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50 lines
1.6 KiB
Go
50 lines
1.6 KiB
Go
// Copyright ©2015 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import "gonum.org/v1/gonum/blas"
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// Dgelq2 computes the LQ factorization of the m×n matrix A.
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//
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// In an LQ factorization, L is a lower triangular m×n matrix, and Q is an n×n
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// orthonormal matrix.
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//
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// a is modified to contain the information to construct L and Q.
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// The lower triangle of a contains the matrix L. The upper triangular elements
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// (not including the diagonal) contain the elementary reflectors. tau is modified
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// to contain the reflector scales. tau must have length of at least k = min(m,n)
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// and this function will panic otherwise.
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//
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// See Dgeqr2 for a description of the elementary reflectors and orthonormal
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// matrix Q. Q is constructed as a product of these elementary reflectors,
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// Q = H_{k-1} * ... * H_1 * H_0.
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//
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// work is temporary storage of length at least m and this function will panic otherwise.
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//
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// Dgelq2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dgelq2(m, n int, a []float64, lda int, tau, work []float64) {
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checkMatrix(m, n, a, lda)
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k := min(m, n)
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if len(tau) < k {
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panic(badTau)
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}
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if len(work) < m {
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panic(badWork)
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}
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for i := 0; i < k; i++ {
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a[i*lda+i], tau[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
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if i < m-1 {
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aii := a[i*lda+i]
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a[i*lda+i] = 1
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impl.Dlarf(blas.Right, m-i-1, n-i,
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a[i*lda+i:], 1,
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tau[i],
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a[(i+1)*lda+i:], lda,
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work)
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a[i*lda+i] = aii
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}
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}
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}
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