zlaic1.f - Man Page
SRC/zlaic1.f
Synopsis
Functions/Subroutines
subroutine zlaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
ZLAIC1 applies one step of incremental condition estimation.
Function/Subroutine Documentation
subroutine zlaic1 (integer job, integer j, complex*16, dimension( j ) x, double precision sest, complex*16, dimension( j ) w, complex*16 gamma, double precision sestpr, complex*16 s, complex*16 c)
ZLAIC1 applies one step of incremental condition estimation.
Purpose:
ZLAIC1 applies one step of incremental condition estimation in its simplest version: Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j lower triangular matrix L, such that twonorm(L*x) = sest Then ZLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w**H gamma ] in the sense that twonorm(Lhat*xhat) = sestpr. Depending on JOB, an estimate for the largest or smallest singular value is computed. Note that [s c]**H and sestpr**2 is an eigenpair of the system diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ] [ conjg(gamma) ] where alpha = x**H * w.
- Parameters
JOB
JOB is INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed.
J
J is INTEGER Length of X and W
X
X is COMPLEX*16 array, dimension (J) The j-vector x.
SEST
SEST is DOUBLE PRECISION Estimated singular value of j by j matrix L
W
W is COMPLEX*16 array, dimension (J) The j-vector w.
GAMMA
GAMMA is COMPLEX*16 The diagonal element gamma.
SESTPR
SESTPR is DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat.
S
S is COMPLEX*16 Sine needed in forming xhat.
C
C is COMPLEX*16 Cosine needed in forming xhat.
- Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 134 of file zlaic1.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Referenced By
The man page zlaic1(3) is an alias of zlaic1.f(3).
Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK