TESTING/EIG/sget53.f(3)

✨ NAME ✨

TESTING/EIG/sget53.f(3) — bestie, this is the manual page for SGET53, the little subroutine that checks the generalized eigenvalues computed by SLAG2. No cap, that’s the whole vibe. 💖

🦋 SYNOPSIS 🦋

🌸 Functions/Subroutines 🌸

• subroutine sget53 (a, lda, b, ldb, scale, wr, wi, result, info) — the callable, and yes it’s giving main character energy.
• SGET53 — the name, iconic, periodt.

💅 Function/Subroutine Documentation 💅

subroutine sget53 (real, dimension( lda, * ) a, integer lda, real,
     dimension( ldb, * ) b, integer ldb, real scale, real wr, real wi, real
     result, integer info)

SGET53

🎀 Purpose 🎀

Ok so SGET53 checks the generalized eigenvalues computed by SLAG2. The basic test for an eigenvalue is literally this:

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

Then “Two are performed:” (yes, the original really has that space, we keep the lore intact 🙈):

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. Slay, resilience. 💪

🍓 Parameters 🍓

• A — A is REAL array, dimension (LDA, 2). The 2x2 matrix A. 💖
• LDA — LDA is INTEGER. The leading dimension of A. It must be at least 2.
• B — B is REAL array, dimension (LDB, N). The 2x2 upper-triangular matrix B.
• LDB — LDB is INTEGER. The leading dimension of B. It must be at least 2.
• SCALE — SCALE is REAL. The s in the formula s A - w B. It is assumed to be non-negative.
• WR — WR is REAL. The real part of the eigenvalue w in the formula s A - w B.
• WI — WI is REAL. The imaginary part of the eigenvalue w in the formula s A - w B.
• RESULT — RESULT is REAL. If INFO is 2 or less, the value computed by the test described above. If INFO=3, this will just be 1/ulp.
• INFO — INFO is INTEGER.
  • =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 sget53.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

---

Sign-off time, bestie: this cutie was brought to you by LAPACK Version 3.12.0 and the TESTING/EIG/sget53.f(3) page, with no separate date line in sight. Mwah 💋✨