# dlaic1.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

dlaic1.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
DLAIC1 applies one step of incremental condition estimation.

## Function/Subroutine Documentation

### subroutine dlaic1 (integer JOB, integer J, double precision, dimension( j ) X, double precision SEST, double precision, dimension( j ) W, double precision GAMMA, double precision SESTPR, double precision S, double precision C)

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