TESTING/LIN/cqpt01.f(3)

🎀 TESTING/LIN/cqpt01.f 🎀

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/cqpt01.f — yes, the filename is basically the whole title vibe here. This one is a LAPACK testing routine, and ngl it’s giving “quietly important math gremlin” in the best way 💅

💖 NAME 💖

TESTING/LIN/cqpt01.f

✨ SYNOPSIS ✨

Functions/Subroutines

       real function cqpt01 (m, n, k, a, af, lda, tau, jpvt, work, lwork)
           CQPT01

🌸 Function/Subroutine Documentation 🌸

   real function cqpt01 (integer m, integer n, integer k, complex, dimension(
       lda, * ) a, complex, dimension( lda, * ) af, integer lda, complex,
       dimension( * ) tau, integer, dimension( * ) jpvt, complex, dimension(
       lwork ) work, integer lwork)
       CQPT01

🦋 Purpose 🦋

CQPT01 tests the QR-factorization with pivoting of a matrix A. The array AF contains the (possibly partial) QR-factorization of A, where the upper triangle of AF(1:k,1:k) is a partial triangular factor, the entries below the diagonal in the first k columns are the Householder vectors, and the rest of AF contains a partially updated matrix.

This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) ) where || . || is matrix one norm. math slay, no cap ✨

🌈 Parameters 🌈

• M — M is INTEGER. The number of rows of the matrices A and AF.
• N — N is INTEGER. The number of columns of the matrices A and AF.
• K — K is INTEGER. The number of columns of AF that have been reduced to upper triangular form.
• A — A is COMPLEX array, dimension (LDA, N). The original matrix A.
• AF — AF is COMPLEX array, dimension (LDA,N). The (possibly partial) output of CGEQPF. The upper triangle of AF(1:k,1:k) is a partial triangular factor, the entries below the diagonal in the first k columns are the Householder vectors, and the rest of AF contains a partially updated matrix.
• LDA — LDA is INTEGER. The leading dimension of the arrays A and AF.
• TAU — TAU is COMPLEX array, dimension (K). Details of the Householder transformations as returned by CGEQPF.
• JPVT — JPVT is INTEGER array, dimension (N). Pivot information as returned by CGEQPF.
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= M*N+N.

🫶 Author 🫶

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

Definition at line 119 of file cqpt01.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie — LAPACK Version 3.12.0, page TESTING/LIN/cqpt01.f(3), from the Library Functions Manual. Stay slay 💅💖🎀