ZGRQTS(3)

💖 ZGRQTS(3) 💖

Okay bestie, welcome to the ZGRQTS(3) page from the Library Functions Manual. The header/footer shorten the file to /home/abui...IG/zgrqts.f(3), and the full path is waiting in NAME below. This is LAPACK test-subroutine territory, and yes, it's giving "I test the factorization so you don't have to" energy. 🦋

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🎀 NAME 🎀

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

That's the whole NAME, no cap. The file is zgrqts.f, and the short header/footer path is /home/abui...IG/zgrqts.f(3). 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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🦋 Function/Subroutine Documentation 🦋

subroutine ZGRQTS (integer m, integer p, integer n, complex*16, dimension(
    lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension(
    lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16,
    dimension( * ) taua, complex*16, dimension( ldb, * ) b, complex*16,
    dimension( ldb, * ) bf, complex*16, dimension( ldb, * ) z, complex*16,
    dimension( ldb, * ) t, complex*16, dimension( ldb, * ) bwk, integer ldb,
    complex*16, dimension( * ) taub, complex*16, dimension( lwork ) work,
    integer lwork, double precision, dimension( * ) rwork, double precision,
    dimension( 4 ) result)
    ZGRQTS

🌟 Purpose 🌟

ZGRQTS is the test bestie for ZGGRQF — the routine that computes the GRQ factorization of an M-by-N matrix A and a P-by-N matrix B, specifically:

A = R*Q and B = Z*T*Q.

It's literally giving "I check the factorization" main-character energy. 👑

🍓 Parameters 🍓

• M — M is INTEGER; the number of rows of the matrix A. Constraint: M >= 0.
• P — P is INTEGER; the number of rows of the matrix B. Constraint: P >= 0.
• N — N is INTEGER; the number of columns of the matrices A and B. Constraint: N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N); the M-by-N matrix A.
• AF — AF is COMPLEX*16 array, dimension (LDA,N); details of the GRQ factorization of A and B, as returned by ZGGRQF, see CGGRQF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N); the N-by-N unitary matrix Q.
• R — R is COMPLEX*16 array, dimension (LDA,MAX(M,N)).
• LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, R and Q. Constraint: LDA >= max(M,N).
• TAUA — TAUA is COMPLEX*16 array, dimension (min(M,N)); the scalar factors of the elementary reflectors, as returned by DGGQRC.
• B — B is COMPLEX*16 array, dimension (LDB,N); on entry, the P-by-N matrix A (yes, the source says A here, bestie — keeping it exactly as written).
• BF — BF is COMPLEX*16 array, dimension (LDB,N); details of the GQR factorization of A and B, as returned by ZGGRQF, see CGGRQF for further details.
• Z — Z is DOUBLE PRECISION array, dimension (LDB,P); the P-by-P unitary matrix Z (the parameter text says DOUBLE PRECISION, so I'm keeping that exactly).
• T — T is COMPLEX*16 array, dimension (LDB,max(P,N)).
• BWK — BWK is COMPLEX*16 array, dimension (LDB,N).
• LDB — LDB is INTEGER; the leading dimension of the arrays B, BF, Z and T. Constraint: LDB >= max(P,N).
• TAUB — TAUB is COMPLEX*16 array, dimension (min(P,N)); the scalar factors of the elementary reflectors, as returned by DGGRQF.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER; the dimension of the array WORK, with 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 are:

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 zgrqts.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! Footer check: LAPACK, Version 3.12.0, and the page path /home/abui...IG/zgrqts.f(3). There's no separate date line in this one, so no invented date — just the source/version vibe. Mwah! 💅✨