SLASD3 - find all the square roots of the roots of the
secular equation, 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 sec
ular 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.
On exit the square roots of the roots of the secu
lar 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) REAL array, dimension(K) The first K
elements of this array contain the old roots of the
deflated updating problem. These are the poles of
the secular equation.
U (input) 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 prob
lem.
LDU2 (input) INTEGER
The leading dimension of the array U2. LDU2 >= N.
VT (input) REAL array, dimension (LDVT, M)
The last M - K columns of VT' contain the deflated
right singular vectors.
LDVT (input) INTEGER
The leading dimension of the array VT. LDVT >= N.
VT2 (input) REAL array, dimension (LDVT2, N)
The first K columns of VT2' contain the non-
deflated right singular vectors for the split prob
lem.
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.
must be likewise permuted before the matrix multi
plies 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) REAL array, dimension (K)
The first K elements of this array contain the com
ponents of the deflation-adjusted updating row vec
tor.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
> 0: if INFO = 1, an singular value did not con
verge
FURTHER DETAILS
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, Uni
versity of
California at Berkeley, USA
Man(1) output converted with
man2html