多点最小二乘法平面方程拟合计算.docx

1、多点最小二乘法平面方程拟合计算多点最小二乘法平面方程拟合计算平面方程拟合计算平面方程的一般表达式为：, ()记：则：平面方程拟合:对于一系列的n个点：要用点拟合计算上述平面方程，则使：最小。 要使得S最小，应满足： 即： 有，或，解上述线形方程组，得：即：下面程序实际求得的是以下的参数：即:AX+BY+CZ+1=0其程序代码如下：#include stdafx.h#include #include #include #define MAX 10void Inverse(double *matrix1,double *matrix2,int n,double d);double Determin

2、ant(double* matrix,int n);double AlCo(double* matrix,int jie,int row,int column);double Cofactor(double* matrix,int jie,int row,int column);int _tmain(int argc, _TCHAR* argv) double array123,Y3; double A,B,C; A = B = C = 0.0; ZeroMemory(array,sizeof(array); ZeroMemory(Y,sizeof(Y); for (int i = 0;i 1

3、2;i+) for (int j = 0;j 3;j+) arrayij = (double)rand(); for (int i = 0; i 12;i+) arrayi0 = 1.0; /设计了12个最简单的数据点，x = 1平面上的点， double *Matrix3,*IMatrix3; for (int i = 0;i 3;i+) Matrixi = new double3; IMatrixi = new double3; for (int i = 0;i 3;i+) for (int j = 0;j 3;j+) *(Matrixi + j) = 0.0; for (int j =

4、0;j 3;j+) for (int i = 0;i 12;i+) *(Matrix0 + j) += arrayi0*arrayij; *(Matrix1 + j) += arrayi1*arrayij; *(Matrix2 + j) += arrayi2*arrayij; Yj -= arrayij; double d = Determinant(Matrix,3); if (abs(d) 0.0001) printf(n矩阵奇异); getchar(); return -1; Inverse(Matrix,IMatrix,3,d); for (int i = 0;i 3;i+) A +=

5、 *(IMatrix0 + i)*Yi; B += *(IMatrix1 + i)*Yi; C += *(IMatrix2 + i)*Yi; printf(n A = %5.3f,B = %5.3f,C= %5.3f,A,B,C); for (int i = 0;i 3;i+) delete Matrixi; delete IMatrixi; getchar(); return 0;void Inverse(double *matrix1,double *matrix2,int n,double d) int i,j; for(i=0;in;i+) matrix2i=(double *)mal

6、loc(n*sizeof(double); for(i=0;in;i+) for(j=0;jn;j+) *(matrix2j+i)=(AlCo(matrix1,n,i,j)/d); double Determinant(double* matrix,int n) double result=0,temp; int i; if(n=1) result=(*matrix0); else for(i=0;in;i+) temp=AlCo(matrix,n,n-1,i); result+=(*(matrixn-1+i)*temp; return result; double AlCo(double*

7、matrix,int jie,int row,int column) double result; if(row+column)%2 = 0) result = Cofactor(matrix,jie,row,column); else result=(-1)*Cofactor(matrix,jie,row,column); return result; double Cofactor(double* matrix,int jie,int row,int column) double result; int i,j; double* smallmatrMAX-1; for(i=0;ijie-1

8、;i+) smallmatri= new doublejie - 1; for(i=0;irow;i+) for(j=0;jcolumn;j+) *(smallmatri+j)=*(matrixi+j); for(i=row;ijie-1;i+) for(j=0;jcolumn;j+) *(smallmatri+j)=*(matrixi+1+j); for(i=0;irow;i+) for(j=column;jjie-1;j+) *(smallmatri+j)=*(matrixi+j+1); for(i=row;ijie-1;i+) for(j=column;jjie-1;j+) *(smallmatri+j)=*(matrixi+1+j+1); result = Determinant(smallmatr,jie-1); for(i=0;ijie-1;i+) delete smallmatri; return result;