TESTING/EIG/csgt01.f(3)

okay bestie, welcome to TESTING/EIG/csgt01.f from the LAPACK Library Functions Manual — yep, the (3) manual-page situation. this whole page is about CSGT01, and it’s giving “testing routine that checks your generalized Hermitian eigen-decomposition” energy. 💅

🌸 NAME

TESTING/EIG/csgt01.f — that’s the page/file name, and the actual subroutine star is CSGT01.

✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine csgt01 (itype, uplo, n, m, a, lda, b, ldb, z, ldz, d, work,
    rwork, result)
    CSGT01

the icon herself: CSGT01.

💅 Function/Subroutine Documentation

here’s the full signature, copied exactly because we do not mess with signatures in this house:

subroutine csgt01 (integer itype, character uplo, integer n, integer m,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *
    ) b, integer ldb, complex, dimension( ldz, * ) z, integer ldz, real,
    dimension( * ) d, complex, dimension( * ) work, real, dimension( * )
    rwork, real, dimension( * ) result)

CSGT01

🎀 Purpose

quick translation: CSGT01 checks a decomposition of the form

!>
!> CSGT01 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 Hermitian matrix, B is Hermitian positive definite,
!> Z is unitary, and D is diagonal.
!>
!> One of the following test ratios is computed:
!>
!> 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 )
!>

so yeah, it’s checking A Z = B Z D, A B Z = Z D, or B A Z = Z D where A is Hermitian, B is Hermitian positive definite, Z is unitary, and D is diagonal. and depending on ITYPE, it computes one of those test ratios. the math is mathing 🧚

🦋 Parameters

parameter roll call, bestie:

• ITYPE — INTEGER. The form of the Hermitian generalized eigenproblem.
  • = 1: A*z = (lambda)*B*z
  • = 2: A*B*z = (lambda)*z
  • = 3: B*A*z = (lambda)*z
• UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the Hermitian matrices A and B is stored.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — INTEGER. The order of the matrix A. N >= 0.
• M — INTEGER. The number of eigenvalues found. M >= 0.
• A — COMPLEX array, dimension (LDA, N). The original Hermitian matrix A.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — COMPLEX array, dimension (LDB, N). The original Hermitian positive definite matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• Z — COMPLEX array, dimension (LDZ, M). The computed eigenvectors of the generalized eigenproblem.
• LDZ — INTEGER. The leading dimension of the array Z. LDZ >= max(1,N).
• D — REAL array, dimension (M). The computed eigenvalues of the generalized eigenproblem.
• WORK — COMPLEX array, dimension (N*N).
• RWORK — REAL array, dimension (N).
• RESULT — REAL array, dimension (1). The test ratio as described above.

👑 Author

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

Definition at line 150 of file csgt01.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 vibe is LAPACK Version 3.12.0, with TESTING/EIG/csgt01.f(3) riding at the bottom. periodt 💖