TESTING/LIN/sqrt01.f(3)

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version 3.12.1 · 3 versions
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💖 TESTING/LIN/sqrt01.f 💖

okay so this is from the Library Functions Manual, and it's the page for TESTING/LIN/sqrt01.f. bestie, it's giving very specific Fortran test energy. 🫶

✨ NAME ✨

TESTING/LIN/sqrt01.f — that's the whole name, no extra lore. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

       subroutine sqrt01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           SQRT01

🫶 Function/Subroutine Documentation 🫶

   subroutine sqrt01 (integer m, integer n, real, dimension( lda, * ) a, real,
       dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension(
       lda, * ) r, integer lda, real, dimension( * ) tau, real, dimension(
       lwork ) work, integer lwork, real, dimension( * ) rwork, real,
       dimension( * ) result)
       SQRT01

🌸 Purpose 🌸

Okay so SQRT01 is out here testing SGEQRF, which computes the QR factorization of an m-by-n matrix A. It also partially tests SORGQR, which forms the m-by-m orthogonal matrix Q. ✨ iconic ✨

And bestie, SQRT01 compares R with Q'*A, and checks that Q is orthogonal. That's the vibe check. 🔥

🎀 Parameters 🎀

M

M is INTEGER The number of rows of the matrix A. M >= 0. (so no negative row chaos, periodt 🫶)

N

N is INTEGER The number of columns of the matrix A. N >= 0. (same energy, keep it nonnegative 💅)

A

A is REAL array, dimension (LDA,N) The m-by-n matrix A.

AF

AF is REAL array, dimension (LDA,N) Details of the QR factorization of A, as returned by SGEQRF. See SGEQRF for further details.

Q

Q is REAL array, dimension (LDA,M) The m-by-m orthogonal matrix Q.

R

R is REAL array, dimension (LDA,max(M,N)) — yep, that's literally all the original says, no extra description. 🎀

LDA

LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N).

TAU

TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by SGEQRF.

WORK

WORK is REAL array, dimension (LWORK)

LWORK

LWORK is INTEGER The dimension of the array WORK.

RWORK

RWORK is REAL array, dimension (M)

RESULT

RESULT is REAL array, dimension (2) The test ratios:

  • RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
  • RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

👑 Author 👑

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

📍 Definition 📍

Definition at line 124 of file sqrt01.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

💖 That's the whole page, bestie — source/version: LAPACK Version 3.12.0; page: TESTING/LIN/sqrt01.f(3); date: not listed in the footer, so no cap, I'm not inventing one. ✨🎀

📦 where this page comes from