DLQT03(3)

🌸 dlqt03.f(3) — Library Functions Manual 🌸

okay bestie, this is the dlqt03.f(3) page, and it’s lowkey a whole Fortran testing era 💅✨

✨ NAME ✨

The NAME here is literally this source path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dlqt03.f

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

subroutine DLQT03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result)
    DLQT03

🎀 Function/Subroutine Documentation 🎀

Here’s the full signature, copied with love and exact characters 🫶

subroutine DLQT03 (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)

DLQT03 💅

✨ Purpose ✨

So DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q' — all four, periodt.

DLQT03 compares the results of a call to DORMLQ with the results of forming Q explicitly by a call to DORGLQ and then performing matrix multiplication by a call to DGEMM. It’s giving “trust but verify” but in Fortran 💖

💖 Parameters 💖

M

M is INTEGER. It’s the number of rows or columns of the matrix C; C is n-by-m if Q is applied from the left, or m-by-n if Q is applied from the right. M >= 0.

N

N is INTEGER. The order of the orthogonal matrix Q. N >= 0.

K

K is INTEGER. The number of elementary reflectors whose product defines the orthogonal matrix Q. N >= K >= 0.

AF

AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the LQ factorization of an m-by-n matrix, as returned by DGELQF. See SGELQF 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,N).

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 LQ 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 n-by-n orthogonal matrix Q.

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

👑 Author 👑

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

Definition at line 134 of file dlqt03.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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