TESTING/EIG/dgqrts.f(3)

💅 NAME 💅

okay so this is the manual page for TESTING/EIG/dgqrts.f, and it's coming at you from the Library Functions Manual. That's the whole NAME section, bestie — it's a file hanging out in the LAPACK testing corner of the universe. 🫶

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✨ SYNOPSIS ✨

Quick vibe check: here's the function/subroutine situation.

🛠 Functions/Subroutines

       subroutine dgqrts (n, m, p, a, af, q, r, lda, taua, b, bf, z, t, bwk,
           ldb, taub, work, lwork, rwork, result)
           DGQRTS

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🧚 Function/Subroutine Documentation 🧚

Here's the full signature, character-for-character, no cap:

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

🎯 Purpose

okay so DGQRTS tests DGGQRF, which computes the GQR factorization of an N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z. That's the whole purpose, and it ate. 💖

🌸 Parameters 🌸

• N — N is INTEGER; the number of rows of the matrices A and B. N >= 0.
• M — M is INTEGER; the number of columns of the matrix A. M >= 0.
• P — P is INTEGER; the number of columns of the matrix B. P >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,M); the N-by-M matrix A.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N); details of the GQR factorization of A and B, as returned by DGGQRF, see SGGQRF for further details.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N); the M-by-M orthogonal matrix Q.
• R — R is DOUBLE PRECISION array, dimension (LDA,MAX(M,N)). That's literally all the original says for this one — no extra description. 🫣
• LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, R and Q. LDA >= max(M,N).
• TAUA — TAUA is DOUBLE PRECISION array, dimension (min(M,N)); the scalar factors of the elementary reflectors, as returned by DGGQRF.
• B — B is DOUBLE PRECISION array, dimension (LDB,P); on entry, the N-by-P matrix A. (Yes, the original literally says A here — I'm not fixing it, bestie. 🙈)
• BF — BF is DOUBLE PRECISION array, dimension (LDB,N); details of the GQR factorization of A and B, as returned by DGGQRF, see SGGQRF for further details.
• Z — Z is DOUBLE PRECISION array, dimension (LDB,P); the P-by-P orthogonal matrix Z.
• T — T is DOUBLE PRECISION array, dimension (LDB,max(P,N)). No extra description in the original.
• BWK — BWK is DOUBLE PRECISION array, dimension (LDB,N). No extra description in the original.
• LDB — LDB is INTEGER; the leading dimension of the arrays B, BF, Z and T. LDB >= max(P,N).
• TAUB — TAUB is DOUBLE PRECISION array, dimension (min(P,N)); the scalar factors of the elementary reflectors, as returned by DGGRQF.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK). No extra description in the original.
• LWORK — LWORK is INTEGER; the dimension of the array WORK, LWORK >= max(N,M,P)**2.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (max(N,M,P)). No extra description in the original.
• RESULT — RESULT is DOUBLE PRECISION array, dimension (4); the test ratios:

RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)
RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)
RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )

👑 Author

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

Definition at line 174 of file dgqrts.f.

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💖 Author 💖

This page was generated automatically by Doxygen for LAPACK from the source code. Slay, automated docs. ✨

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mwah 💋 — source/version tea: LAPACK, Version 3.12.0, and this page is TESTING/EIG/dgqrts.f(3). Bye bestie! 🌈🎀