# claic1.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
CLAIC1 applies one step of incremental condition estimation.

## Function/Subroutine Documentation

### subroutine claic1 (integer JOB, integer J, complex, dimension( j ) X, real SEST, complex, dimension( j ) W, complex GAMMA, real SESTPR, complex S, complex C)

CLAIC1 applies one step of incremental condition estimation.

Purpose:

``` CLAIC1 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 CLAIC1 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 array, dimension (J)
The j-vector x.```

SEST

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

W

```          W is COMPLEX array, dimension (J)
The j-vector w.```

GAMMA

```          GAMMA is COMPLEX
The diagonal element gamma.```

SESTPR

```          SESTPR is REAL
Estimated singular value of (j+1) by (j+1) matrix Lhat.```

S

```          S is COMPLEX
Sine needed in forming xhat.```

C

```          C is COMPLEX
Cosine needed in forming xhat.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Definition at line 137 of file claic1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page claic1(3) is an alias of claic1.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK