ESMF_DLALS0 Subroutine

subroutine ESMF_DLALS0(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO)

\brief \b ESMF_DLALS0 \htmlonly Download ESMF_DLALS0 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach.

For the left singular vector matrix, three types of orthogonal matrices are involved:

(1L) Givens rotations: the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM.

(2L) Permutation. The (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row.

(3L) The left singular vector matrix of the remaining matrix.

For the right singular vector matrix, four types of orthogonal matrices are involved:

(1R) The right singular vector matrix of the remaining matrix.

(2R) If SQRE = 1, one extra Givens rotation to generate the right null space.

(3R) The inverse transformation of (2L).

(4R) The inverse transformation of (1L). \endverbatim \param[in] ICOMPQ \verbatim ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix. \endverbatim

\param[in] NL \verbatim NL is INTEGER The row dimension of the upper block. NL >= 1. \endverbatim

\param[in] NR \verbatim NR is INTEGER The row dimension of the lower block. NR >= 1. \endverbatim

\param[in] SQRE \verbatim SQRE is INTEGER = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

    The bidiagonal matrix has row dimension N = NL + NR + 1,
    and column dimension M = N + SQRE.

\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. LDB must be at least max(1,MAX( M, N ) ). \endverbatim

\param[out] BX \verbatim BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) \endverbatim

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

\param[in] PERM \verbatim PERM is INTEGER array, dimension ( N ) The permutations (from deflation and sorting) applied to the two blocks. \endverbatim

\param[in] GIVPTR \verbatim GIVPTR is INTEGER The number of Givens rotations which took place in this subproblem. \endverbatim

\param[in] GIVCOL \verbatim GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation. \endverbatim

\param[in] LDGCOL \verbatim LDGCOL is INTEGER The leading dimension of GIVCOL, must be at least N. \endverbatim

\param[in] GIVNUM \verbatim GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value used in the corresponding Givens rotation. \endverbatim

\param[in] LDGNUM \verbatim LDGNUM is INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K. \endverbatim

\param[in] POLES \verbatim POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation. \endverbatim

\param[in] DIFL \verbatim DIFL is DOUBLE PRECISION array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value. \endverbatim

\param[in] DIFR \verbatim DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector. \endverbatim

\param[in] Z \verbatim Z is DOUBLE PRECISION array, dimension ( K ) Contain the components of the deflation-adjusted updating row vector. \endverbatim

\param[in] K \verbatim K is INTEGER Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N. \endverbatim

\param[in] C \verbatim C is DOUBLE PRECISION C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1. \endverbatim

\param[in] S \verbatim S is DOUBLE PRECISION S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1. \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension ( K ) \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