TESTING/LIN/dqpt01.f(3)

✨ NAME ✨

okay so bestie, this whole page is about TESTING/LIN/dqpt01.f — that’s the manual name, and it’s giving “LAPACK testing routine” energy. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

double precision function dqpt01 (m, n, k, a, af, lda, tau, jpvt, work,
    lwork)

DQPT01 — yes, that’s the name again, iconic.

🦋 FUNCTION/SUBROUTINE DOCUMENTATION 🦋

double precision function dqpt01 (integer m, integer n, integer k, double
    precision, dimension( lda, * ) a, double precision, dimension( lda, * )
    af, integer lda, double precision, dimension( * ) tau, integer,
    dimension( * ) jpvt, double precision, dimension( lwork ) work, integer
    lwork)

DQPT01

🎯 Purpose 🎯

DQPT01 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; 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 DOUBLE PRECISION array, dimension (LDA, N); the original matrix A.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N); the (possibly partial) output of DGEQPF. 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 DOUBLE PRECISION array, dimension (K); details of the Householder transformations as returned by DGEQPF.
• JPVT — JPVT is INTEGER array, dimension (N); pivot information as returned by DGEQPF.
• WORK — WORK is DOUBLE PRECISION 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 dqpt01.f.

👑 Author 👑

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