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/*
Copyright 2018 Google Inc. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS-IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
#include "ambisonics/associated_legendre_polynomials_generator.h"
#include <cmath>
#include "third_party/googletest/googletest/include/gtest/gtest.h"
#include "base/constants_and_types.h"
#include "base/misc_math.h"
namespace vraudio {
namespace {
// Tolerated test error margin for single-precision floating points.
const float kEpsilon = 1e-5f;
// Generates associated Legendre polynomials up to and including the 4th degree,
// with the Condon-Shortley phase and negative orders included.
std::vector<float> GenerateExpectedValuesFourthDegree(float x) {
// From http://en.wikipedia.org/wiki/Associated_Legendre_polynomials
// Comments are (degree, order).
const std::vector<float> expected_values = {
1.0f, // (0, 0)
0.5f * std::sqrt(1.0f - x * x), // (1, -1)
x, // (1, 0)
-std::sqrt(1.0f - x * x), // (1, 1)
1.0f / 8.0f * (1.0f - x * x), // (2, -2)
0.5f * x * std::sqrt(1.0f - x * x), // (2, -1)
0.5f * (3.0f * x * x - 1.0f), // (2, 0)
-3.0f * x * std::sqrt(1.0f - x * x), // (2, 1)
3.0f * (1.0f - x * x), // (2, 2)
15.0f / 720.0f * std::pow(1.0f - x * x, 3.0f / 2.0f), // (3, -3)
15.0f / 120.0f * x * (1.0f - x * x), // (3, -2)
3.0f / 24.0f * (5.0f * x * x - 1.0f) *
std::sqrt(1.0f - x * x), // (3, -1)
0.5f * (5.0f * IntegerPow(x, 3) - 3.0f * x), // (3, 0)
-3.0f / 2.0f * (5.0f * x * x - 1.0f) * std::sqrt(1.0f - x * x), // (3, 1)
15.0f * x * (1.0f - x * x), // (3, 2)
-15.0f * std::pow(1.0f - x * x, 3.0f / 2.0f), // (3, 3)
105.0f / 40320.0f * IntegerPow(1.0f - x * x, 2), // (4, -4)
105.0f / 5040.0f * x * std::pow(1.0f - x * x, 3.0f / 2.0f), // (4, -3)
15.0f / 720.0f * (7.0f * x * x - 1.0f) * (1.0f - x * x), // (4, -2)
5.0f / 40.0f * (7.0f * IntegerPow(x, 3) - 3.0f * x) *
std::sqrt(1.0f - x * x), // (4, -1)
1.0f / 8.0f *
(35.0f * IntegerPow(x, 4) - 30.0f * x * x + 3.0f), // (4, 0)
-5.0f / 2.0f * (7.0f * IntegerPow(x, 3) - 3.0f * x) *
std::sqrt(1.0f - x * x), // (4, 1)
15.0f / 2.0f * (7.0f * x * x - 1.0f) * (1.0f - x * x), // (4, 2)
-105.0f * x * std::pow(1.0f - x * x, 3.0f / 2.0f), // (4, 3)
105.0f * IntegerPow(1.0f - x * x, 2) // (4, 4)
};
return expected_values;
}
// Tests that the values given by GetIndex are successive indices (n, n+1, n+2,
// and so on).
TEST(AssociatedLegendrePolynomialsGeneratorTest, GetIndex_SuccessiveIndices) {
const int kMaxDegree = 5;
const AssociatedLegendrePolynomialsGenerator alp_generator(kMaxDegree, false,
true);
int last_index = -1;
for (int degree = 0; degree <= kMaxDegree; ++degree) {
for (int order = -degree; order <= degree; ++order) {
int index = static_cast<int>(alp_generator.GetIndex(degree, order));
EXPECT_EQ(last_index + 1, index);
last_index = index;
}
}
}
// Tests that the zeroth-degree, zeroth-order ALP is always 1.
TEST(AssociatedLegendrePolynomialsGeneratorTest, Generate_ZerothElementIsOne) {
const int kMaxDegree = 10;
for (int max_degree = 0; max_degree <= kMaxDegree; ++max_degree) {
for (int condon_shortley_phase = 0; condon_shortley_phase <= 1;
++condon_shortley_phase) {
for (int compute_negative_order = 0; compute_negative_order <= 1;
++compute_negative_order) {
AssociatedLegendrePolynomialsGenerator alp_generator(
max_degree, condon_shortley_phase != 0,
compute_negative_order != 0);
const float kVariableStep = 0.2f;
for (float x = -1.0f; x <= 1.0f; x += kVariableStep) {
const std::vector<float> values = alp_generator.Generate(x);
EXPECT_NEAR(values[0], 1.0f, kEpsilon);
}
}
}
}
}
// Tests that the polynomials generated are correct until the 4th degree.
TEST(AssociatedLegendrePolynomialsGeneratorTest, Generate_CorrectFourthDegree) {
const int kMaxDegree = 4;
const bool kCondonShortleyPhase = true;
const bool kComputeNegativeOrder = true;
const AssociatedLegendrePolynomialsGenerator alp_generator(
kMaxDegree, kCondonShortleyPhase, kComputeNegativeOrder);
const float kVariableStep = 0.05f;
for (float x = -1.0f; x <= 1.0f; x += kVariableStep) {
const std::vector<float> generated_values = alp_generator.Generate(x);
const std::vector<float> expected_values =
GenerateExpectedValuesFourthDegree(x);
ASSERT_EQ(expected_values.size(), generated_values.size());
for (size_t i = 0; i < expected_values.size(); ++i) {
EXPECT_NEAR(generated_values[i], expected_values[i], kEpsilon)
<< " at index " << i;
}
}
}
// Tests that the Condon-Shortley phase is correctly applied.
TEST(AssociatedLegendrePolynomialsGeneratorTest, Generate_CondonShortleyPhase) {
const int kMaxDegree = 10;
const float kValue = 0.12345f;
for (int max_degree = 0; max_degree <= kMaxDegree; ++max_degree) {
for (int compute_negative_order = 0; compute_negative_order <= 1;
++compute_negative_order) {
const AssociatedLegendrePolynomialsGenerator alp_generator_without_phase(
max_degree, false, compute_negative_order != 0);
const std::vector<float> values_without_phase =
alp_generator_without_phase.Generate(kValue);
const AssociatedLegendrePolynomialsGenerator alp_generator_with_phase(
max_degree, true, compute_negative_order != 0);
const std::vector<float> values_with_phase =
alp_generator_with_phase.Generate(kValue);
ASSERT_EQ(values_with_phase.size(), values_without_phase.size());
for (int degree = 0; degree <= max_degree; ++degree) {
const int start_order = compute_negative_order ? -degree : 0;
for (int order = start_order; order <= degree; ++order) {
const size_t index =
alp_generator_without_phase.GetIndex(degree, order);
const float expected = values_without_phase[index] *
std::pow(-1.0f, static_cast<float>(order));
EXPECT_NEAR(values_with_phase[index], expected, kEpsilon)
<< " at degree " << degree << " and order " << order;
}
}
}
}
}
} // namespace
} // namespace vraudio
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