CQPT01(3)

🌸 NAME 🌸

okay so bestie, welcome to the Library Functions Manual — section 3, the ✨library functions✨ zone — and the star of this page is our girl CQPT01. Here's where she lives:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cqpt01.f

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

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

CQPT01 — that's her, that's the function 💅

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🎀 Function/Subroutine Documentation 🎀

the full signature, no cap

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

okay so here's the tea — CQPT01 tests the QR-factorization with pivoting of a matrix A. Your girl AF is holding 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. fr fr that's the whole layout 🧚

This function returns

||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) )

where || . || is the matrix one norm. iconic honestly ✨

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🧮 Parameters

• M — INTEGER, the number of rows of the matrices A and AF. that's it, that's the row count 👑
• N — INTEGER, the number of columns of the matrices A and AF. the column count, we love her 🌸
• K — INTEGER, the number of columns of AF that have been reduced to upper triangular form. so like, how far the reduction got 🎀
• A — COMPLEX array, dimension (LDA, N). the original matrix A. the before picture 📸
• AF — 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. the after picture 💖
• LDA — INTEGER, the leading dimension of the arrays A and AF. yes the leading dimension, she matters 🦋
• TAU — COMPLEX array, dimension (K). details of the Householder transformations as returned by CGEQPF. the receipts 🧾
• JPVT — INTEGER array, dimension (N). pivot information as returned by CGEQPF. who goes where 💫
• WORK — COMPLEX array, dimension (LWORK). the workspace, doing the most as always 💅
• LWORK — INTEGER, the length of the array WORK. and bestie, LWORK >= M*N+N. not negotiable, that's the requirement ❗

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👑 Author

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

slay, four institutions, main character energy 🏛️

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📍 Definition

Definition at line 119 of file cqpt01.f.

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💀 Author

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, a robot wrote this part, don't come for me 🙈)

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okay so that's the whole page, every single parameter accounted for, no details skipped, we ate and left no crumbs 💅✨

byeeeee 🫶 this has been LAPACK, Version 3.12.0, living at /home/abui...IN/cqpt01.f(3) — mwah, see u in the next page 🎀🦋