
NAMEzlaic1.f SYNOPSISFunctions/Subroutinessubroutine zlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) Function/Subroutine Documentationsubroutine zlaic1 (integerJOB, integerJ, complex*16, dimension( j )X, double precisionSEST, complex*16, dimension( j )W, complex*16GAMMA, double precisionSESTPR, complex*16S, complex*16C)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 jbyj 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. JOB
Author:
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 WX X is COMPLEX*16 array, dimension (J) The jvector x.SEST SEST is DOUBLE PRECISION Estimated singular value of j by j matrix LW W is COMPLEX*16 array, dimension (J) The jvector 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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Definition at line 136 of file zlaic1.f.
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