SLASD3(1) LAPACK auxiliary routine (version 3.2) SLASD3(1)NAME
SLASD3 - finds all the square roots of the roots of the secular equa‐
tion, as defined by the values in D and Z
SYNOPSIS
SUBROUTINE SLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2,
LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO )
INTEGER INFO, K, LDQ, LDU, LDU2, LDVT, LDVT2, NL, NR, SQRE
INTEGER CTOT( * ), IDXC( * )
REAL D( * ), DSIGMA( * ), Q( LDQ, * ), U( LDU, * ), U2(
LDU2, * ), VT( LDVT, * ), VT2( LDVT2, * ), Z( * )
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.
This code makes very mild assumptions about floating point arithmetic.
It will work on machines with a guard digit in add/subtract, or on
those binary machines without guard digits which subtract like the Cray
XMP, Cray YMP, Cray C 90, or Cray 2. It could conceivably fail on
hexadecimal or decimal machines without guard digits, but we know of
none.
SLASD3 is called from SLASD1.
ARGUMENTS
NL (input) INTEGER
The row dimension of the upper block. NL >= 1.
NR (input) INTEGER
The row dimension of the lower block. NR >= 1.
SQRE (input) 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 (input) INTEGER
The size of the secular equation, 1 =< K = < N.
D (output) REAL array, dimension(K)
On exit the square roots of the roots of the secular equation,
in ascending order.
Q (workspace) REAL array,
dimension at least (LDQ,K).
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= K. DSIGMA
(input/output) REAL array, dimension(K) The first K elements of
this array contain the old roots of the deflated updating prob‐
lem. These are the poles of the secular equation.
U (output) REAL array, dimension (LDU, N)
The last N - K columns of this matrix contain the deflated left
singular vectors.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= N.
U2 (input) REAL array, dimension (LDU2, N)
The first K columns of this matrix contain the non-deflated left
singular vectors for the split problem.
LDU2 (input) INTEGER
The leading dimension of the array U2. LDU2 >= N.
VT (output) REAL array, dimension (LDVT, M)
The last M - K columns of VT' contain the deflated right singu‐
lar vectors.
LDVT (input) INTEGER
The leading dimension of the array VT. LDVT >= N.
VT2 (input/output) REAL array, dimension (LDVT2, N)
The first K columns of VT2' contain the non-deflated right sin‐
gular vectors for the split problem.
LDVT2 (input) INTEGER
The leading dimension of the array VT2. LDVT2 >= N.
IDXC (input) 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 mul‐
tiplies can take place.
CTOT (input) 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 (input/output) REAL array, dimension (K)
The first K elements of this array contain the components of the
deflation-adjusted updating row vector.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an singular value did not converge
FURTHER DETAILS
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
LAPACK auxiliary routine (versioNovember 2008 SLASD3(1)
