TESTING/MATGEN/slatm6.f(3)

TESTING/MATGEN/slatm6.f(3) 💅✨

okay bestie, welcome to the TESTING/MATGEN/slatm6.f(3) page from the Library Functions Manual — yes it’s giving extremely specific LAPACK test-matrix energy, and we’re gonna read it together, no cap 🫶.

💖 NAME 💖

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 🎀

okay so here’s the whole point: 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. yes, the page says 1th, and we are preserving the lore 💀.

🔥 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.

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okay bestie, that’s the whole page 💖🔥. The footer tags this one as LAPACK Version 3.12.0 and page TESTING/MATGEN/slatm6.f(3). Go forth and slay those generalized eigenvalue tests, periodt ✨🦋.