ZHST01(3)

ZHST01(3) — Library Functions Manual, but make it group chat 💅

okay so bestie, this is the zhst01 page from the Library Functions Manual, and it’s giving “LAPACK test subroutine with main character energy.” The file is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zhst01.f

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zhst01.f

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine ZHST01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork,
    rwork, result)

ZHST01

🦋 Function/Subroutine Documentation 🦋

subroutine ZHST01 (integer n, integer ilo, integer ihi, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldh, * ) h,
    integer ldh, complex*16, dimension( ldq, * ) q, integer ldq, complex*16,
    dimension( lwork ) work, integer lwork, double precision, dimension( * )
    rwork, double precision, dimension( 2 ) result)

ZHST01 — yes, the name appears again, because Doxygen loves an encore 😭💖

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💜 Purpose 💜

ZHST01 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 ZGEHRD + ZUNGHR.

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

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🎀 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*16 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*16 array, dimension (LDH,N). The upper Hessenberg matrix H from the reduction A = Q*H*Q' as computed by ZGEHRD. 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*16 array, dimension (LDQ,N). The orthogonal matrix Q from the reduction A = Q*H*Q' as computed by ZGEHRD + ZUNGHR.
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= 2*N*N.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2).

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

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👑 Author 👑

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

📍 Definition at line 138 of file zhst01.f. 📍

Definition at line 138 of file zhst01.f.

🫶 Author (Doxygen’s auto-generated note) 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the page, bestie — LAPACK Version 3.12.0, source: /home/abui...IG/zhst01.f(3), date: not listed on this copy. 🫶