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|
*> \brief \b SLARHS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SLARHS( 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 )
* REAL A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLARHS 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 REAL 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) REAL 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 REAL 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
*> SLATMS). 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.
*
*> \date December 2016
*
*> \ingroup single_eig
*
* =====================================================================
SUBROUTINE SLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
$ A, LDA, X, LDX, B, LDB, ISEED, INFO )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER TRANS, UPLO, XTYPE
CHARACTER*3 PATH
INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
REAL A( LDA, * ), B( LDB, * ), X( LDX, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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 SGBMV, SGEMM, SLACPY, SLARNV, SSBMV, SSPMV,
$ SSYMM, STBMV, STPMV, STRMM, 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, 'Single 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( 'SLARHS', -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 SLARNV( 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 SGEMM( 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 SSYMM( '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 SGBMV( 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 SSBMV( 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 SSPMV( 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 SLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
IF( KU.EQ.2 ) THEN
DIAG = 'U'
ELSE
DIAG = 'N'
END IF
CALL STRMM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
$ LDB )
*
ELSE IF( LSAMEN( 2, C2, 'TP' ) ) THEN
*
* Triangular matrix, packed storage
*
CALL SLACPY( '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 STPMV( UPLO, TRANS, DIAG, N, A, B( 1, J ), 1 )
50 CONTINUE
*
ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN
*
* Triangular matrix, banded storage
*
CALL SLACPY( '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 STBMV( 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( 'SLARHS', -INFO )
END IF
*
RETURN
*
* End of SLARHS
*
END
|
