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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / lapack / gonum / dgebd2.go

diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgebd2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgebd2.go
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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.
+//  Q^T * 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) {
+       checkMatrix(m, n, a, lda)
+       if len(d) < min(m, n) {
+               panic(badD)
+       }
+       if len(e) < min(m, n)-1 {
+               panic(badE)
+       }
+       if len(tauQ) < min(m, n) {
+               panic(badTauQ)
+       }
+       if len(tauP) < min(m, n) {
+               panic(badTauP)
+       }
+       if len(work) < max(m, n) {
+               panic(badWork)
+       }
+       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
+               }
+       }
+}