i want to create a function (symfun), and i want to divide it to cases, i.e if t> then then answer will be a and if t<0 the answer will be b.
the thing is, that matlab wont allow me to put an if statements after a sym function.
>> l = symfun(0, [m]);
>> l(m) = if m>0 3
also i tried to create a function:
function [x1] = xt_otot_q3(t)
and tried to connect between the two functions:
>> l(m) = xt_otot_q3(m)
Conversion to logical from sym is not possible.
is there any way to break a symfun into cases?
Not sure that I understand what you want.
This code 'combines' the functions symfun and xt+otot_q3 defined below:
function test;
m=randn(4); % N(0,1) random numbers
l=xtotot_q3(symfun(0,m)) % combine xt_otot_q3 and symfun
l=symfun(0,xtotot_q3(m)) % combine symfun and xt_otot_q3
return
function lval=symfun(thr,rval);
lval=ones(size(rval)); % output, size of input, = 1
lval(rval<thr)=-1; % output = -1 if input < thr
return
function lval=xtotot_q3(rval);
lval=3*rval+1; % some function, in this case 3 * input + 1
return
You can save the whole bit as test.m and then call test from the matlab prompt. Maybe if you start with this then you can modify it to fit your needs.
Related
I would like to create a MATLAB function with vector inputs. The problem is that the inputs of a function created by matlabFunction() has only scalar inputs.
x = sym('x',[2 1]);
y = sym('y',[2 1]);
f=x(1)+x(2)+y(1)+y(2);
matlabFunction(f,'file','testFunction.m');
matlabFunction(f,'file','testFunction.m','vars',[x,y]); % tried with different options but doesn't work
This is the result (with x1,x2,y1,y2 inputs instead of x,y):
function f = testFunction(x1,x2,y1,y2)
%TESTFUNCTION
% F = TESTFUNCTION(X1,X2,Y1,Y2)
% This function was generated by the Symbolic Math Toolbox version 8.2.
% 10-Apr-2019 21:28:40
f = x1+x2+y1+y2;
Is there a solution to this problem within MATLAB? Or do I need to write a program opening the file as txt and replacing the words...
Update: I managed to solve the problem. For me, the best solution is the odeToVectorField() function.
Manually it is more difficult to give vector inputs to a function created by matlabFunction(). One way is the following:
syms y;
f=str2sym('y(1)+y(2)');
matlabFunction(f,'File','fFunction','Vars',y);
With this method, you need to manipulate the equation as a string (which is possible but not practical...), then re-convert it to symbolic expression.
If you check the result of f=x(1)+x(2)+y(1)+y(2) you will see that it is also scalar. Do simple test:
x = sym('x',[2 1]);
y = sym('y',[2 1]);
f=x(1)+x(2)+y(1)+y(2);
disp(f)
The results is x1 + x2 + y1 + y2. So there's nothing wrong with your matlabFunction expression, it just save what you give. If you need it to be stored in the form x(1)+x(2)+y(1)+y(2) you need to rewrite your f expression so it will be stored in vector form, until passing it to matlabFunction. Or alternatively you can create your file structure manualy using fprintf, look docs.
Consider the function f(y1,y2,y3,y4,z1)=(-(z1^3)/(y3^2))(3(y2-y1+y3^(-1)-z1/10)^2+(1/5)(y2-y1+y3^(-1)-(z1)/10))-y4 with 5 variables. When I put f(1,1,1,1,1) I find the answer but when I write f(v) in which v=(1,1,1,1,1) matlab does not work. How can I do that (by the second way)?
You could write a wrapper function, that will take a vector as input argument and 'unpacks' this vector before calling your function.
f(y1,y2,y3,y4,z1) = (-(z1^3)/ ...; % your function
fv(v) = f(v(1),v(2),v(3),v(4),v(5));
Or alternatively, make f refer to elements in the input vector by using the appropriate indices:
f(v) = (-(v(5)^3)/(v(3)^2)); ... % etc.
So i'm a little confounded by how to structure my problem.
So the assignment states as following:
Type a m-file numerical_derivative.m that performs numerical derivation. Use
it to calculate f'(-3) when f(x) = 3x^2 /(ln(1-x))
In the m-file you to use h = 10^-6 and have the following mainfunction:
function y = numericalderivative (f, x)
% Calculates the numerical value in the case of f in punk x.
% --- Input ---
% f: function handle f(x)
% x: the point where the derivative is calculated
% --- output ---
% y: the numerical derivative of f on the point x
If I want to save it as a file and run the program in matlab, does't it make it redundant to use handles then?
I won't give you the answer to your homework, but perhaps a simpler example would help.
Consider the following problem
Write a function named fdiff which takes the following two arguments:
A function f represented by a function handle which takes one argument,
and a point x which can be assumed to be in the domain of the f.
Write fdiff so that it returns the value f(x) - f(x-1)
Solution (would be in the file named fdiff.m)
function result = fdiff(f, x)
result = f(x) - f(x-1);
end
Example Use Cases
>> my_function1 = #(x) 3*x^2 /(log(1-x));
>> fdiff(my_function1, -3)
ans =
-10.3477
>> my_function2 = #(x) x^2;
>> fdiff(my_function2, 5)
ans =
9
What you've created with fdiff is a function which takes another function as an input. As you can see it doesn't just work for 3*x^2 /(log(1-x)) but any function you want to define.
The purpose of your assignment is to create something very similar, except instead of computing f(x) - f(x-1), you are asked write a function which approximates f'(x). Your use-case will be nearly identical to the first example except instead of fdiff your function will be named numericalderivative.
Note
In case it's not clear, the second example defines the my_function2 as x^2. The value returned by fdiff(my_function2, 5) is therefore 5^2 - 4^2 = 9.
When you make this as a function file and run this in MATLAB without any input arguments i.e., 'f' and 'x', it will give you the error: 'not enough input arguments'. In order to run the file you have to type something like numericalderivative (3x^2 /(ln(1-x)), 5), which gives the value of the numerical derivative at x = 5.
Functions and, in MATLAB function files are a simple implementation of the DRY programming method. You're being asked to create a function that takes a handle and an x file, then return the derivative of that function handle and that x value. The point of the function file is to be able to re-use your function with either multiple function handles or multiple x values. This is useful as it simply involves passing a function handle and a numeric value to a function.
In your case your script file or command window code would look something like:
func = #(x) (3*x^2)/log(1-x);
x = -3;
num_deriv = numericalderivative(func,x);
You should write the code to make the function numericalderivative work.
I wrote some code that works just fine to evaluate theta on its own with some test input. However, I would like to take this code and turn it into a function that I can call within another matlab file. I keep getting the error message, "Function definitions are not permitted in this context."
I want to be able to define four vectors in another matlab file and call SP1 to evaluate theta for those inputs. I'm not sure where I'm going wrong, though. Please help!
Thanks so much.
clc
clear all
function theta = SP1(p,q1,w1,r)
% INPUT:
%function theta = SP1(p,q1,w1,r)
% p = [5; -7; 12];
% q1 = [17.3037; -3.1128; 2.48175];
% w1 = [1/sqrt(8); sqrt(3/8); 1/sqrt(2)];
% r = [1; 2; -3];
% Define vectors u and v as well as u' and v'.
u = p - r;
v = q1 - r;
w1_t = transpose(w1);
u_prime = u - w1 * w1_t * u;
v_prime = v - w1 * w1_t * v;
% Calculate theta if conditions are met for a solution to exist.
if (abs(norm(u_prime)-norm(v_prime))<0.01) & (abs((w1_t * u)-(w1_t * v))<0.01)
X = w1_t*cross(u_prime,v_prime);
Y = dot(u_prime,v_prime);
theta = atan2(X,Y)
else if (norm(u_prime) == 0 | norm(v_prime) == 0)
disp('Infinite Number of Solutions')
else
disp('Conditions not satisfied to find a solution')
end
end
I think you can just remove the top two lines,
clc
clear all
and save the rest of the code starting with function as SP1.m file.
Then you should be able to call this function as SP1 from other m files.
I think you're confused about how functions work. The first line of a function definition defines how many inputs and outputs MATLAB expects:
function theta = SP1(p,q1,w1,r)
This means that calling a function SP1 will require you to give four inputs, and will return one output. It doesn't mean that:
Your inputs need to be named p, q1 and so on
Your output will be called theta automatically
The function will automatically take in the input variables p, q1, etc if they exist in the workspace.
It also doesn't do any checking on the inputs; so if you require that inputs be of a certain type, size, etc. you need to write your own error checking at the start of the file. You might intend that those inputs be 3x1 vectors, but there's nothing in the function to tell MATLAB that. So, SP1(1,2,3,4) will work, to some extent - it will take those inputs and try to run them through the function, and if they don't cause an error it will give you an output. The output might be wrong, but the computer doesn't know that.
Once you have a function you can call it multiple ways from the command line or from within other functions or scripts. As previously mentioned you don't have to stick to the naming of variables within the function, as long as input variables exist when the function is called MATLAB will accept them:
theta = SP1(p8,q27,w35,not_r);
myoutput = SP1(any,variable,I,like);
I don't necessarily have to give an output (but then the first output will be routed to ans)
SP1(this,will,also,work);
If I have some variables stored in a *.mat file (the case you seem to be asking about), I can do it like this:
load('mydata.mat'); %this file contains stored variables p, q1, w1 and r
theta = SP1(p,q1,w1,r);
I have one file with the following code:
function fx=ff(x)
fx=x;
I have another file with the following code:
function g = LaplaceTransform(s,N)
g = ff(x)*exp(-s*x);
a=0;
b=1;
If=0;
h=(b-a)/N;
If=If+g(a)*h/2+g(b)*h/2;
for i=1:(N-1)
If=If+g(a+h*i)*h;
end;
If
Whenever I run the second file, I get the following error:
Undefined function or variable 'x'.
What I am trying to do is integrate the function g between 0 and 1 using trapezoidal approximations. However, I am unsure how to deal with x and that is clearly causing problems as can be seen with the error.
Any help would be great. Thanks.
Looks like what you're trying to do is create a function in the variable g. That is, you want the first line to mean,
"Let g(x) be a function that is calculated like this: ff(x)*exp(-s*x)",
rather than
"calculate the value of ff(x)*exp(-s*x) and put the result in g".
Solution
You can create a subfunction for this
function result = g(x)
result = ff(x) * exp(-s * x);
end
Or you can create an anonymous function
g = #(x) ff(x) * exp(-s * x);
Then you can use g(a), g(b), etc to calculate what you want.
You can also use the TRAPZ function to perform trapezoidal numerical integration. Here is an example:
%# parameters
a = 0; b = 1;
N = 100; s = 1;
f = #(x) x;
%# integration
X = linspace(a,b,N);
Y = f(X).*exp(-s*X);
If = trapz(X,Y) %# value returned: 0.26423
%# plot
area(X,Y, 'FaceColor',[.5 .8 .9], 'EdgeColor','b', 'LineWidth',2)
grid on, set(gca, 'Layer','top', 'XLim',[a-0.5 b+0.5])
title('$\int_0^1 f(x) e^{-sx} \,dx$', 'Interpreter','latex', 'FontSize',14)
The error message here is about as self-explanatory as it gets. You aren't defining a variable called x, so when you reference it on the first line of your function, MATLAB doesn't know what to use. You need to either define it in the function before referencing it, pass it into the function, or define it somewhere further up the stack so that it will be accessible when you call LaplaceTransform.
Since you're trying to numerically integrate with respect to x, I'm guessing you want x to take on values evenly spaced on your domain [0,1]. You could accomplish this using e.g.
x = linspace(a,b,N);
EDIT: There are a couple of other problems here: first, when you define g, you need to use .* instead of * to multiply the elements in the arrays (by default MATLAB interprets multiplication as matrix multiplication). Second, your calls g(a) and g(b) are treating g as a function instead of as an array of function values. This is something that takes some getting used to in MATLAB; instead of g(a), you really want the first element of the vector g, which is given by g(1). Similarly, instead of g(b), you want the last element of g, which is given by g(length(g)) or g(end). If this doesn't make sense, I'd suggest looking at a basic MATLAB tutorial to get a handle on how vectors and functions are used.