多点最小二乘法平面方程拟合计算.doc

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 Determinant(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 12;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 = 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 += *(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 *)malloc(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* 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;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+) *(