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slaic1.f(3) | LAPACK | slaic1.f(3) |
NAME¶
slaic1.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
Function/Subroutine Documentation¶
subroutine slaic1 (integerJOB, integerJ, real, dimension( j )X, realSEST, real, dimension( j )W, realGAMMA, realSESTPR, realS, realC)¶
SLAIC1 applies one step of incremental condition estimation. Purpose:SLAIC1 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 SLAIC1 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.
JOB
Author:
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 WX
X is REAL array, dimension (J) The j-vector x.SEST
SEST is REAL Estimated singular value of j by j matrix LW
W is REAL array, dimension (J) The j-vector w.GAMMA
GAMMA is REAL The diagonal element gamma.SESTPR
SESTPR is REAL Estimated singular value of (j+1) by (j+1) matrix Lhat.S
S is REAL Sine needed in forming xhat.C
C is REAL Cosine needed in forming xhat.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Definition at line 135 of file slaic1.f.
Author¶
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