算法程序代码

多项式求值和矩阵乘法
1.用MATLAB实现多项式求值的四种运算，针对不同规模的输入值，绘制四种算法时间的比较图
num=[10 50 100 150 200 300 400 500 10000 20000 50000 100000];
x=input('please enter x:')
for m=1:12
a=rand(1,num(m)+1);
tic;
p1(m)=polyval(a,x);
t1(m)=toc;
tic;
p2(m)=0;
for i=1:num(m)+1
p2(m)=p2(m)+a(i)*x^(i-1);
t2(m)=toc;
end
tic;
p3(m)=a(1);
q=1;
for j=2:num(m)+1
q=q*x;
p3(m)=p3(m)+a(j)*q;
t3(m)=toc;
end
tic;
p4(m)=a(num(m)+1);
for k=1:num(m);
p4(m)=x*p4(m)+a(num(m)+1-k);
t4(m)=toc;
end
end
semilogx(num,t1,'b+',num,t2,'gx',num,t3,'r*',num,t4,'ko');
xlabel('num=10,50,100,150,200,300,400,500,10000,20000,50000,100000' ); ylabel('time');
title('The comparison chart of four different methods for polyval')
2.用MATLAB实现矩阵乘法的三种算法，并比较不同规模时的运行时间
num=[2^2,2^3,2^4,2^5,2^6,2^7,2^8,2^9,2^10,2^11]
for m=1:10
A=round(rand(num(m)));
B=round(rand(num(m)));
tic;
C1=A*B;
t1(m)=toc;
tic;
C2=zeros(num(m));
for i=1:num(m)
for k=1:num(m)
for j=1:num(m)
C2(i,j)=C2(i,j)+A(i,k)*B(k,j);
end
end
end
t2(m)=toc;
A11=A(1:num(m)/2,1:num(m)/2);
A12=A(1:num(m)/2,num(m)/2+1:num(m));
A21=A(num(m)/2+1:num(m),1:num(m)/2);
A22=A(num(m)/2+1:num(m),num(m)/2+1:num(m));
B11=B(1:num(m)/2,1:num(m)/2);
B12=B(1:num(m)/2,num(m)/2+1:num(m));
B21=B(num(m)/2+1:num(m),1:num(m)/2);
B22=B(num(m)/2+1:num(m),num(m)/2+1:num(m));
tic;
C3=zeros(num(m));
C11=A11*B11+A12*B21;
C12=A11*B12+A12*B22;
C21=A21*B11+A22*B21;
C22=A21*B12+A22*B22;
C3=[C11 C12;C21 C22];
t3(m)=toc;
tic;
C4=zeros(num(m));
M1=A11*(B12-B22);
M2=(A11+A12)*B22;
M3=(A21+A22)*B11;
M4=A22*(B21-B11);
M5=(A11+A22)*(B11+B22);
M6=(A12-A22)*(B21+B22);
M7=(A11-A21)*(B11+B12);
C11=M5+M4-M2+M6;
C12=M1+M2;
C21=M3+M4;
C22=M5+M1-M3-M7;
C4=[C11 C12;C21 C22];
t4(m)=toc;
end
plot(log(num)/log(2),t1,'b+',log(num)/log(2),t2,'gx',log(num)/log(2),t3,'r*',log(num)/log(2),t4,'ko'); xlabel('log(num)/log(2)=2^2,2^3,2^4,2^5,2^6,2^8,2^9,2^1^0,2^1^1' );
ylabel('time');
title('The comparison chart of four different methods for matrix multiplication')
三、遗传算法代码
%%%*****用遗传算法求函数最大值（双变量单输出）****%%%%%
clc;
clear;
x1min=-3.0; %输入变量1的变化范围
x1max=12.1;
x2min=4.1; %输入变量2的变化范围
x2max=5.8;
pb=0.001; %变异概率
N=300; %初始种群数目＝300
s1=ceil(log2(100000*(x1max-x1min))); %计算二进制串的长度
s2=ceil(log2(100000*(x2max-x2min))); %精确到小数点后面5位
s=s1+s2; %%种群的位数
zq=randi(N,s); %产生初始种群，for循环
for i=1:N
for j=1:s
r=rand(1);
if r>0.5
zq(i,j)=1;
else zq(i,j)=0;
end
end
end
%%*****用于二进制转化为十进制****
for i=1:s1
zhuanhuan(i,1) = 2^(s1-i);
end
for i=s1+1:s
zhuanhuan(i,1) = 2^(s-i);
end
for k=1:1000 %遗传算法的次数
%%********将二进制转换成十进制
for i=1:N
j1(i)=zq(i,1:s1)*zhuanhuan(1:s1);
j2(i)=zq(i,s1+1:s)*zhuanhuan(s1+1:s); end
%%****转化为目标函数值
x1=x1min+j1*(x1max-x1min)/(2^s1-1);
x2=x2min+j2*(x2max-x2min)/(2^s2-1);
%%****计算适应度值
f=21.5+x1.*sin(4*pi*x1)+x2.*sin(20*pi*x2); %%%******依次得到最大值，平均值
f_max(k)=max(f);
f_sum=sum(f);
f_avr(k)=sum(f)/N;
%%******复制********
g=f/f_sum; %计算选择概率
q(1)=g(1); %计算累积概率
for i=2:N
q(i)=q(i-1)+g(i);
end
for i=1:N %轮盘赌法
r=rand(1);
for j=1:N
if r<=q(j)
zq1(i,:)=zq(j,:);
break;
end
end
end
zq = zq1;
%%*****交叉操作*****
zq2 = zq;
zz = randperm(N);%产生交叉顺序
for i=1:N/2
v1 = randperm(s1-1);%产生交叉位
v2 = randperm(s2-1);
for j=v1(1)+1:s1 %交叉
t = zq2(zz(i*2-1),j);
zq2(zz(i*2-1),j) = zq2(zz(i*2),j);
zq2(zz(i*2),j) = t;
end
for j=v2(1)+1:s2
t = zq2(zz(i*2-1),j+s1);
zq2(zz(i*2-1),j+s1) = zq2(zz(i*2),j+s1);
zq2(zz(i*2),j+s1) = t;
end
end
zq = zq2;
%%*********变异操作****
for i=1:N
for j=1:s
if rand(1)<pb
if zq(i,j)==1
zq(i,j)=0;
else zq(i,j)=1;
end
end
end
end
end
figure()%绘图
subplot(1,1,1),plot(f_max),title('函数值最大值');%函数值就是适应度值%subplot(2,1,2),plot(f_avr),title('函数值平均值');。