TESTING/EIG/zget22.f(3)

💅 TESTING/EIG/zget22.f(3) — Library Functions Manual 💅

okay so bestie, gather round, because this is the manual page for TESTING/EIG/zget22.f and honestly? it's giving "eigenvector quality control" and I'm lowkey obsessed 🦋

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✨ NAME ✨

TESTING/EIG/zget22.f — yes that's the whole name, it's just out here living its best file-path life, no cap 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine zget22 (transa, transe, transw, n, a, lda, e, lde, w, work,
    rwork, result)

ZGET22 — that's her, that's the icon, that's the whole subroutine 👑

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🎀 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 💖

🧚 Purpose:

!> !> ZGET22 does an eigenvector check. !> !> 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. !>

so basically, bestie, it does an eigenvector check — two whole tests, no cap. Test one (RESULT(1)) checks | A E - E W | / ( |A| |E| ulp ) using the 1-norm. Test two (RESULT(2)) checks the normalization of E with max | m-norm(E(j)) - 1 | / ( n ulp ) over j. and E(j) is the j-th eigenvector, m-norm is the max-norm of a vector, and for a complex n-vector x that max-norm is literally the maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n. periodt ✨

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🌈 Parameters 🌈

• TRANSA — it's a CHARACTER*1 and it says whether A is transposed or not, bestie:
  • = 'N': No transpose
  • = 'T': Transpose
  • = 'C': Conjugate transpose
• TRANSE — CHARACTER*1, controls whether 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, whether W gets transposed:
  • = 'N': No transpose
  • = 'T': Transpose, same as TRANSW = 'N' (yes, literally the same, don't ask 🙈)
  • = 'C': Conjugate transpose, use -WI(j) instead of WI(j)
• N — INTEGER, the order of the matrix A. N >= 0. keep it non-negative or it's a no from me 💀
• A — COMPLEX*16 array, dimension (LDA,N). it's the matrix whose eigenvectors are chilling in E 🫶
• LDA — INTEGER, the leading dimension of the array A. LDA >= max(1,N). respect the constraint fr fr
• 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', they're stored in the rows of E. iconic either way 💅
• 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), and it holds:
  • RESULT(1) = | A E - E W | / ( |A| |E| ulp )
  • RESULT(2) = max | m-norm(E(j)) - 1 | / ( n ulp ) j

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👑 Author 👑

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

the academic royalty of it all, honestly 🌟

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⭐ Author (again, but different) ⭐

Generated automatically by Doxygen for LAPACK from the source code. so she didn't even write herself, she was born from the source code, main character energy for real 🦋

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💜 Definition

Definition at line 142 of file zget22.f. — that's where she lives, line 142, remember it 📍

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ok that's the whole page bestie, you ate that 🍓

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LAPACK — Version 3.12.0 💖 bye bestie, go check those eigenvectors, and remember: the max-norm is the maximum of |re(x(i)| + |im(x(i)| over i = 1, ..., n, no cap 🎀✨