slasd2.f(3) LAPACK slasd2.f(3)
NAME
slasd2.f -
SYNOPSIS
Functions/Subroutines
subroutine slasd2 (NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO)
SLASD2
Function/Subroutine Documentation
subroutine slasd2 (integerNL, integerNR, integerSQRE, integerK, real, dimension( * )D, real, dimension( * )Z, realALPHA, realBETA, real,
dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )DSIGMA, real, dimension( ldu2, * )U2,
integerLDU2, real, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXP, integer, dimension( * )IDX, integer, dimension( *
)IDXC, integer, dimension( * )IDXQ, integer, dimension( * )COLTYP, integerINFO)
SLASD2
Purpose:
SLASD2 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.
SLASD2 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
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 (N)
On exit Z contains the updating row vector in the secular
equation.
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.
U
U is REAL array, dimension (LDU,N)
On entry U contains the left singular vectors of two
submatrices in the two square blocks with corners at (1,1),
(NL, NL), and (NL+2, NL+2), (N,N).
On exit U contains the trailing (N-K) updated left singular
vectors (those which were deflated) in its last N-K columns.
LDU
LDU is INTEGER
The leading dimension of the array U. LDU >= N.
VT
VT is REAL array, dimension (LDVT,M)
On entry VT**T contains the right singular vectors of two
submatrices in the two square blocks with corners at (1,1),
(NL+1, NL+1), and (NL+2, NL+2), (M,M).
On exit VT**T contains the trailing (N-K) updated right singular
vectors (those which were deflated) in its last N-K columns.
In case SQRE =1, the last row of VT spans the right null
space.
LDVT
LDVT is INTEGER
The leading dimension of the array VT. LDVT >= M.
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.
U2
U2 is REAL array, dimension (LDU2,N)
Contains a copy of the first K-1 left singular vectors which
will be used by SLASD3 in a matrix multiply (SGEMM) to solve
for the new left singular vectors. U2 is arranged into four
blocks. The first block contains a column with 1 at NL+1 and
zero everywhere else; the second block contains non-zero
entries only at and above NL; the third contains non-zero
entries only below NL+1; and the fourth is dense.
LDU2
LDU2 is INTEGER
The leading dimension of the array U2. LDU2 >= N.
VT2
VT2 is REAL array, dimension (LDVT2,N)
VT2**T contains a copy of the first K right singular vectors
which will be used by SLASD3 in a matrix multiply (SGEMM) to
solve for the new right singular vectors. VT2 is arranged into
three blocks. The first block contains a row that corresponds
to the special 0 diagonal element in SIGMA; the second block
contains non-zeros only at and before NL +1; the third block
contains non-zeros only at and after NL +2.
LDVT2
LDVT2 is INTEGER
The leading dimension of the array VT2. LDVT2 >= M.
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.
IDX
IDX is INTEGER array, dimension (N)
This will contain the permutation used to sort the contents of
D into ascending order.
IDXC
IDXC is INTEGER array, dimension (N)
This will contain the permutation used to arrange the columns
of the deflated U matrix into three groups: the first group
contains non-zero entries only at and above NL, the second
contains non-zero entries only below NL+2, and the third is
dense.
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 hlaf 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.
COLTYP
COLTYP is INTEGER array, dimension (N)
As workspace, this will contain a label which will indicate
which of the following types a column in the U2 matrix or a
row in the VT2 matrix is:
1 : non-zero in the upper half only
2 : non-zero in the lower half only
3 : dense
4 : deflated
On exit, it is an array of dimension 4, with COLTYP(I) being
the dimension of the I-th type columns.
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.
Date:
November 2011
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
Definition at line 268 of file slasd2.f.
Author
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Version 3.4.1 Sun May 26 2013 slasd2.f(3)