SRC/slasd1.f(3)

NAME
SRC/slasd1.f

SYNOPSIS

  Functions/Subroutines
subroutine slasd1 (nl, nr, sqre, d, alpha, beta, u, ldu, vt, ldvt, idxq, iwork, work, info)
SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.

Function/Subroutine Documentation

  subroutine slasd1 (integer nl, integer nr, integer sqre, real, dimension( * ) d, real alpha, real beta, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, integer, dimension( * ) idxq, integer, dimension( * ) iwork, real, dimension( * ) work, integer info)

SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.

Purpose:

    !>
    !> SLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B,
    !> where N = NL + NR + 1 and M = N + SQRE. SLASD1 is called from SLASD0.
    !>
    !> A related subroutine SLASD7 handles the case in which the singular
    !> values (and the singular vectors in factored form) are desired.
    !>
    !> SLASD1 computes the SVD as follows:
    !>
    !>               ( D1(in)    0    0       0 )
    !>   B = U(in) * (   Z1**T   a   Z2**T    b ) * VT(in)
    !>               (   0       0   D2(in)   0 )
    !>
    !>     = U(out) * ( D(out) 0) * VT(out)
    !>
    !> where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M
    !> with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
    !> elsewhere; and the entry b is empty if SQRE = 0.
    !>
    !> The left singular vectors of the original matrix are stored in U, and
    !> the transpose of the right singular vectors are stored in VT, and the
    !> singular values are in D.  The algorithm consists of three stages:
    !>
    !>    The first stage consists of deflating the size of the problem
    !>    when there are multiple singular values or when there are zeros in
    !>    the Z vector.  For each such occurrence the dimension of the
    !>    secular equation problem is reduced by one.  This stage is
    !>    performed by the routine SLASD2.
    !>
    !>    The second stage consists of calculating the updated
    !>    singular values. This is done by finding the square roots of the
    !>    roots of the secular equation via the routine SLASD4 (as called
    !>    by SLASD3). This routine also calculates the singular vectors of
    !>    the current problem.
    !>
    !>    The final stage consists of computing the updated singular vectors
    !>    directly using the updated singular values.  The singular vectors
    !>    for the current problem are multiplied with the singular vectors
    !>    from the overall problem.
    !>

Parameters
    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.
    !>

    D

    !>          D is REAL array, dimension (NL+NR+1).
    !>         N = NL+NR+1
    !>         On entry D(1:NL,1:NL) contains the singular values of the
    !>         upper block; and D(NL+2:N) contains the singular values of
    !>         the lower block. On exit D(1:N) contains the singular values
    !>         of the modified matrix.
    !>

    ALPHA

    !>          ALPHA is REAL
    !>         Contains the diagonal element associated with the added row.
    !>

    BETA

    !>          BETA is REAL
    !>         Contains the off-diagonal element associated with the added
    !>         row.
    !>

    U

    !>          U is REAL array, dimension (LDU,N)
    !>         On entry U(1:NL, 1:NL) contains the left singular vectors of
    !>         the upper block; U(NL+2:N, NL+2:N) contains the left singular
    !>         vectors of the lower block. On exit U contains the left
    !>         singular vectors of the bidiagonal matrix.
    !>

    LDU

    !>          LDU is INTEGER
    !>         The leading dimension of the array U.  LDU >= max( 1, N ).
    !>

    VT

    !>          VT is REAL array, dimension (LDVT,M)
    !>         where M = N + SQRE.
    !>         On entry VT(1:NL+1, 1:NL+1)**T contains the right singular
    !>         vectors of the upper block; VT(NL+2:M, NL+2:M)**T contains
    !>         the right singular vectors of the lower block. On exit
    !>         VT**T contains the right singular vectors of the
    !>         bidiagonal matrix.
    !>

    LDVT

    !>          LDVT is INTEGER
    !>         The leading dimension of the array VT.  LDVT >= max( 1, M ).
    !>

    IDXQ

    !>          IDXQ is INTEGER array, dimension (N)
    !>         This contains the permutation which will reintegrate the
    !>         subproblem just solved back into sorted order, i.e.
    !>         D( IDXQ( I = 1, N ) ) will be in ascending order.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (4*N)
    !>

    WORK

    !>          WORK is REAL array, dimension (3*M**2+2*M)
    !>

    INFO

    !>          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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 202 of file slasd1.f.

Author

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