# zlaic1.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **zlaic1** (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)**ZLAIC1** applies one step of incremental condition estimation.

## Function/Subroutine Documentation

### 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.

**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:**December 2016

Definition at line 137 of file zlaic1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaic1(3) is an alias of zlaic1.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK