Defining and plotting a piecewise function

Hi everybody!

I am trying to deifne and plot the function below in matlab, without success. Can anybody point how I could plot this function?

for 0 <= T < Tb, Se(T) = ag*S*?*F0*[(T/Tb) + (1/?*F0)*(1 - T/Tb)]

for Tb <= T < Tc, Se(T) = ag*S*?*F0

for Tc <= T < Td, Se(T) = ag*S*?*F0*(Tc/T)

for Td <= T, Se(T) = ag*S*?*F0*(Tc*Td/(T^2))

Note: I have defined all values of ag, S, n, F0, Tb, Tc, Td in my code.

function S = f(T);

S=0;

if T >= 0 & T < Tb

S = ag*S*n*F0*[(T/Tb) + (1/n*F0)*(1 - T/Tb)];

elseif T >= Tb & T < Tc

S = ag*S*n*F0;

elseif T >= Tc & T < Td

S = ag*S*n*F0*(Tc/T);

else T>=Td

S = ag*S*n*F0*(Tc*Td/(T.^2));

end

end

Thanks!

Answer 1

[Star Strider]

Another option:

S = @(T) (ag*S*n*F0*((T/Tb) + (1/n*F0)*(1 - T/Tb))).*(T >= 0 & T < Tb) + (ag*S*n*F0).*(T >= Tb & T < Tc) + (ag*S*n*F0*(Tc*Td/(T.^2))).*(T >= Tc & T < Td);

If all the other values are scalars, that should work.

.

[Majd Salhab]

Thank you! But when trying to plot it, I am getting an empty figure.

Is this correct?

f = @(T) (ag*S*n*F0*((T/Tb) + (1/n*F0)*(1 - T/Tb))).*(T >= 0 & T < Tb) + (ag*S*n*F0).*(T >= Tb & T < Tc) + (ag*S*n*F0*(Tc/T)).*(T >= Tc & T < Td) + ag*S*n*F0*(Tc*Td/(T.^2)).*(T>=Td);

T = linspace(0, 10, 500);

figure(1);

plot(T,f(T));

Thanks

[Star Strider]

My pleasure.

When ‘T’ appears in the denominator, it is necessary to use element-wise division.

This:

ag*S*n*F0*(Tc*Td/(T.^2))

should be:

ag*S*n*F0*(Tc*Td./(T.^2))
                ↑ ← ELEMENT-WISE DIVISION

so the corrected function is:

S = @(T) (ag*S*n*F0*((T/Tb) + (1/n*F0)*(1 - T/Tb))).*(T >= 0 & T < Tb) + (ag*S*n*F0).*(T >= Tb & T < Tc) + (ag*S*n*F0*(Tc*Td./(T.^2))).*(T >= Tc & T < Td);

That should work. (I did not see that earlier.)

.

[Majd Salhab]

Thanks again :)

There is a problem with the plot function for some reason, I don't know why.

I get this error in the command window:

Error in Exercise0 (line 25)
plot(T,f(T));

Is the code to plot the function below correct?

f = @(T) (ag*S*n*F0*((T/Tb) + (1/n*F0)*(1 - T/Tb))).*(T >= 0 & T < Tb) + (ag*S*n*F0).*(T >= Tb & T < Tc) + (ag*S*n*F0*(Tc/T)).*(T >= Tc & T < Td) + ag*S*n*F0*(Tc*Td./(T.^2)).*(T>=Td);
T = linspace(0, 10, 500);
figure(1);
plot(T,f(T));

Thanks in advance :)

[Star Strider]

My pleasure.

Is there more to the error message?

What are the variables (ag, S, n, F0, Tb, Tc, Td) inside the function?

.

[Majd Salhab]

This is the error:

Error using  / 
Matrix dimensions must agree.

Error in
Exercise0>@(T)(ag*S*n*F0*((T/Tb)+(1/n*F0)*(1-T/Tb))).*(T>=0&T<Tb)+(ag*S*n*F0).*(T>=Tb&T<Tc)+(ag*S*n*F0*(Tc/T)).*(T>=Tc&T<Td)+ag*S*n*F0*(Tc*Td./(T.^2)).*(T>=Td)
(line 22)
f = @(T) (ag*S*n*F0*((T/Tb) + (1/n*F0)*(1 - T/Tb))).*(T >= 0 & T < Tb) + (ag*S*n*F0).*(T >= Tb & T <
Tc) + (ag*S*n*F0*(Tc/T)).*(T >= Tc & T < Td) + ag*S*n*F0*(Tc*Td./(T.^2)).*(T>=Td);

Error in Exercise0 (line 25)
plot(T,f(T));
 
>> 

This is the complete code, maybe it might help to find the error :)

close all;
clear
clc
 
g=9.81;
ag= 0.177*g;
damping = 5;
F0 = 2.544;
Tcstar = 0.281;
St = 1.0;
Cc= 1.25*(Tcstar).^-0.5;
Ss = 2.4 - 1.5*(F0*ag/g);
S = Ss*St;
Tc = Cc*Tcstar;
Tb = Tc/3;
Td = 4*ag/g + 1.6;
n = (10/(5+damping)).^0.5;
 
 
f = @(T) (ag*S*n*F0*((T/Tb) + (1/n*F0)*(1 - T/Tb))).*(T >= 0 & T < Tb) + (ag*S*n*F0).*(T >= Tb & T < Tc) + (ag*S*n*F0*(Tc/T)).*(T >= Tc & T < Td) + ag*S*n*F0*(Tc*Td./(T.^2)).*(T>=Td);
T = linspace(0, 10, 500);
figure(1);
plot(T,f(T));

[Star Strider]

Same problem, different term.

Try this:

f = @(T) (ag*S*n*F0*((T/Tb) + (1/n*F0)*(1 - T/Tb))).*(T >= 0 & T < Tb) + (ag*S*n*F0).*(T >= Tb & T < Tc) + (ag*S*n*F0*(Tc./T)).*(T >= Tc & T < Td) + ag*S*n*F0*(Tc*Td./(T.^2)).*(T>=Td);

.

[Majd Salhab]

Perfect! Thanks a lot! Have a nice day

[Star Strider]

As always, my pleasure!

You, too!

Answer 2

[Ameer Hamza]

See piecewise(): https://www.mathworks.com/help/releases/R2020a/symbolic/piecewise.html. You can use it with symbolic toolbox to define a piecewise function.