lasd3(3)

NAME
lasd3 - lasd3: D&C step: secular equation

SYNOPSIS

  Functions

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.
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.

Detailed Description

Function Documentation

  subroutine dlasd3 (integer nl, integer nr, integer sqre, integer k, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) dsigma, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldu2, * ) u2, integer ldu2, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( ldvt2, * ) vt2, integer ldvt2, integer, dimension( * ) idxc, integer, dimension( * ) ctot, double precision, dimension( * ) z, integer 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.

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.
    !>
    !> 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 (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.

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

  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

Author

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