mirror of
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120 lines
3.1 KiB
Go
120 lines
3.1 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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"math"
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"testing"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/floats"
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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 = 1e-14
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// safmn2 and safmx2 are copied from native.Dlartg.
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// safmn2 ~ 2*10^{-146}
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safmn2 := math.Pow(dlamchB, math.Trunc(math.Log(dlamchS/dlamchE)/math.Log(dlamchB)/2))
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// safmx2 ~ 5*10^145
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safmx2 := 1 / safmn2
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rnd := rand.New(rand.NewSource(1))
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for i := 0; i < 1000; i++ {
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// Generate randomly huge, tiny, and "normal" input arguments to Dlartg.
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var f float64
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var fHuge bool
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switch rnd.Intn(3) {
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case 0:
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// Huge f.
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fHuge = true
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// scale is in the range (10^{-10}, 10^10].
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scale := math.Pow(10, 10-20*rnd.Float64())
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// f is in the range (5*10^135, 5*10^155].
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f = scale * safmx2
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case 1:
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// Tiny f.
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// f is in the range (2*10^{-156}, 2*10^{-136}].
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f = math.Pow(10, 10-20*rnd.Float64()) * safmn2
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default:
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f = rnd.NormFloat64()
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}
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if rnd.Intn(2) == 0 {
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// Sometimes change the sign of f.
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f *= -1
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}
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var g float64
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var gHuge bool
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switch rnd.Intn(3) {
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case 0:
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// Huge g.
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gHuge = true
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g = math.Pow(10, 10-20*rnd.Float64()) * safmx2
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case 1:
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// Tiny g.
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g = math.Pow(10, 10-20*rnd.Float64()) * safmn2
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default:
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g = rnd.NormFloat64()
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}
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if rnd.Intn(2) == 0 {
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g *= -1
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}
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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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cs, sn, r := impl.Dlartg(f, g)
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// Check that the first equation holds.
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rWant := cs*f + sn*g
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if !floats.EqualWithinAbsOrRel(math.Abs(rWant), math.Abs(r), tol, tol) {
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t.Errorf("Case f=%v,g=%v: unexpected r. Want %v, got %v", f, g, rWant, r)
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}
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// Check that cs and sn define a plane rotation. The 2×2 matrix
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// has orthogonal columns by construction, so only check that
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// the columns/rows have unit norm.
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oneTest := cs*cs + sn*sn
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if math.Abs(oneTest-1) > tol {
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t.Errorf("Case f=%v,g=%v: expected cs^2+sn^2==1, got %v", f, g, oneTest)
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}
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if !fHuge && !gHuge {
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// Check that the second equation holds.
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// If both numbers are huge, cancellation errors make
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// this test unreliable.
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zeroTest := -sn*f + cs*g
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if math.Abs(zeroTest) > tol {
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t.Errorf("Case f=%v,g=%v: expected zero, got %v", f, g, zeroTest)
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}
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}
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// Check that cs is positive as documented.
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if math.Abs(f) > math.Abs(g) && cs < 0 {
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t.Errorf("Case f=%v,g=%v: unexpected negative cs %v", f, g, cs)
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}
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}
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// Check other documented special cases.
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for i := 0; i < 100; i++ {
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cs, sn, _ := impl.Dlartg(rnd.NormFloat64(), 0)
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if cs != 1 {
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t.Errorf("Unexpected cs for g=0. Want 1, got %v", cs)
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}
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if sn != 0 {
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t.Errorf("Unexpected sn for g=0. Want 0, got %v", sn)
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}
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}
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for i := 0; i < 100; i++ {
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cs, sn, _ := impl.Dlartg(0, rnd.NormFloat64())
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if cs != 0 {
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t.Errorf("Unexpected cs for f=0. Want 0, got %v", cs)
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}
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if sn != 1 {
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t.Errorf("Unexpected sn for f=0. Want 1, got %v", sn)
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}
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}
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}
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