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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 val-
       ues (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  else-
       where; 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/output) DOUBLE PRECISION
              Contains the diagonal element associated with the added row.

       BETA   (input/output) 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 subprob-
             lem 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

