matlab矩陣應用
clear
%建立矩陣的兩種方式
A1 = [1 2 3 4 5; 6 7 8 9 10];
A2 = [
1 2 3 4 5
6 7 8 9 10
];
%一種是換行用引號，一種是自然寫法
clear
A = [5 4 3 2 1; 6 7 8 9 10;1 2 3 4 5;24 24 24 24 24;25 25 25 25 25];
B = [5 4 3 2 1; 6 7 8 9 10;1 2 3 4 5;24 24 24 24 24;25 25 25 25 25];
A_sqare = [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];
k = 5;
X1 = A'; %A取轉置
X2 = A + B; %求A和B矩陣的和
X3 = A - B; %求A和B矩陣的差
X4 = k * A; %數K乘以A矩陣
X5 = det(A_sqare); %求矩陣A的行列式（注A_sqare必須爲方陣）
X6 = rank(A); %求矩陣A的秩
X7 = inv(A_sqare); %求矩陣A的逆（注A_sqare必須爲方陣）
X8 = B / A; X8 = B * inv(A_sqare); %A右除B = B右乘A的逆
X9 = B / A; X9 = inv(A_sqare) * B; %A左除B = B左乘A的逆
A.*B % .* 是A的每個元素和B相乘，非矩陣相乘，同理 ./ .^
A(2,:) % 取A矩陣的第2行 然後 A(2,:) = [5 5 5 5 5]就對該行進行賦值
A(:,2) % 取A矩陣的第2列 然後 A(:,2) = [5 5 5 5 5]就對該列進行賦值
A(2:1:4,3:1:4) %取A矩陣中的一塊，其語法爲A(起始行:步長:終止行,起始列:步長:終止列)
zeros(5) %生成n階零矩陣
eye(5) %生成n階單位矩陣
eig(A) %矩陣A的特徵值
[X,D] = eig(A) %矩陣A的 特徵向量矩陣X 特徵值組成的對角陣
A([1,2],:) %1,2行互換
A(:,[2,3]) %1,2列互換
A(2,:) = 5 * A(2,:) %第2行乘以5，列上的操作以此類推
K = [A B;B A] %由幾個小矩陣合成一個大矩陣
orth(A) %非奇異矩陣正交化
a1 = A(2,:);
a2 = A(3,:);
a1*a2' %兩個向量內積
rref(A) %A的極大無關向量組
matlab畫圖應用
%while循環
clear
sum = 0;k = 1;
while k<101
sum = sum+k;
k = k + 1;
end
sum
%for循環
clear
sum = 0;n = 1;
for n = 1:100
sum = n + sum;
end
sum
%plot繪圖
x = -10:0.1:10;
y = 3*x.^4+x.^2-1;
figure %開啓新繪圖頁面
plot(x,y)
%fplot繪圖
clear
figure
fplot(@f1, [-10 10]) %調用f1.m裏面的那個function
%ezplot繪圖
clear
syms x
figure
y = 3*x^4 + x^2 - 1;
ezplot(y)
%螺旋線繪圖 題目:x = cost , y = sint , z = t t屬於[0,6pi]
clear
t = 0:0.1:6*pi;
x = cos(t);
y = sin(t);
z = t;
figure
plot3(x,y,z)
%空間曲線繪圖 題目: z = sqrt(1 - x^2 - y^2) , (x - 1/2)^2 + y^2 = (1/2)^2
clear
t = 0:0.1:6;
x = 0.5*cos(t)+0.5;
y = 0.5*sin(t);
z = sqrt(1-x.^2-y.^2);
figure
plot3(x,y,z)
%二次曲面繪圖 題目: x^2 + y^2 = z
clear
s = -10:1:10;
t = -10:1:10;
[x,y] = meshgrid(s,t);
z = x.^2 + y.^2;
figure
mesh(x,y,z);
%旋轉曲面繪圖 題目: y = 1/x 圍繞y軸旋轉
clear
s = -10:0.1:10;
t = -10:0.1:10;
[x,y] = meshgrid(s,t);
r = 1./x;
[x,y,z] = cylinder(r);
figure
mesh(x,y,z)
%輸入數
clear
K = input('請輸入數');
matlab解方程應用
%常微分方程求解 詳細參考PPT（7）
clear
y1 = dsolve('Dy=8-3*y','y(0)=2')
y2 = dsolve('D2y=2*x*Dy/(1+x^2)','y(0)=1,Dy(0)=3')
%微分方程組求解
clear
[X,Y] = dsolve('2*Dx+4*x+Dy-y=exp(t),Dx+3*x+y=0','x(0)=1.5,y(0)=0')
%線性方程組全部解
clear
format rat
A=[1 1 3 -1;0 1 -1 1;1 1 2 2;1 -1 1 -1];
B=[-2;1;4;0];
X = A/B
%方程求解
clear
X = solve('x-exp(-x)=0','x')
%區間裏方程求解
%x=0:0.1:10;
%X = solve('5*x^2*sin(x)-exp(-x)','x')
%求微分方程的特解並且做出函數曲線
y0 = [1,0];
[t,x] = ode45(@vdp,[0,30],y0); %從vdp.m這個文件裏面讀函數
y = x(:,1);
dy=x(:,2);
figure
plot(t,y,t,dy);
%解微分方程
fun=inline('-2*y+2*x*x+2*x');
[x,y]=ode23(fun,[0,0.5],1)
matlab微積分應用
%函數求導
clear
syms x y; %將x y設爲變量
f = cos(x)^3-cos(3*x); %需要求導的式子
dy = diff(f,x); %用diff 函數進行求導
%函數求極限
clear
syms x
f = x*log(1+x)/sin(x*x)
limit(f,'x',0,'left') %語法爲 limit(求極限的式子,求極限的變量,需要逼近的數字,從左還是從右逼近)
%函數求積分
clear
syms x
f = sym('x*exp(x)/(1+x)^2');
int(f) %語法爲 int(求極限的式子,下限,上限) 如果不加上限下限，就是函數式。
int(f,0,1)
pretty(f) %以自然函數形式呈現
%例-求z = x^2 + y^2 , z = 1 , z =2 圍成的曲面
clear
syms x y z
z = x^2+y^2;
f = z;
I = int( int( f, y, sqrt(1-x^2), sqrt(2-x^2) ), x, 1, sqrt(2) )
%級數求和
clear
syms n
f = (n+1)/n*2^n;
j = symsum(f, n, 1, inf) %級數求和，下限爲1,上限爲無窮大
%泰勒展開
clear
syms x
f = cos(x)
taylor(f, 10, x, pi/3) %語法爲taylor(待展開函數,取前幾項, 變量名, 展開中心)
%求傅里葉係數
clear
syms x n
f = x^3+x^2;
n = 5;
a0 = int(f,x,-pi,pi)/pi
a1 = int(f*cos(1*x),x,-pi,pi)/pi
a2 = int(f*cos(2*x),x,-pi,pi)/pi
a3 = int(f*cos(3*x),x,-pi,pi)/pi
a4 = int(f*cos(4*x),x,-pi,pi)/pi
a5 = int(f*cos(5*x),x,-pi,pi)/pi
b1 = int(f*sin(1*x),x,-pi,pi)/pi
b2 = int(f*sin(2*x),x,-pi,pi)/pi
b3 = int(f*sin(3*x),x,-pi,pi)/pi
b4 = int(f*sin(4*x),x,-pi,pi)/pi
b5 = int(f*sin(5*x),x,-pi,pi)/pi
%求山地等三維圖，高線圖
x=0:10:1500;
y=0:10:900;
[x1,y1]=meshgrid(x,y) ;
z= xlsread('ZZchazhi111.xls','sheet1','A1:CM151'); %讀入excel文件數據
Z=z';
figure;
mesh(x1,y1,Z)
figure;
contourf(x1,y1,Z,3)
%生成excel
clear all
%list x,y,z
x = xlsread('shandibiao.xls','sheet1','A3:A37');
y = xlsread('shandibiao.xls','sheet1','B2:AZ2');
z = xlsread('shandibiao.xls','sheet1','B3:AZ37');
Z = z';
%cha zhi. jian ge 10
xx = 0:10:900;
yy = 0:10:1500;
[XX, YY] = meshgrid(xx, yy);
ZZ = interp2(x, y, Z, XX, YY, 'cubic');
xlswrite('chazhi10de',ZZ) %生成excel
%cha zhi. jian ge 1
xxx = 0:1:900;
yyy = 0:1:1500;
[XXX, YYY] = meshgrid(xxx, yyy);
ZZZ = interp2(xx, yy, ZZ, XXX, YYY, 'cubic');
%
clc一種長方體的繪製方法
clear all
x1=zeros(1,10);
y1=zeros(1,10);
z1=zeros(1,10);
x2=linspace(0,50,10);
y2=linspace(0,50,10);
z2=linspace(0,14,10);
x3=50*ones(1,10);
y3=50*ones(1,10);
z3=14*ones(1,10);
figure
plot3(x2,y1,z1,'b',x1,y1,z2,'b',x1,y2,z1,'b',x2,y1,z3,'b',x1,y3,z2,'b',x3,y2,z1,'b',...
x1,y2,z3,'b',x2,y3,z1,'b',x3,y1,z2,'b',x3,y3,z2,'b',x3,y2,z3,'b',x2,y3,z3,'b')