SHST01(3)

🌸 NAME 🌸

okay bestie, this page is SHST01(3) from the Library Functions Manual 💅 — header-path vibes are /home/abui...IG/shst01.f(3).

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/shst01.f

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

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

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💖 Function/Subroutine Documentation 💖

here’s the full signature, no cap:

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 the whole point: SHST01 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 SGEHRD + SORGHR.

Important lil note: in this version, ILO and IHI are not used and are assumed to be 1 and N, respectively. 🫶

🧸 Parameters 🧸

• N — N is INTEGER. The order of the matrix A. N >= 0.
• ILO — ILO is INTEGER.
• IHI — IHI is INTEGER.

Also, 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). 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. 🦋

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. ✨

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💖 that’s the whole page, bestie! Sign-off vibes: LAPACK Version 3.12.0, from /home/abui...IG/shst01.f(3). 💖