103 lines
4.6 KiB
C++
103 lines
4.6 KiB
C++
/********************************************************
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* ██████╗ ██████╗████████╗██╗
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* ██╔════╝ ██╔════╝╚══██╔══╝██║
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* ██║ ███╗██║ ██║ ██║
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* ██║ ██║██║ ██║ ██║
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* ╚██████╔╝╚██████╗ ██║ ███████╗
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* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
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* Geophysical Computational Tools & Library (GCTL)
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*
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* Copyright (c) 2023 Yi Zhang (yizhang-geo@zju.edu.cn)
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*
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* GCTL is distributed under a dual licensing scheme. You can redistribute
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* it and/or modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation, either version 2
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* of the License, or (at your option) any later version. You should have
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* received a copy of the GNU Lesser General Public License along with this
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* program. If not, see <http://www.gnu.org/licenses/>.
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*
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* If the terms and conditions of the LGPL v.2. would prevent you from using
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* the GCTL, please consider the option to obtain a commercial license for a
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* fee. These licenses are offered by the GCTL's original author. As a rule,
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* licenses are provided "as-is", unlimited in time for a one time fee. Please
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* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
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* to include some description of your company and the realm of its activities.
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* Also add information on how to contact you by electronic and paper mail.
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******************************************************/
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#ifndef _GCTL_LEGENDRE_H
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#define _GCTL_LEGENDRE_H
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#include "../core/array.h"
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namespace gctl
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{
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/**
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* @brief 伴随勒让德系数归一化类型
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*/
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enum legendre_norm_e
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{
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One, ///< 归一化总值为1
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Pi4, ///< 归一化总值为4*pi
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};
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/**
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* @brief 利用递推公式计算[-1, 1]内不同阶数的勒让德多项式的值
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*
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* @param order 阶数
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* @param x 坐标位置
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* @param derivative 计算相对于x的导数
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* @return 多项式值
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*/
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double legendre_polynomials(size_t order, double x, bool derivative = false);
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/**
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* @brief 计算向前列推的a系数，避免重复计算。
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*
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* @note Fully normalized associated Legendre functions calculated by standard forward column methods
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* Holmes, S. A., & Featherstone, W. E. (2002). A unified approach to the Clenshaw summation and the recursive computation of
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* very high degree and order normalized associated Legendre functions.
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* Journal of Geodesy, 76(5), 279–299. https://doi.org/10.1007/s00190-002-0216-2
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*
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* @param[in] max_order 最大的计算阶数
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* @param cs 返回的系数
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*/
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void get_a_nm_array(int max_order, array<array<double>> &cs);
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/**
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* @brief 计算向前列推的b系数，避免重复计算。
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*
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* @note Fully normalized associated Legendre functions calculated by standard forward column methods
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* Holmes, S. A., & Featherstone, W. E. (2002). A unified approach to the Clenshaw summation and the recursive computation of
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* very high degree and order normalized associated Legendre functions.
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* Journal of Geodesy, 76(5), 279–299. https://doi.org/10.1007/s00190-002-0216-2
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*
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* @param[in] max_order 最大的计算阶数
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* @param cs 返回的系数
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*/
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void get_b_nm_array(int max_order, array<array<double>> &cs);
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/**
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* @brief 计算标准前向列推法计算规格化的勒让德多项式
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*
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* 二维数组中行数代表阶数列数为次数
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*
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* @note Fully normalized associated Legendre functions calculated by standard forward column methods
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* Holmes, S. A., & Featherstone, W. E. (2002). A unified approach to the Clenshaw summation and the recursive computation of
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* very high degree and order normalized associated Legendre functions.
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* Journal of Geodesy, 76(5), 279–299. https://doi.org/10.1007/s00190-002-0216-2
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*
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* @param nalf 返回的勒让德多项式系数，一个下半三角二维矩阵
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* @param[in] a_nm A系数
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* @param[in] b_nm B系数
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* @param[in] max_order 最大的计算阶数
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* @param[in] theta 计算点的纬度值（度）
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* @param[in] norm 系数的归一化总值大小
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* @param[in] derivative 计算相对于theta的导数
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*/
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void nalf_sfcm(array<array<double>> &nalf, const array<array<double>> &a_nm,
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const array<array<double>> &b_nm, int max_order, double theta,
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legendre_norm_e norm, bool derivative = false);
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};
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#endif //_GCTL_LEGENDRE_H
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