SRC/slasd3.f(3)

NAME
SRC/slasd3.f

SYNOPSIS

  Functions/Subroutines
subroutine slasd3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2, vt, ldvt, vt2, ldvt2, idxc, ctot, z, 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.

Function/Subroutine Documentation

  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.

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

    K

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

    D

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

    Q

              Q is REAL array, dimension (LDQ,K)

    LDQ

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

    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.

    U

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

    LDU

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

    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.

    LDU2

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

    VT

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

    LDVT

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

    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.

    LDVT2

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

    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.

    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.

    Z

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

    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 214 of file slasd3.f.

Author

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