ESMF_DLASDQ Subroutine

subroutine ESMF_DLASDQ(UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)

\brief \b ESMF_DLASDQ \htmlonly Download ESMF_DLASDQ + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired. Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that B = Q * S * PT (PT denotes the transpose of P). The singular values S are overwritten on D.

The input matrix U is changed to U * Q if desired. The input matrix VT is changed to PT * VT if desired. The input matrix C is changed to QT * C if desired.

See “Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy,” by J. Demmel and W. Kahan, LAPACK Working Note #3, for a detailed description of the algorithm. \endverbatim \param[in] UPLO \verbatim UPLO is CHARACTER*1 On entry, UPLO specifies whether the input bidiagonal matrix is upper or lower bidiagonal, and wether it is square are not. UPLO = ‘U’ or ‘u’ B is upper bidiagonal. UPLO = ‘L’ or ‘l’ B is lower bidiagonal. \endverbatim

\param[in] SQRE \verbatim SQRE is INTEGER = 0: then the input matrix is N-by-N. = 1: then the input matrix is N-by-(N+1) if UPLU = ‘U’ and (N+1)-by-N if UPLU = ‘L’.

   The bidiagonal matrix has
   N = NL + NR + 1 rows and
   M = N + SQRE >= N columns.

\endverbatim

\param[in] N \verbatim N is INTEGER On entry, N specifies the number of rows and columns in the matrix. N must be at least 0. \endverbatim

\param[in] NCVT \verbatim NCVT is INTEGER On entry, NCVT specifies the number of columns of the matrix VT. NCVT must be at least 0. \endverbatim

\param[in] NRU \verbatim NRU is INTEGER On entry, NRU specifies the number of rows of the matrix U. NRU must be at least 0. \endverbatim

\param[in] NCC \verbatim NCC is INTEGER On entry, NCC specifies the number of columns of the matrix C. NCC must be at least 0. \endverbatim

\param[in,out] D \verbatim D is DOUBLE PRECISION array, dimension (N) On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in ascending order. \endverbatim

\param[in,out] E \verbatim E is DOUBLE PRECISION array. dimension is (N-1) if SQRE = 0 and N if SQRE = 1. On entry, the entries of E contain the offdiagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, E will contain 0. If the algorithm does not converge, D and E will contain the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input. \endverbatim

\param[in,out] VT \verbatim VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) On entry, contains a matrix which on exit has been premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). \endverbatim

\param[in] LDVT \verbatim LDVT is INTEGER On entry, LDVT specifies the leading dimension of VT as declared in the calling (sub) program. LDVT must be at least 1. If NCVT is nonzero LDVT must also be at least N. \endverbatim

\param[in,out] U \verbatim U is DOUBLE PRECISION array, dimension (LDU, N) On entry, contains a matrix which on exit has been postmultiplied by Q, dimension NRU-by-N if SQRE = 0 and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). \endverbatim

\param[in] LDU \verbatim LDU is INTEGER On entry, LDU specifies the leading dimension of U as declared in the calling (sub) program. LDU must be at least max( 1, NRU ) . \endverbatim

\param[in,out] C \verbatim C is DOUBLE PRECISION array, dimension (LDC, NCC) On entry, contains an N-by-NCC matrix which on exit has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). \endverbatim

\param[in] LDC \verbatim LDC is INTEGER On entry, LDC specifies the leading dimension of C as declared in the calling (sub) program. LDC must be at least 1. If NCC is nonzero, LDC must also be at least N. \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension (4*N) Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at least 2. \endverbatim

\param[out] INFO \verbatim INFO is INTEGER On exit, a value of 0 indicates a successful exit. If INFO < 0, argument number -INFO is illegal. If INFO > 0, the algorithm did not converge, and INFO specifies how many superdiagonals did not converge. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup auxOTHERauxiliary \par Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA

Arguments