# 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 The leading dimension of X.

*Y*Y is REAL 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 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

Univ. of Colorado Denver

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