TESTING/LIN/zqlt03.f(3)

🌸 NAME 🌸

TESTING/LIN/zqlt03.f — that's the file, bestie, from the Library Functions Manual, section 3. It's giving "LAPACK test routine with main character energy." 💖

🌈 SYNOPSIS 🌈

Functions/Subroutines

Serving the signature exactly as requested, no edits, no cap:

   Functions/Subroutines
       subroutine zqlt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
           result)
           ZQLT03

💖 Function/Subroutine Documentation 💖

Full signature, copied with care because we respect the source:

   subroutine zqlt03 (integer m, integer n, integer k, complex*16, dimension(
       lda, * ) af, complex*16, dimension( lda, * ) c, complex*16, dimension(
       lda, * ) cc, complex*16, dimension( lda, * ) q, integer lda, complex*16,
       dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork,
       double precision, dimension( * ) rwork, double precision, dimension( * )
       result)
       ZQLT03

🎯 Purpose:

ZQLT03 is literally the test bestie for ZUNMQL, which computes Q*C, Q'*C, C*Q, or C*Q'. 💅

ZQLT03 compares the results of a call to ZUNMQL with the results of forming Q explicitly by a call to ZUNGQL and then performing matrix multiplication by a call to ZGEMM. Two techniques, one vibe check. ✨

📋 Parameters

• M — M is INTEGER; she's the order of the orthogonal matrix Q, and M >= 0 is the rule. 🌟
• 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, bestie. 🌸
• K — K is INTEGER; the number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0. 🫶
• AF — AF is COMPLEX*16 array, dimension (LDA,N); details of the QL factorization of an m-by-n matrix, as returned by ZGEQLF. See CGEQLF for further details. 🦋
• C — C is COMPLEX*16 array, dimension (LDA,N). That's the whole description, bestie. 💀
• CC — CC is COMPLEX*16 array, dimension (LDA,N). Same energy. 🎀
• Q — Q is COMPLEX*16 array, dimension (LDA,M). Iconic. ✨
• LDA — LDA is INTEGER; the leading dimension of the arrays AF, C, CC, and Q. 👑
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)); the scalar factors of the elementary reflectors corresponding to the QL factorization in AF. 🌺
• WORK — WORK is COMPLEX*16 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 zqlt03.f. 📍

That's where the magic lives, bestie.

🪄 Author 🪄

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