SGET22(3)

🌸 NAME 🌸

Hiii bestie 💖 welcome to SGET22(3), straight outta the Library Functions Manual. This page is all about the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/sget22.f — yes, the whole path, no cap.

✨ 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. Slay. 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 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0, from /home/abui...IG/sget22.f(3) — that's the footer energy, bestie 💖✨👑