claic1.f - Man Page

SRC/claic1.f

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.

Definition at line 134 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 28 2023 12:08:41 Version 3.12.0 LAPACK