Hulk did something

[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / lapack / gonum / dgehd2.go

diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dgehd2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dgehd2.go
new file mode 100644 (file)
index 0000000..3682837
--- /dev/null
+++ b/vendor/gonum.org/v1/gonum/lapack/gonum/dgehd2.go
@@ -0,0 +1,84 @@
+// Copyright ©2016 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"
+
+// Dgehd2 reduces a block of a general n×n matrix A to upper Hessenberg form H
+// by an orthogonal similarity transformation Q^T * A * Q = H.
+//
+// The matrix Q is represented as a product of (ihi-ilo) elementary
+// reflectors
+//  Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
+// Each H_i has the form
+//  H_i = I - tau[i] * v * v^T
+// where v is a real vector with v[0:i+1] = 0, v[i+1] = 1 and v[ihi+1:n] = 0.
+// v[i+2:ihi+1] is stored on exit in A[i+2:ihi+1,i].
+//
+// On entry, a contains the n×n general matrix to be reduced. On return, the
+// upper triangle and the first subdiagonal of A are overwritten with the upper
+// Hessenberg matrix H, and the elements below the first subdiagonal, with the
+// slice tau, represent the orthogonal matrix Q as a product of elementary
+// reflectors.
+//
+// The contents of A are illustrated by the following example, with n = 7, ilo =
+// 1 and ihi = 5.
+// On entry,
+//  [ a   a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [     a   a   a   a   a   a ]
+//  [                         a ]
+// on return,
+//  [ a   a   h   h   h   h   a ]
+//  [     a   h   h   h   h   a ]
+//  [     h   h   h   h   h   h ]
+//  [     v1  h   h   h   h   h ]
+//  [     v1  v2  h   h   h   h ]
+//  [     v1  v2  v3  h   h   h ]
+//  [                         a ]
+// where a denotes an element of the original matrix A, h denotes a
+// modified element of the upper Hessenberg matrix H, and vi denotes an
+// element of the vector defining H_i.
+//
+// ilo and ihi determine the block of A that will be reduced to upper Hessenberg
+// form. It must hold that 0 <= ilo <= ihi <= max(0, n-1), otherwise Dgehd2 will
+// panic.
+//
+// On return, tau will contain the scalar factors of the elementary reflectors.
+// It must have length equal to n-1, otherwise Dgehd2 will panic.
+//
+// work must have length at least n, otherwise Dgehd2 will panic.
+//
+// Dgehd2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgehd2(n, ilo, ihi int, a []float64, lda int, tau, work []float64) {
+       checkMatrix(n, n, a, lda)
+       switch {
+       case ilo < 0 || ilo > max(0, n-1):
+               panic(badIlo)
+       case ihi < min(ilo, n-1) || ihi >= n:
+               panic(badIhi)
+       case len(tau) != n-1:
+               panic(badTau)
+       case len(work) < n:
+               panic(badWork)
+       }
+
+       for i := ilo; i < ihi; i++ {
+               // Compute elementary reflector H_i to annihilate A[i+2:ihi+1,i].
+               var aii float64
+               aii, tau[i] = impl.Dlarfg(ihi-i, a[(i+1)*lda+i], a[min(i+2, n-1)*lda+i:], lda)
+               a[(i+1)*lda+i] = 1
+
+               // Apply H_i to A[0:ihi+1,i+1:ihi+1] from the right.
+               impl.Dlarf(blas.Right, ihi+1, ihi-i, a[(i+1)*lda+i:], lda, tau[i], a[i+1:], lda, work)
+
+               // Apply H_i to A[i+1:ihi+1,i+1:n] from the left.
+               impl.Dlarf(blas.Left, ihi-i, n-i-1, a[(i+1)*lda+i:], lda, tau[i], a[(i+1)*lda+i+1:], lda, work)
+               a[(i+1)*lda+i] = aii
+       }
+}