TESTING/LIN/dqrt03.f(3)

💖 NAME 💖

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🦋 SYNOPSIS 🦋

Here's the cast list, fr fr:

   Functions/Subroutines
       subroutine dqrt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
           result)
           DQRT03

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🌈 Function/Subroutine Documentation 🌈

This is the full signature, character-for-character, because we do not mess with signatures 💅:

subroutine dqrt03 (integer m, integer n, integer k, double precision,
    dimension( lda, * ) af, double precision, dimension( lda, * ) c, double
    precision, dimension( lda, * ) cc, double precision, dimension( lda, * )
    q, integer lda, double precision, dimension( * ) tau, double precision,
    dimension( lwork ) work, integer lwork, double precision, dimension( * )
    rwork, double precision, dimension( * ) result)

DQRT03

🎯 Purpose 🎯

DQRT03 is the vibe check for DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.

It compares the results of a call to DORMQR with the results of forming Q explicitly by a call to DORGQR and then performing matrix multiplication by a call to DGEMM. Two techniques, one showdown 😭🔥

🧸 Parameters 🧸

• M — M is INTEGER. The order of the orthogonal matrix Q. M >= 0.
• N — N is INTEGER. The number of rows or columns of the matrix C; C is m-by-n if Q is applied from the left, or n-by-m if Q is applied from the right. N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the QR factorization of an m-by-n matrix, as returned by DGEQRF. See DGEQRF for further details.
• C — C is DOUBLE PRECISION array, dimension (LDA,N).
• CC — CC is DOUBLE PRECISION array, dimension (LDA,N).
• Q — Q is DOUBLE PRECISION array, dimension (LDA,M).
• LDA — LDA is INTEGER. The leading dimension of the arrays AF, C, CC, and Q.
• TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (4). The test ratios compare two techniques for multiplying a random matrix C by an m-by-m orthogonal matrix Q.

RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )

👑 Author 👑

The academic credits, as listed:

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

Definition at line 134 of file dqrt03.f.

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📜 Author 📜

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