TESTING/EIG/dgrqts.f(3)

💖 TESTING/EIG/dgrqts.f 💖

okay bestie, this is the Library Functions Manual page for TESTING/EIG/dgrqts.f, and it's literally the DGRQTS test routine. Buckle up, we're keeping every flag and every formula exactly as the source says. 💅

🌸 NAME 🌸

TESTING/EIG/dgrqts.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, no cap:

   subroutine dgrqts (integer m, integer p, integer n, 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)

DGRQTS

🧚 Purpose: 🧚

DGRQTS tests DGGRQF, 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 purpose, periodt. ✨

🍓 Parameters 🍓

• 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 DOUBLE PRECISION array, dimension (LDA,N). The M-by-N matrix A.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the GRQ factorization of A and B, as returned by DGGRQF, see SGGRQF for further details.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N). The N-by-N orthogonal matrix Q.
• R — R is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by DGGQRC.
• B — B is DOUBLE PRECISION array, dimension (LDB,N). On entry, the P-by-N matrix A. (Bestie, yes, the source literally says A here — I'm not fixing it. 💀)
• BF — BF is DOUBLE PRECISION array, dimension (LDB,N). Details of the GQR factorization of A and B, as returned by DGGRQF, see SGGRQF 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)).
• BWK — BWK is DOUBLE PRECISION 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 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).
• LWORK — LWORK is INTEGER. The dimension of the array WORK, LWORK >= max(M,P,N)**2.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is DOUBLE PRECISION 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 )

💅 Author 💅

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

Definition at line 174 of file dgrqts.f.

🌈 Author 🌈

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💖 Cute little footer sign-off: LAPACK · Version 3.12.0 · TESTING/EIG/dgrqts.f(3). (No date in the original footer, bestie — keeping it 100.) 💖