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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: keir@google.com (Keir Mierle)
#include "ceres/jet.h"
#include <Eigen/Dense>
#include <algorithm>
#include <cmath>
#include "ceres/stringprintf.h"
#include "ceres/test_util.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
#define VL VLOG(1)
namespace ceres {
namespace internal {
namespace {
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);
}
const double kStep = 1e-8;
const double kNumericalTolerance = 1e-6; // Numeric derivation is quite inexact
// Differentiate using Jet and confirm results with numerical derivation.
template <typename Function>
void NumericalTest(const char* name, const Function& f, const double x) {
const double exact_dx = f(MakeJet(x, 1.0, 0.0)).v[0];
const double estimated_dx =
(f(J(x + kStep)).a - f(J(x - kStep)).a) / (2.0 * kStep);
VL << name << "(" << x << "), exact dx: " << exact_dx
<< ", estimated dx: " << estimated_dx;
ExpectClose(exact_dx, estimated_dx, kNumericalTolerance);
}
// Same as NumericalTest, but given a function taking two arguments.
template <typename Function>
void NumericalTest2(const char* name,
const Function& f,
const double x,
const double y) {
const J exact_delta = f(MakeJet(x, 1.0, 0.0), MakeJet(y, 0.0, 1.0));
const double exact_dx = exact_delta.v[0];
const double exact_dy = exact_delta.v[1];
// Sanity check - these should be equivalent:
EXPECT_EQ(exact_dx, f(MakeJet(x, 1.0, 0.0), MakeJet(y, 0.0, 0.0)).v[0]);
EXPECT_EQ(exact_dx, f(MakeJet(x, 0.0, 1.0), MakeJet(y, 0.0, 0.0)).v[1]);
EXPECT_EQ(exact_dy, f(MakeJet(x, 0.0, 0.0), MakeJet(y, 1.0, 0.0)).v[0]);
EXPECT_EQ(exact_dy, f(MakeJet(x, 0.0, 0.0), MakeJet(y, 0.0, 1.0)).v[1]);
const double estimated_dx =
(f(J(x + kStep), J(y)).a - f(J(x - kStep), J(y)).a) / (2.0 * kStep);
const double estimated_dy =
(f(J(x), J(y + kStep)).a - f(J(x), J(y - kStep)).a) / (2.0 * kStep);
VL << name << "(" << x << ", " << y << "), exact dx: " << exact_dx
<< ", estimated dx: " << estimated_dx;
ExpectClose(exact_dx, estimated_dx, kNumericalTolerance);
VL << name << "(" << x << ", " << y << "), exact dy: " << exact_dy
<< ", estimated dy: " << estimated_dy;
ExpectClose(exact_dy, estimated_dy, kNumericalTolerance);
}
} // namespace
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);
}
NumericalTest("sqrt", sqrt<double, 2>, 0.00001);
NumericalTest("sqrt", sqrt<double, 2>, 1.0);
{ // 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 pow(0, y) == 0 for y > 1, with both arguments Jets.
// This tests special case handling inside pow().
J a = MakeJet(0, 1, 2);
J b = MakeJet(2, 3, 4);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
ExpectJetsClose(c, MakeJet(0, 0, 0));
}
{ // Check that pow(0, y) == 0 for y == 1, with both arguments Jets.
// This tests special case handling inside pow().
J a = MakeJet(0, 1, 2);
J b = MakeJet(1, 3, 4);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
ExpectJetsClose(c, MakeJet(0, 1, 2));
}
{ // Check that pow(0, <1) is not finite, with both arguments Jets.
for (int i = 1; i < 10; i++) {
J a = MakeJet(0, 1, 2);
J b = MakeJet(i * 0.1, 3, 4); // b = 0.1 ... 0.9
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
EXPECT_EQ(c.a, 0.0);
EXPECT_FALSE(IsFinite(c.v[0]));
EXPECT_FALSE(IsFinite(c.v[1]));
}
for (int i = -10; i < 0; i++) {
J a = MakeJet(0, 1, 2);
J b = MakeJet(i * 0.1, 3, 4); // b = -1,-0.9 ... -0.1
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
EXPECT_FALSE(IsFinite(c.a));
EXPECT_FALSE(IsFinite(c.v[0]));
EXPECT_FALSE(IsFinite(c.v[1]));
}
{
// The special case of 0^0 = 1 defined by the C standard.
J a = MakeJet(0, 1, 2);
J b = MakeJet(0, 3, 4);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
EXPECT_EQ(c.a, 1.0);
EXPECT_FALSE(IsFinite(c.v[0]));
EXPECT_FALSE(IsFinite(c.v[1]));
}
}
{ // Check that pow(<0, b) is correct for integer b.
// This tests special case handling inside pow().
J a = MakeJet(-1.5, 3, 4);
// b integer:
for (int i = -10; i <= 10; i++) {
J b = MakeJet(i, 0, 5);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
ExpectClose(c.a, pow(-1.5, i), kTolerance);
EXPECT_TRUE(IsFinite(c.v[0]));
EXPECT_FALSE(IsFinite(c.v[1]));
ExpectClose(c.v[0], i * pow(-1.5, i - 1) * 3.0, kTolerance);
}
}
{ // Check that pow(<0, b) is correct for noninteger b.
// This tests special case handling inside pow().
J a = MakeJet(-1.5, 3, 4);
J b = MakeJet(-2.5, 0, 5);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
EXPECT_FALSE(IsFinite(c.a));
EXPECT_FALSE(IsFinite(c.v[0]));
EXPECT_FALSE(IsFinite(c.v[1]));
}
{
// Check that pow(0,y) == 0 for y == 2, with the second argument a
// Jet. This tests special case handling inside pow().
double a = 0;
J b = MakeJet(2, 3, 4);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
ExpectJetsClose(c, MakeJet(0, 0, 0));
}
{
// Check that pow(<0,y) is correct for integer y. This tests special case
// handling inside pow().
double a = -1.5;
for (int i = -10; i <= 10; i++) {
J b = MakeJet(i, 3, 0);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
ExpectClose(c.a, pow(-1.5, i), kTolerance);
EXPECT_FALSE(IsFinite(c.v[0]));
EXPECT_TRUE(IsFinite(c.v[1]));
ExpectClose(c.v[1], 0, kTolerance);
}
}
{
// Check that pow(<0,y) is correct for noninteger y. This tests special
// case handling inside pow().
double a = -1.5;
J b = MakeJet(-3.14, 3, 0);
VL << "a = " << a;
VL << "b = " << b;
J c = pow(a, b);
VL << "a^b = " << c;
EXPECT_FALSE(IsFinite(c.a));
EXPECT_FALSE(IsFinite(c.v[0]));
EXPECT_FALSE(IsFinite(c.v[1]));
}
{ // Check that 1 + x == x + 1.
J a = x + 1.0;
J b = 1.0 + x;
J c = x;
c += 1.0;
ExpectJetsClose(a, b);
ExpectJetsClose(a, c);
}
{ // Check that 1 - x == -(x - 1).
J a = 1.0 - x;
J b = -(x - 1.0);
J c = x;
c -= 1.0;
ExpectJetsClose(a, b);
ExpectJetsClose(a, -c);
}
{ // Check that (x/s)*s == (x*s)/s.
J a = x / 5.0;
J b = x * 5.0;
J c = x;
c /= 5.0;
J d = x;
d *= 5.0;
ExpectJetsClose(5.0 * a, b / 5.0);
ExpectJetsClose(a, c);
ExpectJetsClose(b, d);
}
{ // 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);
}
{
J zero = J(0.0);
// Check that J0(0) == 1.
ExpectJetsClose(BesselJ0(zero), J(1.0));
// Check that J1(0) == 0.
ExpectJetsClose(BesselJ1(zero), zero);
// Check that J2(0) == 0.
ExpectJetsClose(BesselJn(2, zero), zero);
// Check that J3(0) == 0.
ExpectJetsClose(BesselJn(3, zero), zero);
J z = MakeJet(0.1, -2.7, 1e-3);
// Check that J0(z) == Jn(0,z).
ExpectJetsClose(BesselJ0(z), BesselJn(0, z));
// Check that J1(z) == Jn(1,z).
ExpectJetsClose(BesselJ1(z), BesselJn(1, z));
// Check that J0(z)+J2(z) == (2/z)*J1(z).
// See formula http://dlmf.nist.gov/10.6.E1
ExpectJetsClose(BesselJ0(z) + BesselJn(2, z), (2.0 / z) * BesselJ1(z));
}
{ // Check that floor of a positive number works.
J a = MakeJet(0.1, -2.7, 1e-3);
J b = floor(a);
J expected = MakeJet(floor(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
{ // Check that floor of a negative number works.
J a = MakeJet(-1.1, -2.7, 1e-3);
J b = floor(a);
J expected = MakeJet(floor(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
{ // Check that floor of a positive number works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = floor(a);
J expected = MakeJet(floor(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
{ // Check that ceil of a positive number works.
J a = MakeJet(0.1, -2.7, 1e-3);
J b = ceil(a);
J expected = MakeJet(ceil(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
{ // Check that ceil of a negative number works.
J a = MakeJet(-1.1, -2.7, 1e-3);
J b = ceil(a);
J expected = MakeJet(ceil(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
{ // Check that ceil of a positive number works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = ceil(a);
J expected = MakeJet(ceil(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
{ // Check that erf works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = erf(a);
J expected = MakeJet(erf(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
NumericalTest("erf", erf<double, 2>, -1.0);
NumericalTest("erf", erf<double, 2>, 1e-5);
NumericalTest("erf", erf<double, 2>, 0.5);
NumericalTest("erf", erf<double, 2>, 100.0);
{ // Check that erfc works.
J a = MakeJet(10.123, -2.7, 1e-3);
J b = erfc(a);
J expected = MakeJet(erfc(a.a), 0.0, 0.0);
EXPECT_EQ(expected, b);
}
NumericalTest("erfc", erfc<double, 2>, -1.0);
NumericalTest("erfc", erfc<double, 2>, 1e-5);
NumericalTest("erfc", erfc<double, 2>, 0.5);
NumericalTest("erfc", erfc<double, 2>, 100.0);
{ // Check that cbrt(x * x * x) == x.
J z = x * x * x;
J w = cbrt(z);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, x);
}
{ // Check that cbrt(y) * cbrt(y) * cbrt(y) == y.
J z = cbrt(y);
J w = z * z * z;
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(w, y);
}
{ // Check that cbrt(x) == pow(x, 1/3).
J z = cbrt(x);
J w = pow(x, 1.0 / 3.0);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
NumericalTest("cbrt", cbrt<double, 2>, -1.0);
NumericalTest("cbrt", cbrt<double, 2>, -1e-5);
NumericalTest("cbrt", cbrt<double, 2>, 1e-5);
NumericalTest("cbrt", cbrt<double, 2>, 1.0);
{ // Check that exp2(x) == exp(x * log(2))
J z = exp2(x);
J w = exp(x * log(2.0));
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
NumericalTest("exp2", exp2<double, 2>, -1.0);
NumericalTest("exp2", exp2<double, 2>, -1e-5);
NumericalTest("exp2", exp2<double, 2>, -1e-200);
NumericalTest("exp2", exp2<double, 2>, 0.0);
NumericalTest("exp2", exp2<double, 2>, 1e-200);
NumericalTest("exp2", exp2<double, 2>, 1e-5);
NumericalTest("exp2", exp2<double, 2>, 1.0);
{ // Check that log2(x) == log(x) / log(2)
J z = log2(x);
J w = log(x) / log(2.0);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
NumericalTest("log2", log2<double, 2>, 1e-5);
NumericalTest("log2", log2<double, 2>, 1.0);
NumericalTest("log2", log2<double, 2>, 100.0);
{ // Check that hypot(x, y) == sqrt(x^2 + y^2)
J h = hypot(x, y);
J s = sqrt(x * x + y * y);
VL << "h = " << h;
VL << "s = " << s;
ExpectJetsClose(h, s);
}
{ // Check that hypot(x, x) == sqrt(2) * abs(x)
J h = hypot(x, x);
J s = sqrt(2.0) * abs(x);
VL << "h = " << h;
VL << "s = " << s;
ExpectJetsClose(h, s);
}
{ // Check that the derivative is zero tangentially to the circle:
J h = hypot(MakeJet(2.0, 1.0, 1.0), MakeJet(2.0, 1.0, -1.0));
VL << "h = " << h;
ExpectJetsClose(h, MakeJet(sqrt(8.0), std::sqrt(2.0), 0.0));
}
{ // Check that hypot(x, 0) == x
J zero = MakeJet(0.0, 2.0, 3.14);
J h = hypot(x, zero);
VL << "h = " << h;
ExpectJetsClose(x, h);
}
{ // Check that hypot(0, y) == y
J zero = MakeJet(0.0, 2.0, 3.14);
J h = hypot(zero, y);
VL << "h = " << h;
ExpectJetsClose(y, h);
}
{ // Check that hypot(x, 0) == sqrt(x * x) == x, even when x * x underflows:
EXPECT_EQ(DBL_MIN * DBL_MIN, 0.0); // Make sure it underflows
J huge = MakeJet(DBL_MIN, 2.0, 3.14);
J h = hypot(huge, J(0.0));
VL << "h = " << h;
ExpectJetsClose(h, huge);
}
{ // Check that hypot(x, 0) == sqrt(x * x) == x, even when x * x overflows:
EXPECT_EQ(DBL_MAX * DBL_MAX, std::numeric_limits<double>::infinity());
J huge = MakeJet(DBL_MAX, 2.0, 3.14);
J h = hypot(huge, J(0.0));
VL << "h = " << h;
ExpectJetsClose(h, huge);
}
// clang-format off
NumericalTest2("hypot", hypot<double, 2>, 0.0, 1e-5);
NumericalTest2("hypot", hypot<double, 2>, -1e-5, 0.0);
NumericalTest2("hypot", hypot<double, 2>, 1e-5, 1e-5);
NumericalTest2("hypot", hypot<double, 2>, 0.0, 1.0);
NumericalTest2("hypot", hypot<double, 2>, 1e-3, 1.0);
NumericalTest2("hypot", hypot<double, 2>, 1e-3, -1.0);
NumericalTest2("hypot", hypot<double, 2>, -1e-3, 1.0);
NumericalTest2("hypot", hypot<double, 2>, -1e-3, -1.0);
NumericalTest2("hypot", hypot<double, 2>, 1.0, 2.0);
// clang-format on
{
J z = fmax(x, y);
VL << "z = " << z;
ExpectJetsClose(x, z);
}
{
J z = fmin(x, y);
VL << "z = " << z;
ExpectJetsClose(y, z);
}
}
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));
}
// The following test ensures that Jets have all the appropriate Eigen
// related traits so that they can be used as part of matrix
// decompositions.
TEST(Jet, FullRankEigenLLTSolve) {
Eigen::Matrix<J, 3, 3> A;
Eigen::Matrix<J, 3, 1> b, x;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
A(i, j) = MakeJet(0.0, i, j * j);
}
b(i) = MakeJet(i, i, i);
x(i) = MakeJet(0.0, 0.0, 0.0);
A(i, i) = MakeJet(1.0, i, i * i);
}
x = A.llt().solve(b);
for (int i = 0; i < 3; ++i) {
EXPECT_EQ(x(i).a, b(i).a);
}
}
TEST(Jet, FullRankEigenLDLTSolve) {
Eigen::Matrix<J, 3, 3> A;
Eigen::Matrix<J, 3, 1> b, x;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
A(i, j) = MakeJet(0.0, i, j * j);
}
b(i) = MakeJet(i, i, i);
x(i) = MakeJet(0.0, 0.0, 0.0);
A(i, i) = MakeJet(1.0, i, i * i);
}
x = A.ldlt().solve(b);
for (int i = 0; i < 3; ++i) {
EXPECT_EQ(x(i).a, b(i).a);
}
}
TEST(Jet, FullRankEigenLUSolve) {
Eigen::Matrix<J, 3, 3> A;
Eigen::Matrix<J, 3, 1> b, x;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
A(i, j) = MakeJet(0.0, i, j * j);
}
b(i) = MakeJet(i, i, i);
x(i) = MakeJet(0.0, 0.0, 0.0);
A(i, i) = MakeJet(1.0, i, i * i);
}
x = A.lu().solve(b);
for (int i = 0; i < 3; ++i) {
EXPECT_EQ(x(i).a, b(i).a);
}
}
// ScalarBinaryOpTraits is only supported on Eigen versions >= 3.3
TEST(JetTraitsTest, MatrixScalarUnaryOps) {
const J x = MakeJet(2.3, -2.7, 1e-3);
const J y = MakeJet(1.7, 0.5, 1e+2);
Eigen::Matrix<J, 2, 1> a;
a << x, y;
const J sum = a.sum();
const J sum2 = a(0) + a(1);
ExpectJetsClose(sum, sum2);
}
TEST(JetTraitsTest, MatrixScalarBinaryOps) {
const J x = MakeJet(2.3, -2.7, 1e-3);
const J y = MakeJet(1.7, 0.5, 1e+2);
const J z = MakeJet(5.3, -4.7, 1e-3);
const J w = MakeJet(9.7, 1.5, 10.1);
Eigen::Matrix<J, 2, 2> M;
Eigen::Vector2d v;
M << x, y, z, w;
v << 0.6, -2.1;
// Check that M * v == M * v.cast<J>().
const Eigen::Matrix<J, 2, 1> r1 = M * v;
const Eigen::Matrix<J, 2, 1> r2 = M * v.cast<J>();
ExpectJetsClose(r1(0), r2(0));
ExpectJetsClose(r1(1), r2(1));
// Check that M * a == M * T(a).
const double a = 3.1;
const Eigen::Matrix<J, 2, 2> r3 = M * a;
const Eigen::Matrix<J, 2, 2> r4 = M * J(a);
ExpectJetsClose(r3(0, 0), r4(0, 0));
ExpectJetsClose(r3(1, 0), r4(1, 0));
ExpectJetsClose(r3(0, 1), r4(0, 1));
ExpectJetsClose(r3(1, 1), r4(1, 1));
}
TEST(JetTraitsTest, ArrayScalarUnaryOps) {
const J x = MakeJet(2.3, -2.7, 1e-3);
const J y = MakeJet(1.7, 0.5, 1e+2);
Eigen::Array<J, 2, 1> a;
a << x, y;
const J sum = a.sum();
const J sum2 = a(0) + a(1);
ExpectJetsClose(sum, sum2);
}
TEST(JetTraitsTest, ArrayScalarBinaryOps) {
const J x = MakeJet(2.3, -2.7, 1e-3);
const J y = MakeJet(1.7, 0.5, 1e+2);
Eigen::Array<J, 2, 1> a;
Eigen::Array2d b;
a << x, y;
b << 0.6, -2.1;
// Check that a * b == a * b.cast<T>()
const Eigen::Array<J, 2, 1> r1 = a * b;
const Eigen::Array<J, 2, 1> r2 = a * b.cast<J>();
ExpectJetsClose(r1(0), r2(0));
ExpectJetsClose(r1(1), r2(1));
// Check that a * c == a * T(c).
const double c = 3.1;
const Eigen::Array<J, 2, 1> r3 = a * c;
const Eigen::Array<J, 2, 1> r4 = a * J(c);
ExpectJetsClose(r3(0), r3(0));
ExpectJetsClose(r4(1), r4(1));
}
TEST(Jet, nested3x) {
typedef Jet<J, 2> JJ;
typedef Jet<JJ, 2> JJJ;
JJJ x;
x.a = JJ(J(1, 0), 0);
x.v[0] = JJ(J(1));
JJJ y = x * x * x;
ExpectClose(y.a.a.a, 1, kTolerance);
ExpectClose(y.v[0].a.a, 3., kTolerance);
ExpectClose(y.v[0].v[0].a, 6., kTolerance);
ExpectClose(y.v[0].v[0].v[0], 6., kTolerance);
JJJ e = exp(x);
ExpectClose(e.a.a.a, kE, kTolerance);
ExpectClose(e.v[0].a.a, kE, kTolerance);
ExpectClose(e.v[0].v[0].a, kE, kTolerance);
ExpectClose(e.v[0].v[0].v[0], kE, kTolerance);
}
} // namespace internal
} // namespace ceres