# clatm6.f - Man Page

TESTING/MATGEN/clatm6.f

## Synopsis

### Functions/Subroutines

subroutine clatm6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx, wy, s, dif)
CLATM6

## Function/Subroutine Documentation

### subroutine clatm6 (integer type, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( lda, * ) b, complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldy, * ) y, integer ldy, complex alpha, complex beta, complex wx, complex wy, real, dimension( * ) s, real, dimension( * ) dif)

CLATM6

Purpose:

``` CLATM6 generates test matrices for the generalized eigenvalue
problem, their corresponding right and left eigenvector matrices,
and also reciprocal condition numbers for all eigenvalues and
the reciprocal condition numbers of eigenvectors corresponding to
the 1th and 5th eigenvalues.

Test Matrices
=============

Two kinds of test matrix pairs
(A, B) = inverse(YH) * (Da, Db) * inverse(X)
are used in the tests:

Type 1:
Da = 1+a   0    0    0    0    Db = 1   0   0   0   0
0   2+a   0    0    0         0   1   0   0   0
0    0   3+a   0    0         0   0   1   0   0
0    0    0   4+a   0         0   0   0   1   0
0    0    0    0   5+a ,      0   0   0   0   1
and Type 2:
Da = 1+i   0    0       0       0    Db = 1   0   0   0   0
0   1-i   0       0       0         0   1   0   0   0
0    0    1       0       0         0   0   1   0   0
0    0    0 (1+a)+(1+b)i  0         0   0   0   1   0
0    0    0       0 (1+a)-(1+b)i,   0   0   0   0   1 .

In both cases the same inverse(YH) and inverse(X) are used to compute
(A, B), giving the exact eigenvectors to (A,B) as (YH, X):

YH:  =  1    0   -y    y   -y    X =  1   0  -x  -x   x
0    1   -y    y   -y         0   1   x  -x  -x
0    0    1    0    0         0   0   1   0   0
0    0    0    1    0         0   0   0   1   0
0    0    0    0    1,        0   0   0   0   1 , where

a, b, x and y will have all values independently of each other.```
Parameters

TYPE

```          TYPE is INTEGER
Specifies the problem type (see further details).```

N

```          N is INTEGER
Size of the matrices A and B.```

A

```          A is COMPLEX array, dimension (LDA, N).
On exit A N-by-N is initialized according to TYPE.```

LDA

```          LDA is INTEGER
The leading dimension of A and of B.```

B

```          B is COMPLEX array, dimension (LDA, N).
On exit B N-by-N is initialized according to TYPE.```

X

```          X is COMPLEX array, dimension (LDX, N).
On exit X is the N-by-N matrix of right eigenvectors.```

LDX

```          LDX is INTEGER

Y

```          Y is COMPLEX array, dimension (LDY, N).
On exit Y is the N-by-N matrix of left eigenvectors.```

LDY

```          LDY is INTEGER

ALPHA

`          ALPHA is COMPLEX`

BETA

```          BETA is COMPLEX

Weighting constants for matrix A.```

WX

```          WX is COMPLEX
Constant for right eigenvector matrix.```

WY

```          WY is COMPLEX
Constant for left eigenvector matrix.```

S

```          S is REAL array, dimension (N)
S(i) is the reciprocal condition number for eigenvalue i.```

DIF

```          DIF is REAL array, dimension (N)
DIF(i) is the reciprocal condition number for eigenvector i.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 172 of file clatm6.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clatm6(3) is an alias of clatm6.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK