TESTING/LIN/dqlt03.f(3)

🎀 NAME 🎀

TESTING/LIN/dqlt03.f

okay so bestie, this is the TESTING/LIN/dqlt03.f(3) page from the Library Functions Manual — the one and only DQLT03. It’s giving “Fortran test routine that’s lowkey the moment” 💅.

✨ SYNOPSIS ✨

Functions/Subroutines

   Functions/Subroutines
       subroutine dqlt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
           result)
           DQLT03

🦋 FUNCTION/SUBROUTINE DOCUMENTATION 🦋

   subroutine dqlt03 (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)
       DQLT03

💖 PURPOSE 💖

DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.

DQLT03 compares the results of a call to DORMQL with the results of forming Q explicitly by a call to DORGQL and then performing matrix multiplication by a call to DGEMM.

🌸 PARAMETERS 🌸

• M — M is INTEGER; it’s 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 QL factorization of an m-by-n matrix, as returned by DGEQLF. See SGEQLF for further details.
• C — C is DOUBLE PRECISION array, dimension (LDA,N) — that’s the whole description, no cap.
• CC — CC is DOUBLE PRECISION array, dimension (LDA,N) — same energy as C, bestie.
• 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 QL 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 👑

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

Definition at line 134 of file dqlt03.f.

🖋️ AUTHOR 🖋️

Generated automatically by Doxygen for LAPACK from the source code.

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💖 that’s the whole page, bestie — LAPACK Version 3.12.0, source/version vibes from TESTING/LIN/dqlt03.f(3), and a little periodt for the road. 🫶