Here's the situation:
I need to create a function that takes a function handle fun which is of CONSTANT input-length (that is nargin(fun)>=0), does some transformation on the inputs and then calls fun.
Pseudo-Code:
function g = transformFun(fun)
n = nargin(fun);
g = #(v_1, ..., v_n) ...
% ^ NOT REAL MATLAB - THE MAIN PROBLEM
fun(someCalculationsWithSameSizeOfOutput(v_1,...v_n){:});
% CAN BE ACHIEVED WITH TEMPORARY CELL IN HELPER FUNCTION ^
end
Now the problem: the output function's handle (g = transformFun(concreteFun)) is then passed to other code that relies on the fact that the function is of constant length (assumes nargin(g)>=0), thus a variable-input-length function is unacceptable (the "easy" solution).
This transformation is called with many functions with every possible number of arguments (n is unbounded), so covering a finite number of possibilities is also not possible.
Is there a (simple?) way to achieve that?
[I've searched the internet for a few hours and could only come up with a nasty hack involving the deprecated inline function, which I couldn't make work; maybe I have the wrong terminology].
So typically you could use varargin to handle this sort of thing, but since you need nargin(g) to return the actual number of inputs it's a little trickier.
You could use str2func to create the anonymous function as a string and then convert it to a function handle.
% Create a list or arguments: x1, x2, x3, x4, ...
args = sprintf('x%d,', 1:nargin(func));
args(end) = '';
% Place these arguments into a string which indicates the function call
str = sprintf('#(%s)fun(someCalculationsWithSameSizeOfOutput(%s))', args, args);
% Now create an anonymous function from this string
g = str2func(str);
Based on the attrocity above, it may be worth considering an alternative way of dealing with your function handles.
Related
I have N functions in MATLAB and I can define them using strcat, num2str and eval in a for loop. So without defining by hand I am able to define N functions. Let N=4 and let them be given as follows:
f1=#(x) a1*x+1;
f2=#(x) a2*x+1;
f3=#(x) a3*x+1;
f4=#(x) a4*x+1;
Now I add these four functions and I can do this by hand as follows:
f=#(x)(f1(x)+f2(x)+f3(x)+f4(x));
Here I can do it by hand because I know that N=4. However, in general I never know how many functions I will have. For all cases I cannot write a new function.
Is there any way to do this automatically? I mean if I give N=6 I am expecting to see MATLAB giving me this:
f=#(x)(f1(x)+f2(x)+f3(x)+f4(x)+f5(x)+f6(x));
Whenever I give N=2 then I must have the function f, defined as follows:
f=#(x)(f1(x)+f2(x));
How can we do this?
First of all, you should read this answer that gives a series of reasons to avoid the use of eval. There are very few occasions where eval is necessary, in all other cases it just complicates things. In this case, you use to dynamically generate variable names, which is considered a very bad practice. As detailed in the linked answer and in further writings linked in that answer, dynamic variable names make the code harder to read, harder to maintain, and slower to execute in MATLAB.
So, instead of defining functions f1, f2, f3, ... fN, what you do is define functions f{1}, f{2}, f{3}, ... f{N}. That is, f is a cell array where each element is an anonymous function (or any other function handle).
For example, instead of
f1=#(x) a1*x+1;
f2=#(x) a2*x+1;
f3=#(x) a3*x+1;
f4=#(x) a4*x+1;
you do
N = 4;
a = [4.5, 3.4, 7.1, 2.1];
f = cell(N,1);
for ii=1:N
f{ii} = #(x) a(ii) * x + 1;
end
With these changes, we can easily answer the question. We can now write a function that outputs the sum of the functions in f:
function y = sum_of_functions(f,x)
y = 0;
for ii=1:numel(f)
y = y + f{ii}(x);
end
end
You can put this in a file called sum_of_functions.m, or you can put it at the end of your function file or script file, it doesn't matter. Now, in your code, when you want to evaluate y = f1(x) + f2(x) + f3(x)..., what you write is y = sum_of_functions(f,x).
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 begin with a symbolic function of one variable, calculate the symbolic derivatives of orders 1 through N, and then convert those symbolic functions into function handles and store the function handles in a cell array. I then evaluate each function handle at the same input value using a loop. The problem I have is that it is possible for one of the derivatives to be a constant (with higher order derivatives being zero, of course). As I was trying to give each function handle an input, I face the "Too many input arguments" error. I would like to be able to check, in advance, whether the function handle is a constant so I can avoid the error, but I can't figure out how to do that.
In case a small working example is helpful, I provide the following
symVar = sym('symVar');
startFunc = symVar^4 + symVar^3 + symVar^2;
derivesCell = cell(5);
for J=1:5
derivesCell(J) = {matlabFunction(diff(startFunc,symVar,J))};
end
cumSum = 0;
evalPoint = 2;
for J=1:5
cumSum = cumSum + derivesCell{J}(evalPoint);
end
Execution produces "Error using symengine>#()2.4e1
Too many input arguments."
tl;dr: You can do this with nargin:
>> nargin(derivesCell{5})
ans =
0
>> nargin(derivesCell{3})
ans =
1
Explanation:
Most people are familiar with the use of nargin as a "special variable" inside the function, but it can be used outside the context of a function definition, as a function that takes a function_handle argument, returning the number of input arguments that function handle takes. From the documentation:
NARGIN(FUN) returns the number of declared inputs for the
M-file function FUN. The number of arguments is negative if the
function has a variable number of input arguments. FUN can be
a function handle that maps to a specific function, or a string
containing the name of that function.
Matlab has the function Legendre that returns to an integer m and real number r a vector of length m+1.
Now I want to define another function fun that gives me only the first component of this vector per fixed m, so I want to define a function fun(m,r) that gives me the first component of the vector legendre(m,x). The point is that fun(m,r) should also be a function, just like legendre. Does anybody know how to do this?
Define the function as follows:
function out = fun(n,x)
temp = legendre(n,x); %// store output of "legendre" in a temporary variable
out = temp(1); %// return only desired element
Of course, this should be placed in a file fun.m within Matlab's path.
Alternatively, if you are feeling hackish, you can use
getfield(legendre(n,x), {1})
to extract the first element of legendre(n,x) directly (without a temporary variable). This allows defining fun as an anonymous function as follows:
fun = #(n,x) getfield(legendre(n,x), {1});
As a toy example, I have a class that simply wraps a vector or matrix in an object and includes a timestamp of when it was created. I'm trying to overload subsref so that
() referencing works exactly as it does with the standard vector and matrix types
{} referencing works in exactly the same way as () referencing (nothing to do with cells in other words)
. referencing allows me to access the private properties of the object and other fields that aren't technically properties.
Code:
classdef TimeStampValue
properties (Access = private)
time;
values;
end
methods
%% Constructor
function x = TimeStampValue(values)
x.time = now();
x.values = values;
end
%% Subscripted reference
function x = subsref(B, S)
switch S.type
case '()'
v = builtin('subsref', B.values, S);
x = TimeStampValue(v);
case '{}'
S.type = '()';
v = builtin('subsref', B.values, S);
x = TimeStampValue(v);
case '.'
switch S.subs
case 'time'
x = B.time;
case 'values'
x = B.values;
case 'datestr'
x = datestr(B.time);
end
end
end
function disp(x)
fprintf('\t%d\n', x.time)
disp(x.values)
end
end
end
However brace {} referencing doesn't work. I run this code
clear all
x = TimeStampValue(magic(3));
x{1:2}
and I get this error:
Error using TimeStampValue/subsref
Too many output arguments.
Error in main (line 3)
x{1:2}
MException.last gives me this info:
identifier: 'MATLAB:maxlhs'
message: 'Too many output arguments.'
cause: {0x1 cell}
stack: [1x1 struct]
which isn't helpful because the only thing in the exception stack is the file containing three lines of code that I ran above.
I placed a breakpoint on the first line of the switch statement in subsref but MATLAB never reaches it.
Whats the deal here? Both () and . referencing work as you would expect, so why doesn't {} referencing work?
When overloading the curly braces {} to return a different number of output arguments than usual, it is also necessary to overload numel to return the intended number (1, in this case). UPDATE: As of R2015b, the new function numArgumentsFromSubscript was created to be overloaded instead of numel. The issue remains the same, but this function should be overloaded instead of numel as I describe in the original answer below. See also the page "Modify nargout and nargin for Indexing Methods". Excerpt:
When a class overloads numArgumentsFromSubscript, MATLAB calls this method instead of numel to compute the number of arguments expected for subsref nargout and subsasgn nargin.
If classes do not overload numArgumentsFromSubscript, MATLAB calls numel to compute the values of nargout or nargin.
More explanation of the underlying issue (need to specify number of output arguments) follows.
Original answer (use numArgumentsFromSubscript instead of numel for R2015b+)
To handle the possibility of a comma separated list of output arguments when indexing with curly braces, MATLAB calls numel to determine the number of output arguments from the size of the input indexes (according to this MathWorks answer). If the number of output arguments in the definition of overloaded subsref is inconsistent with (i.e. less than) the number provided by numel, you get the "Too many output arguments" error. As stated by MathWorks:
Therefore, to allow curly brace indexing into your object while returning a number of arguments INCONSISTENT with the size of the input, you will need to overload the NUMEL function inside your class directory.
Since x{1:2} normally provides two outputs (X{1},X{2}), the definition function x = subsref(B, S) is incompatible for this input. The solution is to include in the class a simple numel method to overload the builtin function, as follows:
function n = numel(varargin)
n = 1;
end
Now the {} indexing works as intended, mimicking ():
>> clear all % needed to reset the class definition
>> x = TimeStampValue(magic(3));
>> x(1:2)
ans =
7.355996e+05
8 3
>> x{1:2}
ans =
7.355996e+05
8 3
However, overloading curly braces in this manner is apparently a "specific type of code that we [MathWorks] did not expect customers to be writing". MathWorks recommends:
If you are designing your class to output only one argument, it is not recommended that you use curly brace indexing that requires you to overload NUMEL. Instead, it is recommended you use smooth brace () indexing.
UPDATE: Interestingly, the R2015b release notes state:
Before MATLAB release R2015b, MATLAB incorrectly computed the number of arguments expected for outputs from subsref and inputs to subsasgn for some indexing expressions that return or assign to a comma-separated list.
With release R2015b, MATLAB correctly computes the values of nargout and nargin according to the number of arguments required by the indexing expression.
So perhaps this is now fixed?
An alternative solution that comes to mind is to change function x = subsref(B, S) to function varargout = subsref(B, S) and adding varargout=cell(1,numel(B)); varargout{1} = x;. As Amro noted in comments, pre-allocating the cell is necessary to avoid an error about an unassigned argument.
I just ran into the same problem. What's even worse, is that the number of output arguments is enforced to be equal to what numel() returns not only for the curly braces {}, but also for the dot . operation.
This means that if numel() is overridden to return the usual prod(size(obj)), it becomes impossible to access any properties of the underlying object (such as x.time in the above example), as subsref() is then expected to return multiple outputs.
But if numel() just returns 1 instead, it does not match prod(size(obj)), which is what most code working with numeric values or based on reshape() expects. In fact, the MATLAB editor's balloon help immediately suggests that 'NUMEL(x) is usually faster than PROD(SIZE(x))', which suggest that they are equivalent, but apparently are not.
A possible solution would be to make numel() return prod(size(obj)) and write explicit getter/setter functions for all these properties, e.g.,
x.get_time()
in the example above. This seems to work, because method calls apparently get resolved before subsref() gets called. But then if one of the properties is a matrix it cannot be directly indexed any more because Matlab doesn't understand chained indexing, i.e., instead of writing
x.matrix(1,:)
one would have to write
m = x.get_matrix();
m(1,:)
which is ugly to say the least.
This is starting to get a bit frustrating. I still hope I've just overlooked something obvious, I can't believe that this is how it's supposed to work.
This solution seems to work in 2014b (but not entirely certain why)
classdef TestClass < handle
methods
function n = numel(~,varargin)
n = 1;
end
function varargout = subsref(input,S)
varargout = builtin('subsref',input,S);
end
function out = twoOutputs(~)
out = {}; out{1} = 2; out{2} = 3;
end
end
end
Then via the command window
>> testClass = TestClass();
>> [a,b] = testClass.twoOutouts()
a =
2
b =
3
I am working on a class to handle polynomials and polynomial matrices. I was having the same dificulty because I want different behaviors for the '.' indexing in the cases of scalar polynomials and polynomial matrices.
In my case I want P.coef to return a vector of coefficients if P is a scalar polynomial. If P is a polynomial matrix, P.coef must return a cell array of the same size of P, in which the cell {i,j} contains the coefficient vector of the polynomial P(i,j).
The problem appeared when P.coef was used with a matrix. My desired behavior returns only one object as an answer, but Matlab is expecting the function to return numel(P) objects.
I found a very simple solution. When declaring subsref, I used one mandatory output and a varargout:
function [R,varargout] = subsref(P,S)
The body of the function defines R as needed, according to my design. And at the very end of the function I added:
varargout(1:nargout-1) = cell(1,nargout-1);
To just return empty matrices as the extra outputs that Matlab wants.
This should create no problem if the function is always called with a single output argument, e.g., as in R = P.coef. If the function is called without assigning, the user will see numel(P)-1 empty matrices, which is really not a big deal. Anyway, the user is warned about this in the function help.