*> \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