TESTING/EIG/cgqrts.f(3)

💖 NAME 💖

okay so this page is TESTING/EIG/cgqrts.f, straight out of the Library Functions Manual, and it is literally all about one very specific LAPACK test routine. slay.

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✨ SYNOPSIS ✨

Functions/Subroutines — yes bestie, that's the category:

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

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🎀 Function/Subroutine Documentation 🎀

Here's the full signature, no cap:

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 an N-by-P matrix B:

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

and that's the whole vibe of this routine. 💅

🌈 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)).
• 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. yes, the page literally says A here, and I'm not fixing it, bestie 😭.
• 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)).
• BWK — BWK is COMPLEX 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 COMPLEX array, dimension (min(P,N)). The scalar factors of the elementary reflectors, as returned by SGGRQF. yes, SGGRQF — that's what the page says 🫶.
• 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

Definition at line 174 of file cgqrts.f.

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👑 Author

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