lasd7(3)

NAME
lasd7 - lasd7: D&C step: deflation

SYNOPSIS

  Functions
subroutine dlasd7 (icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw, alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, c, s, info)
DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.
subroutine slasd7 (icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw, alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, c, s, info)
SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.

Detailed Description

Function Documentation

  subroutine dlasd7 (integer icompq, integer nl, integer nr, integer sqre, integer k, double precision, dimension( * ) d, double precision, dimension( * ) z, double precision, dimension( * ) zw, double precision, dimension( * ) vf, double precision, dimension( * ) vfw, double precision, dimension( * ) vl, double precision, dimension( * ) vlw, double precision alpha, double precision beta, double precision, dimension( * ) dsigma, integer, dimension( * ) idx, integer, dimension( * ) idxp, integer, dimension( * ) idxq, integer, dimension( * ) perm, integer givptr, integer, dimension( ldgcol, * ) givcol, integer ldgcol, double precision, dimension( ldgnum, * ) givnum, integer ldgnum, double precision c, double precision s, integer info)

DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.

Purpose:

     DLASD7 merges the two sets of singular values together into a single
     sorted set. Then it tries to deflate the size of the problem. There
     are two ways in which deflation can occur:  when two or more singular
     values are close together or if there is a tiny entry in the Z
     vector. For each such occurrence the order of the related
     secular equation problem is reduced by one.
     DLASD7 is called from DLASD6.

Parameters
    ICOMPQ

              ICOMPQ is INTEGER
              Specifies whether singular vectors are to be computed
              in compact form, as follows:
              = 0: Compute singular values only.
              = 1: Compute singular vectors of upper
                   bidiagonal matrix in compact form.

    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
             Contains the dimension of the non-deflated matrix, this is
             the order of the related secular equation. 1 <= K <=N.

    D

              D is DOUBLE PRECISION array, dimension ( N )
             On entry D contains the singular values of the two submatrices
             to be combined. On exit D contains the trailing (N-K) updated
             singular values (those which were deflated) sorted into
             increasing order.

    Z

              Z is DOUBLE PRECISION array, dimension ( M )
             On exit Z contains the updating row vector in the secular
             equation.

    ZW

              ZW is DOUBLE PRECISION array, dimension ( M )
             Workspace for Z.

    VF

              VF is DOUBLE PRECISION array, dimension ( M )
             On entry, VF(1:NL+1) contains the first components of all
             right singular vectors of the upper block; and VF(NL+2:M)
             contains the first components of all right singular vectors
             of the lower block. On exit, VF contains the first components
             of all right singular vectors of the bidiagonal matrix.

    VFW

              VFW is DOUBLE PRECISION array, dimension ( M )
             Workspace for VF.

    VL

              VL is DOUBLE PRECISION array, dimension ( M )
             On entry, VL(1:NL+1) contains the  last components of all
             right singular vectors of the upper block; and VL(NL+2:M)
             contains the last components of all right singular vectors
             of the lower block. On exit, VL contains the last components
             of all right singular vectors of the bidiagonal matrix.

    VLW

              VLW is DOUBLE PRECISION array, dimension ( M )
             Workspace for VL.

    ALPHA

              ALPHA is DOUBLE PRECISION
             Contains the diagonal element associated with the added row.

    BETA

              BETA is DOUBLE PRECISION
             Contains the off-diagonal element associated with the added
             row.

    DSIGMA

              DSIGMA is DOUBLE PRECISION array, dimension ( N )
             Contains a copy of the diagonal elements (K-1 singular values
             and one zero) in the secular equation.

    IDX

              IDX is INTEGER array, dimension ( N )
             This will contain the permutation used to sort the contents of
             D into ascending order.

    IDXP

              IDXP is INTEGER array, dimension ( N )
             This will contain the permutation used to place deflated
             values of D at the end of the array. On output IDXP(2:K)
             points to the nondeflated D-values and IDXP(K+1:N)
             points to the deflated singular values.

    IDXQ

              IDXQ is INTEGER array, dimension ( N )
             This contains the permutation which separately sorts the two
             sub-problems in D into ascending order.  Note that entries in
             the first half of this permutation must first be moved one
             position backward; and entries in the second half
             must first have NL+1 added to their values.

    PERM

              PERM is INTEGER array, dimension ( N )
             The permutations (from deflation and sorting) to be applied
             to each singular block. Not referenced if ICOMPQ = 0.

    GIVPTR

              GIVPTR is INTEGER
             The number of Givens rotations which took place in this
             subproblem. Not referenced if ICOMPQ = 0.

    GIVCOL

              GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
             Each pair of numbers indicates a pair of columns to take place
             in a Givens rotation. Not referenced if ICOMPQ = 0.

    LDGCOL

              LDGCOL is INTEGER
             The leading dimension of GIVCOL, must be at least N.

    GIVNUM

              GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
             Each number indicates the C or S value to be used in the
             corresponding Givens rotation. Not referenced if ICOMPQ = 0.

    LDGNUM

              LDGNUM is INTEGER
             The leading dimension of GIVNUM, must be at least N.

    C

              C is DOUBLE PRECISION
             C contains garbage if SQRE =0 and the C-value of a Givens
             rotation related to the right null space if SQRE = 1.

    S

              S is DOUBLE PRECISION
             S contains garbage if SQRE =0 and the S-value of a Givens
             rotation related to the right null space if SQRE = 1.

    INFO

              INFO is INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.

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 276 of file dlasd7.f.

  subroutine slasd7 (integer icompq, integer nl, integer nr, integer sqre, integer k, real, dimension( * ) d, real, dimension( * ) z, real, dimension( * ) zw, real, dimension( * ) vf, real, dimension( * ) vfw, real, dimension( * ) vl, real, dimension( * ) vlw, real alpha, real beta, real, dimension( * ) dsigma, integer, dimension( * ) idx, integer, dimension( * ) idxp, integer, dimension( * ) idxq, integer, dimension( * ) perm, integer givptr, integer, dimension( ldgcol, * ) givcol, integer ldgcol, real, dimension( ldgnum, * ) givnum, integer ldgnum, real c, real s, integer info)

SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.

Purpose:

     SLASD7 merges the two sets of singular values together into a single
     sorted set. Then it tries to deflate the size of the problem. There
     are two ways in which deflation can occur:  when two or more singular
     values are close together or if there is a tiny entry in the Z
     vector. For each such occurrence the order of the related
     secular equation problem is reduced by one.
     SLASD7 is called from SLASD6.

Parameters
    ICOMPQ

              ICOMPQ is INTEGER
              Specifies whether singular vectors are to be computed
              in compact form, as follows:
              = 0: Compute singular values only.
              = 1: Compute singular vectors of upper
                   bidiagonal matrix in compact form.

    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
             Contains the dimension of the non-deflated matrix, this is
             the order of the related secular equation. 1 <= K <=N.

    D

              D is REAL array, dimension ( N )
             On entry D contains the singular values of the two submatrices
             to be combined. On exit D contains the trailing (N-K) updated
             singular values (those which were deflated) sorted into
             increasing order.

    Z

              Z is REAL array, dimension ( M )
             On exit Z contains the updating row vector in the secular
             equation.

    ZW

              ZW is REAL array, dimension ( M )
             Workspace for Z.

    VF

              VF is REAL array, dimension ( M )
             On entry, VF(1:NL+1) contains the first components of all
             right singular vectors of the upper block; and VF(NL+2:M)
             contains the first components of all right singular vectors
             of the lower block. On exit, VF contains the first components
             of all right singular vectors of the bidiagonal matrix.

    VFW

              VFW is REAL array, dimension ( M )
             Workspace for VF.

    VL

              VL is REAL array, dimension ( M )
             On entry, VL(1:NL+1) contains the  last components of all
             right singular vectors of the upper block; and VL(NL+2:M)
             contains the last components of all right singular vectors
             of the lower block. On exit, VL contains the last components
             of all right singular vectors of the bidiagonal matrix.

    VLW

              VLW is REAL array, dimension ( M )
             Workspace for VL.

    ALPHA

              ALPHA is REAL
             Contains the diagonal element associated with the added row.

    BETA

              BETA is REAL
             Contains the off-diagonal element associated with the added
             row.

    DSIGMA

              DSIGMA is REAL array, dimension ( N )
             Contains a copy of the diagonal elements (K-1 singular values
             and one zero) in the secular equation.

    IDX

              IDX is INTEGER array, dimension ( N )
             This will contain the permutation used to sort the contents of
             D into ascending order.

    IDXP

              IDXP is INTEGER array, dimension ( N )
             This will contain the permutation used to place deflated
             values of D at the end of the array. On output IDXP(2:K)
             points to the nondeflated D-values and IDXP(K+1:N)
             points to the deflated singular values.

    IDXQ

              IDXQ is INTEGER array, dimension ( N )
             This contains the permutation which separately sorts the two
             sub-problems in D into ascending order.  Note that entries in
             the first half of this permutation must first be moved one
             position backward; and entries in the second half
             must first have NL+1 added to their values.

    PERM

              PERM is INTEGER array, dimension ( N )
             The permutations (from deflation and sorting) to be applied
             to each singular block. Not referenced if ICOMPQ = 0.

    GIVPTR

              GIVPTR is INTEGER
             The number of Givens rotations which took place in this
             subproblem. Not referenced if ICOMPQ = 0.

    GIVCOL

              GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
             Each pair of numbers indicates a pair of columns to take place
             in a Givens rotation. Not referenced if ICOMPQ = 0.

    LDGCOL

              LDGCOL is INTEGER
             The leading dimension of GIVCOL, must be at least N.

    GIVNUM

              GIVNUM is REAL array, dimension ( LDGNUM, 2 )
             Each number indicates the C or S value to be used in the
             corresponding Givens rotation. Not referenced if ICOMPQ = 0.

    LDGNUM

              LDGNUM is INTEGER
             The leading dimension of GIVNUM, must be at least N.

    C

              C is REAL
             C contains garbage if SQRE =0 and the C-value of a Givens
             rotation related to the right null space if SQRE = 1.

    S

              S is REAL
             S contains garbage if SQRE =0 and the S-value of a Givens
             rotation related to the right null space if SQRE = 1.

    INFO

              INFO is INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.

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 276 of file slasd7.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.