// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// modification, are permitted provided that the following conditions are met:
//
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// this list of conditions and the following disclaimer.
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// this list of conditions and the following disclaimer in the documentation
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// Author: keir@google.com (Keir Mierle)
#include "ceres/jet.h"
#include <algorithm>
#include <cmath>
#include "glog/logging.h"
#include "gtest/gtest.h"
#include "ceres/fpclassify.h"
#include "ceres/stringprintf.h"
#include "ceres/test_util.h"
#define VL VLOG(1)
namespace ceres {
namespace internal {
const double kE = 2.71828182845904523536;
typedef Jet<double, 2> J;
// Convenient shorthand for making a jet.
J MakeJet(double a, double v0, double v1) {
J z;
z.a = a;
z.v[0] = v0;
z.v[1] = v1;
return z;
}
// On a 32-bit optimized build, the mismatch is about 1.4e-14.
double const kTolerance = 1e-13;
void ExpectJetsClose(const J &x, const J &y) {
ExpectClose(x.a, y.a, kTolerance);
ExpectClose(x.v[0], y.v[0], kTolerance);
ExpectClose(x.v[1], y.v[1], kTolerance);
}
TEST(Jet, Jet) {
// Pick arbitrary values for x and y.
J x = MakeJet(2.3, -2.7, 1e-3);
J y = MakeJet(1.7, 0.5, 1e+2);
VL << "x = " << x;
VL << "y = " << y;
{ // Check that log(exp(x)) == x.
J z = exp(x);
J w = log(z);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, x);
}
{ // Check that (x * y) / x == y.
J z = x * y;
J w = z / x;
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, y);
}
{ // Check that sqrt(x * x) == x.
J z = x * x;
J w = sqrt(z);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, x);
}
{ // Check that sqrt(y) * sqrt(y) == y.
J z = sqrt(y);
J w = z * z;
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, y);
}
{ // Check that cos(2*x) = cos(x)^2 - sin(x)^2
J z = cos(J(2.0) * x);
J w = cos(x)*cos(x) - sin(x)*sin(x);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, z);
}
{ // Check that sin(2*x) = 2*cos(x)*sin(x)
J z = sin(J(2.0) * x);
J w = J(2.0)*cos(x)*sin(x);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, z);
}
{ // Check that cos(x)*cos(x) + sin(x)*sin(x) = 1
J z = cos(x) * cos(x);
J w = sin(x) * sin(x);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z + w, J(1.0));
}
{ // Check that atan2(r*sin(t), r*cos(t)) = t.
J t = MakeJet(0.7, -0.3, +1.5);
J r = MakeJet(2.3, 0.13, -2.4);
VL << "t = " << t;
VL << "r = " << r;
J u = atan2(r * sin(t), r * cos(t));
VL << "u = " << u;
ExpectJetsClose(u, t);
}
{ // Check that tan(x) = sin(x) / cos(x).
J z = tan(x);
J w = sin(x) / cos(x);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
{ // Check that tan(atan(x)) = x.
J z = tan(atan(x));
J w = x;
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
{ // Check that cosh(x)*cosh(x) - sinh(x)*sinh(x) = 1
J z = cosh(x) * cosh(x);
J w = sinh(x) * sinh(x);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z - w, J(1.0));
}
{ // Check that tanh(x + y) = (tanh(x) + tanh(y)) / (1 + tanh(x) tanh(y))
J z = tanh(x + y);
J w = (tanh(x) + tanh(y)) / (J(1.0) + tanh(x) * tanh(y));
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
{ // Check that pow(x, 1) == x.
VL << "x = " << x;
J u = pow(x, 1.);
VL << "u = " << u;
ExpectJetsClose(x, u);
}
{ // Check that pow(x, 1) == x.
J y = MakeJet(1, 0.0, 0.0);
VL << "x = " << x;
VL << "y = " << y;
J u = pow(x, y);
VL << "u = " << u;
ExpectJetsClose(x, u);
}
{ // Check that pow(e, log(x)) == x.
J logx = log(x);
VL << "x = " << x;
VL << "y = " << y;
J u = pow(kE, logx);
VL << "u = " << u;
ExpectJetsClose(x, u);
}
{ // Check that pow(e, log(x)) == x.
J logx = log(x);
J e = MakeJet(kE, 0., 0.);
VL << "x = " << x;
VL << "log(x) = " << logx;
J u = pow(e, logx);
VL << "u = " << u;
ExpectJetsClose(x, u);
}
{ // Check that pow(e, log(x)) == x.
J logx = log(x);
J e = MakeJet(kE, 0., 0.);
VL << "x = " << x;
VL << "logx = " << logx;
J u = pow(e, logx);
VL << "u = " << u;
ExpectJetsClose(x, u);
}
{ // Check that pow(x,y) = exp(y*log(x)).
J logx = log(x);
J e = MakeJet(kE, 0., 0.);
VL << "x = " << x;
VL << "logx = " << logx;
J u = pow(e, y*logx);
J v = pow(x, y);
VL << "u = " << u;
VL << "v = " << v;
ExpectJetsClose(v, u);
}
{ // Check that 1 + x == x + 1.
J a = x + 1.0;
J b = 1.0 + x;
ExpectJetsClose(a, b);
}
{ // Check that 1 - x == -(x - 1).
J a = 1.0 - x;
J b = -(x - 1.0);
ExpectJetsClose(a, b);
}
{ // Check that x/s == x*s.
J a = x / 5.0;
J b = x * 5.0;
ExpectJetsClose(5.0 * a, b / 5.0);
}
{ // Check that x / y == 1 / (y / x).
J a = x / y;
J b = 1.0 / (y / x);
VL << "a = " << a;
VL << "b = " << b;
ExpectJetsClose(a, b);
}
{ // Check that abs(-x * x) == sqrt(x * x).
ExpectJetsClose(abs(-x), sqrt(x * x));
}
{ // Check that cos(acos(x)) == x.
J a = MakeJet(0.1, -2.7, 1e-3);
ExpectJetsClose(cos(acos(a)), a);
ExpectJetsClose(acos(cos(a)), a);
J b = MakeJet(0.6, 0.5, 1e+2);
ExpectJetsClose(cos(acos(b)), b);
ExpectJetsClose(acos(cos(b)), b);
}
{ // Check that sin(asin(x)) == x.
J a = MakeJet(0.1, -2.7, 1e-3);
ExpectJetsClose(sin(asin(a)), a);
ExpectJetsClose(asin(sin(a)), a);
J b = MakeJet(0.4, 0.5, 1e+2);
ExpectJetsClose(sin(asin(b)), b);
ExpectJetsClose(asin(sin(b)), b);
}
}
TEST(Jet, JetsInEigenMatrices) {
J x = MakeJet(2.3, -2.7, 1e-3);
J y = MakeJet(1.7, 0.5, 1e+2);
J z = MakeJet(5.3, -4.7, 1e-3);
J w = MakeJet(9.7, 1.5, 10.1);
Eigen::Matrix<J, 2, 2> M;
Eigen::Matrix<J, 2, 1> v, r1, r2;
M << x, y, z, w;
v << x, z;
// Check that M * v == (v^T * M^T)^T
r1 = M * v;
r2 = (v.transpose() * M.transpose()).transpose();
ExpectJetsClose(r1(0), r2(0));
ExpectJetsClose(r1(1), r2(1));
}
TEST(JetTraitsTest, ClassificationMixed) {
Jet<double, 3> a(5.5, 0);
a.v[0] = std::numeric_limits<double>::quiet_NaN();
a.v[1] = std::numeric_limits<double>::infinity();
a.v[2] = -std::numeric_limits<double>::infinity();
EXPECT_FALSE(IsFinite(a));
EXPECT_FALSE(IsNormal(a));
EXPECT_TRUE(IsInfinite(a));
EXPECT_TRUE(IsNaN(a));
}
TEST(JetTraitsTest, ClassificationNaN) {
Jet<double, 3> a(5.5, 0);
a.v[0] = std::numeric_limits<double>::quiet_NaN();
a.v[1] = 0.0;
a.v[2] = 0.0;
EXPECT_FALSE(IsFinite(a));
EXPECT_FALSE(IsNormal(a));
EXPECT_FALSE(IsInfinite(a));
EXPECT_TRUE(IsNaN(a));
}
TEST(JetTraitsTest, ClassificationInf) {
Jet<double, 3> a(5.5, 0);
a.v[0] = std::numeric_limits<double>::infinity();
a.v[1] = 0.0;
a.v[2] = 0.0;
EXPECT_FALSE(IsFinite(a));
EXPECT_FALSE(IsNormal(a));
EXPECT_TRUE(IsInfinite(a));
EXPECT_FALSE(IsNaN(a));
}
TEST(JetTraitsTest, ClassificationFinite) {
Jet<double, 3> a(5.5, 0);
a.v[0] = 100.0;
a.v[1] = 1.0;
a.v[2] = 3.14159;
EXPECT_TRUE(IsFinite(a));
EXPECT_TRUE(IsNormal(a));
EXPECT_FALSE(IsInfinite(a));
EXPECT_FALSE(IsNaN(a));
}
} // namespace internal
} // namespace ceres