mirror of
https://github.com/gonum/gonum.git
synced 2025-10-05 15:16:59 +08:00
379 lines
8.8 KiB
Go
379 lines
8.8 KiB
Go
// Copyright ©2020 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 r3
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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/scalar"
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"gonum.org/v1/gonum/mat"
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)
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func TestAdd(t *testing.T) {
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for _, test := range []struct {
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v1, v2 Vec
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want Vec
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}{
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{Vec{0, 0, 0}, Vec{0, 0, 0}, Vec{0, 0, 0}},
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{Vec{1, 0, 0}, Vec{0, 0, 0}, Vec{1, 0, 0}},
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{Vec{1, 2, 3}, Vec{4, 5, 7}, Vec{5, 7, 10}},
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{Vec{1, -3, 5}, Vec{1, -6, -6}, Vec{2, -9, -1}},
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{Vec{1, 2, 3}, Vec{-1, -2, -3}, Vec{}},
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} {
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got := Add(test.v1, test.v2)
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if got != test.want {
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t.Errorf(
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"error: %v + %v: got=%v, want=%v",
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test.v1, test.v2, got, test.want,
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)
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}
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}
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}
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func TestSub(t *testing.T) {
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for _, test := range []struct {
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v1, v2 Vec
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want Vec
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}{
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{Vec{0, 0, 0}, Vec{0, 0, 0}, Vec{0, 0, 0}},
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{Vec{1, 0, 0}, Vec{0, 0, 0}, Vec{1, 0, 0}},
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{Vec{1, 2, 3}, Vec{4, 5, 7}, Vec{-3, -3, -4}},
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{Vec{1, -3, 5}, Vec{1, -6, -6}, Vec{0, 3, 11}},
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{Vec{1, 2, 3}, Vec{1, 2, 3}, Vec{}},
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} {
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got := Sub(test.v1, test.v2)
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if got != test.want {
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t.Errorf(
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"error: %v - %v: got=%v, want=%v",
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test.v1, test.v2, got, test.want,
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)
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}
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}
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}
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func TestScale(t *testing.T) {
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for _, test := range []struct {
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a float64
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v Vec
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want Vec
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}{
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{3, Vec{0, 0, 0}, Vec{0, 0, 0}},
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{1, Vec{1, 0, 0}, Vec{1, 0, 0}},
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{0, Vec{1, 0, 0}, Vec{0, 0, 0}},
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{3, Vec{1, 0, 0}, Vec{3, 0, 0}},
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{-1, Vec{1, -3, 5}, Vec{-1, 3, -5}},
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{2, Vec{1, -3, 5}, Vec{2, -6, 10}},
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{10, Vec{1, 2, 3}, Vec{10, 20, 30}},
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} {
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got := Scale(test.a, test.v)
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if got != test.want {
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t.Errorf(
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"error: %v * %v: got=%v, want=%v",
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test.a, test.v, got, test.want)
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}
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}
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}
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func TestDot(t *testing.T) {
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for _, test := range []struct {
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u, v Vec
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want float64
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}{
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{Vec{1, 2, 3}, Vec{1, 2, 3}, 14},
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{Vec{1, 0, 0}, Vec{1, 0, 0}, 1},
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{Vec{1, 0, 0}, Vec{0, 1, 0}, 0},
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{Vec{1, 0, 0}, Vec{0, 1, 1}, 0},
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{Vec{1, 1, 1}, Vec{-1, -1, -1}, -3},
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{Vec{1, 2, 2}, Vec{-0.3, 0.4, -1.2}, -1.9},
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} {
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{
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got := Dot(test.u, test.v)
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if got != test.want {
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t.Errorf(
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"error: %v · %v: got=%v, want=%v",
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test.u, test.v, got, test.want,
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)
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}
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}
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{
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got := Dot(test.v, test.u)
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if got != test.want {
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t.Errorf(
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"error: %v · %v: got=%v, want=%v",
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test.v, test.u, got, test.want,
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)
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}
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}
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}
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}
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func TestCross(t *testing.T) {
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for _, test := range []struct {
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v1, v2, want Vec
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}{
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{Vec{1, 0, 0}, Vec{1, 0, 0}, Vec{0, 0, 0}},
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{Vec{1, 0, 0}, Vec{0, 1, 0}, Vec{0, 0, 1}},
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{Vec{0, 1, 0}, Vec{1, 0, 0}, Vec{0, 0, -1}},
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{Vec{1, 2, 3}, Vec{-4, 5, -6}, Vec{-27, -6, 13}},
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{Vec{1, 2, 3}, Vec{1, 2, 3}, Vec{}},
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{Vec{1, 2, 3}, Vec{2, 3, 4}, Vec{-1, 2, -1}},
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} {
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got := Cross(test.v1, test.v2)
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if got != test.want {
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t.Errorf(
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"error: %v × %v = %v, want %v",
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test.v1, test.v2, got, test.want,
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)
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}
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}
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}
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func TestNorm(t *testing.T) {
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for _, test := range []struct {
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v Vec
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want float64
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}{
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{Vec{0, 0, 0}, 0},
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{Vec{0, 1, 0}, 1},
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{Vec{3, -4, 12}, 13},
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{Vec{1, 1e-16, 1e-32}, 1},
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{Vec{-0, 4.3145006366056343748277397783556100978621924913975e-196, 4.3145006366056343748277397783556100978621924913975e-196}, 6.101625315155041e-196},
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} {
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if got, want := Norm(test.v), test.want; got != want {
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t.Errorf("|%v| = %v, want %v", test.v, got, want)
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}
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}
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}
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func TestNorm2(t *testing.T) {
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for _, test := range []struct {
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v Vec
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want float64
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}{
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{Vec{0, 0, 0}, 0},
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{Vec{0, 1, 0}, 1},
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{Vec{1, 1, 1}, 3},
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{Vec{1, 2, 3}, 14},
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{Vec{3, -4, 12}, 169},
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{Vec{1, 1e-16, 1e-32}, 1},
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// This will underflow and return zero.
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{Vec{-0, 4.3145006366056343748277397783556100978621924913975e-196, 4.3145006366056343748277397783556100978621924913975e-196}, 0},
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} {
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if got, want := Norm2(test.v), test.want; got != want {
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t.Errorf("|%v|^2 = %v, want %v", test.v, got, want)
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}
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}
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}
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func TestUnit(t *testing.T) {
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for _, test := range []struct {
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v, want Vec
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}{
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{Vec{}, Vec{math.NaN(), math.NaN(), math.NaN()}},
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{Vec{1, 0, 0}, Vec{1, 0, 0}},
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{Vec{0, 1, 0}, Vec{0, 1, 0}},
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{Vec{0, 0, 1}, Vec{0, 0, 1}},
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{Vec{1, 1, 1}, Vec{1. / math.Sqrt(3), 1. / math.Sqrt(3), 1. / math.Sqrt(3)}},
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{Vec{1, 1e-16, 1e-32}, Vec{1, 1e-16, 1e-32}},
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} {
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got := Unit(test.v)
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if !vecEqual(got, test.want) {
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t.Errorf(
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"Normalize(%v) = %v, want %v",
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test.v, got, test.want,
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)
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}
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if test.v == (Vec{}) {
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return
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}
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if n, want := Norm(got), 1.0; n != want {
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t.Errorf("|%v| = %v, want 1", got, n)
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}
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}
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}
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func TestCos(t *testing.T) {
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for _, test := range []struct {
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v1, v2 Vec
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want float64
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}{
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{Vec{1, 1, 1}, Vec{1, 1, 1}, 1},
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{Vec{1, 1, 1}, Vec{-1, -1, -1}, -1},
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{Vec{1, 1, 1}, Vec{1, -1, 1}, 1.0 / 3},
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{Vec{1, 0, 0}, Vec{1, 0, 0}, 1},
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{Vec{1, 0, 0}, Vec{0, 1, 0}, 0},
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{Vec{1, 0, 0}, Vec{0, 1, 1}, 0},
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{Vec{1, 0, 0}, Vec{-1, 0, 0}, -1},
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} {
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tol := 1e-14
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got := Cos(test.v1, test.v2)
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if !scalar.EqualWithinAbs(got, test.want, tol) {
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t.Errorf("cos(%v, %v)= %v, want %v",
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test.v1, test.v2, got, test.want,
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)
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}
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}
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}
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func TestRotate(t *testing.T) {
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const tol = 1e-14
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for _, test := range []struct {
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v, axis Vec
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alpha float64
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want Vec
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}{
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{Vec{1, 0, 0}, Vec{1, 0, 0}, math.Pi / 2, Vec{1, 0, 0}},
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{Vec{1, 0, 0}, Vec{1, 0, 0}, 0, Vec{1, 0, 0}},
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{Vec{1, 0, 0}, Vec{1, 0, 0}, 2 * math.Pi, Vec{1, 0, 0}},
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{Vec{1, 0, 0}, Vec{0, 0, 0}, math.Pi / 2, Vec{math.NaN(), math.NaN(), math.NaN()}},
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{Vec{1, 0, 0}, Vec{0, 1, 0}, math.Pi / 2, Vec{0, 0, -1}},
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{Vec{1, 0, 0}, Vec{0, 1, 0}, math.Pi, Vec{-1, 0, 0}},
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{Vec{2, 0, 0}, Vec{0, 1, 0}, math.Pi, Vec{-2, 0, 0}},
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{Vec{1, 2, 3}, Vec{1, 1, 1}, 2. / 3. * math.Pi, Vec{3, 1, 2}},
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} {
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got := Rotate(test.v, test.alpha, test.axis)
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if !vecApproxEqual(got, test.want, tol) {
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t.Errorf(
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"quat rotate(%v, %v, %v)= %v, want=%v",
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test.v, test.alpha, test.axis, got, test.want,
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)
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}
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var gotv mat.VecDense
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gotv.MulVec(NewRotation(test.alpha, test.axis).Mat(), vecDense(test.v))
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got = vec(gotv)
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if !vecApproxEqual(got, test.want, tol) {
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t.Errorf(
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"matrix rotate(%v, %v, %v)= %v, want=%v",
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test.v, test.alpha, test.axis, got, test.want,
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)
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}
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}
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}
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var vectorFields = []struct {
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field func(Vec) Vec
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divergence func(Vec) float64
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jacobian func(Vec) *Mat
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}{
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{
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field: func(v Vec) Vec {
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// (x*y*z, y*z, z*x)
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return Vec{X: v.X * v.Y * v.Z, Y: v.Y * v.Z, Z: v.Z * v.X}
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},
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divergence: func(v Vec) float64 {
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return v.X + v.Y*v.Z + v.Z
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},
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jacobian: func(v Vec) *Mat {
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return NewMat([]float64{
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v.Y * v.Z, v.X * v.Z, v.X * v.Y,
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0, v.Z, v.Y,
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v.Z, 0, v.X,
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})
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},
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},
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{
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field: func(v Vec) Vec {
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// (x*y*z*cos(y), y*z+sin(x), z*x*sin(y))
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sx := math.Sin(v.X)
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sy, cy := math.Sincos(v.Y)
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return Vec{
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X: v.X * v.Y * v.Z * cy,
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Y: v.Y*v.Z + sx,
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Z: v.Z * v.X * sy,
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}
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},
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divergence: func(v Vec) float64 {
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sy, cy := math.Sincos(v.Y)
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return v.X*sy + v.Y*v.Z*cy + v.Z
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},
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jacobian: func(v Vec) *Mat {
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cx := math.Cos(v.X)
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sy, cy := math.Sincos(v.Y)
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return NewMat([]float64{
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v.Y * v.Z * cy, v.X*v.Z*cy - v.X*v.Y*v.Z*sy, v.X * v.Y * cy,
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cx, v.Z, v.Y,
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v.Z * sy, v.X * v.Z * cy, v.X * sy,
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})
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},
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},
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}
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func TestDivergence(t *testing.T) {
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const (
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tol = 1e-10
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h = 1e-2
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)
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step := Vec{X: h, Y: h, Z: h}
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rnd := rand.New(rand.NewSource(1))
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for _, test := range vectorFields {
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for i := 0; i < 30; i++ {
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p := randomVec(rnd)
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got := Divergence(p, step, test.field)
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want := test.divergence(p)
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if math.Abs(got-want) > tol {
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t.Errorf("result out of tolerance. got %v, want %v", got, want)
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}
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}
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}
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}
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func TestGradient(t *testing.T) {
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const (
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tol = 1e-6
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h = 1e-5
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)
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step := Vec{X: h, Y: h, Z: h}
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rnd := rand.New(rand.NewSource(1))
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for _, test := range scalarFields {
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for i := 0; i < 30; i++ {
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p := randomVec(rnd)
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got := Gradient(p, step, test.field)
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want := test.gradient(p)
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if !vecApproxEqual(got, want, tol) {
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t.Errorf("result out of tolerance. got %v, want %v", got, want)
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}
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}
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}
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}
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func vecDense(v Vec) *mat.VecDense {
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return mat.NewVecDense(3, []float64{v.X, v.Y, v.Z})
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}
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func vec(v mat.VecDense) Vec {
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if v.Len() != 3 {
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panic(mat.ErrShape)
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}
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return Vec{v.AtVec(0), v.AtVec(1), v.AtVec(2)}
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}
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func vecIsNaN(v Vec) bool {
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return math.IsNaN(v.X) && math.IsNaN(v.Y) && math.IsNaN(v.Z)
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}
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func vecIsNaNAny(v Vec) bool {
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return math.IsNaN(v.X) || math.IsNaN(v.Y) || math.IsNaN(v.Z)
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}
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func vecEqual(a, b Vec) bool {
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if vecIsNaNAny(a) || vecIsNaNAny(b) {
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return vecIsNaN(a) && vecIsNaN(b)
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}
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return a == b
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}
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func vecApproxEqual(a, b Vec, tol float64) bool {
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if vecIsNaNAny(a) || vecIsNaNAny(b) {
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return vecIsNaN(a) && vecIsNaN(b)
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}
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return scalar.EqualWithinAbs(a.X, b.X, tol) &&
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scalar.EqualWithinAbs(a.Y, b.Y, tol) &&
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scalar.EqualWithinAbs(a.Z, b.Z, tol)
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}
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