1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
|
/******************************************************************
* Core Library Version 1.7, August 2004
* Copyright (c) 1995-2002 Exact Computation Project
*
* File: LinearAlgebra.h
* Synopsis:
* Linear Algebra Extension of Core Library introducing
* class Vector
* class Matrix
*
* Written by
* Shubin Zhao (shubinz@cs.nyu.edu) (2001)
*
* WWW URL: http://cs.nyu.edu/exact/
* Email: exact@cs.nyu.edu
*
* $Id: linearAlgebra.h 23263 2004-11-14 12:00:19Z efi $
*****************************************************************/
#ifndef CORE_LINEAR_ALGEBRA_H
#define CORE_LINEAR_ALGEBRA_H
#ifndef CORE_LEVEL
# define CORE_LEVEL 3
#endif
#include <cstdarg>
#include <CORE/CORE.h>
class Vector;
class Matrix;
////////////////////////////////////////////////////////////////////////
// Class Vector
// Generic vectors
// Operations implemented: addition, subtraction, dot product
////////////////////////////////////////////////////////////////////////
class Vector {
private:
int dim;
double* _rep;
public:
class RangeException { };
class ArithmeticException { };
explicit Vector(int);
Vector();
Vector(double, double);
Vector(double, double, double);
Vector(const Vector&);
Vector(int, double *);
~Vector();
const Vector& operator=(const Vector&);
bool operator==(const Vector&);
bool operator!=(const Vector&);
const Vector& operator+=(const Vector&);
const Vector& operator-=(const Vector&);
const Vector& operator*=(double);
const double& operator[](int) const;
double& operator[](int);
double norm() const;
double maxnorm() const;
double infnorm() const;
double dimension() const {return dim;}
bool isZero() const;
Vector cross(const Vector &v) const;
static Vector crossProduct(int, ...);
friend Vector operator+(const Vector&, const Vector&);
friend Vector operator-(const Vector&, const Vector&);
friend Vector operator-(const Vector&);
friend Vector operator*(const Vector&, double);
friend Vector operator*(double, const Vector&);
friend Vector operator*(const Matrix&, const Vector&);
friend Vector operator*(const Vector&, const Matrix&);
friend double dotProduct(const Vector&, const Vector&);
friend std::istream& operator>>(std::istream&, Vector&);
friend std::ostream& operator<<(std::ostream&, const Vector&);
};
////////////////////////////////////////////////////////////////////////
// Class Matrix
// Generic matrices
// Operations implemented: addition, subtraction, multiplication
////////////////////////////////////////////////////////////////////////
class Matrix {
private:
int dim1, dim2;
double* _rep;
public:
class RangeException { };
class ArithmeticException { };
explicit Matrix(int);
Matrix(int, int);
Matrix(int, int, double *);
Matrix(double, double,
double, double);
Matrix(double, double, double,
double, double, double,
double, double, double);
Matrix(const Matrix&);
~Matrix();
Matrix& operator=(const Matrix&);
bool operator==(const Matrix&);
bool operator!=(const Matrix&);
const Matrix& operator+=(const Matrix&);
const Matrix& operator-=(const Matrix&);
const Matrix& operator*=(double);
const double& operator()(int, int) const;
double& operator()(int, int);
// added by chen li
// const Vector& row(int i) const;
// const Vector& col(int i) const;
Matrix matrixAlgebraRemainder(int, int) const;
double valueAlgebraRemainder(int, int) const;
const Matrix& transpose();
double determinant() const;
int dimension_1() const { return dim1; }
int dimension_2() const { return dim2; }
friend Matrix operator+(const Matrix&, const Matrix&);
friend Matrix operator-(const Matrix&, const Matrix&);
friend Matrix operator*(const Matrix&, double);
friend Matrix operator*(double, const Matrix&);
friend Vector operator*(const Vector&, const Matrix&);
friend Vector operator*(const Matrix&, const Vector&);
friend Matrix operator*(const Matrix&, const Matrix&);
friend Matrix transpose(const Matrix&);
friend double det(const double a, const double b,
const double c, const double d);
friend double det(const Vector u, const Vector & v); // u,v are 2d vectors
friend std::istream& operator>>(std::istream&, Matrix&);
friend std::ostream& operator<<(std::ostream&, const Matrix&);
}; //Matrix
#endif
|
