+++ /dev/null
-// 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
- }
-}
OSDN Git Service
