dlaic1.f(3) [debian man page]
dlaic1.f(3) LAPACK dlaic1.f(3) NAME
dlaic1.f - SYNOPSIS
Functions/Subroutines subroutine dlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) DLAIC1 Function/Subroutine Documentation subroutine dlaic1 (integerJOB, integerJ, double precision, dimension( j )X, double precisionSEST, double precision, dimension( j )W, double precisionGAMMA, double precisionSESTPR, double precisionS, double precisionC) DLAIC1 Purpose: DLAIC1 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 DLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system diag(sest*sest, 0) + [alpha gamma] * [ alpha ] [ gamma ] where alpha = x**T*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 DOUBLE PRECISION array, dimension (J) The j-vector x. SEST SEST is DOUBLE PRECISION Estimated singular value of j by j matrix L W W is DOUBLE PRECISION array, dimension (J) The j-vector w. GAMMA GAMMA is DOUBLE PRECISION The diagonal element gamma. SESTPR SESTPR is DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat. S S is DOUBLE PRECISION Sine needed in forming xhat. C C is DOUBLE PRECISION 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 135 of file dlaic1.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlaic1.f(3)
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dlaic1.f(3) LAPACK dlaic1.f(3) NAME
dlaic1.f - SYNOPSIS
Functions/Subroutines subroutine dlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) DLAIC1 applies one step of incremental condition estimation. Function/Subroutine Documentation subroutine dlaic1 (integerJOB, integerJ, double precision, dimension( j )X, double precisionSEST, double precision, dimension( j )W, double precisionGAMMA, double precisionSESTPR, double precisionS, double precisionC) DLAIC1 applies one step of incremental condition estimation. Purpose: DLAIC1 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 DLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system diag(sest*sest, 0) + [alpha gamma] * [ alpha ] [ gamma ] where alpha = x**T*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 DOUBLE PRECISION array, dimension (J) The j-vector x. SEST SEST is DOUBLE PRECISION Estimated singular value of j by j matrix L W W is DOUBLE PRECISION array, dimension (J) The j-vector w. GAMMA GAMMA is DOUBLE PRECISION The diagonal element gamma. SESTPR SESTPR is DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat. S S is DOUBLE PRECISION Sine needed in forming xhat. C C is DOUBLE PRECISION Cosine needed in forming xhat. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Definition at line 135 of file dlaic1.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 dlaic1.f(3)