slasd1.f(3)

NAME
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 (integerNL, integerNR, integerSQRE, real, dimension( * )D, realALPHA, realBETA, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, integer, dimension( * )IDXQ, integer, dimension( * )IWORK, real, dimension( * )WORK, integerINFO)

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 occurence 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.

Date:
    September 2012

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

Definition at line 204 of file slasd1.f.

Author

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