dlasd3.f(3)

NAME
dlasd3.f -

SYNOPSIS

  Functions/Subroutines

subroutine dlasd3 (NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO)
DLASD3 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 dlasd3 (integerNL, integerNR, integerSQRE, integerK, double precision, dimension( * )D, double precision, dimension( ldq, * )Q, integerLDQ, double precision, dimension( * )DSIGMA, double precision, dimension( ldu, * )U, integerLDU, double precision, dimension( ldu2, * )U2, integerLDU2, double precision, dimension( ldvt, * )VT, integerLDVT, double precision, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXC, integer, dimension( * )CTOT, double precision, dimension( * )Z, integerINFO)

DLASD3 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:

     DLASD3 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 DLASD4 and then updates the singular
     vectors by matrix multiplication.

     This code makes very mild assumptions about floating point
     arithmetic. It will work on machines with a guard digit in
     add/subtract, or on those binary machines without guard digits
     which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
     It could conceivably fail on hexadecimal or decimal machines
     without guard digits, but we know of none.

     DLASD3 is called from DLASD1.

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 DOUBLE PRECISION array, dimension(K)
             On exit the square roots of the roots of the secular equation,
             in ascending order.

    Q

              Q is DOUBLE PRECISION array,
                         dimension at least (LDQ,K).

    LDQ

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

    DSIGMA

              DSIGMA is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DLASD4
             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 DOUBLE PRECISION 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.

Date:
    September 2012

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

Definition at line 224 of file dlasd3.f.

Author

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