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## slasd3()

subroutine slasd3 | ( | integer | nl,
|  | integer | nr,
|  | integer | sqre,
|  | integer | k,
|  | real, dimension( * ) | d,
|  | real, dimension( ldq, * ) | q,
|  | integer | ldq,
|  | real, dimension( * ) | dsigma,
|  | real, dimension( ldu, * ) | u,
|  | integer | ldu,
|  | real, dimension( ldu2, * ) | u2,
|  | integer | ldu2,
|  | real, dimension( ldvt, * ) | vt,
|  | integer | ldvt,
|  | real, dimension( ldvt2, * ) | vt2,
|  | integer | ldvt2,
|  | integer, dimension( * ) | idxc,
|  | integer, dimension( * ) | ctot,
|  | real, dimension( * ) | z,
|  | integer | info )

SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Download SLASD3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> SLASD3 finds all the square roots of the roots of the secular
      !> equation, as defined by the values in D and Z.  It makes the
      !> appropriate calls to SLASD4 and then updates the singular
      !> vectors by matrix multiplication.
      !>
      !> SLASD3 is called from SLASD1.
      !>

Parameters

  [in]

  NL

      !>          NL is INTEGER
      !>         The row dimension of the upper block.  NL >= 1.
      !>

  [in]

  NR

      !>          NR is INTEGER
      !>         The row dimension of the lower block.  NR >= 1.
      !>

  [in]

  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 N = NL + NR + 1 rows and
      !>         M = N + SQRE >= N columns.
      !>

  [in]

  K

      !>          K is INTEGER
      !>         The size of the secular equation, 1 =< K = < N.
      !>

  [out]

  D

      !>          D is REAL array, dimension(K)
      !>         On exit the square roots of the roots of the secular equation,
      !>         in ascending order.
      !>

  [out]

  Q

      !>          Q is REAL array, dimension (LDQ,K)
      !>

  [in]

  LDQ

      !>          LDQ is INTEGER
      !>         The leading dimension of the array Q.  LDQ >= K.
      !>

  [in]

  DSIGMA

      !>          DSIGMA is REAL array, dimension(K)
      !>         The first K elements of this array contain the old roots
      !>         of the deflated updating problem.  These are the poles
      !>         of the secular equation.
      !>

  [out]

  U

      !>          U is REAL array, dimension (LDU, N)
      !>         The last N - K columns of this matrix contain the deflated
      !>         left singular vectors.
      !>

  [in]

  LDU

      !>          LDU is INTEGER
      !>         The leading dimension of the array U.  LDU >= N.
      !>

  [in]

  U2

      !>          U2 is REAL array, dimension (LDU2, N)
      !>         The first K columns of this matrix contain the non-deflated
      !>         left singular vectors for the split problem.
      !>

  [in]

  LDU2

      !>          LDU2 is INTEGER
      !>         The leading dimension of the array U2.  LDU2 >= N.
      !>

  [out]

  VT

      !>          VT is REAL array, dimension (LDVT, M)
      !>         The last M - K columns of VT**T contain the deflated
      !>         right singular vectors.
      !>

  [in]

  LDVT

      !>          LDVT is INTEGER
      !>         The leading dimension of the array VT.  LDVT >= N.
      !>

  [in,out]

  VT2

      !>          VT2 is REAL array, dimension (LDVT2, N)
      !>         The first K columns of VT2**T contain the non-deflated
      !>         right singular vectors for the split problem.
      !>

  [in]

  LDVT2

      !>          LDVT2 is INTEGER
      !>         The leading dimension of the array VT2.  LDVT2 >= N.
      !>

  [in]

  IDXC

      !>          IDXC is INTEGER array, dimension (N)
      !>         The permutation used to arrange the columns of U (and rows of
      !>         VT) into three groups:  the first group contains non-zero
      !>         entries only at and above (or before) NL +1; the second
      !>         contains non-zero entries only at and below (or after) NL+2;
      !>         and the third is dense. The first column of U and the row of
      !>         VT are treated separately, however.
      !>
      !>         The rows of the singular vectors found by SLASD4
      !>         must be likewise permuted before the matrix multiplies can
      !>         take place.
      !>

  [in]

  CTOT

      !>          CTOT is INTEGER array, dimension (4)
      !>         A count of the total number of the various types of columns
      !>         in U (or rows in VT), as described in IDXC. The fourth column
      !>         type is any column which has been deflated.
      !>

  [in,out]

  Z

      !>          Z is REAL array, dimension (K)
      !>         The first K elements of this array contain the components
      !>         of the deflation-adjusted updating row vector.
      !>

  [out]

  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