CQRT02(3)

💖 CQRT02(3) — Library Functions Manual 💖

okay so bestie, welcome to the CQRT02(3) page from the Library Functions Manual. This is LAPACK testing-routine energy, and she is here to check on CUNGQR like the responsible icon she is. Lowkey obsessed. ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cqrt02.f

That whole source path is the name, no cap. It's giving "I live deep in the LAPACK build tree" and honestly? Respect. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine CQRT02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
           result)

CQRT02 — the subroutine, the moment, the main character. 👑

🦋 Function/Subroutine Documentation 🦋

   subroutine CQRT02 (integer m, integer n, integer k, complex, dimension( lda,
       * ) a, complex, dimension( lda, * ) af, complex, dimension( lda, * ) q,
       complex, dimension( lda, * ) r, integer lda, complex, dimension( * )
       tau, complex, dimension( lwork ) work, integer lwork, real, dimension( *
       ) rwork, real, dimension( * ) result)

CQRT02 — yes, the name again, because she deserves a second entrance. 💅

🎯 Purpose

CQRT02 tests CUNGQR, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors. That's the whole assignment, and she ate. 🔥

Given the QR factorization of an m-by-n matrix A, CQRT02 generates the orthogonal matrix Q defined by the factorization of the first k columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and checks that the columns of Q are orthonormal. Literally the math bestie check-in. 🧮✨

🧮 Parameters

• M — M is INTEGER. The number of rows of the matrix Q to be generated. M >= 0.
• N — N is INTEGER. The number of columns of the matrix Q to be generated. M >= N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
• A — A is COMPLEX array, dimension (LDA,N). The m-by-n matrix A which was factorized by CQRT01.
• AF — AF is COMPLEX array, dimension (LDA,N). Details of the QR factorization of A, as returned by CGEQRF. See CGEQRF for further details.
• Q — Q is COMPLEX array, dimension (LDA,N).
• R — R is COMPLEX array, dimension (LDA,N).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and R. LDA >= M.
• TAU — TAU is COMPLEX array, dimension (N). The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
• RWORK — RWORK is REAL array, dimension (M).
• RESULT — RESULT is REAL array, dimension (2). The test ratios:
  • RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
  • RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 133 of file cqrt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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