MATLAB: ‘Undefined Function or Variable’ Error when Function is Defined

function handlesode

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

Best Answer

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);
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