ESMF_DLASDA Subroutine

subroutine ESMF_DLASDA(ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)

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

\verbatim

Using a divide and conquer approach, ESMF_DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes the singular values in the SVD B = U * S * VT. The orthogonal matrices U and VT are optionally computed in compact form.

A related subroutine, DLASD0, computes the singular values and the singular vectors in explicit form. \endverbatim \param[in] ICOMPQ \verbatim ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in compact form, as follows = 0: Compute singular values only. = 1: Compute singular vectors of upper bidiagonal matrix in compact form. \endverbatim

\param[in] SMLSIZ \verbatim SMLSIZ is INTEGER The maximum size of the subproblems at the bottom of the computation tree. \endverbatim

\param[in] N \verbatim N is INTEGER The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D. \endverbatim

\param[in] SQRE \verbatim SQRE is INTEGER Specifies the column dimension of the bidiagonal matrix. = 0: The bidiagonal matrix has column dimension M = N; = 1: The bidiagonal matrix has column dimension M = N + 1. \endverbatim

\param[in,out] D \verbatim D is DOUBLE PRECISION array, dimension ( N ) On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values. \endverbatim

\param[in] E \verbatim E is DOUBLE PRECISION array, dimension ( M-1 ) Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed. \endverbatim

\param[out] U \verbatim U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left singular vector matrices of all subproblems at the bottom level. \endverbatim

\param[in] LDU \verbatim LDU is INTEGER, LDU = > N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z. \endverbatim

\param[out] VT \verbatim VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right singular vector matrices of all subproblems at the bottom level. \endverbatim

\param[out] K \verbatim K is INTEGER array, dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th secular equation on the computation tree. \endverbatim

\param[out] DIFL \verbatim DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ), where NLVL = floor(log_2 (N/SMLSIZ))). \endverbatim

\param[out] DIFR \verbatim DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) record distances between singular values on the I-th level and singular values on the (I -1)-th level, and DIFR(1:N, 2 * I ) contains the normalizing factors for the right singular vector matrix. See ESMF_DLASD8 for details. \endverbatim

\param[out] Z \verbatim Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. The first K elements of Z(1, I) contain the components of the deflation-adjusted updating row vector for subproblems on the I-th level. \endverbatim

\param[out] POLES \verbatim POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2I - 1) and POLES(1, 2I) contain the new and old singular values involved in the secular equations on the I-th level. \endverbatim

\param[out] GIVPTR \verbatim GIVPTR is INTEGER array, dimension ( N ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records the number of Givens rotations performed on the I-th problem on the computation tree. \endverbatim

\param[out] GIVCOL \verbatim GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVCOL(1, 2 I - 1) and GIVCOL(1, 2 I) record the locations of Givens rotations performed on the I-th level on the computation tree. \endverbatim

\param[in] LDGCOL \verbatim LDGCOL is INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM. \endverbatim

\param[out] PERM \verbatim PERM is INTEGER array, dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records permutations done on the I-th level of the computation tree. \endverbatim

\param[out] GIVNUM \verbatim GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVNUM(1, 2 I - 1) and GIVNUM(1, 2 I) record the C- and S- values of Givens rotations performed on the I-th level on the computation tree. \endverbatim

\param[out] C \verbatim C is DOUBLE PRECISION array, dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the I-th subproblem is not square, on exit, C( I ) contains the C-value of a Givens rotation related to the right null space of the I-th subproblem. \endverbatim

\param[out] S \verbatim S is DOUBLE PRECISION array, dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the I-th subproblem is not square, on exit, S( I ) contains the S-value of a Givens rotation related to the right null space of the I-th subproblem. \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). \endverbatim

\param[out] IWORK \verbatim IWORK is INTEGER array. Dimension must be at least (7 * N). \endverbatim

\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value 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