dlatm6.f - Man Page
TESTING/MATGEN/dlatm6.f
Synopsis
Functions/Subroutines
subroutine dlatm6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx, wy, s, dif)
DLATM6
Function/Subroutine Documentation
subroutine dlatm6 (integer type, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) b, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldy, * ) y, integer ldy, double precision alpha, double precision beta, double precision wx, double precision wy, double precision, dimension( * ) s, double precision, dimension( * ) dif)
DLATM6
Purpose:
DLATM6 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, N). On exit B N-by-N is initialized according to TYPE.
X
X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
BETA
BETA is DOUBLE PRECISION Weighting constants for matrix A.
WX
WX is DOUBLE PRECISION Constant for right eigenvector matrix.
WY
WY is DOUBLE PRECISION Constant for left eigenvector matrix.
S
S is DOUBLE PRECISION array, dimension (N) S(i) is the reciprocal condition number for eigenvalue i.
DIF
DIF is DOUBLE PRECISION 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 dlatm6.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Referenced By
The man page dlatm6(3) is an alias of dlatm6.f(3).
Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK