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54 lines
1.7 KiB
Go
54 lines
1.7 KiB
Go
// Copyright ©2017 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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// Dgerq2 computes an RQ factorization of the m×n matrix A,
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// A = R * Q.
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// On exit, if m <= n, the upper triangle of the subarray
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// A[0:m, n-m:n] contains the m×m upper triangular matrix R.
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// If m >= n, the elements on and above the (m-n)-th subdiagonal
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// contain the m×n upper trapezoidal matrix R.
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// The remaining elements, with tau, represent the
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// orthogonal matrix Q as a product of min(m,n) elementary
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// reflectors.
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//
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// The matrix Q is represented as a product of elementary reflectors
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// Q = H_0 H_1 . . . H_{min(m,n)-1}.
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// Each H(i) has the form
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// H_i = I - tau_i * v * v^T
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// where v is a vector with v[0:n-k+i-1] stored in A[m-k+i, 0:n-k+i-1],
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// v[n-k+i:n] = 0 and v[n-k+i] = 1.
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//
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// tau must have length min(m,n) and work must have length m, otherwise
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// Dgerq2 will panic.
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//
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// Dgerq2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dgerq2(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 := k - 1; i >= 0; i-- {
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// Generate elementary reflector H[i] to annihilate
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// A[m-k+i, 0:n-k+i-1].
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mki := m - k + i
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nki := n - k + i
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var aii float64
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aii, tau[i] = impl.Dlarfg(nki+1, a[mki*lda+nki], a[mki*lda:], 1)
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// Apply H[i] to A[0:m-k+i-1, 0:n-k+i] from the right.
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a[mki*lda+nki] = 1
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impl.Dlarf(blas.Right, mki, nki+1, a[mki*lda:], 1, tau[i], a, lda, work)
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a[mki*lda+nki] = aii
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}
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}
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