DHST01(3)

💖 NAME 💖

okay bestie, you're on DHST01(3) from the Library Functions Manual, and the NAME line is literally this whole path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/dhst01.f.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Here's the subroutine tea:

subroutine DHST01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork,
    result)
    DHST01

🦋 Function/Subroutine Documentation 🦋

Exact signature, bestie — no cap:

subroutine DHST01 (integer n, integer ilo, integer ihi, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( ldh, *
    ) h, integer ldh, double precision, dimension( ldq, * ) q, integer ldq,
    double precision, dimension( lwork ) work, integer lwork, double
    precision, dimension( 2 ) result)
    DHST01

🎀 Purpose 🎀

okay so DHST01 is lowkey the vibe-check for reducing a general matrix A to upper Hessenberg form: A = Q*H*Q'. It computes two test ratios, and yes they're iconic:

• 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, exactly as it would be following DGEHRD + DORGHR.

In this version, ILO and IHI are not used and are assumed to be 1 and N, respectively. periodt. 💅

🌸 Parameters 🌸

• N — N is INTEGER. The order of the matrix A. N >= 0.
• ILO — ILO is INTEGER. That's literally all the original says, bestie.
• 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDH,N). The upper Hessenberg matrix H from the reduction A = Q*H*Q' as computed by DGEHRD. 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 DOUBLE PRECISION array, dimension (LDQ,N). The orthogonal matrix Q from the reduction A = Q*H*Q' as computed by DGEHRD + DORGHR.
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= 2*N*N.
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2). RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS ) and 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 132 of file dhst01.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💅✨ — cute sign-off from the footer: LAPACK Version 3.12.0, source/path /home/abui...IG/dhst01.f(3). That's the footer tea, periodt. 🫶