TESTING/EIG/zhst01.f(3)

💅 TESTING/EIG/zhst01.f(3) — Library Functions Manual 💅

Ok bestie, welcome to the zhst01 page. It's giving test-ratio math, and honestly? Iconic. 💖

🌸 NAME 🌸

TESTING/EIG/zhst01.f — the manual page for the zhst01 subroutine. That's the name, periodt. ✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

There is exactly one star of the show here:

• subroutine zhst01 — yes bestie, that's the whole list. Signature incoming:

       subroutine zhst01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork,
           rwork, result)
           ZHST01

🎀 Function/Subroutine Documentation 🎀

🫶 subroutine zhst01 🫶

   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

🌈 Purpose 🌈

So ZHST01 tests the reduction of a general matrix A to upper Hessenberg form: A = Q*H*Q'. Two test ratios get computed, and they are lowkey the whole point:

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, just like it would be following ZGEHRD + ZUNGHR. Slay. 💅

Also, in this version, ILO and IHI are not used, but they could be used to save some work if this is desired. Cute little future-vibe note. ✨

🍓 Parameters 🍓

• N — N is INTEGER. It's the order of the matrix A, and the constraint is 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. That's the range tea. 🫶
• A — A is COMPLEX*16 array, dimension (LDA,N). It's the original n by n matrix A.
• LDA — LDA is INTEGER, the leading dimension of the array A. Constraint: LDA >= max(1,N). No cap. 💯
• H — H is COMPLEX*16 array, dimension (LDH,N). This is 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. Constraint: LDH >= max(1,N).
• Q — Q is COMPLEX*16 array, dimension (LDQ,N). It's 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. Constraint: LDQ >= max(1,N).
• WORK — WORK is COMPLEX*16 array, dimension (LWORK). Just the work array, doing its thing. 🦋
• LWORK — LWORK is INTEGER, the length of the array WORK. Constraint: LWORK >= 2*N*N. Respect the math. 🔥
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2). Here's exactly what lands in it:

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

👑 Author 👑

The author squad is:

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

Definition at line 138 of file zhst01.f.

📜 Author 📜

This page was generated automatically by Doxygen for LAPACK from the source code. Yes bestie, generated — I just added the sparkle. ✨

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💖 Cute sign-off: this is LAPACK, Version 3.12.0, and the page is TESTING/EIG/zhst01.f(3). Bye bestie, go run those tests! 💅✨