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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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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.
Download ZLAIC1 + dependencies [TGZ] [ZIP] [TXT]
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.
[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*16 array, dimension (J) The j-vector x. |
[in] | SEST | SEST is DOUBLE PRECISION Estimated singular value of j by j matrix L |
[in] | W | W is COMPLEX*16 array, dimension (J) The j-vector w. |
[in] | GAMMA | GAMMA is COMPLEX*16 The diagonal element gamma. |
[out] | SESTPR | SESTPR is DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat. |
[out] | S | S is COMPLEX*16 Sine needed in forming xhat. |
[out] | C | C is COMPLEX*16 Cosine needed in forming xhat. |
Definition at line 137 of file zlaic1.f.