Too many input arguments

clear all; close all;
syms k 
z0=2; r=0.01; K=100;
t=0:20:500;
u=0.75; B=1;
H=@(r) B+r*(1+z0./K)*(u-1); 
F=@(t) r*(1-z0./K)*u*t.^u;
z=(B*z0/H(r))* symsum((F(t)./H(r)).^k/gamma(k*u+1),k,0,20);
zfcn = matlabFunction(z);
figure
semilogy(zfcn(t))

Error using sym/matlabFunction>@()[2.005113038247531,1.0./sqrt(pi).*1.298420190275181e-2+1.863145905367271e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*4.825947247317249e-4)./pi+2.005120920720691,1.0./sqrt(pi).*3.672502285205008e-2+3.133454093356336e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*2.295625548121586e-3)./pi+2.005176098119577,1.0./sqrt(pi).*6.746894298713936e-2+4.24719856221843e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*5.716221725839784e-3)./pi+2.005325866110514,1.0./sqrt(pi).*1.038775353681554e-1+5.270206334681761e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*1.092009584808589e-2)./pi+2.005617522776865,1.0./sqrt(pi).*1.451785737172247e-1+6.230813465160406e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*1.804191350430131e-2)./pi+2.00609837140796,1.0./sqrt(pi).*1.908525940660575e-1+7.144672535509189e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*2.719275779710953e-2)./pi+2.006815724403713,1.0./sqrt(pi).*2.405200513865164e-1+8.021664372626287e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*3.846816503063656e-2)./pi+2.007816908295099,1.0./sqrt(pi).*2.938888891483324e-1+8.8685849809244e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*5.195259229838972e-2)./pi+2.009149269880756,1.0./sqrt(pi).*3.507263460178208e-1+9.690402512763223e-1./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*6.772219848946139e-2)./pi+2.010860183480125,1.0./sqrt(pi).*4.108422544893403e-1+1.049092107875898./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*8.584671431461699e-2)./pi+2.012997059303685,1.0./sqrt(pi).*4.740784362364065e-1+1.127316298296258./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*1.063907735051988e-1)./pi+2.015607352941042,1.0./sqrt(pi).*5.403016069420206e-1+1.203960364494845./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*1.294149034393167e-1)./pi+2.018738575967815,1.0./sqrt(pi).*6.093984311943063e-1+1.279232354188988./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*1.549762892889505e-1)./pi+2.022438307672529,1.0./sqrt(pi).*6.81271961165741e-1+1.353311060554923./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*1.831293813862405e-1)./pi+2.026754207904963,1.0./sqrt(pi).*7.558390022866188e-1+1.426353160774678./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*2.139263904658619e-1)./pi+2.031734031047712,1.0./sqrt(pi).*8.330281208911004e-1+1.498498336177004./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*2.474177005352459e-1)./pi+2.037425641113012,1.0./sqrt(pi).*9.127781090949674e-1+1.569873034774264./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*2.836522198514454e-1)./pi+2.043877027967258,1.0./sqrt(pi).*9.950367832429164e-1+1.640593294671798./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*3.226776844966032e-1)./pi+2.051136324685973,1.0./sqrt(pi).*1.079760030829041+1.710766901903874./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*3.645409250549535e-1)./pi+2.059251826042408,1.0./sqrt(pi).*1.166911045912215+1.780495066505609./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*4.092881041631715e-1)./pi+2.068272008133374,1.0./sqrt(pi).*1.256459709855619+1.849873743343589./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*4.569649307912908e-1)./pi+2.078245549146343,1.0./sqrt(pi).*1.348382085736601+1.918994686672854./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*5.076168557410078e-1)./pi+2.089221351272344,1.0./sqrt(pi).*1.442660002832661+1.987946302180176./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*5.612892518491288e-1)./pi+2.10124856376968,1.0./sqrt(pi).*1.539280713336618+2.056814342993479./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*6.180275816435302e-1)./pi+2.114376607184021,1.0./sqrt(pi).*1.638236607622093+2.125682484065596./gamma(3.0./4.0)+(sqrt(2.0).*gamma(3.0./4.0).*6.77877554642217e-1)./pi+2.128655198730981]
Too many input arguments.

grid on

Answer 1

[Star Strider]

Plotting over ranges of ‘t’ and ‘u’ defines a surface, so create vectors for both of them, and use either ndgrid or meshgrid (the outputs are transposes of each other) to create the appropriately-sized matrices for those vectors. Then, create ‘zfcn’ as a function of both of them, and plot the result.

Try this —

clear all; close all;
syms k t u 
z0=2; r=0.01; K=100;
% t=0:20:500;
% % u=0.75; 
% u = 0.1:0.1:0.75;
% [T,U] = ndgrid(t,u);
B=1;
H=@(r) B+r*(1+z0./K)*(u-1); 
F=@(t) r*(1-z0./K)*u*t.^u;
z(t,u) = (B*z0/H(r))* symsum((F(t)./H(r)).^k/gamma(k*u+1),k,0,20);      % ‘z’ Is Now A Function Of Both ‘t’ and ‘u’ (NOTE: Appropriate Changes In The ‘syms’ Declaration)
zfcn = matlabFunction(z)                                                % ‘zfcn’ Also Is Now A Function Of Both ‘t’ and ‘u’

zfcn = function_handle with value:
    @(t,u)(((t.^u.*u.*9.8e-3)./(gamma(u+1.0).*(u.*1.02e-2+9.898e-1))+(t.^(u.*2.0).*u.^2.*1.0./(u.*1.02e-2+9.898e-1).^2.*9.604e-5)./gamma(u.*2.0+1.0)+(t.^(u.*3.0).*u.^3.*1.0./(u.*1.02e-2+9.898e-1).^3.*9.41192e-7)./gamma(u.*3.0+1.0)+(t.^(u.*4.0).*u.^4.*1.0./(u.*1.02e-2+9.898e-1).^4.*9.2236816e-9)./gamma(u.*4.0+1.0)+(t.^(u.*5.0).*u.^5.*1.0./(u.*1.02e-2+9.898e-1).^5.*9.039207968e-11)./gamma(u.*5.0+1.0)+(t.^(u.*6.0).*u.^6.*1.0./(u.*1.02e-2+9.898e-1).^6.*8.85842380864e-13)./gamma(u.*6.0+1.0)+(t.^(u.*7.0).*u.^7.*1.0./(u.*1.02e-2+9.898e-1).^7.*8.6812553324672e-15)./gamma(u.*7.0+1.0)+(t.^(u.*8.0).*u.^8.*1.0./(u.*1.02e-2+9.898e-1).^8.*8.507630225817856e-17)./gamma(u.*8.0+1.0)+(t.^(u.*9.0).*u.^9.*1.0./(u.*1.02e-2+9.898e-1).^9.*8.337477621301499e-19)./gamma(u.*9.0+1.0)+(t.^(u.*1.0e+1).*u.^10.*1.0./(u.*1.02e-2+9.898e-1).^10.*8.170728068875469e-21)./gamma(u.*1.0e+1+1.0)+(t.^(u.*1.1e+1).*u.^11.*1.0./(u.*1.02e-2+9.898e-1).^11.*8.00731350749796e-23)./gamma(u.*1.1e+1+1.0)+(t.^(u.*1.2e+1).*u.^12.*1.0./(u.*1.02e-2+9.898e-1).^12.*7.847167237348e-25)./gamma(u.*1.2e+1+1.0)+(t.^(u.*1.3e+1).*u.^13.*1.0./(u.*1.02e-2+9.898e-1).^13.*7.69022389260104e-27)./gamma(u.*1.3e+1+1.0)+(t.^(u.*1.4e+1).*u.^14.*1.0./(u.*1.02e-2+9.898e-1).^14.*7.53641941474902e-29)./gamma(u.*1.4e+1+1.0)+(t.^(u.*1.5e+1).*u.^15.*1.0./(u.*1.02e-2+9.898e-1).^15.*7.385691026454039e-31)./gamma(u.*1.5e+1+1.0)+(t.^(u.*1.6e+1).*u.^16.*1.0./(u.*1.02e-2+9.898e-1).^16.*7.237977205924958e-33)./gamma(u.*1.6e+1+1.0)+(t.^(u.*1.7e+1).*u.^17.*1.0./(u.*1.02e-2+9.898e-1).^17.*7.093217661806459e-35)./gamma(u.*1.7e+1+1.0)+(t.^(u.*1.8e+1).*u.^18.*1.0./(u.*1.02e-2+9.898e-1).^18.*6.95135330857033e-37)./gamma(u.*1.8e+1+1.0)+(t.^(u.*1.9e+1).*u.^19.*1.0./(u.*1.02e-2+9.898e-1).^19.*6.812326242398923e-39)./gamma(u.*1.9e+1+1.0)+(t.^(u.*2.0e+1).*u.^20.*1.0./(u.*1.02e-2+9.898e-1).^20.*6.676079717550945e-41)./gamma(u.*2.0e+1+1.0)+1.0).*2.0)./(u.*1.02e-2+9.898e-1)

t=0:20:500;                                                             % Previous Vector unchanged
% u=0.75; 
u = 0.1:0.1:0.75;                                                       % New Vector
[T,U] = ndgrid(t,u);                                                    % Create Matrices

figure
% semilogy(zfcn(t))
surf(T, U, zfcn(T,U))                                                   % Plot Surface
xlabel('t')
ylabel('u')
zlabel('z')
set(gca, 'ZScale','log')                                                % Optional
colormap(turbo)
colorbar

You could also do this with fsurf with the symbolic function, although the results would likeely be a bit different.

See the documentation on the clim funciton to change the colour range.

.

Answer 2

[Sam Chak]

Previously, the symbolic t is undefined in the z(t) function.

clear all; close all;
syms k t
z0=2; r=0.01; K=100;
u=0.75; B=1;
H=@(r) B+r*(1+z0./K)*(u-1); 
F=@(t) r*(1-z0./K)*u*t.^u;
z=(B*z0/H(r))* symsum((F(t)./H(r)).^k/gamma(k*u+1),k,0,20);
zfcn = matlabFunction(z)

zfcn = function_handle with value:
    @(t)t.^3.*9.853089513345264e-10+t.^6.*2.420895258923788e-20+t.^9.*1.416218558303767e-31+t.^12.*3.163305726921127e-43+t.^15.*3.416357717856453e-55+t.^(3.0./2.0).*1.0./sqrt(pi).*1.451677034797244e-4+t.^(9.0./2.0).*1.0./sqrt(pi).*1.087011796854525e-14+t.^(1.5e+1./2.0).*1.0./sqrt(pi).*1.195313337499515e-25+t.^(2.1e+1./2.0).*1.0./sqrt(pi).*4.156566691246514e-37+t.^(2.7e+1./2.0).*1.0./sqrt(pi).*6.315066800643833e-49+(t.^(3.0./4.0).*1.97003436511362e-2)./gamma(3.0./4.0)+(t.^(1.5e+1./4.0).*3.218522944037243e-12)./gamma(3.0./4.0)+(t.^(2.7e+1./4.0).*5.147261113564229e-23)./gamma(3.0./4.0)+(t.^(3.9e+1./4.0).*2.295337998974923e-34)./gamma(3.0./4.0)+(t.^(5.1e+1./4.0).*4.202182874048589e-46)./gamma(3.0./4.0)+(sqrt(2.0).*t.^(9.0./4.0).*gamma(3.0./4.0).*5.705122037601079e-7)./pi+(sqrt(2.0).*t.^(2.1e+1./4.0).*gamma(3.0./4.0).*2.319627036455943e-17)./pi+(sqrt(2.0).*t.^(3.3e+1./4.0).*gamma(3.0./4.0).*1.829494074668569e-28)./pi+(sqrt(2.0).*t.^(4.5e+1./4.0).*gamma(3.0./4.0).*5.057055318288334e-40)./pi+(sqrt(2.0).*t.^(5.7e+1./4.0).*gamma(3.0./4.0).*6.446376853912875e-52)./pi+2.005113038247531

t=0:20:500;
figure
semilogy(t, zfcn(t))
grid on

●

[Mathew]

@ Sam Chak The answer is perfect for 2D.

I would like to view the graph in 3D where

t=[0 500]; % (On x-axis),

u=[0.1 0.75] % (On y-axix),

and the function z on the z-axix.

[Torsten]

z0=2; r=0.01; K=100;
T=0:20:500;
U=0.1:0.05:0.75;
B=1;
H = @(u) B+r*(1+z0/K)*(u-1); 
F = @(t,u) r*(1-z0/K)*u*t^u;
Z = zeros(numel(T),numel(U));
for i = 1:numel(T)
    t = T(i);
    for j = 1:numel(U)
        u = U(j);
        Z(i,j) = 0.0;
        for k = 0:20
          Z(i,j) = Z(i,j) + (F(t,u)/H(u))^k/gamma(k*u+1);
        end
        Z(i,j) = Z(i,j)*B*z0/H(u);
    end
end
surf(T,U,Z.')
zscale("log")

●

[Sam Chak]

@Torsten, Thank you for showing this approach.