CGET52(3)

🌸 NAME 🌸

This is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cget52.f — yes bestie, that exact path, no cap. The title vibe is cget52.f(3), and it lives in the Library Functions Manual 🫶.

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✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

       subroutine CGET52 (left, n, a, lda, b, ldb, e, lde, alpha, beta, work,
           rwork, result)
           CGET52

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🦋 Function/Subroutine Documentation 🦋

   subroutine CGET52 (logical left, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( ldb, * ) b, integer ldb, complex,
       dimension( lde, * ) e, integer lde, complex, dimension( * ) alpha,
       complex, dimension( * ) beta, complex, dimension( * ) work, real,
       dimension( * ) rwork, real, dimension( 2 ) result)
       CGET52

✨ Purpose ✨

okay so CGET52 does an eigenvector check for the generalized eigenvalue problem. It's giving "trust but verify" energy, fr fr.

The basic test for right eigenvectors is:

                          | b(i) A E(i) -  a(i) B E(i) |
        RESULT(1) = max   -------------------------------
                     i    n ulp max( |b(i) A|, |a(i) B| )

using the 1-norm. Here, a(i)/b(i) = w is the i-th generalized eigenvalue of A - w B, or, equivalently, b(i)/a(i) = m is the i-th generalized eigenvalue of m A - B.

For left eigenvectors, A^H, B^H, a, and b are used. bestie, it's giving transpose-conjugate realness 💅.

CGET52 also tests the normalization of E. Each eigenvector is supposed to be normalized so that the maximum of its elements is 1, where in this case, for a complex value x, the measure is |Re(x)| + |Im(x)| ; let us call this maximum norm of a vector v M(v). If a(i)=b(i)=0, then the eigenvector is set to be the jth coordinate vector. The normalization test is:

         RESULT(2) =      max       | M(v(i)) - 1 | / ( n ulp )
                    eigenvectors v(i)

🎀 Parameters 🎀

• LEFT — LEFT is LOGICAL; =.TRUE. means the eigenvectors in the columns of E are assumed to be left eigenvectors; =.FALSE. means the eigenvectors in the columns of E are assumed to be right eigenvectors.
• N — N is INTEGER; the size of the matrices. If it is zero, CGET52 does nothing. It must be at least zero.
• A — A is COMPLEX array, dimension (LDA, N); the matrix A.
• LDA — LDA is INTEGER; the leading dimension of A. It must be at least 1 and at least N.
• B — B is COMPLEX array, dimension (LDB, N); the matrix B.
• LDB — LDB is INTEGER; the leading dimension of B. It must be at least 1 and at least N.
• E — E is COMPLEX array, dimension (LDE, N); the matrix of eigenvectors. It must be O( 1 ).
• LDE — LDE is INTEGER; the leading dimension of E. It must be at least 1 and at least N.
• ALPHA — ALPHA is COMPLEX array, dimension (N); the values a(i) as described above, which, along with b(i), define the generalized eigenvalues.
• BETA — BETA is COMPLEX array, dimension (N); the values b(i) as described above, which, along with a(i), define the generalized eigenvalues.
• WORK — WORK is COMPLEX array, dimension (N**2).
• RWORK — RWORK is REAL array, dimension (N).
• RESULT — RESULT is REAL array, dimension (2); the values computed by the test described above. If A E or B E is likely to overflow, then RESULT(1:2) is set to 10 / ulp.

👑 Author 👑

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

Definition at line 159 of file cget52.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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byeee bestie, this was LAPACK Version 3.12.0, and the footer path is /home/abui...IG/cget52.f(3) 💜✨