# slatm6.f - Man Page

TESTING/MATGEN/slatm6.f

## Synopsis

### Functions/Subroutines

subroutine slatm6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx, wy, s, dif)
SLATM6

## Function/Subroutine Documentation

### subroutine slatm6 (integer type, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( lda, * ) b, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldy, * ) y, integer ldy, real alpha, real beta, real wx, real wy, real, dimension( * ) s, real, dimension( * ) dif)

SLATM6

Purpose:

``` SLATM6 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   -1    0    0    0    Db = 1   0   0   0   0
1    1    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        0   0   0   1   0
0    0    0  -1-b  1+a ,      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 REAL 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 REAL array, dimension (LDA, N).
On exit B N-by-N is initialized according to TYPE.```

X

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

LDX

```          LDX is INTEGER

Y

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

LDY

```          LDY is INTEGER

ALPHA

`          ALPHA is REAL`

BETA

```          BETA is REAL

Weighting constants for matrix A.```

WX

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

WY

```          WY is REAL
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 174 of file slatm6.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slatm6(3) is an alias of slatm6.f(3).

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