INSTINCT Code Coverage Report

Directory: src/
File: Navigation/Gravity/internal/AssociatedLegendre.cpp
Date: 2025-02-07 16:54:41
Exec Total Coverage
Lines: 29 29 100.0%
Functions: 1 1 100.0%
Branches: 38 64 59.4%
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1 // This file is part of INSTINCT, the INS Toolkit for Integrated
2 // Navigation Concepts and Training by the Institute of Navigation of
3 // the University of Stuttgart, Germany.
4 //
5 // This Source Code Form is subject to the terms of the Mozilla Public
6 // License, v. 2.0. If a copy of the MPL was not distributed with this
7 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
8
9 #include "AssociatedLegendre.hpp"
10 #include "util/Logger.hpp"
11
12 #include "Navigation/Constants.hpp"
13 #include <cmath>
14 #include <array>
15 #include <numbers>
16
17 181318 std::pair<Eigen::MatrixXd, Eigen::MatrixXd> NAV::internal::associatedLegendre(double theta, size_t ndegree)
18 {
19 // Index needed for the calculation of all necessary 'Pd' entries up to 'ndegree' (--> Pd(n = ndegree, m = ndegree) is dependent on P(n = ndegree, m = ndegree + 1))
20 181318 int N = static_cast<int>(ndegree + 2);
21
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 181318 Eigen::MatrixXd P = Eigen::MatrixXd::Zero(N, N);
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 181319 Eigen::MatrixXd Pd = Eigen::MatrixXd::Zero(N, N);
24
25 #if defined(__GNUC__) || defined(__clang__)
26 #pragma GCC diagnostic push
27 #pragma GCC diagnostic ignored "-Wnull-dereference"
28 #endif
29 // Recurrence relations for the normalized associated Legendre functions (see 'GUT User Guide' eq. 4.2.2 and eq. 4.2.3)
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 181323 P(0, 0) = 1.0;
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 181320 P(1, 0) = std::numbers::sqrt3 * std::cos(theta);
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 181323 P(1, 1) = std::numbers::sqrt3 * std::sin(theta);
33 #if defined(__GNUC__) || defined(__clang__)
34 #pragma GCC diagnostic pop
35 #endif
36
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 1994381 for (int n = 2; n <= N - 1; n++)
38 {
39 1813185 auto nd = static_cast<double>(n);
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 1813185 P(n, n) = std::sqrt((2.0 * nd + 1.0) / (2.0 * nd)) * std::sin(theta) * P(n - 1, n - 1);
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 15409967 for (int m = 0; m <= n; m++)
43 {
44 13596909 auto md = static_cast<double>(m);
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 13596909 if (n == m + 1)
47 {
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 1813177 P(n, m) = std::sqrt(((2.0 * nd + 1.0) * (2.0 * nd - 1.0)) / ((nd + md) * (nd - md))) * std::cos(theta) * P(n - 1, m);
49 }
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 11783732 else if (n > m + 1)
51 {
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 19942168 P(n, m) = std::sqrt(((2.0 * nd + 1.0) * (2.0 * nd - 1.0)) / ((nd + md) * (nd - md))) * std::cos(theta) * P(n - 1, m)
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 9970968 - std::sqrt(((2.0 * nd + 1.0) * (nd + md - 1.0) * (nd - md - 1.0)) / ((2.0 * nd - 3.0) * (nd + md) * (nd - md))) * std::cos(theta) * P(n - 2, m);
54 }
55 }
56 }
57
58 // Recurrence relations for the derivative of the normalized associated Legendre functions (see 'GUT User Guide' eq. 4.2.6)
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 181196 Pd(0, 0) = 0.0;
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 181323 Pd(1, 0) = -std::numbers::sqrt3 * std::sin(theta);
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 181323 Pd(1, 1) = std::numbers::sqrt3 * std::cos(theta);
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 1994430 for (int n = 2; n <= N - 1; n++) // 2nd for-loop is necessary, because for the calculation of 'Pd', all coefficients of 'P' must be available
64 {
65 1813177 auto nd = static_cast<double>(n);
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 1813177 Pd(n, 0) = -0.5 * std::sqrt(2.0 * nd * (nd + 1.0)) * P(n, 1);
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 1813187 Pd(n, 1) = 0.5 * (std::sqrt(2.0 * nd * (nd + 1.0)) * P(n, 0) - std::sqrt((nd - 1.0) * (nd + 2.0)) * std::pow(P(n, 2), 2.0));
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 9971705 for (int m = 2; m <= n - 1; m++)
71 {
72 8158598 auto md = static_cast<double>(m);
73
74 // else if ((m > 1) && (m < N - 1))
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 8158598 Pd(n, m) = 0.5 * (std::sqrt((nd + md) * (nd - md + 1.0)) * P(n, m - 1) - std::sqrt((nd - md) * (nd + md + 1.0)) * P(n, m + 1));
76 }
77 }
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 362575 return std::make_pair(P, Pd);
80 181322 }
81