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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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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 j-by-j 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 j-vector x. |
[in] | SEST | SEST is REAL Estimated singular value of j by j matrix L |
[in] | W | W is COMPLEX array, dimension (J) The j-vector 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 137 of file claic1.f.