---
name: "slaic1"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slaic1/3lapack"
---

# slaic1(3lapack)

applies one step of incremental condition estimation in its simplest version

## NAME

SLAIC1 - applies one step of incremental condition estimation in its simplest version

## SYNOPSIS

- SUBROUTINE SLAIC1(

  JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )

- INTEGER

  J, JOB

- REAL

  C, GAMMA, S, SEST, SESTPR

- REAL

  W( J ), X( J )

## 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 = \[ w' gamma \]\
 in the sense that\
\
          twonorm(Lhat\*xhat) = sestpr.\
 Depending on JOB, an estimate for the largest or smallest singular value is computed.\
 Note that \[s c\]' and sestpr\*\*2 is an eigenpair of the system\
     diag(sest\*sest, 0) + \[alpha  gamma\] \* \[ alpha \]\
\
                                           \[ gamma \]\
 where  alpha =  x'\*w.\

## ARGUMENTS

- JOB (input) INTEGER

  \= 1: an estimate for the largest singular value is computed.\
   \= 2: an estimate for the smallest singular value is computed.

- J (input) INTEGER

  Length of X and W

- X (input) REAL array, dimension (J)

  The j-vector x.

- SEST (input) REAL

  Estimated singular value of j by j matrix L

- W (input) REAL array, dimension (J)

  The j-vector w.

- GAMMA (input) REAL

  The diagonal element gamma.

- SESTPR (output) REAL

  Estimated singular value of (j+1) by (j+1) matrix Lhat.

- S (output) REAL

  Sine needed in forming xhat.

- C (output) REAL

  Cosine needed in forming xhat.