NAME

       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 (integerNL, integerNR, integerSQRE, integerK, real, dimension( * )D, real,
       dimension( ldq, * )Q, integerLDQ, real, dimension( * )DSIGMA, real, dimension( ldu, * )U,
       integerLDU, real, dimension( ldu2, * )U2, integerLDU2, real, dimension( ldvt, * )VT,
       integerLDVT, real, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXC,
       integer, dimension( * )CTOT, real, dimension( * )Z, integerINFO)
       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.

            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.

            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 at least (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.

       Date:
           September 2012

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

       Definition at line 224 of file slasd3.f.

Author

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