| // 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" |
| |
| // Dgelq2 computes the LQ factorization of the m×n matrix A. |
| // |
| // In an LQ factorization, L is a lower triangular m×n matrix, and Q is an n×n |
| // orthonormal matrix. |
| // |
| // a is modified to contain the information to construct L and Q. |
| // The lower triangle of a contains the matrix L. The upper triangular elements |
| // (not including the diagonal) contain the elementary reflectors. tau is modified |
| // to contain the reflector scales. tau must have length of at least k = min(m,n) |
| // and this function will panic otherwise. |
| // |
| // See Dgeqr2 for a description of the elementary reflectors and orthonormal |
| // matrix Q. Q is constructed as a product of these elementary reflectors, |
| // Q = H_{k-1} * ... * H_1 * H_0. |
| // |
| // work is temporary storage of length at least m and this function will panic otherwise. |
| // |
| // Dgelq2 is an internal routine. It is exported for testing purposes. |
| func (impl Implementation) Dgelq2(m, n int, a []float64, lda int, tau, work []float64) { |
| checkMatrix(m, n, a, lda) |
| k := min(m, n) |
| if len(tau) < k { |
| panic(badTau) |
| } |
| if len(work) < m { |
| panic(badWork) |
| } |
| for i := 0; i < k; i++ { |
| a[i*lda+i], tau[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1) |
| if i < m-1 { |
| aii := a[i*lda+i] |
| a[i*lda+i] = 1 |
| impl.Dlarf(blas.Right, m-i-1, n-i, |
| a[i*lda+i:], 1, |
| tau[i], |
| a[(i+1)*lda+i:], lda, |
| work) |
| a[i*lda+i] = aii |
| } |
| } |
| } |