CGQRTS(3)

✨ NAME ✨

Okay bestie 💖, welcome to CGQRTS(3) from the Library Functions Manual — the vibe is very "LAPACK test routine who knows she's that girl." The actual file is:

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

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🌸 SYNOPSIS 🌸

🫶 Functions/Subroutines 🫶

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

💅 Function/Subroutine Documentation 💅

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

🎀 Purpose 🎀

CGQRTS tests CGGQRF, 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. Periodt. ✨

⭐ 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 COMPLEX array, dimension (LDA,M). The N-by-M matrix A.
• AF — AF is COMPLEX array, dimension (LDA,N). Details of the GQR factorization of A and B, as returned by CGGQRF, see CGGQRF for further details.
• Q — Q is COMPLEX array, dimension (LDA,N). The M-by-M unitary matrix Q.
• R — R is COMPLEX array, dimension (LDA,MAX(M,N)). That's it, that's the description — iconic minimalism 💅.
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, R and Q. LDA >= max(M,N).
• TAUA — TAUA is COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by CGGQRF.
• B — B is COMPLEX array, dimension (LDB,P). On entry, the N-by-P matrix A.

Not me keeping the exact B line that says "matrix A" — yes bestie, that's literally what the page says. Facts are facts. 💀

• BF — BF is COMPLEX array, dimension (LDB,N). Details of the GQR factorization of A and B, as returned by CGGQRF, see CGGQRF for further details.
• Z — Z is COMPLEX array, dimension (LDB,P). The P-by-P unitary matrix Z.
• T — T is COMPLEX array, dimension (LDB,max(P,N)). No extra notes, she's just here for the vibes.
• BWK — BWK is COMPLEX array, dimension (LDB,N). Also no extra notes.
• LDB — LDB is INTEGER. The leading dimension of the arrays B, BF, Z and T. LDB >= max(P,N).
• TAUB — TAUB is COMPLEX array, dimension (min(P,N)). The scalar factors of the elementary reflectors, as returned by SGGRQF.
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK, LWORK >= max(N,M,P)**2.
• RWORK — RWORK is REAL array, dimension (max(N,M,P)).
• RESULT — RESULT is REAL 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 cgqrts.f. 📍

Definition at line 174 of file cgqrts.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the whole page, bestie 🫶. Stay iconic — footer energy is LAPACK Version 3.12.0, page /home/abui...IG/cgqrts.f(3). 💅✨🦋