# zlaic1.f man page

zlaic1.f —

## Synopsis

### Functions/Subroutines

subroutinezlaic1(JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)ZLAIC1applies 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 136 of file zlaic1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlaic1(3) is an alias of zlaic1.f(3).