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