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13102a112c
Also, simplify DlartgTest based on Supplemental Material to: Edward Anderson. 2017. Algorithm 978: Safe Scaling in the Level 1 BLAS. ACM Trans. Math. Softw. 44, 1, Article 12 (July 2017), 28 pages. DOI:https://doi.org/10.1145/3061665
100 lines
2.1 KiB
Go
100 lines
2.1 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 testlapack
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import (
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"fmt"
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"math"
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"testing"
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)
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type Dlartger interface {
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Dlartg(f, g float64) (cs, sn, r float64)
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}
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func DlartgTest(t *testing.T, impl Dlartger) {
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const tol = 20 * dlamchP
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safmin := dlamchS
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safmax := 1 / safmin
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values := []float64{
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-safmax,
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-1 / dlamchP,
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-1,
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-1.0 / 3,
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-dlamchP,
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-safmin,
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0,
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safmin,
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dlamchP,
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1.0 / 3,
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1,
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1 / dlamchP,
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safmax,
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math.Inf(-1),
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math.Inf(1),
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math.NaN(),
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}
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for _, f := range values {
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for _, g := range values {
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name := fmt.Sprintf("Case f=%v,g=%v", f, g)
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// Generate a plane rotation so that
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// [ cs sn] * [f] = [r]
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// [-sn cs] [g] = [0]
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// where cs*cs + sn*sn = 1.
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cs, sn, r := impl.Dlartg(f, g)
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switch {
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case math.IsNaN(f) || math.IsNaN(g):
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if !math.IsNaN(r) {
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t.Errorf("%v: unexpected r=%v; want NaN", name, r)
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}
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case math.IsInf(f, 0) || math.IsInf(g, 0):
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if !math.IsNaN(r) && !math.IsInf(r, 0) {
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t.Errorf("%v: unexpected r=%v; want NaN or Inf", name, r)
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}
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default:
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d := math.Max(math.Abs(f), math.Abs(g))
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d = math.Min(math.Max(safmin, d), safmax)
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fs := f / d
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gs := g / d
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rs := r / d
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// Check that cs*f + sn*g = r.
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rnorm := math.Abs(rs)
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if rnorm == 0 {
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rnorm = math.Max(math.Abs(fs), math.Abs(gs))
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if rnorm == 0 {
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rnorm = 1
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}
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}
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resid := math.Abs(rs-(cs*fs+sn*gs)) / rnorm
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if resid > tol {
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t.Errorf("%v: cs*f + sn*g != r; resid=%v", name, resid)
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}
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// Check that -sn*f + cs*g = 0.
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resid = math.Abs(-sn*fs + cs*gs)
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if resid > tol {
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t.Errorf("%v: -sn*f + cs*g != 0; resid=%v", name, resid)
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}
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// Check that cs*cs + sn*sn = 1.
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resid = math.Abs(1 - (cs*cs + sn*sn))
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if resid > tol {
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t.Errorf("%v: cs*cs + sn*sn != 1; resid=%v", name, resid)
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}
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// Check that cs is non-negative.
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if math.Abs(f) > math.Abs(g) && cs < 0 {
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t.Errorf("%v: cs is negative; cs=%v", name, cs)
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}
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}
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}
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}
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}
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