slals0.f(3)

NAME
slals0.f -

SYNOPSIS

  Functions/Subroutines
subroutine slals0 (ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO)
SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

Function/Subroutine Documentation

  subroutine slals0 (integerICOMPQ, integerNL, integerNR, integerSQRE, integerNRHS, real, dimension( ldb, * )B, integerLDB, real, dimension( ldbx, * )BX, integerLDBX, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, real, dimension( ldgnum, * )GIVNUM, integerLDGNUM, real, dimension( ldgnum, * )POLES, real, dimension( * )DIFL, real, dimension( ldgnum, * )DIFR, real, dimension( * )Z, integerK, realC, realS, real, dimension( * )WORK, integerINFO)

SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.

Purpose:

     SLALS0 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).

Parameters:
    ICOMPQ

              ICOMPQ is INTEGER
             Specifies whether singular vectors are to be computed in
             factored form:
             = 0: Left singular vector matrix.
             = 1: Right singular vector matrix.

    NL

              NL is INTEGER
             The row dimension of the upper block. NL >= 1.

    NR

              NR is INTEGER
             The row dimension of the lower block. NR >= 1.

    SQRE

              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.

    NRHS

              NRHS is INTEGER
             The number of columns of B and BX. NRHS must be at least 1.

    B

              B is REAL 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.

    LDB

              LDB is INTEGER
             The leading dimension of B. LDB must be at least
             max(1,MAX( M, N ) ).

    BX

              BX is REAL array, dimension ( LDBX, NRHS )

    LDBX

              LDBX is INTEGER
             The leading dimension of BX.

    PERM

              PERM is INTEGER array, dimension ( N )
             The permutations (from deflation and sorting) applied
             to the two blocks.

    GIVPTR

              GIVPTR is INTEGER
             The number of Givens rotations which took place in this
             subproblem.

    GIVCOL

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

    LDGCOL

              LDGCOL is INTEGER
             The leading dimension of GIVCOL, must be at least N.

    GIVNUM

              GIVNUM is REAL array, dimension ( LDGNUM, 2 )
             Each number indicates the C or S value used in the
             corresponding Givens rotation.

    LDGNUM

              LDGNUM is INTEGER
             The leading dimension of arrays DIFR, POLES and
             GIVNUM, must be at least K.

    POLES

              POLES is REAL 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.

    DIFL

              DIFL is REAL 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.

    DIFR

              DIFR is REAL 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.

    Z

              Z is REAL array, dimension ( K )
             Contain the components of the deflation-adjusted updating row
             vector.

    K

              K is INTEGER
             Contains the dimension of the non-deflated matrix,
             This is the order of the related secular equation. 1 <= K <=N.

    C

              C is REAL
             C contains garbage if SQRE =0 and the C-value of a Givens
             rotation related to the right null space if SQRE = 1.

    S

              S is REAL
             S contains garbage if SQRE =0 and the S-value of a Givens
             rotation related to the right null space if SQRE = 1.

    WORK

              WORK is REAL array, dimension ( K )

    INFO

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

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

Definition at line 267 of file slals0.f.

Author

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