/home/abui...N/dlatm6.f(3)

okay so bestie, you’ve opened dlatm6.f(3) from the Library Functions Manual — and it’s giving very “deep in the LAPACK build tree” energy 💅✨

✨ NAME ✨

The full path is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/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 🧚

Full signature, no cap:

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 💖

okay so DLATM6 is here to generate test matrices for the generalized eigenvalue problem, plus 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. (Yes, 1th — that’s the page’s lore, and we respect it 🫶)

🧮 Test Matrices 🧮

Two kinds of test matrix pairs are used in the tests:

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

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. iconic behavior honestly 🌸

🎀 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.

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that’s the whole page, bestie 🫶 — LAPACK, Version 3.12.0, page path /home/abui...N/dlatm6.f(3). now go forth and slay those generalized eigenvalue tests 💅✨