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328 lines
9.3 KiB
328 lines
9.3 KiB
*> \brief \b SGQRTS
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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 SGQRTS( N, M, P, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
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* BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LDB, LWORK, M, P, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), AF( LDA, * ), R( LDA, * ),
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* $ Q( LDA, * ), B( LDB, * ), BF( LDB, * ),
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* $ T( LDB, * ), Z( LDB, * ), BWK( LDB, * ),
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* $ TAUA( * ), TAUB( * ), RESULT( 4 ),
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* $ RWORK( * ), WORK( LWORK )
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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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*> SGQRTS tests SGGQRF, which computes the GQR factorization of an
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*> N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.
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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] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows of the matrices A and B. N >= 0.
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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 columns of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] P
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*> \verbatim
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*> P is INTEGER
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*> The number of columns of the matrix B. P >= 0.
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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 REAL array, dimension (LDA,M)
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*> The N-by-M matrix A.
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*> \endverbatim
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*>
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*> \param[out] AF
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*> \verbatim
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*> AF is REAL array, dimension (LDA,N)
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*> Details of the GQR factorization of A and B, as returned
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*> by SGGQRF, see SGGQRF for further details.
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*> \endverbatim
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*>
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*> \param[out] Q
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*> \verbatim
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*> Q is REAL array, dimension (LDA,N)
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*> The M-by-M orthogonal matrix Q.
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*> \endverbatim
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*>
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*> \param[out] R
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*> \verbatim
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*> R is REAL array, dimension (LDA,MAX(M,N))
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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 arrays A, AF, R and Q.
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*> LDA >= max(M,N).
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*> \endverbatim
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*>
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*> \param[out] TAUA
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*> \verbatim
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*> TAUA is REAL array, dimension (min(M,N))
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*> The scalar factors of the elementary reflectors, as returned
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*> by SGGQRF.
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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is REAL array, dimension (LDB,P)
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*> On entry, the N-by-P matrix A.
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*> \endverbatim
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*>
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*> \param[out] BF
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*> \verbatim
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*> BF is REAL array, dimension (LDB,N)
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*> Details of the GQR factorization of A and B, as returned
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*> by SGGQRF, see SGGQRF for further details.
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*> \endverbatim
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*>
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*> \param[out] Z
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*> \verbatim
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*> Z is REAL array, dimension (LDB,P)
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*> The P-by-P orthogonal matrix Z.
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*> \endverbatim
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*>
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*> \param[out] T
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*> \verbatim
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*> T is REAL array, dimension (LDB,max(P,N))
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*> \endverbatim
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*>
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*> \param[out] BWK
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*> \verbatim
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*> BWK is REAL array, dimension (LDB,N)
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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 arrays B, BF, Z and T.
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*> LDB >= max(P,N).
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*> \endverbatim
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*>
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*> \param[out] TAUB
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*> \verbatim
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*> TAUB is REAL array, dimension (min(P,N))
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*> The scalar factors of the elementary reflectors, as returned
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*> by SGGRQF.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK, LWORK >= max(N,M,P)**2.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (max(N,M,P))
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL array, dimension (4)
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*> The test ratios:
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*> RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)
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*> RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)
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*> RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
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*> RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
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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 single_eig
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*
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* =====================================================================
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SUBROUTINE SGQRTS( N, M, P, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
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$ BWK, LDB, TAUB, WORK, LWORK, RWORK, RESULT )
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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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INTEGER LDA, LDB, LWORK, M, P, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), AF( LDA, * ), R( LDA, * ),
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$ Q( LDA, * ), B( LDB, * ), BF( LDB, * ),
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$ T( LDB, * ), Z( LDB, * ), BWK( LDB, * ),
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$ TAUA( * ), TAUB( * ), RESULT( 4 ),
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$ RWORK( * ), WORK( LWORK )
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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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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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REAL ROGUE
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PARAMETER ( ROGUE = -1.0E+10 )
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* ..
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* .. Local Scalars ..
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INTEGER INFO
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REAL ANORM, BNORM, ULP, UNFL, RESID
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGE, SLANSY
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EXTERNAL SLAMCH, SLANGE, SLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMM, SLACPY, SLASET, SORGQR,
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$ SORGRQ, SSYRK
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN, REAL
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* ..
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* .. Executable Statements ..
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*
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ULP = SLAMCH( 'Precision' )
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UNFL = SLAMCH( 'Safe minimum' )
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*
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* Copy the matrix A to the array AF.
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*
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CALL SLACPY( 'Full', N, M, A, LDA, AF, LDA )
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CALL SLACPY( 'Full', N, P, B, LDB, BF, LDB )
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*
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ANORM = MAX( SLANGE( '1', N, M, A, LDA, RWORK ), UNFL )
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BNORM = MAX( SLANGE( '1', N, P, B, LDB, RWORK ), UNFL )
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*
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* Factorize the matrices A and B in the arrays AF and BF.
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*
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CALL SGGQRF( N, M, P, AF, LDA, TAUA, BF, LDB, TAUB, WORK,
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$ LWORK, INFO )
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*
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* Generate the N-by-N matrix Q
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*
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CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
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CALL SLACPY( 'Lower', N-1, M, AF( 2,1 ), LDA, Q( 2,1 ), LDA )
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CALL SORGQR( N, N, MIN( N, M ), Q, LDA, TAUA, WORK, LWORK, INFO )
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*
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* Generate the P-by-P matrix Z
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*
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CALL SLASET( 'Full', P, P, ROGUE, ROGUE, Z, LDB )
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IF( N.LE.P ) THEN
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IF( N.GT.0 .AND. N.LT.P )
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$ CALL SLACPY( 'Full', N, P-N, BF, LDB, Z( P-N+1, 1 ), LDB )
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IF( N.GT.1 )
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$ CALL SLACPY( 'Lower', N-1, N-1, BF( 2, P-N+1 ), LDB,
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$ Z( P-N+2, P-N+1 ), LDB )
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ELSE
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IF( P.GT.1)
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$ CALL SLACPY( 'Lower', P-1, P-1, BF( N-P+2, 1 ), LDB,
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$ Z( 2, 1 ), LDB )
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END IF
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CALL SORGRQ( P, P, MIN( N, P ), Z, LDB, TAUB, WORK, LWORK, INFO )
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*
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* Copy R
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*
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CALL SLASET( 'Full', N, M, ZERO, ZERO, R, LDA )
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CALL SLACPY( 'Upper', N, M, AF, LDA, R, LDA )
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*
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* Copy T
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*
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CALL SLASET( 'Full', N, P, ZERO, ZERO, T, LDB )
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IF( N.LE.P ) THEN
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CALL SLACPY( 'Upper', N, N, BF( 1, P-N+1 ), LDB, T( 1, P-N+1 ),
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$ LDB )
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ELSE
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CALL SLACPY( 'Full', N-P, P, BF, LDB, T, LDB )
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CALL SLACPY( 'Upper', P, P, BF( N-P+1, 1 ), LDB, T( N-P+1, 1 ),
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$ LDB )
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END IF
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*
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* Compute R - Q'*A
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*
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CALL SGEMM( 'Transpose', 'No transpose', N, M, N, -ONE, Q, LDA, A,
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$ LDA, ONE, R, LDA )
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*
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* Compute norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP ) .
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*
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RESID = SLANGE( '1', N, M, R, LDA, RWORK )
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IF( ANORM.GT.ZERO ) THEN
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RESULT( 1 ) = ( ( RESID / REAL( MAX(1,M,N) ) ) / ANORM ) / ULP
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ELSE
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RESULT( 1 ) = ZERO
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END IF
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*
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* Compute T*Z - Q'*B
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*
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CALL SGEMM( 'No Transpose', 'No transpose', N, P, P, ONE, T, LDB,
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$ Z, LDB, ZERO, BWK, LDB )
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CALL SGEMM( 'Transpose', 'No transpose', N, P, N, -ONE, Q, LDA,
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$ B, LDB, ONE, BWK, LDB )
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*
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* Compute norm( T*Z - Q'*B ) / ( MAX(P,N)*norm(A)*ULP ) .
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*
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RESID = SLANGE( '1', N, P, BWK, LDB, RWORK )
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IF( BNORM.GT.ZERO ) THEN
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RESULT( 2 ) = ( ( RESID / REAL( MAX(1,P,N ) ) )/BNORM ) / ULP
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ELSE
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RESULT( 2 ) = ZERO
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END IF
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*
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* Compute I - Q'*Q
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*
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CALL SLASET( 'Full', N, N, ZERO, ONE, R, LDA )
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CALL SSYRK( 'Upper', 'Transpose', N, N, -ONE, Q, LDA, ONE, R,
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$ LDA )
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*
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* Compute norm( I - Q'*Q ) / ( N * ULP ) .
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*
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RESID = SLANSY( '1', 'Upper', N, R, LDA, RWORK )
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RESULT( 3 ) = ( RESID / REAL( MAX( 1, N ) ) ) / ULP
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*
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* Compute I - Z'*Z
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*
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CALL SLASET( 'Full', P, P, ZERO, ONE, T, LDB )
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CALL SSYRK( 'Upper', 'Transpose', P, P, -ONE, Z, LDB, ONE, T,
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$ LDB )
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*
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* Compute norm( I - Z'*Z ) / ( P*ULP ) .
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*
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RESID = SLANSY( '1', 'Upper', P, T, LDB, RWORK )
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RESULT( 4 ) = ( RESID / REAL( MAX( 1, P ) ) ) / ULP
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*
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RETURN
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*
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* End of SGQRTS
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*
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END
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