TESTING/EIG/sget22.f(3)

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💖 TESTING/EIG/sget22.f 💖

okay bestie, this is the Library Functions Manual entry for TESTING/EIG/sget22.f — tiny Fortran file, huge eigenvector-check energy ✨

🎀 NAME 🎀

TESTING/EIG/sget22.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine sget22 (transa, transe, transw, n, a, lda, e, lde, wr, wi,
    work, result)
    SGET22

💅 Function/Subroutine Documentation 💅

subroutine sget22 (character transa, character transe, character transw,
    integer n, real, dimension( lda, * ) a, integer lda, real, dimension(
    lde, * ) e, integer lde, real, dimension( * ) wr, real, dimension( * )
    wi, real, dimension( * ) work, real, dimension( 2 ) result)
    SGET22

Purpose ✨

okay so SGET22 does an eigenvector check. no cap, that's the whole vibe 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. If an eigenvector is complex, as determined from WI(j) nonzero, then the max-norm of the vector ( er + i*ei ) is the maximum of

|er(1)| + |ei(1)|, ... , |er(n)| + |ei(n)|

W is a block diagonal matrix, with a 1 by 1 block for each real eigenvalue and a 2 by 2 block for each complex conjugate pair. If eigenvalues j and j+1 are a complex conjugate pair, so that WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the 2 by 2 block corresponding to the pair will be:

(  wr  wi  )
( -wi  wr  )

Such a block multiplying an n by 2 matrix ( ur ui ) on the right will be the same as multiplying ur + i*ui by wr + i*wi.

To handle various schemes for storage of left eigenvectors, there are options to use A-transpose instead of A, E-transpose instead of E, and/or W-transpose instead of W.

Parameters 💅

TRANSA

TRANSA is CHARACTER*1 — specifies whether or not A is transposed.

  • = 'N': No transpose
  • = 'T': Transpose
  • = 'C': Conjugate transpose (= Transpose)

TRANSE

TRANSE is 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 (= Transpose)

TRANSW

TRANSW is CHARACTER*1 — specifies whether or not W is transposed.

  • = 'N': No transpose
  • = 'T': Transpose, use -WI(j) instead of WI(j)
  • = 'C': Conjugate transpose, use -WI(j) instead of WI(j)

N

N is INTEGER — the order of the matrix A. N >= 0.

A

A is REAL array, dimension (LDA,N) — the matrix whose eigenvectors are in E.

LDA

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N).

E

E is REAL 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

LDE is INTEGER — the leading dimension of the array E. LDE >= max(1,N).

WR

WR is REAL array, dimension (N).

WI

WI is REAL array, dimension (N) — the real and imaginary parts of the eigenvalues of A. Purely real eigenvalues are indicated by WI(j) = 0. Complex conjugate pairs are indicated by WR(j)=WR(j+1) and WI(j) = - WI(j+1) non-zero; the real part is assumed to be stored in the j-th row/column and the imaginary part in the (j+1)-th row/column.

WORK

WORK is REAL array, dimension (N*(N+1)).

RESULT

RESULT is REAL 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 166 of file sget22.f.

Author (auto-generated) 🫶

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