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gctl/lib/algorithm/algorithm_func.cpp
Yi Zhang 4f9864cf6c initial upload
2024-09-10 15:45:07 +08:00

731 lines
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/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2023 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "algorithm_func.h"
double gctl::dist_inverse_weight(std::vector<double> *dis_vec, std::vector<double> *val_vec, int order)
{
if (dis_vec->size() != val_vec->size())
throw runtime_error("The arrays have different sizes. Thrown by gctl::dist_inverse_weight(...)");
double total_dist = 0;
for (int i = 0; i < dis_vec->size(); i++)
{
dis_vec->at(i) = 1.0/(GCTL_ZERO + pow(dis_vec->at(i),order));
total_dist += dis_vec->at(i);
}
double ret = 0.0;
for (int i = 0; i < dis_vec->size(); i++)
{
ret += val_vec->at(i)*dis_vec->at(i)/total_dist;
}
return ret;
}
int gctl::find_index(const double *in_array, int array_size, double in_val, int &index)
{
if (array_size <= 0)
{
index = -1;
return -1;
}
else if (array_size == 1)
{
index = -1;
return -1;
}
else if (in_val < in_array[0] || in_val > in_array[array_size-1])
{
index = -1;
return -1;
}
else if (array_size == 2)
{
index = 0;
return 0;
}
else
{
int low_range = 0;
int high_range = array_size - 1;
int test_index;
bool found = false;
while (high_range - low_range >= 1)
{
test_index = floor(0.5*(low_range + high_range));
if (in_val >= in_array[test_index] && in_val <= in_array[test_index+1])
{
index = test_index;
found = true;
break;
}
else if (in_val < in_array[test_index])
{
high_range = test_index;
}
else if (in_val > in_array[test_index+1])
{
low_range = test_index+1;
}
}
if (found) return 0;
else return -1;
}
}
int gctl::find_index(array<double> *in_array, double in_val, int &index)
{
return find_index(in_array->get(), in_array->size(), in_val, index);
}
void gctl::fractal_model_1d(array<double> &out_arr, int out_size, double l_val,
double r_val, double maxi_range, double smoothness)
{
if (out_size <= 0)
throw invalid_argument("Negative output size. Thrown by gctl::fractal_model_1d(...)");
if (maxi_range <= 0)
throw invalid_argument("Negative maximal range. Thrown by gctl::fractal_model_1d(...)");
if (smoothness <= 0)
throw invalid_argument("Negative smoothness. Thrown by gctl::fractal_model_1d(...)");
out_arr.resize(out_size);
int bigger_num = (int) pow(2, ceil(log(out_arr.size()-1)/log(2))) + 1;
array<double> tmp_arr(bigger_num); // 计算的长度必须为2的次方数
int step_size = (int) (bigger_num-1)/2;
tmp_arr[0] = l_val;
tmp_arr[bigger_num-1] = r_val;
srand(time(0));
while (step_size >= 1)
{
for (int i = step_size; i < bigger_num; i += 2*step_size)
{
tmp_arr[i] = random(-1.0*maxi_range, maxi_range) +
0.5*(tmp_arr[i-step_size] + tmp_arr[i+step_size]);
}
maxi_range = pow(2.0, -1.0*smoothness)*maxi_range;
step_size /= 2;
}
for (int i = 0; i < out_arr.size(); i++)
{
out_arr[i] = tmp_arr[i];
}
return;
}
void gctl::fractal_model_2d(_2d_matrix &out_arr, int r_size, int c_size, double dl_val,
double dr_val, double ul_val, double ur_val, double maxi_range, double smoothness,
unsigned int seed)
{
if (r_size <= 0 || c_size <= 0)
throw invalid_argument("Negative output size. Thrown by gctl::fractal_model_2d(...)");
if (maxi_range <= 0)
throw invalid_argument("Negative maximal range. Thrown by gctl::fractal_model_2d(...)");
if (smoothness <= 0)
throw invalid_argument("Negative smoothness. Thrown by gctl::fractal_model_2d(...)");
int i, j, m, n, R, jmax;
double random_d;
out_arr.resize(r_size, c_size);
int xnum = out_arr.col_size();
int ynum = out_arr.row_size();
int order_x = ceil(log(xnum-1)/log(2));
int order_y = ceil(log(ynum-1)/log(2));
int imax = GCTL_MAX(order_x,order_y);
int ntotal = (int) pow(2.0, imax) + 1; //总数据点数为2的imax次方加1
_2d_matrix topo(ntotal, ntotal, 0.0);
for (i=0; i<ntotal; i++)//设定地形数据初始值，角点数据必须给出
{
for (j=0; j<ntotal; j++)
{
if (i == 0 && j == 0)
{
topo[i][j] = ul_val; //角点初始值；
}
else if (i == ntotal-1 && j==0)
{
topo[i][j] = dl_val; //角点初始值；
}
else if (i==0 && j==ntotal-1)
{
topo[i][j] = ur_val; //角点初始值；
}
else if (i==ntotal-1 && j==ntotal-1)
{
topo[i][j] = dr_val; //角点初始值；
}
else
{
topo[i][j] = GCTL_BDL_MAX;
}
}
}
if (seed == 0) srand(time(0));
else srand(seed);
for (i = 1; i <= imax; i++)//开始迭代，生成正方形区域随机地形
{
R = int(double(ntotal-1)/pow(2.0,i));
jmax=int(pow(4.0,i-1));
for (j=1; j<=jmax; j++)
{
random_d = random(-1.0*maxi_range, maxi_range);
m=2*R*(j-(ceil((double)j/pow(2.0,i-1))-1) * pow(2.0,i-1))-R;
n=2*R*(ceil((double)j/pow(2.0,i-1)))-R;
topo[m][n]=(topo[m-R][n-R]+topo[m+R][n-R]+topo[m-R][n+R]+topo[m+R][n+R])/4+random_d;
}
for (j=1; j<=jmax; j++)
{
m=2*R*(j-(ceil((double)j/pow(2.0,i-1))-1)* pow(2.0,i-1))-R;
n=2*R*(ceil((double)j/pow(2.0,i-1)))-R;
if (topo[m][n-R] == GCTL_BDL_MAX)
{
random_d = random(-1.0*maxi_range, maxi_range);
if ((n-R)!=0)
{
topo[m][n-R]=(topo[m][n-2*R]+topo[m-R][n-R]+topo[m+R][n-R]+topo[m][n])/4+random_d;
}
else
{
topo[m][n-R]=(topo[m-R][n-R]+topo[m+R][n-R]+topo[m][n])/3+random_d;
}
}
if (topo[m-R][n] == GCTL_BDL_MAX)
{
random_d = random(-1.0*maxi_range, maxi_range);
if ((m-R)!=0)
{
topo[m-R][n]=(topo[m-R][n-R]+topo[m-2*R][n]+topo[m][n]+topo[m-R][n+R])/4+random_d;
}
else
{
topo[m-R][n]=(topo[m-R][n-R]+topo[m][n]+topo[m-R][n+R])/3+random_d;
}
}
if (topo[m+R][n] == GCTL_BDL_MAX)
{
random_d = random(-1.0*maxi_range, maxi_range);
if ((m+R)!=(ntotal-1))
{
topo[m+R][n]=(topo[m+R][n-R]+topo[m][n]+topo[m+2*R][n]+topo[m+R][n+R])/4+random_d;
}
else
{
topo[m+R][n]=(topo[m+R][n-R]+topo[m][n]+topo[m+R][n+R])/3+random_d;
}
}
if (topo[m][n+R] == GCTL_BDL_MAX)
{
random_d = random(-1.0*maxi_range, maxi_range);
if ((n+R)!=(ntotal-1))
{
topo[m][n+R]=(topo[m][n]+topo[m-R][n+R]+topo[m+R][n+R]+topo[m][n+2*R])/4+random_d;
}
else
{
topo[m][n+R]=(topo[m][n]+topo[m-R][n+R]+topo[m+R][n+R])/3+random_d;
}
}
}
maxi_range = pow(2.0, -1.0*smoothness)*maxi_range;
}
for (int j = 0; j < ynum; j++)//按预设区域剪裁数组
{
for (int i=0; i < xnum; i++)
{
out_arr[i][j] = topo[i][j];
}
}
return;
}
void gctl::difference_1d(const array<double> &in, array<double> &diff, double spacing, int order)
{
if (order < 1 || order > 4)
throw invalid_argument("The input order can only be 1 to 4. Thrown by gctl::difference_1d(...)");
if (spacing <= 0.0)
throw invalid_argument("The input spacing can't be negative or zero. Thrown by void gctl::difference_1d(...)");
if (order == 1 && in.size() < 3)
throw runtime_error("The input array size must be equal to or bigger than three for the first order derivative. Thrown by gctl::difference_1d(...)");
if (order == 2 && in.size() < 4)
throw runtime_error("The input array size must be equal to or bigger than four for the second order derivative. Thrown by gctl::difference_1d(...)");
if (order == 3 && in.size() < 6)
throw runtime_error("The input array size must be equal to or bigger than six for the third order derivative. Thrown by gctl::difference_1d(...)");
if (order == 4 && in.size() < 7)
throw runtime_error("The input array size must be equal to or bigger than seven for the fourth order derivative. Thrown by gctl::difference_1d(...)");
int t_size = in.size();
diff.resize(t_size);
// 利用向前或向后差分计算边缘元素的导数
if (order == 1)
{
diff[0] = (-3.0*in[0]+4.0*in[1]-in[2])/(2.0*spacing);
diff[t_size-1] = (3.0*in[t_size-1]-4.0*in[t_size-2]+in[t_size-3])/(2.0*spacing);
for (int i = 1; i < t_size-1; i++)
{
diff[i] = (in[i+1] - in[i-1])/(2.0*spacing);
}
}
else if (order == 2)
{
diff[0] = (2.0*in[0]-5.0*in[1]+4.0*in[2]-in[3])/(spacing*spacing);
diff[t_size-1] = (2.0*in[t_size-1]-5.0*in[t_size-2]+4.0*in[t_size-3]-in[t_size-4])/(spacing*spacing);
for (int i = 1; i < t_size-1; i++)
{
diff[i] = (in[i-1]-2.0*in[i]+in[i+1])/(spacing*spacing);
}
}
else if (order == 3)
{
diff[0] = (-5.0*in[0]+18.0*in[1]-24.0*in[2]+14.0*in[3]-3.0*in[4])/(2.0*spacing*spacing*spacing);
diff[1] = (-5.0*in[1]+18.0*in[2]-24.0*in[3]+14.0*in[4]-3.0*in[5])/(2.0*spacing*spacing*spacing);
diff[t_size-1] = (5.0*in[t_size-1]-18.0*in[t_size-2]+24.0*in[t_size-3]-14.0*in[t_size-4]+3.0*in[t_size-5])/(2.0*spacing*spacing*spacing);
diff[t_size-2] = (5.0*in[t_size-2]-18.0*in[t_size-3]+24.0*in[t_size-4]-14.0*in[t_size-5]+3.0*in[t_size-6])/(2.0*spacing*spacing*spacing);
for (int i = 2; i < t_size-2; i++)
{
diff[i] = (-1.0*in[i-2]+2.0*in[i-1]-2.0*in[i+1]+in[i+2])/(2.0*spacing*spacing*spacing);
}
}
else
{
diff[0] = (3.0*in[0]-14.0*in[1]+26.0*in[2]-24.0*in[3]+11.0*in[4]-2.0*in[5])/(spacing*spacing*spacing*spacing);
diff[1] = (3.0*in[1]-14.0*in[2]+26.0*in[3]-24.0*in[4]+11.0*in[5]-2.0*in[6])/(spacing*spacing*spacing*spacing);
diff[t_size-1] = (3.0*in[t_size-1]-14.0*in[t_size-2]+26.0*in[t_size-3]-24.0*in[t_size-4]+11.0*in[t_size-5]-2.0*in[t_size-6])/(spacing*spacing*spacing*spacing);
diff[t_size-2] = (3.0*in[t_size-2]-14.0*in[t_size-3]+26.0*in[t_size-4]-24.0*in[t_size-5]+11.0*in[t_size-6]-2.0*in[t_size-7])/(spacing*spacing*spacing*spacing);
for (int i = 2; i < t_size-2; i++)
{
diff[i] = (in[i-2]-4.0*in[i-1]+6.0*in[i]-4.0*in[i+1]+in[i+2])/(spacing*spacing*spacing*spacing);
}
}
return;
}
void gctl::difference_2d(const _2d_matrix &in, _2d_matrix &diff, double spacing, gradient_type_e d_type, int order)
{
std::string err_str;
if (order < 1 || order > 4)
throw invalid_argument("The input order can only be 1 to 4. Thrown by void gctl::difference_2d(...)");
if (spacing <= 0.0)
throw invalid_argument("The input spacing can't be negative or zero. Thrown by void gctl::difference_2d(...)");
int t_size;
if (d_type == Dx)
{
t_size = in.col_size();
}
else if (d_type == Dy)
{
t_size = in.row_size();
}
else
{
throw logic_error("The calculation type must be Dx or Dy. Thrown by gctl::difference_2d(...)");
}
if (order == 1 && t_size < 3)
throw runtime_error("The input array size must be equal to or bigger than 3x3 for the first order derivative. Thrown by void gctl::difference_2d(...)");
if (order == 2 && t_size < 4)
throw runtime_error("The input array size must be equal to or bigger than 4x4 for the second order derivative. Thrown by gctl::difference_2d(...)");
if (order == 3 && t_size < 6)
throw runtime_error("The input array size must be equal to or bigger than 6x6 for the third order derivative. Thrown by gctl::difference_2d(...)");
if (order == 4 && t_size < 7)
throw runtime_error("The input array size must be equal to or bigger than 7x7 for the fourth order derivative. Thrown by void gctl::difference_2d(...)");
int tr_size = in.row_size(), tl_size = in.col_size();
diff.resize(tr_size, tl_size);
if (d_type == Dx)
{
if (order == 1)
{
for (int i = 0; i < tr_size; i++)
{
diff[i][0] = (-3.0*in[i][0]+4.0*in[i][1]-in[i][2])/(2.0*spacing);
diff[i][tl_size-1] = (3.0*in[i][tl_size-1]-4.0*in[i][tl_size-2]+in[i][tl_size-3])/(2.0*spacing);
for (int j = 1; j < tl_size-1; j++)
{
diff[i][j] = (in[i][j+1] - in[i][j-1])/(2.0*spacing);
}
}
}
else if (order == 2)
{
for (int i = 0; i < tr_size; i++)
{
diff[i][0] = (2.0*in[i][0]-5.0*in[i][1]+4.0*in[i][2]-in[i][3])/(spacing*spacing);
diff[i][tl_size-1] = (2.0*in[i][tl_size-1]-5.0*in[i][tl_size-2]+4.0*in[i][tl_size-3]-in[i][tl_size-4])/(spacing*spacing);
for (int j = 1; j < tl_size-1; j++)
{
diff[i][j] = (in[i][j-1]-2.0*in[i][j]+in[i][j+1])/(spacing*spacing);
}
}
}
else if (order == 3)
{
for (int i = 0; i < tr_size; i++)
{
diff[i][0] = (-5.0*in[i][0]+18.0*in[i][1]-24.0*in[i][2]+14.0*in[i][3]-3.0*in[i][4])/(2.0*spacing*spacing*spacing);
diff[i][1] = (-5.0*in[i][1]+18.0*in[i][2]-24.0*in[i][3]+14.0*in[i][4]-3.0*in[i][5])/(2.0*spacing*spacing*spacing);
diff[i][tl_size-1] = (5.0*in[i][tl_size-1]-18.0*in[i][tl_size-2]+24.0*in[i][tl_size-3]-14.0*in[i][tl_size-4]+3.0*in[i][tl_size-5])/(2.0*spacing*spacing*spacing);
diff[i][tl_size-2] = (5.0*in[i][tl_size-2]-18.0*in[i][tl_size-3]+24.0*in[i][tl_size-4]-14.0*in[i][tl_size-5]+3.0*in[i][tl_size-6])/(2.0*spacing*spacing*spacing);
for (int j = 2; j < tl_size-2; j++)
{
diff[i][j] = (-1.0*in[i][j-2]+2.0*in[i][j-1]-2.0*in[i][j+1]+in[i][j+2])/(2.0*spacing*spacing*spacing);
}
}
}
else
{
for (int i = 0; i < tr_size; i++)
{
diff[i][0] = (3.0*in[i][0]-14.0*in[i][1]+26.0*in[i][2]-24.0*in[i][3]+11.0*in[i][4]-2.0*in[i][5])/(spacing*spacing*spacing*spacing);
diff[i][1] = (3.0*in[i][1]-14.0*in[i][2]+26.0*in[i][3]-24.0*in[i][4]+11.0*in[i][5]-2.0*in[i][6])/(spacing*spacing*spacing*spacing);
diff[i][tl_size-1] = (3.0*in[i][tl_size-1]-14.0*in[i][tl_size-2]+26.0*in[i][tl_size-3]-24.0*in[i][tl_size-4]+11.0*in[i][tl_size-5]-2.0*in[i][tl_size-6])/(spacing*spacing*spacing*spacing);
diff[i][tl_size-2] = (3.0*in[i][tl_size-2]-14.0*in[i][tl_size-3]+26.0*in[i][tl_size-4]-24.0*in[i][tl_size-5]+11.0*in[i][tl_size-6]-2.0*in[i][tl_size-7])/(spacing*spacing*spacing*spacing);
for (int j = 2; j < tl_size-2; j++)
{
diff[i][j] = (in[i][j-2]-4.0*in[i][j-1]+6.0*in[i][j]-4.0*in[i][j+1]+in[i][j+2])/(spacing*spacing*spacing*spacing);
}
}
}
}
else
{
if (order == 1)
{
for (int j = 0; j < tl_size; j++)
{
diff[0][j] = (-3.0*in[0][j]+4.0*in[1][j]-in[2][j])/(2.0*spacing);
diff[tr_size-1][j] = (3.0*in[tr_size-1][j]-4.0*in[tr_size-2][j]+in[tr_size-3][j])/(2.0*spacing);
for (int i = 1; i < tr_size-1; i++)
{
diff[i][j] = (in[i+1][j] - in[i-1][j])/(2.0*spacing);
}
}
}
else if (order == 2)
{
for (int j = 0; j < tl_size; j++)
{
diff[0][j] = (2.0*in[0][j]-5.0*in[1][j]+4.0*in[2][j]-in[3][j])/(spacing*spacing);
diff[tr_size-1][j] = (2.0*in[tr_size-1][j]-5.0*in[tr_size-2][j]+4.0*in[tr_size-3][j]-in[tr_size-4][j])/(spacing*spacing);
for (int i = 1; i < tr_size-1; i++)
{
diff[i][j] = (in[i-1][j]-2.0*in[i][j]+in[i+1][j])/(spacing*spacing);
}
}
}
else if (order == 3)
{
for (int j = 0; j < tl_size; j++)
{
diff[0][j] = (-5.0*in[0][j]+18.0*in[1][j]-24.0*in[2][j]+14.0*in[3][j]-3.0*in[4][j])/(2.0*spacing*spacing*spacing);
diff[1][j] = (-5.0*in[1][j]+18.0*in[2][j]-24.0*in[3][j]+14.0*in[4][j]-3.0*in[5][j])/(2.0*spacing*spacing*spacing);
diff[tr_size-1][j] = (5.0*in[tr_size-1][j]-18.0*in[tr_size-2][j]+24.0*in[tr_size-3][j]-14.0*in[tr_size-4][j]+3.0*in[tr_size-5][j])/(2.0*spacing*spacing*spacing);
diff[tr_size-2][j] = (5.0*in[tr_size-2][j]-18.0*in[tr_size-3][j]+24.0*in[tr_size-4][j]-14.0*in[tr_size-5][j]+3.0*in[tr_size-6][j])/(2.0*spacing*spacing*spacing);
for (int i = 2; i < tr_size-2; i++)
{
diff[i][j] = (-1.0*in[i-2][j]+2.0*in[i-1][j]-2.0*in[i+1][j]+in[i+2][j])/(2.0*spacing*spacing*spacing);
}
}
}
else
{
for (int j = 0; j < tl_size; j++)
{
diff[0][j] = (3.0*in[0][j]-14.0*in[1][j]+26.0*in[2][j]-24.0*in[3][j]+11.0*in[4][j]-2.0*in[5][j])/(spacing*spacing*spacing*spacing);
diff[1][j] = (3.0*in[1][j]-14.0*in[2][j]+26.0*in[3][j]-24.0*in[4][j]+11.0*in[5][j]-2.0*in[6][j])/(spacing*spacing*spacing*spacing);
diff[tr_size-1][j] = (3.0*in[tr_size-1][j]-14.0*in[tr_size-2][j]+26.0*in[tr_size-3][j]-24.0*in[tr_size-4][j]+11.0*in[tr_size-5][j]-2.0*in[tr_size-6][j])/(spacing*spacing*spacing*spacing);
diff[tr_size-2][j] = (3.0*in[tr_size-2][j]-14.0*in[tr_size-3][j]+26.0*in[tr_size-4][j]-24.0*in[tr_size-5][j]+11.0*in[tr_size-6][j]-2.0*in[tr_size-7][j])/(spacing*spacing*spacing*spacing);
for (int i = 2; i < tr_size-2; i++)
{
diff[i][j] = (in[i-2][j]-4.0*in[i-1][j]+6.0*in[i][j]-4.0*in[i+1][j]+in[i+2][j])/(spacing*spacing*spacing*spacing);
}
}
}
}
return;
}
void gctl::difference_2d(const array<double> &in, array<double> &diff, int row_size, int col_size,
double spacing, gradient_type_e d_type, int order)
{
std::string err_str;
if (order < 1 || order > 4)
throw invalid_argument("The input order can only be 1 to 4. Thrown by void gctl::difference_2d(...)");
if (spacing <= 0.0)
throw invalid_argument("The input spacing can't be negative or zero. Thrown by void gctl::difference_2d(...)");
if (row_size*col_size != in.size())
throw invalid_argument("The input array size does not match. Thrown by void gctl::difference_2d(...)");
int t_size;
if (d_type == Dx)
{
t_size = col_size;
}
else if (d_type == Dy)
{
t_size = row_size;
}
else
{
throw logic_error("The calculation type must be Dx or Dy. Thrown by gctl::difference_2d(...)");
}
if (order == 1 && t_size < 3)
throw runtime_error("The input array size must be equal to or bigger than 3x3 for the first order derivative. Thrown by gctl::difference_2d(...)");
if (order == 2 && t_size < 4)
throw runtime_error("The input array size must be equal to or bigger than 4x4 for the second order derivative. Thrown by gctl::difference_2d(...)");
if (order == 3 && t_size < 6)
throw runtime_error("The input array size must be equal to or bigger than 6x6 for the third order derivative. Thrown by gctl::difference_2d(...)");
if (order == 4 && t_size < 7)
throw runtime_error("The input array size must be equal to or bigger than 7x7 for the fourth order derivative. Thrown by gctl::difference_2d(...)");
int tr_size = row_size, tl_size = col_size;
diff.resize(tr_size*tl_size);
int idx;
if (d_type == Dx)
{
if (order == 1)
{
for (int i = 0; i < tr_size; i++)
{
idx = i*tl_size;
diff[idx] = (-3.0*in[idx]+4.0*in[idx+1]-in[idx+2])/(2.0*spacing);
idx = i*tl_size + tl_size-1;
diff[idx] = (3.0*in[idx]-4.0*in[idx-1]+in[idx-2])/(2.0*spacing);
for (int j = 1; j < tl_size-1; j++)
{
idx = i*tl_size + j;
diff[idx] = (in[idx+1] - in[idx-1])/(2.0*spacing);
}
}
}
else if (order == 2)
{
for (int i = 0; i < tr_size; i++)
{
idx = i*tl_size;
diff[idx] = (2.0*in[idx]-5.0*in[idx+1]+4.0*in[idx+2]-in[idx+3])/(spacing*spacing);
idx = i*tl_size + tl_size-1;
diff[idx] = (2.0*in[idx]-5.0*in[idx-1]+4.0*in[idx-2]-in[idx-3])/(spacing*spacing);
for (int j = 1; j < tl_size-1; j++)
{
idx = i*tl_size + j;
diff[idx] = (in[idx-1]-2.0*in[idx]+in[idx+1])/(spacing*spacing);
}
}
}
else if (order == 3)
{
for (int i = 0; i < tr_size; i++)
{
idx = i*tl_size;
diff[idx] = (-5.0*in[idx]+18.0*in[idx+1]-24.0*in[idx+2]+14.0*in[idx+3]-3.0*in[idx+4])/(2.0*spacing*spacing*spacing);
idx = i*tl_size+1;
diff[idx] = (-5.0*in[idx]+18.0*in[idx+1]-24.0*in[idx+2]+14.0*in[idx+3]-3.0*in[idx+4])/(2.0*spacing*spacing*spacing);
idx = i*tl_size + tl_size-1;
diff[idx] = (5.0*in[idx]-18.0*in[idx-1]+24.0*in[idx-2]-14.0*in[idx-3]+3.0*in[idx-4])/(2.0*spacing*spacing*spacing);
idx = i*tl_size + tl_size-2;
diff[idx] = (5.0*in[idx]-18.0*in[idx-1]+24.0*in[idx-2]-14.0*in[idx-3]+3.0*in[idx-4])/(2.0*spacing*spacing*spacing);
for (int j = 2; j < tl_size-2; j++)
{
idx = i*tl_size + j;
diff[idx] = (-1.0*in[idx-2]+2.0*in[idx-1]-2.0*in[idx+1]+in[idx+2])/(2.0*spacing*spacing*spacing);
}
}
}
else
{
for (int i = 0; i < tr_size; i++)
{
idx = i*tl_size;
diff[idx] = (3.0*in[idx]-14.0*in[idx+1]+26.0*in[idx+2]-24.0*in[idx+3]+11.0*in[idx+4]-2.0*in[idx+5])/(spacing*spacing*spacing*spacing);
idx = i*tl_size+1;
diff[idx] = (3.0*in[idx]-14.0*in[idx+1]+26.0*in[idx+2]-24.0*in[idx+3]+11.0*in[idx+4]-2.0*in[idx+5])/(spacing*spacing*spacing*spacing);
idx = i*tl_size + tl_size-1;
diff[idx] = (3.0*in[idx]-14.0*in[idx-1]+26.0*in[idx-2]-24.0*in[idx-3]+11.0*in[idx-4]-2.0*in[idx-5])/(spacing*spacing*spacing*spacing);
idx = i*tl_size + tl_size-2;
diff[idx] = (3.0*in[idx]-14.0*in[idx-1]+26.0*in[idx-2]-24.0*in[idx-3]+11.0*in[idx-4]-2.0*in[idx-5])/(spacing*spacing*spacing*spacing);
for (int j = 2; j < tl_size-2; j++)
{
idx = i*tl_size + j;
diff[idx] = (in[idx-2]-4.0*in[idx-1]+6.0*in[idx]-4.0*in[idx+1]+in[idx+2])/(spacing*spacing*spacing*spacing);
}
}
}
}
else
{
if (order == 1)
{
for (int j = 0; j < tl_size; j++)
{
idx = j;
diff[idx] = (-3.0*in[idx]+4.0*in[idx+tl_size]-in[idx+2*tl_size])/(2.0*spacing);
idx = (tr_size-1)*tl_size + j;
diff[idx] = (3.0*in[idx]-4.0*in[idx-tl_size]+in[idx-2*tl_size])/(2.0*spacing);
for (int i = 1; i < tr_size-1; i++)
{
idx = i*tl_size + j;
diff[idx] = (in[idx+tl_size] - in[idx-tl_size])/(2.0*spacing);
}
}
}
else if (order == 2)
{
for (int j = 0; j < tl_size; j++)
{
idx = j;
diff[idx] = (2.0*in[idx]-5.0*in[idx+tl_size]+4.0*in[idx+2*tl_size]-in[idx+3*tl_size])/(spacing*spacing);
idx = (tr_size-1)*tl_size + j;
diff[idx] = (2.0*in[idx]-5.0*in[idx-tl_size]+4.0*in[idx-2*tl_size]-in[idx-3*tl_size])/(spacing*spacing);
for (int i = 1; i < tr_size-1; i++)
{
idx = i*tl_size + j;
diff[idx] = (in[idx-tl_size]-2.0*in[idx]+in[idx+tl_size])/(spacing*spacing);
}
}
}
else if (order == 3)
{
for (int j = 0; j < tl_size; j++)
{
idx = j;
diff[idx] = (-5.0*in[idx]+18.0*in[idx+tl_size]-24.0*in[idx+2*tl_size]+14.0*in[idx+3*tl_size]-3.0*in[idx+4*tl_size])/(2.0*spacing*spacing*spacing);
idx = tl_size+j;
diff[idx] = (-5.0*in[idx]+18.0*in[idx+tl_size]-24.0*in[idx+2*tl_size]+14.0*in[idx+3*tl_size]-3.0*in[idx+4*tl_size])/(2.0*spacing*spacing*spacing);
idx = (tr_size-1)*tl_size + j;
diff[idx] = (5.0*in[idx]-18.0*in[idx-tl_size]+24.0*in[idx-2*tl_size]-14.0*in[idx-3*tl_size]+3.0*in[idx-4*tl_size])/(2.0*spacing*spacing*spacing);
idx = (tr_size-2)*tl_size + j;
diff[idx] = (5.0*in[idx]-18.0*in[idx-tl_size]+24.0*in[idx-2*tl_size]-14.0*in[idx-3*tl_size]+3.0*in[idx-4*tl_size])/(2.0*spacing*spacing*spacing);
for (int i = 2; i < tr_size-2; i++)
{
idx = i*tl_size + j;
diff[idx] = (-1.0*in[idx-2*tl_size]+2.0*in[idx-tl_size]-2.0*in[idx+tl_size]+in[idx+2*tl_size])/(2.0*spacing*spacing*spacing);
}
}
}
else
{
for (int j = 0; j < tl_size; j++)
{
idx = j;
diff[idx] = (3.0*in[idx]-14.0*in[idx+tl_size]+26.0*in[idx+2*tl_size]-24.0*in[idx+3*tl_size]+11.0*in[idx+4*tl_size]-2.0*in[idx+5*tl_size])/(spacing*spacing*spacing*spacing);
idx = tl_size+j;
diff[idx] = (3.0*in[idx]-14.0*in[idx+tl_size]+26.0*in[idx+2*tl_size]-24.0*in[idx+3*tl_size]+11.0*in[idx+4*tl_size]-2.0*in[idx+5*tl_size])/(spacing*spacing*spacing*spacing);
idx = (tr_size-1)*tl_size + j;
diff[idx] = (3.0*in[idx]-14.0*in[idx-tl_size]+26.0*in[idx-2*tl_size]-24.0*in[idx-3*tl_size]+11.0*in[idx-4*tl_size]-2.0*in[idx-5*tl_size])/(spacing*spacing*spacing*spacing);
idx = (tr_size-2)*tl_size + j;
diff[idx] = (3.0*in[idx]-14.0*in[idx-tl_size]+26.0*in[idx-2*tl_size]-24.0*in[idx-3*tl_size]+11.0*in[idx-4*tl_size]-2.0*in[idx-5*tl_size])/(spacing*spacing*spacing*spacing);
for (int i = 2; i < tr_size-2; i++)
{
idx = i*tl_size + j;
diff[idx] = (in[idx-2*tl_size]-4.0*in[idx-tl_size]+6.0*in[idx]-4.0*in[idx+tl_size]+in[idx+2*tl_size])/(spacing*spacing*spacing*spacing);
}
}
}
}
return;
}
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