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 zlaic1.f(3) LAPACK zlaic1.f(3)

zlaic1.f -

# 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 (integerJOB, integerJ, complex*16, dimension( j )X, double precisionSEST, complex*16, dimension( j )W, complex*16GAMMA, double precisionSESTPR, complex*16S, complex*16C)

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
NAG Ltd.
Date:
September 2012
Definition at line 136 of file zlaic1.f.

# Author

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