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 // 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) { switch { case m < 0: panic(mLT0) case n < 0: panic(nLT0) case lda < max(1, n): panic(badLdA) } // Quick return if possible. k := min(m, n) if k == 0 { return } switch { case len(a) < (m-1)*lda+n: panic(shortA) case len(tau) < k: panic(shortTau) case len(work) < m: panic(shortWork) } 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 } } }