slasd3.f (3)  Linux Manuals
NAME
slasd3.f 
SYNOPSIS
Functions/Subroutines
subroutine slasd3 (NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO)
SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.
Function/Subroutine Documentation
subroutine slasd3 (integerNL, integerNR, integerSQRE, integerK, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, real, dimension( * )DSIGMA, real, dimension( ldu, * )U, integerLDU, real, dimension( ldu2, * )U2, integerLDU2, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXC, integer, dimension( * )CTOT, real, dimension( * )Z, integerINFO)
SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.
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.
Parameters:

NL
NL is INTEGER The row dimension of the upper block. NL >= 1.
NRNR is INTEGER The row dimension of the lower block. NR >= 1.
SQRESQRE is INTEGER = 0: the lower block is an NRbyNR square matrix. = 1: the lower block is an NRby(NR+1) rectangular matrix. The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.
KK is INTEGER The size of the secular equation, 1 =< K = < N.
DD is REAL array, dimension(K) On exit the square roots of the roots of the secular equation, in ascending order.
QQ is REAL array, dimension at least (LDQ,K).
LDQLDQ is INTEGER The leading dimension of the array Q. LDQ >= K.
DSIGMADSIGMA is 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.
UU is REAL array, dimension (LDU, N) The last N  K columns of this matrix contain the deflated left singular vectors.
LDULDU is INTEGER The leading dimension of the array U. LDU >= N.
U2U2 is REAL array, dimension (LDU2, N) The first K columns of this matrix contain the nondeflated left singular vectors for the split problem.
LDU2LDU2 is INTEGER The leading dimension of the array U2. LDU2 >= N.
VTVT is REAL array, dimension (LDVT, M) The last M  K columns of VT**T contain the deflated right singular vectors.
LDVTLDVT is INTEGER The leading dimension of the array VT. LDVT >= N.
VT2VT2 is REAL array, dimension (LDVT2, N) The first K columns of VT2**T contain the nondeflated right singular vectors for the split problem.
LDVT2LDVT2 is INTEGER The leading dimension of the array VT2. LDVT2 >= N.
IDXCIDXC is INTEGER array, dimension (N) The permutation used to arrange the columns of U (and rows of VT) into three groups: the first group contains nonzero entries only at and above (or before) NL +1; the second contains nonzero 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 multiplies can take place.
CTOTCTOT is 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.
ZZ is REAL array, dimension (K) The first K elements of this array contain the components of the deflationadjusted updating row vector.
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: if INFO = 1, a singular value did not converge
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Contributors:
 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
Definition at line 224 of file slasd3.f.
Author
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