csyequb.f - Man Page

SRC/csyequb.f

Synopsis

Functions/Subroutines

subroutine csyequb (uplo, n, a, lda, s, scond, amax, work, info)
CSYEQUB

Function/Subroutine Documentation

subroutine csyequb (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, complex, dimension( * ) work, integer info)

CSYEQUB

Purpose:

``` CSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.```

N

```          N is INTEGER
The order of the matrix A. N >= 0.```

A

```          A is COMPLEX array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling factors are to be
computed.```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).```

S

```          S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.```

SCOND

```          SCOND is REAL
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.```

AMAX

```          AMAX is REAL
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.```

WORK

`          WORK is COMPLEX array, dimension (2*N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the i-th diagonal element is nonpositive.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

Definition at line 131 of file csyequb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK