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// Copyright ©2016 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"
"gonum.org/v1/gonum/blas/blas64"
)
// Dorg2l generates an m×n matrix Q with orthonormal columns which is defined
// as the last n columns of a product of k elementary reflectors of order m.
//
// Q = H_{k-1} * ... * H_1 * H_0
//
// See Dgelqf for more information. It must be that m >= n >= k.
//
// tau contains the scalar reflectors computed by Dgeqlf. tau must have length
// at least k, and Dorg2l will panic otherwise.
//
// work contains temporary memory, and must have length at least n. Dorg2l will
// panic otherwise.
//
// Dorg2l is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dorg2l(m, n, k int, a []float64, lda int, tau, work []float64) {
switch {
case m < 0:
panic(mLT0)
case n < 0:
panic(nLT0)
case n > m:
panic(nGTM)
case k < 0:
panic(kLT0)
case k > n:
panic(kGTN)
case lda < max(1, n):
panic(badLdA)
}
if n == 0 {
return
}
switch {
case len(a) < (m-1)*lda+n:
panic(shortA)
case len(tau) < k:
panic(shortTau)
case len(work) < n:
panic(shortWork)
}
// Initialize columns 0:n-k to columns of the unit matrix.
for j := 0; j < n-k; j++ {
for l := 0; l < m; l++ {
a[l*lda+j] = 0
}
a[(m-n+j)*lda+j] = 1
}
bi := blas64.Implementation()
for i := 0; i < k; i++ {
ii := n - k + i
// Apply H_i to A[0:m-k+i, 0:n-k+i] from the left.
a[(m-n+ii)*lda+ii] = 1
impl.Dlarf(blas.Left, m-n+ii+1, ii, a[ii:], lda, tau[i], a, lda, work)
bi.Dscal(m-n+ii, -tau[i], a[ii:], lda)
a[(m-n+ii)*lda+ii] = 1 - tau[i]
// Set A[m-k+i:m, n-k+i+1] to zero.
for l := m - n + ii + 1; l < m; l++ {
a[l*lda+ii] = 0
}
}
}
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