*
************************************************************************
*
SUBROUTINE ECTPSV( UPLO, TRANS, DIAG, N, AP, X, INCX )
* .. Scalar Arguments ..
INTEGER INCX, N
CHARACTER*1 DIAG, TRANS, UPLO
* .. Array Arguments ..
COMPLEX*16 X( * )
COMPLEX AP( * )
* ..
*
* Purpose
* =======
*
* ECTPSV solves one of the systems of equations
*
* A*x = b, or A'*x = b, or conjg( 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 matrix. Additional precision
* arithmetic is used in the computation.
*
* 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' conjg( 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.
*
* AP - COMPLEX array of DIMENSION at least
* ( ( n*( n + 1 ) )/2 ).
* Before entry with UPLO = 'U' or 'u', the array AP must
* contain the upper triangular matrix packed sequentially,
* column by column, so that AP( 1 ) contains a( 1, 1 ),
* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
* respectively, and so on.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular matrix packed sequentially,
* column by column, so that AP( 1 ) contains a( 1, 1 ),
* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
* respectively, and so on.
* Note that when DIAG = 'U' or 'u', the diagonal elements of
* A are not referenced, but are assumed to be unity.
* Unchanged on exit.
*
* X - COMPLEX*16 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. At least double precision
* arithemtic is used in the computation of 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 20-July-1986.
* Sven Hammarling, Nag Central Office.
* Richard Hanson, Sandia National Labs.
*
*
* .. Parameters ..
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* .. Local Scalars ..
INTEGER I, INFO, IX, J, JX, K, KK, KX
LOGICAL NOCONJ, NOUNIT
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
* .. 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 ( INCX.EQ.0 ) THEN
INFO = 7
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'ECTPSV', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( N.EQ.0 )
$ RETURN
*
NOCONJ = LSAME( TRANS, 'T' )
NOUNIT = ( DIAG .EQ.'N' ).OR.( DIAG .EQ.'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 AP are
* accessed sequentially with one pass through AP.
*
IF( LSAME( TRANS, 'N' ) )THEN
*
* Form x := inv( A )*x.
*
IF( LSAME( UPLO, 'U' ) )THEN
K = ( N*( N + 1 ) )/2
IF( INCX.EQ.1 )THEN
DO 20, J = N, 1, -1
IF( X( J ).NE.ZERO )THEN
IF( NOUNIT )
$ X( J ) = X( J )/AP( K )
K = K - 1
DO 10, I = J - 1, 1, -1
X( I ) = X( I ) - X( J )*AP( K )
K = K - 1
10 CONTINUE
ELSE
K = K - J
END IF
20 CONTINUE
ELSE
JX = KX + ( N - 1 )*INCX
DO 40, J = N, 1, -1
IF( X( JX ).NE.ZERO )THEN
IF( NOUNIT )
$ X( JX ) = X( JX )/AP( K )
IX = JX
KK = K - 1
DO 30, K = KK, KK - J + 2, -1
IX = IX - INCX
X( IX ) = X( IX ) - X( JX )*AP( K )
30 CONTINUE
ELSE
K = K - J
END IF
JX = JX - INCX
40 CONTINUE
END IF
ELSE
K = 1
IF( INCX.EQ.1 )THEN
DO 60, J = 1, N
IF( X( J ).NE.ZERO )THEN
IF( NOUNIT )
$ X( J ) = X( J )/AP( K )
K = K + 1
DO 50, I = J + 1, N
X( I ) = X( I ) - X( J )*AP( K )
K = K + 1
50 CONTINUE
ELSE
K = K + N - J + 1
END IF
60 CONTINUE
ELSE
JX = KX
DO 80, J = 1, N
IF( X( JX ).NE.ZERO )THEN
IF( NOUNIT )
$ X( JX ) = X( JX )/AP( K )
IX = JX
KK = K + 1
DO 70, K = KK, KK + N - ( J + 1 )
IX = IX + INCX
X( IX ) = X( IX ) - X( JX )*AP( K )
70 CONTINUE
ELSE
K = K + N - J + 1
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x.
*
IF( LSAME( UPLO, 'U' ) )THEN
K = 1
IF( INCX.EQ.1 )THEN
DO 110, J = 1, N
IF( NOCONJ )THEN
DO 90, I = 1, J - 1
X( J ) = X( J ) - AP( K )*X( I )
K = K + 1
90 CONTINUE
IF( NOUNIT )
$ X( J ) = X( J )/AP( K )
ELSE
DO 100, I = 1, J - 1
X( J ) = X( J ) - CONJG( AP( K ) )*X( I )
K = K + 1
100 CONTINUE
IF( NOUNIT )
$ X( J ) = X( J )/CONJG( AP( K ) )
END IF
K = K + 1
110 CONTINUE
ELSE
JX = KX
DO 140, J = 1, N
IX = KX
KK = K
IF( NOCONJ )THEN
DO 120, K = KK, KK + J - 2
X( JX ) = X( JX ) - AP( K )*X( IX )
IX = IX + INCX
120 CONTINUE
IF( NOUNIT )
$ X( JX ) = X( JX )/AP( K )
ELSE
DO 130, K = KK, KK + J - 2
X( JX ) = X( JX ) - CONJG( AP( K ) )*X( IX )
IX = IX + INCX
130 CONTINUE
IF( NOUNIT )
$ X( JX ) = X( JX )/CONJG( AP( K ) )
END IF
K = K + 1
JX = JX + INCX
140 CONTINUE
END IF
ELSE
K = ( N*( N + 1 ) )/2
IF( INCX.EQ.1 )THEN
DO 170, J = N, 1, -1
IF( NOCONJ )THEN
DO 150, I = N, J + 1, -1
X( J ) = X( J ) - AP( K )*X( I )
K = K - 1
150 CONTINUE
IF( NOUNIT )
$ X( J ) = X( J )/AP( K )
ELSE
DO 160, I = N, J + 1, -1
X( J ) = X( J ) - CONJG( AP( K ) )*X( I )
K = K - 1
160 CONTINUE
IF( NOUNIT )
$ X( J ) = X( J )/CONJG( AP( K ) )
END IF
K = K - 1
170 CONTINUE
ELSE
KX = KX + ( N - 1 )*INCX
JX = KX
DO 200, J = N, 1, -1
IX = KX
KK = K
IF( NOCONJ )THEN
DO 180, K = KK, KK - ( N - ( J + 1 ) ), -1
X( JX ) = X( JX ) - AP( K )*X( IX )
IX = IX - INCX
180 CONTINUE
IF( NOUNIT )
$ X( JX ) = X( JX )/AP( K )
ELSE
DO 190, K = KK, KK - ( N - ( J + 1 ) ), -1
X( JX ) = X( JX ) - CONJG( AP( K ) )*X( IX )
IX = IX - INCX
190 CONTINUE
IF( NOUNIT )
$ X( JX ) = X( JX )/CONJG( AP( K ) )
END IF
K = K - 1
JX = JX - INCX
200 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of ECTPSV.
*
END