+++ /dev/null
-// Copyright ©2015 The Gonum Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package gonum
-
-import "gonum.org/v1/gonum/blas"
-
-// Dgeqr2 computes a QR factorization of the m×n matrix A.
-//
-// In a QR factorization, Q is an m×m orthonormal matrix, and R is an
-// upper triangular m×n matrix.
-//
-// A is modified to contain the information to construct Q and R.
-// The upper triangle of a contains the matrix R. The lower triangular elements
-// (not including the diagonal) contain the elementary reflectors. tau is modified
-// to contain the reflector scales. tau must have length at least min(m,n), and
-// this function will panic otherwise.
-//
-// The ith elementary reflector can be explicitly constructed by first extracting
-// the
-// v[j] = 0 j < i
-// v[j] = 1 j == i
-// v[j] = a[j*lda+i] j > i
-// and computing H_i = I - tau[i] * v * v^T.
-//
-// The orthonormal matrix Q can be constructed from a product of these elementary
-// reflectors, Q = H_0 * H_1 * ... * H_{k-1}, where k = min(m,n).
-//
-// work is temporary storage of length at least n and this function will panic otherwise.
-//
-// Dgeqr2 is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dgeqr2(m, n int, a []float64, lda int, tau, work []float64) {
- // TODO(btracey): This is oriented such that columns of a are eliminated.
- // This likely could be re-arranged to take better advantage of row-major
- // storage.
- checkMatrix(m, n, a, lda)
- if len(work) < n {
- panic(badWork)
- }
- k := min(m, n)
- if len(tau) < k {
- panic(badTau)
- }
- for i := 0; i < k; i++ {
- // Generate elementary reflector H_i.
- a[i*lda+i], tau[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min((i+1), m-1)*lda+i:], lda)
- if i < n-1 {
- aii := a[i*lda+i]
- a[i*lda+i] = 1
- impl.Dlarf(blas.Left, m-i, n-i-1,
- a[i*lda+i:], lda,
- tau[i],
- a[i*lda+i+1:], lda,
- work)
- a[i*lda+i] = aii
- }
- }
-}