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ec100cf00f
Improved function documentation Fixed dlarfb and dlarft and added full tests Added dgelq2 Working Dgels Fix many comments and tests Many PR comment responses Responded to more PR comments Many PR comments
61 lines
1.4 KiB
Go
61 lines
1.4 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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"github.com/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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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 innacurate, 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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