Suppose I have a column matrix pols containing vectors of [theta, rho, z].
Which means, if I have 9 such vectors, it will be a 9x3 matrix.
It is quite handy to have them arranged as such, because I can just feed any one of them to functions like pol2cart:
cart3 = pol2cart(pols(3,:));
and for a certain vector, I can find its components via the indices 1, 2, 3:
rho5 = pols(5,2);
But sometimes the matrix is actually within another wider matrix, and could be in the middle instead of the beginning, such that the above might become:
rho5 = pols(5,6);
In order to make the code more readable in case someone else has to maintain it, is there anyway to refer to an index via a unique name? Like
rho5 = pols(5).rho;
where it could be defined earlier that .rho maps to the column which has the value of rho.
I've ventured into converting matrices to cells then to array using mat2cell and cell2struct but it doesn't seem practical. Or, I could make an array of structs, but then I lose the ability to do pol2cart(pols), and instead must do
pol2cart(pols.theta, pols.rho, pols.z);
So to repeat the question: can I map the indices to unique names?
For the default MATLAB data types, no, you can't really do that. You could, however, create your own new data type (i.e. class object) to store your data. Within the class definition you would overload the subsref method to define how subscripted referencing (i.e. using (), {}, or .) behaves for your new object. This could get rather tricky with regards to dealing with arrays of objects, but it is possible.
Note that you would also have to create overloaded methods for all the existing functions you want to use on your new data type. Specifically, you would have to create a pol2cart method for your object that could internally call the built-in pol2cart function with the appropriate pieces of data from your object passed as arguments.
...And this brings me to a simpler solution for your current situation. Instead of making a whole new type of class object, you could create a structure array (or scalar structure of arrays) to store your data and simply create a new overloaded pol2cart function specifically for struct data types that will simplify the calling syntax.
I discuss more details of overloading functions for built-in data types in two other answers here and here. In short, you would create a folder called #struct and place it in a folder on your MATLAB path. In this #struct folder you would then put this overloaded function:
function varargout = pol2cart(polarCoordinates)
[varargout{1:nargout}] = pol2cart(polarCoordinates.theta, ...
polarCoordinates.rho, ...
polarCoordinates.z);
end
Note that this is a stream-lined version of the function, without error checks on the input, etc. Now, let's make some sample data:
pols = rand(9, 3); %# A 2-D array of data
polStruct = struct('theta', pols(:, 1), ... %# Convert it to a scalar
'rho', pols(:, 2), ... %# structure of arrays
'z', pols(:, 3));
And you could access the rho value of the fifth row as follows:
rho5 = pols(5,2);
rho5 = polStruct.rho(5);
If you wanted to convert from polar to cartesian coordinates, here's how you would do it for each data type:
[X,Y,Z] = pol2cart(pols(:,1), pols(:,2), pols(:,3)); %# Calls the built-in one
[X2,Y2,Z2] = pol2cart(polStruct); %# Calls the overloaded one
And you can check that they each give identical results as follows:
>> isequal([X Y Z],[X2 Y2 Z2])
ans =
1 %# True!
OK, the formal answer is probably "no" as given by woodchips above. However, if you really want to do something like that, you might be able to use a semi-hack. Specifically, you can define a class and overload an operator to achieve (almost) what you want. Unfortunately, I see that Matlab doesn't allow overloading ., so you have to use some other operator. (see edit below)
Just to give you the idea, here is a class that returns the i-th row of a matrix M by M^i.
classdef Test
properties
M;
end
methods
function this = Test(M)
this.M = M;
end
function res = mpower(this, i)
res = this.M(i, :);
end
end
end
And it can be run like this:
>> tmp = Test([1 2; 3 4]);
>> tmp^1
ans =
1 2
>> tmp^2
ans =
3 4
Use at your own risk! :)
Edit:
I was wrong above. As mentioned in gnovice's answer you can actually define the . operator for a custom class using method subsref.
No. You cannot do so. As simple as that.
Related
I have to run a Matlab loop indexed by x. At each iteration, I have to load and work with an array, A_x.mat, where the subscript x follows the loop index. How can I do that? Let me give you and example to highlight my issue. The example is very silly but serves my purposes.
X=10;
C=cell(X,1)
for x=1:X
load(['A_' num2str(x) '.mat']); %here I load A_x.mat
%C{x}=A_x*3;
end
I don't know how to compute A_x*3 in a way that allows the subscript x to vary. Could you advise?
To solve my issue I also tried
for x=1:X
B=load(['A_' num2str(x) '.mat']); %here I load A_x.mat and "rename" it B
%C{x}=B*3;
end
but B turns out to be a 1x1 struct with 1 field that is again A_x. Hence, I have not solved anything.
You can save the structure subfield name as a char and access the structure with it directly:
X=10;
C=cell(X,1)
for x=1:X
name = ['A_', num2str(x)];
data_structure = load([name, '.mat']); %here I load A_x.mat
C{x} = data_structure.(name) * 3;
end
Note that you could achieve something similar with eval() but that is not recommended. If ever you need to access variables dynamically like this, use a structure.
Good evening everyone,
I want to create a function
f(x) = [f1(x), f2(x), ... , fn(x)]
in MatLab, with an arbitrary form and number for the fi. In my current case they are meant to be basis elements for a finite-dimensional function space, so for example a number of multi variable polynomials. I want to able to be able to set form (e.g. hermite/lagrange polynomials, ...) and number via arguments in some sort of "function creating" function, so I would like to solve this for arbitrary functions fi.
Assume for now that the fi are fi:R^d -> R, so vector input to scalar output. This means the result from f should be a n-dim vector containing the output of all n functions. The number of functions n could be fairly large, as there is permutation involved. I also need to evaluate the resulting function very often, so I hope to do it as efficiently as possible.
Currently I see two ways to do this:
Create a cell with each fi using a loop, using something like
funcell{i}=matlabFunction(createpoly(degree, x),'vars',{x})
and one of the functions from the symbolic toolbox and a symbolic x (vector). It is then possible to create the desired function with cellfun, e.g.
f=#(x) cellfun(#(v) v(x), funcell)
This is relatively short, easy and what can be found when doing searches. It even allows extension to vector output using 'UniformOutput',false and cell2mat. On the downside it is very inefficient, first during creation because of matlabFunction and then during evaluation because of cellfun.
The other idea I had is to create a string and use eval. One way to do this would be
stringcell{i}=[char(createpoly(degree, x)),';']
and then use strjoin. In theory this should yield an efficient function. There are two problems however. The first is the use of eval (mostly on principle), the second is inserting the correct arguments. The symbolic toolbox does not allow symbols of the form x(i), so the resulting string will not contain them either. The only remedy I have so far is some sort of string replacement on the xi that are allowed, but this is also far from elegant.
So I do have ways to do what I need right now, but I would appreciate any ideas for a better solution.
From my understanding of the problem, you could do the straightforward:
Initialization step:
my_fns = cell(n, 1); %where n is number of functions
my_fns{1} = #f1; % Assuming f1 is defined in f1.m etc...
my_fns{2} = #f2;
Evaluation at x:
z = zeros(n, 1);
for i=1:n,
z(i) = my_fns{i}(x)
end
For example if you put it in my_evaluate.m:
function z = my_evaluate(my_fns, x)
z = zeros(n, 1);
for i=1:n,
z(i) = my_fns{i}(x)
end
How might this possibly be sped up?
Depends on if you have special structure than can be exploited.
Are there calculations common to some subset of f1 through fn that need not be repeated with each function call? Eg. if the common calculation step is costly, you could do y = f_helper(x) and z(i) = fi(x, y).
Can the functions f1...fn be vector / matrix friendly, allowing evaluation of multiple points with each function call?
The big issue is how fast your function calls f1 through fn are, not how you collect the results from those calls in a vector.
I am trying to understand the following commands of a MATLAB script :
global operatorObj
calcEVR_handles = operatorObj.calcEVR_handles;
m = operatorObj.nInputs
E = zeros(m,1);
V = zeros(m,1);
R = zeros(m,m);
for i=1:m
[E(i), V(i), R(i,i)] = calcEVR_handles{i}(t,x);
end
What can calcEVR_handles be, if t is a float and x is a vector?
calcEVR_handles (to me) looks like a cell array where each element is a handle to a function. Each element in calcEVR_handles is an anonymous function that takes in a single value t and a single vector x. As such, by doing calcEVR_handles{i}, you would access the corresponding function stored at the ith element in the cell array. Once you have access, you then pass your parameters to this function and it gives you those three outputs.
To show you an example of this working, consider the following cell array that works similarly to calcEVR_handles.
calcCellFunc = {#sin, #cos, #tan};
This is a three element cell array, where each element is a handle to a function. The # is a special character in MATLAB that denotes that you are creating a handle to a function. It's also used to create anonymous functions, but let's shelve that for this answer. You can read more about it here if you want to delve into more detail regarding this.
Back to our cell array of handles, we will make handles for sin, cos and tan. You can then iterate over your cell array by accessing the function you want by calcCellFunc{idx} where idx is the element you want in the cell array. This will ultimately give you the function stored at index idx. Once you do that, you can then call the function and specify whatever inputs you want (or none if it doesn't take any inputs). Here's a quick example for you. Let's create a random 5 x 5 matrix, and run through each function with this matrix serving as the input. We then take each of these outputs and store them into a corresponding slot in an output cell array. As such:
rng(123); %// Set seed for reproducibility
M = rand(5);
calcCellFunc = {#sin, #cos, #tan};
out = cell(1, numel(calcCellFunc)); %// To store the results for each function
for idx = 1 : numel(calcCellFunc)
out{idx} = calcCellFunc{idx}(M); %// Get the function, then pass
%// the matrix M to it
end
If you want to make things clear, you could split up the out statement to this instead:
func = calcCellFunc{idx}; %// Get access to the function
out{idx} = func(M); %// Pass M to this function
If you're new to handles / anonymous functions, you should probably use the above code first to make it explicitly clear on what MATLAB is doing. You are first getting access to the function you want that is stored in the cell array, and then you pass your arguments to this function.
If we display the output, we get:
>> celldisp(out)
out{1} =
0.6415 0.4106 0.3365 0.6728 0.5927
0.2823 0.8309 0.6662 0.1815 0.7509
0.2249 0.6325 0.4246 0.1746 0.6627
0.5238 0.4626 0.0596 0.5069 0.5737
0.6590 0.3821 0.3876 0.5071 0.6612
out{2} =
0.7671 0.9118 0.9417 0.7398 0.8054
0.9593 0.5564 0.7458 0.9834 0.6604
0.9744 0.7745 0.9054 0.9846 0.7489
0.8518 0.8866 0.9982 0.8620 0.8191
0.7522 0.9241 0.9218 0.8619 0.7502
out{3} =
0.8363 0.4503 0.3573 0.9094 0.7359
0.2942 1.4934 0.8932 0.1845 1.1370
0.2308 0.8167 0.4690 0.1773 0.8850
0.6149 0.5218 0.0597 0.5880 0.7004
0.8761 0.4135 0.4205 0.5884 0.8814
The first element of the output cell array has the output when you pass M to sin, the second when you pass M to cos, and the third when you pass M to tan.
So the next question you're asking... why is this useful?
Point #1 - Nix the copying and pasting
This kind of code writing is very useful because if you want to use the same inputs and supply them to many different functions, we would naturally be inclined to do some copying and pasting. Take each of your function names, and create a single line for each. Each line would call the corresponding function you want, followed by the input arguments. This can become quite tedious, and so one smart way to do it would be to place your function name as a handle into a cell array, and to write one for loop that goes over all of the functions dynamically. You could even explore cellfun and escape using the for loop to iterate over all of the function handles too, but I'll leave that for you to read up on.
In this way, you have very maintainable code and if you want to remove functions that don't need to be run, just remove the handles from the cell array rather than scrolling down to where the line that invokes this function is located and removing that.
This is actually a very common technique in computer science / software engineering in general. In fact, this is actually quite close to what are known as function pointers. This is MATLAB's cheap way of doing it, but the logic behind this is essentially the same.
Point #2 - Higher Order Functions
Another way this is useful is if you have a function where one (or more than one!) of the inputs is a function, and you also specify inputs into this function as additional parameters to this function. This is what is known as a higher order function. The outputs would be based on using this input function, and the additional inputs you specify to it and the outputs are based on using this input function and the inputs you specify for this function.
One very good example is the fzero function in MATLAB. The goal is to find the root of a non-linear function, and the first parameter is a handle to a function that you specify. The base behaviour behind how fzero works is the same no matter what the function is. All you have to do is specify the function you want to solve and the initial guess of where you think this root is.
All in all, anonymous functions are very useful.
I am trying to store a set of object handles in an array. The objects are a series of lines generated by imline(.). I want to store the handles in order to be able to change the property of a desired line (in this case, position).
I know how to do this - however, when I try to fill a matrix with the handles of lines, an error occurs - MATLAB states that conversion from IMLINE to DOUBLE is not possible. This does not happen with other types of objects. Is there a way to circumvent this?
Here is some pseudocode to clarify:
lines=zeros(1,x); % defining empty storage matrix
for idx=1:x
line=imline(ax_handl,[x_1 y_1; x_2 y_2])
set(line,'UserData',idx) % in order to identify independent lines with the number
lines(idx)=line; % here I try to store a line handle as it's made
end
% now in the function responsible for motion of objects, I assign new position to line
line_num=get(gco,'UserData'); % this relates other objects associated with line number
setPosition(lines(line_num),[a b; c d]);
Use the empty static method to create an empty array of the class type:
lines = imline.empty(0,10);
for idx=1:10
line = imline(gca, sortrows(rand(2,2)));
set(line,'UserData',idx)
lines(idx) = line;
end
You may need to fill your matrix with default valued lines in order to create it. The typical approach to preallocating a matrix of objects of size N would be to simply assign an object to the last element in the matrix.
M(N,N)=imline(gca,[NaN NaN],[NaN NaN]); %# set non-displayable vals for x and y
NOTE, the line above will not work with imline as it will call the default constructor for each of the other N*N-1 imline objects in the matrix and a call of imline with no arguments forces user interaction with the current axis.
My advice (if you are pre-allocating) is to define all the default lines explicitly in the matrix:
for k=1:N*N
M(k)=imline(gca,[NaN NaN],[NaN NaN]);
end
%# Reshape (if necessary)
M = reshape(M,[N N]);
Alternatively, you could let Matlab fill the array for you. If you find that you will need this code often, derive a new class from imline. The following example shows the very least that would need to happen. It merely defines a constructor. This example allows you to pass optional arguments to imline as well. If no arguments are specified, the imline object is created with position values as above.
classdef myimline<imline
methods
function obj = myimline(varargin)
if isempty(varargin)
varargin = {gca,[NaN NaN],[NaN NaN]};
end
obj = obj#imline(varargin{:});
end
end
end
Example usage:
%# Generate a 100 element array of `imline` objects,
%# but define the last one explicitly
mat(100)=myimline(gca,[0 1],[0 1]);
The last myimline object in the array has points specified as in the assignment, but the rest of the elements have the default position values [NaN NaN] as above.
I have a system of equations contained in an anonymous equation. Instead of defining all of the equations when i create the function, I would like to add one in each step of a for loop. Is this possible?
I suppose if you have a linear set of equations, you can construct it using a matrix, then you're free to include new operations by adding rows and columns to the matrix and/or its accompanying right hand side vector.
If you're really trying to use anonymous functions, say if your functions are non-linear, then I would suggest you to look into arrays of anonymous functions. For example,
A = cell(3,1); % Preallocate a 3 by 1 cell array
for ii = 1:3
A{ii} = #(x) x^2+ii; % Fill up the array with anonymous functions
end
Now if you check what's contained in cell array 'A',
A = #(x)x^2+ii
#(x)x^2+ii
#(x)x^2+ii
Don't worry about the display of 'ii' instead of the actual number of the loop variable as we gave it earlier, MATLAB has internally replaced them with those values. Changing 'ii' in the current function scope will also not affect their values in 'A' either. Thus,
A{1}(2) = 5, A{2}(2) = 6 and A{3}(2) = 7
If you're not familiar with cell arrays, you can read up on its usage here.
Again, what you're trying to achieve might be different. I hope this works for you.