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+// 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/
+//
+// 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 <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 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
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