dlarhs.f

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*> \brief \b DLARHS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLARHS( 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 )
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLARHS 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 ) may be A or A' (transpose of A).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] PATH
*> \verbatim
*>          PATH is CHARACTER*3
*>          The type of the real matrix A.  PATH may be given in any
*>          combination of upper and lower case.  Valid types include
*>             xGE:  General m x n matrix
*>             xGB:  General banded matrix
*>             xPO:  Symmetric positive definite, 2-D storage
*>             xPP:  Symmetric positive definite packed
*>             xPB:  Symmetric positive definite 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
*>          Specifies whether the upper or lower triangular part of the
*>          matrix A is stored, if A is symmetric.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          Specifies the operation applied to the matrix A.
*>          = 'N':  System is  A * x = b
*>          = 'T':  System is  A'* x = b
*>          = 'C':  System is  A'* x = b
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number or 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 DOUBLE PRECISION 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) DOUBLE PRECISION 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 DOUBLE PRECISION 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
*>          DLATMS).  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 double_eig
*
*  =====================================================================
      SUBROUTINE dlarhs( 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 )
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 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           dgbmv, dgemm, dlacpy, dlarnv, dsbmv, dspmv,
     $                   dsymm, dtbmv, dtpmv, dtrmm, xerbla
*     ..
*     .. 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' )
      tri = lsame( path( 2: 2 ), 'T' )
      band = lsame( path( 3: 3 ), 'B' )
      IF( .NOT.lsame( c1, 'Double 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( 'DLARHS', -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 dlarnv( 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 dgemm( trans, 'N', mb, nrhs, nx, one, a, lda, x, ldx,
     $               zero, b, ldb )
*
      ELSE IF( lsamen( 2, c2, 'PO' ) .OR. lsamen( 2, c2, 'SY' ) ) THEN
*
*        Symmetric matrix, 2-D storage
*
         CALL dsymm( '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 dgbmv( trans, mb, nx, kl, ku, one, a, lda, x( 1, j ),
     $                  1, zero, b( 1, j ), 1 )
   20    CONTINUE
*
      ELSE IF( lsamen( 2, c2, 'PB' ) ) THEN
*
*        Symmetric matrix, band storage
*
         DO 30 j = 1, nrhs
            CALL dsbmv( uplo, n, kl, one, a, lda, x( 1, j ), 1, zero,
     $                  b( 1, j ), 1 )
   30    CONTINUE
*
      ELSE IF( lsamen( 2, c2, 'PP' ) .OR. lsamen( 2, c2, 'SP' ) ) THEN
*
*        Symmetric matrix, packed storage
*
         DO 40 j = 1, nrhs
            CALL dspmv( uplo, n, one, a, x( 1, j ), 1, zero, b( 1, j ),
     $                  1 )
   40    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 dlacpy( 'Full', n, nrhs, x, ldx, b, ldb )
         IF( ku.EQ.2 ) THEN
            diag = 'U'
         ELSE
            diag = 'N'
         END IF
         CALL dtrmm( 'Left', uplo, trans, diag, n, nrhs, one, a, lda, b,
     $               ldb )
*
      ELSE IF( lsamen( 2, c2, 'TP' ) ) THEN
*
*        Triangular matrix, packed storage
*
         CALL dlacpy( 'Full', n, nrhs, x, ldx, b, ldb )
         IF( ku.EQ.2 ) THEN
            diag = 'U'
         ELSE
            diag = 'N'
         END IF
         DO 50 j = 1, nrhs
            CALL dtpmv( uplo, trans, diag, n, a, b( 1, j ), 1 )
   50    CONTINUE
*
      ELSE IF( lsamen( 2, c2, 'TB' ) ) THEN
*
*        Triangular matrix, banded storage
*
         CALL dlacpy( 'Full', n, nrhs, x, ldx, b, ldb )
         IF( ku.EQ.2 ) THEN
            diag = 'U'
         ELSE
            diag = 'N'
         END IF
         DO 60 j = 1, nrhs
            CALL dtbmv( uplo, trans, diag, n, kl, a, lda, b( 1, j ), 1 )
   60    CONTINUE
*
      ELSE
*
*        If PATH is none of the above, return with an error code.
*
         info = -1
         CALL xerbla( 'DLARHS', -info )
      END IF
*
      RETURN
*
*     End of DLARHS
*
      END