# 'Undefined Function or Variable' Error when Function is Defined

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árbol on 2 Nov 2017
Edited: Stephen23 on 22 Dec 2017
My model contains two functions, cp(t) and ct(t). In my original (working) code (see below), cp(t) and ct(t) are each defined by one functional form. Now, I would like to study the behavior of the dependent variables for different functional forms of cp(t) and ct(t). How can I do this?
My Attempt: I created two matrices in the ODE solver; in the first matrix, each column represents a function for cp(t), and in the second matrix, each column represents a function for ct(t). When I run the ODE solver, I get the error "Undefined Function or Variable" for cp(t).
Thank you!
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ORIGINAL, WORKING CODE
ODE File:
function dy = short_ODE(t,y)
b = 21.5;
d = 0.167;
qe = 0.0542;
q1 = 0.000257;
q2 = 0.0008;
dy(1,1) = 10*b*y(9)*(cp(t)/(cp(t)+ct(t)))-ne(t)*y(1)-qe*y(1);
dy(2,1) = ne(t)*y(1)-n1(t)*y(2)-f1(t)*y(2)-q1*(y(2)^2)/cp(t);
dy(3,1) = n1(t)*y(2)-n2(t)*y(3)-f2(t)*y(3)-q2*(y(3)^2)/cp(t);
dy(4,1) = n2(t)*y(3)-np(t)*y(4)-fp(t)*y(4);
dy(5,1) = np(t)*y(4)/2-(1+d)*y(5)+y(9);
dy(6,1) = -(1+d)*y(6)+y(5);
dy(7,1) = -(1+d)*y(7)+y(6);
dy(8,1) = -(1+d)*y(8)+y(7);
dy(9,1) = -(1+d)*y(9)+y(8);
function y = T(t)
T0 = 21.5;
y = T0 + 0.6346*cos(t*2*pi/365) + 0.7731*sin(t*2*pi/365);
end
% Nested cp(t)
function y = cp(t)
y = 135000-35000*(1.446*cos(t*2*pi/365)+0.7109*sin(t*2*pi/365)...
+1.347*cos(2*t*2*pi/365)+1.408*sin(2*t*2*pi/365)...
-0.9942*cos(3*t*2*pi/365)-0.2396*sin(3*t*2*pi/365));
end
% Nested ct(t)
function y = ct(t)
epsilon = 1e-10;
y = 0*t + epsilon;
end
% Nested ne
function y = ne(t)
y = 0.693/(1.10316852+12.55262944/(1+(T(t)/15.21894679)^6.468691289));
end
% Nested n1
function y = n1(t)
y = 0.693/(2.711278535+18.35202441/(1+(T(t)/15.61912844)^5.845513817));
end
% Nested f1
function y = f1(t)
y = 0.666733-0.056977*T(t)+0.00125224*T(t)^2;
end
% Nested n2
function y = n2(t)
y = 0.693/(4.244561306+136.3457233/(1+(T(t)/10.3599642)^4.783523801));
end
% Nested f2
function y = f2(t)
y = 0.666733-0.056977*T(t)+0.00125224*T(t)^2;
end
% Nested np
function y = np(t)
y = 0.693/(8.583819474+18.15593517/(1+(T(t)/21.5533767)^7.852462638));
end
% Nested fp
function y = fp(t)
y = 0.666733-0.056977*T(t)+0.00125224*T(t)^2;
end
end
ODE Solver:
clear all;
tf = 1000;
dt = 1;
t = 0:dt:tf;
y0 = [3954200.8835438923;2310300.5386356956;2007000.7121853685;
103780.6956163843;1289400.7821495022/100/5;
1289400.7821495022/100/5;1289400.7821495022/100/5;
1289400.7821495022/100/5;1289400.7821495022/100/5];
[t,y] = ode15s(@short_ODE,t,y0);
A = y(:,5)+y(:,6)+y(:,7)+y(:,8)+y(:,9);
plot(t,A,'b');
xlabel('Time (in days)');
ylabel('Population');
h_xlabel = get(gca,'XLabel');
set(h_xlabel,'FontSize',14);
h_ylabel = get(gca,'YLabel');
set(h_ylabel,'FontSize',14);
set(gca,'fontName','Helvetica');
MODIFIED CODE WITH ERROR
ODE Solver:
clear;
tf = 1000;
dt = 1;
t = 1:dt:tf;
y0 = [3954200.8835438923;2310300.5386356956;2007000.7121853685;
103780.6956163843;1289400.7821495022/100/5;
1289400.7821495022/100/5;1289400.7821495022/100/5;
1289400.7821495022/100/5;1289400.7821495022/100/5];
m = min(c(t));
d = m/10;
i = 0;
for p = 0:d:m % This is where I created matrices cp(:,i) and ct(:,i)
i = i + 1;
a(1:length(c(t))) = p;
cp(:,i) = transpose(a); %#ok<*SAGROW>
ct(:,i) = transpose(c(t)) - transpose(a);
end
for j = 1:11
calle1 = @(t,y) e1_ODE(t,y,j);
[t,y] = ode15s(calle1,t,y0);
A(:,j) = y(:,5)+y(:,6)+y(:,7)+y(:,8)+y(:,9);
plot(t,A,'b');
xlabel('Time (in days)');
ylabel('Population');
h_xlabel = get(gca,'XLabel');
set(h_xlabel,'FontSize',14);
h_ylabel = get(gca,'YLabel');
set(h_ylabel,'FontSize',14);
set(gca,'fontName','Helvetica');
hold on
end
% Nested c(t)
function y = c(t)
y = 135000-35000*(1.446*cos(t*2*pi/365)+0.7109*sin(t*2*pi/365)...
+1.347*cos(2*t*2*pi/365)+1.408*sin(2*t*2*pi/365)...
-0.9942*cos(3*t*2*pi/365)-0.2396*sin(3*t*2*pi/365));
end
ODE File:
function dy = e1_ODE(t,y,j) % Here, I have index as an input, which wasn't needed
% for the working code
b = 21.5;
d = 0.167;
qe = 0.0542;
q1 = 0.000257;
q2 = 0.0008;
epsilon = 1e-10;
dy(1,1) = 10*b*y(9)*(cp(t,j)/(cp(t,j)+ct(t,j)))-ne(t)*y(1)-qe*y(1);
dy(2,1) = ne(t)*y(1)-n1(t)*y(2)-f1(t)*y(2)-q1*(y(2)^2)/cp(t,j)+epsilon;
dy(3,1) = n1(t)*y(2)-n2(t)*y(3)-f2(t)*y(3)-q2*(y(3)^2)/cp(t,j)+epsilon;
dy(4,1) = n2(t)*y(3)-np(t)*y(4)-fp(t)*y(4);
dy(5,1) = np(t)*y(4)/2-(1+d)*y(5)+y(9);
dy(6,1) = -(1+d)*y(6)+y(5);
dy(7,1) = -(1+d)*y(7)+y(6);
dy(8,1) = -(1+d)*y(8)+y(7);
dy(9,1) = -(1+d)*y(9)+y(8);
function y = T(t)
T0 = 21.5;
y = T0 + 0.6346*cos(t*2*pi/365) + 0.7731*sin(t*2*pi/365);
end
% Nested ne
function y = ne(t)
y = 0.693/(1.10316852+12.55262944/(1+(T(t)/15.21894679)^6.468691289));
end
% Nested n1
function y = n1(t)
y = 0.693/(2.711278535+18.35202441/(1+(T(t)/15.61912844)^5.845513817));
end
% Nested f1
function y = f1(t)
y = 0.666733-0.056977*T(t)+0.00125224*T(t)^2;
end
% Nested n2
function y = n2(t)
y = 0.693/(4.244561306+136.3457233/(1+(T(t)/10.3599642)^4.783523801));
end
% Nested f2
function y = f2(t)
y = 0.666733-0.056977*T(t)+0.00125224*T(t)^2;
end
% Nested np
function y = np(t)
y = 0.693/(8.583819474+18.15593517/(1+(T(t)/21.5533767)^7.852462638));
end
% Nested fp
function y = fp(t)
y = 0.666733-0.056977*T(t)+0.00125224*T(t)^2;
end
end

Josh Meyer on 3 Nov 2017
Looks like the issue is you define cp in the workspace and the function can't access that variable when it gets called. So, try passing cp to the ode function:
calle1 = @(t,y) e1_ODE(t,y,j,cp);
árbol on 22 Dec 2017
@Stephen Cobeldick: Thank you for recommending function handles! My code is working as intended.