TESTING/EIG/dget22.f(3)

🎀 TESTING/EIG/dget22.f(3) — Library Functions Manual 🎀

okay so bestie, this is TESTING/EIG/dget22.f(3) from the Library Functions Manual, and it's giving extremely specific LAPACK testing routine energy. We're gonna go through every single flag, every dimension, every formula — no skips, no cap. 💅✨

📛 NAME

TESTING/EIG/dget22.f

✨ SYNOPSIS

🧚 Functions/Subroutines

       subroutine dget22 (transa, transe, transw, n, a, lda, e, lde, wr, wi,
           work, result)
           DGET22

🌈 Function/Subroutine Documentation

       subroutine dget22 (character transa, character transe, character transw,
       integer n, double precision, dimension( lda, * ) a, integer lda, double
       precision, dimension( lde, * ) e, integer lde, double precision,
       dimension( * ) wr, double precision, dimension( * ) wi, double
       precision, dimension( * ) work, double precision, dimension( 2 ) result)

💖 DGET22

DGET22 is the routine name, and yes, it's the star of this page. 👑

🔥 Purpose

okay so the purpose is literally this: DGET22 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. 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. iykyk 🦋

🧸 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
• WI — WI is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N*(N+1))
• RESULT — RESULT is 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 166 of file dget22.f.

💌 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie. the footer says LAPACK Version 3.12.0 and TESTING/EIG/dget22.f(3) — no separate date is listed, so I'm not gonna invent one, periodt. mwah 💖🎀