MATLAB: How to represent function which is defined on different interval

functionmatlab functionplot

I'm trying to plot function that defined on different intervals like following.

Let

phi_i(x)=M*(x-(i-1)/M) on [(i-1)/M,i/M] and M*((i+1)/M-x) on [i/M,(i+1)/M] and 0 on other values.

I got values u_1, u_2 …u_(M-1) and note u(x)=u_1 phi_1(x)+u_2 phi_2(x) +…+u_(M-1) phi(x)

How to plot u(x)?

Best Answer

You can use a for-loop to compose the function out of the parts using anonymous functions:

phi_part_i=@(x,i) ...
    M*(x-(i-1)/M)*( (i-1)/M <x & x<     i/M ) + ...
    M*((i+1)/M-x)*(     i/M <x & x< (i+1)/M );
phi_1=@(x) phi_part_i(x,1);
phi_1_10=@(x) 0;
for m=1:10
    phi_1_10=@(x) phi_1_10(x) + phi_part_i(x,m);
end

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MATLAB: I am not able to get passed through shape function in matlab. Shape function contains symbolic variable which needs to be converted to vpa function and how to do that

syms pi p q E A l x
n=3;
k=(n:n);
r=(1:n);
a=(1:n);
N = sym(1:n);
pi=eval(pi);
p=q*x/E*A*l;
for i=1:n  
        syms x
        N(i)=(x.^2-2*x).^i;  %Shape function
        %N(i)=sin((2*i-1)/2*pi*x);
        %N(i)=piecewise(x>=(i-1)/n & x<1/n+(i-1)/n,n*(x-(i-1)/n),x>=i/n & x<=(i+1)/n & x<1,-n*x+i+1,0);
        Y1=(N(i));
        Y2=diff(N(i),x);
        Y3=diff(N(i),x,2);
        x=linspace(0,1);
        plot(x,subs(Y1))
        hold on
        plot(x,subs(Y2))
        hold on
        plot(x,subs(Y3))
        hold off
        legend('N','N''','N''''');
        pause(1);
end

MATLAB: Variable x must be of data type double. It is currently of type sym. Check where the variable is assigned a value.

You need to substitute a value for symbolic variable t to get a numeric value

U = [3,2,1;
     0,1,2;
     0,0,1];
b = [0;0;0];
syms t;
x = backsub_syms(U,b);
y = subs(x, t, 1) % t = 1
double(y)
function x = backsub_syms(U,b)
n = length(b);
syms t
x=sym(zeros(n,1))
x(n)=sym('t')
b=(sym(b))
for i = n:-1:1
    x(i)=b(i);
    x(n)=sym('t')
    if i<n
        for j = n:-1:i+1
            
            x(i)=x(i)-U(i,j)*x(j);
            
        end
    end
    
    x(i)=x(i)/U(i,i);
end
end

Best Answer

Related Solutions

MATLAB: I am not able to get passed through shape function in matlab. Shape function contains symbolic variable which needs to be converted to vpa function and how to do that

MATLAB: Variable x must be of data type double. It is currently of type sym. Check where the variable is assigned a value.

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