TESTING/EIG/dget53.f(3)

💅 TESTING/EIG/dget53.f 💅

okay so this is the Library Functions Manual page TESTING/EIG/dget53.f(3) — the manual name is folded right in here instead of copy-pasting the header line. 🫶

🌸 NAME 🌸

TESTING/EIG/dget53.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine dget53 (a, lda, b, ldb, scale, wr, wi, result, info) — DGET53

💖 Function/Subroutine Documentation 💖

🌟 subroutine dget53 🌟

subroutine dget53 (double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( ldb, * ) b, integer ldb, double precision
    scale, double precision wr, double precision wi, double precision
    result, integer info)

DGET53

💫 Purpose 💫

okay so DGET53 checks the generalized eigenvalues that DLAG2 computed. No cap, that’s literally the job. ✨

The basic test for an eigenvalue is:

                             | det( s A - w B ) |
    RESULT =  ---------------------------------------------------
              ulp max( s norm(A), |w| norm(B) )*norm( s A - w B )

Two are performed:

1. ulp*max( s*norm(A), |w|*norm(B) ) must be at least safe_minimum. This insures that the test performed is not essentially det(0*A + 0*B)=0.
2. s*norm(A) + |w|*norm(B) must be less than 1/safe_minimum. This insures that s*A - w*B will not overflow.

If these tests are not passed, then s and w are scaled and tested anyway, if this is possible. 🦋

🎀 Parameters 🎀

• A — A is DOUBLE PRECISION array, dimension (LDA, 2). It’s the 2x2 matrix A. 💅
• LDA — INTEGER. The leading dimension of A. It must be at least 2. ✨
• B — B is DOUBLE PRECISION array, dimension (LDB, N). It’s the 2x2 upper-triangular matrix B. 🎀
• LDB — INTEGER. The leading dimension of B. It must be at least 2. 🌸
• SCALE — DOUBLE PRECISION. The s in the formula s A - w B. It is assumed to be non-negative. 🫶
• WR — DOUBLE PRECISION. The real part of the eigenvalue w in the formula s A - w B. 💜
• WI — DOUBLE PRECISION. The imaginary part of the eigenvalue w in the formula s A - w B. 🦋
• RESULT — DOUBLE PRECISION. If INFO is 2 or less, the value computed by the test described above. If INFO=3, this will just be 1/ulp. 😭
• INFO — INTEGER. The status tea is:
  • =0: The input data pass the .
  • =1: s*norm(A) + |w|*norm(B) > 1/safe_minimum.
  • =2: ulp*max( s*norm(A), |w|*norm(B) ) < safe_minimum
  • =3: same as INFO=2, but s and w could not be scaled so as to compute the test.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 125 of file dget53.f. 📌

🌟 Author 🌟

Yep, the auto-generated tea: Generated automatically by Doxygen for LAPACK from the source code. ☕✨

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byeeee bestie 🫶💖 — source/version energy: LAPACK, Version 3.12.0, for page TESTING/EIG/dget53.f(3). The original footer doesn’t print a separate date, so I’m not inventing one — periodt. 🌈✨