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63 lines
1.5 KiB
Go
63 lines
1.5 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 native
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import (
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"math"
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"gonum.org/v1/gonum/blas/blas64"
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)
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// Dlarfg generates an elementary reflector for a Householder matrix. It creates
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// a real elementary reflector of order n such that
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// H * (alpha) = (beta)
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// ( x) ( 0)
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// H^T * H = I
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// H is represented in the form
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// H = 1 - tau * (1; v) * (1 v^T)
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// where tau is a real scalar.
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//
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// On entry, x contains the vector x, on exit it contains v.
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//
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// Dlarfg is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dlarfg(n int, alpha float64, x []float64, incX int) (beta, tau float64) {
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if n < 0 {
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panic(nLT0)
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}
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if n <= 1 {
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return alpha, 0
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}
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checkVector(n-1, x, incX)
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bi := blas64.Implementation()
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xnorm := bi.Dnrm2(n-1, x, incX)
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if xnorm == 0 {
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return alpha, 0
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}
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beta = -math.Copysign(impl.Dlapy2(alpha, xnorm), alpha)
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safmin := dlamchS / dlamchE
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knt := 0
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if math.Abs(beta) < safmin {
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// xnorm and beta may be inaccurate, scale x and recompute.
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rsafmn := 1 / safmin
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for {
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knt++
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bi.Dscal(n-1, rsafmn, x, incX)
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beta *= rsafmn
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alpha *= rsafmn
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if math.Abs(beta) >= safmin {
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break
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}
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}
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xnorm = bi.Dnrm2(n-1, x, incX)
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beta = -math.Copysign(impl.Dlapy2(alpha, xnorm), alpha)
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}
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tau = (beta - alpha) / beta
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bi.Dscal(n-1, 1/(alpha-beta), x, incX)
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for j := 0; j < knt; j++ {
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beta *= safmin
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}
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return beta, tau
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}
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