TESTING/EIG/sgrqts.f(3)

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version 3.12.1 · 2 versions
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okay bestie, this is the manual page for TESTING/EIG/sgrqts.f — from the Library Functions Manual, section (3), no cap. grab a strawberry 🍓 and let’s get into this test-routine energy.

🌸 NAME 🌸

TESTING/EIG/sgrqts.f — that’s literally the name, bestie. 💅

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

  • subroutine sgrqts (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result) — SGRQTS 🫶

💖 Function/Subroutine Documentation 💖

🦋 SGRQTS (main character) 🦋

subroutine sgrqts (integer m, integer p, integer n, real, dimension( lda, *
    ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real,
    dimension( lda, * ) r, integer lda, real, dimension( * ) taua, real,
    dimension( ldb, * ) b, real, dimension( ldb, * ) bf, real, dimension(
    ldb, * ) z, real, dimension( ldb, * ) t, real, dimension( ldb, * ) bwk,
    integer ldb, real, dimension( * ) taub, real, dimension( lwork ) work,
    integer lwork, real, dimension( * ) rwork, real, dimension( 4 ) result)

SGRQTS — iconic, honestly. 💖

🎀 Purpose 🎀

SGRQTS tests SGGRQF, which computes the GRQ factorization of an M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q. That’s the whole vibe. ✨

🍓 Parameters 🍓

okay, parameter time — buckle up, bestie, because there are a lot of them and every single one matters. 💅

  • M — M is INTEGER; the number of rows of the matrix A. M >= 0. 💖
  • P — P is INTEGER; the number of rows of the matrix B. P >= 0. 🌸
  • N — N is INTEGER; the number of columns of the matrices A and B. N >= 0. 🦋
  • 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 GRQ factorization of A and B, as returned by SGGRQF, see SGGRQF for further details. 🫶
  • Q — Q is REAL array, dimension (LDA,N); the N-by-N orthogonal matrix Q. ✨
  • R — R is REAL array, dimension (LDA,MAX(M,N)). 💜
  • LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, R and Q. LDA >= max(M,N). 💅
  • TAUA — TAUA is REAL array, dimension (min(M,N)); the scalar factors of the elementary reflectors, as returned by SGGQRC. 🌈
  • B — B is REAL array, dimension (LDB,N); on entry, the P-by-N matrix A. 🙈
  • BF — BF is REAL array, dimension (LDB,N); details of the GQR factorization of A and B, as returned by SGGRQF, see SGGRQF for further details. 💖
  • Z — Z is REAL array, dimension (LDB,P); the P-by-P orthogonal matrix Z. ⭐
  • T — T is REAL array, dimension (LDB,max(P,N)). 🔥
  • BWK — BWK is REAL array, dimension (LDB,N). 👑
  • LDB — LDB is INTEGER; the leading dimension of the arrays B, BF, Z and T. LDB >= max(P,N). 🎀
  • TAUB — TAUB is REAL array, dimension (min(P,N)); the scalar factors of the elementary reflectors, as returned by SGGRQF. 🌸
  • WORK — WORK is REAL array, dimension (LWORK). 🦋
  • LWORK — LWORK is INTEGER; the dimension of the array WORK, LWORK >= max(M,P,N)**2. 💀
  • RWORK — RWORK is REAL array, dimension (M). 💜
  • RESULT — RESULT is REAL array, dimension (4); the test ratios:
    • RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)
    • RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)
    • RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )
    • RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )

slay. 🧚

👑 Author 👑

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

Definition at line 175 of file sgrqts.f. 📌

🌟 Author 🌟

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💖 that’s a wrap, bestie — LAPACK Version 3.12.0. stay slay! 💅

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