I have a bunch of anonymous functions stored in a cell array as follows:
F = {#(x) x + 1, #(x) x * x}
I want to create a new anonymous function to add them all up and average the result given an input x. F can have arbitrary number of function handles and is generated at run time. If F is known, then it is simply f = #(x) (F{1}(x) + F{2}(x)) / length(F). But I don't know how to append all elements of F onto this new anonymous function (presumably in a loop?) How would I do this?
Use cellfun to define a function that evaluates each function f in F using just one line. An anonymous function handle for arbitrary F and x is as follows:
F = {#(x) x + 1, #(x) x * x};
%// Build anonymous function that evaluates each function, sums,
%// divides by length of F
new_F = #(x,F)sum(cellfun(#(f)f(x), F)) / length(F);
Then, to evaluate, simply call:
x = 2; %// data to apply fcns on
result = new_F(x, F)
Related
I want to integrate x^2 from 2 to 4 with the trapezoidal integration method. For this, I defined a function trap that takes 4 arguments:
function y = trap( fn, a, b, h )
n = (b-a)/h;
x = a + [1:n-1]*h;
y = h/2*(feval(fn, a) + feval(fn, b) + 2*sum(feval(fn,x)));
and a function f
function y= f(x)
y=x^2
end
Now, by executing trap(f,2,4,0.1), I get the following error:
Not enough input arguments.
Error in f (line 2)
y=x^2
What is the origin of that error?
You have to call trap using the function handle #f, not f.
trap(#f,2,4,0.1)
function y = trap( fn, a, b, h )
n = (b-a)/h;
x = a + [1:n-1]*h;
y = h/2*(fn(a) + fn(b) + 2*sum(fn(x)));
end
function y= f(x)
y = x.^2;
end
which gives, as expected,
ans =
18.67
Also you needed element-wise multiplication in f(x) to compute y = x.^2.
And feval is not necessary. You can directly call fn(a) to evaluate the function.
syms c A(t) v(t)
A(t) =
0
c*sin(tt(t))
c*cos(tt(t))
How I can get X = A(2) = c*sin(tt(t)); (the function at second row)? If I type A(2), the result will be as below (it substitutes a constant for the function, which is not my desire):
>> A(2)
ans =
0
c*sin(tt(2))
c*cos(tt(2))
The problem is that you've defined A as a symbolic function (symfun), not as an array of symbolic expressions. Instead:
syms c A tt(t)
A = [0;
c*sin(tt(t));
c*sin(tt(t))];
Now A(2) will return c*sin(tt(t)).
Alternatively, if you can't change the definition of A(t), you'll need to assign it to an intermediate variable to convert it to an array of symbolic expressions:
syms c A(t) tt(t)
A(t) = [0;
c*sin(tt(t));
c*cos(tt(t))];
B = A(t);
Then, B(2) will return c*sin(tt(t)). You can also use formula to extract the underlying expressions:
B = formula(A):
In matlab you must to use "subs(f)" function to evaluate functions.
First create the function:
syms g(x)
g(x) = x^3;
After that asign the X value:
x=2;
then if you evaluate g using the subs function, the result is the expected value 8, but it is assigned to a symbolic function, gnew. This new symbolic function formally depends on the variable x.
gnew = subs(g)
The function call, g(x), returns the value of g for the current value of x. For example, if you assigned the value 2 to the variable x, then calling g(x) is equivalent to calling g(2)
g2 = g(x)
g2 =
4
g2 = g(2)
g2 =
4
I am having trouble with printing out h_a_b. I am able to get functions f and g but not this one. I need to use h_a_b function so i can do h(f(x),g(x)) and calculate the sqrt of h(a,b). see equations
I am always getting this error
Undefined function 'h_a_b' for input arguments of type 'function_handle'.
I am suppose to write a program that create 3 anonymous functions representing the function
Equations needed
f(x) = 10*cos x ,
g(x) = 5*sin * x, and
h(a,b) = \sqrt(a^2 + b^2).
Here is my code
f = # (x) 5*sin(x);
g = # (x) 10*cos(x);
h_a_b = # (a,b) sqrt(a.^2 + b.^2);
then I plot it with this function that was given to me.
function plotfunc(fun,points)
%PLOTFUNC Plots a function between the specified points.
% Function PLOTFUNC accepts a function handle, and
% plots the function at the points specified.
% Define variables:
% fun -- Function handle
% msg -- Error message
%
msg = nargchk(2,2,nargin);
error(msg);
% Get function name
fname = func2str(fun);
% Plot the data and label the plot
plot(points,fun(points));
title(['\bfPlot of ' fname '(x) vs x']);
xlabel('\bfx');
ylabel(['\bf' fname '(x)']);
grid on;
end
Because your function (h_a_b) takes a vector as input and gives scalar as output it represents a surface, thus plot cannot be used to visualize it (that is only for 2D, scalar-scalar plots).
Are you looking for something like this?:
f = # (x) 5*sin(x);
g = # (x) 10*cos(x);
h_a_b = # (a,b) sqrt(a.^2 + b.^2);
z = #(a,b) sqrt(h_a_b(f(a),g(b)));
[A, B] = meshgrid(0:0.1:8, 0:0.1:9);
Z = z(A,B);
surfc(A,B,Z)
xlabel('a')
ylabel('b')
figure
contourf(A,B,Z)
xlabel('a')
ylabel('b')
Second option, considering z as scalar-scalar function and using your plotfunc function:
f = # (x) 5*sin(x);
g = # (x) 10*cos(x);
h_a_b = # (a,b) sqrt(a.^2 + b.^2);
z = #(x) sqrt(h_a_b(f(x),g(x)));
points = 0:0.1:8;
plotfunc(z,points)
Which is one slice of the above surface.
I'm trying to define g function in matlab and should be like this g(x) = x + f(x);
x is a number
f is an inline function
None of the following works:
g = x + f(x)
g = inline(x+f);
g = inline(sum(x,f));
Issue: You need to Nest an inline function inside another function
Problems with your code:
Enclose items inside the parenthesis of an inline function in single quotes
Do Not enclose items in parenthesis of an anonymous function in single quotes
Use f(x) when nesting it inside another function to indicate that its a function
Solution: You can either Nest an anonymous function or an inline function inside another anonymous or inline function, like so:
>> f = inline('x.^2') %Or: f = #(x) (x.^2)
>> g = inline('x + f(x)') %Or: g = #(x) (x + f(x))
Now,
>> g(2.5)
ans = 8.75
This is a part of my code.
clear all;
clc;
p = 50;
t = [-6 : 0.01 : 6];
f = inline('(t+2).*sin(t)', 't')
v = inline('3*f(p*t+2)','t','f','p')
plot(t,f(t));
v(t,f,p);
figure;
plot(t,v(t,f,p));
Here I have two questions.
Why I have to pass p into the function v even though p is a constant which has already declared ?
How I can get an expression for v completely in terms of t as 3*[(50*t+2)*sin(50*t+2)] or in its simplified form ?
Update
This is an update for the second question
Let
f(x) = 1 + x - x^2
g(x) = sin(x)
If I give f(g(x)), I wanna get the output in words, like this
f(g(x)) = (cos(X))^2 + sin(x)
not in numerical value. Is there any function capable to do that?
1) Why do I have to pass p to v even though p is a constant which has already been declared?
Well, a MATLAB's inline function object has an eval wrapper, so the only variables in its scope are those which were automatically captured from the expression or explicitly specified.
In other words, if you want v to recognize p, you have no other option but declaring it when creating the inline object and passing it to v explicitly. The same goes for f as well!
2) How I can get an expression for v completely in terms of t as 3*[(50*t+2)*sin(50*t+2)] or in its simplified form?
Use anonymous functions, like Shai suggested. They are more powerful, more elegant and much faster. For instance:
v = #(t)(3*(50*t+2)*sin(50*t+2))
Note that if you use a name, which is already in use by a variable, as an argument, the anonymous function will treat it as an argument first. It does see other variables in the scope, so doing something like g = #(x)(x + p) is also possible.
EDIT #1:
Here's another example, this time a function of a function:
x = 1:5;
f = #(x)(x .^ 3); %// Here x is a local variable, not as defined above
g = #(x)(x + 2); %// Here x is also a local variable
result = f(g(x));
or alternatively define yet another function that implements that:
h = #(x)f(g(x)); %// Same result as h = #(x)((x + 2) .^ 3)
result = h(x);
The output should be the same.
EDIT #2:
If you want to make an anonymous function out of the expression string, concatenate the '#(x)' (or the correct anonymous header, as you see fit) to the beginning and apply eval, for example:
expr = '(x + 2) .^ 3';
f = eval(['#(x)', expr]) %// Same result as f = #(x)((x + 2) .^ 3)
Note that you can also do char(f) to convert it back into a string, but you'll have to manually get rid of the '#(...)' part.
EDIT #3:
If you're looking for a different solution, you can explore the Symbolic Toolbox. For example, try:
syms x
f(x) = x + 2
g(x) = x ^ 3
or can also use sym, like so:
f(x) = sym('x + 2');
g(x) = sym('x ^ 3');
Use subs to substitute values and evaluate the symbolic expression.
How about using anonymous functions:
p = 50;
t = -6:0.01:6;
f = #(x) (x+2).*sin(x);
v = #(x) 3*f(p*x+2);
figure;
subplot(1,2,1); plot( t, f(t) ); title('f(t)');
subplot(1,2,2); plot( t, v(t) ); title('v(t)');
Is this what you wanted?
Adding a constant into an inline can be done during its definition.
Instead of
p = 50;
v = inline('3*f(p*t+2)','t','f','p')
You can write
p = 50;
v = inline( sprintf('3*f(%f*t+2)', p), 't','f')