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75 lines
2.1 KiB
Go
75 lines
2.1 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 "github.com/gonum/blas"
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// Dgebd2 reduces an m×n matrix A to upper or lower bidiagonal form by an orthogonal
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// transformation.
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// Q^T * A * P = B
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// if m >= n, B is upper diagonal, otherwise B is lower bidiagonal.
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// d is the diagonal, len = min(m,n)
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// e is the off-diagonal len = min(m,n)-1
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//
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// Dgebd2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dgebd2(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64) {
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checkMatrix(m, n, a, lda)
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if len(d) < min(m, n) {
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panic(badD)
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}
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if len(e) < min(m, n)-1 {
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panic(badE)
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}
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if len(tauQ) < min(m, n) {
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panic(badTauQ)
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}
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if len(tauP) < min(m, n) {
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panic(badTauP)
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}
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if len(work) < max(m, n) {
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panic(badWork)
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}
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if m >= n {
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for i := 0; i < n; i++ {
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a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
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d[i] = a[i*lda+i]
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a[i*lda+i] = 1
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// Apply H_i to A[i:m, i+1:n] from the left.
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if i < n-1 {
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impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tauQ[i], a[i*lda+i+1:], lda, work)
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}
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a[i*lda+i] = d[i]
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if i < n-1 {
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a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
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e[i] = a[i*lda+i+1]
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a[i*lda+i+1] = 1
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impl.Dlarf(blas.Right, m-i-1, n-i-1, a[i*lda+i+1:], 1, tauP[i], a[(i+1)*lda+i+1:], lda, work)
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a[i*lda+i+1] = e[i]
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} else {
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tauP[i] = 0
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}
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}
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return
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}
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for i := 0; i < m; i++ {
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a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
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d[i] = a[i*lda+i]
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a[i*lda+i] = 1
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if i < m-1 {
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impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tauP[i], a[(i+1)*lda+i:], lda, work)
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}
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a[i*lda+i] = d[i]
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if i < m-1 {
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a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
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e[i] = a[(i+1)*lda+i]
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a[(i+1)*lda+i] = 1
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impl.Dlarf(blas.Left, m-i-1, n-i-1, a[(i+1)*lda+i:], lda, tauQ[i], a[(i+1)*lda+i+1:], lda, work)
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a[(i+1)*lda+i] = e[i]
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} else {
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tauQ[i] = 0
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}
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}
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}
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