TESTING/EIG/chst01.f(3)

💖 TESTING/EIG/chst01.f(3) 💖

okay so bestie, welcome to the Library Functions Manual glow-up for TESTING/EIG/chst01.f — yes, the page title is TESTING/EIG/chst01.f(3), and it’s giving “CHST01 testing subroutine” main character energy. 🎀✨

🌸 NAME 🌸

TESTING/EIG/chst01.f — that’s the file, and the subroutine inside is chst01. no cap. 💅

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

• subroutine chst01 — the icon itself, with the full arg list below:

subroutine chst01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork,
           rwork, result)

CHST01 — periodt. 💖

💅 Function/Subroutine Documentation 💅

💜 subroutine chst01 💜

subroutine chst01 (integer n, integer ilo, integer ihi, complex, dimension(
       lda, * ) a, integer lda, complex, dimension( ldh, * ) h, integer ldh,
       complex, dimension( ldq, * ) q, integer ldq, complex, dimension( lwork )
       work, integer lwork, real, dimension( * ) rwork, real, dimension( 2 )
       result)

CHST01 — yes, that’s the name again, and it’s iconic. 🫶

💖 Purpose 💖

okay so CHST01 tests the reduction of a general matrix A to upper Hessenberg form: A = Q*H*Q'. Two test ratios are computed:

RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )

The matrix Q is assumed to be given explicitly as it would be following CGEHRD + CUNGHR.

In this version, ILO and IHI are not used, but they could be used to save some work if this is desired. 👑

🎀 Parameters 🎀

• N — N is INTEGER. The order of the matrix A. N >= 0. 🌸
• ILO — ILO is INTEGER.
• IHI — IHI is INTEGER. A is assumed to be upper triangular in rows and columns 1:ILO-1 and IHI+1:N, so Q differs from the identity only in rows and columns ILO+1:IHI.
• A — A is COMPLEX array, dimension (LDA,N). The original n by n matrix A. 🦋
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• H — H is COMPLEX array, dimension (LDH,N). The upper Hessenberg matrix H from the reduction A = Q*H*Q' as computed by CGEHRD. H is assumed to be zero below the first subdiagonal.
• LDH — LDH is INTEGER. The leading dimension of the array H. LDH >= max(1,N).
• Q — Q is COMPLEX array, dimension (LDQ,N). The orthogonal matrix Q from the reduction A = Q*H*Q' as computed by CGEHRD + CUNGHR. ✨
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= 2*N*N. 🔥
• RWORK — RWORK is REAL array, dimension (N).
• RESULT — RESULT is REAL array, dimension (2). RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS ). RESULT(2) = norm( I - Q'*Q ) / ( N * EPS ). 💖

👑 Author 👑

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

Definition at line 138 of file chst01.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole page, bestie: source/version/page check is LAPACK, Version 3.12.0, and TESTING/EIG/chst01.f(3) — no separate date is printed in this footer. Go off and test that reduction. periodt. 💅✨