628 lines
17 KiB
C++
628 lines
17 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) 2022 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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#include "gm_regular_grid.h"
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#ifdef GCTL_POTENTIAL_FFTW3
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// include fftw head files
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#include "fftw3.h"
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#endif //GCTL_POTENTIAL_FFTW3
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gctl::gm_regular_grid::gm_regular_grid(){}
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gctl::gm_regular_grid::~gm_regular_grid(){}
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gctl::gm_regular_grid::gm_regular_grid(std::string in_name, std::string in_info, int xnum, int ynum,
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double xmin, double ymin, double dx, double dy) : regular_grid::regular_grid(in_name, in_info, xnum,
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ynum, xmin, ymin, dx, dy){}
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#ifdef GCTL_POTENTIAL_FFTW3
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void gctl::gm_regular_grid::gradient(std::string datname, std::string gradname, gravitational_field_type_e c_type, int order)
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{
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meshdata &data = get_data(datname);
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mesh_data_value_e value_type = data.valtype_;
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mesh_data_type_e data_type = data.loctype_;
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if(value_type != Scalar)
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{
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throw std::runtime_error("[gctl::gm_regular_grid::gradient] Invalid value type.");
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}
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if (c_type != Tzz && c_type != Tzx && c_type != Tzy)
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{
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throw std::runtime_error("[gctl::gm_regular_grid::gradient] The gradient type must be Tzz, Tzx and Tzy.");
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}
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// 检查是否存在与梯度数据同名的数据 若有则检查是否需要重新建立数据
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meshdata &new_data = add_data(data_type, value_type, gradname, 0.0);
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gctl::array<double> ingrid_ex;
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int M = -1, N = -1;
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int ori_row, ori_col;
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if (data_type == NodeData) gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum, rg_xnum, M, N, ori_row, ori_col);
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else gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum-1, rg_xnum-1, M, N, ori_row, ori_col);
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fftw_complex *in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
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fftw_complex *out= (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
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for (int i = 0; i < M*N; i++)
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{
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in[i][0] = ingrid_ex[i];
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in[i][1] = 0.0;
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}
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fftw_plan p = fftw_plan_dft_2d(M, N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
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fftw_execute(p);
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int half_M = ceil(M/2);
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int half_N = ceil(N/2);
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double du = 2.0*GCTL_Pi/((M-1)*rg_dy);
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double dv = 2.0*GCTL_Pi/((N-1)*rg_dx);
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int idx1, idx2, idx3, idx4;
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double u, v;
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if (c_type == Tzx)
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{
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for (int i = 0; i < M; i++)
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{
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for (int j = 0; j < half_N; j++)
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{
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v = dv*(j+1);
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idx1 = i*N+j;
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idx2 = i*N+N-1-j;
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in[idx1][0] = -1.0*out[idx1][1]*pow(v, order);
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in[idx1][1] = out[idx1][0]*pow(v, order);
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in[idx2][0] = -1.0*out[idx2][1]*pow(-1.0*v, order);
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in[idx2][1] = out[idx2][0]*pow(-1.0*v, order);
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}
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}
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}
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else if (c_type == Tzy)
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{
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for (int i = 0; i < half_M; i++)
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{
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u = du*(i+1);
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for (int j = 0; j < N; j++)
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{
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idx1 = i*N+j;
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idx3 = (M-1-i)*N+j;
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in[idx1][0] = -1.0*out[idx1][1]*pow(u, order);
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in[idx1][1] = out[idx1][0]*pow(u, order);
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in[idx3][0] = -1.0*out[idx3][1]*pow(-1.0*u, order);
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in[idx3][1] = out[idx3][0]*pow(-1.0*u, order);
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}
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}
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}
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else
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{
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for (int i = 0; i < half_M; i++)
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{
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u = du*(i+1);
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for (int j = 0; j < half_N; j++)
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{
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v = dv*(j+1);
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idx1 = i*N+j;
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idx2 = i*N+N-1-j;
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idx3 = (M-1-i)*N+j;
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idx4 = (M-1-i)*N+N-1-j;
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in[idx1][0] = out[idx1][0]*pow(sqrt(u*u+v*v), order);
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in[idx1][1] = out[idx1][1]*pow(sqrt(u*u+v*v), order);
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in[idx2][0] = out[idx2][0]*pow(sqrt(u*u+v*v), order);
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in[idx2][1] = out[idx2][1]*pow(sqrt(u*u+v*v), order);
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in[idx3][0] = out[idx3][0]*pow(sqrt(u*u+v*v), order);
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in[idx3][1] = out[idx3][1]*pow(sqrt(u*u+v*v), order);
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in[idx4][0] = out[idx4][0]*pow(sqrt(u*u+v*v), order);
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in[idx4][1] = out[idx4][1]*pow(sqrt(u*u+v*v), order);
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}
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}
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}
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p = fftw_plan_dft_2d(M, N, in, out, FFTW_BACKWARD, FFTW_ESTIMATE);
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fftw_execute(p);
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for (int i = 0; i < M; i++)
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{
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for (int j = 0; j < N; j++)
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{
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ingrid_ex[i*N+j] = out[i*N+j][0]/(M*N);
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}
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}
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if (data_type == NodeData)
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{
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for (int i = 0; i < rg_ynum; i++)
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{
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for (int j = 0; j < rg_xnum; j++)
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{
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new_data.datval_[i*rg_xnum+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
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}
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}
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}
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else
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{
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for (int i = 0; i < rg_ynum-1; i++)
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{
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for (int j = 0; j < rg_xnum-1; j++)
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{
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new_data.datval_[i*(rg_xnum-1)+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
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}
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}
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}
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fftw_destroy_plan(p);
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fftw_free(in);
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fftw_free(out);
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return;
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}
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void gctl::gm_regular_grid::rtp(std::string datname, std::string rtpname, double inc, double dec)
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{
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meshdata &data = get_data(datname);
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mesh_data_value_e value_type = data.valtype_;
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mesh_data_type_e data_type = data.loctype_;
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if(value_type != Scalar)
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{
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std::string err_str = "Invalid value type. From gctl::gm_regular_grid::rtp(...)";
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throw runtime_error(err_str);
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}
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// 检查是否存在与梯度数据同名的数据 若有则检查是否需要重新建立数据
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meshdata &new_data = add_data(data_type, value_type, rtpname, 0.0);
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gctl::array<double> ingrid_ex;
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int M = -1, N = -1;
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int ori_row, ori_col;
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if (data_type == NodeData) gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum, rg_xnum, M, N, ori_row, ori_col);
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else gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum-1, rg_xnum-1, M, N, ori_row, ori_col);
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fftw_complex *in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
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fftw_complex *out= (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
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for (int i = 0; i < M*N; i++)
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{
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in[i][0] = ingrid_ex[i];
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in[i][1] = 0.0;
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}
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fftw_plan p = fftw_plan_dft_2d(M, N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
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fftw_execute(p);
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int half_M = ceil(M/2);
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int half_N = ceil(N/2);
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double du = 2.0*GCTL_Pi/((M-1)*rg_dy);
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double dv = 2.0*GCTL_Pi/((N-1)*rg_dx);
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double cc = cosd(dec)*cosd(inc);
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double sc = sind(dec)*cosd(inc);
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double s = sind(inc);
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int idx;
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double U, V, Rpart, Ipart;
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double temp, temp1, temp2, temp3, temp4, base;
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for (int i = 0; i < half_M; i++)
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{
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for (int j = 0; j < half_N; j++)
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{
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U = (i+1)*du; V = (j+1)*dv;
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temp = U*U+V*V;
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idx = i*N+j;
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temp1 = cc*U+sc*V;
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temp2 = s*s*temp-temp1*temp1;
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base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
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Rpart = temp*temp2/base;
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Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
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temp3 = out[idx][0];
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temp4 = out[idx][1];
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in[idx][0] = Rpart*temp3-temp4*Ipart;
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in[idx][1] = Rpart*temp4+Ipart*temp3;
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idx = (M-1-i)*N+j;
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temp1 = -cc*U+sc*V;
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temp2 = s*s*temp-temp1*temp1;
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base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
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Rpart = temp*temp2/base;
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Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
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temp3 = out[idx][0];
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temp4 = out[idx][1];
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in[idx][0] = Rpart*temp3-temp4*Ipart;
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in[idx][1] = Rpart*temp4+Ipart*temp3;
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idx = i*N+N-1-j;
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temp1 = cc*U-sc*V;
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temp2 = s*s*temp-temp1*temp1;
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base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
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Rpart = temp*temp2/base;
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Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
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temp3 = out[idx][0];
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temp4 = out[idx][1];
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in[idx][0] = Rpart*temp3-temp4*Ipart;
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in[idx][1] = Rpart*temp4+Ipart*temp3;
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idx = (M-1-i)*N+N-1-j;
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temp1 = -cc*U-sc*V;
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temp2 = s*s*temp-temp1*temp1;
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base = temp2*temp2+4.0*s*s*temp1*temp1*temp;
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Rpart = temp*temp2/base;
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Ipart = -2.0*s*temp1*pow(temp,1.5)/base;
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temp3 = out[idx][0];
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temp4 = out[idx][1];
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in[idx][0] = Rpart*temp3-temp4*Ipart;
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in[idx][1] = Rpart*temp4+Ipart*temp3;
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}
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}
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p = fftw_plan_dft_2d(M, N, in, out, FFTW_BACKWARD, FFTW_ESTIMATE);
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fftw_execute(p);
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for (int i = 0; i < M; i++)
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{
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for (int j = 0; j < N; j++)
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{
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ingrid_ex[i*N+j] = out[i*N+j][0]/(M*N);
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}
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}
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if (data_type == NodeData)
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{
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for (int i = 0; i < rg_ynum; i++)
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{
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for (int j = 0; j < rg_xnum; j++)
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{
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new_data.datval_[i*rg_xnum+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
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}
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}
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}
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else
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{
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for (int i = 0; i < rg_ynum-1; i++)
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{
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for (int j = 0; j < rg_xnum-1; j++)
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{
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new_data.datval_[i*(rg_xnum-1)+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
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}
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}
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}
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fftw_destroy_plan(p);
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fftw_free(in);
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fftw_free(out);
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return;
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}
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void gctl::gm_regular_grid::drtp(std::string datname, std::string incname,
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std::string decname, std::string drtpname, int order)
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{
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// 首先获取数据并确定所有数据类型和格式都是一致的
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meshdata *md_ptr = get_data_ptr(datname);
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mesh_data_value_e dat_valtype = md_ptr->valtype_;
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mesh_data_type_e dat_datype = md_ptr->loctype_;
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md_ptr = get_data_ptr(incname);
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mesh_data_value_e inc_valtype = md_ptr->valtype_;
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mesh_data_type_e inc_datype = md_ptr->loctype_;
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md_ptr = get_data_ptr(decname);
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mesh_data_value_e dec_valtype = md_ptr->valtype_;
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mesh_data_type_e dec_datype = md_ptr->loctype_;
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std::string err_str;
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if (dat_valtype != Scalar)
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{
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err_str = "Invalid value type. From gctl::gm_regular_grid::drtp(...)";
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throw runtime_error(err_str);
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}
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if (dat_datype != inc_datype || dat_datype != dec_datype)
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{
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err_str = "Incompatible data type. From gctl::gm_regular_grid::drtp(...)";
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throw runtime_error(err_str);
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}
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// 获取数据指针
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md_ptr = get_data_ptr(datname);
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array<double> *dat_ptr = &md_ptr->datval_;
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md_ptr = get_data_ptr(incname);
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array<double> *inc_ptr = &md_ptr->datval_;
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md_ptr = get_data_ptr(decname);
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array<double> *dec_ptr = &md_ptr->datval_;
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// 检查是否存在同名的数据 若有则检查是否需要重新建立数据
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add_data(dat_datype, dat_valtype, drtpname, 0.0);
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md_ptr = get_data_ptr(drtpname);
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// 获取数据指针
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array<double> *drtp_ptr = &md_ptr->datval_;
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// 新建临时数据并获取数据指针
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std::string tmp_name = drtpname+"tmp";
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add_data(dat_datype, dat_valtype, tmp_name, 0.0);
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md_ptr = get_data_ptr(tmp_name);
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array<double> *tmp_ptr = &md_ptr->datval_;
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std::string diff1_name = drtpname+"diff1";
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add_data(dat_datype, dat_valtype, diff1_name, 0.0);
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md_ptr = get_data_ptr(diff1_name);
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array<double> *diff1_ptr = &md_ptr->datval_;
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std::string diff2_name = drtpname+"diff2";
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add_data(dat_datype, dat_valtype, diff2_name, 0.0);
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array<double> *diff2_ptr = &md_ptr->datval_;
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// 计算平均磁化参数
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double meaninc = 0.0, meandec = 0.0;
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for (int i = 0; i < inc_ptr->size(); i++)
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{
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meaninc += inc_ptr->at(i);
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meandec += dec_ptr->at(i);
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}
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meaninc /= inc_ptr->size();
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meandec /= dec_ptr->size();
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// 计算平均化极结果
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rtp(datname, tmp_name, meaninc, meandec);
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for (int i = 0; i < drtp_ptr->size(); i++)
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{
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drtp_ptr->at(i) = tmp_ptr->at(i);
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}
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// 使用微小扰动计算RTP相对与倾角与偏角的导数
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double dinc = 0.01, ddec = 0.01;
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// 计算一阶变角度化极结果
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rtp(datname, diff1_name, meaninc+dinc, meandec);
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rtp(datname, diff2_name, meaninc, meandec+ddec);
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for (int i = 0; i < drtp_ptr->size(); i++)
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{
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diff1_ptr->at(i) = (inc_ptr->at(i) - meaninc)
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*(diff1_ptr->at(i) - tmp_ptr->at(i))/dinc;
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drtp_ptr->at(i) += diff1_ptr->at(i);
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diff2_ptr->at(i) = (dec_ptr->at(i) - meandec)
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*(diff2_ptr->at(i) - tmp_ptr->at(i))/ddec;
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drtp_ptr->at(i) += diff2_ptr->at(i);
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}
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|
|
|
double factor;
|
|
for (int o = 2; o <= order; o++)
|
|
{
|
|
factor = 1.0;
|
|
for (int n = o; n > 1; n--)
|
|
{
|
|
factor *= n;
|
|
}
|
|
factor = 1.0/factor;
|
|
|
|
rtp(diff1_name, tmp_name, meaninc, meandec);
|
|
rtp(diff1_name, diff1_name, meaninc+dinc, meandec);
|
|
for (int i = 0; i < drtp_ptr->size(); i++)
|
|
{
|
|
diff1_ptr->at(i) = factor*pow(inc_ptr->at(i) - meaninc, o)
|
|
*(diff1_ptr->at(i) - tmp_ptr->at(i))/dinc;
|
|
drtp_ptr->at(i) += diff1_ptr->at(i);
|
|
}
|
|
|
|
rtp(diff2_name, tmp_name, meaninc, meandec);
|
|
rtp(diff2_name, diff2_name, meaninc, meandec+ddec);
|
|
for (int i = 0; i < drtp_ptr->size(); i++)
|
|
{
|
|
diff2_ptr->at(i) = factor*pow(dec_ptr->at(i) - meandec, o)
|
|
*(diff2_ptr->at(i) - tmp_ptr->at(i))/ddec;
|
|
drtp_ptr->at(i) += diff2_ptr->at(i);
|
|
}
|
|
}
|
|
|
|
// 删除临时数据
|
|
remove_data(tmp_name);
|
|
remove_data(diff1_name);
|
|
remove_data(diff2_name);
|
|
return;
|
|
}
|
|
|
|
void gctl::gm_regular_grid::conti(std::string datname, std::string retname, double height)
|
|
{
|
|
meshdata &data = get_data(datname);
|
|
mesh_data_value_e value_type = data.valtype_;
|
|
mesh_data_type_e data_type = data.loctype_;
|
|
|
|
if(value_type != Scalar)
|
|
{
|
|
throw std::runtime_error("[gctl::gm_regular_grid::conti] Invalid value type.");
|
|
}
|
|
|
|
// 检查是否存在与梯度数据同名的数据 若有则检查是否需要重新建立数据
|
|
meshdata &new_data = add_data(data_type, value_type, retname, 0.0);
|
|
gctl::array<double> ingrid_ex;
|
|
|
|
int M = -1, N = -1;
|
|
int ori_row, ori_col;
|
|
if (data_type == NodeData) gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum, rg_xnum, M, N, ori_row, ori_col);
|
|
else gctl::cosine_extrapolate_2d(data.datval_, ingrid_ex, rg_ynum-1, rg_xnum-1, M, N, ori_row, ori_col);
|
|
|
|
fftw_complex *in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
|
|
fftw_complex *out= (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*M*N);
|
|
|
|
for (int i = 0; i < M*N; i++)
|
|
{
|
|
in[i][0] = ingrid_ex[i];
|
|
in[i][1] = 0.0;
|
|
}
|
|
|
|
fftw_plan p = fftw_plan_dft_2d(M, N, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
|
|
fftw_execute(p);
|
|
|
|
int half_M = ceil(M/2);
|
|
int half_N = ceil(N/2);
|
|
double du = 2.0*GCTL_Pi/((M-1)*rg_dy);
|
|
double dv = 2.0*GCTL_Pi/((N-1)*rg_dx);
|
|
|
|
int idx1, idx2, idx3, idx4;
|
|
double u, v;
|
|
for (int i = 0; i < half_M; i++)
|
|
{
|
|
u = du*(i+1);
|
|
for (int j = 0; j < half_N; j++)
|
|
{
|
|
v = dv*(j+1);
|
|
|
|
idx1 = i*N+j;
|
|
idx2 = i*N+N-1-j;
|
|
idx3 = (M-1-i)*N+j;
|
|
idx4 = (M-1-i)*N+N-1-j;
|
|
|
|
in[idx1][0] = out[idx1][0]*exp(sqrt(u*u+v*v)*height);
|
|
in[idx1][1] = out[idx1][1]*exp(sqrt(u*u+v*v)*height);
|
|
|
|
in[idx2][0] = out[idx2][0]*exp(sqrt(u*u+v*v)*height);
|
|
in[idx2][1] = out[idx2][1]*exp(sqrt(u*u+v*v)*height);
|
|
|
|
in[idx3][0] = out[idx3][0]*exp(sqrt(u*u+v*v)*height);
|
|
in[idx3][1] = out[idx3][1]*exp(sqrt(u*u+v*v)*height);
|
|
|
|
in[idx4][0] = out[idx4][0]*exp(sqrt(u*u+v*v)*height);
|
|
in[idx4][1] = out[idx4][1]*exp(sqrt(u*u+v*v)*height);
|
|
}
|
|
}
|
|
|
|
p = fftw_plan_dft_2d(M, N, in, out, FFTW_BACKWARD, FFTW_ESTIMATE);
|
|
fftw_execute(p);
|
|
|
|
for (int i = 0; i < M; i++)
|
|
{
|
|
for (int j = 0; j < N; j++)
|
|
{
|
|
ingrid_ex[i*N+j] = out[i*N+j][0]/(M*N);
|
|
}
|
|
}
|
|
|
|
if (data_type == NodeData)
|
|
{
|
|
for (int i = 0; i < rg_ynum; i++)
|
|
{
|
|
for (int j = 0; j < rg_xnum; j++)
|
|
{
|
|
new_data.datval_[i*rg_xnum+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (int i = 0; i < rg_ynum-1; i++)
|
|
{
|
|
for (int j = 0; j < rg_xnum-1; j++)
|
|
{
|
|
new_data.datval_[i*(rg_xnum-1)+j] = ingrid_ex[(i+ori_row)*N+j+ori_col];
|
|
}
|
|
}
|
|
}
|
|
|
|
fftw_destroy_plan(p);
|
|
fftw_free(in);
|
|
fftw_free(out);
|
|
return;
|
|
}
|
|
|
|
#endif //GCTL_POTENTIAL_FFTW3
|
|
|
|
void gctl::gm_regular_grid::trend(std::string datname, std::string regname, std::string resname, int wx_size, int wy_size, int x_order, int y_order)
|
|
{
|
|
meshdata &data = get_data(datname);
|
|
mesh_data_value_e value_type = data.valtype_;
|
|
mesh_data_type_e data_type = data.loctype_;
|
|
|
|
if(value_type != Scalar)
|
|
{
|
|
throw std::runtime_error("Invalid value type. From gctl::gm_regular_grid::trend(...)");
|
|
}
|
|
|
|
// 检查是否存在与趋势场局部场数据同名的数据 若有则检查是否需要重新建立数据
|
|
meshdata ®_data = add_data(data_type, value_type, regname, 0.0);
|
|
meshdata &res_data = add_data(data_type, value_type, resname, 0.0);
|
|
|
|
matrix<double> data_mat;
|
|
if (data_type == NodeData)
|
|
{
|
|
data_mat.resize(rg_ynum, rg_xnum);
|
|
for (size_t i = 0; i < rg_ynum; i++)
|
|
{
|
|
for (size_t j = 0; j < rg_xnum; j++)
|
|
{
|
|
data_mat[i][j] = data.datval_[i*rg_xnum+j];
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
data_mat.resize(rg_ynum-1, rg_xnum-1);
|
|
for (size_t i = 0; i < rg_ynum-1; i++)
|
|
{
|
|
for (size_t j = 0; j < rg_xnum-1; j++)
|
|
{
|
|
data_mat[i][j] = data.datval_[i*(rg_xnum-1)+j];
|
|
}
|
|
}
|
|
}
|
|
|
|
trend_2d(data_mat, wy_size, wx_size, y_order, x_order);
|
|
|
|
if (data_type == NodeData)
|
|
{
|
|
for (size_t i = 0; i < rg_ynum; i++)
|
|
{
|
|
for (size_t j = 0; j < rg_xnum; j++)
|
|
{
|
|
reg_data.datval_[i*rg_xnum+j] = data_mat[i][j];
|
|
res_data.datval_[i*rg_xnum+j] = data.datval_[i*rg_xnum+j] - data_mat[i][j];
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (size_t i = 0; i < rg_ynum-1; i++)
|
|
{
|
|
for (size_t j = 0; j < rg_xnum-1; j++)
|
|
{
|
|
reg_data.datval_[i*(rg_xnum-1)+j] = data_mat[i][j];
|
|
res_data.datval_[i*(rg_xnum-1)+j] = data.datval_[i*(rg_xnum-1)+j] - data_mat[i][j];
|
|
}
|
|
}
|
|
}
|
|
return;
|
|
} |