# slaic1.f - Man Page

SRC/slaic1.f

## Synopsis

### Functions/Subroutines

subroutine **slaic1** (job, j, x, sest, w, gamma, sestpr, s, c)**SLAIC1** applies one step of incremental condition estimation.

## Function/Subroutine Documentation

### subroutine slaic1 (integer job, integer j, real, dimension( j ) x, real sest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)

**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.

**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 REAL array, dimension (J) The j-vector x.

*SEST*SEST is REAL Estimated singular value of j by j matrix L

*W*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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **133** of file **slaic1.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slaic1(3) is an alias of slaic1.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK