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dlasd1 examples
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Man Page Details
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NAME
       DLASD1 - the SVD of an upper bidiagonal N-by-M matrix B,

SYNOPSIS
       SUBROUTINE DLASD1( NL,  NR,  SQRE,  D,  ALPHA,  BETA, U, LDU, VT, LDVT,
                          IDXQ, IWORK, WORK, INFO )

           INTEGER        INFO, LDU, LDVT, NL, NR, SQRE

           DOUBLE         PRECISION ALPHA, BETA

           INTEGER        IDXQ( * ), IWORK( * )

           DOUBLE         PRECISION D( * ), U( LDU, * ), VT( LDVT, * ),  WORK(
                          * )

  Purpose
  =======

  DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B,
  where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0.

  A related subroutine DLASD7 handles the case in which the singular
  values (and the singular vectors in factored form) are desired.

  DLASD1 computes the SVD as follows:

                ( D1(in)  0    0     0 )
    B = U(in) * (   Z1'   a   Z2'    b ) * VT(in)
                (   0     0   D2(in) 0 )

      = U(out) * ( D(out) 0) * VT(out)

  where Z' = (Z1' a Z2' b) = u' VT', 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 DLASD2.

     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 DLASD4 (as called
     by DLASD3). 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.

  Arguments
  =========

  NL     (input) INTEGER
         The row dimension of the upper block.  NL >= 1.

  NR     (input) INTEGER
         The row dimension of the lower block.  NR >= 1.

  SQRE   (input) 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      (input/output) DOUBLE PRECISION array,
                        dimension (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  (input) DOUBLE PRECISION
         Contains the diagonal element associated with the added row.

  BETA   (input) DOUBLE PRECISION
         Contains the off-diagonal element associated with the added
         row.

  U      (input/output) DOUBLE PRECISION 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    (input) INTEGER
         The leading dimension of the array U.  LDU >= max( 1, N ).

  VT     (input/output) DOUBLE PRECISION array, dimension(LDVT,M)
         where M = N + SQRE.
         On entry VT(1:NL+1, 1:NL+1)' contains the right singular
         vectors of the upper block; VT(NL+2:M, NL+2:M)' contains
         the right singular vectors of the lower block. On exit
         VT' contains the right singular vectors of the
         bidiagonal matrix.

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

  IDXQ  (output) 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  (workspace) INTEGER array, dimension( 4 * N )

  WORK   (workspace) DOUBLE PRECISION array, dimension( 3*M**2 + 2*M )

  INFO   (output) INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if INFO = 1, an singular value did not converge

  Further Details
  ===============

  Based on contributions by
     Ming Gu and Huan Ren, Computer Science Division, University of
     California at Berkeley, USA

