SRC/slalsa.f(3)

NAME
SRC/slalsa.f

SYNOPSIS

  Functions/Subroutines
subroutine slalsa (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)
SLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.

Function/Subroutine Documentation

  subroutine slalsa (integer icompq, integer smlsiz, integer n, integer nrhs, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldbx, * ) bx, integer ldbx, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldu, * ) vt, integer, dimension( * ) k, real, dimension( ldu, * ) difl, real, dimension( ldu, * ) difr, real, dimension( ldu, * ) z, real, dimension( ldu, * ) poles, integer, dimension( * ) givptr, integer, dimension( ldgcol, * ) givcol, integer ldgcol, integer, dimension( ldgcol, * ) perm, real, dimension( ldu, * ) givnum, real, dimension( * ) c, real, dimension( * ) s, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.

Purpose:

     SLALSA is an intermediate 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 orthogonal
     matrices.).
     If ICOMPQ = 0, SLALSA applies the inverse of the left singular vector
     matrix of an upper bidiagonal matrix to the right hand side; and if
     ICOMPQ = 1, SLALSA applies the right singular vector matrix to the
     right hand side. The singular vector matrices were generated in
     compact form by SLALSA.

Parameters
    ICOMPQ

              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

    SMLSIZ

              SMLSIZ is INTEGER
             The maximum size of the subproblems at the bottom of the
             computation tree.

    N

              N is INTEGER
             The row and column dimensions of the upper bidiagonal matrix.

    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 in the calling subprogram.
             LDB must be at least max(1,MAX( M, N ) ).

    BX

              BX is REAL array, dimension ( LDBX, NRHS )
             On exit, the result of applying the left or right singular
             vector matrix to B.

    LDBX

              LDBX is INTEGER
             The leading dimension of BX.

    U

              U is REAL array, dimension ( LDU, SMLSIZ ).
             On entry, U contains the left singular vector matrices of all
             subproblems at the bottom level.

    LDU

              LDU is INTEGER, LDU = > N.
             The leading dimension of arrays U, VT, DIFL, DIFR,
             POLES, GIVNUM, and Z.

    VT

              VT is REAL array, dimension ( LDU, SMLSIZ+1 ).
             On entry, VT**T contains the right singular vector matrices of
             all subproblems at the bottom level.

    K

              K is INTEGER array, dimension ( N ).

    DIFL

              DIFL is REAL array, dimension ( LDU, NLVL ).
             where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.

    DIFR

              DIFR is REAL 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.

    Z

              Z is REAL 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.

    POLES

              POLES is REAL 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.

    GIVPTR

              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.

    GIVCOL

              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.

    LDGCOL

              LDGCOL is INTEGER, LDGCOL = > N.
             The leading dimension of arrays GIVCOL and PERM.

    PERM

              PERM is INTEGER array, dimension ( LDGCOL, NLVL ).
             On entry, PERM(*, I) records permutations done on the I-th
             level of the computation tree.

    GIVNUM

              GIVNUM is REAL 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.

    C

              C is REAL 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.

    S

              S is REAL 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.

    WORK

              WORK is REAL array, dimension (N)

    IWORK

              IWORK is INTEGER array, dimension (3*N)

    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.

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

Definition at line 263 of file slalsa.f.

Author

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