SSGT01(3)

💖 NAME 💖

Okay so bestie, welcome to SSGT01(3) — a LAPACK Library Functions Manual page, and the name section is literally serving source-file realness:

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ssgt01.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SSGT01 (itype, uplo, n, m, a, lda, b, ldb, z, ldz, d, work,
    result)
    SSGT01

🛠️ Function/Subroutine Documentation 🛠️

subroutine SSGT01 (integer itype, character uplo, integer n, integer m,
       real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,
       integer ldb, real, dimension( ldz, * ) z, integer ldz, real, dimension(
       * ) d, real, dimension( * ) work, real, dimension( * ) result)
       SSGT01

This is the full signature, and yes it is giving old-school Fortran with the dimension(...) energy. Slay.

🎯 Purpose 🎯

SSGT01 checks a decomposition of the form:

A Z   =  B Z D or
A B Z =  Z D or
B A Z =  Z D

Where A is a symmetric matrix, B is symmetric positive definite, Z is orthogonal, and D is diagonal.

One of the following test ratios is computed, and the accuracy check is literally the main character:

ITYPE = 1:  RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )

ITYPE = 2:  RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )

ITYPE = 3:  RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )

🧸 Parameters 🧸

• ITYPE — ITYPE is INTEGER. This says which form of the symmetric generalized eigenproblem you are checking:
  • = 1: A*z = (lambda)*B*z
  • = 2: A*B*z = (lambda)*z
  • = 3: B*A*z = (lambda)*z
• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrices A and B is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The order of the matrix A. Hard rule: N >= 0.
• M — M is INTEGER. The number of eigenvalues found. Range check: 0 <= M <= N.
• A — A is REAL array, dimension (LDA, N). The original symmetric matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N).
• B — B is REAL array, dimension (LDB, N). The original symmetric positive definite matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B. Constraint: LDB >= max(1,N).
• Z — Z is REAL array, dimension (LDZ, M). The computed eigenvectors of the generalized eigenproblem.
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. Constraint: LDZ >= max(1,N).
• D — D is REAL array, dimension (M). The computed eigenvalues of the generalized eigenproblem.
• WORK — WORK is REAL array, dimension (N*N).
• RESULT — RESULT is REAL array, dimension (1). The test ratio as described above. This is where the tea gets reported.

🫶 Author 🫶

The credit list is:

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

Definition at line 144 of file ssgt01.f.

📝 Author 📝

This page was generated automatically by Doxygen for LAPACK from the source code. Periodt.

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That is the whole page, bestie 💖 — footer deets: LAPACK Version 3.12.0, source path /home/abui...IG/ssgt01.f(3), and the date slot is lowkey not printed in this footer, so no invented date energy here. Bye babes 🫶✨