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 // Copyright ©2015 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" // Dgebd2 reduces an m×n matrix A to upper or lower bidiagonal form by an orthogonal // transformation. // Qᵀ * A * P = B // if m >= n, B is upper diagonal, otherwise B is lower bidiagonal. // d is the diagonal, len = min(m,n) // e is the off-diagonal len = min(m,n)-1 // // Dgebd2 is an internal routine. It is exported for testing purposes. func (impl Implementation) Dgebd2(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64) { switch { case m < 0: panic(mLT0) case n < 0: panic(nLT0) case lda < max(1, n): panic(badLdA) } // Quick return if possible. minmn := min(m, n) if minmn == 0 { return } switch { case len(d) < minmn: panic(shortD) case len(e) < minmn-1: panic(shortE) case len(tauQ) < minmn: panic(shortTauQ) case len(tauP) < minmn: panic(shortTauP) case len(work) < max(m, n): panic(shortWork) } if m >= n { for i := 0; i < n; i++ { a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda) d[i] = a[i*lda+i] a[i*lda+i] = 1 // Apply H_i to A[i:m, i+1:n] from the left. if i < n-1 { impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tauQ[i], a[i*lda+i+1:], lda, work) } a[i*lda+i] = d[i] if i < n-1 { 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) e[i] = a[i*lda+i+1] a[i*lda+i+1] = 1 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) a[i*lda+i+1] = e[i] } else { tauP[i] = 0 } } return } for i := 0; i < m; i++ { a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1) d[i] = a[i*lda+i] a[i*lda+i] = 1 if i < m-1 { impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tauP[i], a[(i+1)*lda+i:], lda, work) } a[i*lda+i] = d[i] if i < m-1 { 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) e[i] = a[(i+1)*lda+i] a[(i+1)*lda+i] = 1 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) a[(i+1)*lda+i] = e[i] } else { tauQ[i] = 0 } } }