TESTING/MATGEN/clatm6.f(3)

💅 TESTING/MATGEN/clatm6.f(3) 💅

okay bestie, this is the TESTING/MATGEN/clatm6.f(3) page from the Library Functions Manual — yes, we’re deep in LAPACK test-matrix territory, and it’s giving “math but make it fashion” ✨

🌸 NAME 🌸

TESTING/MATGEN/clatm6.f

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

• CLATM6 — the subroutine in question, and the vibe is very much “I generate test matrices” 💅

subroutine clatm6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx,
     wy, s, dif)

🦋 Function/Subroutine Documentation 🦋

🎀 subroutine clatm6 🎀

CLATM6

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)

⭐ Purpose ⭐

So, CLATM6 generates test matrices for the generalized eigenvalue problem, their corresponding right and left eigenvector matrices, and it also gives reciprocal condition numbers for all eigenvalues plus the reciprocal condition numbers of eigenvectors corresponding to the 1th and 5th eigenvalues. Iconic behavior 💖

Test Matrices — okay so there are two kinds of test matrix pairs, and they’re built like this:

(A, B) = inverse(YH) * (Da, Db) * inverse(X)

These are used in the tests:

Type 1:

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:

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; it 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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that’s the whole page, bestie 🫶 — source/version: LAPACK Version 3.12.0; footer tag: TESTING/MATGEN/clatm6.f(3) ✨