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

  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

Author

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