TESTING/EIG/cget22.f(3)

🎀 NAME 🎀

The name on the tin is TESTING/EIG/cget22.f — and yes, the header title is TESTING/EIG/cget22.f(3). This page lives in the Library Functions Manual, which we’re folding in right here near the top instead of copying the header line, bestie. 💅

This is the page for CGET22, an eigenvector-checking subroutine. It’s giving “test the eigenvectors carefully” energy, no cap. ✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine cget22 (character transa, character transe, character transw,
    integer n, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( lde, * ) e, integer lde, complex, dimension( * ) w, complex,
    dimension( * ) work, real, dimension( * ) rwork, real, dimension( 2 )
    result)

And the subroutine’s name is CGET22 — main character energy, obviously. 👑

💖 Function/Subroutine Documentation 💖

🌸 subroutine cget22 🌸

subroutine cget22 (character transa, character transe, character transw,
    integer n, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( lde, * ) e, integer lde, complex, dimension( * ) w, complex,
    dimension( * ) work, real, dimension( * ) rwork, real, dimension( 2 )
    result)

CGET22

🦋 Purpose 🦋

CGET22 does an eigenvector check, and it is lowkey thorough. The basic test is:

RESULT(1) = | A E  -  E W | / ( |A| |E| ulp )

using the 1-norm. It also tests the normalization of E:

RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
                 j

where E(j) is the j-th eigenvector, and m-norm is the max-norm of a vector. The max-norm of a complex n-vector x in this case is the maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n.

🌈 Parameters 🌈

• TRANSA — CHARACTER*1. Specifies whether or not A is transposed.
  • 'N': No transpose
  • 'T': Transpose
  • 'C': Conjugate transpose
• TRANSE — CHARACTER*1. Specifies whether or not E is transposed.
  • 'N': No transpose, eigenvectors are in columns of E
  • 'T': Transpose, eigenvectors are in rows of E
  • 'C': Conjugate transpose, eigenvectors are in rows of E
• TRANSW — CHARACTER*1. Specifies whether or not W is transposed.
  • 'N': No transpose
  • 'T': Transpose, same as TRANSW = 'N'
  • 'C': Conjugate transpose, use -WI(j) instead of WI(j)
• N — INTEGER. The order of the matrix A. N >= 0.
• A — COMPLEX array, dimension (LDA,N). The matrix whose eigenvectors are in E.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• E — COMPLEX array, dimension (LDE,N). The matrix of eigenvectors. If TRANSE = 'N', the eigenvectors are stored in the columns of E, if TRANSE = 'T' or 'C', the eigenvectors are stored in the rows of E.
• LDE — INTEGER. The leading dimension of the array E. LDE >= max(1,N).
• W — COMPLEX array, dimension (N). The eigenvalues of A.
• WORK — COMPLEX array, dimension (N*N).
• RWORK — REAL array, dimension (N).
• RESULT — REAL array, dimension (2). The two result slots are defined like this:

RESULT(1) = | A E  -  E W | / ( |A| |E| ulp )
RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp )
                 j

👑 Author 👑

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

📍 Definition at line 142 of file cget22.f. 📍

💌 Author 💌

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶 — the footer notes are LAPACK Version 3.12.0 and the page is TESTING/EIG/cget22.f(3). No date is listed on that footer, so we’re not inventing one. periodt 💜✨