TESTING/EIG/dhst01.f(3)

✨ NAME ✨

okay so bestie, welcome to TESTING/EIG/dhst01.f(3) from the Library Functions Manual. This page is all about DHST01, a subroutine that runs the vibe check on a Hessenberg reduction. 💅

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🌸 SYNOPSIS 🌸

🫶 Functions/Subroutines 🫶

• subroutine dhst01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork, result) — DHST01

subroutine dhst01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork, result)
    DHST01

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🫶 Function/Subroutine Documentation 🫶

💅 subroutine dhst01 💅

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 tests the reduction of a general matrix A to upper Hessenberg form, and the whole energy is:

A = Q*H*Q'.

Two test ratios get computed, and they are literally:

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 like it would be following DGEHRD + DORGHR. 🫶

In this version, ILO and IHI are not used and are assumed to be 1 and N, respectively. no cap.

🎀 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 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 ). 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. 💖

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