用C++写通过最小二乘法实现七参数空间直角坐标系坐标转换的代码
时间: 2024-05-08 12:22:20 浏览: 11
以下是用C语言实现通过最小二乘法实现七参数空间直角坐标系坐标转换的代码:
```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define N 4 // 样本点数
#define M 7 // 参数个数
// 定义结构体存储样本点坐标
typedef struct {
double X, Y, Z; // 直角坐标系坐标
double x, y, z; // 大地坐标系坐标
} POINT;
// 定义样本点
POINT P[N] = {
{ 3272048.600, 549052.240, 4922028.220, 120.215, 31.023, 100.000 },
{ 3272040.790, 549054.470, 4922033.450, 120.215, 31.023, 100.000 },
{ 3272041.710, 549042.030, 4922036.690, 120.215, 31.023, 100.000 },
{ 3272047.800, 549045.560, 4922028.310, 120.215, 31.023, 100.000 }
};
// 定义函数
double getA(int i, int j);
double getB(int i);
void Gauss();
void calc();
// 定义全局变量
double A[M][M]; // 系数矩阵
double B[M]; // 常数矩阵
double X[M]; // 参数矩阵
int main() {
// 初始化参数矩阵
for (int i = 0; i < M; i++) {
X[i] = 0;
}
// 构造系数矩阵和常数矩阵
for (int i = 0; i < M; i++) {
for (int j = 0; j < M; j++) {
A[i][j] = 0;
for (int k = 0; k < N; k++) {
A[i][j] += getA(k, i) * getA(k, j);
}
}
B[i] = 0;
for (int k = 0; k < N; k++) {
B[i] += getB(k) * getA(k, i);
}
}
// 高斯消元求解参数矩阵
Gauss();
// 计算样本点坐标转换
calc();
// 输出结果
for (int i = 0; i < N; i++) {
printf("样本点%d:\n", i + 1);
printf("直角坐标系坐标:X=%lf, Y=%lf, Z=%lf\n", P[i].X, P[i].Y, P[i].Z);
printf("大地坐标系坐标:x=%lf, y=%lf, z=%lf\n\n", P[i].x, P[i].y, P[i].z);
}
return 0;
}
// 计算系数矩阵A的元素
double getA(int i, int j) {
switch (j) {
case 0:
return 1;
case 1:
return P[i].X;
case 2:
return P[i].Y;
case 3:
return P[i].Z;
case 4:
return P[i].Y * P[i].Z;
case 5:
return P[i].X * P[i].Z;
case 6:
return P[i].X * P[i].Y;
default:
return 0;
}
}
// 计算常数矩阵B的元素
double getB(int i) {
switch (i) {
case 0:
return P[i].x;
case 1:
return P[i].y;
case 2:
return P[i].z;
case 3:
return P[i].x * P[i].y;
case 4:
return P[i].x * P[i].z;
case 5:
return P[i].y * P[i].z;
case 6:
return P[i].x * P[i].x - P[i].y * P[i].y;
default:
return 0;
}
}
// 高斯消元求解参数矩阵
void Gauss() {
// 高斯消元
for (int i = 0; i < M - 1; i++) {
if (A[i][i] == 0) {
printf("系数矩阵出现0,无法继续计算!\n");
exit(0);
}
for (int j = i + 1; j < M; j++) {
double t = A[j][i] / A[i][i];
for (int k = i; k < M; k++) {
A[j][k] = A[j][k] - t * A[i][k];
}
B[j] = B[j] - t * B[i];
}
}
if (A[M - 1][M - 1] == 0) {
printf("系数矩阵出现0,无法继续计算!\n");
exit(0);
}
// 回带求解
X[M - 1] = B[M - 1] / A[M - 1][M - 1];
for (int i = M - 2; i >= 0; i--) {
double sum = 0;
for (int j = i + 1; j < M; j++) {
sum += A[i][j] * X[j];
}
X[i] = (B[i] - sum) / A[i][i];
}
}
// 计算样本点坐标转换
void calc() {
for (int i = 0; i < N; i++) {
double dx = X[0] + X[1] * P[i].X + X[2] * P[i].Y + X[3] * P[i].Z + X[4] * P[i].Y * P[i].Z + X[5] * P[i].X * P[i].Z + X[6] * P[i].X * P[i].Y;
double dy = X[0] + X[1] * P[i].X + X[2] * P[i].Y + X[3] * P[i].Z - X[4] * P[i].X * P[i].Z + X[5] * P[i].Y * P[i].Z - X[6] * P[i].X * P[i].Y;
double dz = X[0] + X[1] * P[i].X + X[2] * P[i].Y + X[3] * P[i].Z - X[4] * P[i].X * P[i].Y + X[5] * P[i].X * P[i].Z + X[6] * P[i].Y * P[i].Z;
P[i].x = dx;
P[i].y = dy;
P[i].z = dz;
}
}
```
其中,样本点的坐标和参数个数可以根据实际情况进行修改。