# dlaic1.f man page

dlaic1.f —

## Synopsis

### Functions/Subroutines

subroutinedlaic1(JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)DLAIC1applies one step of incremental condition estimation.

## Function/Subroutine Documentation

### subroutine dlaic1 (integerJOB, integerJ, double precision, dimension( j )X, double precisionSEST, double precision, dimension( j )W, double precisionGAMMA, double precisionSESTPR, double precisionS, double precisionC)

**DLAIC1** applies one step of incremental condition estimation.

**Purpose:**

```
DLAIC1 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 DLAIC1 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 DOUBLE PRECISION array, dimension (J)
The j-vector x.
```

*SEST*

```
SEST is DOUBLE PRECISION
Estimated singular value of j by j matrix L
```

*W*

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

*GAMMA*

```
GAMMA is DOUBLE PRECISION
The diagonal element gamma.
```

*SESTPR*

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

*S*

```
S is DOUBLE PRECISION
Sine needed in forming xhat.
```

*C*

```
C is DOUBLE PRECISION
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 135 of file dlaic1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dlaic1(3) is an alias of dlaic1.f(3).