Ubuntu Manpage: lasd7 - lasd7: D&C step: deflation

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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 is INTEGER
The row dimension of the upper block. NL >= 1.

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

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

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

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 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 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 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

NL is INTEGER
The row dimension of the upper block. NL >= 1.

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

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

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

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 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

IDXQ

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 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 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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