testdata/lapack/TESTING/EIG/dgsvts3.f
*> \brief \b DGSVTS3
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGSVTS3( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
* LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK,
* LWORK, RWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDB, LDQ, LDR, LDU, LDV, LWORK, M, N, P
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), ALPHA( * ),
* $ B( LDB, * ), BETA( * ), BF( LDB, * ),
* $ Q( LDQ, * ), R( LDR, * ), RESULT( 6 ),
* $ RWORK( * ), U( LDU, * ), V( LDV, * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGSVTS3 tests DGGSVD3, which computes the GSVD of an M-by-N matrix A
*> and a P-by-N matrix B:
*> U'*A*Q = D1*R and V'*B*Q = D2*R.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] P
*> \verbatim
*> P is INTEGER
*> The number of rows of the matrix B. P >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,M)
*> The M-by-N matrix A.
*> \endverbatim
*>
*> \param[out] AF
*> \verbatim
*> AF is DOUBLE PRECISION array, dimension (LDA,N)
*> Details of the GSVD of A and B, as returned by DGGSVD3,
*> see DGGSVD3 for further details.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A and AF.
*> LDA >= max( 1,M ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,P)
*> On entry, the P-by-N matrix B.
*> \endverbatim
*>
*> \param[out] BF
*> \verbatim
*> BF is DOUBLE PRECISION array, dimension (LDB,N)
*> Details of the GSVD of A and B, as returned by DGGSVD3,
*> see DGGSVD3 for further details.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the arrays B and BF.
*> LDB >= max(1,P).
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*> U is DOUBLE PRECISION array, dimension(LDU,M)
*> The M by M orthogonal matrix U.
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of the array U. LDU >= max(1,M).
*> \endverbatim
*>
*> \param[out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension(LDV,M)
*> The P by P orthogonal matrix V.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V. LDV >= max(1,P).
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is DOUBLE PRECISION array, dimension(LDQ,N)
*> The N by N orthogonal matrix Q.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= max(1,N).
*> \endverbatim
*>
*> \param[out] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] BETA
*> \verbatim
*> BETA is DOUBLE PRECISION array, dimension (N)
*>
*> The generalized singular value pairs of A and B, the
*> ``diagonal'' matrices D1 and D2 are constructed from
*> ALPHA and BETA, see subroutine DGGSVD3 for details.
*> \endverbatim
*>
*> \param[out] R
*> \verbatim
*> R is DOUBLE PRECISION array, dimension(LDQ,N)
*> The upper triangular matrix R.
*> \endverbatim
*>
*> \param[in] LDR
*> \verbatim
*> LDR is INTEGER
*> The leading dimension of the array R. LDR >= max(1,N).
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N)
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK,
*> LWORK >= max(M,P,N)*max(M,P,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (max(M,P,N))
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (6)
*> The test ratios:
*> RESULT(1) = norm( U'*A*Q - D1*R ) / ( MAX(M,N)*norm(A)*ULP)
*> RESULT(2) = norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP)
*> RESULT(3) = norm( I - U'*U ) / ( M*ULP )
*> RESULT(4) = norm( I - V'*V ) / ( P*ULP )
*> RESULT(5) = norm( I - Q'*Q ) / ( N*ULP )
*> RESULT(6) = 0 if ALPHA is in decreasing order;
*> = ULPINV otherwise.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date August 2015
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGSVTS3( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
$ LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK,
$ LWORK, RWORK, RESULT )
*
* -- 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..--
* August 2015
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LDQ, LDR, LDU, LDV, LWORK, M, N, P
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), ALPHA( * ),
$ B( LDB, * ), BETA( * ), BF( LDB, * ),
$ Q( LDQ, * ), R( LDR, * ), RESULT( 6 ),
$ RWORK( * ), U( LDU, * ), V( LDV, * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J, K, L
DOUBLE PRECISION ANORM, BNORM, RESID, TEMP, ULP, ULPINV, UNFL
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
EXTERNAL DLAMCH, DLANGE, DLANSY
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMM, DGGSVD3, DLACPY, DLASET, DSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
ULP = DLAMCH( 'Precision' )
ULPINV = ONE / ULP
UNFL = DLAMCH( 'Safe minimum' )
*
* Copy the matrix A to the array AF.
*
CALL DLACPY( 'Full', M, N, A, LDA, AF, LDA )
CALL DLACPY( 'Full', P, N, B, LDB, BF, LDB )
*
ANORM = MAX( DLANGE( '1', M, N, A, LDA, RWORK ), UNFL )
BNORM = MAX( DLANGE( '1', P, N, B, LDB, RWORK ), UNFL )
*
* Factorize the matrices A and B in the arrays AF and BF.
*
CALL DGGSVD3( 'U', 'V', 'Q', M, N, P, K, L, AF, LDA, BF, LDB,
$ ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, LWORK,
$ IWORK, INFO )
*
* Copy R
*
DO 20 I = 1, MIN( K+L, M )
DO 10 J = I, K + L
R( I, J ) = AF( I, N-K-L+J )
10 CONTINUE
20 CONTINUE
*
IF( M-K-L.LT.0 ) THEN
DO 40 I = M + 1, K + L
DO 30 J = I, K + L
R( I, J ) = BF( I-K, N-K-L+J )
30 CONTINUE
40 CONTINUE
END IF
*
* Compute A:= U'*A*Q - D1*R
*
CALL DGEMM( 'No transpose', 'No transpose', M, N, N, ONE, A, LDA,
$ Q, LDQ, ZERO, WORK, LDA )
*
CALL DGEMM( 'Transpose', 'No transpose', M, N, M, ONE, U, LDU,
$ WORK, LDA, ZERO, A, LDA )
*
DO 60 I = 1, K
DO 50 J = I, K + L
A( I, N-K-L+J ) = A( I, N-K-L+J ) - R( I, J )
50 CONTINUE
60 CONTINUE
*
DO 80 I = K + 1, MIN( K+L, M )
DO 70 J = I, K + L
A( I, N-K-L+J ) = A( I, N-K-L+J ) - ALPHA( I )*R( I, J )
70 CONTINUE
80 CONTINUE
*
* Compute norm( U'*A*Q - D1*R ) / ( MAX(1,M,N)*norm(A)*ULP ) .
*
RESID = DLANGE( '1', M, N, A, LDA, RWORK )
*
IF( ANORM.GT.ZERO ) THEN
RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M, N ) ) ) / ANORM ) /
$ ULP
ELSE
RESULT( 1 ) = ZERO
END IF
*
* Compute B := V'*B*Q - D2*R
*
CALL DGEMM( 'No transpose', 'No transpose', P, N, N, ONE, B, LDB,
$ Q, LDQ, ZERO, WORK, LDB )
*
CALL DGEMM( 'Transpose', 'No transpose', P, N, P, ONE, V, LDV,
$ WORK, LDB, ZERO, B, LDB )
*
DO 100 I = 1, L
DO 90 J = I, L
B( I, N-L+J ) = B( I, N-L+J ) - BETA( K+I )*R( K+I, K+J )
90 CONTINUE
100 CONTINUE
*
* Compute norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP ) .
*
RESID = DLANGE( '1', P, N, B, LDB, RWORK )
IF( BNORM.GT.ZERO ) THEN
RESULT( 2 ) = ( ( RESID / DBLE( MAX( 1, P, N ) ) ) / BNORM ) /
$ ULP
ELSE
RESULT( 2 ) = ZERO
END IF
*
* Compute I - U'*U
*
CALL DLASET( 'Full', M, M, ZERO, ONE, WORK, LDQ )
CALL DSYRK( 'Upper', 'Transpose', M, M, -ONE, U, LDU, ONE, WORK,
$ LDU )
*
* Compute norm( I - U'*U ) / ( M * ULP ) .
*
RESID = DLANSY( '1', 'Upper', M, WORK, LDU, RWORK )
RESULT( 3 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / ULP
*
* Compute I - V'*V
*
CALL DLASET( 'Full', P, P, ZERO, ONE, WORK, LDV )
CALL DSYRK( 'Upper', 'Transpose', P, P, -ONE, V, LDV, ONE, WORK,
$ LDV )
*
* Compute norm( I - V'*V ) / ( P * ULP ) .
*
RESID = DLANSY( '1', 'Upper', P, WORK, LDV, RWORK )
RESULT( 4 ) = ( RESID / DBLE( MAX( 1, P ) ) ) / ULP
*
* Compute I - Q'*Q
*
CALL DLASET( 'Full', N, N, ZERO, ONE, WORK, LDQ )
CALL DSYRK( 'Upper', 'Transpose', N, N, -ONE, Q, LDQ, ONE, WORK,
$ LDQ )
*
* Compute norm( I - Q'*Q ) / ( N * ULP ) .
*
RESID = DLANSY( '1', 'Upper', N, WORK, LDQ, RWORK )
RESULT( 5 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / ULP
*
* Check sorting
*
CALL DCOPY( N, ALPHA, 1, WORK, 1 )
DO 110 I = K + 1, MIN( K+L, M )
J = IWORK( I )
IF( I.NE.J ) THEN
TEMP = WORK( I )
WORK( I ) = WORK( J )
WORK( J ) = TEMP
END IF
110 CONTINUE
*
RESULT( 6 ) = ZERO
DO 120 I = K + 1, MIN( K+L, M ) - 1
IF( WORK( I ).LT.WORK( I+1 ) )
$ RESULT( 6 ) = ULPINV
120 CONTINUE
*
RETURN
*
* End of DGSVTS3
*
END