LAPACK: SRC/dlangb.f Source File

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00001       DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
00002      $                 WORK )
00003 *
00004 *  -- LAPACK auxiliary routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          NORM
00011       INTEGER            KL, KU, LDAB, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  DLANGB  returns the value of the one norm,  or the Frobenius norm, or
00021 *  the  infinity norm,  or the element of  largest absolute value  of an
00022 *  n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
00023 *
00024 *  Description
00025 *  ===========
00026 *
00027 *  DLANGB returns the value
00028 *
00029 *     DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00030 *              (
00031 *              ( norm1(A),         NORM = '1', 'O' or 'o'
00032 *              (
00033 *              ( normI(A),         NORM = 'I' or 'i'
00034 *              (
00035 *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00036 *
00037 *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
00038 *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00039 *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
00040 *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00041 *
00042 *  Arguments
00043 *  =========
00044 *
00045 *  NORM    (input) CHARACTER*1
00046 *          Specifies the value to be returned in DLANGB as described
00047 *          above.
00048 *
00049 *  N       (input) INTEGER
00050 *          The order of the matrix A.  N >= 0.  When N = 0, DLANGB is
00051 *          set to zero.
00052 *
00053 *  KL      (input) INTEGER
00054 *          The number of sub-diagonals of the matrix A.  KL >= 0.
00055 *
00056 *  KU      (input) INTEGER
00057 *          The number of super-diagonals of the matrix A.  KU >= 0.
00058 *
00059 *  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
00060 *          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
00061 *          column of A is stored in the j-th column of the array AB as
00062 *          follows:
00063 *          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
00064 *
00065 *  LDAB    (input) INTEGER
00066 *          The leading dimension of the array AB.  LDAB >= KL+KU+1.
00067 *
00068 *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
00069 *          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00070 *          referenced.
00071 *
00072 * =====================================================================
00073 *
00074 *
00075 *     .. Parameters ..
00076       DOUBLE PRECISION   ONE, ZERO
00077       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00078 *     ..
00079 *     .. Local Scalars ..
00080       INTEGER            I, J, K, L
00081       DOUBLE PRECISION   SCALE, SUM, VALUE
00082 *     ..
00083 *     .. External Subroutines ..
00084       EXTERNAL           DLASSQ
00085 *     ..
00086 *     .. External Functions ..
00087       LOGICAL            LSAME
00088       EXTERNAL           LSAME
00089 *     ..
00090 *     .. Intrinsic Functions ..
00091       INTRINSIC          ABS, MAX, MIN, SQRT
00092 *     ..
00093 *     .. Executable Statements ..
00094 *
00095       IF( N.EQ.0 ) THEN
00096          VALUE = ZERO
00097       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00098 *
00099 *        Find max(abs(A(i,j))).
00100 *
00101          VALUE = ZERO
00102          DO 20 J = 1, N
00103             DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
00104                VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00105    10       CONTINUE
00106    20    CONTINUE
00107       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00108 *
00109 *        Find norm1(A).
00110 *
00111          VALUE = ZERO
00112          DO 40 J = 1, N
00113             SUM = ZERO
00114             DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
00115                SUM = SUM + ABS( AB( I, J ) )
00116    30       CONTINUE
00117             VALUE = MAX( VALUE, SUM )
00118    40    CONTINUE
00119       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00120 *
00121 *        Find normI(A).
00122 *
00123          DO 50 I = 1, N
00124             WORK( I ) = ZERO
00125    50    CONTINUE
00126          DO 70 J = 1, N
00127             K = KU + 1 - J
00128             DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
00129                WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
00130    60       CONTINUE
00131    70    CONTINUE
00132          VALUE = ZERO
00133          DO 80 I = 1, N
00134             VALUE = MAX( VALUE, WORK( I ) )
00135    80    CONTINUE
00136       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00137 *
00138 *        Find normF(A).
00139 *
00140          SCALE = ZERO
00141          SUM = ONE
00142          DO 90 J = 1, N
00143             L = MAX( 1, J-KU )
00144             K = KU + 1 - J + L
00145             CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
00146    90    CONTINUE
00147          VALUE = SCALE*SQRT( SUM )
00148       END IF
00149 *
00150       DLANGB = VALUE
00151       RETURN
00152 *
00153 *     End of DLANGB
00154 *
00155       END