*> \brief \b DBDT05 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DBDT05( M, N, A, LDA, S, NS, U, LDU, * VT, LDVT, WORK, RESID ) * * .. Scalar Arguments .. * INTEGER LDA, LDU, LDVT, N, NS * DOUBLE PRECISION RESID * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ), S( * ), U( LDU, * ), * $ VT( LDVT, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DBDT05 reconstructs a bidiagonal matrix B from its (partial) SVD: *> S = U' * B * V *> where U and V are orthogonal matrices and S is diagonal. *> *> The test ratio to test the singular value decomposition is *> RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS ) *> where VT = V' and EPS is the machine precision. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrices A and U. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrices A and VT. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The m by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] S *> \verbatim *> S is DOUBLE PRECISION array, dimension (NS) *> The singular values from the (partial) SVD of B, sorted in *> decreasing order. *> \endverbatim *> *> \param[in] NS *> \verbatim *> NS is INTEGER *> The number of singular values/vectors from the (partial) *> SVD of B. *> \endverbatim *> *> \param[in] U *> \verbatim *> U is DOUBLE PRECISION array, dimension (LDU,NS) *> The n by ns orthogonal matrix U in S = U' * B * V. *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> The leading dimension of the array U. LDU >= max(1,N) *> \endverbatim *> *> \param[in] VT *> \verbatim *> VT is DOUBLE PRECISION array, dimension (LDVT,N) *> The n by ns orthogonal matrix V in S = U' * B * V. *> \endverbatim *> *> \param[in] LDVT *> \verbatim *> LDVT is INTEGER *> The leading dimension of the array VT. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (M,N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> The test ratio: norm(S - U' * A * V) / ( n * norm(A) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_eig * * ===================================================================== SUBROUTINE DBDT05( M, N, A, LDA, S, NS, U, LDU, $ VT, LDVT, WORK, RESID ) * * -- 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 .. INTEGER LDA, LDU, LDVT, M, N, NS DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), $ VT( LDVT, * ), WORK( * ) * .. * * ====================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX DOUBLE PRECISION DASUM, DLAMCH, DLANGE EXTERNAL LSAME, IDAMAX, DASUM, DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DGEMM * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN * .. * .. Executable Statements .. * * Quick return if possible. * RESID = ZERO IF( MIN( M, N ).LE.0 .OR. NS.LE.0 ) $ RETURN * EPS = DLAMCH( 'Precision' ) ANORM = DLANGE( 'M', M, N, A, LDA, WORK ) * * Compute U' * A * V. * CALL DGEMM( 'N', 'T', M, NS, N, ONE, A, LDA, VT, $ LDVT, ZERO, WORK( 1+NS*NS ), M ) CALL DGEMM( 'T', 'N', NS, NS, M, -ONE, U, LDU, WORK( 1+NS*NS ), $ M, ZERO, WORK, NS ) * * norm(S - U' * B * V) * J = 0 DO 10 I = 1, NS WORK( J+I ) = WORK( J+I ) + S( I ) RESID = MAX( RESID, DASUM( NS, WORK( J+1 ), 1 ) ) J = J + NS 10 CONTINUE * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE IF( ANORM.GE.RESID ) THEN RESID = ( RESID / ANORM ) / ( DBLE( N )*EPS ) ELSE IF( ANORM.LT.ONE ) THEN RESID = ( MIN( RESID, DBLE( N )*ANORM ) / ANORM ) / $ ( DBLE( N )*EPS ) ELSE RESID = MIN( RESID / ANORM, DBLE( N ) ) / $ ( DBLE( N )*EPS ) END IF END IF END IF * RETURN * * End of DBDT05 * END