C      ALGORITHM 828, COLLECTED ALGORITHMS FROM ACM.
C      THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C      VOL. 29,NO. 4,  December, 2003, P.  458--468.
#! /bin/sh
# This is a shell archive, meaning:
# 1. Remove everything above the #! /bin/sh line.
# 2. Save the resulting text in a file.
# 3. Execute the file with /bin/sh (not csh) to create the files:
#	Fortran77/
#	Fortran77/Dp/
#	Fortran77/Dp/Drivers/
#	Fortran77/Dp/Drivers/Makefile
#	Fortran77/Dp/Drivers/data1
#	Fortran77/Dp/Drivers/data2
#	Fortran77/Dp/Drivers/data3
#	Fortran77/Dp/Drivers/data4
#	Fortran77/Dp/Drivers/data5
#	Fortran77/Dp/Drivers/dblas.f
#	Fortran77/Dp/Drivers/driver.f
#	Fortran77/Dp/Drivers/interactive.f
#	Fortran77/Dp/Drivers/lapack.f
#	Fortran77/Dp/Drivers/res1
#	Fortran77/Dp/Drivers/res1_1
#	Fortran77/Dp/Drivers/res1_2
#	Fortran77/Dp/Drivers/res2
#	Fortran77/Dp/Drivers/res2_1
#	Fortran77/Dp/Drivers/res2_2
#	Fortran77/Dp/Drivers/res3
#	Fortran77/Dp/Drivers/res3_1
#	Fortran77/Dp/Drivers/res3_2
#	Fortran77/Dp/Drivers/res4
#	Fortran77/Dp/Drivers/res4_1
#	Fortran77/Dp/Drivers/res4_2
#	Fortran77/Dp/Drivers/res5
#	Fortran77/Dp/Drivers/res5_1
#	Fortran77/Dp/Drivers/res5_2
#	Fortran77/Dp/Src/
#	Fortran77/Dp/Src/src.f
# This archive created: Fri Jan 23 09:47:26 2004
export PATH; PATH=/bin:$PATH
if test ! -d 'Fortran77'
then
	mkdir 'Fortran77'
fi
cd 'Fortran77'
if test ! -d 'Dp'
then
	mkdir 'Dp'
fi
cd 'Dp'
if test ! -d 'Drivers'
then
	mkdir 'Drivers'
fi
cd 'Drivers'
if test -f 'Makefile'
then
	echo shar: will not over-write existing file "'Makefile'"
else
cat << "SHAR_EOF" > 'Makefile'
# This makefile is primarily for checking the implementation 
# against results already obtained. To do this efficiently the
# interactive driver has been editted to take input from stdin
# and put output on stdout. All the other files for PS plots are
# generated by default and then overwritten. 
#
# The file interactive.f is the original driver that prompts for 
# a data file and aske the user whether various other files should
# be created.

include makefile.inc

all: Res1 Res2 Res3 Res4 Res5

SRCLIBS= $(LAPACK) $(BLAS)

src.o: $(INCSRC)/src.f
	$(F77) $(F77OPTS) -c $(INCSRC)/src.f

DRIVERS= driver
RESULTS= Res1 Res2 Res3 Res4 Res5

Objs1= driver.o src.o
driver: $(Objs1)
	$(F77LINK) $(F77LINKOPTS) -o driver $(Objs1) $(SRCLIBS)
Res1: driver data1
	./driver <data1 >Res1_1
	mv dnsplin1.prt Res1_2

Res2: driver data2
	./driver <data2 >Res2_1
	mv dnsplin1.prt Res2_2

Res3: driver data3
	./driver <data3 >Res3_1
	mv dnsplin1.prt Res3_2

Res4: driver data4
	./driver <data4 >Res4_1
	mv dnsplin1.prt Res4_2

Res5: driver data5
	./driver <data5 >Res5_1
	mv dnsplin1.prt Res5_2

diffres: Res1 res1 Res1 res1 Res3 res3 Res4 res4 Res5 res5
	echo "Differences in results from driver"
	$(DIFF)  Res1 res1
	echo "Differences in results from driver"
	$(DIFF)  Res2 res2
	echo "Differences in results from driver"
	$(DIFF)  Res3 res3
	echo "Differences in results from driver"
	$(DIFF)  Res4 res4
	echo "Differences in results from driver"
	$(DIFF)  Res5 res5

clean: 
	rm -rf *.o $(DRIVERS) $(CLEANUP) $(RESULTS) dnsplin1.ps\
                   dnsplin1.ps0 dnsplin1.ps2
SHAR_EOF
fi # end of overwriting check
if test -f 'data1'
then
	echo shar: will not over-write existing file "'data1'"
else
cat << "SHAR_EOF" > 'data1'
   7                   Number of data points N (format I4)
0.0                    Abscissa of first point (format D22.15)
1.0                    Abscissa of second point (format D22.15)
2.0
3.0
4.0
5.0
6.0
0.0                    Ordinate of first point (format D22.15)
1.9                    Ordinate of second point (format D22.15)
2.7
2.6
1.6
0.8
1.2
0.025                  Mesh width H (format D22.15)
SHAR_EOF
fi # end of overwriting check
if test -f 'data2'
then
	echo shar: will not over-write existing file "'data2'"
else
cat << "SHAR_EOF" > 'data2'
  11
0.0
2.0
3.0
5.0
6.0
8.0
9.0
11.0
12.0
14.0
15.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
1.0
7.0
8.0
15.0
0.0625
SHAR_EOF
fi # end of overwriting check
if test -f 'data3'
then
	echo shar: will not over-write existing file "'data3'"
else
cat << "SHAR_EOF" > 'data3'
   9
7.99
8.09
8.19
8.70
9.20
10.0
12.0
15.0
20.0
0.0
.276429e-3
.437498
1.69183
4.69428
9.43740
9.98636
9.99919
9.99994
.05
SHAR_EOF
fi # end of overwriting check
if test -f 'data4'
then
	echo shar: will not over-write existing file "'data4'"
else
cat << "SHAR_EOF" > 'data4'
  10
0.0
1.0
1.5
2.5
4.0
4.5
5.5
6.0
8.0
10.0
10.0
8.0
5.0
4.0
3.5
3.4
6.0
7.1
8.0
8.5
.04
SHAR_EOF
fi # end of overwriting check
if test -f 'data5'
then
	echo shar: will not over-write existing file "'data5'"
else
cat << "SHAR_EOF" > 'data5'
  11
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.15
1.015
1.0
0.515
0.5
0.5
0.5
0.5
0.18
0.0
0.004
SHAR_EOF
fi # end of overwriting check
if test -f 'dblas.f'
then
	echo shar: will not over-write existing file "'dblas.f'"
else
cat << "SHAR_EOF" > 'dblas.f'
      SUBROUTINE DGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        TRANSA, TRANSB
      INTEGER            M, N, K, LDA, LDB, LDC
      DOUBLE PRECISION   ALPHA, BETA
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  DGEMM  performs one of the matrix-matrix operations
*
*     C := alpha*op( A )*op( B ) + beta*C,
*
*  where  op( X ) is one of
*
*     op( X ) = X   or   op( X ) = X',
*
*  alpha and beta are scalars, and A, B and C are matrices, with op( A )
*  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
*
*  Parameters
*  ==========
*
*  TRANSA - CHARACTER*1.
*           On entry, TRANSA specifies the form of op( A ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSA = 'N' or 'n',  op( A ) = A.
*
*              TRANSA = 'T' or 't',  op( A ) = A'.
*
*              TRANSA = 'C' or 'c',  op( A ) = A'.
*
*           Unchanged on exit.
*
*  TRANSB - CHARACTER*1.
*           On entry, TRANSB specifies the form of op( B ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSB = 'N' or 'n',  op( B ) = B.
*
*              TRANSB = 'T' or 't',  op( B ) = B'.
*
*              TRANSB = 'C' or 'c',  op( B ) = B'.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry,  M  specifies  the number  of rows  of the  matrix
*           op( A )  and of the  matrix  C.  M  must  be at least  zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N  specifies the number  of columns of the matrix
*           op( B ) and the number of columns of the matrix C. N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry,  K  specifies  the number of columns of the matrix
*           op( A ) and the number of rows of the matrix op( B ). K must
*           be at least  zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
*           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by m  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
*           LDA must be at least  max( 1, m ), otherwise  LDA must be at
*           least  max( 1, k ).
*           Unchanged on exit.
*
*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
*           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
*           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
*           part of the array  B  must contain the matrix  B,  otherwise
*           the leading  n by k  part of the array  B  must contain  the
*           matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
*           LDB must be at least  max( 1, k ), otherwise  LDB must be at
*           least  max( 1, n ).
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
*           supplied as zero then C need not be set on input.
*           Unchanged on exit.
*
*  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
*           Before entry, the leading  m by n  part of the array  C must
*           contain the matrix  C,  except when  beta  is zero, in which
*           case C need not be set on entry.
*           On exit, the array  C  is overwritten by the  m by n  matrix
*           ( alpha*op( A )*op( B ) + beta*C ).
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            NOTA, NOTB
      INTEGER            I, INFO, J, L, NCOLA, NROWA, NROWB
      DOUBLE PRECISION   TEMP
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Executable Statements ..
*
*     Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
*     transposed and set  NROWA, NCOLA and  NROWB  as the number of rows
*     and  columns of  A  and the  number of  rows  of  B  respectively.
*
      NOTA  = LSAME( TRANSA, 'N' )
      NOTB  = LSAME( TRANSB, 'N' )
      IF( NOTA )THEN
         NROWA = M
         NCOLA = K
      ELSE
         NROWA = K
         NCOLA = M
      END IF
      IF( NOTB )THEN
         NROWB = K
      ELSE
         NROWB = N
      END IF
*
*     Test the input parameters.
*
      INFO = 0
      IF(      ( .NOT.NOTA                 ).AND.
     $         ( .NOT.LSAME( TRANSA, 'C' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'T' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.NOTB                 ).AND.
     $         ( .NOT.LSAME( TRANSB, 'C' ) ).AND.
     $         ( .NOT.LSAME( TRANSB, 'T' ) )      )THEN
         INFO = 2
      ELSE IF( M  .LT.0               )THEN
         INFO = 3
      ELSE IF( N  .LT.0               )THEN
         INFO = 4
      ELSE IF( K  .LT.0               )THEN
         INFO = 5
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 8
      ELSE IF( LDB.LT.MAX( 1, NROWB ) )THEN
         INFO = 10
      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN
         INFO = 13
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DGEMM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And if  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( BETA.EQ.ZERO )THEN
            DO 20, J = 1, N
               DO 10, I = 1, M
                  C( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
               DO 30, I = 1, M
                  C( I, J ) = BETA*C( I, J )
   30          CONTINUE
   40       CONTINUE
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( NOTB )THEN
         IF( NOTA )THEN
*
*           Form  C := alpha*A*B + beta*C.
*
            DO 90, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 50, I = 1, M
                     C( I, J ) = ZERO
   50             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 60, I = 1, M
                     C( I, J ) = BETA*C( I, J )
   60             CONTINUE
               END IF
               DO 80, L = 1, K
                  IF( B( L, J ).NE.ZERO )THEN
                     TEMP = ALPHA*B( L, J )
                     DO 70, I = 1, M
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
   70                CONTINUE
                  END IF
   80          CONTINUE
   90       CONTINUE
         ELSE
*
*           Form  C := alpha*A'*B + beta*C
*
            DO 120, J = 1, N
               DO 110, I = 1, M
                  TEMP = ZERO
                  DO 100, L = 1, K
                     TEMP = TEMP + A( L, I )*B( L, J )
  100             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  110          CONTINUE
  120       CONTINUE
         END IF
      ELSE
         IF( NOTA )THEN
*
*           Form  C := alpha*A*B' + beta*C
*
            DO 170, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 130, I = 1, M
                     C( I, J ) = ZERO
  130             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 140, I = 1, M
                     C( I, J ) = BETA*C( I, J )
  140             CONTINUE
               END IF
               DO 160, L = 1, K
                  IF( B( J, L ).NE.ZERO )THEN
                     TEMP = ALPHA*B( J, L )
                     DO 150, I = 1, M
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  150                CONTINUE
                  END IF
  160          CONTINUE
  170       CONTINUE
         ELSE
*
*           Form  C := alpha*A'*B' + beta*C
*
            DO 200, J = 1, N
               DO 190, I = 1, M
                  TEMP = ZERO
                  DO 180, L = 1, K
                     TEMP = TEMP + A( L, I )*B( J, L )
  180             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  190          CONTINUE
  200       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DGEMM .
*
      END
      SUBROUTINE DSYMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO
      INTEGER            M, N, LDA, LDB, LDC
      DOUBLE PRECISION   ALPHA, BETA
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  DSYMM  performs one of the matrix-matrix operations
*
*     C := alpha*A*B + beta*C,
*
*  or
*
*     C := alpha*B*A + beta*C,
*
*  where alpha and beta are scalars,  A is a symmetric matrix and  B and
*  C are  m by n matrices.
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry,  SIDE  specifies whether  the  symmetric matrix  A
*           appears on the  left or right  in the  operation as follows:
*
*              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
*
*              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
*
*           Unchanged on exit.
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of  the  symmetric  matrix   A  is  to  be
*           referenced as follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of the
*                                  symmetric matrix is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of the
*                                  symmetric matrix is to be referenced.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry,  M  specifies the number of rows of the matrix  C.
*           M  must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix C.
*           N  must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
*           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
*           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
*           the array  A  must contain the  symmetric matrix,  such that
*           when  UPLO = 'U' or 'u', the leading m by m upper triangular
*           part of the array  A  must contain the upper triangular part
*           of the  symmetric matrix and the  strictly  lower triangular
*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
*           the leading  m by m  lower triangular part  of the  array  A
*           must  contain  the  lower triangular part  of the  symmetric
*           matrix and the  strictly upper triangular part of  A  is not
*           referenced.
*           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
*           the array  A  must contain the  symmetric matrix,  such that
*           when  UPLO = 'U' or 'u', the leading n by n upper triangular
*           part of the array  A  must contain the upper triangular part
*           of the  symmetric matrix and the  strictly  lower triangular
*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
*           the leading  n by n  lower triangular part  of the  array  A
*           must  contain  the  lower triangular part  of the  symmetric
*           matrix and the  strictly upper triangular part of  A  is not
*           referenced.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
*           LDA must be at least  max( 1, m ), otherwise  LDA must be at
*           least  max( 1, n ).
*           Unchanged on exit.
*
*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
*           Before entry, the leading  m by n part of the array  B  must
*           contain the matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   LDB  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
*           supplied as zero then C need not be set on input.
*           Unchanged on exit.
*
*  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
*           Before entry, the leading  m by n  part of the array  C must
*           contain the matrix  C,  except when  beta  is zero, in which
*           case C need not be set on entry.
*           On exit, the array  C  is overwritten by the  m by n updated
*           matrix.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, K, NROWA
      DOUBLE PRECISION   TEMP1, TEMP2
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Executable Statements ..
*
*     Set NROWA as the number of rows of A.
*
      IF( LSAME( SIDE, 'L' ) )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
*     Test the input parameters.
*
      INFO = 0
      IF(      ( .NOT.LSAME( SIDE, 'L' ) ).AND.
     $         ( .NOT.LSAME( SIDE, 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER              ).AND.
     $         ( .NOT.LSAME( UPLO, 'L' ) )      )THEN
         INFO = 2
      ELSE IF( M  .LT.0               )THEN
         INFO = 3
      ELSE IF( N  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 9
      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN
         INFO = 12
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DSYMM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( BETA.EQ.ZERO )THEN
            DO 20, J = 1, N
               DO 10, I = 1, M
                  C( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
               DO 30, I = 1, M
                  C( I, J ) = BETA*C( I, J )
   30          CONTINUE
   40       CONTINUE
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( SIDE, 'L' ) )THEN
*
*        Form  C := alpha*A*B + beta*C.
*
         IF( UPPER )THEN
            DO 70, J = 1, N
               DO 60, I = 1, M
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 50, K = 1, I - 1
                     C( K, J ) = C( K, J ) + TEMP1    *A( K, I )
                     TEMP2     = TEMP2     + B( K, J )*A( K, I )
   50             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           TEMP1*A( I, I ) + ALPHA*TEMP2
                  END IF
   60          CONTINUE
   70       CONTINUE
         ELSE
            DO 100, J = 1, N
               DO 90, I = M, 1, -1
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 80, K = I + 1, M
                     C( K, J ) = C( K, J ) + TEMP1    *A( K, I )
                     TEMP2     = TEMP2     + B( K, J )*A( K, I )
   80             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           TEMP1*A( I, I ) + ALPHA*TEMP2
                  END IF
   90          CONTINUE
  100       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*B*A + beta*C.
*
         DO 170, J = 1, N
            TEMP1 = ALPHA*A( J, J )
            IF( BETA.EQ.ZERO )THEN
               DO 110, I = 1, M
                  C( I, J ) = TEMP1*B( I, J )
  110          CONTINUE
            ELSE
               DO 120, I = 1, M
                  C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J )
  120          CONTINUE
            END IF
            DO 140, K = 1, J - 1
               IF( UPPER )THEN
                  TEMP1 = ALPHA*A( K, J )
               ELSE
                  TEMP1 = ALPHA*A( J, K )
               END IF
               DO 130, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  130          CONTINUE
  140       CONTINUE
            DO 160, K = J + 1, N
               IF( UPPER )THEN
                  TEMP1 = ALPHA*A( J, K )
               ELSE
                  TEMP1 = ALPHA*A( K, J )
               END IF
               DO 150, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  150          CONTINUE
  160       CONTINUE
  170    CONTINUE
      END IF
*
      RETURN
*
*     End of DSYMM .
*
      END
      SUBROUTINE DSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        UPLO, TRANS
      INTEGER            N, K, LDA, LDB, LDC
      DOUBLE PRECISION   ALPHA, BETA
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  DSYR2K  performs one of the symmetric rank 2k operations
*
*     C := alpha*A*B' + alpha*B*A' + beta*C,
*
*  or
*
*     C := alpha*A'*B + alpha*B'*A + beta*C,
*
*  where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
*  and  A and B  are  n by k  matrices  in the  first  case  and  k by n
*  matrices in the second case.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of the  array  C  is to be  referenced  as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry,  TRANS  specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   C := alpha*A*B' + alpha*B*A' +
*                                        beta*C.
*
*              TRANS = 'T' or 't'   C := alpha*A'*B + alpha*B'*A +
*                                        beta*C.
*
*              TRANS = 'C' or 'c'   C := alpha*A'*B + alpha*B'*A +
*                                        beta*C.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N specifies the order of the matrix C.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
*           of  columns  of the  matrices  A and B,  and on  entry  with
*           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
*           of rows of the matrices  A and B.  K must be at least  zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by n  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDA must be at least  max( 1, n ), otherwise  LDA must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  B  must contain the matrix  B,  otherwise
*           the leading  k by n  part of the array  B  must contain  the
*           matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDB must be at least  max( 1, n ), otherwise  LDB must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
*           upper triangular part of the array C must contain the upper
*           triangular part  of the  symmetric matrix  and the strictly
*           lower triangular part of C is not referenced.  On exit, the
*           upper triangular part of the array  C is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
*           lower triangular part of the array C must contain the lower
*           triangular part  of the  symmetric matrix  and the strictly
*           upper triangular part of C is not referenced.  On exit, the
*           lower triangular part of the array  C is overwritten by the
*           lower triangular part of the updated matrix.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, L, NROWA
      DOUBLE PRECISION   TEMP1, TEMP2
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      IF( LSAME( TRANS, 'N' ) )THEN
         NROWA = N
      ELSE
         NROWA = K
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
      INFO = 0
      IF(      ( .NOT.UPPER               ).AND.
     $         ( .NOT.LSAME( UPLO , 'L' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANS, 'T' ) ).AND.
     $         ( .NOT.LSAME( TRANS, 'C' ) )      )THEN
         INFO = 2
      ELSE IF( N  .LT.0               )THEN
         INFO = 3
      ELSE IF( K  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDB.LT.MAX( 1, NROWA ) )THEN
         INFO = 9
      ELSE IF( LDC.LT.MAX( 1, N     ) )THEN
         INFO = 12
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DSYR2K', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.
     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( UPPER )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 20, J = 1, N
                  DO 10, I = 1, J
                     C( I, J ) = ZERO
   10             CONTINUE
   20          CONTINUE
            ELSE
               DO 40, J = 1, N
                  DO 30, I = 1, J
                     C( I, J ) = BETA*C( I, J )
   30             CONTINUE
   40          CONTINUE
            END IF
         ELSE
            IF( BETA.EQ.ZERO )THEN
               DO 60, J = 1, N
                  DO 50, I = J, N
                     C( I, J ) = ZERO
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 80, J = 1, N
                  DO 70, I = J, N
                     C( I, J ) = BETA*C( I, J )
   70             CONTINUE
   80          CONTINUE
            END IF
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  C := alpha*A*B' + alpha*B*A' + C.
*
         IF( UPPER )THEN
            DO 130, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 90, I = 1, J
                     C( I, J ) = ZERO
   90             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 100, I = 1, J
                     C( I, J ) = BETA*C( I, J )
  100             CONTINUE
               END IF
               DO 120, L = 1, K
                  IF( ( A( J, L ).NE.ZERO ).OR.
     $                ( B( J, L ).NE.ZERO )     )THEN
                     TEMP1 = ALPHA*B( J, L )
                     TEMP2 = ALPHA*A( J, L )
                     DO 110, I = 1, J
                        C( I, J ) = C( I, J ) +
     $                              A( I, L )*TEMP1 + B( I, L )*TEMP2
  110                CONTINUE
                  END IF
  120          CONTINUE
  130       CONTINUE
         ELSE
            DO 180, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 140, I = J, N
                     C( I, J ) = ZERO
  140             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 150, I = J, N
                     C( I, J ) = BETA*C( I, J )
  150             CONTINUE
               END IF
               DO 170, L = 1, K
                  IF( ( A( J, L ).NE.ZERO ).OR.
     $                ( B( J, L ).NE.ZERO )     )THEN
                     TEMP1 = ALPHA*B( J, L )
                     TEMP2 = ALPHA*A( J, L )
                     DO 160, I = J, N
                        C( I, J ) = C( I, J ) +
     $                              A( I, L )*TEMP1 + B( I, L )*TEMP2
  160                CONTINUE
                  END IF
  170          CONTINUE
  180       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*A'*B + alpha*B'*A + C.
*
         IF( UPPER )THEN
            DO 210, J = 1, N
               DO 200, I = 1, J
                  TEMP1 = ZERO
                  TEMP2 = ZERO
                  DO 190, L = 1, K
                     TEMP1 = TEMP1 + A( L, I )*B( L, J )
                     TEMP2 = TEMP2 + B( L, I )*A( L, J )
  190             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           ALPHA*TEMP1 + ALPHA*TEMP2
                  END IF
  200          CONTINUE
  210       CONTINUE
         ELSE
            DO 240, J = 1, N
               DO 230, I = J, N
                  TEMP1 = ZERO
                  TEMP2 = ZERO
                  DO 220, L = 1, K
                     TEMP1 = TEMP1 + A( L, I )*B( L, J )
                     TEMP2 = TEMP2 + B( L, I )*A( L, J )
  220             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           ALPHA*TEMP1 + ALPHA*TEMP2
                  END IF
  230          CONTINUE
  240       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DSYR2K.
*
      END
      SUBROUTINE DSYRK ( UPLO, TRANS, N, K, ALPHA, A, LDA,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        UPLO, TRANS
      INTEGER            N, K, LDA, LDC
      DOUBLE PRECISION   ALPHA, BETA
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  DSYRK  performs one of the symmetric rank k operations
*
*     C := alpha*A*A' + beta*C,
*
*  or
*
*     C := alpha*A'*A + beta*C,
*
*  where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
*  and  A  is an  n by k  matrix in the first case and a  k by n  matrix
*  in the second case.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of the  array  C  is to be  referenced  as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry,  TRANS  specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   C := alpha*A*A' + beta*C.
*
*              TRANS = 'T' or 't'   C := alpha*A'*A + beta*C.
*
*              TRANS = 'C' or 'c'   C := alpha*A'*A + beta*C.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N specifies the order of the matrix C.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
*           of  columns   of  the   matrix   A,   and  on   entry   with
*           TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
*           of rows of the matrix  A.  K must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by n  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDA must be at least  max( 1, n ), otherwise  LDA must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
*           upper triangular part of the array C must contain the upper
*           triangular part  of the  symmetric matrix  and the strictly
*           lower triangular part of C is not referenced.  On exit, the
*           upper triangular part of the array  C is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
*           lower triangular part of the array C must contain the lower
*           triangular part  of the  symmetric matrix  and the strictly
*           upper triangular part of C is not referenced.  On exit, the
*           lower triangular part of the array  C is overwritten by the
*           lower triangular part of the updated matrix.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, L, NROWA
      DOUBLE PRECISION   TEMP
*     .. Parameters ..
      DOUBLE PRECISION   ONE ,         ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      IF( LSAME( TRANS, 'N' ) )THEN
         NROWA = N
      ELSE
         NROWA = K
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
      INFO = 0
      IF(      ( .NOT.UPPER               ).AND.
     $         ( .NOT.LSAME( UPLO , 'L' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANS, 'T' ) ).AND.
     $         ( .NOT.LSAME( TRANS, 'C' ) )      )THEN
         INFO = 2
      ELSE IF( N  .LT.0               )THEN
         INFO = 3
      ELSE IF( K  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDC.LT.MAX( 1, N     ) )THEN
         INFO = 10
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DSYRK ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.
     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( UPPER )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 20, J = 1, N
                  DO 10, I = 1, J
                     C( I, J ) = ZERO
   10             CONTINUE
   20          CONTINUE
            ELSE
               DO 40, J = 1, N
                  DO 30, I = 1, J
                     C( I, J ) = BETA*C( I, J )
   30             CONTINUE
   40          CONTINUE
            END IF
         ELSE
            IF( BETA.EQ.ZERO )THEN
               DO 60, J = 1, N
                  DO 50, I = J, N
                     C( I, J ) = ZERO
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 80, J = 1, N
                  DO 70, I = J, N
                     C( I, J ) = BETA*C( I, J )
   70             CONTINUE
   80          CONTINUE
            END IF
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  C := alpha*A*A' + beta*C.
*
         IF( UPPER )THEN
            DO 130, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 90, I = 1, J
                     C( I, J ) = ZERO
   90             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 100, I = 1, J
                     C( I, J ) = BETA*C( I, J )
  100             CONTINUE
               END IF
               DO 120, L = 1, K
                  IF( A( J, L ).NE.ZERO )THEN
                     TEMP = ALPHA*A( J, L )
                     DO 110, I = 1, J
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  110                CONTINUE
                  END IF
  120          CONTINUE
  130       CONTINUE
         ELSE
            DO 180, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 140, I = J, N
                     C( I, J ) = ZERO
  140             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 150, I = J, N
                     C( I, J ) = BETA*C( I, J )
  150             CONTINUE
               END IF
               DO 170, L = 1, K
                  IF( A( J, L ).NE.ZERO )THEN
                     TEMP      = ALPHA*A( J, L )
                     DO 160, I = J, N
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  160                CONTINUE
                  END IF
  170          CONTINUE
  180       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*A'*A + beta*C.
*
         IF( UPPER )THEN
            DO 210, J = 1, N
               DO 200, I = 1, J
                  TEMP = ZERO
                  DO 190, L = 1, K
                     TEMP = TEMP + A( L, I )*A( L, J )
  190             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  200          CONTINUE
  210       CONTINUE
         ELSE
            DO 240, J = 1, N
               DO 230, I = J, N
                  TEMP = ZERO
                  DO 220, L = 1, K
                     TEMP = TEMP + A( L, I )*A( L, J )
  220             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  230          CONTINUE
  240       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DSYRK .
*
      END
      SUBROUTINE DTRMM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
     $                   B, LDB )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO, TRANSA, DIAG
      INTEGER            M, N, LDA, LDB
      DOUBLE PRECISION   ALPHA
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  DTRMM  performs one of the matrix-matrix operations
*
*     B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
*
*  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
*
*     op( A ) = A   or   op( A ) = A'.
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry,  SIDE specifies whether  op( A ) multiplies B from
*           the left or right as follows:
*
*              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
*
*              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
*
*           Unchanged on exit.
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix A is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANSA - CHARACTER*1.
*           On entry, TRANSA specifies the form of op( A ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSA = 'N' or 'n'   op( A ) = A.
*
*              TRANSA = 'T' or 't'   op( A ) = A'.
*
*              TRANSA = 'C' or 'c'   op( A ) = A'.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit triangular
*           as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of B. M must be at
*           least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of B.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
*           zero then  A is not referenced and  B need not be set before
*           entry.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
*           upper triangular part of the array  A must contain the upper
*           triangular matrix  and the strictly lower triangular part of
*           A is not referenced.
*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
*           lower triangular part of the array  A must contain the lower
*           triangular matrix  and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
*           A  are not referenced either,  but are assumed to be  unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
*           then LDA must be at least max( 1, n ).
*           Unchanged on exit.
*
*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
*           Before entry,  the leading  m by n part of the array  B must
*           contain the matrix  B,  and  on exit  is overwritten  by the
*           transformed matrix.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   LDB  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            LSIDE, NOUNIT, UPPER
      INTEGER            I, INFO, J, K, NROWA
      DOUBLE PRECISION   TEMP
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      LSIDE  = LSAME( SIDE  , 'L' )
      IF( LSIDE )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      NOUNIT = LSAME( DIAG  , 'N' )
      UPPER  = LSAME( UPLO  , 'U' )
*
      INFO   = 0
      IF(      ( .NOT.LSIDE                ).AND.
     $         ( .NOT.LSAME( SIDE  , 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER                ).AND.
     $         ( .NOT.LSAME( UPLO  , 'L' ) )      )THEN
         INFO = 2
      ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'T' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'C' ) )      )THEN
         INFO = 3
      ELSE IF( ( .NOT.LSAME( DIAG  , 'U' ) ).AND.
     $         ( .NOT.LSAME( DIAG  , 'N' ) )      )THEN
         INFO = 4
      ELSE IF( M  .LT.0               )THEN
         INFO = 5
      ELSE IF( N  .LT.0               )THEN
         INFO = 6
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 9
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DTRMM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         DO 20, J = 1, N
            DO 10, I = 1, M
               B( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSIDE )THEN
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*A*B.
*
            IF( UPPER )THEN
               DO 50, J = 1, N
                  DO 40, K = 1, M
                     IF( B( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*B( K, J )
                        DO 30, I = 1, K - 1
                           B( I, J ) = B( I, J ) + TEMP*A( I, K )
   30                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP*A( K, K )
                        B( K, J ) = TEMP
                     END IF
   40             CONTINUE
   50          CONTINUE
            ELSE
               DO 80, J = 1, N
                  DO 70 K = M, 1, -1
                     IF( B( K, J ).NE.ZERO )THEN
                        TEMP      = ALPHA*B( K, J )
                        B( K, J ) = TEMP
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )*A( K, K )
                        DO 60, I = K + 1, M
                           B( I, J ) = B( I, J ) + TEMP*A( I, K )
   60                   CONTINUE
                     END IF
   70             CONTINUE
   80          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*A'*B.
*
            IF( UPPER )THEN
               DO 110, J = 1, N
                  DO 100, I = M, 1, -1
                     TEMP = B( I, J )
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( I, I )
                     DO 90, K = 1, I - 1
                        TEMP = TEMP + A( K, I )*B( K, J )
   90                CONTINUE
                     B( I, J ) = ALPHA*TEMP
  100             CONTINUE
  110          CONTINUE
            ELSE
               DO 140, J = 1, N
                  DO 130, I = 1, M
                     TEMP = B( I, J )
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( I, I )
                     DO 120, K = I + 1, M
                        TEMP = TEMP + A( K, I )*B( K, J )
  120                CONTINUE
                     B( I, J ) = ALPHA*TEMP
  130             CONTINUE
  140          CONTINUE
            END IF
         END IF
      ELSE
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*B*A.
*
            IF( UPPER )THEN
               DO 180, J = N, 1, -1
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( J, J )
                  DO 150, I = 1, M
                     B( I, J ) = TEMP*B( I, J )
  150             CONTINUE
                  DO 170, K = 1, J - 1
                     IF( A( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*A( K, J )
                        DO 160, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  160                   CONTINUE
                     END IF
  170             CONTINUE
  180          CONTINUE
            ELSE
               DO 220, J = 1, N
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( J, J )
                  DO 190, I = 1, M
                     B( I, J ) = TEMP*B( I, J )
  190             CONTINUE
                  DO 210, K = J + 1, N
                     IF( A( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*A( K, J )
                        DO 200, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  200                   CONTINUE
                     END IF
  210             CONTINUE
  220          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*B*A'.
*
            IF( UPPER )THEN
               DO 260, K = 1, N
                  DO 240, J = 1, K - 1
                     IF( A( J, K ).NE.ZERO )THEN
                        TEMP = ALPHA*A( J, K )
                        DO 230, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  230                   CONTINUE
                     END IF
  240             CONTINUE
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( K, K )
                  IF( TEMP.NE.ONE )THEN
                     DO 250, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  250                CONTINUE
                  END IF
  260          CONTINUE
            ELSE
               DO 300, K = N, 1, -1
                  DO 280, J = K + 1, N
                     IF( A( J, K ).NE.ZERO )THEN
                        TEMP = ALPHA*A( J, K )
                        DO 270, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  270                   CONTINUE
                     END IF
  280             CONTINUE
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( K, K )
                  IF( TEMP.NE.ONE )THEN
                     DO 290, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  290                CONTINUE
                  END IF
  300          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of DTRMM .
*
      END
      SUBROUTINE DTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
     $                   B, LDB )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO, TRANSA, DIAG
      INTEGER            M, N, LDA, LDB
      DOUBLE PRECISION   ALPHA
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  DTRSM  solves one of the matrix equations
*
*     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
*
*  where alpha is a scalar, X and B are m by n matrices, A is a unit, or
*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
*
*     op( A ) = A   or   op( A ) = A'.
*
*  The matrix X is overwritten on B.
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry, SIDE specifies whether op( A ) appears on the left
*           or right of X as follows:
*
*              SIDE = 'L' or 'l'   op( A )*X = alpha*B.
*
*              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
*
*           Unchanged on exit.
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix A is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANSA - CHARACTER*1.
*           On entry, TRANSA specifies the form of op( A ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSA = 'N' or 'n'   op( A ) = A.
*
*              TRANSA = 'T' or 't'   op( A ) = A'.
*
*              TRANSA = 'C' or 'c'   op( A ) = A'.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit triangular
*           as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of B. M must be at
*           least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of B.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
*           zero then  A is not referenced and  B need not be set before
*           entry.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
*           upper triangular part of the array  A must contain the upper
*           triangular matrix  and the strictly lower triangular part of
*           A is not referenced.
*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
*           lower triangular part of the array  A must contain the lower
*           triangular matrix  and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
*           A  are not referenced either,  but are assumed to be  unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
*           then LDA must be at least max( 1, n ).
*           Unchanged on exit.
*
*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
*           Before entry,  the leading  m by n part of the array  B must
*           contain  the  right-hand  side  matrix  B,  and  on exit  is
*           overwritten by the solution matrix  X.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   LDB  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            LSIDE, NOUNIT, UPPER
      INTEGER            I, INFO, J, K, NROWA
      DOUBLE PRECISION   TEMP
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      LSIDE  = LSAME( SIDE  , 'L' )
      IF( LSIDE )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      NOUNIT = LSAME( DIAG  , 'N' )
      UPPER  = LSAME( UPLO  , 'U' )
*
      INFO   = 0
      IF(      ( .NOT.LSIDE                ).AND.
     $         ( .NOT.LSAME( SIDE  , 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER                ).AND.
     $         ( .NOT.LSAME( UPLO  , 'L' ) )      )THEN
         INFO = 2
      ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'T' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'C' ) )      )THEN
         INFO = 3
      ELSE IF( ( .NOT.LSAME( DIAG  , 'U' ) ).AND.
     $         ( .NOT.LSAME( DIAG  , 'N' ) )      )THEN
         INFO = 4
      ELSE IF( M  .LT.0               )THEN
         INFO = 5
      ELSE IF( N  .LT.0               )THEN
         INFO = 6
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 9
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DTRSM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         DO 20, J = 1, N
            DO 10, I = 1, M
               B( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSIDE )THEN
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*inv( A )*B.
*
            IF( UPPER )THEN
               DO 60, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 30, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
   30                CONTINUE
                  END IF
                  DO 50, K = M, 1, -1
                     IF( B( K, J ).NE.ZERO )THEN
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )/A( K, K )
                        DO 40, I = 1, K - 1
                           B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
   40                   CONTINUE
                     END IF
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 100, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 70, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
   70                CONTINUE
                  END IF
                  DO 90 K = 1, M
                     IF( B( K, J ).NE.ZERO )THEN
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )/A( K, K )
                        DO 80, I = K + 1, M
                           B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
   80                   CONTINUE
                     END IF
   90             CONTINUE
  100          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*inv( A' )*B.
*
            IF( UPPER )THEN
               DO 130, J = 1, N
                  DO 120, I = 1, M
                     TEMP = ALPHA*B( I, J )
                     DO 110, K = 1, I - 1
                        TEMP = TEMP - A( K, I )*B( K, J )
  110                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( I, I )
                     B( I, J ) = TEMP
  120             CONTINUE
  130          CONTINUE
            ELSE
               DO 160, J = 1, N
                  DO 150, I = M, 1, -1
                     TEMP = ALPHA*B( I, J )
                     DO 140, K = I + 1, M
                        TEMP = TEMP - A( K, I )*B( K, J )
  140                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( I, I )
                     B( I, J ) = TEMP
  150             CONTINUE
  160          CONTINUE
            END IF
         END IF
      ELSE
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*B*inv( A ).
*
            IF( UPPER )THEN
               DO 210, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 170, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
  170                CONTINUE
                  END IF
                  DO 190, K = 1, J - 1
                     IF( A( K, J ).NE.ZERO )THEN
                        DO 180, I = 1, M
                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
  180                   CONTINUE
                     END IF
  190             CONTINUE
                  IF( NOUNIT )THEN
                     TEMP = ONE/A( J, J )
                     DO 200, I = 1, M
                        B( I, J ) = TEMP*B( I, J )
  200                CONTINUE
                  END IF
  210          CONTINUE
            ELSE
               DO 260, J = N, 1, -1
                  IF( ALPHA.NE.ONE )THEN
                     DO 220, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
  220                CONTINUE
                  END IF
                  DO 240, K = J + 1, N
                     IF( A( K, J ).NE.ZERO )THEN
                        DO 230, I = 1, M
                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
  230                   CONTINUE
                     END IF
  240             CONTINUE
                  IF( NOUNIT )THEN
                     TEMP = ONE/A( J, J )
                     DO 250, I = 1, M
                       B( I, J ) = TEMP*B( I, J )
  250                CONTINUE
                  END IF
  260          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*B*inv( A' ).
*
            IF( UPPER )THEN
               DO 310, K = N, 1, -1
                  IF( NOUNIT )THEN
                     TEMP = ONE/A( K, K )
                     DO 270, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  270                CONTINUE
                  END IF
                  DO 290, J = 1, K - 1
                     IF( A( J, K ).NE.ZERO )THEN
                        TEMP = A( J, K )
                        DO 280, I = 1, M
                           B( I, J ) = B( I, J ) - TEMP*B( I, K )
  280                   CONTINUE
                     END IF
  290             CONTINUE
                  IF( ALPHA.NE.ONE )THEN
                     DO 300, I = 1, M
                        B( I, K ) = ALPHA*B( I, K )
  300                CONTINUE
                  END IF
  310          CONTINUE
            ELSE
               DO 360, K = 1, N
                  IF( NOUNIT )THEN
                     TEMP = ONE/A( K, K )
                     DO 320, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  320                CONTINUE
                  END IF
                  DO 340, J = K + 1, N
                     IF( A( J, K ).NE.ZERO )THEN
                        TEMP = A( J, K )
                        DO 330, I = 1, M
                           B( I, J ) = B( I, J ) - TEMP*B( I, K )
  330                   CONTINUE
                     END IF
  340             CONTINUE
                  IF( ALPHA.NE.ONE )THEN
                     DO 350, I = 1, M
                        B( I, K ) = ALPHA*B( I, K )
  350                CONTINUE
                  END IF
  360          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of DTRSM .
*
      END
      SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, BETA
      INTEGER            INCX, INCY, LDA, M, N
      CHARACTER*1        TRANS
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  DGEMV  performs one of the matrix-vector operations
*
*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,
*
*  where alpha and beta are scalars, x and y are vectors and A is an
*  m by n matrix.
*
*  Parameters
*  ==========
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
*
*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
*
*              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry, the leading m by n part of the array A must
*           contain the matrix of coefficients.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, m ).
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*           Before entry with BETA non-zero, the incremented array Y
*           must contain the vector y. On exit, Y is overwritten by the
*           updated vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   TEMP
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 1
      ELSE IF( M.LT.0 )THEN
         INFO = 2
      ELSE IF( N.LT.0 )THEN
         INFO = 3
      ELSE IF( LDA.LT.MAX( 1, M ) )THEN
         INFO = 6
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 8
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DGEMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
*     up the start points in  X  and  Y.
*
      IF( LSAME( TRANS, 'N' ) )THEN
         LENX = N
         LENY = M
      ELSE
         LENX = M
         LENY = N
      END IF
      IF( INCX.GT.0 )THEN
         KX = 1
      ELSE
         KX = 1 - ( LENX - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
         KY = 1
      ELSE
         KY = 1 - ( LENY - 1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE )THEN
         IF( INCY.EQ.1 )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 10, I = 1, LENY
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20, I = 1, LENY
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         ELSE
            IY = KY
            IF( BETA.EQ.ZERO )THEN
               DO 30, I = 1, LENY
                  Y( IY ) = ZERO
                  IY      = IY   + INCY
   30          CONTINUE
            ELSE
               DO 40, I = 1, LENY
                  Y( IY ) = BETA*Y( IY )
                  IY      = IY           + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  y := alpha*A*x + y.
*
         JX = KX
         IF( INCY.EQ.1 )THEN
            DO 60, J = 1, N
               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  DO 50, I = 1, M
                     Y( I ) = Y( I ) + TEMP*A( I, J )
   50             CONTINUE
               END IF
               JX = JX + INCX
   60       CONTINUE
         ELSE
            DO 80, J = 1, N
               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  IY   = KY
                  DO 70, I = 1, M
                     Y( IY ) = Y( IY ) + TEMP*A( I, J )
                     IY      = IY      + INCY
   70             CONTINUE
               END IF
               JX = JX + INCX
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y := alpha*A'*x + y.
*
         JY = KY
         IF( INCX.EQ.1 )THEN
            DO 100, J = 1, N
               TEMP = ZERO
               DO 90, I = 1, M
                  TEMP = TEMP + A( I, J )*X( I )
   90          CONTINUE
               Y( JY ) = Y( JY ) + ALPHA*TEMP
               JY      = JY      + INCY
  100       CONTINUE
         ELSE
            DO 120, J = 1, N
               TEMP = ZERO
               IX   = KX
               DO 110, I = 1, M
                  TEMP = TEMP + A( I, J )*X( IX )
                  IX   = IX   + INCX
  110          CONTINUE
               Y( JY ) = Y( JY ) + ALPHA*TEMP
               JY      = JY      + INCY
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DGEMV .
*
      END
      SUBROUTINE DSYR  ( UPLO, N, ALPHA, X, INCX, A, LDA )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA
      INTEGER            INCX, LDA, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  DSYR   performs the symmetric rank 1 operation
*
*     A := alpha*x*x' + A,
*
*  where alpha is a real scalar, x is an n element vector and A is an
*  n by n symmetric matrix.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the array A is to be referenced as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of A
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of A
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular part of the symmetric matrix and the strictly
*           lower triangular part of A is not referenced. On exit, the
*           upper triangular part of the array A is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular part of the symmetric matrix and the strictly
*           upper triangular part of A is not referenced. On exit, the
*           lower triangular part of the array A is overwritten by the
*           lower triangular part of the updated matrix.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER        ( ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   TEMP
      INTEGER            I, INFO, IX, J, JX, KX
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 5
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
         INFO = 7
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DSYR  ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
     $   RETURN
*
*     Set the start point in X if the increment is not unity.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  A  when A is stored in upper triangle.
*
         IF( INCX.EQ.1 )THEN
            DO 20, J = 1, N
               IF( X( J ).NE.ZERO )THEN
                  TEMP = ALPHA*X( J )
                  DO 10, I = 1, J
                     A( I, J ) = A( I, J ) + X( I )*TEMP
   10             CONTINUE
               END IF
   20       CONTINUE
         ELSE
            JX = KX
            DO 40, J = 1, N
               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  IX   = KX
                  DO 30, I = 1, J
                     A( I, J ) = A( I, J ) + X( IX )*TEMP
                     IX        = IX        + INCX
   30             CONTINUE
               END IF
               JX = JX + INCX
   40       CONTINUE
         END IF
      ELSE
*
*        Form  A  when A is stored in lower triangle.
*
         IF( INCX.EQ.1 )THEN
            DO 60, J = 1, N
               IF( X( J ).NE.ZERO )THEN
                  TEMP = ALPHA*X( J )
                  DO 50, I = J, N
                     A( I, J ) = A( I, J ) + X( I )*TEMP
   50             CONTINUE
               END IF
   60       CONTINUE
         ELSE
            JX = KX
            DO 80, J = 1, N
               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  IX   = JX
                  DO 70, I = J, N
                     A( I, J ) = A( I, J ) + X( IX )*TEMP
                     IX        = IX        + INCX
   70             CONTINUE
               END IF
               JX = JX + INCX
   80       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of DSYR  .
*
      END
      SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, K, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  DTBSV  solves one of the systems of equations
*
*     A*x = b,   or   A'*x = b,
*
*  where b and x are n element vectors and A is an n by n unit, or
*  non-unit, upper or lower triangular band matrix, with ( k + 1 )
*  diagonals.
*
*  No test for singularity or near-singularity is included in this
*  routine. Such tests must be performed before calling this routine.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the equations to be solved as
*           follows:
*
*              TRANS = 'N' or 'n'   A*x = b.
*
*              TRANS = 'T' or 't'   A'*x = b.
*
*              TRANS = 'C' or 'c'   A'*x = b.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with UPLO = 'U' or 'u', K specifies the number of
*           super-diagonals of the matrix A.
*           On entry with UPLO = 'L' or 'l', K specifies the number of
*           sub-diagonals of the matrix A.
*           K must satisfy  0 .le. K.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
*           by n part of the array A must contain the upper triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row
*           ( k + 1 ) of the array, the first super-diagonal starting at
*           position 2 in row k, and so on. The top left k by k triangle
*           of the array A is not referenced.
*           The following program segment will transfer an upper
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 DO 20, J = 1, N
*                    M = K + 1 - J
*                    DO 10, I = MAX( 1, J - K ), J
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
*           by n part of the array A must contain the lower triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row 1 of
*           the array, the first sub-diagonal starting at position 1 in
*           row 2, and so on. The bottom right k by k triangle of the
*           array A is not referenced.
*           The following program segment will transfer a lower
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 DO 20, J = 1, N
*                    M = 1 - J
*                    DO 10, I = J, MIN( N, J + K )
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Note that when DIAG = 'U' or 'u' the elements of the array A
*           corresponding to the diagonal elements of the matrix are not
*           referenced, but are assumed to be unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           ( k + 1 ).
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element right-hand side vector b. On exit, X is overwritten
*           with the solution vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER        ( ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   TEMP
      INTEGER            I, INFO, IX, J, JX, KPLUS1, KX, L
      LOGICAL            NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
         INFO = 1
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 2
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
         INFO = 3
      ELSE IF( N.LT.0 )THEN
         INFO = 4
      ELSE IF( K.LT.0 )THEN
         INFO = 5
      ELSE IF( LDA.LT.( K + 1 ) )THEN
         INFO = 7
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 9
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DTBSV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
      NOUNIT = LSAME( DIAG, 'N' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed by sequentially with one pass through A.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  x := inv( A )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KPLUS1 = K + 1
            IF( INCX.EQ.1 )THEN
               DO 20, J = N, 1, -1
                  IF( X( J ).NE.ZERO )THEN
                     L = KPLUS1 - J
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( KPLUS1, J )
                     TEMP = X( J )
                     DO 10, I = J - 1, MAX( 1, J - K ), -1
                        X( I ) = X( I ) - TEMP*A( L + I, J )
   10                CONTINUE
                  END IF
   20          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 40, J = N, 1, -1
                  KX = KX - INCX
                  IF( X( JX ).NE.ZERO )THEN
                     IX = KX
                     L  = KPLUS1 - J
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( KPLUS1, J )
                     TEMP = X( JX )
                     DO 30, I = J - 1, MAX( 1, J - K ), -1
                        X( IX ) = X( IX ) - TEMP*A( L + I, J )
                        IX      = IX      - INCX
   30                CONTINUE
                  END IF
                  JX = JX - INCX
   40          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 60, J = 1, N
                  IF( X( J ).NE.ZERO )THEN
                     L = 1 - J
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( 1, J )
                     TEMP = X( J )
                     DO 50, I = J + 1, MIN( N, J + K )
                        X( I ) = X( I ) - TEMP*A( L + I, J )
   50                CONTINUE
                  END IF
   60          CONTINUE
            ELSE
               JX = KX
               DO 80, J = 1, N
                  KX = KX + INCX
                  IF( X( JX ).NE.ZERO )THEN
                     IX = KX
                     L  = 1  - J
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( 1, J )
                     TEMP = X( JX )
                     DO 70, I = J + 1, MIN( N, J + K )
                        X( IX ) = X( IX ) - TEMP*A( L + I, J )
                        IX      = IX      + INCX
   70                CONTINUE
                  END IF
                  JX = JX + INCX
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := inv( A')*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KPLUS1 = K + 1
            IF( INCX.EQ.1 )THEN
               DO 100, J = 1, N
                  TEMP = X( J )
                  L    = KPLUS1 - J
                  DO 90, I = MAX( 1, J - K ), J - 1
                     TEMP = TEMP - A( L + I, J )*X( I )
   90             CONTINUE
                  IF( NOUNIT )
     $               TEMP = TEMP/A( KPLUS1, J )
                  X( J ) = TEMP
  100          CONTINUE
            ELSE
               JX = KX
               DO 120, J = 1, N
                  TEMP = X( JX )
                  IX   = KX
                  L    = KPLUS1  - J
                  DO 110, I = MAX( 1, J - K ), J - 1
                     TEMP = TEMP - A( L + I, J )*X( IX )
                     IX   = IX   + INCX
  110             CONTINUE
                  IF( NOUNIT )
     $               TEMP = TEMP/A( KPLUS1, J )
                  X( JX ) = TEMP
                  JX      = JX   + INCX
                  IF( J.GT.K )
     $               KX = KX + INCX
  120          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 140, J = N, 1, -1
                  TEMP = X( J )
                  L    = 1      - J
                  DO 130, I = MIN( N, J + K ), J + 1, -1
                     TEMP = TEMP - A( L + I, J )*X( I )
  130             CONTINUE
                  IF( NOUNIT )
     $               TEMP = TEMP/A( 1, J )
                  X( J ) = TEMP
  140          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 160, J = N, 1, -1
                  TEMP = X( JX )
                  IX   = KX
                  L    = 1       - J
                  DO 150, I = MIN( N, J + K ), J + 1, -1
                     TEMP = TEMP - A( L + I, J )*X( IX )
                     IX   = IX   - INCX
  150             CONTINUE
                  IF( NOUNIT )
     $               TEMP = TEMP/A( 1, J )
                  X( JX ) = TEMP
                  JX      = JX   - INCX
                  IF( ( N - J ).GE.K )
     $               KX = KX - INCX
  160          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of DTBSV .
*
      END
      SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE  DCOPY
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A5
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SCOPY-S DCOPY-D CCOPY-C),COPY,
C             LINEAR ALGEBRA,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  D.P. vector copy y = x
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C       DY  double precision vector with N elements
C     INCY  storage spacing between elements of DY
C
C     --Output--
C       DY  copy of vector DX (unchanged if N .LE. 0)
C
C     Copy double precision DX to double precision DY.
C     For I = 0 to N-1, copy DX(LX+I*INCX) to DY(LY+I*INCY),
C     where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and LY is
C     defined in a similar way using INCY.
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DCOPY
C
      DOUBLE PRECISION DX(1),DY(1)
C***FIRST EXECUTABLE STATEMENT  DCOPY
      IF(N.LE.0)RETURN
      IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
    5 CONTINUE
C
C        CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
        DY(IY) = DX(IX)
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C        CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 7.
C
   20 M = MOD(N,7)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DY(I) = DX(I)
   30 CONTINUE
      IF( N .LT. 7 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,7
        DY(I) = DX(I)
        DY(I + 1) = DX(I + 1)
        DY(I + 2) = DX(I + 2)
        DY(I + 3) = DX(I + 3)
        DY(I + 4) = DX(I + 4)
        DY(I + 5) = DX(I + 5)
        DY(I + 6) = DX(I + 6)
   50 CONTINUE
      RETURN
C
C        CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
C
   60 CONTINUE
      NS=N*INCX
          DO 70 I=1,NS,INCX
          DY(I) = DX(I)
   70     CONTINUE
      RETURN
      END

      SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE  DAXPY
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A7
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SAXPY-S DAXPY-D CAXPY-C),
C             LINEAR ALGEBRA,TRIAD,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  D.P computation y = a*x + y
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DA  double precision scalar multiplier
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C       DY  double precision vector with N elements
C     INCY  storage spacing between elements of DY
C
C     --Output--
C       DY  double precision result (unchanged if N .LE. 0)
C
C     Overwrite double precision DY with double precision DA*DX + DY.
C     For I = 0 to N-1, replace  DY(LY+I*INCY) with DA*DX(LX+I*INCX) +
C       DY(LY+I*INCY), where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N
C       and LY is defined in a similar way using INCY.
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DAXPY
C
      DOUBLE PRECISION DX(1),DY(1),DA
C***FIRST EXECUTABLE STATEMENT  DAXPY
      IF(N.LE.0.OR.DA.EQ.0.D0) RETURN
      IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
    5 CONTINUE
C
C        CODE FOR NONEQUAL OR NONPOSITIVE INCREMENTS.
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
        DY(IY) = DY(IY) + DA*DX(IX)
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C        CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 4.
C
   20 M = MOD(N,4)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DY(I) = DY(I) + DA*DX(I)
   30 CONTINUE
      IF( N .LT. 4 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,4
        DY(I) = DY(I) + DA*DX(I)
        DY(I + 1) = DY(I + 1) + DA*DX(I + 1)
        DY(I + 2) = DY(I + 2) + DA*DX(I + 2)
        DY(I + 3) = DY(I + 3) + DA*DX(I + 3)
   50 CONTINUE
      RETURN
C
C        CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
C
   60 CONTINUE
      NS = N*INCX
          DO 70 I=1,NS,INCX
          DY(I) = DA*DX(I) + DY(I)
   70     CONTINUE
      RETURN
      END

      DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
C
C     FORMS THE DOT PRODUCT OF TWO VECTORS.
C     USES UNROLLED LOOPS FOR INCREMENTS EQUAL TO ONE.
C     JACK DONGARRA, LINPACK, 3/11/78.
C
      DOUBLE PRECISION DX(1),DY(1),DTEMP
      INTEGER I,INCX,INCY,IX,IY,M,MP1,N
C
      DDOT = 0.0D0
      DTEMP = 0.0D0
      IF(N.LE.0)RETURN
      IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20
C
C	 CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS
C	   NOT EQUAL TO 1
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
	DTEMP = DTEMP + DX(IX)*DY(IY)
	IX = IX + INCX
	IY = IY + INCY
   10 CONTINUE
      DDOT = DTEMP
      RETURN
C
C	 CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C	 CLEAN-UP LOOP
C
   20 M = MOD(N,5)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
	DTEMP = DTEMP + DX(I)*DY(I)
   30 CONTINUE
      IF( N .LT. 5 ) GO TO 60
   40 MP1 = M + 1
      DO 50 I = MP1,N,5
	DTEMP = DTEMP + DX(I)*DY(I) + DX(I + 1)*DY(I + 1) +
     *	 DX(I + 2)*DY(I + 2) + DX(I + 3)*DY(I + 3) + DX(I + 4)*DY(I + 4)
   50 CONTINUE
   60 DDOT = DTEMP
      RETURN
      END

      DOUBLE PRECISION FUNCTION DNRM2(N,DX,INCX)
C***BEGIN PROLOGUE  DNRM2
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A3B
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SNRM2-S DNRM2-D SCNRM2-C),
C             EUCLIDEAN LENGTH,EUCLIDEAN NORM,L2,LINEAR ALGEBRA,UNITARY,
C             VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Euclidean length (L2 norm) of d.p. vector
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C    DNRM2  double precision result (zero if N .LE. 0)
C
C     Euclidean norm of the N-vector stored in DX() with storage
C     increment INCX .
C     If    N .LE. 0 return with result = 0.
C     If N .GE. 1 then INCX must be .GE. 1
C
C           C.L. Lawson, 1978 Jan 08
C
C     Four phase method     using two built-in constants that are
C     hopefully applicable to all machines.
C         CUTLO = maximum of  DSQRT(U/EPS)  over all known machines.
C         CUTHI = minimum of  DSQRT(V)      over all known machines.
C     where
C         EPS = smallest no. such that EPS + 1. .GT. 1.
C         U   = smallest positive no.   (underflow limit)
C         V   = largest  no.            (overflow  limit)
C
C     Brief outline of algorithm..
C
C     Phase 1    scans zero components.
C     move to phase 2 when a component is nonzero and .LE. CUTLO
C     move to phase 3 when a component is .GT. CUTLO
C     move to phase 4 when a component is .GE. CUTHI/M
C     where M = N for X() real and M = 2*N for complex.
C
C     Values for CUTLO and CUTHI..
C     From the environmental parameters listed in the IMSL converter
C     document the limiting values are as followS..
C     CUTLO, S.P.   U/EPS = 2**(-102) for  Honeywell.  Close seconds are
C                   Univac and DEC at 2**(-103)
C                   Thus CUTLO = 2**(-51) = 4.44089E-16
C     CUTHI, S.P.   V = 2**127 for Univac, Honeywell, and DEC.
C                   Thus CUTHI = 2**(63.5) = 1.30438E19
C     CUTLO, D.P.   U/EPS = 2**(-67) for Honeywell and DEC.
C                   Thus CUTLO = 2**(-33.5) = 8.23181D-11
C     CUTHI, D.P.   same as S.P.  CUTHI = 1.30438D19
      SAVE CUTLO, CUTHI, ZERO, ONE
C     DATA CUTLO, CUTHI / 8.232D-11,  1.304D19 /
C     DATA CUTLO, CUTHI / 4.441E-16,  1.304E19 /
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DNRM2
      INTEGER          NEXT
      DOUBLE PRECISION   DX(1), CUTLO, CUTHI, HITEST, SUM, XMAX,ZERO,ONE
      DATA   ZERO, ONE /0.0D0, 1.0D0/
C
      DATA CUTLO, CUTHI / 8.232D-11,  1.304D19 /
C***FIRST EXECUTABLE STATEMENT  DNRM2
      IF(N .GT. 0) GO TO 10
         DNRM2  = ZERO
         GO TO 300
C
   10 ASSIGN 30 TO NEXT
      SUM = ZERO
      NN = N * INCX
C                                                 BEGIN MAIN LOOP
      I = 1
   20    GO TO NEXT,(30, 50, 70, 110)
   30 IF( DABS(DX(I)) .GT. CUTLO) GO TO 85
      ASSIGN 50 TO NEXT
      XMAX = ZERO
C
C                        PHASE 1.  SUM IS ZERO
C
   50 IF( DX(I) .EQ. ZERO) GO TO 200
      IF( DABS(DX(I)) .GT. CUTLO) GO TO 85
C
C                                PREPARE FOR PHASE 2.
      ASSIGN 70 TO NEXT
      GO TO 105
C
C                                PREPARE FOR PHASE 4.
C
  100 I = J
      ASSIGN 110 TO NEXT
      SUM = (SUM / DX(I)) / DX(I)
  105 XMAX = DABS(DX(I))
      GO TO 115
C
C                   PHASE 2.  SUM IS SMALL.
C                             SCALE TO AVOID DESTRUCTIVE UNDERFLOW.
C
   70 IF( DABS(DX(I)) .GT. CUTLO ) GO TO 75
C
C                     COMMON CODE FOR PHASES 2 AND 4.
C                     IN PHASE 4 SUM IS LARGE.  SCALE TO AVOID OVERFLOW.
C
  110 IF( DABS(DX(I)) .LE. XMAX ) GO TO 115
         SUM = ONE + SUM * (XMAX / DX(I))**2
         XMAX = DABS(DX(I))
         GO TO 200
C
  115 SUM = SUM + (DX(I)/XMAX)**2
      GO TO 200
C
C
C                  PREPARE FOR PHASE 3.
C
   75 SUM = (SUM * XMAX) * XMAX
C
C
C     FOR REAL OR D.P. SET HITEST = CUTHI/N
C     FOR COMPLEX      SET HITEST = CUTHI/(2*N)
C
   85 HITEST = CUTHI/FLOAT( N )
C
C                   PHASE 3.  SUM IS MID-RANGE.  NO SCALING.
C
      DO 95 J =I,NN,INCX
      IF(DABS(DX(J)) .GE. HITEST) GO TO 100
   95    SUM = SUM + DX(J)**2
      DNRM2 = DSQRT( SUM )
      GO TO 300
C
  200 CONTINUE
      I = I + INCX
      IF ( I .LE. NN ) GO TO 20
C
C              END OF MAIN LOOP.
C
C              COMPUTE SQUARE ROOT AND ADJUST FOR SCALING.
C
      DNRM2 = XMAX * DSQRT(SUM)
  300 CONTINUE
      RETURN
      END

      SUBROUTINE DSWAP(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE  DSWAP
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A5
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SSWAP-S DSWAP-D CSWAP-C ISWAP-I),
C             INTERCHANGE,LINEAR ALGEBRA,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Interchange d.p. vectors
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C       DY  double precision vector with N elements
C     INCY  storage spacing between elements of DY
C
C     --Output--
C       DX  input vector DY (unchanged if N .LE. 0)
C       DY  input vector DX (unchanged if N .LE. 0)
C
C     Interchange double precision DX and double precision DY.
C     For I = 0 to N-1, interchange  DX(LX+I*INCX) and DY(LY+I*INCY),
C     where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and LY is
C     defined in a similar way using INCY.
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DSWAP
C
      DOUBLE PRECISION DX(1),DY(1),DTEMP1,DTEMP2,DTEMP3
C***FIRST EXECUTABLE STATEMENT  DSWAP
      IF(N.LE.0)RETURN
      IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
    5 CONTINUE
C
C       CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
C
      IX = 1
      IY = 1
      IF(INCX.LT.0)IX = (-N+1)*INCX + 1
      IF(INCY.LT.0)IY = (-N+1)*INCY + 1
      DO 10 I = 1,N
        DTEMP1 = DX(IX)
        DX(IX) = DY(IY)
        DY(IY) = DTEMP1
        IX = IX + INCX
        IY = IY + INCY
   10 CONTINUE
      RETURN
C
C       CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C       CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 3.
C
   20 M = MOD(N,3)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DTEMP1 = DX(I)
        DX(I) = DY(I)
        DY(I) = DTEMP1
   30 CONTINUE
      IF( N .LT. 3 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,3
        DTEMP1 = DX(I)
        DTEMP2 = DX(I+1)
        DTEMP3 = DX(I+2)
        DX(I) = DY(I)
        DX(I+1) = DY(I+1)
        DX(I+2) = DY(I+2)
        DY(I) = DTEMP1
        DY(I+1) = DTEMP2
        DY(I+2) = DTEMP3
   50 CONTINUE
      RETURN
   60 CONTINUE
C
C     CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
C
      NS = N*INCX
        DO 70 I=1,NS,INCX
        DTEMP1 = DX(I)
        DX(I) = DY(I)
        DY(I) = DTEMP1
   70   CONTINUE
      RETURN
      END

      SUBROUTINE DSCAL(N,DA,DX,INCX)
C***BEGIN PROLOGUE  DSCAL
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A6
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SSCAL-S DSCAL-D CSCAL-C),
C             LINEAR ALGEBRA,SCALE,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  D.P. vector scale x = a*x
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DA  double precision scale factor
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C       DX  double precision result (unchanged if N.LE.0)
C
C     Replace double precision DX by double precision DA*DX.
C     For I = 0 to N-1, replace DX(1+I*INCX) with  DA * DX(1+I*INCX)
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DSCAL
C
      DOUBLE PRECISION DA,DX(1)
C***FIRST EXECUTABLE STATEMENT  DSCAL
      IF(N.LE.0)RETURN
      IF(INCX.EQ.1)GOTO 20
C
C        CODE FOR INCREMENTS NOT EQUAL TO 1.
C
      NS = N*INCX
          DO 10 I = 1,NS,INCX
          DX(I) = DA*DX(I)
   10     CONTINUE
      RETURN
C
C        CODE FOR INCREMENTS EQUAL TO 1.
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 5.
C
   20 M = MOD(N,5)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
        DX(I) = DA*DX(I)
   30 CONTINUE
      IF( N .LT. 5 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,5
        DX(I) = DA*DX(I)
        DX(I + 1) = DA*DX(I + 1)
        DX(I + 2) = DA*DX(I + 2)
        DX(I + 3) = DA*DX(I + 3)
        DX(I + 4) = DA*DX(I + 4)
   50 CONTINUE
      RETURN
      END
      DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX)
C***BEGIN PROLOGUE  DASUM
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A3A
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(SASUM-S DASUM-D SCASUM-C),ADD,
C             LINEAR ALGEBRA,MAGNITUDE,SUM,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Sum of magnitudes of d.p. vector components
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C    DASUM  double precision result (zero if N .LE. 0)
C
C     Returns sum of magnitudes of double precision DX.
C     DASUM = sum from 0 to N-1 of DABS(DX(1+I*INCX))
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  DASUM
C
      DOUBLE PRECISION DX(1)
C***FIRST EXECUTABLE STATEMENT  DASUM
      DASUM = 0.D0
      IF(N.LE.0)RETURN
      IF(INCX.EQ.1)GOTO 20
C
C        CODE FOR INCREMENTS NOT EQUAL TO 1.
C
      NS = N*INCX
          DO 10 I=1,NS,INCX
          DASUM = DASUM + DABS(DX(I))
   10     CONTINUE
      RETURN
C
C        CODE FOR INCREMENTS EQUAL TO 1.
C
C
C        CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 6.
C
   20 M = MOD(N,6)
      IF( M .EQ. 0 ) GO TO 40
      DO 30 I = 1,M
         DASUM = DASUM + DABS(DX(I))
   30 CONTINUE
      IF( N .LT. 6 ) RETURN
   40 MP1 = M + 1
      DO 50 I = MP1,N,6
         DASUM = DASUM + DABS(DX(I)) + DABS(DX(I+1)) + DABS(DX(I+2))
     1   + DABS(DX(I+3)) + DABS(DX(I+4)) + DABS(DX(I+5))
   50 CONTINUE
      RETURN
      END
      INTEGER FUNCTION IDAMAX(N,DX,INCX)
C***BEGIN PROLOGUE  IDAMAX
C***DATE WRITTEN   791001   (YYMMDD)
C***REVISION DATE  861211   (YYMMDD)
C***CATEGORY NO.  D1A2
C***KEYWORDS  LIBRARY=SLATEC(BLAS),
C             TYPE=DOUBLE PRECISION(ISAMAX-S IDAMAX-D ICAMAX-C),
C             LINEAR ALGEBRA,MAXIMUM COMPONENT,VECTOR
C***AUTHOR  LAWSON, C. L., (JPL)
C           HANSON, R. J., (SNLA)
C           KINCAID, D. R., (U. OF TEXAS)
C           KROGH, F. T., (JPL)
C***PURPOSE  Find the smallest index of that component of a d.p. vector
C            having the maximum magnitude.
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of Parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C   IDAMAX  smallest index (zero if N .LE. 0)
C
C     Find smallest index of maximum magnitude of double precision DX.
C     IDAMAX =  first I, I = 1 to N, to minimize  ABS(DX(1-INCX+I*INCX)
C***REFERENCES  LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C                 *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C                 ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C                 SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  IDAMAX
C
      DOUBLE PRECISION DX(*),DMAX,XMAG
C***FIRST EXECUTABLE STATEMENT  IDAMAX
      IDAMAX = 0
      IF(N.LE.0) RETURN
      IDAMAX = 1
      IF(N.LE.1)RETURN
      IF(INCX.EQ.1)GOTO 20
C
C        CODE FOR INCREMENTS NOT EQUAL TO 1.
C
      DMAX = DABS(DX(1))
      NS = N*INCX
      II = 1
          DO 10 I = 1,NS,INCX
          XMAG = DABS(DX(I))
          IF(XMAG.LE.DMAX) GO TO 5
          IDAMAX = II
          DMAX = XMAG
    5     II = II + 1
   10     CONTINUE
      RETURN
C
C        CODE FOR INCREMENTS EQUAL TO 1.
C
   20 DMAX = DABS(DX(1))
      DO 30 I = 2,N
          XMAG = DABS(DX(I))
          IF(XMAG.LE.DMAX) GO TO 30
          IDAMAX = I
          DMAX = XMAG
   30 CONTINUE
      RETURN
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'driver.f'
then
	echo shar: will not over-write existing file "'driver.f'"
else
cat << "SHAR_EOF" > 'driver.f'
C
C
C ARRAY length and grid parameters:
C
C   LDA = Row dimension of array ABD used to store D**T*D
C         (and the matrix associated with the cubic spline
C         interpolant) in LAPACK band storage (packed)
C         format for the linear solver DPBSV (and CSPLIN).
C
C   MMAX = Maximum number of grid points.  The array storage
C          requirement is approximately 112*MMAX bytes for
C          8-byte double precision numbers.
C
C   NMAX = Maximum number of data points.
C
      INTEGER LDA, MMAX, NMAX
      PARAMETER (LDA=3, NMAX=100, MMAX=900)
C
C Arrays:
C
      DOUBLE PRECISION D(NMAX), S(NMAX), T(NMAX)
      DOUBLE PRECISION A(MMAX), ABD(LDA,MMAX), D1Y(MMAX),
     .                 D2Y(MMAX), G(MMAX), G0(MMAX),
     .                 P(MMAX), WK(MMAX,3), Y0(MMAX),
     .                 Y(MMAX)
      INTEGER IND(NMAX)
C
C Scalars and functions:
C
      CHARACTER CHR
      CHARACTER*60 FNAME
      DOUBLE PRECISION DDOT, PHI
      DOUBLE PRECISION ALPHA, C2, C3, DD, DG, DGG, DPHI, DT,
     .                 DY, FMTOL, GG, GNRM1, GNRMM, H, PHI0,
     .                 PHIY, PHTOL, PLTSIZ, Q, SSIZ0, SSIZ1,
     .                 YMAX
      INTEGER I, IER, J, J1, J2, LIN, LOUT, LPLT, LPRT, M,
     .        MAXCG, N, NCG, NG, NGMAX, NPHSM, NPHVAL, NPRNT
      LOGICAL L2G, OPT, PLT0, PRNT
C
C Parameters:
C
C   FMTOL = Nonnegative tolerance for the line search:
C           length of the interval of uncertainty.  Refer
C           to Function FMIN.
C
C   L2G = Flag with value TRUE iff the L2-gradient is to be
C         used in place of the Sobolev gradient.
C
C   MAXCG = Number of Polak-Ribiere conjugate gradient steps
C           between restarts with a steepest descent step.
C
C   NGMAX = Maximum number of descent steps (outer itera-
C           tions) before termination without convergence.
C           NGMAX > 0.
C
C   NPRNT = Number of descent steps between print steps.
C           For each print step, several lines of statistics
C           describing the step are written to unit LPRT.
C           The first and last descent steps are necessarily
C           print steps.  NPRNT .GE. 1.
C
C   OPT = Flag with value TRUE iff the optimal step-size
C         (computed by a line search) is to be used at each
C         descent step.
C
C   PHTOL = Nonnegative tolerance which defines convergence
C           of the descent method:  bound on Max(DPHI,DY**2,
C           DG**3), where
C             DPHI = abs(change in phi)/(1+phi),
C             DY = max-norm(change in Y)/(1+max-norm(Y)),
C             DG = max-norm(S-gradient)/(1+max-norm(Y)).
C
C   PLT0 = Flag with value TRUE iff the initial estimate is
C          to be plotted.
C
C   PLTSIZ = Plot size in inches for Postscript plots.
C            1.0 <= PLTSIZ <= 6.5.
C
C   SSIZ0 = Descent step size used if OPT = FALSE.
C
C   SSIZ1 = Initial descent step size used if OPT = TRUE.
C
      DATA FMTOL/1.D-6/,  L2G/.FALSE./,  MAXCG/3/,
     .     NGMAX/200/,    NPRNT/1/,      OPT/.TRUE./,
     .     PHTOL/1.D-3/,  PLT0/.TRUE./,  PLTSIZ/6.5/,
     .     SSIZ0/1.D-3/,  SSIZ1/1.D-5/
C
C Logical unit numbers:
C
C   LIN = Logical unit number for an input data set contain-
C         ing N, (T(I), I = 1,N), (D(I), I = 1,N), and H.
C
C   LOUT = Logical unit number for writing the solution
C          M, (Y(I), I = 1,M), (D1Y(I), I = 1,M), and
C          (D2Y(I), I = 1,M):  Subroutine WRITF.
C
C   LPLT = Logical unit number for files containing
C          Postscript plots:  initial estimate, spline
C          curve, and/or curvature.  Refer to Subroutine
C          PLTCRV.
C
C   LPRT = Logical unit number for output other than the
C          solution.
C
      DATA LIN/5/,  LOUT/6/,  LPLT/3/,  LPRT/4/
C
C Open print file, delete it, and reopen it.  This is
C   necessary on some systems (Microsoft) which ignore
C   end-of-file records.
C
      OPEN (LPRT,FILE='dnsplin1.prt')
      CLOSE (LPRT,STATUS='DELETE')
      OPEN (LPRT,FILE='dnsplin1.prt')
C
C Get an input data set file name.
C
C   1 WRITE (*,200)
C 200 FORMAT (//5X,'Specify the name of a file containing ',
C    .        'an input data set'/
C    .        5X,'(at most 60 characters):'/)
C     READ (*,205,ERR=1) FNAME
C 205 FORMAT (A60)
C     OPEN (LIN,FILE=FNAME,STATUS='OLD',ERR=1)
C
C Read input data, and compute indexes (1 to M=IND(N)) of
C   data points.
C
      CALL READF (LIN,NMAX, N,T,D,H,IND,IER)
      IF (IER .NE. 0) GO TO 21
      M = IND(N)
      IF (M .LT. 6  .OR.  M .GT. MMAX  .OR.  M-N .LT. 1)
     .  GO TO 22
C
C Print a heading with parameter values.
C
      WRITE (LPRT,100)
  100 FORMAT (///27X,'DNSPLIN1 Output'/)
      WRITE (LPRT,110) T(1), T(N), N, M, H, MAXCG, FMTOL,
     .                 PHTOL, NGMAX
  110 FORMAT (//5X,'Domain:  T(1) = ',D10.3,', T(N) = ',
     .             D10.3/
     .        5X,'Number of data points:  N = ',I4//
     .        5X,'Number of grid points:  M = ',I5/
     .        5X,'Mesh width:  H = ',D12.6//1P,
     .        5X,'# CG steps between restarts:  MAXCG = ',
     .           I4/
     .        5X,'Line search tolerance:  FMTOL = ',D9.3/
     .        5X,'Convergence tolerance:  PHTOL = ',D9.3/
     .        5X,'Max number of iterations:  NGMAX = ',I6)
C
C Set Y0 to the gridpoint values of the Hermite cubic
C   interpolant with derivatives S at the data abscissae
C   obtained from the natural cubic spline.
C
      CALL CSPLIN (LDA,N,T,D, ABD, S,IER)
      IF (IER .NE. 0) GO TO 23
C
      J2 = 1
      DO 3 I = 1,N-1
        J1 = J2
        J2 = IND(I+1)
        Y0(J1) = D(I)
        DT = T(I+1)-T(I)
        DD = (D(I+1)-D(I))/DT
        C2 = (3.D0*DD-2.D0*S(I)-S(I+1))/DT
        C3 = (-2.D0*DD+S(I)+S(I+1))/(DT*DT)
        DT = 0.D0
        DO 2 J = J1+1,J2-1
          DT = DT + H
          Y0(J) = ((C3*DT + C2)*DT + S(I))*DT + D(I)
    2     CONTINUE
    3   CONTINUE
      Y0(J2) = D(N)
C
C Copy Y0 into Y.
C
      DO 4 I = 1,M
        Y(I) = Y0(I)
    4   CONTINUE
C
C Prompt for optional plot of initial estimate.
C
C   5 WRITE (*,210)
C 210 FORMAT (//5X,'Create file dnsplin1.ps0 containing a ',
C    .        'plot '/
C    .        5X,'of the initial estimate? (y/n)'/)
C     READ (*,215,ERR=5) CHR
C 215 FORMAT (A1)
C     IF (CHR .NE. 'Y'  .AND.  CHR .NE. 'y'  .AND.
C    .    CHR .NE. 'N'  .AND.  CHR .NE. 'n') GO TO 5
C     IF (CHR .EQ. 'Y'  .OR.  CHR .EQ. 'y') THEN
        OPEN (LPLT,FILE='dnsplin1.ps0')
        CLOSE (LPLT,STATUS='DELETE')
        OPEN (LPLT,FILE='dnsplin1.ps0')
        CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y0,.FALSE.,Y0,
     .               PLTSIZ, IER)
        CLOSE (LPLT)
        IF (IER .NE. 0) GO TO 26
C     ENDIF
C
C Compute PHI0 = phi(Y0).  Grid-point values D1y(i), D2y(i),
C   and a(i) are also computed.
C
      PHI0 = PHI (M,H,Y0, D1Y,D2Y,A)
C
C Initialize iteration counts:
C
C   NCG = Number of conjugate gradient steps since the
C         previous restart with a steepest descent step.
C
C   NG = Number of iterations (gradient evaluations).
C
C   NPHSM = Total number of evaluations of phi in the line
C           searches.
C
C   PRNT = TRUE iff statistics describing the iteration are
C          to be printed.
C
      NCG = MAXCG
      NG = 0
      NPHSM = 0
      PRNT = .TRUE.
C
C Top of loop:  compute the L2-gradient G = grad(phi), its
C               1-norm GNRM1, and its max-norm GNRMM, and
C               overwrite G with the Sobolev gradient unless
C               L2G = TRUE.
C
    7 CALL GRADL2 (N,H,IND,M,D1Y,D2Y,A, WK, G,GNRM1,
     .             GNRMM,IER)
      IF (IER .NE. 0) GO TO 24
      IF (.NOT. L2G) THEN
        CALL GRADS4 (N,H,IND,M,D1Y,D2Y,LDA, ABD,G,
     .               WK, IER)
        IF (IER .GT. 0) WRITE (LPRT,125) IER
  125   FORMAT (//5X,'GRADS4 Failure:  IER = ',I1)
      ENDIF
C
C Compute mean absolute L2-gradient component GNRM1.
C
      GNRM1 = GNRM1/DBLE(M-N)
C
C Update iteration count.
C
      NG = NG + 1
C
C Print statistics associated with the step.
C
      IF (PRNT) THEN
        IF (NCG .GE. MAXCG) THEN
          WRITE (LPRT,130) NG
        ELSE
          WRITE (LPRT,135) NG
        ENDIF
        WRITE (LPRT,140) PHI0, GNRM1, GNRMM
      ENDIF
  130 FORMAT (//15X,'Iteration ',I6,' (Steepest descent)')
  135 FORMAT (//15X,'Iteration ',I6,' (Conjugate gradient)')
  140 FORMAT (5X,'Functional:                  phi(F) = ',
     .           1P,D21.15/
     .        5X,'Mean absolute L2-gradient:    GNRM1 = ',
     .           D8.2/
     .        5X,'Max-norm of L2-gradient:      GNRMM = ',
     .           D8.2)
      PRNT = (NPRNT*(NG/NPRNT) .EQ. NG)  .OR.  (NG .EQ. 1)
C
      IF (NCG .GE. MAXCG) THEN
C
C Steepest descent step.
C
        Q = 0.D0
        NCG = 0
      ELSE
C
C Conjugate gradient step.
C
        GG = DDOT(M,G0,1,G0,1)
        DGG = DDOT(M,G,1,G,1) - DDOT(M,G0,1,G,1)
        Q = DGG/GG
        NCG = NCG + 1
      ENDIF
C
C Compute the search direction p = -G + Q*p.
C
      DO 8 I = 1,M
        P(I) = -G(I) + Q*P(I)
    8   CONTINUE
C
C Copy Y into Y1 (WK column 1), compute the optimal step-
C   size ALPHA, and update Y to Y1+ALPHA*p.  Difference
C   approximations to derivatives and terms defining phi(Y)
C   are returned in D1Y, D2Y, and A.  The Max-norm of Y is
C   returned in YMAX, and DY is the relative change in Y:
C   Max-norm(Y-Y1)/(1+YMAX) = ALPHA*Max-norm(p)/(1+YMAX).
C
C The initial estimate for ALPHA should be small.  Using
C   the step-size computed at the previously iteration can
C   result in an incorrect step-size caused by finding a
C   local minimum which is not a global minimum.
C
      DO 9 I = 1,M
        WK(I,1) = Y(I)
    9   CONTINUE
      IF (OPT) THEN
        ALPHA = SSIZ1
      ELSE
C
C   Use small constant step-size.
C
        ALPHA = SSIZ0
      ENDIF
      CALL LNSRCH (M,H,WK,PHI0,P,FMTOL,OPT, ALPHA,Y,D1Y,
     .             D2Y,A, PHIY,NPHVAL,YMAX,DY,IER)
      IF (IER .NE. 0) GO TO 25
      NPHSM = NPHSM + NPHVAL
C
C Adjust DY to the relative change in Y squared.
C
      DY = DY**2
C
C Compute the max-norm of the Sobolev gradient relative to
C   the solution y.
C
      DG = 0.D0
      DO 10 I = 1,M
        DG = MAX(DG,ABS(G(I)))
   10   CONTINUE
      DG = (DG/(1.D0+YMAX))**3
C
C Save a copy of the Sobolev gradient G in G0 for computing
C   the search direction in the next conjugate gradient
C   step.
C
      IF (NCG .LT. MAXCG) THEN
        DO 11 I = 1,M
          G0(I) = G(I)
   11     CONTINUE
      ENDIF
C
C Compute the relative change DPHI in phi and update PHI0.
C   Terminate on an increase in phi.
C
      DPHI = (PHI0-PHIY)/(1.D0+PHI0)
      PHI0 = PHIY
      IF (DPHI .LT. 0.D0) NGMAX = NG
C
C Print statistics.
C
      IF (PRNT) WRITE (LPRT,150) NPHVAL, ALPHA, PHIY, DPHI,
     .                           DY, DG
  150 FORMAT (/5X,'Line search:     No. phi evals NPHV = ',
     .            I3/
     .         5X,'                Optimal step-size S = ',
     .            1P,D9.3/
     .         5X,'                  Functional phi(Y) = ',
     .            D21.15/
     .         5X,'     Relative change in phi(Y) DPHI = ',
     .            D9.2/
     .         5X,'  Squared relative change in Y:  DY = ',
     .            D9.2/
     .         5X,'    Cubed S-gradient rel. to Y:  DG = ',
     .            D9.2/
     .         1X,'______________________________________',
     .            '___________________________')
C
C Test for termination.
C
      IF ((DPHI .GE. PHTOL  .OR.  DY .GE. PHTOL  .OR.
     .     DG .GE. PHTOL)  .AND.  NG .LT. NGMAX) GO TO 7
      IF (.NOT. PRNT) THEN
C
C Print parameter values.
C
        IF (NCG .EQ. 0) THEN
          WRITE (LPRT,130) NG
        ELSE
          WRITE (LPRT,135) NG
        ENDIF
        WRITE (LPRT,140) PHI0, GNRM1, GNRMM
        WRITE (LPRT,150) NPHVAL, ALPHA, PHIY, DPHI, DY, DG
      ENDIF
C
C Compute the curve length in DY.
C
      C2 = H*H
      DY = 0.D0
      DO 12 I = 2,M
        DY = DY + SQRT(C2 + (Y(I)-Y(I-1))**2)
   12   CONTINUE
C
C Print iteration counts and statistics.
C
      WRITE (LPRT,160) NG
  160 FORMAT (//5X,'Number of descent ',
     .        'iterations: ',I6)
      WRITE (LPRT,170) NPHSM
  170 FORMAT (/5X,'Total number of phi evaluations ',
     .        'in the line searches: ',I7)
      WRITE (LPRT,180) DY
  180 FORMAT (/5X,'Total polygonal curve length: ',D9.3)
C
C Write the solution to disk.
C
C     OPEN (LOUT,FILE='dnsplin1.out')
C     CLOSE (LOUT,STATUS='DELETE')
C     OPEN (LOUT,FILE='dnsplin1.out')
      CALL WRITF (LOUT,M,Y,D1Y,D2Y)
C
C Plot the solution.
C
      OPEN (LPLT,FILE='dnsplin1.ps')
      CLOSE (LPLT,STATUS='DELETE')
      OPEN (LPLT,FILE='dnsplin1.ps')
      CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y,PLT0,Y0,
     .             PLTSIZ, IER)
      CLOSE (LPLT)
      IF (IER .NE. 0) GO TO 26
C
C Prompt for optional plot of curvature.
C
C  13 WRITE (*,220)
C 220 FORMAT (//5X,'Create file dnsplin1.ps2 containing a ',
C    .        'curvature plot? (y/n)'/)
C     READ (*,215,ERR=13) CHR
C     IF (CHR .NE. 'Y'  .AND.  CHR .NE. 'y'  .AND.
C    .    CHR .NE. 'N'  .AND.  CHR .NE. 'n') GO TO 13
C     IF (CHR .EQ. 'Y'  .OR.  CHR .EQ. 'y') THEN
        OPEN (LPLT,FILE='dnsplin1.ps2')
        CLOSE (LPLT,STATUS='DELETE')
        OPEN (LPLT,FILE='dnsplin1.ps2')
        Y(1) = 0.D0
        DO 14 I = 2,M-1
          Y(I) = D2Y(I)/(1.D0+D1Y(I)**2)**1.5D0
   14     CONTINUE
        Y(M) = 0.D0
        DO 15 J = 1,N
          I = IND(J)
          D(J) = Y(I)
   15     CONTINUE
        CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y,.FALSE.,Y0,
     .               PLTSIZ, IER)
        CLOSE (LPLT)
        IF (IER .NE. 0) GO TO 26
C     ENDIF
      STOP
C
C Error encountered in Subroutine READF.
C
   21 WRITE (LPRT,421) IER
  421 FORMAT (///10X,'*** Error in READF:  IER = ',
     .        I1,' ***')
      STOP
C
C Invalid data:  M < 6 or M > MMAX or M-N < 1.
C
   22 WRITE (LPRT,422) M, MMAX, N
  422 FORMAT (///10X,'*** Error in data:  M = ',I5,
     .        ', MMAX = ',I5,', N = ',I4,' ***')
      STOP
C
C Error encountered in Subroutine CSPLIN.
C
   23 WRITE (LPRT,423) IER
  423 FORMAT (///10X,'*** Error in CSPLIN:  IER = ',
     .        I1,' ***')
      STOP
C
C Error encountered in Subroutine GRADL2.
C
   24 WRITE (LPRT,424) IER
  424 FORMAT (///10X,'*** Error in GRADL2:  IER = ',
     .        I1,' ***')
      STOP
C
C Error encountered in Subroutine LNSRCH.
C
   25 WRITE (LPRT,425) IER
  425 FORMAT (///10X,'*** Error in LNSRCH:  IER = ',
     .        I1,' ***')
      STOP
C
C Error encountered in Subroutine PLTCRV.
C
   26 WRITE (LPRT,426) IER
  426 FORMAT (///10X,'*** Error in PLTCRV:  IER = ',
     .        I1,' ***')
      STOP
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'interactive.f'
then
	echo shar: will not over-write existing file "'interactive.f'"
else
cat << "SHAR_EOF" > 'interactive.f'
C
C ARRAY length and grid parameters:
C
C   LDA = Row dimension of array ABD used to store D**T*D
C         (and the matrix associated with the cubic spline
C         interpolant) in LAPACK band storage (packed)
C         format for the linear solver DPBSV (and CSPLIN).
C
C   MMAX = Maximum number of grid points.  The array storage
C          requirement is approximately 112*MMAX bytes for
C          8-byte double precision numbers.
C
C   NMAX = Maximum number of data points.
C
      INTEGER LDA, MMAX, NMAX
      PARAMETER (LDA=3, NMAX=100, MMAX=900)
C
C Arrays:
C
      DOUBLE PRECISION D(NMAX), S(NMAX), T(NMAX)
      DOUBLE PRECISION A(MMAX), ABD(LDA,MMAX), D1Y(MMAX),
     .                 D2Y(MMAX), G(MMAX), G0(MMAX),
     .                 P(MMAX), WK(MMAX,3), Y0(MMAX),
     .                 Y(MMAX)
      INTEGER IND(NMAX)
C
C Scalars and functions:
C
      CHARACTER CHR
      CHARACTER*60 FNAME
      DOUBLE PRECISION DDOT, PHI
      DOUBLE PRECISION ALPHA, C2, C3, DD, DG, DGG, DPHI, DT,
     .                 DY, FMTOL, GG, GNRM1, GNRMM, H, PHI0,
     .                 PHIY, PHTOL, PLTSIZ, Q, SSIZ0, SSIZ1,
     .                 YMAX
      INTEGER I, IER, J, J1, J2, LIN, LOUT, LPLT, LPRT, M,
     .        MAXCG, N, NCG, NG, NGMAX, NPHSM, NPHVAL, NPRNT
      LOGICAL L2G, OPT, PLT0, PRNT
C
C Parameters:
C
C   FMTOL = Nonnegative tolerance for the line search:
C           length of the interval of uncertainty.  Refer
C           to Function FMIN.
C
C   L2G = Flag with value TRUE iff the L2-gradient is to be
C         used in place of the Sobolev gradient.
C
C   MAXCG = Number of Polak-Ribiere conjugate gradient steps
C           between restarts with a steepest descent step.
C
C   NGMAX = Maximum number of descent steps (outer itera-
C           tions) before termination without convergence.
C           NGMAX > 0.
C
C   NPRNT = Number of descent steps between print steps.
C           For each print step, several lines of statistics
C           describing the step are written to unit LPRT.
C           The first and last descent steps are necessarily
C           print steps.  NPRNT .GE. 1.
C
C   OPT = Flag with value TRUE iff the optimal step-size
C         (computed by a line search) is to be used at each
C         descent step.
C
C   PHTOL = Nonnegative tolerance which defines convergence
C           of the descent method:  bound on Max(DPHI,DY**2,
C           DG**3), where
C             DPHI = abs(change in phi)/(1+phi),
C             DY = max-norm(change in Y)/(1+max-norm(Y)),
C             DG = max-norm(S-gradient)/(1+max-norm(Y)).
C
C   PLT0 = Flag with value TRUE iff the initial estimate is
C          to be plotted.
C
C   PLTSIZ = Plot size in inches for Postscript plots.
C            1.0 <= PLTSIZ <= 6.5.
C
C   SSIZ0 = Descent step size used if OPT = FALSE.
C
C   SSIZ1 = Initial descent step size used if OPT = TRUE.
C
      DATA FMTOL/1.D-6/,  L2G/.FALSE./,  MAXCG/3/,
     .     NGMAX/200/,    NPRNT/1/,      OPT/.TRUE./,
     .     PHTOL/1.D-3/,  PLT0/.TRUE./,  PLTSIZ/6.5/,
     .     SSIZ0/1.D-3/,  SSIZ1/1.D-5/
C
C Logical unit numbers:
C
C   LIN = Logical unit number for an input data set contain-
C         ing N, (T(I), I = 1,N), (D(I), I = 1,N), and H.
C
C   LOUT = Logical unit number for writing the solution
C          M, (Y(I), I = 1,M), (D1Y(I), I = 1,M), and
C          (D2Y(I), I = 1,M):  Subroutine WRITF.
C
C   LPLT = Logical unit number for files containing
C          Postscript plots:  initial estimate, spline
C          curve, and/or curvature.  Refer to Subroutine
C          PLTCRV.
C
C   LPRT = Logical unit number for output other than the
C          solution.
C
      DATA LIN/1/,  LOUT/2/,  LPLT/3/,  LPRT/4/
C
C Open print file, delete it, and reopen it.  This is
C   necessary on some systems (Microsoft) which ignore
C   end-of-file records.
C
      OPEN (LPRT,FILE='dnsplin1.prt')
      CLOSE (LPRT,STATUS='DELETE')
      OPEN (LPRT,FILE='dnsplin1.prt')
C
C Get an input data set file name.
C
    1 WRITE (*,200)
  200 FORMAT (//5X,'Specify the name of a file containing ',
     .        'an input data set'/
     .        5X,'(at most 60 characters):'/)
      READ (*,205,ERR=1) FNAME
  205 FORMAT (A60)
      OPEN (LIN,FILE=FNAME,STATUS='OLD',ERR=1)
C
C Read input data, and compute indexes (1 to M=IND(N)) of
C   data points.
C
      CALL READF (LIN,NMAX, N,T,D,H,IND,IER)
      IF (IER .NE. 0) GO TO 21
      M = IND(N)
      IF (M .LT. 6  .OR.  M .GT. MMAX  .OR.  M-N .LT. 1)
     .  GO TO 22
C
C Print a heading with parameter values.
C
      WRITE (LPRT,100)
  100 FORMAT (///27X,'DNSPLIN1 Output'/)
      WRITE (LPRT,110) T(1), T(N), N, M, H, MAXCG, FMTOL,
     .                 PHTOL, NGMAX
  110 FORMAT (//5X,'Domain:  T(1) = ',D10.3,', T(N) = ',
     .             D10.3/
     .        5X,'Number of data points:  N = ',I4//
     .        5X,'Number of grid points:  M = ',I5/
     .        5X,'Mesh width:  H = ',D12.6//1P,
     .        5X,'# CG steps between restarts:  MAXCG = ',
     .           I4/
     .        5X,'Line search tolerance:  FMTOL = ',D9.3/
     .        5X,'Convergence tolerance:  PHTOL = ',D9.3/
     .        5X,'Max number of iterations:  NGMAX = ',I6)
C
C Set Y0 to the gridpoint values of the Hermite cubic
C   interpolant with derivatives S at the data abscissae
C   obtained from the natural cubic spline.
C
      CALL CSPLIN (LDA,N,T,D, ABD, S,IER)
      IF (IER .NE. 0) GO TO 23
C
      J2 = 1
      DO 3 I = 1,N-1
        J1 = J2
        J2 = IND(I+1)
        Y0(J1) = D(I)
        DT = T(I+1)-T(I)
        DD = (D(I+1)-D(I))/DT
        C2 = (3.D0*DD-2.D0*S(I)-S(I+1))/DT
        C3 = (-2.D0*DD+S(I)+S(I+1))/(DT*DT)
        DT = 0.D0
        DO 2 J = J1+1,J2-1
          DT = DT + H
          Y0(J) = ((C3*DT + C2)*DT + S(I))*DT + D(I)
    2     CONTINUE
    3   CONTINUE
      Y0(J2) = D(N)
C
C Copy Y0 into Y.
C
      DO 4 I = 1,M
        Y(I) = Y0(I)
    4   CONTINUE
C
C Prompt for optional plot of initial estimate.
C
    5 WRITE (*,210)
  210 FORMAT (//5X,'Create file dnsplin1.ps0 containing a ',
     .        'plot '/
     .        5X,'of the initial estimate? (y/n)'/)
      READ (*,215,ERR=5) CHR
  215 FORMAT (A1)
      IF (CHR .NE. 'Y'  .AND.  CHR .NE. 'y'  .AND.
     .    CHR .NE. 'N'  .AND.  CHR .NE. 'n') GO TO 5
      IF (CHR .EQ. 'Y'  .OR.  CHR .EQ. 'y') THEN
        OPEN (LPLT,FILE='dnsplin1.ps0')
        CLOSE (LPLT,STATUS='DELETE')
        OPEN (LPLT,FILE='dnsplin1.ps0')
        CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y0,.FALSE.,Y0,
     .               PLTSIZ, IER)
        CLOSE (LPLT)
        IF (IER .NE. 0) GO TO 26
      ENDIF
C
C Compute PHI0 = phi(Y0).  Grid-point values D1y(i), D2y(i),
C   and a(i) are also computed.
C
      PHI0 = PHI (M,H,Y0, D1Y,D2Y,A)
C
C Initialize iteration counts:
C
C   NCG = Number of conjugate gradient steps since the
C         previous restart with a steepest descent step.
C
C   NG = Number of iterations (gradient evaluations).
C
C   NPHSM = Total number of evaluations of phi in the line
C           searches.
C
C   PRNT = TRUE iff statistics describing the iteration are
C          to be printed.
C
      NCG = MAXCG
      NG = 0
      NPHSM = 0
      PRNT = .TRUE.
C
C Top of loop:  compute the L2-gradient G = grad(phi), its
C               1-norm GNRM1, and its max-norm GNRMM, and
C               overwrite G with the Sobolev gradient unless
C               L2G = TRUE.
C
    7 CALL GRADL2 (N,H,IND,M,D1Y,D2Y,A, WK, G,GNRM1,
     .             GNRMM,IER)
      IF (IER .NE. 0) GO TO 24
      IF (.NOT. L2G) THEN
        CALL GRADS4 (N,H,IND,M,D1Y,D2Y,LDA, ABD,G,
     .               WK, IER)
        IF (IER .GT. 0) WRITE (LPRT,125) IER
  125   FORMAT (//5X,'GRADS4 Failure:  IER = ',I1)
      ENDIF
C
C Compute mean absolute L2-gradient component GNRM1.
C
      GNRM1 = GNRM1/DBLE(M-N)
C
C Update iteration count.
C
      NG = NG + 1
C
C Print statistics associated with the step.
C
      IF (PRNT) THEN
        IF (NCG .GE. MAXCG) THEN
          WRITE (LPRT,130) NG
        ELSE
          WRITE (LPRT,135) NG
        ENDIF
        WRITE (LPRT,140) PHI0, GNRM1, GNRMM
      ENDIF
  130 FORMAT (//15X,'Iteration ',I6,' (Steepest descent)')
  135 FORMAT (//15X,'Iteration ',I6,' (Conjugate gradient)')
  140 FORMAT (5X,'Functional:                  phi(F) = ',
     .           1P,D21.15/
     .        5X,'Mean absolute L2-gradient:    GNRM1 = ',
     .           D8.2/
     .        5X,'Max-norm of L2-gradient:      GNRMM = ',
     .           D8.2)
      PRNT = (NPRNT*(NG/NPRNT) .EQ. NG)  .OR.  (NG .EQ. 1)
C
      IF (NCG .GE. MAXCG) THEN
C
C Steepest descent step.
C
        Q = 0.D0
        NCG = 0
      ELSE
C
C Conjugate gradient step.
C
        GG = DDOT(M,G0,1,G0,1)
        DGG = DDOT(M,G,1,G,1) - DDOT(M,G0,1,G,1)
        Q = DGG/GG
        NCG = NCG + 1
      ENDIF
C
C Compute the search direction p = -G + Q*p.
C
      DO 8 I = 1,M
        P(I) = -G(I) + Q*P(I)
    8   CONTINUE
C
C Copy Y into Y1 (WK column 1), compute the optimal step-
C   size ALPHA, and update Y to Y1+ALPHA*p.  Difference
C   approximations to derivatives and terms defining phi(Y)
C   are returned in D1Y, D2Y, and A.  The Max-norm of Y is
C   returned in YMAX, and DY is the relative change in Y:
C   Max-norm(Y-Y1)/(1+YMAX) = ALPHA*Max-norm(p)/(1+YMAX).
C
C The initial estimate for ALPHA should be small.  Using
C   the step-size computed at the previously iteration can
C   result in an incorrect step-size caused by finding a
C   local minimum which is not a global minimum.
C
      DO 9 I = 1,M
        WK(I,1) = Y(I)
    9   CONTINUE
      IF (OPT) THEN
        ALPHA = SSIZ1
      ELSE
C
C   Use small constant step-size.
C
        ALPHA = SSIZ0
      ENDIF
      CALL LNSRCH (M,H,WK,PHI0,P,FMTOL,OPT, ALPHA,Y,D1Y,
     .             D2Y,A, PHIY,NPHVAL,YMAX,DY,IER)
      IF (IER .NE. 0) GO TO 25
      NPHSM = NPHSM + NPHVAL
C
C Adjust DY to the relative change in Y squared.
C
      DY = DY**2
C
C Compute the max-norm of the Sobolev gradient relative to
C   the solution y.
C
      DG = 0.D0
      DO 10 I = 1,M
        DG = MAX(DG,ABS(G(I)))
   10   CONTINUE
      DG = (DG/(1.D0+YMAX))**3
C
C Save a copy of the Sobolev gradient G in G0 for computing
C   the search direction in the next conjugate gradient
C   step.
C
      IF (NCG .LT. MAXCG) THEN
        DO 11 I = 1,M
          G0(I) = G(I)
   11     CONTINUE
      ENDIF
C
C Compute the relative change DPHI in phi and update PHI0.
C   Terminate on an increase in phi.
C
      DPHI = (PHI0-PHIY)/(1.D0+PHI0)
      PHI0 = PHIY
      IF (DPHI .LT. 0.D0) NGMAX = NG
C
C Print statistics.
C
      IF (PRNT) WRITE (LPRT,150) NPHVAL, ALPHA, PHIY, DPHI,
     .                           DY, DG
  150 FORMAT (/5X,'Line search:     No. phi evals NPHV = ',
     .            I3/
     .         5X,'                Optimal step-size S = ',
     .            1P,D9.3/
     .         5X,'                  Functional phi(Y) = ',
     .            D21.15/
     .         5X,'     Relative change in phi(Y) DPHI = ',
     .            D9.2/
     .         5X,'  Squared relative change in Y:  DY = ',
     .            D9.2/
     .         5X,'    Cubed S-gradient rel. to Y:  DG = ',
     .            D9.2/
     .         1X,'______________________________________',
     .            '___________________________')
C
C Test for termination.
C
      IF ((DPHI .GE. PHTOL  .OR.  DY .GE. PHTOL  .OR.
     .     DG .GE. PHTOL)  .AND.  NG .LT. NGMAX) GO TO 7
      IF (.NOT. PRNT) THEN
C
C Print parameter values.
C
        IF (NCG .EQ. 0) THEN
          WRITE (LPRT,130) NG
        ELSE
          WRITE (LPRT,135) NG
        ENDIF
        WRITE (LPRT,140) PHI0, GNRM1, GNRMM
        WRITE (LPRT,150) NPHVAL, ALPHA, PHIY, DPHI, DY, DG
      ENDIF
C
C Compute the curve length in DY.
C
      C2 = H*H
      DY = 0.D0
      DO 12 I = 2,M
        DY = DY + SQRT(C2 + (Y(I)-Y(I-1))**2)
   12   CONTINUE
C
C Print iteration counts and statistics.
C
      WRITE (LPRT,160) NG
  160 FORMAT (//5X,'Number of descent ',
     .        'iterations: ',I6)
      WRITE (LPRT,170) NPHSM
  170 FORMAT (/5X,'Total number of phi evaluations ',
     .        'in the line searches: ',I7)
      WRITE (LPRT,180) DY
  180 FORMAT (/5X,'Total polygonal curve length: ',D9.3)
C
C Write the solution to disk.
C
      OPEN (LOUT,FILE='dnsplin1.out')
      CLOSE (LOUT,STATUS='DELETE')
      OPEN (LOUT,FILE='dnsplin1.out')
      CALL WRITF (LOUT,M,Y,D1Y,D2Y)
C
C Plot the solution.
C
      OPEN (LPLT,FILE='dnsplin1.ps')
      CLOSE (LPLT,STATUS='DELETE')
      OPEN (LPLT,FILE='dnsplin1.ps')
      CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y,PLT0,Y0,
     .             PLTSIZ, IER)
      CLOSE (LPLT)
      IF (IER .NE. 0) GO TO 26
C
C Prompt for optional plot of curvature.
C
   13 WRITE (*,220)
  220 FORMAT (//5X,'Create file dnsplin1.ps2 containing a ',
     .        'curvature plot? (y/n)'/)
      READ (*,215,ERR=13) CHR
      IF (CHR .NE. 'Y'  .AND.  CHR .NE. 'y'  .AND.
     .    CHR .NE. 'N'  .AND.  CHR .NE. 'n') GO TO 13
      IF (CHR .EQ. 'Y'  .OR.  CHR .EQ. 'y') THEN
        OPEN (LPLT,FILE='dnsplin1.ps2')
        CLOSE (LPLT,STATUS='DELETE')
        OPEN (LPLT,FILE='dnsplin1.ps2')
        Y(1) = 0.D0
        DO 14 I = 2,M-1
          Y(I) = D2Y(I)/(1.D0+D1Y(I)**2)**1.5D0
   14     CONTINUE
        Y(M) = 0.D0
        DO 15 J = 1,N
          I = IND(J)
          D(J) = Y(I)
   15     CONTINUE
        CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y,.FALSE.,Y0,
     .               PLTSIZ, IER)
        CLOSE (LPLT)
        IF (IER .NE. 0) GO TO 26
      ENDIF
      STOP
C
C Error encountered in Subroutine READF.
C
   21 WRITE (LPRT,421) IER
  421 FORMAT (///10X,'*** Error in READF:  IER = ',
     .        I1,' ***')
      STOP
C
C Invalid data:  M < 6 or M > MMAX or M-N < 1.
C
   22 WRITE (LPRT,422) M, MMAX, N
  422 FORMAT (///10X,'*** Error in data:  M = ',I5,
     .        ', MMAX = ',I5,', N = ',I4,' ***')
      STOP
C
C Error encountered in Subroutine CSPLIN.
C
   23 WRITE (LPRT,423) IER
  423 FORMAT (///10X,'*** Error in CSPLIN:  IER = ',
     .        I1,' ***')
      STOP
C
C Error encountered in Subroutine GRADL2.
C
   24 WRITE (LPRT,424) IER
  424 FORMAT (///10X,'*** Error in GRADL2:  IER = ',
     .        I1,' ***')
      STOP
C
C Error encountered in Subroutine LNSRCH.
C
   25 WRITE (LPRT,425) IER
  425 FORMAT (///10X,'*** Error in LNSRCH:  IER = ',
     .        I1,' ***')
      STOP
C
C Error encountered in Subroutine PLTCRV.
C
   26 WRITE (LPRT,426) IER
  426 FORMAT (///10X,'*** Error in PLTCRV:  IER = ',
     .        I1,' ***')
      STOP
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'lapack.f'
then
	echo shar: will not over-write existing file "'lapack.f'"
else
cat << "SHAR_EOF" > 'lapack.f'
      SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
*  -- LAPACK driver routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     March 31, 1993
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  DPBSV computes the solution to a real system of linear equations
*     A * X = B,
*  where A is an N-by-N symmetric positive definite band matrix and X
*  and B are N-by-NRHS matrices.
*
*  The Cholesky decomposition is used to factor A as
*     A = U**T * U,  if UPLO = 'U', or
*     A = L * L**T,  if UPLO = 'L',
*  where U is an upper triangular band matrix, and L is a lower
*  triangular band matrix, with the same number of superdiagonals or
*  subdiagonals as A.  The factored form of A is then used to solve the
*  system of equations A * X = B.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The number of linear equations, i.e., the order of the
*          matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrix B.  NRHS >= 0.
*
*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the symmetric band
*          matrix A, stored in the first KD+1 rows of the array.  The
*          j-th column of A is stored in the j-th column of the array AB
*          as follows:
*          if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
*          See below for further details.
*
*          On exit, if INFO = 0, the triangular factor U or L from the
*          Cholesky factorization A = U**T*U or A = L*L**T of the band
*          matrix A, in the same storage format as A.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
*          On entry, the N-by-NRHS right hand side matrix B.
*          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  if INFO = i, the leading minor of order i of A is not
*                positive definite, so the factorization could not be
*                completed, and the solution has not been computed.
*
*  Further Details
*  ===============
*
*  The band storage scheme is illustrated by the following example, when
*  N = 6, KD = 2, and UPLO = 'U':
*
*  On entry:                       On exit:
*
*      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
*
*  Similarly, if UPLO = 'L' the format of A is as follows:
*
*  On entry:                       On exit:
*
*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
*
*  Array elements marked * are not used by the routine.
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DPBTRF, DPBTRS, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KD.LT.0 ) THEN
         INFO = -3
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -6
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPBSV ', -INFO )
         RETURN
      END IF
*
*     Compute the Cholesky factorization A = U'*U or A = L*L'.
*
      CALL DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
      IF( INFO.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
      END IF
      RETURN
*
*     End of DPBSV
*
      END
      SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     March 31, 1993
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * )
*     ..
*
*  Purpose
*  =======
*
*  DPBTRF computes the Cholesky factorization of a real symmetric
*  positive definite band matrix A.
*
*  The factorization has the form
*     A = U**T * U,  if UPLO = 'U', or
*     A = L  * L**T,  if UPLO = 'L',
*  where U is an upper triangular matrix and L is lower triangular.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the symmetric band
*          matrix A, stored in the first KD+1 rows of the array.  The
*          j-th column of A is stored in the j-th column of the array AB
*          as follows:
*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*
*          On exit, if INFO = 0, the triangular factor U or L from the
*          Cholesky factorization A = U**T*U or A = L*L**T of the band
*          matrix A, in the same storage format as A.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  if INFO = i, the leading minor of order i is not
*                positive definite, and the factorization could not be
*                completed.
*
*  Further Details
*  ===============
*
*  The band storage scheme is illustrated by the following example, when
*  N = 6, KD = 2, and UPLO = 'U':
*
*  On entry:                       On exit:
*
*      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
*
*  Similarly, if UPLO = 'L' the format of A is as follows:
*
*  On entry:                       On exit:
*
*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
*
*  Array elements marked * are not used by the routine.
*
*  Contributed by
*  Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
      INTEGER            NBMAX, LDWORK
      PARAMETER          ( NBMAX = 32, LDWORK = NBMAX+1 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, I2, I3, IB, II, J, JJ, NB
*     ..
*     .. Local Arrays ..
      DOUBLE PRECISION   WORK( LDWORK, NBMAX )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           LSAME, ILAENV
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMM, DPBTF2, DPOTF2, DSYRK, DTRSM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF( ( .NOT.LSAME( UPLO, 'U' ) ) .AND.
     $    ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KD.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -5
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPBTRF', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Determine the block size for this environment
*
      NB = ILAENV( 1, 'DPBTRF', UPLO, N, KD, -1, -1 )
*
*     The block size must not exceed the semi-bandwidth KD, and must not
*     exceed the limit set by the size of the local array WORK.
*
      NB = MIN( NB, NBMAX )
*
      IF( NB.LE.1 .OR. NB.GT.KD ) THEN
*
*        Use unblocked code
*
         CALL DPBTF2( UPLO, N, KD, AB, LDAB, INFO )
      ELSE
*
*        Use blocked code
*
         IF( LSAME( UPLO, 'U' ) ) THEN
*
*           Compute the Cholesky factorization of a symmetric band
*           matrix, given the upper triangle of the matrix in band
*           storage.
*
*           Zero the upper triangle of the work array.
*
            DO 20 J = 1, NB
               DO 10 I = 1, J - 1
                  WORK( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
*
*           Process the band matrix one diagonal block at a time.
*
            DO 70 I = 1, N, NB
               IB = MIN( NB, N-I+1 )
*
*              Factorize the diagonal block
*
               CALL DPOTF2( UPLO, IB, AB( KD+1, I ), LDAB-1, II )
               IF( II.NE.0 ) THEN
                  INFO = I + II - 1
                  GO TO 150
               END IF
               IF( I+IB.LE.N ) THEN
*
*                 Update the relevant part of the trailing submatrix.
*                 If A11 denotes the diagonal block which has just been
*                 factorized, then we need to update the remaining
*                 blocks in the diagram:
*
*                    A11   A12   A13
*                          A22   A23
*                                A33
*
*                 The numbers of rows and columns in the partitioning
*                 are IB, I2, I3 respectively. The blocks A12, A22 and
*                 A23 are empty if IB = KD. The upper triangle of A13
*                 lies outside the band.
*
                  I2 = MIN( KD-IB, N-I-IB+1 )
                  I3 = MIN( IB, N-I-KD+1 )
*
                  IF( I2.GT.0 ) THEN
*
*                    Update A12
*
                     CALL DTRSM( 'Left', 'Upper', 'Transpose',
     $                           'Non-unit', IB, I2, ONE, AB( KD+1, I ),
     $                           LDAB-1, AB( KD+1-IB, I+IB ), LDAB-1 )
*
*                    Update A22
*
                     CALL DSYRK( 'Upper', 'Transpose', I2, IB, -ONE,
     $                           AB( KD+1-IB, I+IB ), LDAB-1, ONE,
     $                           AB( KD+1, I+IB ), LDAB-1 )
                  END IF
*
                  IF( I3.GT.0 ) THEN
*
*                    Copy the lower triangle of A13 into the work array.
*
                     DO 40 JJ = 1, I3
                        DO 30 II = JJ, IB
                           WORK( II, JJ ) = AB( II-JJ+1, JJ+I+KD-1 )
   30                   CONTINUE
   40                CONTINUE
*
*                    Update A13 (in the work array).
*
                     CALL DTRSM( 'Left', 'Upper', 'Transpose',
     $                           'Non-unit', IB, I3, ONE, AB( KD+1, I ),
     $                           LDAB-1, WORK, LDWORK )
*
*                    Update A23
*
                     IF( I2.GT.0 )
     $                  CALL DGEMM( 'Transpose', 'No Transpose', I2, I3,
     $                              IB, -ONE, AB( KD+1-IB, I+IB ),
     $                              LDAB-1, WORK, LDWORK, ONE,
     $                              AB( 1+IB, I+KD ), LDAB-1 )
*
*                    Update A33
*
                     CALL DSYRK( 'Upper', 'Transpose', I3, IB, -ONE,
     $                           WORK, LDWORK, ONE, AB( KD+1, I+KD ),
     $                           LDAB-1 )
*
*                    Copy the lower triangle of A13 back into place.
*
                     DO 60 JJ = 1, I3
                        DO 50 II = JJ, IB
                           AB( II-JJ+1, JJ+I+KD-1 ) = WORK( II, JJ )
   50                   CONTINUE
   60                CONTINUE
                  END IF
               END IF
   70       CONTINUE
         ELSE
*
*           Compute the Cholesky factorization of a symmetric band
*           matrix, given the lower triangle of the matrix in band
*           storage.
*
*           Zero the lower triangle of the work array.
*
            DO 90 J = 1, NB
               DO 80 I = J + 1, NB
                  WORK( I, J ) = ZERO
   80          CONTINUE
   90       CONTINUE
*
*           Process the band matrix one diagonal block at a time.
*
            DO 140 I = 1, N, NB
               IB = MIN( NB, N-I+1 )
*
*              Factorize the diagonal block
*
               CALL DPOTF2( UPLO, IB, AB( 1, I ), LDAB-1, II )
               IF( II.NE.0 ) THEN
                  INFO = I + II - 1
                  GO TO 150
               END IF
               IF( I+IB.LE.N ) THEN
*
*                 Update the relevant part of the trailing submatrix.
*                 If A11 denotes the diagonal block which has just been
*                 factorized, then we need to update the remaining
*                 blocks in the diagram:
*
*                    A11
*                    A21   A22
*                    A31   A32   A33
*
*                 The numbers of rows and columns in the partitioning
*                 are IB, I2, I3 respectively. The blocks A21, A22 and
*                 A32 are empty if IB = KD. The lower triangle of A31
*                 lies outside the band.
*
                  I2 = MIN( KD-IB, N-I-IB+1 )
                  I3 = MIN( IB, N-I-KD+1 )
*
                  IF( I2.GT.0 ) THEN
*
*                    Update A21
*
                     CALL DTRSM( 'Right', 'Lower', 'Transpose',
     $                           'Non-unit', I2, IB, ONE, AB( 1, I ),
     $                           LDAB-1, AB( 1+IB, I ), LDAB-1 )
*
*                    Update A22
*
                     CALL DSYRK( 'Lower', 'No Transpose', I2, IB, -ONE,
     $                           AB( 1+IB, I ), LDAB-1, ONE,
     $                           AB( 1, I+IB ), LDAB-1 )
                  END IF
*
                  IF( I3.GT.0 ) THEN
*
*                    Copy the upper triangle of A31 into the work array.
*
                     DO 110 JJ = 1, IB
                        DO 100 II = 1, MIN( JJ, I3 )
                           WORK( II, JJ ) = AB( KD+1-JJ+II, JJ+I-1 )
  100                   CONTINUE
  110                CONTINUE
*
*                    Update A31 (in the work array).
*
                     CALL DTRSM( 'Right', 'Lower', 'Transpose',
     $                           'Non-unit', I3, IB, ONE, AB( 1, I ),
     $                           LDAB-1, WORK, LDWORK )
*
*                    Update A32
*
                     IF( I2.GT.0 )
     $                  CALL DGEMM( 'No transpose', 'Transpose', I3, I2,
     $                              IB, -ONE, WORK, LDWORK,
     $                              AB( 1+IB, I ), LDAB-1, ONE,
     $                              AB( 1+KD-IB, I+IB ), LDAB-1 )
*
*                    Update A33
*
                     CALL DSYRK( 'Lower', 'No Transpose', I3, IB, -ONE,
     $                           WORK, LDWORK, ONE, AB( 1, I+KD ),
     $                           LDAB-1 )
*
*                    Copy the upper triangle of A31 back into place.
*
                     DO 130 JJ = 1, IB
                        DO 120 II = 1, MIN( JJ, I3 )
                           AB( KD+1-JJ+II, JJ+I-1 ) = WORK( II, JJ )
  120                   CONTINUE
  130                CONTINUE
                  END IF
               END IF
  140       CONTINUE
         END IF
      END IF
      RETURN
*
  150 CONTINUE
      RETURN
*
*     End of DPBTRF
*
      END
      SUBROUTINE DPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * )
*     ..
*
*  Purpose
*  =======
*
*  DPBTF2 computes the Cholesky factorization of a real symmetric
*  positive definite band matrix A.
*
*  The factorization has the form
*     A = U' * U ,  if UPLO = 'U', or
*     A = L  * L',  if UPLO = 'L',
*  where U is an upper triangular matrix, U' is the transpose of U, and
*  L is lower triangular.
*
*  This is the unblocked version of the algorithm, calling Level 2 BLAS.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          symmetric matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of super-diagonals of the matrix A if UPLO = 'U',
*          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
*
*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the symmetric band
*          matrix A, stored in the first KD+1 rows of the array.  The
*          j-th column of A is stored in the j-th column of the array AB
*          as follows:
*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*
*          On exit, if INFO = 0, the triangular factor U or L from the
*          Cholesky factorization A = U'*U or A = L*L' of the band
*          matrix A, in the same storage format as A.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -k, the k-th argument had an illegal value
*          > 0: if INFO = k, the leading minor of order k is not
*               positive definite, and the factorization could not be
*               completed.
*
*  Further Details
*  ===============
*
*  The band storage scheme is illustrated by the following example, when
*  N = 6, KD = 2, and UPLO = 'U':
*
*  On entry:                       On exit:
*
*      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
*
*  Similarly, if UPLO = 'L' the format of A is as follows:
*
*  On entry:                       On exit:
*
*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
*
*  Array elements marked * are not used by the routine.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J, KLD, KN
      DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DSCAL, DSYR, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KD.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -5
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPBTF2', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
      KLD = MAX( 1, LDAB-1 )
*
      IF( UPPER ) THEN
*
*        Compute the Cholesky factorization A = U'*U.
*
         DO 10 J = 1, N
*
*           Compute U(J,J) and test for non-positive-definiteness.
*
            AJJ = AB( KD+1, J )
            IF( AJJ.LE.ZERO )
     $         GO TO 30
            AJJ = SQRT( AJJ )
            AB( KD+1, J ) = AJJ
*
*           Compute elements J+1:J+KN of row J and update the
*           trailing submatrix within the band.
*
            KN = MIN( KD, N-J )
            IF( KN.GT.0 ) THEN
               CALL DSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD )
               CALL DSYR( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD,
     $                    AB( KD+1, J+1 ), KLD )
            END IF
   10    CONTINUE
      ELSE
*
*        Compute the Cholesky factorization A = L*L'.
*
         DO 20 J = 1, N
*
*           Compute L(J,J) and test for non-positive-definiteness.
*
            AJJ = AB( 1, J )
            IF( AJJ.LE.ZERO )
     $         GO TO 30
            AJJ = SQRT( AJJ )
            AB( 1, J ) = AJJ
*
*           Compute elements J+1:J+KN of column J and update the
*           trailing submatrix within the band.
*
            KN = MIN( KD, N-J )
            IF( KN.GT.0 ) THEN
               CALL DSCAL( KN, ONE / AJJ, AB( 2, J ), 1 )
               CALL DSYR( 'Lower', KN, -ONE, AB( 2, J ), 1,
     $                    AB( 1, J+1 ), KLD )
            END IF
   20    CONTINUE
      END IF
      RETURN
*
   30 CONTINUE
      INFO = J
      RETURN
*
*     End of DPBTF2
*
      END
      SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * )
*     ..
*
*  Purpose
*  =======
*
*  DPOTF2 computes the Cholesky factorization of a real symmetric
*  positive definite matrix A.
*
*  The factorization has the form
*     A = U' * U ,  if UPLO = 'U', or
*     A = L  * L',  if UPLO = 'L',
*  where U is an upper triangular matrix and L is lower triangular.
*
*  This is the unblocked version of the algorithm, calling Level 2 BLAS.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          symmetric matrix A is stored.
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
*          n by n upper triangular part of A contains the upper
*          triangular part of the matrix A, and the strictly lower
*          triangular part of A is not referenced.  If UPLO = 'L', the
*          leading n by n lower triangular part of A contains the lower
*          triangular part of the matrix A, and the strictly upper
*          triangular part of A is not referenced.
*
*          On exit, if INFO = 0, the factor U or L from the Cholesky
*          factorization A = U'*U  or A = L*L'.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -k, the k-th argument had an illegal value
*          > 0: if INFO = k, the leading minor of order k is not
*               positive definite, and the factorization could not be
*               completed.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J
      DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DDOT
      EXTERNAL           LSAME, DDOT
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMV, DSCAL, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPOTF2', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
      IF( UPPER ) THEN
*
*        Compute the Cholesky factorization A = U'*U.
*
         DO 10 J = 1, N
*
*           Compute U(J,J) and test for non-positive-definiteness.
*
            AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
            IF( AJJ.LE.ZERO ) THEN
               A( J, J ) = AJJ
               GO TO 30
            END IF
            AJJ = SQRT( AJJ )
            A( J, J ) = AJJ
*
*           Compute elements J+1:N of row J.
*
            IF( J.LT.N ) THEN
               CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
     $                     LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
               CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
            END IF
   10    CONTINUE
      ELSE
*
*        Compute the Cholesky factorization A = L*L'.
*
         DO 20 J = 1, N
*
*           Compute L(J,J) and test for non-positive-definiteness.
*
            AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
     $            LDA )
            IF( AJJ.LE.ZERO ) THEN
               A( J, J ) = AJJ
               GO TO 30
            END IF
            AJJ = SQRT( AJJ )
            A( J, J ) = AJJ
*
*           Compute elements J+1:N of column J.
*
            IF( J.LT.N ) THEN
               CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
     $                     LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
               CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
            END IF
   20    CONTINUE
      END IF
      GO TO 40
*
   30 CONTINUE
      INFO = J
*
   40 CONTINUE
      RETURN
*
*     End of DPOTF2
*
      END
      SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  DPBTRS solves a system of linear equations A*X = B with a symmetric
*  positive definite band matrix A using the Cholesky factorization
*  A = U**T*U or A = L*L**T computed by DPBTRF.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangular factor stored in AB;
*          = 'L':  Lower triangular factor stored in AB.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
*  NRHS    (input) INTEGER
*          The number of right hand sides, i.e., the number of columns
*          of the matrix B.  NRHS >= 0.
*
*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
*          The triangular factor U or L from the Cholesky factorization
*          A = U**T*U or A = L*L**T of the band matrix A, stored in the
*          first KD+1 rows of the array.  The j-th column of U or L is
*          stored in the j-th column of the array AB as follows:
*          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
*          On entry, the right hand side matrix B.
*          On exit, the solution matrix X.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DTBSV, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KD.LT.0 ) THEN
         INFO = -3
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -6
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPBTRS', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 .OR. NRHS.EQ.0 )
     $   RETURN
*
      IF( UPPER ) THEN
*
*        Solve A*X = B where A = U'*U.
*
         DO 10 J = 1, NRHS
*
*           Solve U'*X = B, overwriting B with X.
*
            CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
*
*           Solve U*X = B, overwriting B with X.
*
            CALL DTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
   10    CONTINUE
      ELSE
*
*        Solve A*X = B where A = L*L'.
*
         DO 20 J = 1, NRHS
*
*           Solve L*X = B, overwriting B with X.
*
            CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
*
*           Solve L'*X = B, overwriting B with X.
*
            CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
     $                  LDAB, B( 1, J ), 1 )
   20    CONTINUE
      END IF
*
      RETURN
*
*     End of DPBTRS
*
      END
      SUBROUTINE DPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
     $                   IWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, KD, LDAB, N
      DOUBLE PRECISION   ANORM, RCOND
*     ..
*     .. Array Arguments ..
      INTEGER            IWORK( * )
      DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DPBCON estimates the reciprocal of the condition number (in the
*  1-norm) of a real symmetric positive definite band matrix using the
*  Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF.
*
*  An estimate is obtained for norm(inv(A)), and the reciprocal of the
*  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangular factor stored in AB;
*          = 'L':  Lower triangular factor stored in AB.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of superdiagonals of the matrix A if UPLO = 'U',
*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
*
*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
*          The triangular factor U or L from the Cholesky factorization
*          A = U**T*U or A = L*L**T of the band matrix A, stored in the
*          first KD+1 rows of the array.  The j-th column of U or L is
*          stored in the j-th column of the array AB as follows:
*          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  ANORM   (input) DOUBLE PRECISION
*          The 1-norm (or infinity-norm) of the symmetric band matrix A.
*
*  RCOND   (output) DOUBLE PRECISION
*          The reciprocal of the condition number of the matrix A,
*          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
*          estimate of the 1-norm of inv(A) computed in this routine.
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
*
*  IWORK   (workspace) INTEGER array, dimension (N)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      CHARACTER          NORMIN
      INTEGER            IX, KASE
      DOUBLE PRECISION   AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            IDAMAX
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           LSAME, IDAMAX, DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLACON, DLATBS, DRSCL, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KD.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -5
      ELSE IF( ANORM.LT.ZERO ) THEN
         INFO = -6
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DPBCON', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      RCOND = ZERO
      IF( N.EQ.0 ) THEN
         RCOND = ONE
         RETURN
      ELSE IF( ANORM.EQ.ZERO ) THEN
         RETURN
      END IF
*
      SMLNUM = DLAMCH( 'Safe minimum' )
*
*     Estimate the 1-norm of the inverse.
*
      KASE = 0
      NORMIN = 'N'
   10 CONTINUE
      CALL DLACON( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE )
      IF( KASE.NE.0 ) THEN
         IF( UPPER ) THEN
*
*           Multiply by inv(U').
*
            CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
     $                   KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
     $                   INFO )
            NORMIN = 'Y'
*
*           Multiply by inv(U).
*
            CALL DLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
     $                   KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
     $                   INFO )
         ELSE
*
*           Multiply by inv(L).
*
            CALL DLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
     $                   KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
     $                   INFO )
            NORMIN = 'Y'
*
*           Multiply by inv(L').
*
            CALL DLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
     $                   KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
     $                   INFO )
         END IF
*
*        Multiply by 1/SCALE if doing so will not cause overflow.
*
         SCALE = SCALEL*SCALEU
         IF( SCALE.NE.ONE ) THEN
            IX = IDAMAX( N, WORK, 1 )
            IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
     $         GO TO 20
            CALL DRSCL( N, SCALE, WORK, 1 )
         END IF
         GO TO 10
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( AINVNM.NE.ZERO )
     $   RCOND = ( ONE / AINVNM ) / ANORM
*
   20 CONTINUE
*
      RETURN
*
*     End of DPBCON
*
      END
      SUBROUTINE DLABAD( SMALL, LARGE )
*
*  -- LAPACK auxiliary routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   LARGE, SMALL
*     ..
*
*  Purpose
*  =======
*
*  DLABAD takes as input the values computed by SLAMCH for underflow and
*  overflow, and returns the square root of each of these values if the
*  log of LARGE is sufficiently large.  This subroutine is intended to
*  identify machines with a large exponent range, such as the Crays, and
*  redefine the underflow and overflow limits to be the square roots of
*  the values computed by DLAMCH.  This subroutine is needed because
*  DLAMCH does not compensate for poor arithmetic in the upper half of
*  the exponent range, as is found on a Cray.
*
*  Arguments
*  =========
*
*  SMALL   (input/output) DOUBLE PRECISION
*          On entry, the underflow threshold as computed by DLAMCH.
*          On exit, if LOG10(LARGE) is sufficiently large, the square
*          root of SMALL, otherwise unchanged.
*
*  LARGE   (input/output) DOUBLE PRECISION
*          On entry, the overflow threshold as computed by DLAMCH.
*          On exit, if LOG10(LARGE) is sufficiently large, the square
*          root of LARGE, otherwise unchanged.
*
*  =====================================================================
*
*     .. Intrinsic Functions ..
      INTRINSIC          LOG10, SQRT
*     ..
*     .. Executable Statements ..
*
*     If it looks like we're on a Cray, take the square root of
*     SMALL and LARGE to avoid overflow and underflow problems.
*
      IF( LOG10( LARGE ).GT.2000.D0 ) THEN
         SMALL = SQRT( SMALL )
         LARGE = SQRT( LARGE )
      END IF
*
      RETURN
*
*     End of DLABAD
*
      END
      SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. Scalar Arguments ..
      INTEGER            KASE, N
      DOUBLE PRECISION   EST
*     ..
*     .. Array Arguments ..
      INTEGER            ISGN( * )
      DOUBLE PRECISION   V( * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  DLACON estimates the 1-norm of a square, real matrix A.
*  Reverse communication is used for evaluating matrix-vector products.
*
*  Arguments
*  =========
*
*  N      (input) INTEGER
*         The order of the matrix.  N >= 1.
*
*  V      (workspace) DOUBLE PRECISION array, dimension (N)
*         On the final return, V = A*W,  where  EST = norm(V)/norm(W)
*         (W is not returned).
*
*  X      (input/output) DOUBLE PRECISION array, dimension (N)
*         On an intermediate return, X should be overwritten by
*               A * X,   if KASE=1,
*               A' * X,  if KASE=2,
*         and DLACON must be re-called with all the other parameters
*         unchanged.
*
*  ISGN   (workspace) INTEGER array, dimension (N)
*
*  EST    (output) DOUBLE PRECISION
*         An estimate (a lower bound) for norm(A).
*
*  KASE   (input/output) INTEGER
*         On the initial call to DLACON, KASE should be 0.
*         On an intermediate return, KASE will be 1 or 2, indicating
*         whether X should be overwritten by A * X  or A' * X.
*         On the final return from DLACON, KASE will again be 0.
*
*  Further Details
*  ======= =======
*
*  Contributed by Nick Higham, University of Manchester.
*  Originally named SONEST, dated March 16, 1988.
*
*  Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
*  a real or complex matrix, with applications to condition estimation",
*  ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
*
*  =====================================================================
*
*     .. Parameters ..
      INTEGER            ITMAX
      PARAMETER          ( ITMAX = 5 )
      DOUBLE PRECISION   ZERO, ONE, TWO
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, ITER, J, JLAST, JUMP
      DOUBLE PRECISION   ALTSGN, ESTOLD, TEMP
*     ..
*     .. External Functions ..
      INTEGER            IDAMAX
      DOUBLE PRECISION   DASUM
      EXTERNAL           IDAMAX, DASUM
*     ..
*     .. External Subroutines ..
      EXTERNAL           DCOPY
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, NINT, SIGN
*     ..
*     .. Save statement ..
      SAVE
*     ..
*     .. Executable Statements ..
*
      IF( KASE.EQ.0 ) THEN
         DO 10 I = 1, N
            X( I ) = ONE / DBLE( N )
   10    CONTINUE
         KASE = 1
         JUMP = 1
         RETURN
      END IF
*
      GO TO ( 20, 40, 70, 110, 140 )JUMP
*
*     ................ ENTRY   (JUMP = 1)
*     FIRST ITERATION.  X HAS BEEN OVERWRITTEN BY A*X.
*
   20 CONTINUE
      IF( N.EQ.1 ) THEN
         V( 1 ) = X( 1 )
         EST = ABS( V( 1 ) )
*        ... QUIT
         GO TO 150
      END IF
      EST = DASUM( N, X, 1 )
*
      DO 30 I = 1, N
         X( I ) = SIGN( ONE, X( I ) )
         ISGN( I ) = NINT( X( I ) )
   30 CONTINUE
      KASE = 2
      JUMP = 2
      RETURN
*
*     ................ ENTRY   (JUMP = 2)
*     FIRST ITERATION.  X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X.
*
   40 CONTINUE
      J = IDAMAX( N, X, 1 )
      ITER = 2
*
*     MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
*
   50 CONTINUE
      DO 60 I = 1, N
         X( I ) = ZERO
   60 CONTINUE
      X( J ) = ONE
      KASE = 1
      JUMP = 3
      RETURN
*
*     ................ ENTRY   (JUMP = 3)
*     X HAS BEEN OVERWRITTEN BY A*X.
*
   70 CONTINUE
      CALL DCOPY( N, X, 1, V, 1 )
      ESTOLD = EST
      EST = DASUM( N, V, 1 )
      DO 80 I = 1, N
         IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
     $      GO TO 90
   80 CONTINUE
*     REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
      GO TO 120
*
   90 CONTINUE
*     TEST FOR CYCLING.
      IF( EST.LE.ESTOLD )
     $   GO TO 120
*
      DO 100 I = 1, N
         X( I ) = SIGN( ONE, X( I ) )
         ISGN( I ) = NINT( X( I ) )
  100 CONTINUE
      KASE = 2
      JUMP = 4
      RETURN
*
*     ................ ENTRY   (JUMP = 4)
*     X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X.
*
  110 CONTINUE
      JLAST = J
      J = IDAMAX( N, X, 1 )
      IF( ( X( JLAST ).NE.ABS( X( J ) ) ) .AND. ( ITER.LT.ITMAX ) ) THEN
         ITER = ITER + 1
         GO TO 50
      END IF
*
*     ITERATION COMPLETE.  FINAL STAGE.
*
  120 CONTINUE
      ALTSGN = ONE
      DO 130 I = 1, N
         X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
         ALTSGN = -ALTSGN
  130 CONTINUE
      KASE = 1
      JUMP = 5
      RETURN
*
*     ................ ENTRY   (JUMP = 5)
*     X HAS BEEN OVERWRITTEN BY A*X.
*
  140 CONTINUE
      TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
      IF( TEMP.GT.EST ) THEN
         CALL DCOPY( N, X, 1, V, 1 )
         EST = TEMP
      END IF
*
  150 CONTINUE
      KASE = 0
      RETURN
*
*     End of DLACON
*
      END
      DOUBLE PRECISION FUNCTION DLAMCH( CMACH )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      CHARACTER          CMACH
*     ..
*
*  Purpose
*  =======
*
*  DLAMCH determines double precision machine parameters.
*
*  Arguments
*  =========
*
*  CMACH   (input) CHARACTER*1
*          Specifies the value to be returned by DLAMCH:
*          = 'E' or 'e',   DLAMCH := eps
*          = 'S' or 's ,   DLAMCH := sfmin
*          = 'B' or 'b',   DLAMCH := base
*          = 'P' or 'p',   DLAMCH := eps*base
*          = 'N' or 'n',   DLAMCH := t
*          = 'R' or 'r',   DLAMCH := rnd
*          = 'M' or 'm',   DLAMCH := emin
*          = 'U' or 'u',   DLAMCH := rmin
*          = 'L' or 'l',   DLAMCH := emax
*          = 'O' or 'o',   DLAMCH := rmax
*
*          where
*
*          eps   = relative machine precision
*          sfmin = safe minimum, such that 1/sfmin does not overflow
*          base  = base of the machine
*          prec  = eps*base
*          t     = number of (base) digits in the mantissa
*          rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise
*          emin  = minimum exponent before (gradual) underflow
*          rmin  = underflow threshold - base**(emin-1)
*          emax  = largest exponent before overflow
*          rmax  = overflow threshold  - (base**emax)*(1-eps)
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            FIRST, LRND
      INTEGER            BETA, IMAX, IMIN, IT
      DOUBLE PRECISION   BASE, EMAX, EMIN, EPS, PREC, RMACH, RMAX, RMIN,
     $                   RND, SFMIN, SMALL, T
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLAMC2
*     ..
*     .. Save statement ..
      SAVE               FIRST, EPS, SFMIN, BASE, T, RND, EMIN, RMIN,
     $                   EMAX, RMAX, PREC
*     ..
*     .. Data statements ..
      DATA               FIRST / .TRUE. /
*     ..
*     .. Executable Statements ..
*
      IF( FIRST ) THEN
         FIRST = .FALSE.
         CALL DLAMC2( BETA, IT, LRND, EPS, IMIN, RMIN, IMAX, RMAX )
         BASE = BETA
         T = IT
         IF( LRND ) THEN
            RND = ONE
            EPS = ( BASE**( 1-IT ) ) / 2
         ELSE
            RND = ZERO
            EPS = BASE**( 1-IT )
         END IF
         PREC = EPS*BASE
         EMIN = IMIN
         EMAX = IMAX
         SFMIN = RMIN
         SMALL = ONE / RMAX
         IF( SMALL.GE.SFMIN ) THEN
*
*           Use SMALL plus a bit, to avoid the possibility of rounding
*           causing overflow when computing  1/sfmin.
*
            SFMIN = SMALL*( ONE+EPS )
         END IF
      END IF
*
      IF( LSAME( CMACH, 'E' ) ) THEN
         RMACH = EPS
      ELSE IF( LSAME( CMACH, 'S' ) ) THEN
         RMACH = SFMIN
      ELSE IF( LSAME( CMACH, 'B' ) ) THEN
         RMACH = BASE
      ELSE IF( LSAME( CMACH, 'P' ) ) THEN
         RMACH = PREC
      ELSE IF( LSAME( CMACH, 'N' ) ) THEN
         RMACH = T
      ELSE IF( LSAME( CMACH, 'R' ) ) THEN
         RMACH = RND
      ELSE IF( LSAME( CMACH, 'M' ) ) THEN
         RMACH = EMIN
      ELSE IF( LSAME( CMACH, 'U' ) ) THEN
         RMACH = RMIN
      ELSE IF( LSAME( CMACH, 'L' ) ) THEN
         RMACH = EMAX
      ELSE IF( LSAME( CMACH, 'O' ) ) THEN
         RMACH = RMAX
      END IF
*
      DLAMCH = RMACH
      RETURN
*
*     End of DLAMCH
*
      END
*
************************************************************************
*
      SUBROUTINE DLAMC1( BETA, T, RND, IEEE1 )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      LOGICAL            IEEE1, RND
      INTEGER            BETA, T
*     ..
*
*  Purpose
*  =======
*
*  DLAMC1 determines the machine parameters given by BETA, T, RND, and
*  IEEE1.
*
*  Arguments
*  =========
*
*  BETA    (output) INTEGER
*          The base of the machine.
*
*  T       (output) INTEGER
*          The number of ( BETA ) digits in the mantissa.
*
*  RND     (output) LOGICAL
*          Specifies whether proper rounding  ( RND = .TRUE. )  or
*          chopping  ( RND = .FALSE. )  occurs in addition. This may not
*          be a reliable guide to the way in which the machine performs
*          its arithmetic.
*
*  IEEE1   (output) LOGICAL
*          Specifies whether rounding appears to be done in the IEEE
*          'round to nearest' style.
*
*  Further Details
*  ===============
*
*  The routine is based on the routine  ENVRON  by Malcolm and
*  incorporates suggestions by Gentleman and Marovich. See
*
*     Malcolm M. A. (1972) Algorithms to reveal properties of
*        floating-point arithmetic. Comms. of the ACM, 15, 949-951.
*
*     Gentleman W. M. and Marovich S. B. (1974) More on algorithms
*        that reveal properties of floating point arithmetic units.
*        Comms. of the ACM, 17, 276-277.
*
* =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            FIRST, LIEEE1, LRND
      INTEGER            LBETA, LT
      DOUBLE PRECISION   A, B, C, F, ONE, QTR, SAVEC, T1, T2
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMC3
      EXTERNAL           DLAMC3
*     ..
*     .. Save statement ..
      SAVE               FIRST, LIEEE1, LBETA, LRND, LT
*     ..
*     .. Data statements ..
      DATA               FIRST / .TRUE. /
*     ..
*     .. Executable Statements ..
*
      IF( FIRST ) THEN
         FIRST = .FALSE.
         ONE = 1
*
*        LBETA,  LIEEE1,  LT and  LRND  are the  local values  of  BETA,
*        IEEE1, T and RND.
*
*        Throughout this routine  we use the function  DLAMC3  to ensure
*        that relevant values are  stored and not held in registers,  or
*        are not affected by optimizers.
*
*        Compute  a = 2.0**m  with the  smallest positive integer m such
*        that
*
*           fl( a + 1.0 ) = a.
*
         A = 1
         C = 1
*
*+       WHILE( C.EQ.ONE )LOOP
   10    CONTINUE
         IF( C.EQ.ONE ) THEN
            A = 2*A
            C = DLAMC3( A, ONE )
            C = DLAMC3( C, -A )
            GO TO 10
         END IF
*+       END WHILE
*
*        Now compute  b = 2.0**m  with the smallest positive integer m
*        such that
*
*           fl( a + b ) .gt. a.
*
         B = 1
         C = DLAMC3( A, B )
*
*+       WHILE( C.EQ.A )LOOP
   20    CONTINUE
         IF( C.EQ.A ) THEN
            B = 2*B
            C = DLAMC3( A, B )
            GO TO 20
         END IF
*+       END WHILE
*
*        Now compute the base.  a and c  are neighbouring floating point
*        numbers  in the  interval  ( beta**t, beta**( t + 1 ) )  and so
*        their difference is beta. Adding 0.25 to c is to ensure that it
*        is truncated to beta and not ( beta - 1 ).
*
         QTR = ONE / 4
         SAVEC = C
         C = DLAMC3( C, -A )
         LBETA = C + QTR
*
*        Now determine whether rounding or chopping occurs,  by adding a
*        bit  less  than  beta/2  and a  bit  more  than  beta/2  to  a.
*
         B = LBETA
         F = DLAMC3( B / 2, -B / 100 )
         C = DLAMC3( F, A )
         IF( C.EQ.A ) THEN
            LRND = .TRUE.
         ELSE
            LRND = .FALSE.
         END IF
         F = DLAMC3( B / 2, B / 100 )
         C = DLAMC3( F, A )
         IF( ( LRND ) .AND. ( C.EQ.A ) )
     $      LRND = .FALSE.
*
*        Try and decide whether rounding is done in the  IEEE  'round to
*        nearest' style. B/2 is half a unit in the last place of the two
*        numbers A and SAVEC. Furthermore, A is even, i.e. has last  bit
*        zero, and SAVEC is odd. Thus adding B/2 to A should not  change
*        A, but adding B/2 to SAVEC should change SAVEC.
*
         T1 = DLAMC3( B / 2, A )
         T2 = DLAMC3( B / 2, SAVEC )
         LIEEE1 = ( T1.EQ.A ) .AND. ( T2.GT.SAVEC ) .AND. LRND
*
*        Now find  the  mantissa, t.  It should  be the  integer part of
*        log to the base beta of a,  however it is safer to determine  t
*        by powering.  So we find t as the smallest positive integer for
*        which
*
*           fl( beta**t + 1.0 ) = 1.0.
*
         LT = 0
         A = 1
         C = 1
*
*+       WHILE( C.EQ.ONE )LOOP
   30    CONTINUE
         IF( C.EQ.ONE ) THEN
            LT = LT + 1
            A = A*LBETA
            C = DLAMC3( A, ONE )
            C = DLAMC3( C, -A )
            GO TO 30
         END IF
*+       END WHILE
*
      END IF
*
      BETA = LBETA
      T = LT
      RND = LRND
      IEEE1 = LIEEE1
      RETURN
*
*     End of DLAMC1
*
      END
*
************************************************************************
*
      SUBROUTINE DLAMC2( BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      LOGICAL            RND
      INTEGER            BETA, EMAX, EMIN, T
      DOUBLE PRECISION   EPS, RMAX, RMIN
*     ..
*
*  Purpose
*  =======
*
*  DLAMC2 determines the machine parameters specified in its argument
*  list.
*
*  Arguments
*  =========
*
*  BETA    (output) INTEGER
*          The base of the machine.
*
*  T       (output) INTEGER
*          The number of ( BETA ) digits in the mantissa.
*
*  RND     (output) LOGICAL
*          Specifies whether proper rounding  ( RND = .TRUE. )  or
*          chopping  ( RND = .FALSE. )  occurs in addition. This may not
*          be a reliable guide to the way in which the machine performs
*          its arithmetic.
*
*  EPS     (output) DOUBLE PRECISION
*          The smallest positive number such that
*
*             fl( 1.0 - EPS ) .LT. 1.0,
*
*          where fl denotes the computed value.
*
*  EMIN    (output) INTEGER
*          The minimum exponent before (gradual) underflow occurs.
*
*  RMIN    (output) DOUBLE PRECISION
*          The smallest normalized number for the machine, given by
*          BASE**( EMIN - 1 ), where  BASE  is the floating point value
*          of BETA.
*
*  EMAX    (output) INTEGER
*          The maximum exponent before overflow occurs.
*
*  RMAX    (output) DOUBLE PRECISION
*          The largest positive number for the machine, given by
*          BASE**EMAX * ( 1 - EPS ), where  BASE  is the floating point
*          value of BETA.
*
*  Further Details
*  ===============
*
*  The computation of  EPS  is based on a routine PARANOIA by
*  W. Kahan of the University of California at Berkeley.
*
* =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            FIRST, IEEE, IWARN, LIEEE1, LRND
      INTEGER            GNMIN, GPMIN, I, LBETA, LEMAX, LEMIN, LT,
     $                   NGNMIN, NGPMIN
      DOUBLE PRECISION   A, B, C, HALF, LEPS, LRMAX, LRMIN, ONE, RBASE,
     $                   SIXTH, SMALL, THIRD, TWO, ZERO
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMC3
      EXTERNAL           DLAMC3
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLAMC1, DLAMC4, DLAMC5
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, MIN
*     ..
*     .. Save statement ..
      SAVE               FIRST, IWARN, LBETA, LEMAX, LEMIN, LEPS, LRMAX,
     $                   LRMIN, LT
*     ..
*     .. Data statements ..
      DATA               FIRST / .TRUE. / , IWARN / .FALSE. /
*     ..
*     .. Executable Statements ..
*
      IF( FIRST ) THEN
         FIRST = .FALSE.
         ZERO = 0
         ONE = 1
         TWO = 2
*
*        LBETA, LT, LRND, LEPS, LEMIN and LRMIN  are the local values of
*        BETA, T, RND, EPS, EMIN and RMIN.
*
*        Throughout this routine  we use the function  DLAMC3  to ensure
*        that relevant values are stored  and not held in registers,  or
*        are not affected by optimizers.
*
*        DLAMC1 returns the parameters  LBETA, LT, LRND and LIEEE1.
*
         CALL DLAMC1( LBETA, LT, LRND, LIEEE1 )
*
*        Start to find EPS.
*
         B = LBETA
         A = B**( -LT )
         LEPS = A
*
*        Try some tricks to see whether or not this is the correct  EPS.
*
         B = TWO / 3
         HALF = ONE / 2
         SIXTH = DLAMC3( B, -HALF )
         THIRD = DLAMC3( SIXTH, SIXTH )
         B = DLAMC3( THIRD, -HALF )
         B = DLAMC3( B, SIXTH )
         B = ABS( B )
         IF( B.LT.LEPS )
     $      B = LEPS
*
         LEPS = 1
*
*+       WHILE( ( LEPS.GT.B ).AND.( B.GT.ZERO ) )LOOP
   10    CONTINUE
         IF( ( LEPS.GT.B ) .AND. ( B.GT.ZERO ) ) THEN
            LEPS = B
            C = DLAMC3( HALF*LEPS, ( TWO**5 )*( LEPS**2 ) )
            C = DLAMC3( HALF, -C )
            B = DLAMC3( HALF, C )
            C = DLAMC3( HALF, -B )
            B = DLAMC3( HALF, C )
            GO TO 10
         END IF
*+       END WHILE
*
         IF( A.LT.LEPS )
     $      LEPS = A
*
*        Computation of EPS complete.
*
*        Now find  EMIN.  Let A = + or - 1, and + or - (1 + BASE**(-3)).
*        Keep dividing  A by BETA until (gradual) underflow occurs. This
*        is detected when we cannot recover the previous A.
*
         RBASE = ONE / LBETA
         SMALL = ONE
         DO 20 I = 1, 3
            SMALL = DLAMC3( SMALL*RBASE, ZERO )
   20    CONTINUE
         A = DLAMC3( ONE, SMALL )
         CALL DLAMC4( NGPMIN, ONE, LBETA )
         CALL DLAMC4( NGNMIN, -ONE, LBETA )
         CALL DLAMC4( GPMIN, A, LBETA )
         CALL DLAMC4( GNMIN, -A, LBETA )
         IEEE = .FALSE.
*
         IF( ( NGPMIN.EQ.NGNMIN ) .AND. ( GPMIN.EQ.GNMIN ) ) THEN
            IF( NGPMIN.EQ.GPMIN ) THEN
               LEMIN = NGPMIN
*            ( Non twos-complement machines, no gradual underflow;
*              e.g.,  VAX )
            ELSE IF( ( GPMIN-NGPMIN ).EQ.3 ) THEN
               LEMIN = NGPMIN - 1 + LT
               IEEE = .TRUE.
*            ( Non twos-complement machines, with gradual underflow;
*              e.g., IEEE standard followers )
            ELSE
               LEMIN = MIN( NGPMIN, GPMIN )
*            ( A guess; no known machine )
               IWARN = .TRUE.
            END IF
*
         ELSE IF( ( NGPMIN.EQ.GPMIN ) .AND. ( NGNMIN.EQ.GNMIN ) ) THEN
            IF( ABS( NGPMIN-NGNMIN ).EQ.1 ) THEN
               LEMIN = MAX( NGPMIN, NGNMIN )
*            ( Twos-complement machines, no gradual underflow;
*              e.g., CYBER 205 )
            ELSE
               LEMIN = MIN( NGPMIN, NGNMIN )
*            ( A guess; no known machine )
               IWARN = .TRUE.
            END IF
*
         ELSE IF( ( ABS( NGPMIN-NGNMIN ).EQ.1 ) .AND.
     $            ( GPMIN.EQ.GNMIN ) ) THEN
            IF( ( GPMIN-MIN( NGPMIN, NGNMIN ) ).EQ.3 ) THEN
               LEMIN = MAX( NGPMIN, NGNMIN ) - 1 + LT
*            ( Twos-complement machines with gradual underflow;
*              no known machine )
            ELSE
               LEMIN = MIN( NGPMIN, NGNMIN )
*            ( A guess; no known machine )
               IWARN = .TRUE.
            END IF
*
         ELSE
            LEMIN = MIN( NGPMIN, NGNMIN, GPMIN, GNMIN )
*         ( A guess; no known machine )
            IWARN = .TRUE.
         END IF
***
* Comment out this if block if EMIN is ok
         IF( IWARN ) THEN
            FIRST = .TRUE.
            WRITE( 6, FMT = 9999 )LEMIN
         END IF
***
*
*        Assume IEEE arithmetic if we found denormalised  numbers above,
*        or if arithmetic seems to round in the  IEEE style,  determined
*        in routine DLAMC1. A true IEEE machine should have both  things
*        true; however, faulty machines may have one or the other.
*
         IEEE = IEEE .OR. LIEEE1
*
*        Compute  RMIN by successive division by  BETA. We could compute
*        RMIN as BASE**( EMIN - 1 ),  but some machines underflow during
*        this computation.
*
         LRMIN = 1
         DO 30 I = 1, 1 - LEMIN
            LRMIN = DLAMC3( LRMIN*RBASE, ZERO )
   30    CONTINUE
*
*        Finally, call DLAMC5 to compute EMAX and RMAX.
*
         CALL DLAMC5( LBETA, LT, LEMIN, IEEE, LEMAX, LRMAX )
      END IF
*
      BETA = LBETA
      T = LT
      RND = LRND
      EPS = LEPS
      EMIN = LEMIN
      RMIN = LRMIN
      EMAX = LEMAX
      RMAX = LRMAX
*
      RETURN
*
 9999 FORMAT( / / ' WARNING. The value EMIN may be incorrect:-',
     $      '  EMIN = ', I8, /
     $      ' If, after inspection, the value EMIN looks',
     $      ' acceptable please comment out ',
     $      / ' the IF block as marked within the code of routine',
     $      ' DLAMC2,', / ' otherwise supply EMIN explicitly.', / )
*
*     End of DLAMC2
*
      END
*
************************************************************************
*
      DOUBLE PRECISION FUNCTION DLAMC3( A, B )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   A, B
*     ..
*
*  Purpose
*  =======
*
*  DLAMC3  is intended to force  A  and  B  to be stored prior to doing
*  the addition of  A  and  B ,  for use in situations where optimizers
*  might hold one of these in a register.
*
*  Arguments
*  =========
*
*  A, B    (input) DOUBLE PRECISION
*          The values A and B.
*
* =====================================================================
*
*     .. Executable Statements ..
*
      DLAMC3 = A + B
*
      RETURN
*
*     End of DLAMC3
*
      END
*
************************************************************************
*
      SUBROUTINE DLAMC4( EMIN, START, BASE )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      INTEGER            BASE, EMIN
      DOUBLE PRECISION   START
*     ..
*
*  Purpose
*  =======
*
*  DLAMC4 is a service routine for DLAMC2.
*
*  Arguments
*  =========
*
*  EMIN    (output) EMIN
*          The minimum exponent before (gradual) underflow, computed by
*          setting A = START and dividing by BASE until the previous A
*          can not be recovered.
*
*  START   (input) DOUBLE PRECISION
*          The starting point for determining EMIN.
*
*  BASE    (input) INTEGER
*          The base of the machine.
*
* =====================================================================
*
*     .. Local Scalars ..
      INTEGER            I
      DOUBLE PRECISION   A, B1, B2, C1, C2, D1, D2, ONE, RBASE, ZERO
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMC3
      EXTERNAL           DLAMC3
*     ..
*     .. Executable Statements ..
*
      A = START
      ONE = 1
      RBASE = ONE / BASE
      ZERO = 0
      EMIN = 1
      B1 = DLAMC3( A*RBASE, ZERO )
      C1 = A
      C2 = A
      D1 = A
      D2 = A
*+    WHILE( ( C1.EQ.A ).AND.( C2.EQ.A ).AND.
*    $       ( D1.EQ.A ).AND.( D2.EQ.A )      )LOOP
   10 CONTINUE
      IF( ( C1.EQ.A ) .AND. ( C2.EQ.A ) .AND. ( D1.EQ.A ) .AND.
     $    ( D2.EQ.A ) ) THEN
         EMIN = EMIN - 1
         A = B1
         B1 = DLAMC3( A / BASE, ZERO )
         C1 = DLAMC3( B1*BASE, ZERO )
         D1 = ZERO
         DO 20 I = 1, BASE
            D1 = D1 + B1
   20    CONTINUE
         B2 = DLAMC3( A*RBASE, ZERO )
         C2 = DLAMC3( B2 / RBASE, ZERO )
         D2 = ZERO
         DO 30 I = 1, BASE
            D2 = D2 + B2
   30    CONTINUE
         GO TO 10
      END IF
*+    END WHILE
*
      RETURN
*
*     End of DLAMC4
*
      END
*
************************************************************************
*
      SUBROUTINE DLAMC5( BETA, P, EMIN, IEEE, EMAX, RMAX )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      LOGICAL            IEEE
      INTEGER            BETA, EMAX, EMIN, P
      DOUBLE PRECISION   RMAX
*     ..
*
*  Purpose
*  =======
*
*  DLAMC5 attempts to compute RMAX, the largest machine floating-point
*  number, without overflow.  It assumes that EMAX + abs(EMIN) sum
*  approximately to a power of 2.  It will fail on machines where this
*  assumption does not hold, for example, the Cyber 205 (EMIN = -28625,
*  EMAX = 28718).  It will also fail if the value supplied for EMIN is
*  too large (i.e. too close to zero), probably with overflow.
*
*  Arguments
*  =========
*
*  BETA    (input) INTEGER
*          The base of floating-point arithmetic.
*
*  P       (input) INTEGER
*          The number of base BETA digits in the mantissa of a
*          floating-point value.
*
*  EMIN    (input) INTEGER
*          The minimum exponent before (gradual) underflow.
*
*  IEEE    (input) LOGICAL
*          A logical flag specifying whether or not the arithmetic
*          system is thought to comply with the IEEE standard.
*
*  EMAX    (output) INTEGER
*          The largest exponent before overflow
*
*  RMAX    (output) DOUBLE PRECISION
*          The largest machine floating-point number.
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
*     ..
*     .. Local Scalars ..
      INTEGER            EXBITS, EXPSUM, I, LEXP, NBITS, TRY, UEXP
      DOUBLE PRECISION   OLDY, RECBAS, Y, Z
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMC3
      EXTERNAL           DLAMC3
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MOD
*     ..
*     .. Executable Statements ..
*
*     First compute LEXP and UEXP, two powers of 2 that bound
*     abs(EMIN). We then assume that EMAX + abs(EMIN) will sum
*     approximately to the bound that is closest to abs(EMIN).
*     (EMAX is the exponent of the required number RMAX).
*
      LEXP = 1
      EXBITS = 1
   10 CONTINUE
      TRY = LEXP*2
      IF( TRY.LE.( -EMIN ) ) THEN
         LEXP = TRY
         EXBITS = EXBITS + 1
         GO TO 10
      END IF
      IF( LEXP.EQ.-EMIN ) THEN
         UEXP = LEXP
      ELSE
         UEXP = TRY
         EXBITS = EXBITS + 1
      END IF
*
*     Now -LEXP is less than or equal to EMIN, and -UEXP is greater
*     than or equal to EMIN. EXBITS is the number of bits needed to
*     store the exponent.
*
      IF( ( UEXP+EMIN ).GT.( -LEXP-EMIN ) ) THEN
         EXPSUM = 2*LEXP
      ELSE
         EXPSUM = 2*UEXP
      END IF
*
*     EXPSUM is the exponent range, approximately equal to
*     EMAX - EMIN + 1 .
*
      EMAX = EXPSUM + EMIN - 1
      NBITS = 1 + EXBITS + P
*
*     NBITS is the total number of bits needed to store a
*     floating-point number.
*
      IF( ( MOD( NBITS, 2 ).EQ.1 ) .AND. ( BETA.EQ.2 ) ) THEN
*
*        Either there are an odd number of bits used to store a
*        floating-point number, which is unlikely, or some bits are
*        not used in the representation of numbers, which is possible,
*        (e.g. Cray machines) or the mantissa has an implicit bit,
*        (e.g. IEEE machines, Dec Vax machines), which is perhaps the
*        most likely. We have to assume the last alternative.
*        If this is true, then we need to reduce EMAX by one because
*        there must be some way of representing zero in an implicit-bit
*        system. On machines like Cray, we are reducing EMAX by one
*        unnecessarily.
*
         EMAX = EMAX - 1
      END IF
*
      IF( IEEE ) THEN
*
*        Assume we are on an IEEE machine which reserves one exponent
*        for infinity and NaN.
*
         EMAX = EMAX - 1
      END IF
*
*     Now create RMAX, the largest machine number, which should
*     be equal to (1.0 - BETA**(-P)) * BETA**EMAX .
*
*     First compute 1.0 - BETA**(-P), being careful that the
*     result is less than 1.0 .
*
      RECBAS = ONE / BETA
      Z = BETA - ONE
      Y = ZERO
      DO 20 I = 1, P
         Z = Z*RECBAS
         IF( Y.LT.ONE )
     $      OLDY = Y
         Y = DLAMC3( Y, Z )
   20 CONTINUE
      IF( Y.GE.ONE )
     $   Y = OLDY
*
*     Now multiply by BETA**EMAX to get RMAX.
*
      DO 30 I = 1, EMAX
         Y = DLAMC3( Y*BETA, ZERO )
   30 CONTINUE
*
      RMAX = Y
      RETURN
*
*     End of DLAMC5
*
      END
      SUBROUTINE DLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X,
     $                   SCALE, CNORM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1992
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, NORMIN, TRANS, UPLO
      INTEGER            INFO, KD, LDAB, N
      DOUBLE PRECISION   SCALE
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AB( LDAB, * ), CNORM( * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  DLATBS solves one of the triangular systems
*
*     A *x = s*b  or  A'*x = s*b
*
*  with scaling to prevent overflow, where A is an upper or lower
*  triangular band matrix.  Here A' denotes the transpose of A, x and b
*  are n-element vectors, and s is a scaling factor, usually less than
*  or equal to 1, chosen so that the components of x will be less than
*  the overflow threshold.  If the unscaled problem will not cause
*  overflow, the Level 2 BLAS routine DTBSV is called.  If the matrix A
*  is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*  non-trivial solution to A*x = 0 is returned.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the matrix A is upper or lower triangular.
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  TRANS   (input) CHARACTER*1
*          Specifies the operation applied to A.
*          = 'N':  Solve A * x = s*b  (No transpose)
*          = 'T':  Solve A'* x = s*b  (Transpose)
*          = 'C':  Solve A'* x = s*b  (Conjugate transpose = Transpose)
*
*  DIAG    (input) CHARACTER*1
*          Specifies whether or not the matrix A is unit triangular.
*          = 'N':  Non-unit triangular
*          = 'U':  Unit triangular
*
*  NORMIN  (input) CHARACTER*1
*          Specifies whether CNORM has been set or not.
*          = 'Y':  CNORM contains the column norms on entry
*          = 'N':  CNORM is not set on entry.  On exit, the norms will
*                  be computed and stored in CNORM.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of subdiagonals or superdiagonals in the
*          triangular matrix A.  KD >= 0.
*
*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
*          The upper or lower triangular band matrix A, stored in the
*          first KD+1 rows of the array. The j-th column of A is stored
*          in the j-th column of the array AB as follows:
*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  X       (input/output) DOUBLE PRECISION array, dimension (N)
*          On entry, the right hand side b of the triangular system.
*          On exit, X is overwritten by the solution vector x.
*
*  SCALE   (output) DOUBLE PRECISION
*          The scaling factor s for the triangular system
*             A * x = s*b  or  A'* x = s*b.
*          If SCALE = 0, the matrix A is singular or badly scaled, and
*          the vector x is an exact or approximate solution to A*x = 0.
*
*  CNORM   (input or output) DOUBLE PRECISION array, dimension (N)
*
*          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
*          contains the norm of the off-diagonal part of the j-th column
*          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
*          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
*          must be greater than or equal to the 1-norm.
*
*          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
*          returns the 1-norm of the offdiagonal part of the j-th column
*          of A.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -k, the k-th argument had an illegal value
*
*  Further Details
*  ======= =======
*
*  A rough bound on x is computed; if that is less than overflow, DTBSV
*  is called, otherwise, specific code is used which checks for possible
*  overflow or divide-by-zero at every operation.
*
*  A columnwise scheme is used for solving A*x = b.  The basic algorithm
*  if A is lower triangular is
*
*       x[1:n] := b[1:n]
*       for j = 1, ..., n
*            x(j) := x(j) / A(j,j)
*            x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j]
*       end
*
*  Define bounds on the components of x after j iterations of the loop:
*     M(j) = bound on x[1:j]
*     G(j) = bound on x[j+1:n]
*  Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}.
*
*  Then for iteration j+1 we have
*     M(j+1) <= G(j) / | A(j+1,j+1) |
*     G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] |
*            <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | )
*
*  where CNORM(j+1) is greater than or equal to the infinity-norm of
*  column j+1 of A, not counting the diagonal.  Hence
*
*     G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | )
*                  1<=i<=j
*  and
*
*     |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| )
*                                   1<=i< j
*
*  Since |x(j)| <= M(j), we use the Level 2 BLAS routine DTBSV if the
*  reciprocal of the largest M(j), j=1,..,n, is larger than
*  max(underflow, 1/overflow).
*
*  The bound on x(j) is also used to determine when a step in the
*  columnwise method can be performed without fear of overflow.  If
*  the computed bound is greater than a large constant, x is scaled to
*  prevent overflow, but if the bound overflows, x is set to 0, x(j) to
*  1, and scale to 0, and a non-trivial solution to A*x = 0 is found.
*
*  Similarly, a row-wise scheme is used to solve A'*x = b.  The basic
*  algorithm for A upper triangular is
*
*       for j = 1, ..., n
*            x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j)
*       end
*
*  We simultaneously compute two bounds
*       G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j
*       M(j) = bound on x(i), 1<=i<=j
*
*  The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we
*  add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1.
*  Then the bound on x(j) is
*
*       M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) |
*
*            <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| )
*                      1<=i<=j
*
*  and we can safely call DTBSV if 1/M(n) and 1/G(n) are both greater
*  than max(underflow, 1/overflow).
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, HALF, ONE
      PARAMETER          ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOTRAN, NOUNIT, UPPER
      INTEGER            I, IMAX, J, JFIRST, JINC, JLAST, JLEN, MAIND
      DOUBLE PRECISION   BIGNUM, GROW, REC, SMLNUM, SUMJ, TJJ, TJJS,
     $                   TMAX, TSCAL, USCAL, XBND, XJ, XMAX
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            IDAMAX
      DOUBLE PRECISION   DASUM, DDOT, DLAMCH
      EXTERNAL           LSAME, IDAMAX, DASUM, DDOT, DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DAXPY, DSCAL, DTBSV, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, MIN
*     ..
*     .. Executable Statements ..
*
      INFO = 0
      UPPER = LSAME( UPLO, 'U' )
      NOTRAN = LSAME( TRANS, 'N' )
      NOUNIT = LSAME( DIAG, 'N' )
*
*     Test the input parameters.
*
      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
     $         LSAME( TRANS, 'C' ) ) THEN
         INFO = -2
      ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
         INFO = -3
      ELSE IF( .NOT.LSAME( NORMIN, 'Y' ) .AND. .NOT.
     $         LSAME( NORMIN, 'N' ) ) THEN
         INFO = -4
      ELSE IF( N.LT.0 ) THEN
         INFO = -5
      ELSE IF( KD.LT.0 ) THEN
         INFO = -6
      ELSE IF( LDAB.LT.KD+1 ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DLATBS', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Determine machine dependent parameters to control overflow.
*
      SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
      BIGNUM = ONE / SMLNUM
      SCALE = ONE
*
      IF( LSAME( NORMIN, 'N' ) ) THEN
*
*        Compute the 1-norm of each column, not including the diagonal.
*
         IF( UPPER ) THEN
*
*           A is upper triangular.
*
            DO 10 J = 1, N
               JLEN = MIN( KD, J-1 )
               CNORM( J ) = DASUM( JLEN, AB( KD+1-JLEN, J ), 1 )
   10       CONTINUE
         ELSE
*
*           A is lower triangular.
*
            DO 20 J = 1, N
               JLEN = MIN( KD, N-J )
               IF( JLEN.GT.0 ) THEN
                  CNORM( J ) = DASUM( JLEN, AB( 2, J ), 1 )
               ELSE
                  CNORM( J ) = ZERO
               END IF
   20       CONTINUE
         END IF
      END IF
*
*     Scale the column norms by TSCAL if the maximum element in CNORM is
*     greater than BIGNUM.
*
      IMAX = IDAMAX( N, CNORM, 1 )
      TMAX = CNORM( IMAX )
      IF( TMAX.LE.BIGNUM ) THEN
         TSCAL = ONE
      ELSE
         TSCAL = ONE / ( SMLNUM*TMAX )
         CALL DSCAL( N, TSCAL, CNORM, 1 )
      END IF
*
*     Compute a bound on the computed solution vector to see if the
*     Level 2 BLAS routine DTBSV can be used.
*
      J = IDAMAX( N, X, 1 )
      XMAX = ABS( X( J ) )
      XBND = XMAX
      IF( NOTRAN ) THEN
*
*        Compute the growth in A * x = b.
*
         IF( UPPER ) THEN
            JFIRST = N
            JLAST = 1
            JINC = -1
            MAIND = KD + 1
         ELSE
            JFIRST = 1
            JLAST = N
            JINC = 1
            MAIND = 1
         END IF
*
         IF( TSCAL.NE.ONE ) THEN
            GROW = ZERO
            GO TO 50
         END IF
*
         IF( NOUNIT ) THEN
*
*           A is non-unit triangular.
*
*           Compute GROW = 1/G(j) and XBND = 1/M(j).
*           Initially, G(0) = max{x(i), i=1,...,n}.
*
            GROW = ONE / MAX( XBND, SMLNUM )
            XBND = GROW
            DO 30 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
               IF( GROW.LE.SMLNUM )
     $            GO TO 50
*
*              M(j) = G(j-1) / abs(A(j,j))
*
               TJJ = ABS( AB( MAIND, J ) )
               XBND = MIN( XBND, MIN( ONE, TJJ )*GROW )
               IF( TJJ+CNORM( J ).GE.SMLNUM ) THEN
*
*                 G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) )
*
                  GROW = GROW*( TJJ / ( TJJ+CNORM( J ) ) )
               ELSE
*
*                 G(j) could overflow, set GROW to 0.
*
                  GROW = ZERO
               END IF
   30       CONTINUE
            GROW = XBND
         ELSE
*
*           A is unit triangular.
*
*           Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
*
            GROW = MIN( ONE, ONE / MAX( XBND, SMLNUM ) )
            DO 40 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
               IF( GROW.LE.SMLNUM )
     $            GO TO 50
*
*              G(j) = G(j-1)*( 1 + CNORM(j) )
*
               GROW = GROW*( ONE / ( ONE+CNORM( J ) ) )
   40       CONTINUE
         END IF
   50    CONTINUE
*
      ELSE
*
*        Compute the growth in A' * x = b.
*
         IF( UPPER ) THEN
            JFIRST = 1
            JLAST = N
            JINC = 1
            MAIND = KD + 1
         ELSE
            JFIRST = N
            JLAST = 1
            JINC = -1
            MAIND = 1
         END IF
*
         IF( TSCAL.NE.ONE ) THEN
            GROW = ZERO
            GO TO 80
         END IF
*
         IF( NOUNIT ) THEN
*
*           A is non-unit triangular.
*
*           Compute GROW = 1/G(j) and XBND = 1/M(j).
*           Initially, M(0) = max{x(i), i=1,...,n}.
*
            GROW = ONE / MAX( XBND, SMLNUM )
            XBND = GROW
            DO 60 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
               IF( GROW.LE.SMLNUM )
     $            GO TO 80
*
*              G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) )
*
               XJ = ONE + CNORM( J )
               GROW = MIN( GROW, XBND / XJ )
*
*              M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j))
*
               TJJ = ABS( AB( MAIND, J ) )
               IF( XJ.GT.TJJ )
     $            XBND = XBND*( TJJ / XJ )
   60       CONTINUE
            GROW = MIN( GROW, XBND )
         ELSE
*
*           A is unit triangular.
*
*           Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
*
            GROW = MIN( ONE, ONE / MAX( XBND, SMLNUM ) )
            DO 70 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
               IF( GROW.LE.SMLNUM )
     $            GO TO 80
*
*              G(j) = ( 1 + CNORM(j) )*G(j-1)
*
               XJ = ONE + CNORM( J )
               GROW = GROW / XJ
   70       CONTINUE
         END IF
   80    CONTINUE
      END IF
*
      IF( ( GROW*TSCAL ).GT.SMLNUM ) THEN
*
*        Use the Level 2 BLAS solve if the reciprocal of the bound on
*        elements of X is not too small.
*
         CALL DTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, X, 1 )
      ELSE
*
*        Use a Level 1 BLAS solve, scaling intermediate results.
*
         IF( XMAX.GT.BIGNUM ) THEN
*
*           Scale X so that its components are less than or equal to
*           BIGNUM in absolute value.
*
            SCALE = BIGNUM / XMAX
            CALL DSCAL( N, SCALE, X, 1 )
            XMAX = BIGNUM
         END IF
*
         IF( NOTRAN ) THEN
*
*           Solve A * x = b
*
            DO 110 J = JFIRST, JLAST, JINC
*
*              Compute x(j) = b(j) / A(j,j), scaling x if necessary.
*
               XJ = ABS( X( J ) )
               IF( NOUNIT ) THEN
                  TJJS = AB( MAIND, J )*TSCAL
               ELSE
                  TJJS = TSCAL
                  IF( TSCAL.EQ.ONE )
     $               GO TO 100
               END IF
               TJJ = ABS( TJJS )
               IF( TJJ.GT.SMLNUM ) THEN
*
*                    abs(A(j,j)) > SMLNUM:
*
                  IF( TJJ.LT.ONE ) THEN
                     IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                          Scale x by 1/b(j).
*
                        REC = ONE / XJ
                        CALL DSCAL( N, REC, X, 1 )
                        SCALE = SCALE*REC
                        XMAX = XMAX*REC
                     END IF
                  END IF
                  X( J ) = X( J ) / TJJS
                  XJ = ABS( X( J ) )
               ELSE IF( TJJ.GT.ZERO ) THEN
*
*                    0 < abs(A(j,j)) <= SMLNUM:
*
                  IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                       Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM
*                       to avoid overflow when dividing by A(j,j).
*
                     REC = ( TJJ*BIGNUM ) / XJ
                     IF( CNORM( J ).GT.ONE ) THEN
*
*                          Scale by 1/CNORM(j) to avoid overflow when
*                          multiplying x(j) times column j.
*
                        REC = REC / CNORM( J )
                     END IF
                     CALL DSCAL( N, REC, X, 1 )
                     SCALE = SCALE*REC
                     XMAX = XMAX*REC
                  END IF
                  X( J ) = X( J ) / TJJS
                  XJ = ABS( X( J ) )
               ELSE
*
*                    A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and
*                    scale = 0, and compute a solution to A*x = 0.
*
                  DO 90 I = 1, N
                     X( I ) = ZERO
   90             CONTINUE
                  X( J ) = ONE
                  XJ = ONE
                  SCALE = ZERO
                  XMAX = ZERO
               END IF
  100          CONTINUE
*
*              Scale x if necessary to avoid overflow when adding a
*              multiple of column j of A.
*
               IF( XJ.GT.ONE ) THEN
                  REC = ONE / XJ
                  IF( CNORM( J ).GT.( BIGNUM-XMAX )*REC ) THEN
*
*                    Scale x by 1/(2*abs(x(j))).
*
                     REC = REC*HALF
                     CALL DSCAL( N, REC, X, 1 )
                     SCALE = SCALE*REC
                  END IF
               ELSE IF( XJ*CNORM( J ).GT.( BIGNUM-XMAX ) ) THEN
*
*                 Scale x by 1/2.
*
                  CALL DSCAL( N, HALF, X, 1 )
                  SCALE = SCALE*HALF
               END IF
*
               IF( UPPER ) THEN
                  IF( J.GT.1 ) THEN
*
*                    Compute the update
*                       x(max(1,j-kd):j-1) := x(max(1,j-kd):j-1) -
*                                             x(j)* A(max(1,j-kd):j-1,j)
*
                     JLEN = MIN( KD, J-1 )
                     CALL DAXPY( JLEN, -X( J )*TSCAL,
     $                           AB( KD+1-JLEN, J ), 1, X( J-JLEN ), 1 )
                     I = IDAMAX( J-1, X, 1 )
                     XMAX = ABS( X( I ) )
                  END IF
               ELSE IF( J.LT.N ) THEN
*
*                 Compute the update
*                    x(j+1:min(j+kd,n)) := x(j+1:min(j+kd,n)) -
*                                          x(j) * A(j+1:min(j+kd,n),j)
*
                  JLEN = MIN( KD, N-J )
                  IF( JLEN.GT.0 )
     $               CALL DAXPY( JLEN, -X( J )*TSCAL, AB( 2, J ), 1,
     $                           X( J+1 ), 1 )
                  I = J + IDAMAX( N-J, X( J+1 ), 1 )
                  XMAX = ABS( X( I ) )
               END IF
  110       CONTINUE
*
         ELSE
*
*           Solve A' * x = b
*
            DO 160 J = JFIRST, JLAST, JINC
*
*              Compute x(j) = b(j) - sum A(k,j)*x(k).
*                                    k<>j
*
               XJ = ABS( X( J ) )
               USCAL = TSCAL
               REC = ONE / MAX( XMAX, ONE )
               IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN
*
*                 If x(j) could overflow, scale x by 1/(2*XMAX).
*
                  REC = REC*HALF
                  IF( NOUNIT ) THEN
                     TJJS = AB( MAIND, J )*TSCAL
                  ELSE
                     TJJS = TSCAL
                  END IF
                  TJJ = ABS( TJJS )
                  IF( TJJ.GT.ONE ) THEN
*
*                       Divide by A(j,j) when scaling x if A(j,j) > 1.
*
                     REC = MIN( ONE, REC*TJJ )
                     USCAL = USCAL / TJJS
                  END IF
                  IF( REC.LT.ONE ) THEN
                     CALL DSCAL( N, REC, X, 1 )
                     SCALE = SCALE*REC
                     XMAX = XMAX*REC
                  END IF
               END IF
*
               SUMJ = ZERO
               IF( USCAL.EQ.ONE ) THEN
*
*                 If the scaling needed for A in the dot product is 1,
*                 call DDOT to perform the dot product.
*
                  IF( UPPER ) THEN
                     JLEN = MIN( KD, J-1 )
                     SUMJ = DDOT( JLEN, AB( KD+1-JLEN, J ), 1,
     $                      X( J-JLEN ), 1 )
                  ELSE
                     JLEN = MIN( KD, N-J )
                     IF( JLEN.GT.0 )
     $                  SUMJ = DDOT( JLEN, AB( 2, J ), 1, X( J+1 ), 1 )
                  END IF
               ELSE
*
*                 Otherwise, use in-line code for the dot product.
*
                  IF( UPPER ) THEN
                     JLEN = MIN( KD, J-1 )
                     DO 120 I = 1, JLEN
                        SUMJ = SUMJ + ( AB( KD+I-JLEN, J )*USCAL )*
     $                         X( J-JLEN-1+I )
  120                CONTINUE
                  ELSE
                     JLEN = MIN( KD, N-J )
                     DO 130 I = 1, JLEN
                        SUMJ = SUMJ + ( AB( I+1, J )*USCAL )*X( J+I )
  130                CONTINUE
                  END IF
               END IF
*
               IF( USCAL.EQ.TSCAL ) THEN
*
*                 Compute x(j) := ( x(j) - sumj ) / A(j,j) if 1/A(j,j)
*                 was not used to scale the dotproduct.
*
                  X( J ) = X( J ) - SUMJ
                  XJ = ABS( X( J ) )
                  IF( NOUNIT ) THEN
*
*                    Compute x(j) = x(j) / A(j,j), scaling if necessary.
*
                     TJJS = AB( MAIND, J )*TSCAL
                  ELSE
                     TJJS = TSCAL
                     IF( TSCAL.EQ.ONE )
     $                  GO TO 150
                  END IF
                  TJJ = ABS( TJJS )
                  IF( TJJ.GT.SMLNUM ) THEN
*
*                       abs(A(j,j)) > SMLNUM:
*
                     IF( TJJ.LT.ONE ) THEN
                        IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                             Scale X by 1/abs(x(j)).
*
                           REC = ONE / XJ
                           CALL DSCAL( N, REC, X, 1 )
                           SCALE = SCALE*REC
                           XMAX = XMAX*REC
                        END IF
                     END IF
                     X( J ) = X( J ) / TJJS
                  ELSE IF( TJJ.GT.ZERO ) THEN
*
*                       0 < abs(A(j,j)) <= SMLNUM:
*
                     IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                          Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM.
*
                        REC = ( TJJ*BIGNUM ) / XJ
                        CALL DSCAL( N, REC, X, 1 )
                        SCALE = SCALE*REC
                        XMAX = XMAX*REC
                     END IF
                     X( J ) = X( J ) / TJJS
                  ELSE
*
*                       A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and
*                       scale = 0, and compute a solution to A'*x = 0.
*
                     DO 140 I = 1, N
                        X( I ) = ZERO
  140                CONTINUE
                     X( J ) = ONE
                     SCALE = ZERO
                     XMAX = ZERO
                  END IF
  150             CONTINUE
               ELSE
*
*                 Compute x(j) := x(j) / A(j,j) - sumj if the dot
*                 product has already been divided by 1/A(j,j).
*
                  X( J ) = X( J ) / TJJS - SUMJ
               END IF
               XMAX = MAX( XMAX, ABS( X( J ) ) )
  160       CONTINUE
         END IF
         SCALE = SCALE / TSCAL
      END IF
*
*     Scale the column norms by 1/TSCAL for return.
*
      IF( TSCAL.NE.ONE ) THEN
         CALL DSCAL( N, ONE / TSCAL, CNORM, 1 )
      END IF
*
      RETURN
*
*     End of DLATBS
*
      END
      SUBROUTINE DRSCL( N, SA, SX, INCX )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SA
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   SX( * )
*     ..
*
*  Purpose
*  =======
*
*  DRSCL multiplies an n-element real vector x by the real scalar 1/a.
*  This is done without overflow or underflow as long as
*  the final result x/a does not overflow or underflow.
*
*  Arguments
*  =========
*
*  N       (input) INTEGER
*          The number of components of the vector x.
*
*  SA      (input) DOUBLE PRECISION
*          The scalar a which is used to divide each component of x.
*          SA must be >= 0, or the subroutine will divide by zero.
*
*  SX      (input/output) DOUBLE PRECISION array, dimension
*                         (1+(N-1)*abs(INCX))
*          The n-element vector x.
*
*  INCX    (input) INTEGER
*          The increment between successive values of the vector SX.
*          > 0:  SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i),     1< i<= n
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            DONE
      DOUBLE PRECISION   BIGNUM, CDEN, CDEN1, CNUM, CNUM1, MUL, SMLNUM
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DSCAL
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( N.LE.0 )
     $   RETURN
*
*     Get machine parameters
*
      SMLNUM = DLAMCH( 'S' )
      BIGNUM = ONE / SMLNUM
      CALL DLABAD( SMLNUM, BIGNUM )
*
*     Initialize the denominator to SA and the numerator to 1.
*
      CDEN = SA
      CNUM = ONE
*
   10 CONTINUE
      CDEN1 = CDEN*SMLNUM
      CNUM1 = CNUM / BIGNUM
      IF( ABS( CDEN1 ).GT.ABS( CNUM ) .AND. CNUM.NE.ZERO ) THEN
*
*        Pre-multiply X by SMLNUM if CDEN is large compared to CNUM.
*
         MUL = SMLNUM
         DONE = .FALSE.
         CDEN = CDEN1
      ELSE IF( ABS( CNUM1 ).GT.ABS( CDEN ) ) THEN
*
*        Pre-multiply X by BIGNUM if CDEN is small compared to CNUM.
*
         MUL = BIGNUM
         DONE = .FALSE.
         CNUM = CNUM1
      ELSE
*
*        Multiply X by CNUM / CDEN and return.
*
         MUL = CNUM / CDEN
         DONE = .TRUE.
      END IF
*
*     Scale the vector X by MUL
*
      CALL DSCAL( N, MUL, SX, INCX )
*
      IF( .NOT.DONE )
     $   GO TO 10
*
      RETURN
*
*     End of DRSCL
*
      END
      INTEGER          FUNCTION IEEECK( ISPEC, ZERO, ONE )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1998
*
*     .. Scalar Arguments ..
      INTEGER            ISPEC
      REAL               ONE, ZERO
*     ..
*
*  Purpose
*  =======
*
*  IEEECK is called from the ILAENV to verify that Infinity and
*  possibly NaN arithmetic is safe (i.e. will not trap).
*
*  Arguments
*  =========
*
*  ISPEC   (input) INTEGER
*          Specifies whether to test just for inifinity arithmetic
*          or whether to test for infinity and NaN arithmetic.
*          = 0: Verify infinity arithmetic only.
*          = 1: Verify infinity and NaN arithmetic.
*
*  ZERO    (input) REAL
*          Must contain the value 0.0
*          This is passed to prevent the compiler from optimizing
*          away this code.
*
*  ONE     (input) REAL
*          Must contain the value 1.0
*          This is passed to prevent the compiler from optimizing
*          away this code.
*
*  RETURN VALUE:  INTEGER
*          = 0:  Arithmetic failed to produce the correct answers
*          = 1:  Arithmetic produced the correct answers
*
*     .. Local Scalars ..
      REAL               NAN1, NAN2, NAN3, NAN4, NAN5, NAN6, NEGINF,
     $                   NEGZRO, NEWZRO, POSINF
*     ..
*     .. Executable Statements ..
      IEEECK = 1
*
      POSINF = ONE / ZERO
      IF( POSINF.LE.ONE ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      NEGINF = -ONE / ZERO
      IF( NEGINF.GE.ZERO ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      NEGZRO = ONE / ( NEGINF+ONE )
      IF( NEGZRO.NE.ZERO ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      NEGINF = ONE / NEGZRO
      IF( NEGINF.GE.ZERO ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      NEWZRO = NEGZRO + ZERO
      IF( NEWZRO.NE.ZERO ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      POSINF = ONE / NEWZRO
      IF( POSINF.LE.ONE ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      NEGINF = NEGINF*POSINF
      IF( NEGINF.GE.ZERO ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      POSINF = POSINF*POSINF
      IF( POSINF.LE.ONE ) THEN
         IEEECK = 0
         RETURN
      END IF
*
*
*
*
*     Return if we were only asked to check infinity arithmetic
*
      IF( ISPEC.EQ.0 )
     $   RETURN
*
      NAN1 = POSINF + NEGINF
*
      NAN2 = POSINF / NEGINF
*
      NAN3 = POSINF / POSINF
*
      NAN4 = POSINF*ZERO
*
      NAN5 = NEGINF*NEGZRO
*
      NAN6 = NAN5*0.0
*
      IF( NAN1.EQ.NAN1 ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      IF( NAN2.EQ.NAN2 ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      IF( NAN3.EQ.NAN3 ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      IF( NAN4.EQ.NAN4 ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      IF( NAN5.EQ.NAN5 ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      IF( NAN6.EQ.NAN6 ) THEN
         IEEECK = 0
         RETURN
      END IF
*
      RETURN
      END
      INTEGER          FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3,
     $                 N4 )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. Scalar Arguments ..
      CHARACTER*( * )    NAME, OPTS
      INTEGER            ISPEC, N1, N2, N3, N4
*     ..
*
*  Purpose
*  =======
*
*  ILAENV is called from the LAPACK routines to choose problem-dependent
*  parameters for the local environment.  See ISPEC for a description of
*  the parameters.
*
*  This version provides a set of parameters which should give good,
*  but not optimal, performance on many of the currently available
*  computers.  Users are encouraged to modify this subroutine to set
*  the tuning parameters for their particular machine using the option
*  and problem size information in the arguments.
*
*  This routine will not function correctly if it is converted to all
*  lower case.  Converting it to all upper case is allowed.
*
*  Arguments
*  =========
*
*  ISPEC   (input) INTEGER
*          Specifies the parameter to be returned as the value of
*          ILAENV.
*          = 1: the optimal blocksize; if this value is 1, an unblocked
*               algorithm will give the best performance.
*          = 2: the minimum block size for which the block routine
*               should be used; if the usable block size is less than
*               this value, an unblocked routine should be used.
*          = 3: the crossover point (in a block routine, for N less
*               than this value, an unblocked routine should be used)
*          = 4: the number of shifts, used in the nonsymmetric
*               eigenvalue routines
*          = 5: the minimum column dimension for blocking to be used;
*               rectangular blocks must have dimension at least k by m,
*               where k is given by ILAENV(2,...) and m by ILAENV(5,...)
*          = 6: the crossover point for the SVD (when reducing an m by n
*               matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds
*               this value, a QR factorization is used first to reduce
*               the matrix to a triangular form.)
*          = 7: the number of processors
*          = 8: the crossover point for the multishift QR and QZ methods
*               for nonsymmetric eigenvalue problems.
*          = 9: maximum size of the subproblems at the bottom of the
*               computation tree in the divide-and-conquer algorithm
*               (used by xGELSD and xGESDD)
*          =10: ieee NaN arithmetic can be trusted not to trap
*          =11: infinity arithmetic can be trusted not to trap
*
*  NAME    (input) CHARACTER*(*)
*          The name of the calling subroutine, in either upper case or
*          lower case.
*
*  OPTS    (input) CHARACTER*(*)
*          The character options to the subroutine NAME, concatenated
*          into a single character string.  For example, UPLO = 'U',
*          TRANS = 'T', and DIAG = 'N' for a triangular routine would
*          be specified as OPTS = 'UTN'.
*
*  N1      (input) INTEGER
*  N2      (input) INTEGER
*  N3      (input) INTEGER
*  N4      (input) INTEGER
*          Problem dimensions for the subroutine NAME; these may not all
*          be required.
*
* (ILAENV) (output) INTEGER
*          >= 0: the value of the parameter specified by ISPEC
*          < 0:  if ILAENV = -k, the k-th argument had an illegal value.
*
*  Further Details
*  ===============
*
*  The following conventions have been used when calling ILAENV from the
*  LAPACK routines:
*  1)  OPTS is a concatenation of all of the character options to
*      subroutine NAME, in the same order that they appear in the
*      argument list for NAME, even if they are not used in determining
*      the value of the parameter specified by ISPEC.
*  2)  The problem dimensions N1, N2, N3, N4 are specified in the order
*      that they appear in the argument list for NAME.  N1 is used
*      first, N2 second, and so on, and unused problem dimensions are
*      passed a value of -1.
*  3)  The parameter value returned by ILAENV is checked for validity in
*      the calling subroutine.  For example, ILAENV is used to retrieve
*      the optimal blocksize for STRTRI as follows:
*
*      NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
*      IF( NB.LE.1 ) NB = MAX( 1, N )
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            CNAME, SNAME
      CHARACTER*1        C1
      CHARACTER*2        C2, C4
      CHARACTER*3        C3
      CHARACTER*6        SUBNAM
      INTEGER            I, IC, IZ, NB, NBMIN, NX
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          CHAR, ICHAR, INT, MIN, REAL
*     ..
*     .. External Functions ..
      INTEGER            IEEECK
      EXTERNAL           IEEECK
*     ..
*     .. Executable Statements ..
*
      GO TO ( 100, 100, 100, 400, 500, 600, 700, 800, 900, 1000,
     $        1100 ) ISPEC
*
*     Invalid value for ISPEC
*
      ILAENV = -1
      RETURN
*
  100 CONTINUE
*
*     Convert NAME to upper case if the first character is lower case.
*
      ILAENV = 1
      SUBNAM = NAME
      IC = ICHAR( SUBNAM( 1:1 ) )
      IZ = ICHAR( 'Z' )
      IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN
*
*        ASCII character set
*
         IF( IC.GE.97 .AND. IC.LE.122 ) THEN
            SUBNAM( 1:1 ) = CHAR( IC-32 )
            DO 10 I = 2, 6
               IC = ICHAR( SUBNAM( I:I ) )
               IF( IC.GE.97 .AND. IC.LE.122 )
     $            SUBNAM( I:I ) = CHAR( IC-32 )
   10       CONTINUE
         END IF
*
      ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN
*
*        EBCDIC character set
*
         IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
     $       ( IC.GE.145 .AND. IC.LE.153 ) .OR.
     $       ( IC.GE.162 .AND. IC.LE.169 ) ) THEN
            SUBNAM( 1:1 ) = CHAR( IC+64 )
            DO 20 I = 2, 6
               IC = ICHAR( SUBNAM( I:I ) )
               IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR.
     $             ( IC.GE.145 .AND. IC.LE.153 ) .OR.
     $             ( IC.GE.162 .AND. IC.LE.169 ) )
     $            SUBNAM( I:I ) = CHAR( IC+64 )
   20       CONTINUE
         END IF
*
      ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN
*
*        Prime machines:  ASCII+128
*
         IF( IC.GE.225 .AND. IC.LE.250 ) THEN
            SUBNAM( 1:1 ) = CHAR( IC-32 )
            DO 30 I = 2, 6
               IC = ICHAR( SUBNAM( I:I ) )
               IF( IC.GE.225 .AND. IC.LE.250 )
     $            SUBNAM( I:I ) = CHAR( IC-32 )
   30       CONTINUE
         END IF
      END IF
*
      C1 = SUBNAM( 1:1 )
      SNAME = C1.EQ.'S' .OR. C1.EQ.'D'
      CNAME = C1.EQ.'C' .OR. C1.EQ.'Z'
      IF( .NOT.( CNAME .OR. SNAME ) )
     $   RETURN
      C2 = SUBNAM( 2:3 )
      C3 = SUBNAM( 4:6 )
      C4 = C3( 2:3 )
*
      GO TO ( 110, 200, 300 ) ISPEC
*
  110 CONTINUE
*
*     ISPEC = 1:  block size
*
*     In these examples, separate code is provided for setting NB for
*     real and complex.  We assume that NB will take the same value in
*     single or double precision.
*
      NB = 1
*
      IF( C2.EQ.'GE' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         ELSE IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR.
     $            C3.EQ.'QLF' ) THEN
            IF( SNAME ) THEN
               NB = 32
            ELSE
               NB = 32
            END IF
         ELSE IF( C3.EQ.'HRD' ) THEN
            IF( SNAME ) THEN
               NB = 32
            ELSE
               NB = 32
            END IF
         ELSE IF( C3.EQ.'BRD' ) THEN
            IF( SNAME ) THEN
               NB = 32
            ELSE
               NB = 32
            END IF
         ELSE IF( C3.EQ.'TRI' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         END IF
      ELSE IF( C2.EQ.'PO' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         END IF
      ELSE IF( C2.EQ.'SY' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN
            NB = 32
         ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN
            NB = 64
         END IF
      ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            NB = 64
         ELSE IF( C3.EQ.'TRD' ) THEN
            NB = 32
         ELSE IF( C3.EQ.'GST' ) THEN
            NB = 64
         END IF
      ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
         IF( C3( 1:1 ).EQ.'G' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NB = 32
            END IF
         ELSE IF( C3( 1:1 ).EQ.'M' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NB = 32
            END IF
         END IF
      ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
         IF( C3( 1:1 ).EQ.'G' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NB = 32
            END IF
         ELSE IF( C3( 1:1 ).EQ.'M' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NB = 32
            END IF
         END IF
      ELSE IF( C2.EQ.'GB' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( SNAME ) THEN
               IF( N4.LE.64 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            ELSE
               IF( N4.LE.64 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            END IF
         END IF
      ELSE IF( C2.EQ.'PB' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( SNAME ) THEN
               IF( N2.LE.64 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            ELSE
               IF( N2.LE.64 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            END IF
         END IF
      ELSE IF( C2.EQ.'TR' ) THEN
         IF( C3.EQ.'TRI' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         END IF
      ELSE IF( C2.EQ.'LA' ) THEN
         IF( C3.EQ.'UUM' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         END IF
      ELSE IF( SNAME .AND. C2.EQ.'ST' ) THEN
         IF( C3.EQ.'EBZ' ) THEN
            NB = 1
         END IF
      END IF
      ILAENV = NB
      RETURN
*
  200 CONTINUE
*
*     ISPEC = 2:  minimum block size
*
      NBMIN = 2
      IF( C2.EQ.'GE' ) THEN
         IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR.
     $       C3.EQ.'QLF' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
         ELSE IF( C3.EQ.'HRD' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
         ELSE IF( C3.EQ.'BRD' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
         ELSE IF( C3.EQ.'TRI' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
         END IF
      ELSE IF( C2.EQ.'SY' ) THEN
         IF( C3.EQ.'TRF' ) THEN
            IF( SNAME ) THEN
               NBMIN = 8
            ELSE
               NBMIN = 8
            END IF
         ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN
            NBMIN = 2
         END IF
      ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
         IF( C3.EQ.'TRD' ) THEN
            NBMIN = 2
         END IF
      ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
         IF( C3( 1:1 ).EQ.'G' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NBMIN = 2
            END IF
         ELSE IF( C3( 1:1 ).EQ.'M' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NBMIN = 2
            END IF
         END IF
      ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
         IF( C3( 1:1 ).EQ.'G' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NBMIN = 2
            END IF
         ELSE IF( C3( 1:1 ).EQ.'M' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NBMIN = 2
            END IF
         END IF
      END IF
      ILAENV = NBMIN
      RETURN
*
  300 CONTINUE
*
*     ISPEC = 3:  crossover point
*
      NX = 0
      IF( C2.EQ.'GE' ) THEN
         IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR.
     $       C3.EQ.'QLF' ) THEN
            IF( SNAME ) THEN
               NX = 128
            ELSE
               NX = 128
            END IF
         ELSE IF( C3.EQ.'HRD' ) THEN
            IF( SNAME ) THEN
               NX = 128
            ELSE
               NX = 128
            END IF
         ELSE IF( C3.EQ.'BRD' ) THEN
            IF( SNAME ) THEN
               NX = 128
            ELSE
               NX = 128
            END IF
         END IF
      ELSE IF( C2.EQ.'SY' ) THEN
         IF( SNAME .AND. C3.EQ.'TRD' ) THEN
            NX = 32
         END IF
      ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN
         IF( C3.EQ.'TRD' ) THEN
            NX = 32
         END IF
      ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN
         IF( C3( 1:1 ).EQ.'G' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NX = 128
            END IF
         END IF
      ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN
         IF( C3( 1:1 ).EQ.'G' ) THEN
            IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR.
     $          C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR.
     $          C4.EQ.'BR' ) THEN
               NX = 128
            END IF
         END IF
      END IF
      ILAENV = NX
      RETURN
*
  400 CONTINUE
*
*     ISPEC = 4:  number of shifts (used by xHSEQR)
*
      ILAENV = 6
      RETURN
*
  500 CONTINUE
*
*     ISPEC = 5:  minimum column dimension (not used)
*
      ILAENV = 2
      RETURN
*
  600 CONTINUE 
*
*     ISPEC = 6:  crossover point for SVD (used by xGELSS and xGESVD)
*
      ILAENV = INT( REAL( MIN( N1, N2 ) )*1.6E0 )
      RETURN
*
  700 CONTINUE
*
*     ISPEC = 7:  number of processors (not used)
*
      ILAENV = 1
      RETURN
*
  800 CONTINUE
*
*     ISPEC = 8:  crossover point for multishift (used by xHSEQR)
*
      ILAENV = 50
      RETURN
*
  900 CONTINUE
*
*     ISPEC = 9:  maximum size of the subproblems at the bottom of the
*                 computation tree in the divide-and-conquer algorithm
*                 (used by xGELSD and xGESDD)
*
      ILAENV = 25
      RETURN
*
 1000 CONTINUE
*
*     ISPEC = 10: ieee NaN arithmetic can be trusted not to trap
*
C     ILAENV = 0
      ILAENV = 1
      IF( ILAENV.EQ.1 ) THEN
         ILAENV = IEEECK( 0, 0.0, 1.0 ) 
      END IF
      RETURN
*
 1100 CONTINUE
*
*     ISPEC = 11: infinity arithmetic can be trusted not to trap
*
C     ILAENV = 0
      ILAENV = 1
      IF( ILAENV.EQ.1 ) THEN
         ILAENV = IEEECK( 1, 0.0, 1.0 ) 
      END IF
      RETURN
*
*     End of ILAENV
*
      END
      LOGICAL          FUNCTION LSAME( CA, CB )
*
*  -- LAPACK auxiliary routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     January 31, 1994
*
*     .. Scalar Arguments ..
      CHARACTER          CA, CB
*     ..
*
*  Purpose
*  =======
*
*  LSAME returns .TRUE. if CA is the same letter as CB regardless of
*  case.
*
*  Arguments
*  =========
*
*  CA      (input) CHARACTER*1
*  CB      (input) CHARACTER*1
*          CA and CB specify the single characters to be compared.
*
* =====================================================================
*
*     .. Intrinsic Functions ..
      INTRINSIC          ICHAR
*     ..
*     .. Local Scalars ..
      INTEGER            INTA, INTB, ZCODE
*     ..
*     .. Executable Statements ..
*
*     Test if the characters are equal
*
      LSAME = CA.EQ.CB
      IF( LSAME )
     $   RETURN
*
*     Now test for equivalence if both characters are alphabetic.
*
      ZCODE = ICHAR( 'Z' )
*
*     Use 'Z' rather than 'A' so that ASCII can be detected on Prime
*     machines, on which ICHAR returns a value with bit 8 set.
*     ICHAR('A') on Prime machines returns 193 which is the same as
*     ICHAR('A') on an EBCDIC machine.
*
      INTA = ICHAR( CA )
      INTB = ICHAR( CB )
*
      IF( ZCODE.EQ.90 .OR. ZCODE.EQ.122 ) THEN
*
*        ASCII is assumed - ZCODE is the ASCII code of either lower or
*        upper case 'Z'.
*
         IF( INTA.GE.97 .AND. INTA.LE.122 ) INTA = INTA - 32
         IF( INTB.GE.97 .AND. INTB.LE.122 ) INTB = INTB - 32
*
      ELSE IF( ZCODE.EQ.233 .OR. ZCODE.EQ.169 ) THEN
*
*        EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or
*        upper case 'Z'.
*
         IF( INTA.GE.129 .AND. INTA.LE.137 .OR.
     $       INTA.GE.145 .AND. INTA.LE.153 .OR.
     $       INTA.GE.162 .AND. INTA.LE.169 ) INTA = INTA + 64
         IF( INTB.GE.129 .AND. INTB.LE.137 .OR.
     $       INTB.GE.145 .AND. INTB.LE.153 .OR.
     $       INTB.GE.162 .AND. INTB.LE.169 ) INTB = INTB + 64
*
      ELSE IF( ZCODE.EQ.218 .OR. ZCODE.EQ.250 ) THEN
*
*        ASCII is assumed, on Prime machines - ZCODE is the ASCII code
*        plus 128 of either lower or upper case 'Z'.
*
         IF( INTA.GE.225 .AND. INTA.LE.250 ) INTA = INTA - 32
         IF( INTB.GE.225 .AND. INTB.LE.250 ) INTB = INTB - 32
      END IF
      LSAME = INTA.EQ.INTB
*
*     RETURN
*
*     End of LSAME
*
      END
      SUBROUTINE XERBLA( SRNAME, INFO )
*
*  -- LAPACK auxiliary routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     September 30, 1994
*
*     .. Scalar Arguments ..
      CHARACTER*6        SRNAME
      INTEGER            INFO
*     ..
*
*  Purpose
*  =======
*
*  XERBLA  is an error handler for the LAPACK routines.
*  It is called by an LAPACK routine if an input parameter has an
*  invalid value.  A message is printed and execution stops.
*
*  Installers may consider modifying the STOP statement in order to
*  call system-specific exception-handling facilities.
*
*  Arguments
*  =========
*
*  SRNAME  (input) CHARACTER*6
*          The name of the routine which called XERBLA.
*
*  INFO    (input) INTEGER
*          The position of the invalid parameter in the parameter list
*          of the calling routine.
*
* =====================================================================
*
*     .. Executable Statements ..
*
      WRITE( *, FMT = 9999 )SRNAME, INFO
*
      STOP
*
 9999 FORMAT( ' ** On entry to ', A6, ' parameter number ', I2, ' had ',
     $      'an illegal value' )
*
*     End of XERBLA
*
      END
SHAR_EOF
fi # end of overwriting check
if test -f 'res1'
then
	echo shar: will not over-write existing file "'res1'"
else
cat << "SHAR_EOF" > 'res1'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res1_1'
then
	echo shar: will not over-write existing file "'res1_1'"
else
cat << "SHAR_EOF" > 'res1_1'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res1_2'
then
	echo shar: will not over-write existing file "'res1_2'"
else
cat << "SHAR_EOF" > 'res1_2'



                           DNSPLIN1 Output



     Domain:  T(1) =  0.000D+00, T(N) =  0.600D+01
     Number of data points:  N =    7

     Number of grid points:  M =   241
     Mesh width:  H = 0.250000D-01

     # CG steps between restarts:  MAXCG =    3
     Line search tolerance:  FMTOL = 1.000D-06
     Convergence tolerance:  PHTOL = 1.000D-03
     Max number of iterations:  NGMAX =    200


               Iteration      1 (Steepest descent)
     Functional:                  phi(F) = 2.695861118877437D+00
     Mean absolute L2-gradient:    GNRM1 = 9.31D-02
     Max-norm of L2-gradient:      GNRMM = 1.73D+00

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 2.753D+01
                       Functional phi(Y) = 2.545851221875195D+00
          Relative change in phi(Y) DPHI =  4.06D-02
       Squared relative change in Y:  DY =  1.76D-04
         Cubed S-gradient rel. to Y:  DG =  1.12D-10
 _________________________________________________________________


               Iteration      2 (Conjugate gradient)
     Functional:                  phi(F) = 2.545851221875195D+00
     Mean absolute L2-gradient:    GNRM1 = 5.41D-02
     Max-norm of L2-gradient:      GNRMM = 7.98D-01

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 2.454D+01
                       Functional phi(Y) = 2.534168663474722D+00
          Relative change in phi(Y) DPHI =  3.29D-03
       Squared relative change in Y:  DY =  2.94D-06
         Cubed S-gradient rel. to Y:  DG =  1.07D-12
 _________________________________________________________________


               Iteration      3 (Conjugate gradient)
     Functional:                  phi(F) = 2.534168663474722D+00
     Mean absolute L2-gradient:    GNRM1 = 2.31D-02
     Max-norm of L2-gradient:      GNRMM = 3.97D-01

     Line search:     No. phi evals NPHV =  37
                     Optimal step-size S = 3.964D+01
                       Functional phi(Y) = 2.526798539947565D+00
          Relative change in phi(Y) DPHI =  2.09D-03
       Squared relative change in Y:  DY =  1.77D-05
         Cubed S-gradient rel. to Y:  DG =  9.68D-13
 _________________________________________________________________


               Iteration      4 (Conjugate gradient)
     Functional:                  phi(F) = 2.526798539947565D+00
     Mean absolute L2-gradient:    GNRM1 = 1.33D-02
     Max-norm of L2-gradient:      GNRMM = 1.71D-01

     Line search:     No. phi evals NPHV =  41
                     Optimal step-size S = 3.502D+01
                       Functional phi(Y) = 2.526225131925866D+00
          Relative change in phi(Y) DPHI =  1.63D-04
       Squared relative change in Y:  DY =  1.46D-06
         Cubed S-gradient rel. to Y:  DG =  3.59D-14
 _________________________________________________________________


     Number of descent iterations:      4

     Total number of phi evaluations in the line searches:     150

     Total polygonal curve length: 0.834D+01
SHAR_EOF
fi # end of overwriting check
if test -f 'res2'
then
	echo shar: will not over-write existing file "'res2'"
else
cat << "SHAR_EOF" > 'res2'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res2_1'
then
	echo shar: will not over-write existing file "'res2_1'"
else
cat << "SHAR_EOF" > 'res2_1'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res2_2'
then
	echo shar: will not over-write existing file "'res2_2'"
else
cat << "SHAR_EOF" > 'res2_2'



                           DNSPLIN1 Output



     Domain:  T(1) =  0.000D+00, T(N) =  0.150D+02
     Number of data points:  N =   11

     Number of grid points:  M =   241
     Mesh width:  H = 0.625000D-01

     # CG steps between restarts:  MAXCG =    3
     Line search tolerance:  FMTOL = 1.000D-06
     Convergence tolerance:  PHTOL = 1.000D-03
     Max number of iterations:  NGMAX =    200


               Iteration      1 (Steepest descent)
     Functional:                  phi(F) = 1.847022230448302D+01
     Mean absolute L2-gradient:    GNRM1 = 1.43D+00
     Max-norm of L2-gradient:      GNRMM = 4.04D+01

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 9.945D+00
                       Functional phi(Y) = 3.108584884343124D+00
          Relative change in phi(Y) DPHI =  7.89D-01
       Squared relative change in Y:  DY =  5.14D-03
         Cubed S-gradient rel. to Y:  DG =  3.74D-07
 _________________________________________________________________


               Iteration      2 (Conjugate gradient)
     Functional:                  phi(F) = 3.108584884343124D+00
     Mean absolute L2-gradient:    GNRM1 = 6.23D-01
     Max-norm of L2-gradient:      GNRMM = 1.18D+01

     Line search:     No. phi evals NPHV =  32
                     Optimal step-size S = 1.075D+01
                       Functional phi(Y) = 2.734542807953708D+00
          Relative change in phi(Y) DPHI =  9.10D-02
       Squared relative change in Y:  DY =  1.53D-04
         Cubed S-gradient rel. to Y:  DG =  1.76D-09
 _________________________________________________________________


               Iteration      3 (Conjugate gradient)
     Functional:                  phi(F) = 2.734542807953708D+00
     Mean absolute L2-gradient:    GNRM1 = 1.79D-01
     Max-norm of L2-gradient:      GNRMM = 2.19D+00

     Line search:     No. phi evals NPHV =  26
                     Optimal step-size S = 3.434D-01
                       Functional phi(Y) = 2.727705979535965D+00
          Relative change in phi(Y) DPHI =  1.83D-03
       Squared relative change in Y:  DY =  3.39D-06
         Cubed S-gradient rel. to Y:  DG =  2.69D-08
 _________________________________________________________________


               Iteration      4 (Conjugate gradient)
     Functional:                  phi(F) = 2.727705979535965D+00
     Mean absolute L2-gradient:    GNRM1 = 2.38D-01
     Max-norm of L2-gradient:      GNRMM = 3.05D+00

     Line search:     No. phi evals NPHV =  35
                     Optimal step-size S = 1.140D+01
                       Functional phi(Y) = 2.440207353380296D+00
          Relative change in phi(Y) DPHI =  7.71D-02
       Squared relative change in Y:  DY =  1.60D-03
         Cubed S-gradient rel. to Y:  DG =  3.23D-08
 _________________________________________________________________


               Iteration      5 (Steepest descent)
     Functional:                  phi(F) = 2.440207353380296D+00
     Mean absolute L2-gradient:    GNRM1 = 3.07D-01
     Max-norm of L2-gradient:      GNRMM = 4.93D+00

     Line search:     No. phi evals NPHV =  32
                     Optimal step-size S = 8.656D+00
                       Functional phi(Y) = 2.305872979351708D+00
          Relative change in phi(Y) DPHI =  3.90D-02
       Squared relative change in Y:  DY =  6.97D-05
         Cubed S-gradient rel. to Y:  DG =  8.96D-10
 _________________________________________________________________


               Iteration      6 (Conjugate gradient)
     Functional:                  phi(F) = 2.305872979351708D+00
     Mean absolute L2-gradient:    GNRM1 = 8.71D-02
     Max-norm of L2-gradient:      GNRMM = 3.01D+00

     Line search:     No. phi evals NPHV =  28
                     Optimal step-size S = 8.767D-01
                       Functional phi(Y) = 2.300097411948204D+00
          Relative change in phi(Y) DPHI =  1.75D-03
       Squared relative change in Y:  DY =  5.12D-06
         Cubed S-gradient rel. to Y:  DG =  7.79D-09
 _________________________________________________________________


               Iteration      7 (Conjugate gradient)
     Functional:                  phi(F) = 2.300097411948204D+00
     Mean absolute L2-gradient:    GNRM1 = 8.46D-02
     Max-norm of L2-gradient:      GNRMM = 2.50D+00

     Line search:     No. phi evals NPHV =  41
                     Optimal step-size S = 1.359D+01
                       Functional phi(Y) = 2.149679131926205D+00
          Relative change in phi(Y) DPHI =  4.56D-02
       Squared relative change in Y:  DY =  1.53D-03
         Cubed S-gradient rel. to Y:  DG =  1.14D-08
 _________________________________________________________________


               Iteration      8 (Conjugate gradient)
     Functional:                  phi(F) = 2.149679131926205D+00
     Mean absolute L2-gradient:    GNRM1 = 2.53D-01
     Max-norm of L2-gradient:      GNRMM = 3.91D+00

     Line search:     No. phi evals NPHV =  34
                     Optimal step-size S = 1.549D+01
                       Functional phi(Y) = 2.058102703980385D+00
          Relative change in phi(Y) DPHI =  2.91D-02
       Squared relative change in Y:  DY =  8.46D-05
         Cubed S-gradient rel. to Y:  DG =  1.78D-10
 _________________________________________________________________


               Iteration      9 (Steepest descent)
     Functional:                  phi(F) = 2.058102703980385D+00
     Mean absolute L2-gradient:    GNRM1 = 1.27D-01
     Max-norm of L2-gradient:      GNRMM = 1.96D+00

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 1.182D+01
                       Functional phi(Y) = 2.024316039436485D+00
          Relative change in phi(Y) DPHI =  1.10D-02
       Squared relative change in Y:  DY =  1.23D-04
         Cubed S-gradient rel. to Y:  DG =  8.28D-10
 _________________________________________________________________


               Iteration     10 (Conjugate gradient)
     Functional:                  phi(F) = 2.024316039436485D+00
     Mean absolute L2-gradient:    GNRM1 = 5.30D-02
     Max-norm of L2-gradient:      GNRMM = 1.17D+00

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 3.172D+01
                       Functional phi(Y) = 1.945852149825856D+00
          Relative change in phi(Y) DPHI =  2.59D-02
       Squared relative change in Y:  DY =  5.80D-04
         Cubed S-gradient rel. to Y:  DG =  1.16D-10
 _________________________________________________________________


               Iteration     11 (Conjugate gradient)
     Functional:                  phi(F) = 1.945852149825856D+00
     Mean absolute L2-gradient:    GNRM1 = 1.88D-01
     Max-norm of L2-gradient:      GNRMM = 2.07D+00

     Line search:     No. phi evals NPHV =  31
                     Optimal step-size S = 2.817D+00
                       Functional phi(Y) = 1.935709121934864D+00
          Relative change in phi(Y) DPHI =  3.44D-03
       Squared relative change in Y:  DY =  9.64D-05
         Cubed S-gradient rel. to Y:  DG =  1.01D-09
 _________________________________________________________________


               Iteration     12 (Conjugate gradient)
     Functional:                  phi(F) = 1.935709121934864D+00
     Mean absolute L2-gradient:    GNRM1 = 2.15D-01
     Max-norm of L2-gradient:      GNRMM = 3.31D+00

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 9.001D+00
                       Functional phi(Y) = 1.904346612904878D+00
          Relative change in phi(Y) DPHI =  1.07D-02
       Squared relative change in Y:  DY =  1.53D-05
         Cubed S-gradient rel. to Y:  DG =  5.07D-10
 _________________________________________________________________


               Iteration     13 (Steepest descent)
     Functional:                  phi(F) = 1.904346612904878D+00
     Mean absolute L2-gradient:    GNRM1 = 7.29D-02
     Max-norm of L2-gradient:      GNRMM = 1.70D+00

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 1.537D+01
                       Functional phi(Y) = 1.889710783473111D+00
          Relative change in phi(Y) DPHI =  5.04D-03
       Squared relative change in Y:  DY =  2.23D-05
         Cubed S-gradient rel. to Y:  DG =  2.90D-11
 _________________________________________________________________


               Iteration     14 (Conjugate gradient)
     Functional:                  phi(F) = 1.889710783473111D+00
     Mean absolute L2-gradient:    GNRM1 = 3.98D-02
     Max-norm of L2-gradient:      GNRMM = 1.05D+00

     Line search:     No. phi evals NPHV =  28
                     Optimal step-size S = 1.153D+00
                       Functional phi(Y) = 1.888299483028042D+00
          Relative change in phi(Y) DPHI =  4.88D-04
       Squared relative change in Y:  DY =  3.55D-06
         Cubed S-gradient rel. to Y:  DG =  4.35D-10
 _________________________________________________________________


     Number of descent iterations:     14

     Total number of phi evaluations in the line searches:     458

     Total polygonal curve length: 0.269D+02
SHAR_EOF
fi # end of overwriting check
if test -f 'res3'
then
	echo shar: will not over-write existing file "'res3'"
else
cat << "SHAR_EOF" > 'res3'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res3_1'
then
	echo shar: will not over-write existing file "'res3_1'"
else
cat << "SHAR_EOF" > 'res3_1'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res3_2'
then
	echo shar: will not over-write existing file "'res3_2'"
else
cat << "SHAR_EOF" > 'res3_2'



                           DNSPLIN1 Output



     Domain:  T(1) =  0.799D+01, T(N) =  0.200D+02
     Number of data points:  N =    9

     Number of grid points:  M =   241
     Mesh width:  H = 0.500000D-01

     # CG steps between restarts:  MAXCG =    3
     Line search tolerance:  FMTOL = 1.000D-06
     Convergence tolerance:  PHTOL = 1.000D-03
     Max number of iterations:  NGMAX =    200


               Iteration      1 (Steepest descent)
     Functional:                  phi(F) = 6.962522789884859D+01
     Mean absolute L2-gradient:    GNRM1 = 1.23D+01
     Max-norm of L2-gradient:      GNRMM = 2.79D+03

     Line search:     No. phi evals NPHV =  32
                     Optimal step-size S = 9.670D+00
                       Functional phi(Y) = 9.285783480988394D+00
          Relative change in phi(Y) DPHI =  8.54D-01
       Squared relative change in Y:  DY =  4.56D-03
         Cubed S-gradient rel. to Y:  DG =  3.40D-07
 _________________________________________________________________


               Iteration      2 (Conjugate gradient)
     Functional:                  phi(F) = 9.285783480988394D+00
     Mean absolute L2-gradient:    GNRM1 = 4.74D-01
     Max-norm of L2-gradient:      GNRMM = 6.97D+01

     Line search:     No. phi evals NPHV =  31
                     Optimal step-size S = 3.737D+00
                       Functional phi(Y) = 8.137932191760390D+00
          Relative change in phi(Y) DPHI =  1.12D-01
       Squared relative change in Y:  DY =  2.60D-05
         Cubed S-gradient rel. to Y:  DG =  1.46D-08
 _________________________________________________________________


               Iteration      3 (Conjugate gradient)
     Functional:                  phi(F) = 8.137932191760390D+00
     Mean absolute L2-gradient:    GNRM1 = 1.77D+00
     Max-norm of L2-gradient:      GNRMM = 3.51D+02

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 1.499D+01
                       Functional phi(Y) = 4.539893067805838D+00
          Relative change in phi(Y) DPHI =  3.94D-01
       Squared relative change in Y:  DY =  1.07D-03
         Cubed S-gradient rel. to Y:  DG =  1.16D-08
 _________________________________________________________________


               Iteration      4 (Conjugate gradient)
     Functional:                  phi(F) = 4.539893067805838D+00
     Mean absolute L2-gradient:    GNRM1 = 8.26D-01
     Max-norm of L2-gradient:      GNRMM = 1.47D+02

     Line search:     No. phi evals NPHV =  35
                     Optimal step-size S = 1.707D+01
                       Functional phi(Y) = 3.045988277936966D+00
          Relative change in phi(Y) DPHI =  2.70D-01
       Squared relative change in Y:  DY =  2.07D-04
         Cubed S-gradient rel. to Y:  DG =  7.61D-10
 _________________________________________________________________


               Iteration      5 (Steepest descent)
     Functional:                  phi(F) = 3.045988277936966D+00
     Mean absolute L2-gradient:    GNRM1 = 6.68D-01
     Max-norm of L2-gradient:      GNRMM = 1.33D+02

     Line search:     No. phi evals NPHV =  34
                     Optimal step-size S = 1.036D+01
                       Functional phi(Y) = 2.779376523757108D+00
          Relative change in phi(Y) DPHI =  6.59D-02
       Squared relative change in Y:  DY =  9.05D-05
         Cubed S-gradient rel. to Y:  DG =  7.76D-10
 _________________________________________________________________


               Iteration      6 (Conjugate gradient)
     Functional:                  phi(F) = 2.779376523757108D+00
     Mean absolute L2-gradient:    GNRM1 = 7.64D-02
     Max-norm of L2-gradient:      GNRMM = 4.13D+00

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 8.066D+00
                       Functional phi(Y) = 2.762935338981907D+00
          Relative change in phi(Y) DPHI =  4.35D-03
       Squared relative change in Y:  DY =  1.47D-05
         Cubed S-gradient rel. to Y:  DG =  2.69D-10
 _________________________________________________________________


               Iteration      7 (Conjugate gradient)
     Functional:                  phi(F) = 2.762935338981907D+00
     Mean absolute L2-gradient:    GNRM1 = 2.30D-01
     Max-norm of L2-gradient:      GNRMM = 4.16D+01

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 2.264D+01
                       Functional phi(Y) = 2.666259732184198D+00
          Relative change in phi(Y) DPHI =  2.57D-02
       Squared relative change in Y:  DY =  6.68D-04
         Cubed S-gradient rel. to Y:  DG =  5.27D-10
 _________________________________________________________________


               Iteration      8 (Conjugate gradient)
     Functional:                  phi(F) = 2.666259732184198D+00
     Mean absolute L2-gradient:    GNRM1 = 1.49D-01
     Max-norm of L2-gradient:      GNRMM = 2.25D+01

     Line search:     No. phi evals NPHV =  35
                     Optimal step-size S = 1.594D+01
                       Functional phi(Y) = 2.639868745953409D+00
          Relative change in phi(Y) DPHI =  7.20D-03
       Squared relative change in Y:  DY =  7.77D-05
         Cubed S-gradient rel. to Y:  DG =  6.09D-11
 _________________________________________________________________


               Iteration      9 (Steepest descent)
     Functional:                  phi(F) = 2.639868745953409D+00
     Mean absolute L2-gradient:    GNRM1 = 1.09D-01
     Max-norm of L2-gradient:      GNRMM = 1.50D+01

     Line search:     No. phi evals NPHV =  37
                     Optimal step-size S = 2.124D+01
                       Functional phi(Y) = 2.626303197085885D+00
          Relative change in phi(Y) DPHI =  3.73D-03
       Squared relative change in Y:  DY =  6.13D-05
         Cubed S-gradient rel. to Y:  DG =  5.01D-11
 _________________________________________________________________


               Iteration     10 (Conjugate gradient)
     Functional:                  phi(F) = 2.626303197085885D+00
     Mean absolute L2-gradient:    GNRM1 = 9.32D-02
     Max-norm of L2-gradient:      GNRMM = 1.66D+01

     Line search:     No. phi evals NPHV =  39
                     Optimal step-size S = 3.616D+01
                       Functional phi(Y) = 2.603300113231649D+00
          Relative change in phi(Y) DPHI =  6.34D-03
       Squared relative change in Y:  DY =  2.61D-04
         Cubed S-gradient rel. to Y:  DG =  2.02D-11
 _________________________________________________________________


               Iteration     11 (Conjugate gradient)
     Functional:                  phi(F) = 2.603300113231649D+00
     Mean absolute L2-gradient:    GNRM1 = 1.08D-01
     Max-norm of L2-gradient:      GNRMM = 1.75D+01

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 8.393D+00
                       Functional phi(Y) = 2.596794197414559D+00
          Relative change in phi(Y) DPHI =  1.81D-03
       Squared relative change in Y:  DY =  1.44D-04
         Cubed S-gradient rel. to Y:  DG =  4.93D-11
 _________________________________________________________________


               Iteration     12 (Conjugate gradient)
     Functional:                  phi(F) = 2.596794197414559D+00
     Mean absolute L2-gradient:    GNRM1 = 1.45D-01
     Max-norm of L2-gradient:      GNRMM = 2.17D+01

     Line search:     No. phi evals NPHV =  35
                     Optimal step-size S = 1.191D+01
                       Functional phi(Y) = 2.586424242456628D+00
          Relative change in phi(Y) DPHI =  2.88D-03
       Squared relative change in Y:  DY =  3.55D-06
         Cubed S-gradient rel. to Y:  DG =  1.95D-11
 _________________________________________________________________


               Iteration     13 (Steepest descent)
     Functional:                  phi(F) = 2.586424242456628D+00
     Mean absolute L2-gradient:    GNRM1 = 4.88D-02
     Max-norm of L2-gradient:      GNRMM = 4.51D+00

     Line search:     No. phi evals NPHV =  38
                     Optimal step-size S = 3.938D+01
                       Functional phi(Y) = 2.579400085251667D+00
          Relative change in phi(Y) DPHI =  1.96D-03
       Squared relative change in Y:  DY =  5.51D-05
         Cubed S-gradient rel. to Y:  DG =  6.70D-12
 _________________________________________________________________


               Iteration     14 (Conjugate gradient)
     Functional:                  phi(F) = 2.579400085251667D+00
     Mean absolute L2-gradient:    GNRM1 = 7.30D-02
     Max-norm of L2-gradient:      GNRMM = 1.30D+01

     Line search:     No. phi evals NPHV =  38
                     Optimal step-size S = 9.520D+00
                       Functional phi(Y) = 2.575430230011021D+00
          Relative change in phi(Y) DPHI =  1.11D-03
       Squared relative change in Y:  DY =  1.08D-04
         Cubed S-gradient rel. to Y:  DG =  1.82D-11
 _________________________________________________________________


               Iteration     15 (Conjugate gradient)
     Functional:                  phi(F) = 2.575430230011021D+00
     Mean absolute L2-gradient:    GNRM1 = 1.34D-01
     Max-norm of L2-gradient:      GNRMM = 1.94D+01

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 1.442D+01
                       Functional phi(Y) = 2.564267530101878D+00
          Relative change in phi(Y) DPHI =  3.12D-03
       Squared relative change in Y:  DY =  6.05D-05
         Cubed S-gradient rel. to Y:  DG =  1.49D-11
 _________________________________________________________________


               Iteration     16 (Conjugate gradient)
     Functional:                  phi(F) = 2.564267530101878D+00
     Mean absolute L2-gradient:    GNRM1 = 6.52D-02
     Max-norm of L2-gradient:      GNRMM = 5.73D+00

     Line search:     No. phi evals NPHV =  40
                     Optimal step-size S = 4.147D+01
                       Functional phi(Y) = 2.555298148712444D+00
          Relative change in phi(Y) DPHI =  2.52D-03
       Squared relative change in Y:  DY =  1.59D-04
         Cubed S-gradient rel. to Y:  DG =  1.43D-12
 _________________________________________________________________


               Iteration     17 (Steepest descent)
     Functional:                  phi(F) = 2.555298148712444D+00
     Mean absolute L2-gradient:    GNRM1 = 7.87D-02
     Max-norm of L2-gradient:      GNRMM = 8.89D+00

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 1.820D+01
                       Functional phi(Y) = 2.551693290633654D+00
          Relative change in phi(Y) DPHI =  1.01D-03
       Squared relative change in Y:  DY =  4.82D-06
         Cubed S-gradient rel. to Y:  DG =  1.76D-12
 _________________________________________________________________


               Iteration     18 (Conjugate gradient)
     Functional:                  phi(F) = 2.551693290633654D+00
     Mean absolute L2-gradient:    GNRM1 = 4.82D-02
     Max-norm of L2-gradient:      GNRMM = 7.16D+00

     Line search:     No. phi evals NPHV =  38
                     Optimal step-size S = 2.077D+01
                       Functional phi(Y) = 2.549515142933999D+00
          Relative change in phi(Y) DPHI =  6.13D-04
       Squared relative change in Y:  DY =  2.59D-05
         Cubed S-gradient rel. to Y:  DG =  2.33D-12
 _________________________________________________________________


     Number of descent iterations:     18

     Total number of phi evaluations in the line searches:     642

     Total polygonal curve length: 0.200D+02
SHAR_EOF
fi # end of overwriting check
if test -f 'res4'
then
	echo shar: will not over-write existing file "'res4'"
else
cat << "SHAR_EOF" > 'res4'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res4_1'
then
	echo shar: will not over-write existing file "'res4_1'"
else
cat << "SHAR_EOF" > 'res4_1'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res4_2'
then
	echo shar: will not over-write existing file "'res4_2'"
else
cat << "SHAR_EOF" > 'res4_2'



                           DNSPLIN1 Output



     Domain:  T(1) =  0.000D+00, T(N) =  0.100D+02
     Number of data points:  N =   10

     Number of grid points:  M =   251
     Mesh width:  H = 0.400000D-01

     # CG steps between restarts:  MAXCG =    3
     Line search tolerance:  FMTOL = 1.000D-06
     Convergence tolerance:  PHTOL = 1.000D-03
     Max number of iterations:  NGMAX =    200


               Iteration      1 (Steepest descent)
     Functional:                  phi(F) = 1.204285303543998D+01
     Mean absolute L2-gradient:    GNRM1 = 8.93D-01
     Max-norm of L2-gradient:      GNRMM = 2.11D+01

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 1.525D+01
                       Functional phi(Y) = 4.210114047965495D+00
          Relative change in phi(Y) DPHI =  6.01D-01
       Squared relative change in Y:  DY =  1.85D-03
         Cubed S-gradient rel. to Y:  DG =  2.25D-08
 _________________________________________________________________


               Iteration      2 (Conjugate gradient)
     Functional:                  phi(F) = 4.210114047965495D+00
     Mean absolute L2-gradient:    GNRM1 = 4.80D-01
     Max-norm of L2-gradient:      GNRMM = 1.21D+01

     Line search:     No. phi evals NPHV =  35
                     Optimal step-size S = 2.276D+01
                       Functional phi(Y) = 3.616846786346256D+00
          Relative change in phi(Y) DPHI =  1.14D-01
       Squared relative change in Y:  DY =  4.18D-04
         Cubed S-gradient rel. to Y:  DG =  8.84D-10
 _________________________________________________________________


               Iteration      3 (Conjugate gradient)
     Functional:                  phi(F) = 3.616846786346256D+00
     Mean absolute L2-gradient:    GNRM1 = 3.60D-01
     Max-norm of L2-gradient:      GNRMM = 1.01D+01

     Line search:     No. phi evals NPHV =  35
                     Optimal step-size S = 2.140D+01
                       Functional phi(Y) = 3.378654389247692D+00
          Relative change in phi(Y) DPHI =  5.16D-02
       Squared relative change in Y:  DY =  2.32D-04
         Cubed S-gradient rel. to Y:  DG =  3.30D-10
 _________________________________________________________________


               Iteration      4 (Conjugate gradient)
     Functional:                  phi(F) = 3.378654389247692D+00
     Mean absolute L2-gradient:    GNRM1 = 2.51D-01
     Max-norm of L2-gradient:      GNRMM = 8.09D+00

     Line search:     No. phi evals NPHV =  35
                     Optimal step-size S = 2.526D+01
                       Functional phi(Y) = 3.254592507777017D+00
          Relative change in phi(Y) DPHI =  2.83D-02
       Squared relative change in Y:  DY =  8.05D-05
         Cubed S-gradient rel. to Y:  DG =  3.54D-11
 _________________________________________________________________


               Iteration      5 (Steepest descent)
     Functional:                  phi(F) = 3.254592507777017D+00
     Mean absolute L2-gradient:    GNRM1 = 2.09D-01
     Max-norm of L2-gradient:      GNRMM = 7.18D+00

     Line search:     No. phi evals NPHV =  32
                     Optimal step-size S = 2.019D+01
                       Functional phi(Y) = 3.182797745867247D+00
          Relative change in phi(Y) DPHI =  1.69D-02
       Squared relative change in Y:  DY =  7.66D-05
         Cubed S-gradient rel. to Y:  DG =  8.13D-11
 _________________________________________________________________


               Iteration      6 (Conjugate gradient)
     Functional:                  phi(F) = 3.182797745867247D+00
     Mean absolute L2-gradient:    GNRM1 = 1.33D-01
     Max-norm of L2-gradient:      GNRMM = 5.08D+00

     Line search:     No. phi evals NPHV =  40
                     Optimal step-size S = 2.636D+01
                       Functional phi(Y) = 3.128928284031733D+00
          Relative change in phi(Y) DPHI =  1.29D-02
       Squared relative change in Y:  DY =  3.26D-05
         Cubed S-gradient rel. to Y:  DG =  9.64D-12
 _________________________________________________________________


               Iteration      7 (Conjugate gradient)
     Functional:                  phi(F) = 3.128928284031733D+00
     Mean absolute L2-gradient:    GNRM1 = 1.32D-01
     Max-norm of L2-gradient:      GNRMM = 5.58D+00

     Line search:     No. phi evals NPHV =  36
                     Optimal step-size S = 1.392D+01
                       Functional phi(Y) = 3.095857069635267D+00
          Relative change in phi(Y) DPHI =  8.01D-03
       Squared relative change in Y:  DY =  9.83D-05
         Cubed S-gradient rel. to Y:  DG =  3.52D-11
 _________________________________________________________________


               Iteration      8 (Conjugate gradient)
     Functional:                  phi(F) = 3.095857069635267D+00
     Mean absolute L2-gradient:    GNRM1 = 2.32D-01
     Max-norm of L2-gradient:      GNRMM = 8.85D+00

     Line search:     No. phi evals NPHV =  34
                     Optimal step-size S = 1.474D+01
                       Functional phi(Y) = 3.042483566893213D+00
          Relative change in phi(Y) DPHI =  1.30D-02
       Squared relative change in Y:  DY =  1.91D-05
         Cubed S-gradient rel. to Y:  DG =  1.84D-11
 _________________________________________________________________


               Iteration      9 (Steepest descent)
     Functional:                  phi(F) = 3.042483566893213D+00
     Mean absolute L2-gradient:    GNRM1 = 7.36D-02
     Max-norm of L2-gradient:      GNRMM = 2.00D+00

     Line search:     No. phi evals NPHV =  38
                     Optimal step-size S = 5.026D+01
                       Functional phi(Y) = 3.012634184165759D+00
          Relative change in phi(Y) DPHI =  7.38D-03
       Squared relative change in Y:  DY =  2.96D-05
         Cubed S-gradient rel. to Y:  DG =  1.27D-12
 _________________________________________________________________


               Iteration     10 (Conjugate gradient)
     Functional:                  phi(F) = 3.012634184165759D+00
     Mean absolute L2-gradient:    GNRM1 = 1.34D-01
     Max-norm of L2-gradient:      GNRMM = 5.58D+00

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 5.515D+00
                       Functional phi(Y) = 3.004014685340456D+00
          Relative change in phi(Y) DPHI =  2.15D-03
       Squared relative change in Y:  DY =  2.25D-05
         Cubed S-gradient rel. to Y:  DG =  1.35D-11
 _________________________________________________________________


               Iteration     11 (Conjugate gradient)
     Functional:                  phi(F) = 3.004014685340456D+00
     Mean absolute L2-gradient:    GNRM1 = 2.02D-01
     Max-norm of L2-gradient:      GNRMM = 7.62D+00

     Line search:     No. phi evals NPHV =  34
                     Optimal step-size S = 1.666D+01
                       Functional phi(Y) = 2.962390005206303D+00
          Relative change in phi(Y) DPHI =  1.04D-02
       Squared relative change in Y:  DY =  6.47D-05
         Cubed S-gradient rel. to Y:  DG =  1.79D-11
 _________________________________________________________________


               Iteration     12 (Conjugate gradient)
     Functional:                  phi(F) = 2.962390005206303D+00
     Mean absolute L2-gradient:    GNRM1 = 1.04D-01
     Max-norm of L2-gradient:      GNRMM = 4.11D+00

     Line search:     No. phi evals NPHV =  37
                     Optimal step-size S = 3.052D+01
                       Functional phi(Y) = 2.949053121332670D+00
          Relative change in phi(Y) DPHI =  3.37D-03
       Squared relative change in Y:  DY =  2.35D-06
         Cubed S-gradient rel. to Y:  DG =  4.38D-13
 _________________________________________________________________


               Iteration     13 (Steepest descent)
     Functional:                  phi(F) = 2.949053121332670D+00
     Mean absolute L2-gradient:    GNRM1 = 8.56D-02
     Max-norm of L2-gradient:      GNRMM = 2.91D+00

     Line search:     No. phi evals NPHV =  37
                     Optimal step-size S = 2.008D+01
                       Functional phi(Y) = 2.940464310249708D+00
          Relative change in phi(Y) DPHI =  2.17D-03
       Squared relative change in Y:  DY =  5.51D-06
         Cubed S-gradient rel. to Y:  DG =  1.60D-12
 _________________________________________________________________


               Iteration     14 (Conjugate gradient)
     Functional:                  phi(F) = 2.940464310249708D+00
     Mean absolute L2-gradient:    GNRM1 = 5.35D-02
     Max-norm of L2-gradient:      GNRMM = 1.92D+00

     Line search:     No. phi evals NPHV =  38
                     Optimal step-size S = 5.226D+01
                       Functional phi(Y) = 2.926268282662580D+00
          Relative change in phi(Y) DPHI =  3.60D-03
       Squared relative change in Y:  DY =  1.70D-05
         Cubed S-gradient rel. to Y:  DG =  2.10D-13
 _________________________________________________________________


               Iteration     15 (Conjugate gradient)
     Functional:                  phi(F) = 2.926268282662580D+00
     Mean absolute L2-gradient:    GNRM1 = 8.96D-02
     Max-norm of L2-gradient:      GNRMM = 4.14D+00

     Line search:     No. phi evals NPHV =  34
                     Optimal step-size S = 4.680D+00
                       Functional phi(Y) = 2.923118283615815D+00
          Relative change in phi(Y) DPHI =  8.02D-04
       Squared relative change in Y:  DY =  1.08D-05
         Cubed S-gradient rel. to Y:  DG =  2.98D-12
 _________________________________________________________________


     Number of descent iterations:     15

     Total number of phi evaluations in the line searches:     531

     Total polygonal curve length: 0.174D+02
SHAR_EOF
fi # end of overwriting check
if test -f 'res5'
then
	echo shar: will not over-write existing file "'res5'"
else
cat << "SHAR_EOF" > 'res5'
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SHAR_EOF
fi # end of overwriting check
if test -f 'res5_1'
then
	echo shar: will not over-write existing file "'res5_1'"
else
cat << "SHAR_EOF" > 'res5_1'
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 0.960246296887977D+02
 0.121629379078225D+03
 0.134253645583355D+03
 0.135526935342852D+03
 0.127813908213224D+03
 0.954918231392248D+02
 0.728739815384002D+02
 0.568510168187687D+02
 0.451958937452025D+02
 0.365217328939967D+02
 0.299339592752662D+02
 0.248380488675846D+02
 0.208286948482272D+02
 0.176234796618732D+02
 0.150218459641369D+02
 0.128789658929967D+02
 0.110886685909008D+02
 0.957203534770936D+01
 0.826963225851896D+01
 0.713613002534860D+01
 0.613652074106692D+01
 0.524342068586227D+01
 0.443512189607712D+01
 0.369416587943849D+01
 0.300628471143743D+01
 0.235960222723657D+01
 0.174401980672628D+01
 0.115073270409802D+01
 0.571837378495746D+00
 0.000000000000000D+00
SHAR_EOF
fi # end of overwriting check
if test -f 'res5_2'
then
	echo shar: will not over-write existing file "'res5_2'"
else
cat << "SHAR_EOF" > 'res5_2'



                           DNSPLIN1 Output



     Domain:  T(1) =  0.000D+00, T(N) =  0.100D+01
     Number of data points:  N =   11

     Number of grid points:  M =   251
     Mesh width:  H = 0.400000D-02

     # CG steps between restarts:  MAXCG =    3
     Line search tolerance:  FMTOL = 1.000D-06
     Convergence tolerance:  PHTOL = 1.000D-03
     Max number of iterations:  NGMAX =    200


               Iteration      1 (Steepest descent)
     Functional:                  phi(F) = 3.226669631958785D+02
     Mean absolute L2-gradient:    GNRM1 = 3.63D+02
     Max-norm of L2-gradient:      GNRMM = 2.45D+04

     Line search:     No. phi evals NPHV =  42
                     Optimal step-size S = 1.453D+02
                       Functional phi(Y) = 1.142444537470714D+02
          Relative change in phi(Y) DPHI =  6.44D-01
       Squared relative change in Y:  DY =  1.61D-03
         Cubed S-gradient rel. to Y:  DG =  2.11D-11
 _________________________________________________________________


               Iteration      2 (Conjugate gradient)
     Functional:                  phi(F) = 1.142444537470714D+02
     Mean absolute L2-gradient:    GNRM1 = 1.34D+02
     Max-norm of L2-gradient:      GNRMM = 4.24D+03

     Line search:     No. phi evals NPHV =  40
                     Optimal step-size S = 3.446D+01
                       Functional phi(Y) = 1.103124983940659D+02
          Relative change in phi(Y) DPHI =  3.41D-02
       Squared relative change in Y:  DY =  5.97D-05
         Cubed S-gradient rel. to Y:  DG =  1.40D-11
 _________________________________________________________________


               Iteration      3 (Conjugate gradient)
     Functional:                  phi(F) = 1.103124983940659D+02
     Mean absolute L2-gradient:    GNRM1 = 1.51D+02
     Max-norm of L2-gradient:      GNRMM = 4.05D+03

     Line search:     No. phi evals NPHV =  38
                     Optimal step-size S = 1.064D+02
                       Functional phi(Y) = 9.275145093428233D+01
          Relative change in phi(Y) DPHI =  1.58D-01
       Squared relative change in Y:  DY =  1.85D-03
         Cubed S-gradient rel. to Y:  DG =  3.65D-11
 _________________________________________________________________


               Iteration      4 (Conjugate gradient)
     Functional:                  phi(F) = 9.275145093428233D+01
     Mean absolute L2-gradient:    GNRM1 = 9.03D+01
     Max-norm of L2-gradient:      GNRMM = 1.17D+03

     Line search:     No. phi evals NPHV =  40
                     Optimal step-size S = 1.103D+02
                       Functional phi(Y) = 8.543327504399396D+01
          Relative change in phi(Y) DPHI =  7.81D-02
       Squared relative change in Y:  DY =  1.75D-05
         Cubed S-gradient rel. to Y:  DG =  1.04D-12
 _________________________________________________________________


               Iteration      5 (Steepest descent)
     Functional:                  phi(F) = 8.543327504399396D+01
     Mean absolute L2-gradient:    GNRM1 = 3.89D+01
     Max-norm of L2-gradient:      GNRMM = 7.52D+02

     Line search:     No. phi evals NPHV =  43
                     Optimal step-size S = 2.857D+02
                       Functional phi(Y) = 7.491685718459338D+01
          Relative change in phi(Y) DPHI =  1.22D-01
       Squared relative change in Y:  DY =  1.93D-03
         Cubed S-gradient rel. to Y:  DG =  3.63D-12
 _________________________________________________________________


               Iteration      6 (Conjugate gradient)
     Functional:                  phi(F) = 7.491685718459338D+01
     Mean absolute L2-gradient:    GNRM1 = 4.62D+01
     Max-norm of L2-gradient:      GNRMM = 9.69D+02

     Line search:     No. phi evals NPHV =  44
                     Optimal step-size S = 1.972D+02
                       Functional phi(Y) = 7.144463993956479D+01
          Relative change in phi(Y) DPHI =  4.57D-02
       Squared relative change in Y:  DY =  4.08D-05
         Cubed S-gradient rel. to Y:  DG =  3.28D-14
 _________________________________________________________________


               Iteration      7 (Conjugate gradient)
     Functional:                  phi(F) = 7.144463993956479D+01
     Mean absolute L2-gradient:    GNRM1 = 2.58D+01
     Max-norm of L2-gradient:      GNRMM = 5.39D+02

     Line search:     No. phi evals NPHV =  33
                     Optimal step-size S = 4.411D+00
                       Functional phi(Y) = 7.139845536224045D+01
          Relative change in phi(Y) DPHI =  6.38D-04
       Squared relative change in Y:  DY =  8.90D-07
         Cubed S-gradient rel. to Y:  DG =  1.31D-12
 _________________________________________________________________


     Number of descent iterations:      7

     Total number of phi evaluations in the line searches:     280

     Total polygonal curve length: 0.264D+01
SHAR_EOF
fi # end of overwriting check
cd ..
if test ! -d 'Src'
then
	mkdir 'Src'
fi
cd 'Src'
if test -f 'src.f'
then
	echo shar: will not over-write existing file "'src.f'"
else
cat << "SHAR_EOF" > 'src.f'
C
C      DNSPLIN1:  Discrete Nonlinear Spline Interpolation
C
C                         02/18/03
C
C
C   Given a sequence of n data ordinates D1, D2, ..., Dn
C associated with strictly increasing abscissae T1, T2, ...,
C Tn, n >= 2, this program constructs a discrete approxima-
C tion to a nonlinear interpolating spline function y:  the
C graph of y is a continuous curve with continuous tangent
C and piecewise continuous curvature (with discontinuities
C allowed only at the knots (Ti,Di)) such that y(Tj) = Dj
C and y is a local minimum of the functional
C
C       E(y) = I[ K**2 ds],
C
C where I[_] is the integral with respect to arc length s,
C and K(s) denotes signed curvature.  The natural boundary
C conditions associated with minimizing E over nonlinear
C interpolating splines imply continuous curvature at the
C interior knots, K = 0 at the endpoints, and the Euler
C equation
C
C       K''(s) + 0.5*K**3 = 0
C
C is satisfied in each open interval (Ti,Ti+1).
C
C   The spline curve y models a thin beam (elastica) of
C homogeneous material and uniform cross sectional area
C with frictionlessly rotating sliders at the knots.  E(y)
C is proportional to the elastic strain energy.
C
C Reference:  Michael A. Malcolm, "On the computation of
C             nonlinear spline functions", SIAM J. Numerical
C             Analysis, Vol. 14, No. 2, April 1977.
C
C
C DISCRETIZATION:
C
C   Using K(t) = y''(t)/[1+y'(t)**2]**(3/2) and s'(t) =
C [1+y'(t)**2]**(1/2), we obtain
C
C       E(y) = I[ y''(t)**2/[1+y'(t)**2]**(5/2) dt],
C
C where I[_] denotes the integral from T1 to Tn.  The domain
C [T1,Tn] is uniformly partitioned with constant mesh width
C H, resulting in m grid points T1+(i-1)*H, i = 1,...,m with
C corresponding function values y(i) = y(T1+(i-1)*H).  The
C data points are perturbed if necessary so that, for j = 1,
C ...,n, Tj = T1+(i-1)*H for some integer i = IND(j), and
C y(i) = y(IND(j)) = y(Tj) = Dj.
C
C   We use central difference approximations to derivatives,
C and approximate the integral by the composite trapezoidal
C rule to obtain the discretized functional
C
C       phi(y) = H*Sum[ D2y(i)*a(i) ],
C
C where
C
C       D1y(i) = (y(i+1)-y(i-1))/(2*H),
C
C       D2y(i) = (y(i+1)-2*y(i)+y(i-1))/H**2,
C
C       a(i) = D2y(i)/[1+D1y(i)**2]**(5/2),
C
C and Sum[_] denotes the sum over i = 2 to m-1.
C
C   Denote by S0 the set of m-vectors h such that h(i) = 0
C if i = IND(j) for j = 1 to n.  This is the space of
C perturbations for y, chosen to preserve the interpolation
C conditions provided the initial estimate of y satisfies
C the conditions.  Let P0 denote the orthogonal projection
C onto S0.  P0 is applied by simply zeroing the appropriate
C components.
C
C The components of the gradient are
C
C grad(phi)(i) = (2/H)*[a(i-1)-2*a(i)+a(i+1)-b(i-1)+b(i+1)],
C
C where
C
C       b(i) = (5/4)*H*D1y(i)*D2y(i)*a(i)/[1+D1y(i)**2],
C
C for i = 2 to m-1.  grad(phi)(1) = grad(phi)(m) = 0 since
C the endpoint values y(1) and y(m) are fixed by the inter-
C polation conditions.  The gradient is projected onto S0 by
C zeroing the appropriate components.
C
C
C METHOD:
C
C   The functional phi is minimized subject to the interpo-
C lation constraints by the Polak-Ribiere nonlinear conjugate
C gradient method using the Sobolev gradient defined below.
C
C   The Sobolev inner product associated with a curve (the
C current approximation to the solution) y is
C
C       <g,h>_y = I[ g''(s)*h''(s) ds ],
C
C where s(t) is the arc length associated with y, and
C
C       g'(s) = g'(t)/(1+y'(t)**2)**(1/2),
C
C       g''(s) = [ (1+y'(t)**2)*g''(t) -
C                  y'(t)*y''(t)*g'(t) ]/(1+y'(t)**2)**2.
C
C Note that <g,h>_y is positive (defines an inner product)
C on functions with two or more zeros (and square integrable
C second derivatives).  The discretized inner product
C on S0 is
C
C       <g,h>_y = Sum[ Dg(i)*Dh(i) ],
C
C where the sum is over i = 2 to m-1, and Dg is the dis-
C cretization of
C
C       g''(s)*Sqrt(s') = [s'(t)*g''(t)-s''(t)*g'(t)]/
C                         [s'(t)**(5/2)]
C
C              = [ [1+y'(t)**2]*g''(t)-y'(t)*y''(t)*g'(t) ]/
C                [ [1+y'(t)**2]**(7/4) ].
C
C Denote the discretized L2 inner product by
C
C       <r,s>_(m-2) = Sum[ r(i)*s(i) ].
C
C with the sum over i = 2 to m-1.
C
C   Then <g,h>_y = <Dg,Dh>_(m-2) = <D**T*Dg,h>_m =
C <D**T*Dg,P0*h>_m = <P0*D**T*Dg,h>_S0, where P0 is the
C orthogonal projection onto S0 (and the adjoint of D is
C P0*D**T).  Now let g be the Sobolev gradient (S-gradient)
C of phi at y.  Then by the Rietz Representation Theorem,
C
C       phi'(y)h = <grad(phi),h>_S0 = <g,h>_y
C                = <P0*D**T*Dg,h>_S0
C
C for all h in S0, so that the Sobolev gradient g is defined
C by
C
C       DTD*g = grad(phi),
C
C where DTD is the restriction of P0*D**T*D to S0.
C
C   Note that D**T*D is a pentadiagonal symmetric positive
C semi-definite matrix of order m, but we implicitly omit
C the rows and columns associated with constraints (zeros in
C grad(phi)) to obtain a positive definite matrix of order
C m-n.  More precisely, we omit the first and last rows and
C columns, and treat the other constraints by zeroing the
C row and column elements other than the diagonal (which is
C retained in order to preserve the scaling and condition
C number).  The resulting order-(m-2) system is solved by a
C direct method (using a U**T*U factorization for upper
C triangular matrix U).  DTD may be thought of as a precon-
C ditioner for the standard gradient.
C
C
C REQUIRED LIBRARY:
C
C   This program must be linked with a library providing the
C LAPACK subroutine DPBSV and the double precision BLAS.
      SUBROUTINE CSPLIN (LDA,N,T,D, ABD, S,IER)
      INTEGER LDA, N, IER
      DOUBLE PRECISION T(N), D(N), ABD(LDA,N), S(N)
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   08/17/01
C
C   Given a sequence of N data points (T(i),D(i)) with
C strictly increasing abscissae, this routine solves the
C symmetric positive definite tridiagonal linear system for
C the knot-derivative values S(i) defining the C2 Hermite
C cubic spline interpolant with natural end conditions.
C
C On input:
C
C       LDA = Row dimension of ABD.  LDA >= 2.
C
C       N = Number of data points.  N >= 2.
C
C       T,D = Arrays of length N containing the data points
C             (abscissae and ordinates, respectively, of the
C             knots) with strictly increasing abscissae.  T
C             is not tested for validity.
C
C The above parameters are not altered by this routine.
C
C       ABD = Array dimensioned LDA by M for M >= N.
C
C       S = Array of length at least N.
C
C On output:
C
C       ABD = Garbage.
C
C       S = Knot-derivative values of the cubic spline if
C           IER = 0.
C
C       IER = Error indicator:
C             IER = 0 if no errors were encountered.
C             IER = 1 if LDA or N is outside its valid
C                     range.
C
C Modules required by CSPLIN:  None
C
C***********************************************************
C
      DOUBLE PRECISION A1, A2, DD1, DD2
      INTEGER J
C
C Test for valid input parameters.
C
      IF (LDA .LT. 2  .OR.  N .LT. 2) GO TO 11
C
C Store the symmetric tridiagonal matrix in ABD and right
C   hand side in S.  The first row of ABD contains the off-
C   diagonal elements 1/h(i) = 1/(T(i+1)-T(i)) in column
C   i+1 for i = 1 to N-1.  The second row contains the
C   diagonal elements 2/h(i-1) + 2/h(i) in column i for
C   i = 1 to N, where 2/h(0) = 2/h(N) = 0.  The right hand
C   side is S(i) = 3*[dd(i-1)/h(i-1) + dd(i)/h(i)], where
C   dd(i) = (D(i+1)-D(i))/h(i) and dd(0) = dd(N) = 0.
C
      A2 = 1.D0/(T(2)-T(1))
      DD2 = (D(2)-D(1))*A2*A2
      ABD(2,1) = 2.D0*A2
      S(1) = 3.D0*DD2
      DO 1 J = 2,N-1
        A1 = A2
        A2 = 1.D0/(T(J+1)-T(J))
        DD1 = DD2
        DD2 = (D(J+1)-D(J))*A2*A2
        ABD(1,J) = A1
        ABD(2,J) = 2.D0*(A1+A2)
        S(J) = 3.D0*(DD1+DD2)
    1   CONTINUE
      ABD(1,N) = A2
      ABD(2,N) = 2.D0*A2
      S(N) = 3.D0*DD2
C
C Forward elimination:
C
      DO 2 J = 2,N
        A1 = ABD(1,J)/ABD(2,J-1)
        ABD(2,J) = ABD(2,J) - A1*ABD(1,J)
        S(J) = S(J) - A1*S(J-1)
    2   CONTINUE
C
C Back solve:
C
      S(N) = S(N)/ABD(2,N)
      DO 3 J = N-1,1,-1
        S(J) = (S(J) - ABD(1,J+1)*S(J+1))/ABD(2,J)
    3   CONTINUE
C
C No error encountered.
C
      IER = 0
      RETURN
C
C Invalid input parameter.
C
   11 IER = 1
      RETURN
      END
      DOUBLE PRECISION FUNCTION DSTORE (X)
      DOUBLE PRECISION X
C
C***********************************************************
C
C                                                 From GLRH2
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   02/25/96
C
C   This function forces its argument X to be stored in a
C memory location, thus providing a means of determining
C floating point number characteristics (such as the machine
C precision) when it is necessary to avoid computation in
C high precision registers.
C
C On input:
C
C       X = Double precision value to be stored.
C
C X is not altered by this function.
C
C On output:
C
C       DSTORE = Value of X after it has been stored and
C                possibly truncated or rounded to the double
C                precision word length.
C
C Modules required by DSTORE:  None
C
C***********************************************************
C
      DOUBLE PRECISION Y
      COMMON/STCOM/Y
      Y = X
      DSTORE = Y
      RETURN
      END
      DOUBLE PRECISION FUNCTION FMIN (AX,BX,TOL,F, IFLG )
      DOUBLE PRECISION AX, BX, TOL, F
      INTEGER IFLG
C
C***********************************************************
C
C                                                  From GLRH
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   11/23/95
C
C   This function returns an approximation to the point at
C which a real-valued function F attains a minimum on the
C interval (AX,BX).  It is based on the function by the same
C name by R. Brent (01/01/73), modified to use reverse
C communication.
C
C   The method used is a combination of golden section
C search and successive parabolic interpolation.  Conver-
C gence is never much slower than that for a Fibonacci
C search.  If F has a continuous second derivative which is
C positive at the minimum (which is not at AX or BX), then
C convergence is superlinear, and usually of the order of
C about 1.324....
C
C   The function F is never evaluated at two points closer
C together than EPS*Abs(FMIN) + (TOL/3), where EPS is
C approximately the square root of the relative machine
C precision.  If F is a unimodal function and the computed
C values of F are always unimodal when separated by at least
C EPS*Abs(X*) + (TOL/3), then FMIN approximates the abscissa
C of the global minimum of F on the interval (AX,BX) with
C an error less than 3*EPS*Abs(FMIN) + TOL.  If F is not
C unimodal, then FMIN may approximate a local, but perhaps
C non-global, minimum to the same accuracy.
C
C On input:
C
C       AX,BX = Endpoints of the initial interval -- the
C               interval over which F is to be minimized.
C
C       TOL = Desired length of the interval of uncertainty
C             of the final result.  TOL .GE. 0.
C
C       F = Function value F(FMIN) if IFLG .NE. 0, or unused
C           dummy parameter on the first call.
C
C The above parameters are not altered by this function.
C
C       IFLG = Reverse communication flag:
C              IFLG = 0 if this is the first call to FMIN
C                       for a given minimization problem.
C              IFLG > 0 if F contains a function value
C                       at the point FMIN returned by the
C                       previously call.  The value of
C                       IFLG must be the value returned
C                       by the previous call.
C
C On Output:
C
C       IFLG = Reverse communication flag:
C              IFLG = 0 if FMIN is the solution.
C              IFLG > 0 if FMIN contains a point at which
C                       F is to be evaluated.  FMIN must
C                       be called again.
C              IFLG < 0 if FMIN was called with an invalid
C                       value of IFLG (neither 0 nor the
C                       returned value).
C
C       FMIN = Approximation to the point at which F is
C              minimized (IFLG = 0), or point at which F
C              is to be evaluated (IFLG > 0).
C
C Module required by FMIN:  DSTORE
C
C Intrinsic functions called by FMIN:  ABS, SIGN, SQRT
C
C Reference:  Richard Brent, Algorithms for Minimization
C             Without Derivatives, Prentice-Hall, Inc.
C             (1973).
C
C***********************************************************
C
      DOUBLE PRECISION A, B, C, D, E, FU, FV, FW, FX, EPS,
     .                 P, Q, R, TOL1, TOL2, U, V, W, X, XM
      DOUBLE PRECISION DSTORE
      SAVE
C
C Test IFLG.
C
      IF (IFLG .EQ. 1) GO TO 2
      IF (IFLG .EQ. 2) GO TO 6
      IF (IFLG .NE. 0) THEN
        IFLG = -ABS(IFLG)
        RETURN
      ENDIF
C
C C is the squared inverse of the golden ratio.
C
      C = 0.5D0*(3.D0 - SQRT(5.D0))
C
C EPS is approximately the square root of the relative
C   machine precision.
C
      EPS = 1.D0
    1 EPS = EPS/2.D0
        TOL1 = DSTORE(1.D0 + EPS)
        IF (TOL1 .GT. 1.D0) GO TO 1
      EPS = SQRT(EPS)
C
C Initialization:
C
      A = AX
      B = BX
      V = A + C*(B - A)
      W = V
      X = V
      E = 0.D0
C
C Get F(X):  IFLG = 1.
C
      IFLG = 1
      FMIN = X
      RETURN
    2 FX = F
      FV = FX
      FW = FX
C
C Main loop:
C
    3 XM = 0.5D0*(A + B)
        TOL1 = EPS*ABS(X) + TOL/3.D0
        TOL2 = 2.D0*TOL1
C
C Test for termination.
C
        IF (ABS(X - XM) .LE. (TOL2 - 0.5D0*(B - A)))
     .    GO TO 7
C
C Test for golden-section necessary.
C
        IF (ABS(E) .LE. TOL1) GO TO 4
C
C Fit a parabola.
C
        R = (X - W)*(FX - FV)
        Q = (X - V)*(FX - FW)
        P = (X - V)*Q - (X - W)*R
        Q = 2.D0*(Q - R)
        IF (Q .GT. 0.D0) P = -P
        Q =  ABS(Q)
        R = E
        E = D
C
C Test for parabola acceptable.
C
        IF ( ABS(P) .GE. ABS(0.5D0*Q*R)  .OR.
     .       P .LE. Q*(A - X) .OR.  P .GE. Q*(B - X) )
     .    GO TO 4
C
C Take a parabolic interpolation step.
C
        D = P/Q
        U = X + D
C
C F must not be evaluated too close to AX or BX.
C
        IF ((U - A) .LT. TOL2) D = SIGN(TOL1, XM - X)
        IF ((B - U) .LT. TOL2) D = SIGN(TOL1, XM - X)
        GO TO 5
C
C Take a golden-section step.
C
    4   IF (X .GE. XM) E = A - X
        IF (X .LT. XM) E = B - X
        D = C*E
C
C F must not be evaluated too close to X.
C
    5   IF (ABS(D) .GE. TOL1) THEN
          U = X + D
        ELSE
          U = X + SIGN(TOL1, D)
        ENDIF
C
C Get F(U).  IFLG = 2.
C
        IFLG = 2
        FMIN = U
        RETURN
    6   FU = F
C
C Update A, B, V, W, and X.
C
        IF (FU .LE. FX) THEN
          IF (U .GE. X) A = X
          IF (U .LT. X) B = X
          V = W
          FV = FW
          W = X
          FW = FX
          X = U
          FX = FU
          GO TO 3
        ENDIF
C
        IF (U .LT. X) THEN
          A = U
        ELSE
          B = U
        ENDIF
        IF (FU .LE. FW  .OR.  W .EQ. X) THEN
          V = W
          FV = FW
          W = U
          FW = FU
          GO TO 3
        ENDIF
        IF (FU .LE. FV  .OR.  V .EQ. X  .OR.  V .EQ. W) THEN
          V = U
          FV = FU
        ENDIF
        GO TO 3
C
C Return the solution.
C
    7 IFLG = 0
      FMIN = X
      RETURN
      END
      SUBROUTINE GRADL2 (N,H,IND,M,D1Y,D2Y,A, WK, G,GNRM1,
     .                   GNRMM,IER)
      INTEGER N, IND(N), M, IER
      DOUBLE PRECISION H, D1Y(M), D2Y(M), A(M), WK(M), G(M),
     .                 GNRM1, GNRMM
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   06/18/02
C
C   This subroutine computes the L2 gradient grad(phi) of
C the energy functional phi associated with a nonlinear
C spline interpolant (Function PHI).
C
C On input:
C
C       N = Number of data points.  2 <= N <= M-1.
C
C       H = Mesh width.  H > 0.
C
C       IND = Array of length N containing a strictly
C             increasing sequence of indexes (1 to M) of
C             the data values to be interpolated, with
C             IND(1) = 1 and IND(N) = M.
C
C       M = Number of grid points.  M = IND(N) >= 6.
C
C       D1Y,D2Y,A = Arrays of length M containing difference
C                   approximations to derivatives and terms
C                   defining phi(y) computed by Function
C                   PHI.
C
C The above parameters are not altered by this routine.
C
C       WK = Work array of length at least M.
C
C       G = Array of length at least M.
C
C On output:
C
C       WK = Garbage.
C
C       G = Components of the L2-gradient grad(phi) (partial
C           derivatives of phi with respect to the function
C           values Y(i)) unless IER > 0.  G is an element of
C           S0:  G(i) = 0 for i = IND(j), j = 1 to N.
C
C       GNRM1 = Vector 1-norm of grad(phi):  sum of absolute
C               values of the components.
C
C       GNRMM = Vector max-norm of grad(phi):  maximum of
C               the absolute values of the components.
C
C       IER = Error indicator:
C             IER = 0 if no errors were encountered.
C             IER = 1 if N, H, IND, or M is outside its
C                      valid range on input.  Output para-
C                      meters are not altered in this case.
C
C Modules required by GRADL2:  None
C
C Intrinsic functions called by GRADL2:  ABS, MAX
C
C***********************************************************
C
      DOUBLE PRECISION C1, C2, GMAX, SUM
      INTEGER I, J
C
C Test for invalid input parameters.
C
      IF (N .LT. 2  .OR.  H .LE. 0.D0  .OR.  M .LT. 6  .OR.
     .    M-N .LT. 1  .OR.  IND(1) .NE. 1  .OR.
     .    IND(N) .NE. M) GO TO 11
      DO 1 I = 2,N
        IF (IND(I) .LE. IND(I-1)) GO TO 11
    1   CONTINUE
C
C Store constants.
C
      C1 = 1.25D0*H
      C2 = 2.D0/H
C
C L2 gradient:  G(i) = (2/H)*[a(i-1)-2*a(i)+a(i+1)
C                             -b(i-1)+b(i+1)]
C
C   where a(i) = D2y(i)/[1+D1y(i)**2]**(5/2),
C
C         b(i) = (5/4)*H*D1y(i)*D2y(i)**2/
C                     [1+D1y(i)**2]**(7/2),
C
C for i = 2 to m-1.
C
C Store b(i) in WK.
C
      DO 2 I = 1,M
        WK(I) = C1*D1Y(I)*D2Y(I)*A(I)/(1.D0+D1Y(I)**2)
    2   CONTINUE
C
C Store grad(phi) in G.
C
      DO 3 I = 2,M-1
        G(I) = C2*(A(I-1)-2.D0*A(I)+A(I+1)-WK(I-1)+WK(I+1))
    3   CONTINUE
C
C Project G onto S0 by zeroing the components associated
C   with data points.
C
      DO 4 J = 1,N
        I = IND(J)
        G(I) = 0.D0
    4   CONTINUE
C
C Accumulate GNRM1 and GNRMM in SUM and GMAX, respectively.
C
      SUM = 0.D0
      GMAX = 0.D0
      DO 5 I = 2,M-1
        SUM = SUM + ABS(G(I))
        GMAX = MAX( GMAX,ABS(G(I)) )
    5   CONTINUE
      GNRM1 = SUM
      GNRMM = GMAX
C
C No errors encountered.
C
      IER = 0
      RETURN
C
C Invalid input parameter.
C
   11 IER = 1
      RETURN
      END
      SUBROUTINE GRADS4 (N,H,IND,M,D1Y,D2Y,LDA, ABD,G,
     .                   WK, IER)
      INTEGER N, IND(N), M, LDA, IER
      DOUBLE PRECISION H, D1Y(M), D2Y(M), ABD(LDA,M), G(M),
     .                 WK(M,3)
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   07/12/02
C
C   This subroutine applies a 4-th order smoother DTD**(-1)
C to the L2 gradient grad(phi), returning a Sobolev gradi-
C ent G of the functional phi associated with a nonlinear
C spline interpolant (Function PHI).  The linear system is
C solved by LAPACK Subroutine DPBSV.
C
C   DTD is the restriction to S0 of P0*D**T*D, where D is
C the discrete differential operator corresponding to Dg =
C g''(s)*Sqrt(s').  The Sobolev gradient is therefore the
C gradient associated with the following discretized inner
C product on S0:
C
C       <g,h>_y = <Dg,Dh>_(m-2),
C
C               = Sum[ Dg(i)*Dh(i) ],
C
C where the sum is over i = 2 to m-1.  This is the discrete
C analog of
C
C       <g,h>_y = I[ g''(s)*h''(s) ds ],
C
C where s(t) is the arc length associated with y, and
C
C       g'(s) = g'(t)/(1+y'(t)**2)**(1/2),
C
C       g''(s) = [ (1+y'(t)**2)*g''(t) -
C                  y'(t)*y''(t)*g'(t) ]/(1+y'(t)**2)**2.
C
C On input:
C
C       N = Number of data points.  2 <= N <= M-1.
C
C       H = Mesh width.  H > 0.
C
C       IND = Array of length N containing a strictly
C             increasing sequence of indexes (1 to M) of
C             the data values to be interpolated, with
C             IND(1) = 1 and IND(N) = M.
C
C       M = Number of grid points.  M = IND(N) >= 6.
C
C       D1Y,D2Y = Arrays of length M containing difference
C                 approximations to derivatives defining
C                 phi(y) (computed by Function PHI).
C
C       LDA = Row dimension of ABD.  LDA >= 3.
C
C The above parameters are not altered by this routine.
C
C       ABD = Array dimensioned LDA by M used to store the
C             symmetric positive semi-definite pentadiagonal
C             order-(M-2) matrix D**T*D.
C
C       G = Array of length M containing the components of
C           the L2-gradient grad(phi) (partial derivatives
C           of phi with respect to the function values
C           Y(i)).  G must be an element of S0:  G(i) = 0
C           for i = IND(j), j = 1 to N.  G may be computed
C           by Subroutine GRADL2.
C
C       WK = Work array of length at least 3*M.
C
C On output:
C
C       ABD = U**T*U factorization of the upper triangle
C             of D**T*D in LAPACK band storage format
C             (incomplete if IER = 2).
C
C       G = Sobolev gradient (an element of S0) unless
C           IER > 0, in which case G is not altered.
C
C       WK = Garbage.
C
C       IER = Error indicator:
C             IER = 0 if no errors were encountered.
C             IER = 1 if N, H, IND, M, or LDA is outside
C                     its valid range on input.  Output
C                     parameters are not altered in this
C                     case.
C             IER = 2 if DTD is not positive definite
C                     (singular to working precision).
C
C LAPACK subprograms required by GRADS4:  DPBSV, DPBTF2,
C                    DPBTRF, DPBTRS, DPOTF2, LSAME, XERBLA
C
C BLAS subprograms required by GRADS4:  DGEMM, DGEMV, DSYR,
C                                       DSYRK, DTBSV, DTRSM
C
C Intrinsic function called by GRADS4:  SQRT
C
C***********************************************************
C
      DOUBLE PRECISION H4, T1, T2
      INTEGER I, J
C
C Test for invalid input parameters.
C
      IF (N .LT. 2  .OR.  H .LE. 0.D0  .OR.  M .LT. 6  .OR.
     .    M-N .LT. 1  .OR.  IND(1) .NE. 1  .OR.
     .    IND(N) .NE. M  .OR.  LDA .LT. 3) GO TO 11
      DO 1 I = 2,N
        IF (IND(I) .LE. IND(I-1)) GO TO 11
    1   CONTINUE
C
C Compute terms defining D**T*D, where D is the second
C   derivative with respect to arc length scaled by
C   Sqrt(s')):
C
C   H4 = H**4
C
C   T1 = 1 + D1y(j)**2
C   T2 = 1/(H**4*(1+D1y(j)**2)**(7/2)) = 1/(H4*T1**3.5)
C
C   WK(j,1) = T1**2*T2
C   WK(j,2) = -H*T1*D1y(j)*D2y(j)*T2
C   WK(j,3) = (H*D1y(j)*D2y(j)/2)**2*T2
C
      H4 = H**4
      DO 2 J = 2,M-1
        T1 = 1.D0 + D1Y(J)*D1Y(J)
        T2 = 1.D0/(H4*T1**3.5D0)
        WK(J,1) = T1*T1*T2
        WK(J,2) = -H*T1*D1Y(J)*D2Y(J)*T2
        WK(J,3) = (H*D1Y(J)*D2Y(J)/2.D0)**2*T2
    2   CONTINUE
C
C Store the upper triangle of D**T*D in the first three rows
C   of ABD in LAPACK band storage format:
C
C       ABD(1,j+1) = (D**T*D)(j,j+2)  for j = 2 to m-3,
C       ABD(2,j) =   (D**T*D)(j,j+1)  for j = 2 to m-2,
C       ABD(3,j-1) = (D**T*D)(j,j)    for j = 2 to m-1.
C
      DO 3 J = 2,M-3
        ABD(1,J+1) = WK(J+1,1)-WK(J+1,3)
    3   CONTINUE
C
      DO 4 J = 2,M-2
        ABD(2,J) = -2.D0*WK(J,1)-WK(J,2)-2.D0*WK(J+1,1)+
     .             WK(J+1,2)
    4   CONTINUE
C
      ABD(3,1) = 4.D0*WK(2,1)+WK(3,1)-WK(3,2)+WK(3,3)
      DO 5 J = 3,M-2
        ABD(3,J-1) = WK(J-1,1)+WK(J-1,2)+WK(J-1,3)+
     .               4.D0*WK(J,1)+WK(J+1,1)-WK(J+1,2)+
     .               WK(J+1,3)
    5   CONTINUE
      ABD(3,M-2) = WK(M-2,1)+WK(M-2,2)+WK(M-2,3)+
     .             4.D0*WK(M-1,1)
C
C Convert D**T*D to DTD as follows:  the rows and columns
C   associated with a data point (zero element in G) are
C   zeroed except for the diagonal element which is retained
C   in order to preserve the scaling (and condition number).
C
      DO 6 J = 2,N-1
        I = IND(J)
        ABD(1,I-1) = 0.D0
        ABD(2,I-1) = 0.D0
        ABD(2,I) = 0.D0
        ABD(1,I+1) = 0.D0
    6   CONTINUE
C
C Overwrite ABD with a U**T*U factorization (for upper
C   triangular matrix U) stored in band format, and solve
C   the system.
C
      CALL DPBSV ('U',M-2,2,1,ABD,LDA,G(2),M-2,IER)
      IF (IER .NE. 0) THEN
        IER = 2
      ENDIF
      RETURN
C
C Invalid input parameter.
C
   11 IER = 1
      RETURN
      END
      SUBROUTINE LNSRCH (M,H,Y0,PHI0,P,FMTOL,OPT, S,Y,D1Y,
     .                   D2Y,A, PHIY,NEVAL,YMAX,DY,IER)
      INTEGER M, NEVAL, IER
      LOGICAL OPT
      DOUBLE PRECISION H, Y0(M), PHI0, P(M), FMTOL, S, Y(M),
     .                 D1Y(M), D2Y(M), A(M), PHIY, YMAX, DY
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   06/18/02
C
C   This subroutine minimizes phi(Y0+S*P) over positive
C step-sizes S (unless OPT = FALSE), where phi is the
C functional defined by Function PHI.
C
C On input:
C
C       M = Number of grid points.  M >= 2.
C
C       H = Mesh width.  H > 0.
C
C       Y0 = Array of length M containing the current
C            estimate of the minimizer of phi:  gridpoint
C            function values y(i).
C
C       PHI0 = phi(Y0).
C
C       P = Array of length M defining the search
C           direction for the descent method.
C
C       FMTOL = Nonnegative tolerance for Function FMIN:
C               the desired length of the interval of
C               uncertainty for the optimal step-size.
C
C       OPT = Flag with value TRUE iff the optimal step-
C             size is to be computed.
C
C The above parameters are not altered by this routine.
C
C       S = Step-size to be used if OPT = FALSE, or initial
C           estimate of the optimal step-size if OPT = TRUE.
C           The value S = 1 or the output from a previous
C           call is a reasonable choice for the initial
C           estimate.  S > 0.
C
C       Y = Array of length M.
C
C       D1Y,D2Y,A = Arrays of length at least M.
C
C On output:
C
C       S = Estimate of the optimal step-size (not altered
C           if OPT = FALSE).
C
C       Y = Minimizer of phi:  Y0 + S*P.
C
C       D1Y,D2Y,A = Finite difference approximations to
C                   derivatives and terms defining the
C                   integrand associated with phi(Y).
C
C       PHIY = phi(Y).
C
C       NEVAL = Number of evaluations of phi.
C
C       YMAX = Max-norm of Y.
C
C       DY = Relative change in Y:  Max-norm(Y-Y0)/(1+YMAX)
C            = S*Max-norm(P)/(1+YMAX).
C
C       IER = Error indicator:
C             IER = 0 if no errors were encountered.
C             IER = 1 if M, H, FMTOL, or S is outside its
C                     valid range on input.
C             IER = 2 if P = 0.
C             Output parameters are not altered if IER > 0.
C
C Modules required by LNSRCH:  FMIN, PHI
C
C Intrinsic function called by LNSRCH:  ABS
C
C***********************************************************
C
      DOUBLE PRECISION PH2, PHS, S1, S2
      DOUBLE PRECISION FMIN, PHI
      INTEGER I, IFLG, NEV
C
C Test for invalid input.
C
      IF (M .LT. 2  .OR.  H .LE. 0.D0  .OR.
     .    FMTOL .LT. 0.D0  .OR.  S .LE. 0.D0) THEN
        NEVAL = 0
        IER = 1
        RETURN
      ENDIF
C
C Compute DY = Max-norm(P), and test for P = 0.
C
      DY = 0.D0
      DO 1 I = 1,M
        IF (ABS(P(I)) .GT. DY) DY = ABS(P(I))
    1   CONTINUE
      IF (DY .EQ. 0.D0) THEN
        NEVAL = 0
        IER = 2
        RETURN
      ENDIF
      NEV = 0
      IF (.NOT. OPT) GO TO 6
C
C Find a bracketing interval [S1,S2] = [0,S2] such that
C   phi(Y0+S2*P) > PHI0 = phi(Y0).  S2 is initialized to
C   2*S and doubled at each step as necessary.
C
      S1 = 0.D0
      S2 = S
    2 S2 = 2.D0*S2
        DO 3 I = 1,M
          Y(I) = Y0(I) + S2*P(I)
    3     CONTINUE
        PH2 = PHI (M,H,Y, D1Y,D2Y,A)
        NEV = NEV + 1
        IF (PH2 .LE. PHI0) GO TO 2
C
C Compute the optimal step-size S.
C
      IFLG = 0
      PHS = 0.D0
    4 S = FMIN (S1,S2,FMTOL,PHS, IFLG )
        IF (IFLG .EQ. 0) GO TO 6
        DO 5 I = 1,M
          Y(I) = Y0(I) + S*P(I)
    5     CONTINUE
        PHS = PHI (M,H,Y, D1Y,D2Y,A)
        NEV = NEV + 1
        GO TO 4
C
C Update Y and compute the final value PHIY = phi(Y), YMAX,
C   and DY = Max-norm(Y-Y0)/(1+YMAX) for Y = Y0+S*P.
C
    6 YMAX = 0.D0
      DO 7 I = 1,M
        Y(I) = Y0(I) + S*P(I)
        IF (ABS(Y(I)) .GT. YMAX) YMAX = ABS(Y(I))
    7   CONTINUE
      PHIY = PHI (M,H,Y, D1Y,D2Y,A)
      DY = S*DY/(1.D0+YMAX)
      NEVAL = NEV + 1
      IER = 0
      RETURN
      END
      DOUBLE PRECISION FUNCTION PHI (M,H,Y, D1Y,D2Y,A)
      INTEGER M
      DOUBLE PRECISION H, Y(M), D1Y(M), D2Y(M), A(M)
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   06/18/02
C
C   Given a discrete sequence of function values Y = y(1),
C y(2), ..., y(M) on a uniform grid with mesh width H, this
C function returns the value at Y of the discretized energy
C functional which approximates the integral with respect to
C arc length of squared curvature, along with the terms
C defining the functional and difference approximations to
C derivatives at the grid points:
C
C       PHI = H*Sum[ D2y(i)*a(i) ],
C
C where
C
C       D1y(i) = (y(i+1)-y(i-1))/(2*H),
C
C       D2y(i) = (y(i+1)-2*y(i)+y(i-1))/H**2,
C
C       a(i) = D2y(i)/[1+D1y(i)**2]**(5/2),
C
C and Sum[_] denotes the sum over i = 2 to m-1.  The end
C conditions give D2y(1) = D2y(m) = 0.
C
C On input:
C
C       M = Number of grid points.  M >= 2.
C
C       H = Mesh width.  H > 0.
C
C       Y = Array of length M containing the function
C           values y(i).
C
C The above parameters are not altered by this function.
C
C       D1Y,D2Y,A = Arrays of length at least M.
C
C On output:
C
C       D1Y,D2Y,A = Arrays containing the finite difference
C                   approximations defined above, along with
C                   the endpoint values associated with
C                   natural end conditions:  D2y(1) = D2y(M)
C                   = 0, and thus D1y(1) = (y(2)-y(1))/H and
C                   D1y(M) = (y(M)-y(M-1))/H.
C
C       PHI = Value of the discretized energy functional.
C
C The program is terminated with an error message written to
C the standard output unit if an input parameter is invalid.
C
C Modules required by PHI:  None
C
C Intrinsic function called by PHI:  SQRT
C
C***********************************************************
C
      DOUBLE PRECISION S1, S2, SUM, T
      INTEGER I
      IF (M .LT. 2  .OR.  H .LE. 0.D0) GO TO 11
C
C Initialization:
C
      S1 = 1.D0/(2.D0*H)
      S2 = 1.D0/(H*H)
C
C i = 1:  the terms defining phi(Y) are accumulated in SUM.
C
      D1Y(1) = (Y(2)-Y(1))/H
      D2Y(1) = 0.D0
      A(1) = 0.D0
      SUM = 0.D0
C
C i = 2 to m-1:
C
      DO 1 I = 2,M-1
        D1Y(I) = (Y(I+1)-Y(I-1))*S1
        D2Y(I) = (Y(I+1)-2.D0*Y(I)+Y(I-1))*S2
        T = 1.D0 + D1Y(I)*D1Y(I)
        A(I) = D2Y(I)/(T*T*SQRT(T))
        SUM = SUM + D2Y(I)*A(I)
    1   CONTINUE
C
C i = m:
C
      D1Y(M) = (Y(M)-Y(M-1))/H
      D2Y(M) = 0.D0
      A(M) = 0.D0
C
      PHI = H*SUM
      RETURN
C
C M < 2 or H <= 0.
C
   11 WRITE (*,100) M, H
  100 FORMAT (//' *** Error in PHI:  M = ',I4,', H = ',
     .        D10.3)
      STOP
      END
      SUBROUTINE PLTCRV (LUN,N,A,B,XS,YS,M,Y,PLT0,Y0,
     .                   PLTSIZ, IER)
      INTEGER LUN, N, M, IER
      LOGICAL PLT0
      DOUBLE PRECISION A, B, XS(N), YS(N), Y(M), Y0(M),
     .                 PLTSIZ
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   06/20/02
C
C   Given one or two sequences of function values y(1), ...,
C y(M), and optionally y0(1), ..., y0(M), associated with
C uniformly distributed grid points T(i) = A + (i-1)*H for
C H = (B-A)/(M-1), i = 1 to M, and a sequence of N data
C points (xs(i),ys(i)), this subroutine creates a level-2
C Encapsulated PostScript (EPS) file containing a plot of
C the curve (or curves) with marker symbols centered at the
C data points.  If the second curve y0 is included, it it
C drawn with dashed lines.  It is assumed that the data
C points lie inside the containing rectangle of the curves.
C
C On input:
C
C       LUN = Logical unit number in the range 0 to 99.
C             The unit should be opened with an appropriate
C             file name before the call to this routine.
C
C       N = Number of data points to be marked.
C           0 <= N <= M.
C
C       A,B = Left and right endpoints defining the domain.
C             B-A > 0.
C
C       XS,YS = Arrays of length N containing the abscissae
C               and ordinates of the data points to be
C               marked.
C
C       M = Number of grid points and function values.
C           M >= 2.
C
C       Y = Array of length M containing the function
C           values.
C
C       PLT0 = Logical variable with value TRUE iff the
C              second curve is to be drawn.
C
C       Y0 = Array of length M containing function values
C            defining the second curve if PLT0 = TRUE, or
C            dummy variable otherwise.
C
C       PLTSIZ = Plot size in inches.  The view volume
C                (bounding box defined by the function
C                domain and range) is mapped to a rectangu-
C                lar viewport with maximum side-length equal
C                to .88*PLTSIZ.  The containing rectangle is
C                centered on the 8.5 by 11 inch page, and
C                its boundary is drawn.  Labels below, to
C                the left of, and to the right of the rec-
C                tangle extend its dimensions by 1/4 inch,
C                2/3 inches, and 1/6 inch, respectively, for
C                FSIZ = 12 pts.  1.0 <= PLTSIZ <= 6.5.
C
C Input parameters are not altered by this routine.
C
C On output:
C
C       IER = Error indicator:
C             IER = 0 if no errors were encountered.
C             IER = 1 if LUN, N, A, B, M, or PLTSIZ is
C                     outside its valid range.
C             IER = 2 if all function values are identical.
C             IER = 3 if an error was encountered in writing
C                     to unit LUN.
C
C   Various plotting options can be controlled by altering
C the data statement below.
C
C Modules required by PLTCRV:  None
C
C Intrinsic functions called by PLTCRV:  CHAR, MAX, MIN,
C                                        NINT, REAL
C
C***********************************************************
C
      INTEGER I, IH, IPX1, IPX2, IPY1, IPY2, IW
      LOGICAL ASPECT, AXES, SQUARE
      REAL    BSIZ, DASHL, DX, DY, FSIZ, H, R, SFX, SFY,
     .        T, TX, TY, WX1, WX2, WY1, WY2, X, XM, YM
C
      DATA    ASPECT/.TRUE./, AXES/.TRUE./, BSIZ/6.0/,
     .        DASHL/4.0/, FSIZ/12.0/, SQUARE/.FALSE./
C
C Local parameters:
C
C ASPECT =    Logical variable with value TRUE if the
C               aspect ratio of the view volume is to be
C               preserved in the viewport, FALSE if the
C               viewport is to be square.  Note the limit-
C               ation on the size of the aspect ratio R
C AXES =      Logical variable with value TRUE if the x and
C               y axes (intersected with the view volume)
C               are to be drawn
C BSIZ =      Box size in points for marker symbols
C DASHL =     Length (in points, at 72 points per inch) of
C               dashes and spaces in a dashed line pattern
C               used for connecting pseudo-vertices
C DX =        View volume width WX2-WX1
C DY =        View volume height WY2-WY1
C FSIZ =      Font size in points for labels
C H =         Mesh width
C I =         Array index
C IH =        Height of the viewport in points
C IPX1,IPY1 = X and y coordinates (in points) of the lower
C               left corner of the containing rectangle
C IPX2,IPY2 = X and y coordinates (in points) of the upper
C               right corner of the containing rectangle
C IW =        Width of the viewport in points
C R =         Aspect ratio of the viewport:
C               Max(1/2,Min(2,DX/DY)) if ASPECT = TRUE,
C               1 otherwise
C SFX,SFY =   Scale factors for mapping world coordinates
C               (window coordinates in [WX1,WX2] X [WY1,WY2])
C               to viewport coordinates
C SQUARE =    Logical variable with value TRUE if markers
C               are to be square boxes, FALSE if markers are
C               to be X's
C T =         Temporary variable
C TX,TY =     Translation vector for mapping world coordi-
C               nates to viewport coordinates
C WX1,WY1 =   X and y (world) coordinates of the lower left
C               corner of the window (view volume)
C WX2,WY2 =   X and y (world) coordinates of the upper right
C               corner of the window (view volume)
C X =         Grid point abscissae value
C XM,YM =     Location in world coordinates of the center of
C               a marker symbol or beginning of a label
C
C
C Test for error 1.
C
      IF (LUN .LT. 0  .OR.  LUN .GT. 99  .OR.  N .LT. 0
     .    .OR.  N .GT. M  .OR.  B-A .LE. 0.0  .OR.  M .LT. 2
     .    .OR.  PLTSIZ .LT. 1.0  .OR.  PLTSIZ .GT. 6.5D0)
     .   GO TO 11
C
C Compute the window (view volume) corner coordinates
C   (WX1,WY1) and WX2,WY2).
C
      WX1 = A
      WX2 = B
      WY1 = REAL(Y(1))
      WY2 = WY1
      DO 1 I = 2,M
        WY1 = MIN(WY1,REAL(Y(I)))
        WY2 = MAX(WY2,REAL(Y(I)))
    1   CONTINUE
      IF (PLT0) THEN
        DO 2 I = 1,M
          WY1 = MIN(WY1,REAL(Y0(I)))
          WY2 = MAX(WY2,REAL(Y0(I)))
    2     CONTINUE
      ENDIF
C
C Compute the dimensions and aspect ratio of the view
C   volume.
C
      DX = WX2 - WX1
      DY = WY2 - WY1
      IF (DY .LE. 0.0) GO TO 12
      R = 1.0
      IF (ASPECT) R = MAX(0.5,MIN(2.0,DX/DY))
C
C Compute the lower left (IPX1,IPY1) and upper right
C   (IPX2,IPY2) corner coordinates of the containing
C   rectangle.  The coordinates, specified in default user
C   space units (points, at 72 points/inch with origin at
C   the lower left corner of the page), are chosen to have
C   aspect ratio R, and to center the plot on the 8.5 by 11
C   inch page.  The center of the page is (306,396), and
C   T = PLTSIZ/2 in points.
C
      T = 36.0*PLTSIZ
      IF (R .GE. 1.0) THEN
        IPX1 = 306 - NINT(T)
        IPX2 = 306 + NINT(T)
        IPY1 = 396 - NINT(T/R)
        IPY2 = 396 + NINT(T/R)
      ELSE
        IPX1 = 306 - NINT(T*R)
        IPX2 = 306 + NINT(T*R)
        IPY1 = 396 - NINT(T)
        IPY2 = 396 + NINT(T)
      ENDIF
C
C Output header comments.  The bounding box corner coordi-
C   nates are obtained by extending the containing rectangle
C   to include its boundary and the labels.
C
      WRITE (LUN,100,ERR=13) IPX1-NINT(4.0*FSIZ),
     .                       IPY1-NINT(1.5*FSIZ),
     .                       IPX2+NINT(FSIZ), IPY2+1
  100 FORMAT ('%!PS-Adobe-3.0 EPSF-3.0'/
     .        '%%BoundingBox:',4I4/
     .        '%%Title:  Nonlinear Spline'/
     .        '%%Creator:  DNSPLIN1'/
     .        '%%EndComments')
C
C Set the line thickness to 2 points, and draw the boundary
C   of the containing rectangle.
C
      T = 2.0
      WRITE (LUN,110,ERR=13) T
      WRITE (LUN,120,ERR=13) IPX1, IPY1
      WRITE (LUN,130,ERR=13) IPX1, IPY2
      WRITE (LUN,130,ERR=13) IPX2, IPY2
      WRITE (LUN,130,ERR=13) IPX2, IPY1
      WRITE (LUN,140,ERR=13)
      WRITE (LUN,150,ERR=13)
  110 FORMAT (F12.6,' setlinewidth')
  120 FORMAT (2I4,' moveto')
  130 FORMAT (2I4,' lineto')
  140 FORMAT ('closepath')
  150 FORMAT ('stroke')
C
C Set IW and IH to the width and height of a viewport
C   obtained by shrinking the containing rectangle by 12%
C   in each direction.
C
      IW = NINT(0.88*REAL(IPX2-IPX1))
      IH = NINT(0.88*REAL(IPY2-IPY1))
C
C Set up a viewport mapping.
C
      SFX = REAL(IW)/DX
      SFY = REAL(IH)/DY
      TX = REAL(306-IW/2) - SFX*WX1
      TY = REAL(396-IH/2) - SFY*WY1
C
C Set the line thickness to 1 point.
C
      T = 1.0
      WRITE (LUN,110,ERR=13) T
C
C Draw the first curve Y (by creating and painting a path).
C
      H = DX/REAL(M-1)
      X = A
      WRITE (LUN,160,ERR=13) SFX*X+TX, SFY*REAL(Y(1))+TY
      DO 3 I = 2,M
        X = X + H
        WRITE (LUN,170,ERR=13) SFX*X+TX, SFY*REAL(Y(I))+TY
    3   CONTINUE
      WRITE (LUN,150,ERR=13)
  160 FORMAT (2F12.6,' moveto')
  170 FORMAT (2F12.6,' lineto')
      IF (PLT0) THEN
C
C Set the dashed line attribute.
C
        WRITE (LUN,180,ERR=13) DASHL, DASHL
  180   FORMAT ('[',2F12.6,'] 0 setdash')
C
C Draw the second curve Y0.
C
        X = A
        WRITE (LUN,160,ERR=13) SFX*X+TX, SFY*REAL(Y0(1))+TY
        DO 4 I = 2,M
          X = X + H
          WRITE (LUN,170,ERR=13) SFX*X+TX, SFY*REAL(Y0(I))+TY
    4     CONTINUE
        WRITE (LUN,150,ERR=13)
      ENDIF
C
C Restore the solid line attribute.
C
      WRITE (LUN,190,ERR=13)
  190 FORMAT ('[] 0 setdash')
      IF (AXES) THEN
C
C Draw x and y axes (if contained in the view volume).
C
        IF (WX1 .LT. 0.0  .AND.  WX2 .GT. 0.0) THEN
          WRITE (LUN,160,ERR=13) TX, SFY*WY1+TY
          WRITE (LUN,170,ERR=13) TX, SFY*WY2+TY
        ENDIF
        IF (WY1 .LT. 0.0  .AND.  WY2 .GT. 0.0) THEN
          WRITE (LUN,160,ERR=13) SFX*WX1+TX, TY
          WRITE (LUN,170,ERR=13) SFX*WX2+TX, TY
        ENDIF
      ENDIF
C
C Draw marker symbols (squares or X's) at the data points.
C
C   T = BSIZ/2,
C   (XM,YM) = Location of symbol center.
C
      T = BSIZ/2.0
      DO 5 I = 1,N
        XM = SFX*REAL(XS(I))+TX
        YM = SFY*REAL(YS(I))+TY
        WRITE (LUN,160,ERR=13) XM-T, YM-T
        IF (SQUARE) THEN
          WRITE (LUN,170,ERR=13) XM+T, YM-T
          WRITE (LUN,170,ERR=13) XM+T, YM+T
          WRITE (LUN,170,ERR=13) XM-T, YM+T
          WRITE (LUN,140,ERR=13)
        ELSE
          WRITE (LUN,170,ERR=13) XM+T, YM+T
          WRITE (LUN,160,ERR=13) XM+T, YM-T
          WRITE (LUN,170,ERR=13) XM-T, YM+T
        ENDIF
    5   CONTINUE
C
C Paint the path.
C
      WRITE (LUN,150,ERR=13)
C
C Select a font and scale it.
C
      T = FSIZ
      WRITE (LUN,200,ERR=13) T
  200 FORMAT ('/Helvetica findfont'/
     .        F12.6,' scalefont setfont')
C
C Draw tick marks and labels at the extreme points of the
C   domain and range.  The tick mark length is T/2.
C
      XM = SFX*WX1+TX
      YM = REAL(IPY1)
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,170,ERR=13) XM, YM-T/2.0
      XM = XM - 1.5*T
      YM = YM - 1.5*T
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,210,ERR=13) WX1
  210 FORMAT ('(',F6.2,') show')
C
      XM = SFX*WX2+TX
      YM = REAL(IPY1)
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,170,ERR=13) XM, YM-T/2.0
      XM = XM - 1.5*T
      YM = YM - 1.5*T
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,210,ERR=13) WX2
C
      XM = REAL(IPX1)
      YM = SFY*WY1+TY
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,170,ERR=13) XM-T/2.0, YM
      XM = XM - 4.0*T
      YM = YM - 0.25*T
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,210,ERR=13) WY1
C
      XM = REAL(IPX1)
      YM = SFY*WY2+TY
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,170,ERR=13) XM-T/2.0, YM
      XM = XM - 4.0*T
      YM = YM - 0.25*T
      WRITE (LUN,160,ERR=13) XM, YM
      WRITE (LUN,210,ERR=13) WY2
C
C Paint the path and output the showpage command and
C   end-of-file indicator.
C
      WRITE (LUN,220,ERR=13)
  220 FORMAT ('stroke'/
     .        'showpage'/
     .        '%%EOF')
C
C HP's interpreters require a one-byte End-of-PostScript-Job
C   indicator (to eliminate a timeout error message):
C   ASCII 4.
C
      WRITE (LUN,230,ERR=13) CHAR(4)
  230 FORMAT (A1)
C
C No error encountered.
C
      IER = 0
      RETURN
C
C Invalid input parameter LUN, N, A, B, M, or PLTSIZ.
C
   11 IER = 1
      RETURN
C
C DY = 0:  constant function.
C
   12 IER = 2
      RETURN
C
C Error writing to unit LUN.
C
   13 IER = 3
      RETURN
      END
      SUBROUTINE READF (LIN,NMAX, N,T,D,H,IND,IER)
      INTEGER LIN, NMAX, N, IND(NMAX), IER
      DOUBLE PRECISION T(NMAX), D(NMAX), H
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   01/02/02
C
C   This routine reads a data set consisting of the number
C of data points N, the abscissae T, ordinates D, and mesh
C width H for the finite difference grid.  The indexes IND
C of the data points in the uniform grid are also computed.
C Format I4 is used for N, format D22.15 for the other
C values.
C
C On input:
C
C       LIN = Logical unit number for input.  0 .LE. LIN
C             .LE. 99.
C
C       NMAX = Maximum value of N.  NMAX >= 2.
C
C The above parameters are not altered by this routine.
C
C       T,D,IND = Arrays of length at least NMAX.
C
C On output:
C
C       N = Number of data points.  2 <= N <= NMAX.
C
C       T,D = Ordered sequence of data abscissae and ordi-
C             nates, respectively.  The abscissae must be
C             strictly increasing with separation between
C             adjacent values greater than H/2.
C
C       H = Positive mesh width for the uniform finite
C           difference grid.  The local discretization error
C           is O(H**2), and the data abscissae are perturbed
C           if necessary so that T(i)-T(1) is a multiple of
C           H for i = 1 to N.
C
C       IND = Indexes of the (perturbed) data points in the
C             grid:
C               IND(i) = NINT((T(i)-T(1))/H) + 1
C             for i = 1 to N.
C
C       IER = Error indicator:
C             IER = 0 if no errors were encountered.
C             IER = 1 if LIN or NMAX is outside its
C                     valid range.
C             IER = 2 if a read error occurred.
C             IER = 3 if N < 2 or N > NMAX.
C             IER = 4 if H <= 0.
C             IER = 5 if the abscissae are not strictly
C                     increasing or the separation between
C                     adjacent abscissae is too small to
C                     produce distinct indexes.
C
C             The error conditions are tested in the above-
C             specified order, and processing is terminated
C             immediately on encountering an error.
C
C Modules required by READF:  None
C
C Intrinsic functions called by READF:  DBLE, NINT
C
C***********************************************************
C
      INTEGER I
C
C Input formats:
C
  100 FORMAT (I4)
  110 FORMAT (D22.15)
C
C Test for invalid input parameters.
C
      IF (LIN .LT. 0  .OR.  LIN .GT. 99  .OR.  NMAX .LT. 2)
     .  GO TO 11
C
C Read the data set and test for errors.
C
      READ (LIN,100,ERR=12) N
      IF (N .LT. 2  .OR.  N .GT. NMAX) GO TO 13
      READ (LIN,110,ERR=12) (T(I), I = 1,N)
      READ (LIN,110,ERR=12) (D(I), I = 1,N)
      READ (LIN,110,ERR=12) H
      IF (H .LE. 0.D0) GO TO 14
C
C Compute IND.
C
      IND(1) = 1
      DO 1 I = 2,N
        IND(I) = NINT((T(I)-T(1))/H) + 1
        IF (IND(I) .LT. IND(I-1)) GO TO 15
        T(I) = T(1) + DBLE(IND(I)-1)*H
    1   CONTINUE
C
C No error encountered.
C
      IER = 0
      RETURN
C
C Input parameter LIN or NMAX is outside its valid range.
C
   11 IER = 1
      RETURN
C
C Read error encountered.
C
   12 IER = 2
      RETURN
C
C N < 2 or N > NMAX.
C
   13 IER = 3
      RETURN
C
C H is not positive.
C
   14 IER = 4
      RETURN
C
C Abscissae not strictly increasing or too close together.
C
   15 IER = 5
      RETURN
      END
      SUBROUTINE WRITF (LOUT,M,Y,D1Y,D2Y)
      INTEGER LOUT, M
      DOUBLE PRECISION Y(M), D1Y(M), D2Y(M)
C
C***********************************************************
C
C                                              From DNSPLIN1
C                                            Robert J. Renka
C                                  Dept. of Computer Science
C                                       Univ. of North Texas
C                                           renka@cs.unt.edu
C                                                   06/20/02
C
C   This routine creates an output data set consisting of
C the number of grid points m (format I5) followed by the
C sequence of gridpoint function values (y(i), i = 1,m),
C the first derivative values (D1y(i), i = 1,m), and the
C second derivative values (D2y(i), i = 1,m) written with
C format D22.15.
C
C On input:
C
C       LOUT = Logical unit number for writing the solution.
C              0 .LE. LOUT .LE. 99.
C
C       M = Number of grid points.  M > 0.
C
C       Y = Array of length M containing the function
C           values.
C
C       D1Y,D2Y = Arrays of length M containing difference
C                 approximations to derivatives defining
C                 phi(y) (computed by Function PHI).
C
C Input parameters are not altered by this routine.
C
C An error message is written to the standard output unit
C if an input parameter is invalid or a write error is
C encountered writing to unit LOUT.
C
C Modules required by WRITF:  None
C
C***********************************************************
C
      INTEGER I
C
C Output formats:
C
  100 FORMAT (I5)
  110 FORMAT (D22.15)
C
C Test for invalid parameters.
C
      IF (LOUT .LT. 0  .OR.  LOUT .GT. 99  .OR.  M .LE. 0)
     .  GO TO 11
C
C Create the data set.
C
      WRITE (LOUT,100,ERR=12) M
      DO 1 I = 1,M
        WRITE (LOUT,110,ERR=12) Y(I)
    1   CONTINUE
      DO 2 I = 1,M
        WRITE (LOUT,110,ERR=12) D1Y(I)
    2   CONTINUE
      DO 3 I = 1,M
        WRITE (LOUT,110,ERR=12) D2Y(I)
    3   CONTINUE
      RETURN
C
C Invalid input parameter.
C
   11 WRITE (*,210)
  210 FORMAT (///10X,'*** Error in WRITF:  invalid input ',
     .               'parameter ***')
      RETURN
C
C Error writing to unit LOUT.
C
   12 WRITE (*,220)
  220 FORMAT (///10X,'*** Error in WRITF writing to unit ',
     .               'LOUT ***')
      RETURN
      END
SHAR_EOF
fi # end of overwriting check
cd ..
cd ..
cd ..
#       End of shell archive
exit 0