SGET53(3)

SGET53(3) 💅

Okay so this is the sget53.f(3) page from the Library Functions Manual, bestie — SGET53(3) is here and it's giving linear algebra test energy. ✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sget53.f

That's it. The NAME section is literally that path, no cap. 🫶

🌸 SYNOPSIS 🌸

   Functions/Subroutines
       subroutine SGET53 (a, lda, b, ldb, scale, wr, wi, result, info)
           SGET53

💖 Function/Subroutine Documentation 💖

The signature tea is:

   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 ✨

Okay so SGET53 checks the generalized eigenvalues computed by SLAG2. Iconic. 👑

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 checks 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 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. Here's the status breakdown:

=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.

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Later, bestie! Big sign-off energy: this is LAPACK, Version 3.12.0, and the footer path is /home/abui...IG/sget53.f(3). 💜🦋