SQPT01(3)

🌸 SQPT01(3) — Library Functions Manual 🌸

okay so bestie, this is the Library Functions Manual page for SQPT01(3), and it's giving “let's verify a pivoted QR factorization” energy. 🦋

✨ NAME ✨

The source file behind this page is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqpt01.f

✨ SYNOPSIS ✨

Functions/Subroutines

• real function SQPT01 (m, n, k, a, af, lda, tau, jpvt, work, lwork) — yup, that's the whole function, and its name is SQPT01. 💅

real function SQPT01 (integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( * ) tau, integer, dimension( * ) jpvt, real, dimension( lwork ) work, integer lwork)

💖 Function/Subroutine Documentation 💖

Purpose

Okay so SQPT01 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. 🎀

Parameters

• M — M is INTEGER; it's the number of rows of the matrices A and AF. 💖
• N — N is INTEGER; it's the number of columns of the matrices A and AF. ✨
• K — K is INTEGER; it's the number of columns of AF that have been reduced to upper triangular form. 🦋
• A — A is a REAL array with dimension (LDA, N); it's the original matrix A. 🌸
• AF — AF is a REAL array with dimension (LDA,N); it's the (possibly partial) output of SGEQPF. 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; it's the leading dimension of the arrays A and AF. 🫶
• TAU — TAU is a REAL array with dimension (K); it holds details of the Householder transformations as returned by SGEQPF. 😭
• JPVT — JPVT is an INTEGER array with dimension (N); it holds pivot information as returned by SGEQPF. 🔥
• WORK — WORK is a REAL array with dimension (LWORK). 👑
• LWORK — LWORK is INTEGER; it's 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 sqpt01.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 💖 This one's footer vibe is LAPACK Version 3.12.0, page path /home/abui...IN/sqpt01.f(3). Slay. 🎀