I have a vector v and would like to define a function x using following formular:
Now I try to define this in Matlab, but for some reason I can't access an array within a symsum.
v = [1 2 3 4];
syms k
x = #(t) symsum(v(k) * exp(2*pi*i*k*t/size(v)), k, 1, size(x_n));
When I try to evaluate this Function x(4) I get an exception:
Error using sym/subsindex (line 796)
Invalid indexing or function definition. When defining a function, ensure that the arguments are
symbolic variables and the body of the function is a SYM expression. When indexing, the input
must be numeric, logical, or ':'.
Do you know, why? Do you have a solution or workaround?
Related
I want to define a vector,X, with five elements:
syms a
X = zeros(1,5)
X(1) = 1;
for k=1:4
X(k+1)=X(k)+a^2;
end
Actually I need to have the vector X, that its elements should be based on variable a. But I face an error in Matlab, when I write the code above:
The following error occurred converting from sym to double:
Error using symengine (line 58)
DOUBLE cannot convert the input expression into a double array.
If the input expression contains a symbolic variable, use VPA.
Error in Code2 (line 5)
X(k+1)=X(k)*a^2;
How to fix this?
You are mixing between symbolic variables to doubles,
Doubles holds a value, you can use the loop that you wrote only if a is a double and already holds a value (the value can be the input of a function) .
for example :
function ret=testFunc(a)
X = zeros(1,5)
X(1) = 1;
for k=1:4
X(k+1)=X(k)+a^2;
end
ret=X
end
if you want to work with syms (for other symbolic analysis) you can define x as a symbol too, for example :
syms a x
x(1)=1;
for i=2:5
x(i)=x(i-1)+a.^2;
end
now, x is a function of a, and if you print x you will get :
[ 1, a^2 + 1, 2*a^2 + 1, 3*a^2 + 1, 4*a^2 + 1]
to evaluate the value of x, you will still need to input a value for a.
Matlab help suggest subs function for replacing a in wanted value as follows:
y = subs(x,a,4)
in that point y is still a symbol and you will need to make it a double by using
double(y)
I am having trouble using fminsearch: getting the error that there were not enough input arguments for my function.
f = #(x1,x2,x3) x1.^2 + 3.*x2.^2 + 4.*x3.^2 - 2.*x1.*x2 + 5.*x1 + 3.*x2 + 2.*x3;
[x, val] = fminsearch(f,0)
Is there something wrong with my function? I keep getting errors anytime I want to use it as an input function with any other command.
I am having trouble using fminsearch [...]
Stop right there and think some more about the function you're trying to minimize.
Numerical optimization (which is what fminsearch does) is unnecessary, here. Your function is a quadratic function of vector x; in other words, its value at x can be expressed as
x^T A x + b^T x
where matrix A and vector b are defined as follows (using MATLAB notation):
A = [ 1 -1 0;
-1 3 0;
0 0 4]
and
b = [5 3 2].'
Because A is positive definite, your function has one and only one minimum, which can be computed in MATLAB with
x_sol = -0.5 * A \ b;
Now, if you're curious about the cause of the error you ran into, have a look at fuesika's answer; but do without fminsearch whenever you can.
It is exactly what Matlab is telling you: your function expects three arguments. You are passing only one.
Instead of
[x, val] = fminsearch(f,0)
you should call it like
[x, val] = fminsearch(f,[0,0,0])
since you define the function f to accept a three dimensional vector as input only.
You can read more about the specification of fminsearch in the online documentation at http://mathworks.com/help/matlab/ref/fminsearch.html:
x = fminsearch(fun,x0) starts at the point x0 and returns a value x
that is a local minimizer of the function described in fun. x0 can be
a scalar, vector, or matrix. fun is a function_handle.
I have a symbolic ODE:
syms x1 x2 cs ks ms t2 real
xx=[x1 x2];
fun_sym=[xx(2); (cs/ms)*(xx(1)^2-1)*xx(2) - (ks/ms)*xx(1)];
I want to solve it using ODE function, but first I need to convert it into function handle:
v=matlabFunction(fun_sym,'vars', [t2,xx,cs,ks,ms]);
[T,x]= ode15s(#(t2,xx) v,t,[1 0]);
where t=[0:0.1:1]. Matlab gives an error:
#(T2,XX)V returns a vector of length 1, but the length of initial conditions vector is 2.
I think this is because it interpret v as: #(t2,x1,x2,cs,ks,ms), so it expects the second argument to be x1, which is a 1-by-1 element, even though I have defined v as [t2,xx,...], where xx is a 1-by-2 element. How can I solve this issue?
This works, but you need to give values to the other parameters as well (cs, ks, and ms)
v=matlabFunction(fun_sym,'vars', [t2,x1,x2,cs,ks,ms]);
[T,x]= ode15s(#(t2,xx) v(t2,xx(1),xx(2),cs,ks,ms),t,[1 0]);
I need help figuring out how to code the following problem. Any help would be greatly appreciated!
Create a function that will take a vector/array input for x (1 by n) and a scalar input for a, and produce the output defined by the following equation:
y(x,a)=((xsin(ax-2))/(sqrt(1+(ax)^2)
-π ≤ x ≤ π
a={.5 1 1.5 2}
The equation must be vectorized in terms of x and the output from the function is the array y which has the same dimension as the array x.
Write a script that calls this function to compute y(x,a) for the range of x defined above and each value of the parameter a. Results should be stored in a solution matrix using a different row of the solution matrix for each value of a.
So far for my function I have:
function [y] = part1(a,x)
y=((x*sin(a*x-2))/(sqrt(1+(a*x).^2)));
end
I'm not sure how to output this into the solution matrix
For my script I have:
%%
clear,clc
a={0.5 1 1.5 2};
x=-pi:0.1:pi;
for
part1(x,a)
end
I'm getting the following errors when I run this now:
Undefined function 'mtimes' for input arguments of type 'cell'.
Error in part1 (line 4)
y=((x*sin(a*x-2))/(sqrt(1+(a*x).^2)));
Error in labtest2 (line 8)
y(i,:)=part1(x,a(i));
EDIT
I've made some changes and am still getting some errors that I cannot resolve.
Here is my full code for function followed by full code for script:
Function
function [y] = part1(x,a)
nx=numel(x);
na=numel(a);
y=((x.*sin(a.*x-2))./(sqrt(1+(a.*x).^2)));
size(y)=[nx na]
end
Script
%%
clear,clc
a={0.5 1 1.5 2};
x=-pi:0.1:pi;
for i = 1:length(a)
y(i,:)=part1(x,a(i));
end
Errors
Undefined function 'times' for input arguments of type 'cell'.
Error in part1 (line 6)
y=((x.*sin(a.*x-2))./(sqrt(1+(a.*x).^2)));
Error in labtest2 (line 8)
y(i,:)=part1(x,a(i));
The reason you're getting Undefined function 'times' for input arguments of type 'cell' is because your variable a is a cell array. You need to change your assignment of a from
a={0.5 1 1.5 2};
to
a=[0.5 1 1.5 2];
which will make it just a normal array. Alternatively, you need to reference it with cell array notation: a{i} instead of a(i).
You're almost there. Note that you've written
function [y] = part1(a,x)
but you call it in your script as
part1(x,a)
so you should probably correct that.
A few things jump out at me:
You never assign the output of part1(x,a) to anything. You're told that
Results should be stored in a solution matrix using a different row of the solution matrix for each value of a.
What I take this to mean is that the 1st row corresponds to part1() evaluated for the 1st element of a. Since we're operating on x which is a vector, that row will have multiple columns. Your output is indeed a matrix. In your case, length(-pi:0.1:pi) == 63, therefore size(y) == [4 63], where y is your output matrix.
Your for loop is backwards. You're told to accept scalar a and vector x. Therefore, your script should be something like:
a = 0.5:0.5:2;
x = -pi:0.1:pi;
for i = 1:length(a)
y(i,:) = part1(x, a(i));
end
Note the use of length and the : operator. I want to iterate between 1 to length(a) (in this case, length(a) == 4) so that I can use the current a(i) value as an index into my output matrix, y. The : operator in y(i,:) signifies "The ith row and all columns of y will take the value output by part1(x,a(i))."
Your function needs to be changed up for element-by-element operations. Notice that, for instance, x*sin(a*x-2) works for scalar x but not vectors. This is because x is a vector and sin(a*x-2) is also a vector (since the sin call will operate element-by-element and a is a scalar). Trying to multiply two vectors together will result in errors since MATLAB will try to perform a matrix multiplication. Resolve this by replacing * with .*. This way it is unambiguous that you are going to multiply these two vectors element-by-element. You'll also need to change / to ./.
On another note, thank you for attempting to do your homework before asking SO for help. We've been getting a huge influx of questions from students that have made no attempt to do their own work before dumping it on us, so it's refreshing that we regulars of the MATLAB tag get to actual help out instead of telling people to do their own work.
Finally got the whole thing worked out.
Function
function [y] = part1(x,a)
y=((x.*sin(a.*x - 2))./(sqrt(1 + (a.*x).^2)));
end
Script
%%
clear all;
clc;
close all;
x=[-pi:.1:pi];
a=[.5:.5:2];
for i=1:length(a)
y(i,:)=part1(x,a(i));
plot(x,y)
end
Sol=[y]
I want to put a function in feval(f,x) that has a vector as input
e.g.
function [ ret ] = f (x)
ret = x(1)^2 - x(2)^2;
end
and
x = [1,2]
but octave always gives an error code:
`x' undefined near line 6 column 18
evaluating argument list element number 1
evaluating argument list element number 1
It seems feval can only evaluate numbers and not vectors. Is there any way to do this?
Create a handle to your function and then call feval on the handle, passing it your vector as its argument:
h = #(x)myfun(x);
x = [1, 2];
y = feval(h, x);
I tried this out in Octave on your function and it seems to work.