claic1(3) [debian man page]
claic1.f(3) LAPACK claic1.f(3) NAME
claic1.f - SYNOPSIS
Functions/Subroutines subroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) CLAIC1 Function/Subroutine Documentation subroutine claic1 (integerJOB, integerJ, complex, dimension( j )X, realSEST, complex, dimension( j )W, complexGAMMA, realSESTPR, complexS, complexC) CLAIC1 Purpose: 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. 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 array, dimension (J) The j-vector x. SEST SEST is REAL Estimated singular value of j by j matrix L W W is COMPLEX array, dimension (J) The j-vector w. GAMMA GAMMA is COMPLEX The diagonal element gamma. SESTPR SESTPR is REAL Estimated singular value of (j+1) by (j+1) matrix Lhat. S S is COMPLEX Sine needed in forming xhat. C C is COMPLEX Cosine needed in forming xhat. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 136 of file claic1.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 claic1.f(3)
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zlaic1.f(3) LAPACK zlaic1.f(3) NAME
zlaic1.f - SYNOPSIS
Functions/Subroutines subroutine zlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) ZLAIC1 Function/Subroutine Documentation subroutine zlaic1 (integerJOB, integerJ, complex*16, dimension( j )X, double precisionSEST, complex*16, dimension( j )W, complex*16GAMMA, double precisionSESTPR, complex*16S, complex*16C) ZLAIC1 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. Date: November 2011 Definition at line 136 of file zlaic1.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 zlaic1.f(3)