---
name: "clatm6.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/clatm6.f"
---

# clatm6.f(3)

## NAME

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
!>          The leading dimension of X.
!>
```

*Y*

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

*LDY*

```
!>          LDY is INTEGER
!>          The leading dimension of Y.
!>
```

*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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **172** of file **clatm6.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.