ESMF_DLALSA Subroutine

subroutine ESMF_DLALSA(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)

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

\verbatim

ESMF_DLALSA is an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.).

If ICOMPQ = 0, ESMF_DLALSA applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ = 1, ESMF_DLALSA applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in compact form by ESMF_DLALSA. \endverbatim \param[in] ICOMPQ \verbatim ICOMPQ is INTEGER Specifies whether the left or the right singular vector matrix is involved. = 0: Left singular vector matrix = 1: Right singular vector matrix \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 and column dimensions of the upper bidiagonal matrix. \endverbatim

\param[in] NRHS \verbatim NRHS is INTEGER The number of columns of B and BX. NRHS must be at least 1. \endverbatim

\param[in,out] B \verbatim B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N. \endverbatim

\param[in] LDB \verbatim LDB is INTEGER The leading dimension of B in the calling subprogram. LDB must be at least max(1,MAX( M, N ) ). \endverbatim

\param[out] BX \verbatim BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) On exit, the result of applying the left or right singular vector matrix to B. \endverbatim

\param[in] LDBX \verbatim LDBX is INTEGER The leading dimension of BX. \endverbatim

\param[in] U \verbatim U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). On entry, 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[in] VT \verbatim VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). On entry, VT**T contains the right singular vector matrices of all subproblems at the bottom level. \endverbatim

\param[in] K \verbatim K is INTEGER array, dimension ( N ). \endverbatim

\param[in] DIFL \verbatim DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ). where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. \endverbatim

\param[in] DIFR \verbatim DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). On entry, DIFL(, I) and DIFR(, 2 * I -1) record distances between singular values on the I-th level and singular values on the (I -1)-th level, and DIFR(*, 2 * I) record the normalizing factors of the right singular vectors matrices of subproblems on I-th level. \endverbatim

\param[in] Z \verbatim Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ). On entry, Z(1, I) contains the components of the deflation- adjusted updating row vector for subproblems on the I-th level. \endverbatim

\param[in] POLES \verbatim POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old singular values involved in the secular equations on the I-th level. \endverbatim

\param[in] GIVPTR \verbatim GIVPTR is INTEGER array, dimension ( N ). On entry, GIVPTR( I ) records the number of Givens rotations performed on the I-th problem on the computation tree. \endverbatim

\param[in] GIVCOL \verbatim GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records 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[in] PERM \verbatim PERM is INTEGER array, dimension ( LDGCOL, NLVL ). On entry, PERM(*, I) records permutations done on the I-th level of the computation tree. \endverbatim

\param[in] GIVNUM \verbatim GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). On entry, GIVNUM(, 2 I -1 : 2 * I) records the C- and S- values of Givens rotations performed on the I-th level on the computation tree. \endverbatim

\param[in] C \verbatim C is DOUBLE PRECISION array, dimension ( N ). On entry, if the I-th subproblem is not square, C( I ) contains the C-value of a Givens rotation related to the right null space of the I-th subproblem. \endverbatim

\param[in] S \verbatim S is DOUBLE PRECISION array, dimension ( N ). On entry, if the I-th subproblem is not square, 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. The dimension must be at least N. \endverbatim

\param[out] IWORK \verbatim IWORK is INTEGER array. The dimension must be at least 3 * N \endverbatim

\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup doubleOTHERcomputational \par Contributors:

Ming Gu and Ren-Cang Li, Computer Science Division, University of
  California at Berkeley, USA \n
Osni Marques, LBNL/NERSC, USA \n

Arguments