I'm pretty new on Julia and have a question that may appear simple. Say I have a function, which I will name test(x::Vector, arg1, arg2) where x is a vector of variables and the function has two arguments arg1 & arg2.
I would like to optimize (minimize) the function test with respect to the vector x. I can't figure out how to use the optimize function from the Optim package that accepts two arguments values. In R, one may do as following:
optim(initial guest, test, arg1=value1,arg2=value2)
Is there a similar way to declare argument value in Julia?
You can define another function that fixes the value of those arguments.
# Function to minimize
f(x::Vector, a, b) = (x[1] - a)^2 + (x[2] - b)^2
using Optim
g(x::Vector) = f(x, 3, 4)
optimize(g, [0.,0.])
You could also use an anonymous function (but it may be less efficient).
optimize(x -> f(x,3,4), [0.,0.])
Related
I'd like to do something like this:
>> foo = #() functionCall1() functionCall2()
So that when I said:
>> foo()
It would execute functionCall1() and then execute functionCall2(). (I feel that I need something like the C , operator)
EDIT:
functionCall1 and functionCall2 are not necessarily functions that return values.
Trying to do everything via the command line without saving functions in m-files may be a complicated and messy endeavor, but here's one way I came up with...
First, make your anonymous functions and put their handles in a cell array:
fcn1 = #() ...;
fcn2 = #() ...;
fcn3 = #() ...;
fcnArray = {fcn1 fcn2 fcn3};
...or, if you have functions already defined (like in m-files), place the function handles in a cell array like so:
fcnArray = {#fcn1 #fcn2 #fcn3};
Then you can make a new anonymous function that calls each function in the array using the built-in functions cellfun and feval:
foo = #() cellfun(#feval,fcnArray);
Although funny-looking, it works.
EDIT: If the functions in fcnArray need to be called with input arguments, you would first have to make sure that ALL of the functions in the array require THE SAME number of inputs. In that case, the following example shows how to call the array of functions with one input argument each:
foo = #(x) cellfun(#feval,fcnArray,x);
inArgs = {1 'a' [1 2 3]};
foo(inArgs); %# Passes 1 to fcn1, 'a' to fcn2, and [1 2 3] to fcn3
WORD OF WARNING: The documentation for cellfun states that the order in which the output elements are computed is not specified and should not be relied upon. This means that there are no guarantees that fcn1 gets evaluated before fcn2 or fcn3. If order matters, the above solution shouldn't be used.
The anonymous function syntax in Matlab (like some other languages) only allows a single expression. Furthermore, it has different variable binding semantics (variables which are not in the argument list have their values lexically bound at function creation time, instead of references being bound). This simplicity allows Mathworks to do some optimizations behind the scenes and avoid a lot of messy scoping and object lifetime issues when using them in scripts.
If you are defining this anonymous function within a function (not a script), you can create named inner functions. Inner functions have normal lexical reference binding and allow arbitrary numbers of statements.
function F = createfcn(a,...)
F = #myfunc;
function b = myfunc(...)
a = a+1;
b = a;
end
end
Sometimes you can get away with tricks like gnovice's suggestion.
Be careful about using eval... it's very inefficient (it bypasses the JIT), and Matlab's optimizer can get confused between variables and functions from the outer scope that are used inside the eval expression. It's also hard to debug and/or extent code that uses eval.
Here is a method that will guarantee execution order and, (with modifications mentioned at the end) allows passing different arguments to different functions.
call1 = #(a,b) a();
call12 = #(a,b) call1(b,call1(a,b));
The key is call1 which calls its first argument and ignores its second. call12 calls its first argument and then its second, returning the value from the second. It works because a function cannot be evaluated before its arguments. To create your example, you would write:
foo = #() call12(functionCall1, functionCall2);
Test Code
Here is the test code I used:
>> print1=#()fprintf('1\n');
>> print2=#()fprintf('2\n');
>> call12(print1,print2)
1
2
Calling more functions
To call 3 functions, you could write
call1(print3, call1(print2, call1(print1,print2)));
4 functions:
call1(print4, call1(print3, call1(print2, call1(print1,print2))));
For more functions, continue the nesting pattern.
Passing Arguments
If you need to pass arguments, you can write a version of call1 that takes arguments and then make the obvious modification to call12.
call1arg1 = #(a,arg_a,b) a(arg_a);
call12arg1 = #(a, arg_a, b, arg_b) call1arg1(b, arg_b, call1arg1(a, arg_a, b))
You can also make versions of call1 that take multiple arguments and mix and match them as appropriate.
It is possible, using the curly function which is used to create a comma separated list.
curly = #(x, varargin) x{varargin{:}};
f=#(x)curly({exp(x),log(x)})
[a,b]=f(2)
If functionCall1() and functionCall2() return something and those somethings can be concatenated, then you can do this:
>> foo = #() [functionCall1(), functionCall2()]
or
>> foo = #() [functionCall1(); functionCall2()]
A side effect of this is that foo() will return the concatenation of whatever functionCall1() and functionCall2() return.
I don't know if the execution order of functionCall1() and functionCall2() is guaranteed.
It was suggested in this comment that there is a difference between how Matlab and Python pass around functions. From what I can tell by looking and using the two, there is no difference between the two, but maybe I'm missing something?
In Matlab, you would create a quick function handle like this:
fun = #(x) x.^2 + 1;
In Python, using a lambda function, you could create a similar function like this:
def fun(x):
return x^2
In both languages, it's possible to send the term 'fun' to another function as an argument - but the commenter I linked to insinuated that they are not the same and/or need to be used differently.
What am I missing?
The first comment seems to simply reiterate the idea that you can pass a MATLAB function handle as an argument (although the answer didn't state anything that would make me think otherwise). The second comment seemed to interpret this to mean that the first commenter thought that you couldn't do this in Python and responded to state that you can use either a lambda or pass the function directly.
Regardless, assuming that you use them correctly, a function handle in MATLAB is functionally equivalent to using either a lambda or function object as an input argument in Python.
In python, if you don't append the () to the end of the function, it doesn't execute the function and instead yields the function object which can then be passed to another function.
# Function which accepts a function as an input
def evalute(func, val)
# Execute the function that's passed in
return func(val)
# Standard function definition
def square_and_add(x):
return x**2 + 1
# Create a lambda function which does the same thing.
lambda_square_and_add = lambda x: x**2 + 1
# Now pass the function to another function directly
evaluate(square_and_add, 2)
# Or pass a lambda function to the other function
evaluate(lambda_square_and_add, 2)
In MATLAB, you have to use a function handle because MATLAB attempts to execute a function even if you omit the ().
function res = evaluate(func, val)
res = func(val)
end
function y = square_and_add(x)
y = x^2 + 1;
end
%// Will try to execute square_and_add with no inputs resulting in an error
evaluate(square_and_add)
%// Must use a function handle
evaluate(#square_and_add, 2)
Could you please help me with the following issue: I have the following function handle:
r1 = #(lambda) b + lambda*(r - b); % r and b are vectors of return data
I want to find the optimal lambdas that set me a mean function to zero, for a given set of powers within that function. What I tried to do and didn't work, as it returns me an error for undefined operators for input arguments of type 'function_handle' is:
lambda0 = 0.3;
for a = 2:10 %power coefficient
S1(a) = fzero(mean((r - b)*r1.^(1/(a - 1))),lambda0);
end
Any suggestion as to how to go about this problem is highly appreciated! Thank you in advance.
fzero accepts a function handle as the first input. As you currently have it, you're trying to pass a statement as the first input. This statement can't even be properly evaluated because you are trying to perform numerical operations on a function handle (more on this in a bit).
You need to instead do something like this where we create a new function handle that evaluates the original function handle and performs the other operations you need.
S1(a) = fzero(#(lambda)mean((r - b)*r1(lambda).^(1/(a - 1))),lambda0);
Further Explanation
Performing operations on a function handle is not the same as performing them on the result.
So for example, if we had a function handle:
func = #(x)2*x;
If we evaluation this, by calling it with an input value for x
func(2)
4
This works as we would expect. If now we really want the value (2*x)^2, we could try to write it the way that you wrote your statement in your question
func2 = func^2;
We will get an error!
Undefined operator '^' for input arguments of type 'function_handle'.
This does not work because MATLAB attempts to apply the ^ operation to the function handle itself and not the value of the evaluated function handle.
Instead, we would need to create a new function handle that essentially wraps the other one and performs any additional options:
func2 = #(x)func(x)^2;
func2(2)
16
Bringing it Full-Circle
So if we go back to your question, you defined your anonymous function r1 like this.
r1 = #(lambda) b + lambda*(r - b); % r and b are vectors of return data
This all looks great. You have one input argument and you reference r and b from the parent workspace.
Now when you call fzero you try to perform operations on this function handle in hopes of creating a new function handle.
mean((r - b)*r1.^(1/(a - 1)))
Like we just showed this will result in a very similar error
Undefined operator .^ for input arguments of type 'function_handle'
So we need to wrap this into a new function.
newfunc = #(lambda)mean((r - b)*r1(lambda).^(1 / (a - 1)));
Now we can safely pass this to fzero.
result = fzero(newfunc, lambda0);
I'd like to do something like this:
>> foo = #() functionCall1() functionCall2()
So that when I said:
>> foo()
It would execute functionCall1() and then execute functionCall2(). (I feel that I need something like the C , operator)
EDIT:
functionCall1 and functionCall2 are not necessarily functions that return values.
Trying to do everything via the command line without saving functions in m-files may be a complicated and messy endeavor, but here's one way I came up with...
First, make your anonymous functions and put their handles in a cell array:
fcn1 = #() ...;
fcn2 = #() ...;
fcn3 = #() ...;
fcnArray = {fcn1 fcn2 fcn3};
...or, if you have functions already defined (like in m-files), place the function handles in a cell array like so:
fcnArray = {#fcn1 #fcn2 #fcn3};
Then you can make a new anonymous function that calls each function in the array using the built-in functions cellfun and feval:
foo = #() cellfun(#feval,fcnArray);
Although funny-looking, it works.
EDIT: If the functions in fcnArray need to be called with input arguments, you would first have to make sure that ALL of the functions in the array require THE SAME number of inputs. In that case, the following example shows how to call the array of functions with one input argument each:
foo = #(x) cellfun(#feval,fcnArray,x);
inArgs = {1 'a' [1 2 3]};
foo(inArgs); %# Passes 1 to fcn1, 'a' to fcn2, and [1 2 3] to fcn3
WORD OF WARNING: The documentation for cellfun states that the order in which the output elements are computed is not specified and should not be relied upon. This means that there are no guarantees that fcn1 gets evaluated before fcn2 or fcn3. If order matters, the above solution shouldn't be used.
The anonymous function syntax in Matlab (like some other languages) only allows a single expression. Furthermore, it has different variable binding semantics (variables which are not in the argument list have their values lexically bound at function creation time, instead of references being bound). This simplicity allows Mathworks to do some optimizations behind the scenes and avoid a lot of messy scoping and object lifetime issues when using them in scripts.
If you are defining this anonymous function within a function (not a script), you can create named inner functions. Inner functions have normal lexical reference binding and allow arbitrary numbers of statements.
function F = createfcn(a,...)
F = #myfunc;
function b = myfunc(...)
a = a+1;
b = a;
end
end
Sometimes you can get away with tricks like gnovice's suggestion.
Be careful about using eval... it's very inefficient (it bypasses the JIT), and Matlab's optimizer can get confused between variables and functions from the outer scope that are used inside the eval expression. It's also hard to debug and/or extent code that uses eval.
Here is a method that will guarantee execution order and, (with modifications mentioned at the end) allows passing different arguments to different functions.
call1 = #(a,b) a();
call12 = #(a,b) call1(b,call1(a,b));
The key is call1 which calls its first argument and ignores its second. call12 calls its first argument and then its second, returning the value from the second. It works because a function cannot be evaluated before its arguments. To create your example, you would write:
foo = #() call12(functionCall1, functionCall2);
Test Code
Here is the test code I used:
>> print1=#()fprintf('1\n');
>> print2=#()fprintf('2\n');
>> call12(print1,print2)
1
2
Calling more functions
To call 3 functions, you could write
call1(print3, call1(print2, call1(print1,print2)));
4 functions:
call1(print4, call1(print3, call1(print2, call1(print1,print2))));
For more functions, continue the nesting pattern.
Passing Arguments
If you need to pass arguments, you can write a version of call1 that takes arguments and then make the obvious modification to call12.
call1arg1 = #(a,arg_a,b) a(arg_a);
call12arg1 = #(a, arg_a, b, arg_b) call1arg1(b, arg_b, call1arg1(a, arg_a, b))
You can also make versions of call1 that take multiple arguments and mix and match them as appropriate.
It is possible, using the curly function which is used to create a comma separated list.
curly = #(x, varargin) x{varargin{:}};
f=#(x)curly({exp(x),log(x)})
[a,b]=f(2)
If functionCall1() and functionCall2() return something and those somethings can be concatenated, then you can do this:
>> foo = #() [functionCall1(), functionCall2()]
or
>> foo = #() [functionCall1(); functionCall2()]
A side effect of this is that foo() will return the concatenation of whatever functionCall1() and functionCall2() return.
I don't know if the execution order of functionCall1() and functionCall2() is guaranteed.
I am working on a project and have many functions to create and they do need lots of debugging so instead of just hitting the run button i have to go to command window and give a function call.
does MATLAB support assignment of default values to input arguments like python does?
In python
def some_fcn(arg1 = a, arg2 = b)
% THE CODE
if you now call it without passing the arguments it doesn't give errors but if you try the same in MATLAB it gives an error.
For assigning default values, one might find it easier to manage if you use exist function instead of nargin.
function f(arg1, arg2, arg3)
if ~exist('arg2', 'var')
arg2 = arg2Default;
end
The advantage is that if you change the order of arguments, you don't need to update this part of the code, but when you use nargin you have to start counting and updating numbers.
If you are writing a complex function that requires validation of inputs, default argument values, key-value pairs, passing options as structs etc., you could use the inputParser object. This solution is probably overkill for simple functions, but you might keep it in mind for your monster-function that solves equations, plots results and brings you coffee. It resembles a bit the things you can do with python's argparse module.
You configure an inputParser like so:
>> p = inputParser();
>> p.addRequired('x', #isfinite) % validation function
>> p.addOptional('y', 123) % default value
>> p.addParamValue('label', 'default') % default value
Inside a function, you would typically call it with p.parse(varargin{:}) and look for your parameters in p.Results. Some quick demonstration on the command line:
>> p.parse(44); disp(p.Results)
label: 'default'
x: 44
y: 123
>> p.parse()
Not enough input arguments.
>> p.parse(Inf)
Argument 'x' failed validation isfinite.
>> p.parse(44, 55); disp(p.Results)
label: 'default'
x: 44
y: 55
>> p.parse(13, 'label', 'hello'); disp(p.Results)
label: 'hello'
x: 13
y: 123
>> p.parse(88, 13, 'option', 12)
Argument 'option' did not match any valid parameter of the parser.
You can kind of do this with nargin
function out = some_fcn(arg1, arg2)
switch nargin
case 0
arg1 = a;
arg2 = b;
%//etc
end
but where are a and b coming from? Are they dynamically assigned? Because that effects the validity of this solution
After a few seconds of googling I found that as is often the case, Loren Shure has already solved this problem for us. In this article she outlines exactly my method above, why it is ugly and bad and how to do better.
You can use nargin in your function code to detect when no arguments are passed, and assign default values or do whatever you want in that case.
MathWorks has a new solution for this in R2019b, namely, the arguments block. There are a few rules for the arguments block, naturally, so I would encourage you to learn more by viewing the Function Argument Validation help page. Here is a quick example:
function ret = someFunction( x, y )
%SOMEFUNCTION Calculates some stuff.
arguments
x (1, :) double {mustBePositive}
y (2, 3) logical = true(2, 3)
end
% ...stuff is done, ret is defined, etc.
end
Wrapped into this is narginchk, inputParser, validateattributes, varargin, etc. It can be very convenient. Regarding default values, they are very simply defined as those arguments that equal something. In the example above, x isn't given an assignment, whereas y = true(2, 3) if no value is given when the function is called. If you wanted x to also have a default value, you could change it to, say, x (1, :) double {mustBePositive} = 0.5 * ones(1, 4).
There is a more in-depth answer at How to deal with name/value pairs of function arguments in MATLAB
that hopefully can spare you some headache in getting acquainted with the new functionality.