numeric-linalg

Educational material on the SciPy implementation of numerical linear algebra algorithms

Name	Size	Mode
..
lapack/TESTING/LIN/zlarhs.f	13463B	-rw-r--r--

*> \brief \b ZLARHS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
*                          A, LDA, X, LDX, B, LDB, ISEED, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANS, UPLO, XTYPE
*       CHARACTER*3        PATH
*       INTEGER            INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
*       ..
*       .. Array Arguments ..
*       INTEGER            ISEED( 4 )
*       COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*>    op(A) * X = B,
*> where op(A) = A, A**T, or A**H, depending on TRANS.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] PATH
*> \verbatim
*>          PATH is CHARACTER*3
*>          The type of the complex matrix A.  PATH may be given in any
*>          combination of upper and lower case.  Valid paths include
*>             xGE:  General m x n matrix
*>             xGB:  General banded matrix
*>             xPO:  Hermitian positive definite, 2-D storage
*>             xPP:  Hermitian positive definite packed
*>             xPB:  Hermitian positive definite banded
*>             xHE:  Hermitian indefinite, 2-D storage
*>             xHP:  Hermitian indefinite packed
*>             xHB:  Hermitian indefinite banded
*>             xSY:  Symmetric indefinite, 2-D storage
*>             xSP:  Symmetric indefinite packed
*>             xSB:  Symmetric indefinite banded
*>             xTR:  Triangular
*>             xTP:  Triangular packed
*>             xTB:  Triangular banded
*>             xQR:  General m x n matrix
*>             xLQ:  General m x n matrix
*>             xQL:  General m x n matrix
*>             xRQ:  General m x n matrix
*>          where the leading character indicates the precision.
*> \endverbatim
*>
*> \param[in] XTYPE
*> \verbatim
*>          XTYPE is CHARACTER*1
*>          Specifies how the exact solution X will be determined:
*>          = 'N':  New solution; generate a random X.
*>          = 'C':  Computed; use value of X on entry.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Used only if A is symmetric or triangular; specifies whether
*>          the upper or lower triangular part of the matrix A is stored.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          Used only if A is nonsymmetric; specifies the operation
*>          applied to the matrix A.
*>          = 'N':  B := A    * X  (No transpose)
*>          = 'T':  B := A**T * X  (Transpose)
*>          = 'C':  B := A**H * X  (Conjugate transpose)
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*>          KL is INTEGER
*>          Used only if A is a band matrix; specifies the number of
*>          subdiagonals of A if A is a general band matrix or if A is
*>          symmetric or triangular and UPLO = 'L'; specifies the number
*>          of superdiagonals of A if A is symmetric or triangular and
*>          UPLO = 'U'.  0 <= KL <= M-1.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*>          KU is INTEGER
*>          Used only if A is a general band matrix or if A is
*>          triangular.
*>
*>          If PATH = xGB, specifies the number of superdiagonals of A,
*>          and 0 <= KU <= N-1.
*>
*>          If PATH = xTR, xTP, or xTB, specifies whether or not the
*>          matrix has unit diagonal:
*>          = 1:  matrix has non-unit diagonal (default)
*>          = 2:  matrix has unit diagonal
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand side vectors in the system A*X = B.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (LDA,N)
*>          The test matrix whose type is given by PATH.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          If PATH = xGB, LDA >= KL+KU+1.
*>          If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
*>          Otherwise, LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*>          X is or output) COMPLEX*16 array, dimension (LDX,NRHS)
*>          On entry, if XTYPE = 'C' (for 'Computed'), then X contains
*>          the exact solution to the system of linear equations.
*>          On exit, if XTYPE = 'N' (for 'New'), then X is initialized
*>          with random values.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.  If TRANS = 'N',
*>          LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
*>          The right hand side vector(s) for the system of equations,
*>          computed from B = op(A) * X, where op(A) is determined by
*>          TRANS.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  If TRANS = 'N',
*>          LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension (4)
*>          The seed vector for the random number generator (used in
*>          ZLATMS).  Modified on exit.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE ZLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
     $                   A, LDA, X, LDX, B, LDB, ISEED, INFO )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE, ZERO
      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
     $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI
      CHARACTER          C1, DIAG
      CHARACTER*2        C2
      INTEGER            J, MB, NX
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, LSAMEN
      EXTERNAL           LSAME, LSAMEN
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, ZGBMV, ZGEMM, ZHBMV, ZHEMM, ZHPMV,
     $                   ZLACPY, ZLARNV, ZSBMV, ZSPMV, ZSYMM, ZTBMV,
     $                   ZTPMV, ZTRMM
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      C1 = PATH( 1: 1 )
      C2 = PATH( 2: 3 )
      TRAN = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' )
      NOTRAN = .NOT.TRAN
      GEN = LSAME( PATH( 2: 2 ), 'G' )
      QRS = LSAME( PATH( 2: 2 ), 'Q' ) .OR. LSAME( PATH( 3: 3 ), 'Q' )
      SYM = LSAME( PATH( 2: 2 ), 'P' ) .OR.
     $      LSAME( PATH( 2: 2 ), 'S' ) .OR. LSAME( PATH( 2: 2 ), 'H' )
      TRI = LSAME( PATH( 2: 2 ), 'T' )
      BAND = LSAME( PATH( 3: 3 ), 'B' )
      IF( .NOT.LSAME( C1, 'Zomplex precision' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.( LSAME( XTYPE, 'N' ) .OR. LSAME( XTYPE, 'C' ) ) )
     $          THEN
         INFO = -2
      ELSE IF( ( SYM .OR. TRI ) .AND. .NOT.
     $         ( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) THEN
         INFO = -3
      ELSE IF( ( GEN .OR. QRS ) .AND. .NOT.
     $         ( TRAN .OR. LSAME( TRANS, 'N' ) ) ) THEN
         INFO = -4
      ELSE IF( M.LT.0 ) THEN
         INFO = -5
      ELSE IF( N.LT.0 ) THEN
         INFO = -6
      ELSE IF( BAND .AND. KL.LT.0 ) THEN
         INFO = -7
      ELSE IF( BAND .AND. KU.LT.0 ) THEN
         INFO = -8
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -9
      ELSE IF( ( .NOT.BAND .AND. LDA.LT.MAX( 1, M ) ) .OR.
     $         ( BAND .AND. ( SYM .OR. TRI ) .AND. LDA.LT.KL+1 ) .OR.
     $         ( BAND .AND. GEN .AND. LDA.LT.KL+KU+1 ) ) THEN
         INFO = -11
      ELSE IF( ( NOTRAN .AND. LDX.LT.MAX( 1, N ) ) .OR.
     $         ( TRAN .AND. LDX.LT.MAX( 1, M ) ) ) THEN
         INFO = -13
      ELSE IF( ( NOTRAN .AND. LDB.LT.MAX( 1, M ) ) .OR.
     $         ( TRAN .AND. LDB.LT.MAX( 1, N ) ) ) THEN
         INFO = -15
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZLARHS', -INFO )
         RETURN
      END IF
*
*     Initialize X to NRHS random vectors unless XTYPE = 'C'.
*
      IF( TRAN ) THEN
         NX = M
         MB = N
      ELSE
         NX = N
         MB = M
      END IF
      IF( .NOT.LSAME( XTYPE, 'C' ) ) THEN
         DO 10 J = 1, NRHS
            CALL ZLARNV( 2, ISEED, N, X( 1, J ) )
   10    CONTINUE
      END IF
*
*     Multiply X by op(A) using an appropriate
*     matrix multiply routine.
*
      IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
     $    LSAMEN( 2, C2, 'LQ' ) .OR. LSAMEN( 2, C2, 'QL' ) .OR.
     $    LSAMEN( 2, C2, 'RQ' ) ) THEN
*
*        General matrix
*
         CALL ZGEMM( TRANS, 'N', MB, NRHS, NX, ONE, A, LDA, X, LDX,
     $               ZERO, B, LDB )
*
      ELSE IF( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'HE' ) ) THEN
*
*        Hermitian matrix, 2-D storage
*
         CALL ZHEMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO,
     $               B, LDB )
*
      ELSE IF( LSAMEN( 2, C2, 'SY' ) ) THEN
*
*        Symmetric matrix, 2-D storage
*
         CALL ZSYMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO,
     $               B, LDB )
*
      ELSE IF( LSAMEN( 2, C2, 'GB' ) ) THEN
*
*        General matrix, band storage
*
         DO 20 J = 1, NRHS
            CALL ZGBMV( TRANS, M, N, KL, KU, ONE, A, LDA, X( 1, J ), 1,
     $                  ZERO, B( 1, J ), 1 )
   20    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'PB' ) .OR. LSAMEN( 2, C2, 'HB' ) ) THEN
*
*        Hermitian matrix, band storage
*
         DO 30 J = 1, NRHS
            CALL ZHBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO,
     $                  B( 1, J ), 1 )
   30    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'SB' ) ) THEN
*
*        Symmetric matrix, band storage
*
         DO 40 J = 1, NRHS
            CALL ZSBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO,
     $                  B( 1, J ), 1 )
   40    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'PP' ) .OR. LSAMEN( 2, C2, 'HP' ) ) THEN
*
*        Hermitian matrix, packed storage
*
         DO 50 J = 1, NRHS
            CALL ZHPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ),
     $                  1 )
   50    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'SP' ) ) THEN
*
*        Symmetric matrix, packed storage
*
         DO 60 J = 1, NRHS
            CALL ZSPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ),
     $                  1 )
   60    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'TR' ) ) THEN
*
*        Triangular matrix.  Note that for triangular matrices,
*           KU = 1 => non-unit triangular
*           KU = 2 => unit triangular
*
         CALL ZLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
         IF( KU.EQ.2 ) THEN
            DIAG = 'U'
         ELSE
            DIAG = 'N'
         END IF
         CALL ZTRMM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
     $               LDB )
*
      ELSE IF( LSAMEN( 2, C2, 'TP' ) ) THEN
*
*        Triangular matrix, packed storage
*
         CALL ZLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
         IF( KU.EQ.2 ) THEN
            DIAG = 'U'
         ELSE
            DIAG = 'N'
         END IF
         DO 70 J = 1, NRHS
            CALL ZTPMV( UPLO, TRANS, DIAG, N, A, B( 1, J ), 1 )
   70    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN
*
*        Triangular matrix, banded storage
*
         CALL ZLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
         IF( KU.EQ.2 ) THEN
            DIAG = 'U'
         ELSE
            DIAG = 'N'
         END IF
         DO 80 J = 1, NRHS
            CALL ZTBMV( UPLO, TRANS, DIAG, N, KL, A, LDA, B( 1, J ), 1 )
   80    CONTINUE
*
      ELSE
*
*        If none of the above, set INFO = -1 and return
*
         INFO = -1
         CALL XERBLA( 'ZLARHS', -INFO )
      END IF
*
      RETURN
*
*     End of ZLARHS
*
      END