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66 lines
1.6 KiB
Go
66 lines
1.6 KiB
Go
// Copyright ©2016 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 (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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)
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// Dorg2l generates an m×n matrix Q with orthonormal columns which is defined
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// as the last n columns of a product of k elementary reflectors of order m.
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// Q = H_{k-1} * ... * H_1 * H_0
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// See Dgelqf for more information. It must be that m >= n >= k.
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//
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// tau contains the scalar reflectors computed by Dgeqlf. tau must have length
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// at least k, and Dorg2l will panic otherwise.
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//
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// work contains temporary memory, and must have length at least n. Dorg2l will
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// panic otherwise.
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//
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// Dorg2l is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dorg2l(m, n, k int, a []float64, lda int, tau, work []float64) {
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checkMatrix(m, n, a, lda)
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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) < n {
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panic(badWork)
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}
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if m < n {
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panic(mLTN)
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}
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if k > n {
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panic(kGTN)
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}
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if n == 0 {
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return
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}
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// Initialize columns 0:n-k to columns of the unit matrix.
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for j := 0; j < n-k; j++ {
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for l := 0; l < m; l++ {
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a[l*lda+j] = 0
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}
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a[(m-n+j)*lda+j] = 1
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}
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bi := blas64.Implementation()
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for i := 0; i < k; i++ {
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ii := n - k + i
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// Apply H_i to A[0:m-k+i, 0:n-k+i] from the left.
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a[(m-n+ii)*lda+ii] = 1
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impl.Dlarf(blas.Left, m-n+ii+1, ii, a[ii:], lda, tau[i], a, lda, work)
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bi.Dscal(m-n+ii, -tau[i], a[ii:], lda)
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a[(m-n+ii)*lda+ii] = 1 - tau[i]
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// Set A[m-k+i:m, n-k+i+1] to zero.
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for l := m - n + ii + 1; l < m; l++ {
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a[l*lda+ii] = 0
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}
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}
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}
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