matrix1.txt

几个算法程序

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发信人: sweeping (simon), 信区: Algorithm WWW-POST 
标  题: 一些矩阵运算源码1 
发信站: 武汉白云黄鹤站 (Thu Nov  8 17:38:01 2001) , 转信 
 
 
/////////////////////////////// 
// CMatrix.h 
 
// Jacob eigenvalue and eigenvector 
// QR eigenvalue 
#define MATRIXEPSILON 0.000001 
// QR eigenvalue 
// Seidel iterations 
#define MATRIXITERATION 60 
// 
class CSymmetricalMatrix; 
 
class CMatrix 
{ 
protected: // for subclass to access 
int m_rows; // rows 
int m_cols; // columns 
double *m_a; // elements 
 
public: 
CMatrix() { m_rows=0;  m_cols=0;  m_a=NULL; } 
CMatrix(int rows, int cols); 
~CMatrix(); 
BOOL Resize(int rows, int cols); 
int GetRows(); 
int GetColumns(); 
void SetElement(int row, int col, double e); 
double GetElement(int row, int col); 
void SetAllElements(double e);  
double *GetBuffer(); // return m_a: begin address 
 
// return a copy of a matrix 
CMatrix *Copy(); 
 
// add pB to current, and return the result matrix 
CMatrix *AddMatrix(CMatrix *pB); 
// subtract pB from current, and return the result matrix 
CMatrix *SubMatrix(CMatrix *pB); 
// multiply pB with current, and return the result matrix 
CMatrix *Multiply(CMatrix *pB); 
// return the transpose of current matrix 
CMatrix *Transpose(); 
// return At*A, A: current matrix 
CSymmetricalMatrix *LeftTransposeMultiply(); 
// return A*At, A: current matrix 
CSymmetricalMatrix *RightTransposeMultiply(); 
 
BOOL WriteToFile(char *filename); 
BOOL ReadFromFile(char *filename); 
}; 
 
class CSquareMatrix : public CMatrix 
{ 
 
public: 
CSquareMatrix() : CMatrix() {}; 
CSquareMatrix(int rows) : CMatrix(rows, rows) {}; 
~CSquareMatrix() {}; 
BOOL Resize(int rows) { return CMatrix::Resize(rows, rows); }; 
 
void SetToIdentity();  
 
double Determinantal(); 
 
// calculate the inverse matrix of a nxn matrix 
// the original matrix will be destroyed 
// and become the inverse matrix 
// if the inverse does not exist, return FALSE 
BOOL Inverse(); 
 
// calculate the LU decomposition of matrix 
// the results are put into pL and pU 
// pL and pU are allocated outside of this method 
// the original matrix will be destroyed 
// if can not decompose, return FALSE 
BOOL LUDecompose(CSquareMatrix *pL, CSquareMatrix *pU); 
 
// calculate the QR decomposition of matrix 
// the results are put into pQ and original matrix 
// pQ is allocated outside of this method 
// the original matrix will be destroyed 
// if can not decompose, return FALSE 
BOOL QRDecompose(CSquareMatrix *pQ); 
 
// transform matrix into H matrix 
// the original matrix will be destroyed 
// if can not transform, return FALSE 
BOOL Hessenberg(); 
 
// calculate the eigenvalues of nxn real matrix  
// the result eigenvalues are in the returned nx2 matrix 
// the first column is the real part of eigenvalues 
// the second column is the imaginary part of eigenvalues 
// for a eigenvalue lambda,  
// solve the equation (A-lambda*I)X=0 to get the corresponding eigenvector 
// original matrix is destroyed! 
// if can not get the eigenvalues, return FALSE 
CMatrix *QREigenvalue(); 
}; 
 
class CSymmetricalMatrix : public CSquareMatrix 
{ 
// calculate the eigenvalue and eigenvictor of  
// nnxnn symmetric real matrix aa 
// the result eigenvictors are ss, 
// the result eigenvalues are in the diagonal of aa 
void jacobian(double *aa, double *ss, int nn); 
 
public: 
CSymmetricalMatrix() : CSquareMatrix() {}; 
CSymmetricalMatrix(int rows) : CSquareMatrix(rows) {}; 
~CSymmetricalMatrix() {}; 
 
// calculate the eigenvalue and eigenvictor of  
// nxn symmetric real matrix  
// the result eigenvectors are in returned matrix, 
// the result eigenvalues are in the diagonal of original matrix 
// original matrix is destroyed! 
// if original matrix is not symmetrical, 
// we will use the upper-right to fill out down-left to make it symmetrical 
CSymmetricalMatrix *Jacob(); 
 
}; 
 
class CEquationMatrix : public CMatrix 
{ 
public: 
CEquationMatrix() : CMatrix() {}; 
CEquationMatrix(int rows) : CMatrix(rows, rows+1) {}; 
~CEquationMatrix() {}; 
BOOL Resize(int rows) { return CMatrix::Resize(rows, rows+1); }; 
 
// solve nx(n+1) equations using Gaussian method 
// the matrix ia n rows and n+1 columns 
// the first n columns are matrix A 
// the last column is the constant vector B 
// after solving, matrix will be destroied, 
// the solution will be put into the last column 
// if can not solve the equations, FALSE will be returned 
BOOL Gauss(); 
 
// solve nx(n+1) equations using Jordan's method 
// the matrix ia n rows and n+1 columns 
// the first n columns are matrix A 
// the last column is the constant vector B 
// after solving, matrix will be destroied, 
// the solution will be put into the last column 
// if can not solve the equations, FALSE will be returned 
BOOL Jordan(); 
 
// solve nx(n+1) equations using Seidel's method 
// the matrix ia n rows and n+1 columns 
// the first n columns are matrix A 
// the last column is the constant vector B 
// after solving, matrix will be destroied, 
// the solution will be put into the last column 
// if can not solve the equations, FALSE will be returned 
BOOL Seidel(); 
 
}; 
 

 
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