/home/abui...N/clatm6.f(3)

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/clatm6.f

This page is from the Library Functions Manual, and it's the clatm6.f(3) page. We're talking about the subroutine CLATM6, and honestly it's giving test-matrix main character energy. 💅

✨ 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 🦋

Okay so 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.

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