TESTING/LIN/sqpt01.f(3)

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🌸 NAME 🌸

TESTING/LIN/sqpt01.f

✨ SYNOPSIS ✨

Functions/Subroutines

  • real function sqpt01 (m, n, k, a, af, lda, tau, jpvt, work, lwork) — SQPT01

💅 Function/Subroutine Documentation 💅

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)

SQPT01

Purpose

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 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 REAL array, dimension (LDA, N) The original matrix A.

AF

AF is REAL array, dimension (LDA,N) 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 The leading dimension of the arrays A and AF.

TAU

TAU is REAL array, dimension (K) Details of the Householder transformations as returned by SGEQPF.

JPVT

JPVT is INTEGER array, dimension (N) Pivot information as returned by SGEQPF.

WORK

WORK is REAL 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 sqpt01.f.

Author

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