LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) 
CLAIC1 applies one step of incremental condition estimation. 
subroutine claic1  (  integer  JOB, 
integer  J,  
complex, dimension( j )  X,  
real  SEST,  
complex, dimension( j )  W,  
complex  GAMMA,  
real  SESTPR,  
complex  S,  
complex  C  
) 
CLAIC1 applies one step of incremental condition estimation.
Download CLAIC1 + dependencies [TGZ] [ZIP] [TXT]CLAIC1 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 CLAIC1 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.
[in]  JOB  JOB is INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed. 
[in]  J  J is INTEGER Length of X and W 
[in]  X  X is COMPLEX array, dimension (J) The jvector x. 
[in]  SEST  SEST is REAL Estimated singular value of j by j matrix L 
[in]  W  W is COMPLEX array, dimension (J) The jvector w. 
[in]  GAMMA  GAMMA is COMPLEX The diagonal element gamma. 
[out]  SESTPR  SESTPR is REAL Estimated singular value of (j+1) by (j+1) matrix Lhat. 
[out]  S  S is COMPLEX Sine needed in forming xhat. 
[out]  C  C is COMPLEX Cosine needed in forming xhat. 
Definition at line 136 of file claic1.f.