ZGET22(3)

ZGET22(3) 💅✨

okay so bestie, welcome to the Library Functions Manual — this page is ZGET22(3), and the header path is /home/abui...IG/zget22.f(3) (yes, the truncated-looking one, iykyk). It’s giving “LAPACK test routine that checks eigenvectors,” and we’re gonna get through every single detail together. 🫶

📛 NAME 📛

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zget22.f

✨ SYNOPSIS ✨

Functions/Subroutines 🧚

subroutine ZGET22 (transa, transe, transw, n, a, lda, e, lde, w, work,
    rwork, result)
    ZGET22

🌸 Function/Subroutine Documentation 🌸

subroutine ZGET22 (character transa, character transe, character transw,
    integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( lde, * ) e, integer lde, complex*16, dimension( * ) w,
    complex*16, dimension( * ) work, double precision, dimension( * ) rwork,
    double precision, dimension( 2 ) result)
    ZGET22

ZGET22

Purpose 💖

ZGET22 does an eigenvector check. No cap. 👑

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. (Keeping that exactly as written, bestie — character for character. 💅)

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*16 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*16 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*16 array, dimension (N). The eigenvalues of A.
• WORK — COMPLEX*16 array, dimension (N*N).
• RWORK — DOUBLE PRECISION array, dimension (N).
• RESULT — DOUBLE PRECISION array, dimension (2).

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 zget22.f.

Author (Doxygen's little auto-note) ✨

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 bestie, this page is signed off as LAPACK, Version 3.12.0, with footer path /home/abui...IG/zget22.f(3). Byeeee! 💖✨🎀