DGET53(3)

DGET53(3) 💅

okay so this is DGET53(3), straight out of the Library Functions Manual — and yes, bestie, we're about to get into some eigenvalue-checking lore. 🦋

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🎀 NAME 🎀

the name on this page is literally this source path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dget53.f

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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💖 Function/Subroutine Documentation 💖

here's the full signature, bestie:

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 computed by DLAG2. iconic behavior. 💜

The basic test for an eigenvalue is this absolute cinema:

                              | 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. resilient queen energy. ✨

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🧸 Parameters

• A — A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. The s in the formula s A - w B. It is assumed to be non-negative.
• WR — WR is DOUBLE PRECISION. The real part of the eigenvalue w in the formula s A - w B.
• WI — WI is DOUBLE PRECISION. The imaginary part of the eigenvalue w in the formula s A - w B.
• RESULT — RESULT is 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 — INFO is INTEGER. Here's the tea:
  • =0: The input data pass the . (yes, the page says the . — mysterious main character behavior)
  • =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.

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👑 Author

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

Definition at line 125 of file dget53.f.

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🌸 AUTHOR 🌸

This page was generated automatically by Doxygen for LAPACK from the source code.

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Catch you later, bestie — this was LAPACK Version 3.12.0, from /home/abui...IG/dget53.f(3). The footer didn't give us a date, so that's the whole story. Mwah 💋✨