CGRQTS(3)

💅 NAME 💅

okay so bestie, welcome to cgrqts.f(3), straight out of the Library Functions Manual. This page is literally about the file at:

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

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✨ SYNOPSIS ✨

Functions/Subroutines:

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

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🦋 Function/Subroutine Documentation 🦋

The signature, exactly as the page gives it:

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

🌸 Purpose 🌸

No cap, CGRQTS tests CGGRQF, 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 of this subroutine. 💖

🎀 Parameters 🎀

• M — M is INTEGER. It's the number of rows of the matrix A. Constraint: M >= 0.
• P — P is INTEGER. It's the number of rows of the matrix B. Constraint: P >= 0.
• N — N is INTEGER. It's the number of columns of the matrices A and B. Constraint: N >= 0.
• A — A is COMPLEX array, dimension (LDA,N). It's the M-by-N matrix A.
• AF — AF is COMPLEX array, dimension (LDA,N). It holds details of the GRQ factorization of A and B, as returned by CGGRQF; see CGGRQF for further details.
• Q — Q is COMPLEX array, dimension (LDA,N). It's the N-by-N unitary matrix Q.
• R — R is COMPLEX array, dimension (LDA,MAX(M,N)).
• LDA — LDA is INTEGER. It's the leading dimension of the arrays A, AF, R and Q. Constraint: LDA >= max(M,N).
• TAUA — TAUA is COMPLEX array, dimension (min(M,N)). These are the scalar factors of the elementary reflectors, as returned by SGGQRC.
• B — B is COMPLEX array, dimension (LDB,N). On entry, the P-by-N matrix A. (yes, it says A right there in the source — I'm just relaying the exact words, bestie 🙈)
• BF — BF is COMPLEX array, dimension (LDB,N). It holds details of the GQR factorization of A and B, as returned by CGGRQF; see CGGRQF for further details.
• Z — Z is REAL array, dimension (LDB,P). It's the P-by-P unitary matrix Z.
• T — T is COMPLEX array, dimension (LDB,max(P,N)).
• BWK — BWK is COMPLEX array, dimension (LDB,N).
• LDB — LDB is INTEGER. It's the leading dimension of the arrays B, BF, Z and T. Constraint: LDB >= max(P,N).
• TAUB — TAUB is COMPLEX array, dimension (min(P,N)). These are the scalar factors of the elementary reflectors, as returned by SGGRQF.
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. It's the dimension of the array WORK. Constraint: LWORK >= max(M,P,N)**2.
• RWORK — RWORK is REAL array, dimension (M).
• RESULT — RESULT is REAL array, dimension (4). These are 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 cgrqts.f.

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off, bestie: source LAPACK, version Version 3.12.0, and the footer date line — which in the source page is the path-ish bit /home/abui...IG/cgrqts.f(3) with no separate calendar date shown — mwah 💅💖🫶