slaic1.f man page

slaic1.f

Synopsis

Functions/Subroutines

subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
SLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

subroutine slaic1 (integer JOB, integer J, real, dimension( j ) X, real SEST, real, dimension( j ) W, real GAMMA, real SESTPR, real S, real C)

SLAIC1 applies one step of incremental condition estimation.

Purpose:

``` SLAIC1 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 SLAIC1 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 REAL array, dimension (J)
The j-vector x.```

SEST

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

W

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

GAMMA

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

SESTPR

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

S

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

C

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Definition at line 136 of file slaic1.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page slaic1(3) is an alias of slaic1.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK