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5f0141ca4c
Changes made in dsp/fourier/internal/fftpack break the formatting used there, so these are reverted. There will be complaints in CI. [git-generate] gofmt -w . go generate gonum.org/v1/gonum/blas go generate gonum.org/v1/gonum/blas/gonum go generate gonum.org/v1/gonum/unit go generate gonum.org/v1/gonum/unit/constant go generate gonum.org/v1/gonum/graph/formats/dot go generate gonum.org/v1/gonum/graph/formats/rdf go generate gonum.org/v1/gonum/stat/card git checkout -- dsp/fourier/internal/fftpack
89 lines
2.3 KiB
Go
89 lines
2.3 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 gonum
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import "gonum.org/v1/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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//
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// Qᵀ * A * P = B
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//
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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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switch {
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case m < 0:
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panic(mLT0)
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case n < 0:
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panic(nLT0)
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case lda < max(1, n):
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panic(badLdA)
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}
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// Quick return if possible.
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minmn := min(m, n)
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if minmn == 0 {
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return
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}
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switch {
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case len(d) < minmn:
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panic(shortD)
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case len(e) < minmn-1:
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panic(shortE)
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case len(tauQ) < minmn:
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panic(shortTauQ)
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case len(tauP) < minmn:
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panic(shortTauP)
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case len(work) < max(m, n):
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panic(shortWork)
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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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