TESTING/LIN/zqpt01.f(3)

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version 3.12.1 · 2 versions
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💅 NAME 💅

okay so bestie, this is TESTING/LIN/zqpt01.f — manual page TESTING/LIN/zqpt01.f(3) from the Library Functions Manual. We're in iconic LAPACK territory. ✨

✨ SYNOPSIS ✨

Functions/Subroutines

double precision function zqpt01 (m, n, k, a, af, lda, tau, jpvt, work,
    lwork)
ZQPT01

🫶 Function/Subroutine Documentation 🫶

double precision function zqpt01 (integer m, integer n, integer k,
    complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af,
    integer lda, complex*16, dimension( * ) tau, integer, dimension( * )
    jpvt, complex*16, dimension( lwork ) work, integer lwork)

ZQPT01

🎯 Purpose

okay so ZQPT01 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) )

📋 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*16 array, dimension (LDA, N). The original matrix A.
  • AF — AF is COMPLEX*16 array, dimension (LDA,N). The (possibly partial) output of ZGEQPF. 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*16 array, dimension (K). Details of the Householder transformations as returned by ZGEQPF.
  • JPVT — JPVT is INTEGER array, dimension (N). Pivot information as returned by ZGEQPF.
  • WORK — WORK is COMPLEX*16 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

Definition at line 118 of file zqpt01.f.

🌸 Author 🌸

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