常用数学函数矩阵版本的C++实现
头文件：
/* * Copyright (c) 2008-2011 Zhang Ming (M. Zhang), [email protected] * * This program is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 2 or any later version. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * 1. Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * This program is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for * more details. A copy of the GNU General Public License is available at: * http://www.fsf.org/licensing/licenses */ /***************************************************************************** * matrixmath.h * * This file provides the basic math functions such as: * cos sin tan acos asin atan * abs exp log log10 sqrt pow * * When debugging, use #define BOUNDS_CHECK above your "#include matrix.h" * line. When done debugging, comment out #define BOUNDS_CHECK for better * performance. * * Zhang Ming, 2010-01 (revised 2010-08), Xi'an Jiaotong University. *****************************************************************************/ #ifndef MATRIXMATH_H #define MATRIXMATH_H #include <matrix.h> namespace splab { template<typename Type> Matrix<Type> abs( const Matrix<Type>& ); template<typename Type> Matrix<Type> cos( const Matrix<Type>& ); template<typename Type> Matrix<Type> sin( const Matrix<Type>& ); template<typename Type> Matrix<Type> tan( const Matrix<Type>& ); template<typename Type> Matrix<Type> acos( const Matrix<Type>& ); template<typename Type> Matrix<Type> asin( const Matrix<Type>& ); template<typename Type> Matrix<Type> atan( const Matrix<Type>& ); template<typename Type> Matrix<Type> exp( const Matrix<Type>& ); template<typename Type> Matrix<Type> log( const Matrix<Type>& ); template<typename Type> Matrix<Type> log10( const Matrix<Type>& ); template<typename Type> Matrix<Type> sqrt( const Matrix<Type>& ); template<typename Type> Matrix<Type> pow( const Matrix<Type>&, const Matrix<Type>& ); template<typename Type> Matrix<Type> pow( const Matrix<Type>&, const Type& ); template<typename Type> Matrix<Type> pow( const Type&, const Matrix<Type>& ); #include <matrixmath-impl.h> } // namespace splab #endif // MATRIXMATH_H
实现文件：
/* * Copyright (c) 2008-2011 Zhang Ming (M. Zhang), [email protected] * * This program is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 2 or any later version. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * 1. Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * This program is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for * more details. A copy of the GNU General Public License is available at: * http://www.fsf.org/licensing/licenses */ /***************************************************************************** * vector-impl.h * * Implementation for Matrix math functions. * * Zhang Ming, 2010-08, Xi'an Jiaotong University. *****************************************************************************/ template <typename Type> Matrix<Type> abs( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = abs( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> cos( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = cos( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> sin( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = sin( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> tan( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = tan( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> acos( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = acos( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> asin( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = asin( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> atan( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = atan( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> exp( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = exp( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> log( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = log( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> log10( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = log10( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> sqrt( const Matrix<Type> &A ) { int m = A.rows(), n = A.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = sqrt( A[i][j] ); return tmp; } template <typename Type> Matrix<Type> pow( const Matrix<Type> &B, const Matrix<Type> &E ) { int m = B.rows(), n = B.cols(); assert( m == E.rows() ); assert( n == E.cols() ); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = pow( B[i][j], E[i][j] ); return tmp; } template <typename Type> Matrix<Type> pow( const Matrix<Type> &B, const Type &e ) { int m = B.rows(), n = B.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = pow( B[i][j], e ); return tmp; } template <typename Type> Matrix<Type> pow( const Type &b, const Matrix<Type> &E ) { int m = E.rows(), n = E.cols(); Matrix<Type> tmp( m, n ); for( int i=0; i<m; ++i ) for( int j=0; j<n; ++j ) tmp[i][j] = pow( b, E[i][j] ); return tmp; }
测试代码：
/*****************************************************************************
* matrixmath_test.cpp
*
* Math functions of matrix testing.
*
* Zhang Ming, 2010-08, Xi'an Jiaotong University.
*****************************************************************************/
#define BOUNDS_CHECK
#include <iostream>
#include <iomanip>
#include <matrixmath.h>
using namespace std;
using namespace splab;
typedef double Type;
int main()
{
int N = 9;
Type a = 0, b = 2*PI;
Vector<Type> array = linspace( a, b, N );
Matrix<Type> x( 3, 3, array );
cout << setiosflags(ios::fixed) << setprecision(4);
cout << x << endl;
cout << "sin of x : " << sin(x) << endl;
cout << "cos of x : "<< cos(x) << endl;
cout << "tan of x : " << tan(x) << endl;
cout << "asin of x : "<< asin(x) << endl;
cout << "acos of x : " << acos(x) << endl;
cout << "atan of x : " << atan(x) << endl;
cout << "exp of x : "<< exp(x) << endl;
cout << "log of x : " << log(x) << endl;
cout << "log10 of x : " << log10(x) << endl;
a = 2.0;
cout << "sqrt of x : "<< sqrt(x) << endl;
cout << "pow of x : " << pow(x,x) << endl;
cout << "pow of x : " << pow(x,a) << endl;
cout << "pow of x : " << pow(a,x) << endl;
return 0;
}
运行结果：
size: 3 by 3 0.0000 0.7854 1.5708 2.3562 3.1416 3.9270 4.7124 5.4978 6.2832 sin of x : size: 3 by 3 0.0000 0.7071 1.0000 0.7071 0.0000 -0.7071 -1.0000 -0.7071 -0.0000 cos of x : size: 3 by 3 1.0000 0.7071 0.0000 -0.7071 -1.0000 -0.7071 -0.0000 0.7071 1.0000 tan of x : size: 3 by 3 0.0000 1.0000 16331778728383844.0000 -1.0000 -0.0000 1.0000 5443926242794615.0000 -1.0000 -0.0000 asin of x : size: 3 by 3 0.0000 0.9033 nan nan nan nan nan nan nan acos of x : size: 3 by 3 1.5708 0.6675 nan nan nan nan nan nan nan atan of x : size: 3 by 3 0.0000 0.6658 1.0039 1.1694 1.2626 1.3214 1.3617 1.3909 1.4130 exp of x : size: 3 by 3 1.0000 2.1933 4.8105 10.5507 23.1407 50.7540 111.3178 244.1511 535.4917 log of x : size: 3 by 3 -inf -0.2416 0.4516 0.8570 1.1447 1.3679 1.5502 1.7043 1.8379 log10 of x : size: 3 by 3 -inf -0.1049 0.1961 0.3722 0.4971 0.5941 0.6732 0.7402 0.7982 sqrt of x : size: 3 by 3 0.0000 0.8862 1.2533 1.5350 1.7725 1.9817 2.1708 2.3447 2.5066 pow of x : size: 3 by 3 1.0000 0.8272 2.0327 7.5336 36.4622 215.2126 1487.9012 11732.6371 103540.9204 pow of x : size: 3 by 3 0.0000 0.6169 2.4674 5.5517 9.8696 15.4213 22.2066 30.2257 39.4784 pow of x : size: 3 by 3 1.0000 1.7236 2.9707 5.1202 8.8250 15.2104 26.2162 45.1855 77.8802 Process returned 0 (0x0) execution time : 0.109 s Press any key to continue.