/home/abui...N/slatm6.f(3)

okay bestie, welcome to the Library Functions Manual page for /home/abui...N/slatm6.f(3) 💅✨. This one is all about the SLATM6 subroutine, and it’s giving test-matrix construction realness.

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/slatm6.f — that’s the name, bestie. Yes, it’s a whole path. Periodt.

✨ SYNOPSIS ✨

Here’s the signature screenshot, no cap:

       subroutine SLATM6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx,
           wy, s, dif)
           SLATM6

🎀 Functions/Subroutines 🎀

The star of the show is literally this:

       subroutine SLATM6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx,
           wy, s, dif)
           SLATM6

🦋 Function/Subroutine Documentation 🦋

Full signature with all the types, because we respect the details:

   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 tea: 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 original says 1th — we respect the lore 💀.

Test Matrices — the original underlines it with =============, iconic:

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 🍓

Every parameter, bestie, no skips:

• 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 📌

Definition at line 174 of file slatm6.f.

💖 Author 💖

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Final footer sign-off: LAPACK Version 3.12.0, source page /home/abui...N/slatm6.f(3). That’s the whole manual page — slay, bye 💖🫶👑