TESTING/EIG/shst01.f(3)

💖 TESTING/EIG/shst01.f — Library Functions Manual 💖

🌸 NAME 🌸

TESTING/EIG/shst01.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine shst01 (n, ilo, ihi, a, lda, h, ldh, q, ldq, work, lwork,
    result)
    SHST01

📚 Function/Subroutine Documentation 📚

💅 SHST01 💅

subroutine shst01 (integer n, integer ilo, integer ihi, real, dimension(
    lda, * ) a, integer lda, real, dimension( ldh, * ) h, integer ldh, real,
    dimension( ldq, * ) q, integer ldq, real, dimension( lwork ) work,
    integer lwork, real, dimension( 2 ) result)

SHST01

🎯 Purpose

Okay so SHST01 tests the reduction of a general matrix A to upper Hessenberg form: A = Q*H*Q'. Two test ratios are computed, and here they are exactly:

• 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 SGEHRD + SORGHR.

In this version, ILO and IHI are not used and are assumed to be 1 and N, respectively. Lowkey iconic that they just say it like that.

🧾 Parameters

• N — N is INTEGER; it's the order of the matrix A. N >= 0.
• ILO — ILO is INTEGER. That's the whole note here, 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 REAL array, dimension (LDA,N). It's 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 REAL array, dimension (LDH,N). The upper Hessenberg matrix H from the reduction A = Q*H*Q' as computed by SGEHRD. 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 REAL array, dimension (LDQ,N). The orthogonal matrix Q from the reduction A = Q*H*Q' as computed by SGEHRD + SORGHR.
• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= max(1,N).
• WORK — WORK is REAL array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= 2*N*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 132 of file shst01.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

---

Sign-off: LAPACK Version 3.12.0 · TESTING/EIG/shst01.f(3) — love u, bye! 💜