# 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 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.

## 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