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version 0.7.5 release
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+214
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10 files changed

+214
-5
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‎lib/mathalgorithm.h‎

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@@ -1,4 +1,4 @@
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// version 0.7.5 pre-release
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// version 0.7.5 release
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#ifndef MATHALGORITHM_H
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#define MATHALGORITHM_H
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#include "numbertheory.h"

‎lib/numerical.h‎

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -658,17 +658,17 @@ template <class DD> DD D(std::function<DD(DD)> f,DD x,string str)
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{
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if(str=="center")
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{
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const DD h = 1e-7;
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const DD h = 1e-8;
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return (f(x + h) - f(x - h)) / (2 * h);
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}
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if(str=="forward")
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{
666-
const DD h = 1e-7;
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const DD h = 1e-8;
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return (f(x + h) - f(x))/h;
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}
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if(str=="backward")
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{
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const DD h = 1e-7;
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const DD h = 1e-8;
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return (f(x) - f(x-h))/h;
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}
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cerr << "错误：没有定义该方法。" << '\n';
@@ -699,7 +699,7 @@ template<class DD> DD D(std::function<DD(Matrix<DD>)>f,int n,const Matrix<DD> &x
699699
cerr << "错误：求偏导的分量越界" << '\n';
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return f(x);
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}
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const DD h=1e-7;
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const DD h=1e-8;
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auto y=x;
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y(n,0)=Get(x,n,0)+h;
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return (f(y) - f(x)) / h;

‎src/hpc and nbt example.cpp‎

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#include <iostream>
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#include <ctime>
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#include <chrono>
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#include "../lib/mathalgorithm.h"
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using namespace mal;
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/* minimal inclusion:
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#include "../lib/highprecision.h"
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#include "../lib/numbertheory.h"
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using namespace hpc;
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using namespace nbt; */
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int main()
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{
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auto start = std::chrono::system_clock::now();
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BigInt a("23948576235");
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BigInt b("823761298");
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BigInt c("2");
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BigInt m("986732000000000000000123761");
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BigInt n("5000000009");
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BigInt x = Fibonacci(1000000);
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BigInt y = Fibonacci(100000);
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std::cout << "a * b = " << a*b << std::endl;
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std::cout << "c ^ 100 = " << (c^100) << std::endl;
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std::cout << "Prime test for m: " << PrimeQ(m) << std::endl;
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std::cout << "Find a factor of n: " << FindAFactor(n) << std::endl;
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std::cout << "integer length of x is " << IntegerLength(x) << std::endl;
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std::cout << "x mod y is " << x % y << std::endl;
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std::cout << "log2 of a is " << log2(a) << std::endl;
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auto end = std::chrono::system_clock::now();
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std::cout << "total time=" << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count()
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<< "ms"<<std::endl;
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system("pause");
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return 0;
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}
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‎src/lag example.cpp‎

Lines changed: 16 additions & 0 deletions
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#include <iostream>
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#include "../lib/mathalgorithm.h"
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using namespace mal;
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/* minimal inclusion:
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#include "../lib/linearalgebra.h"
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using namespace lag; */
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int main()
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{
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Matrix<double> A({{1,1,-1},{1,2,-2},{-2,1,1}},3,3);
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Matrix<double> b({{1}, {0}, {1}}, 3, 1);
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std::cout << LinearSolve(A, b) <<std::endl;
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system("pause");
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return 0;
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}

‎src/nmr example.cpp‎

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#include <iostream>
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#include "../lib/mathalgorithm.h"
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using namespace mal;
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/* minimal inclusion:
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#include "../lib/numerical.h"
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using namespace nmr; */
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int main()
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{
11+
Matrix<double> base(
12+
{{0.4,-0.916},{0.5,-0.693},{0.8,-0.223},{0.9,-0.105}});
13+
Matrix<double> data({{0.6},{0.7}},2,1);
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Matrix<double> result=Interpolation(base,data);
15+
std::cout<<result<<std::endl;
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17+
auto p = [](double x) { return 4.0 / (1 + x * x); };
18+
auto q = Integrate<double>(p, 0, 1);
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N(q, 10);
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21+
auto f=[](double x){ return x*x*exp(x); };
22+
auto g=D<double>(2,f);
23+
std::cout<<g(0)<<std::endl;
24+
25+
system("pause");
26+
return 0;
27+
}

‎src/ode example.cpp‎

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#include <iostream>
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#include "../lib/mathalgorithm.h"
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using namespace mal;
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/* minimal inclusion:
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#include "../lib/ode.h"
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using namespace ode; */
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9+
int main()
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{
11+
function<double(double, double)> f = [](double x, double y) { return y; };
12+
std::cout << DSolve(f, {0., 1.}, 1.) << std::endl;
13+
system("pause");
14+
return 0;
15+
}

‎src/opt example.cpp‎

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#include <iostream>
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#include "../lib/mathalgorithm.h"
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using namespace mal;
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/* minimal inclusion:
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#include "../lib/optimization.h"
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using namespace opt; */
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9+
int main()
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{
11+
double epsilon = 1e-6;
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std::cout << "约束优化问题：" << std::endl;
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function<double(double,double)> f_pre = [](double x, double y)
15+
{
16+
return x + sqrt(3.) * y;
17+
};
18+
auto f = MatrizeInputs(f_pre);
19+
function<Matrix<double>(double,double)> c_pre = [](double x, double y)
20+
{
21+
return Matrix<double>(x*x+y*y-1.,1,1);
22+
};
23+
auto c = MatrizeInputs(c_pre);
24+
Matrix<double> initial(1.,2,1);
25+
std::cout << "AugmentedLagrangian"<<std::endl<<
26+
Transpose(AugmentedLagrangian<double>(f, c, initial, epsilon, BFGS<double>))
27+
<<std::endl;
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29+
std::cout << "无约束优化问题：" << std::endl;
30+
function<double(double,double)> g_pre = [](double x,double y)
31+
{
32+
return x * x + 10. * y * y;
33+
};
34+
auto g = MatrizeInputs(g_pre);
35+
Matrix<double> initial2(vector<vector<double>>({{-10.}, {-1.}}));
36+
double step = 0.085;
37+
std::cout << "GradientDescentFixedStepsize"<<std::endl<<
38+
Transpose(GradientDescentFixedStepsize(g, initial2, epsilon, step)) << std::endl;
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std::cout << "GradientDescentWolfe"<<std::endl<<
40+
Transpose(GradientDescentWolfe(g, initial2, epsilon)) << std::endl;
41+
std::cout << "GradientDescentGoldstein"<<std::endl<<
42+
Transpose(GradientDescentGoldstein(g, initial2, epsilon)) << std::endl;
43+
std::cout << "BarzilarBorwein"<<std::endl<<
44+
Transpose(BarzilarBorwein(g, initial2, epsilon)) << std::endl;
45+
std::cout << "FletcherReeves" << std::endl<<
46+
Transpose(FletcherReeves(g, initial2, epsilon)) << std::endl;
47+
std::cout << "PolakRibiere" << std::endl<<
48+
Transpose(PolakRibiere(g, initial2, epsilon)) << std::endl;
49+
std::cout << "SR1"<<std::endl<<
50+
Transpose(SR1(g, initial2, epsilon)) << std::endl;
51+
std::cout << "DFP"<<std::endl<<
52+
Transpose(DFP(g, initial2, epsilon)) << std::endl;
53+
std::cout << "BFGS"<<std::endl<<
54+
Transpose(BFGS(g, initial2, epsilon)) << std::endl;
55+
56+
Matrix<double> initial3(vector<vector<double>>({{-0.1}, {-0.1}}));
57+
std::cout << "ClassicNewton"<<std::endl<<
58+
Transpose(ClassicNewton(g, initial3, epsilon)) << std::endl;
59+
std::cout << "ModifiedNewtonGoldstein"<<std::endl<<
60+
Transpose(ModifiedNewtonGoldstein(g, initial2, epsilon)) << std::endl;
61+
system("pause");
62+
return 0;
63+
}
64+

‎src/plt example.cpp‎

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1+
#include <iostream>
2+
#include "../lib/mathalgorithm.h"
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using namespace mal;
4+
5+
/* minimal inclusion:
6+
#include "../lib/plot.h"
7+
using namespace plt; */
8+
9+
int main()
10+
{
11+
function<double(double)> f = [](double x)
12+
{ return sin(x); };
13+
Plot<double>(f, vector<double>({0., 2*Pi<double>}));
14+
system("pause");
15+
return 0;
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}
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‎src/ply example.cpp‎

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#include <iostream>
2+
#include "../lib/mathalgorithm.h"
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using namespace mal;
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5+
/* minimal inclusion:
6+
#include "../lib/polynomial.h"
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using namespace ply; */
8+
9+
int main()
10+
{
11+
Polynomial<int> f({1,1,1},2);
12+
Polynomial<int> g({5,-3,0,1},3);
13+
Polynomial<int> h=f*g;
14+
std::cout<<"h(x)="<<h<<std::endl;
15+
std::cout<<"h(5)="<<h(5)<<std::endl;
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system("pause");
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return 0;
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}

‎src/prb example.cpp‎

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1+
#include <iostream>
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#include "../lib/mathalgorithm.h"
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using namespace mal;
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/* minimal inclusion:
6+
#include "../lib/probability.h"
7+
using namespace prb; */
8+
9+
int main()
10+
{
11+
std::cout << CDF(NormalDistribution(1, 1), 1) << std::endl;
12+
system("pause");
13+
return 0;
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}

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