Improving code to reduce run-time

Question

AH2019 2019-4-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/456840-improving-code-to-reduce-run-time

评论： Stephen23 2019-4-17

Hi

I need to improve following code for decreasing run-time.

The main deficiencies are

The run-time, especially for Ln 137 [ i.e. bc(2) = solve(subs(fd1,[psi(1),X],[bc(1),1/2+sqrt(1/4-(z/h)^2)]),psi(N)) ] is too much.
In the case of N>10, the

Please hint me

clc;
clear all
tic
N = 10;
L = 5;
h = 1;
n = 1;
md = 1;
P = 0;
rhom = 2702;
rhoc = 3960;
Em = 70e9;
Ec = 380e9;
nu = 0.3;
% X =(y/h+1/2);
sc = 1/h;
syms X z omega
om = sym('om',[1,N]);
om(1) = 0;
phi1 = sym('phi1',[1,N]);
x = zeros(1,N);
A = zeros(2,N,N);
l = sym('l',[1,N]);
df = sym('df',[1,N]);
df1 = sym('df1',[1,N]);
df1o = sym('df1o',[1,N]);
df2 = sym('df2',[1,N]);
psi = sym('psi',[1,N]);
dis = sym('dis',[1,N]);
M = zeros(N-2,N-2);
bc = sym('bc',[1,2]);
mm = sym('mm',[1,N-2]);
F = sym('F',[1,N]);
q = 1:N;
Vc =(X)^n;
Vm = 1-Vc;
rho = rhom*Vm+rhoc*Vc;
E = Em*Vm+Ec*Vc;
G = E/(2*(1+nu));
m0 = int(int(rho/sc,X,1/2-sqrt(1/4-(z/h)^2),1/2+sqrt(1/4-(z/h)^2)),z,-h/2,h/2);
for i=1:N
    x(i) = 1/2*(1-cos((i-1)*vpa(pi)/(N-1)));
end
for m=1:N
    phi1(m) = (X-x(m));
end
aphi = cumprod(phi1);
for r=1:2
for j=1:N
for m=1:N
    if j==m
        phi1(m) = 1;
    else
        phi1(m) = (x(j)-x(m));
    end
end
dphi = cumprod(phi1);
l(j) = aphi(N)/((X-x(j))*dphi(N));
for i=1:N
A(r,i,j) = limit(diff(l(j),X,r),X,x(i));
end
end
end
for i=1:N
for j=1:N
    df(j) = A(1,i,j)*psi(j);
end
df1o(i) = sum(df);
end
for i=1:N
for j=1:N
    df(j) = A(2,i,j)*psi(j);
end
df2(i) = sum(df);
end
for i=1:N
df2(i) = df2(i)*subs(G,X,x(i));
end
for i=1:N
df1(i) = df1o(i)*sc*subs(diff(G,X),X,x(i));
end
for i=1:N
dis(i)= subs((rho*om(1)^2*L^2-md^2*vpa(pi^2)*E)*(L^2*psi(i)+md^2*vpa(pi^2)*(X-1/2)*h),X,x(i));
end
ode = L^4*sc^2*df2+L^4*sc*df1+dis;
for j=1:N-2
for i=1:N-2
    M(i,j)= diff(ode(i+1),psi(j+1));
end
end
for j=1:N-2
    mm(j) = ode(j+1);
for i=1:N-2
    mm(j)= subs(mm(j),psi(i+1),0);
end
end
mat = -(M^(-1)*mm');
df1s = subs(df1o,psi(2:N-1),mat');
fd1 = polyfit(x,df1s,N-1)*(X.^(N-q))';
bc(1) = solve(subs(fd1,X,1/2-sqrt(1/4-(z/h)^2)),psi(1));
bc(2) = solve(subs(fd1,[psi(1),X],[bc(1),1/2+sqrt(1/4-(z/h)^2)]),psi(N));
bc(1) = subs(bc(1),psi(N),bc(2));
F(1) = bc(1);
F(N) = bc(2);
F = subs(F,F(2:N-1), subs(mat',[psi(1),psi(N)],[bc(1),bc(2)]));
f = polyfit(x,F,N-1)*(X.^(N-q))';
INT = int(G*diff(f,X),X,1/2-sqrt(1/4-(z/h)^2),1/2+sqrt(1/4-(z/h)^2))*L^2;
INT = matlabFunction(INT);
INT = integral(INT,-h/2,h/2,'ArrayValued',1);
solve(INT+m0*omega^2*L^2+md^2*vpa(pi^2)*P,omega);
om(2) = abs(ans(1));
lp=1;
while abs(om(lp+1)-om(lp))>1e-10
    lp=lp+1;
for i=1:N
dis(i)= subs((rho*om(lp)^2*L^2-md^2*vpa(pi^2)*E)*(L^2*psi(i)+md^2*vpa(pi^2)*(X-1/2)*h),X,x(i));
end
ode = L^4*sc^2*df2+L^4*sc*df1+dis;
ode = subs(ode,[psi(1),psi(N)],[bc(1),bc(2)]);
for j=1:N-2
for i=1:N-2
    M(i,j)= diff(ode(i+1),psi(j+1));
end
end
for j=1:N-2
    mm(j) = ode(j+1);
for i=1:N-2
    mm(j)= subs(mm(j),psi(i+1),0);
end
end
mat = -(M^(-1)*mm');
df1s = subs(df1o,psi(2:N-1),mat');
fd1 = polyfit(x,df1s,N-1)*(X.^(N-q))';
bc(1) = solve(subs(fd1,X,1/2-sqrt(1/4-(z/h)^2)),psi(1));
bc(2) = solve(subs(fd1,[psi(1),X],[bc(1),1/2+sqrt(1/4-(z/h)^2)]),psi(N));
bc(1) = subs(bc(1),psi(N),bc(2));
F(1) = bc(1);
F(N) = bc(2);
F = subs(F,F(2:N-1), mat');
f = polyfit(x,F,N-1)*(X.^(N-q))';
INT = int(G*diff(f,X),X,1/2-sqrt(1/4-(z/h)^2),1/2+sqrt(1/4-(z/h)^2))*L^2;
INT = matlabFunction(INT);
INT = integral(INT,-h/2,h/2,'ArrayValued',1);
solve(INT+m0*omega^2*L^2+md^2*vpa(pi^2)*P,omega);
om(1+lp) = abs(ans(1));
end
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