| 1 | /* |
| 2 | Copyright 2018 Google Inc. All Rights Reserved. |
| 3 | |
| 4 | Licensed under the Apache License, Version 2.0 (the "License"); |
| 5 | you may not use this file except in compliance with the License. |
| 6 | You may obtain a copy of the License at |
| 7 | |
| 8 | http://www.apache.org/licenses/LICENSE-2.0 |
| 9 | |
| 10 | Unless required by applicable law or agreed to in writing, software |
| 11 | distributed under the License is distributed on an "AS-IS" BASIS, |
| 12 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 13 | See the License for the specific language governing permissions and |
| 14 | limitations under the License. |
| 15 | */ |
| 16 | |
| 17 | #include "ambisonics/associated_legendre_polynomials_generator.h" |
| 18 | |
| 19 | #include <cmath> |
| 20 | |
| 21 | #include "base/logging.h" |
| 22 | #include "base/misc_math.h" |
| 23 | |
| 24 | namespace vraudio { |
| 25 | |
| 26 | AssociatedLegendrePolynomialsGenerator::AssociatedLegendrePolynomialsGenerator( |
| 27 | int max_degree, bool condon_shortley_phase, bool compute_negative_order) |
| 28 | : max_degree_(max_degree), |
| 29 | condon_shortley_phase_(condon_shortley_phase), |
| 30 | compute_negative_order_(compute_negative_order) { |
| 31 | DCHECK_GE(max_degree_, 0); |
| 32 | } |
| 33 | |
| 34 | std::vector<float> AssociatedLegendrePolynomialsGenerator::Generate( |
| 35 | float x) const { |
| 36 | std::vector<float> values(GetNumValues()); |
| 37 | |
| 38 | // Bases for the recurrence relations. |
| 39 | values[GetIndex(degree: 0, order: 0)] = ComputeValue(degree: 0, order: 0, x, values); |
| 40 | if (max_degree_ >= 1) values[GetIndex(degree: 1, order: 0)] = ComputeValue(degree: 1, order: 0, x, values); |
| 41 | |
| 42 | // Using recurrence relations, we now compute the rest of the values needed. |
| 43 | // (degree, 0), based on (degree - 1, 0) and (degree - 2, 0): |
| 44 | for (int degree = 2; degree <= max_degree_; ++degree) { |
| 45 | const int order = 0; |
| 46 | values[GetIndex(degree, order)] = ComputeValue(degree, order, x, values); |
| 47 | } |
| 48 | // (degree, degree): |
| 49 | for (int degree = 1; degree <= max_degree_; ++degree) { |
| 50 | const int order = degree; |
| 51 | values[GetIndex(degree, order)] = ComputeValue(degree, order, x, values); |
| 52 | } |
| 53 | // (degree, degree - 1): |
| 54 | for (int degree = 2; degree <= max_degree_; ++degree) { |
| 55 | const int order = degree - 1; |
| 56 | values[GetIndex(degree, order)] = ComputeValue(degree, order, x, values); |
| 57 | } |
| 58 | // The remaining positive orders, based on (degree - 1, order) and |
| 59 | // (degree - 2, order): |
| 60 | for (int degree = 3; degree <= max_degree_; ++degree) { |
| 61 | for (int order = 1; order <= degree - 2; ++order) { |
| 62 | values[GetIndex(degree, order)] = ComputeValue(degree, order, x, values); |
| 63 | } |
| 64 | } |
| 65 | // (degree, -order): |
| 66 | if (compute_negative_order_) { |
| 67 | for (int degree = 1; degree <= max_degree_; ++degree) { |
| 68 | for (int order = 1; order <= degree; ++order) { |
| 69 | values[GetIndex(degree, order: -order)] = |
| 70 | ComputeValue(degree, order: -order, x, values); |
| 71 | } |
| 72 | } |
| 73 | } |
| 74 | if (!condon_shortley_phase_) { |
| 75 | for (int degree = 1; degree <= max_degree_; ++degree) { |
| 76 | const int start_order = compute_negative_order_ ? -degree : 0; |
| 77 | for (int order = start_order; order <= degree; ++order) { |
| 78 | // Undo the Condon-Shortley phase. |
| 79 | values[GetIndex(degree, order)] *= |
| 80 | static_cast<float>(std::pow(x: -1, y: order)); |
| 81 | } |
| 82 | } |
| 83 | } |
| 84 | return values; |
| 85 | } |
| 86 | |
| 87 | size_t AssociatedLegendrePolynomialsGenerator::GetNumValues() const { |
| 88 | if (compute_negative_order_) |
| 89 | return (max_degree_ + 1) * (max_degree_ + 1); |
| 90 | else |
| 91 | return ((max_degree_ + 1) * (max_degree_ + 2)) / 2; |
| 92 | } |
| 93 | |
| 94 | size_t AssociatedLegendrePolynomialsGenerator::GetIndex(int degree, |
| 95 | int order) const { |
| 96 | CheckIndexValidity(degree, order); |
| 97 | size_t result; |
| 98 | if (compute_negative_order_) { |
| 99 | result = static_cast<size_t>(degree * (degree + 1) + order); |
| 100 | } else { |
| 101 | result = static_cast<size_t>((degree * (degree + 1)) / 2 + order); |
| 102 | } |
| 103 | DCHECK_GE(result, 0U); |
| 104 | DCHECK_LT(result, GetNumValues()); |
| 105 | return result; |
| 106 | } |
| 107 | |
| 108 | float AssociatedLegendrePolynomialsGenerator::ComputeValue( |
| 109 | int degree, int order, float x, const std::vector<float>& values) const { |
| 110 | CheckIndexValidity(degree, order); |
| 111 | if (degree == 0 && order == 0) { |
| 112 | return 1; |
| 113 | } else if (degree == 1 && order == 0) { |
| 114 | return x; |
| 115 | } else if (degree == order) { |
| 116 | return std::pow(x: -1.0f, y: static_cast<float>(degree)) * |
| 117 | DoubleFactorial(x: 2 * degree - 1) * |
| 118 | std::pow(x: (1.0f - x * x), y: 0.5f * static_cast<float>(degree)); |
| 119 | } else if (order == degree - 1) { |
| 120 | return x * static_cast<float>(2 * degree - 1) * |
| 121 | values[GetIndex(degree: degree - 1, order: degree - 1)]; |
| 122 | } else if (order < 0) { |
| 123 | return std::pow(x: -1.0f, y: static_cast<float>(order)) * |
| 124 | Factorial(x: degree + order) / Factorial(x: degree - order) * |
| 125 | values[GetIndex(degree, order: -order)]; |
| 126 | } else { |
| 127 | return (static_cast<float>(2 * degree - 1) * x * |
| 128 | values[GetIndex(degree: degree - 1, order)] - |
| 129 | static_cast<float>(degree - 1 + order) * |
| 130 | values[GetIndex(degree: degree - 2, order)]) / |
| 131 | static_cast<float>(degree - order); |
| 132 | } |
| 133 | } |
| 134 | |
| 135 | void AssociatedLegendrePolynomialsGenerator::CheckIndexValidity( |
| 136 | int degree, int order) const { |
| 137 | DCHECK_GE(degree, 0); |
| 138 | DCHECK_LE(degree, max_degree_); |
| 139 | if (compute_negative_order_) { |
| 140 | DCHECK_LE(-degree, order); |
| 141 | } else { |
| 142 | DCHECK_GE(order, 0); |
| 143 | } |
| 144 | DCHECK_LE(order, degree); |
| 145 | } |
| 146 | |
| 147 | } // namespace vraudio |
| 148 | |