If I have a function f(x,y), I want to know how to define another function (say g) where g(x) = f(x,y), where y has been defined beforehand, either explicitly or as the input of another function.
I know this is probably quite simple but my code does not seem to work and I cannot find a solution in the documentation.
You are probably looking for anonymous functions.
A very common use-case is minimiziation. You often need to minimize a function of multiple variables along a single parameter. This leaves you without the option of just passing in constants for the remaining parameters.
An anonymous definition of g would look like this:
g = #(x) f(x, y)
y would have to be a variable defined in the current workspace. The value of y is bound permanently to the function. Whether you do clear y or assign a different value to it, the value of y used in g will be whatever it was when you first created the function handle.
As another, now deleted, answer mentioned, you could use the much uglier approach of using global variables.
The disadvantages are that your code will be hard to read and maintain. The value of the variable can change in many places. Finally, there are simply better ways of doing it available in modern versions of MATLAB like nested functions, even if anonymous functions don't work for you for some reason.
The advantages are that you can make g a simple stand alone function. Unlike the anonymous version, you will get different results if you change the value of y in the base workspace, just be careful not to clear it.
The main thing to remember with globals is that each function/workspace wishing to share the value must declare the name global (before assigning to it to avoid a warning).
In the base workspace:
global y
y = ...
In g.m:
function [z] = g(x)
global y;
z = f(x, y);
I am not particularly recommending this technique, but it helps to be aware of it in case you can't express g as a single statement.
A note about warnings. Both anonymous functions and globals will warn you about assigning to a variable that already exists. That is why putting a global declaration as the first line of a function is generally good practice.
f = #(a,b) a^2 + b^2;
y = 4;
g = #(x) f(x,y);
g(2)
ans = 20
Related
I have defined several anonymous functions which normally depend on three variables eta1, eta2, y. There is the following relationship between eta1 eta2 and y
eta1=#(y) ((i*alpha1*lambda_0)^(1/3))*y+eta01;
eta2=#(y) ((i*alpha2*lambda_0)^(1/3))*y+eta02;
So I basically give values for y and then I am able to plot h1b(y=whatever) via arrayfun:
DW1=#(eta) blablabla
N3Y=#(y) i*alpha1*(DW1(eta1(y))*conj(U2(eta2(y)))+W1(eta1(y))...
*conj(DU2(eta2(y))));
h1b=#(y) -(1/(lambda_0*alphats))*(betats*N3Y(y));
vec=arrayfun(h1b,eta1(0:0.01:N));
plot(abs(vec),0:0.01:N)
My question: is there a way to retrieve h1b formally depending on eta1 instead of y, as an anonymous function? Without evaluating y, subsequently eta1,eta2 and then h1b, which is what I do.
Lets clarify. So you currently have:
syms y eta1 eta2;
eta1(y), eta2(y)
W1(eta1), DW1(eta1)
U2(eta2) DU2(eta2)
Hence you also have:
N3Y(W1,DW1,U2,DW2)
or:
N3Y(eta1,eta2)
or:
N3Y(y)
Hence, you have:
h1b(N3Y)
or:
h1b(eta1,eta2)
or:
h1b(y)
So, h1b depends solely on eta1 and eta2, so if you dot want to manipulate kinky eval and simplify calls, why you just dont create two versions of your functions, one with y and other with etas?.
You dont need to rewrite, the ys versions are just evaluated from the etas versions.
I have a statement in my MATLAB program:
f = #(A)DistanceGauss(A,x_axis,Y_target,Y_initial,numOf,modus);
I understood that f is defined as the function handle to the function distancegauss which contains the parameters/arg list present inside the parentheses.
What does the variable A in #(A) do? Does it have any importance? While browsing I found that the variables within parentheses after # would be the input arguments for an anonymous function..
Can anyone explain what does that A do? Will this handle work even without that A after the # symbol ? Because it is already present as an argument to be passed after the function name.
Your code will create an anonymous function f which accepts one input A. In particular f will call the function DistanceGauss(A,x_axis,Y_target,Y_initial,numOf,modus); where the value of A is whatever you input with f(A) and the other inputs must already exist in your workspace and will be passed to the function. Note: if the other variables don't exist you should get an error when calling f.
Now a reasonable question is why would you want to do this you could just call DistanceGauss(A,x_axis,Y_target,Y_initial,numOf,modus); directly with whatever values you want, without having to worry about whether some of them exist.
There are two main reasons I can think of why you would do this (I'm sure there are others). Firstly for simplicity where your other inputs don't change and you don't want to have to keep retyping them or have users accidentally change them.
The other reason where you would want this is when optimizing/minimizing a function, for example with fminsearch. The matlab optimization functions will vary all inputs. If you want only vary some of them you can use this sort of syntax to reduce the number of input variables.
As to what A actually is in your case this will depend on what it does in DistanceGauss, which is not a standard MATLAB function so I suggest you look at the code for that.
"f(A)" or "f of A" or "The function of A" here has the handle "f"
DistanceGauss() here is another function that was defined elsewhere in your code.
You would set x_axis, Y_target, Y_initial, numOf, & modus before creating the function f. These arguments would stay the same for Function f, even if you try and set them again later.
'A' though, is different. You don't set it before you make the function. You can later operate on all values of A, such as if you plot the function or get the integral of the function. In that case, it would be performing the DistanceGauss function on every value of 'A', (though we can't see here what DistanceGauss function does. )
Anonymous function should be defined such as:
sqr = #(x) x.^2;
in which x shows the variable of the the function and there is no name for it (it is called anonymous!).
Although you can do something like this:
c = 10;
mygrid = #(x,y) ndgrid((-x:x/c:x),(-y:y/c:y));
[x,y] = mygrid(pi,2*pi);
in which you are modifying an existing function ndgrid to make a new anonymous function.
In your case also:
f = #(A)DistanceGauss(A,x_axis,Y_target,Y_initial,numOf,modus);
This is a new anonymous function by modifying the function DistanceGauss that you may want to have a single variable A.
If you remove (A) from the code, then f would be a handle to the existing function DistanceGauss:
f = #DistanceGauss;
Now you can evaluate the function simply by using the handle:
f(A,x_axis,...)
I'm trying to use the MATLAB function fzero properly but my program keeps returning an error message. This is my code (made up of two m-files):
friction_zero.m
function fric_zero = friction_zero(reynolds)
fric_zero = 0.25*power(log10(5.74/(power(reynolds,0.9))),-2);
flow.m
function f = flow(fric)
f = 1/(sqrt(fric))-1.873*log10(reynolds*sqrt(fric))-233/((reynolds*sqrt(fric))^0.9)-0.2361;
f_initial = friction_zero(power(10,4));
z = fzero(#flow,f_initial)
The goal is to return z as the root for the equation specified by f when flow.m is run.
I believe I have the correct syntax as I have spent a couple of hours online looking at examples. What happens is that it returns the following error message:
"Undefined function or variable 'fric'."
(Of course it's undefined, it's the variable I'm trying to solve!)
Can someone point out to me what I've done wrong? Thanks
EDIT
Thanks to all who helped! You have assisted me to eventually figure out my problem.
I had to add another file. Here is a full summary of the completed code with output.
friction_zero.m
function fric_zero = friction_zero(re)
fric_zero = 0.25*power(log10(5.74/(power(re,0.9))),-2); %starting value for fric
flow.m
function z = flow(fric)
re = power(10,4);
z = 1/(sqrt(fric))-1.873*log10(re*sqrt(fric))-233/((re*sqrt(fric))^0.9)-0.2361;
flow2.m
f_initial = friction_zero(re); %arbitrary starting value (Reynolds)
x = #flow;
fric_root = fzero(x,f_initial)
This returns an output of:
fric_root = 0.0235
Which seems to be the correct answer (phew!)
I realised that (1) I didn't define reynolds (which is now just re) in the right place, and (2) I was trying to do too much and thus skipped out on the line x = #flow;, for some reason when I added the extra line in, MATLAB stopped complaining. Not sure why it wouldn't have just taken #flow straight into fzero().
Once again, thanks :)
You need to make sure that f is a function in your code. This is simply an expression with reynolds being a constant when it isn't defined. As such, wrap this as an anonymous function with fric as the input variable. Also, you need to make sure the output variable from your function is z, not f. Since you're solving for fric, you don't need to specify this as the input variable into flow. Also, you need to specify f as the input into fzero, not flow. flow is the name of your main function. In addition, reynolds in flow is not defined, so I'm going to assume that it's the same as what you specified to friction_zero. With these edits, try doing this:
function z = flow()
reynolds = power(10,4);
f = #(fric) 1/(sqrt(fric))-1.873*log10(reynolds*sqrt(fric))-233/((reynolds*sqrt(fric))^0.9)-0.2361;
f_initial = friction_zero(reynolds);
z = fzero(#f, f_initial); %// You're solving for `f`, not flow. flow is your function name
The reason that you have a problem is because flow is called without argument I think. You should read a little more about matlab functions. By the way, reynolds is not defined either.
I am afraid I cannot help you completely since I have not been doing fluid mechanics. However, I can tell you about functions.
A matlab function definition looks something like this:
function x0 = f(xGuess)
a = 2;
fcn =#(t) a*t.^3+t; % t must not be an input to f.
disp(fcn);
a = 3;
disp(fcn);
x0 = fsolve(fcn1,xGuess); % x0 is calculated here
The function can then ne called as myX0 = f(myGuess). When you define a matlab function with arguments and return values, you must tell matlab what to do with them. Matlab cannot guess that. In this function you tell matlab to use xGuess as an initial guess to fsolve, when solving the anonymous function fcn. Notice also that matlab does not assume that an undefined variable is an independent variable. You need to tell matlab that now I want to create an anonymous function fcn which have an independent variable t.
Observation 1: I use .^. This is since the function will take an argument an evaluate it and this argument can also be a vector. In this particulat case I want pointwise evaluation. This is not really necessary when using fsolve but it is good practice if f is not a matrix equation, since "vectorization" is often used in matlab.
Observation 2: notice that even if a changes its value the function does not change. This is since matlab passes the value of a variable when defining a function and not the variable itself. A c programmer would say that a variable is passed by its value and not by a pointer. This means that fcn is really defined as fcn = #(x) 2*t.^3+t;. Using the variable a is just a conveniance (constants can may also be complicated to find, but when found they are just a value).
Armed with this knowledge, you should be able to tackle the problem in front of you. Also, the recursive call to flow in your function will eventuallt cause a crash. When you write a function that calls itself like this you must have a stopping criterium, something to tell the program when to stop. As it is now, flow will call ifself in the last row, like z = fzero(#flow,f_initial) for 500 times and then crash. Alos it is possible as well to define functions with zero inputs:
function plancksConstant = h()
plancksConstant = 6.62606957eā34;
Where the call h or h() will return Plancks constant.
Good luck!
I'm trying to model the effect of different filter "building blocks" on a system which is a construct based on these filters.
I would like the basic filters to be "modular", i.e. they should be "replaceable", without rewriting the construct which is based upon the basic filters.
For example, I have a system of filters G_0, G_1, which is defined in terms of some basic filters called H_0 and H_1.
I'm trying to do the following:
syms z
syms H_0(z) H_1(z)
G_0(z)=H_0(z^(4))*H_0(z^(2))*H_0(z)
G_1(z)=H_1(z^(4))*H_0(z^(2))*H_0(z)
This declares the z-domain I'd like to work in, and a construct of two filters G_0,G_1, based on the basic filters H_0,H_1.
Now, I'm trying to evaluate the construct in terms of some basic filters:
H_1(z) = 1+z^-1
H_0(z) = 1+0*z^-1
What I would like to get at this point is an expanded polynomial of z.
E.g. for the declarations above, I'd like to see that G_0(z)=1, and that G_1(z)=1+z^(-4).
I've tried stuff like "subs(G_0(z))", "formula(G_0(z))", "formula(subs(subs(G_0(z))))", but I keep getting result in terms of H_0 and H_1.
Any advice? Many thanks in advance.
Edit - some clarifications:
In reality, I have 10-20 transfer functions like G_0 and G_1, so I'm trying to avoid re-declaring all of them every time I change the basic blocks H_0 and H_1. The basic blocks H_0 and H_1 would actually be of a much higher degree than they are in the example here.
G_0 and G_1 will not change after being declared, only H_0 and H_1 will.
H_0(z^2) means using z^2 as an argument for H_0(z). So wherever z appears in the declaration of H_0, z^2 should be plugged in
The desired output is a function in terms of z, not H_0 and H_1.
A workable hack is having an m-File containing the declarations of the construct (G_0 and G_1 in this example), which is run every time H_0 and H_1 are redefined. I was wondering if there's a more elegant way of doing it, along the lines of the (non-working) code shown above.
This seems to work quite nicely, and is very easily extendable. I redefined H_0 to H_1 as an example only.
syms z
H_1(z) = 1+z^-1;
H_0(z) = 1+0*z^-1;
G_0=#(Ha,z) Ha(z^(4))*Ha(z^(2))*Ha(z);
G_1=#(Ha,Hb,z) Hb(z^(4))*Ha(z^(2))*Ha(z);
G_0(H_0,z)
G_1(H_0,H_1,z)
H_0=#(z) H_1(z);
G_0(H_0,z)
G_1(H_0,H_1,z)
This seems to be a namespace issue. You can't define a symbolic expression or function in terms of arbitrary/abstract symfuns and then later on define these symfuns explicitly and be able to use them to obtain an exploit form of the original symbolic expression or function (at least not easily). Here's an example of how a symbolic function can be replaced by name:
syms z y(z)
x(z) = y(z);
y(z) = z^2; % Redefines y(z)
subs(x,'y(z)',y)
Unfortunately, this method depends on specifying the function(s) to be substituted exactly ā because strings are used, Matlab sees arbitrary/abstract symfuns with different arguments as different functions. So the following example does not work as it returns y(z^2):
syms z y(z)
x(z) = y(z^2); % Function of z^2 instead
y(z) = z^2;
subs(x,'y(z)',y)
But if the last line was changed to subs(x,'y(z^2)',y) it would work.
So one option might be to form strings for case, but that seems overly complex and inelegant. I think that it would make more sense to simply not explicitly (re)define your arbitrary/abstract H_0, H_1, etc. functions and instead use other variables. In terms of the simple example:
syms z y(z)
x(z) = y(z^2);
y_(z) = z^2; % Create new explicit symfun
subs(x,y,y_)
which returns z^4. For your code:
syms z H_0(z) H_1(z)
G_0(z) = H_0(z^4)*H_0(z^2)*H_0(z);
G_1(z) = H_1(z^4)*H_0(z^2)*H_0(z);
H_0_(z) = 1+0*z^-1;
H_1_(z) = 1+z^-1;
subs(G_0, {H_0, H_1}, {H_0_, H_1_})
subs(G_1, {H_0, H_1}, {H_0_, H_1_})
which returns
ans(z) =
1
ans(z) =
1/z^4 + 1
You can then change H_0_ and H_1_, etc. at will and use subs to evaluateG_1andG_2` again.
when I am doing a function in Matlab. Sometimes I have equations and every one of these have constants. Then, I have to declare these constants inside my function. I wonder if there is a way to call the values of that constants from outside of the function, if I have their values on the workspace.
I don't want to write this values as inputs of my function in the function declaration.
In addition to the solutions provided by Iterator, which are all great, I think you have some other options.
First of all, I would like to warn you about global variables (as Iterator also did): these introduce hidden dependencies and make it much more cumbersome to reuse and debug your code. If your only concern is ease of use when calling the functions, I would suggest you pass along a struct containing those constants. That has the advantage that you can easily save those constants together. Unless you know what you're doing, do yourself a favor and stay away from global variables (and functions such as eval, evalin and assignin).
Next to global, evalin and passing structs, there is another mechanism for global state: preferences. These are to be used when it concerns a nearly immutable setting of your code. These are unfit for passing around actual raw data.
If all you want is a more or less clean syntax for calling a certain function, this can be achieved in a few different ways:
You could use a variable number of parameters. This is the best option when your constants have a default value. I will explain by means of an example, e.g. a regular sine wave y = A*sin(2*pi*t/T) (A is the amplitude, T the period). In MATLAB one would implement this as:
function y = sinewave(t,A,T)
y = A*sin(2*pi*t/T);
When calling this function, we need to provide all parameters. If we extend this function to something like the following, we can omit the A and T parameters:
function y = sinewave(t,A,T)
if nargin < 3
T = 1; % default period is 1
if nargin < 2
A = 1; % default amplitude 1
end
end
y = A*sin(2*pi*t/T);
This uses the construct nargin, if you want to know more, it is worthwhile to consult the MATLAB help for nargin, varargin, varargout and nargout. However, do note that you have to provide a value for A when you want to provide the value of T. There is a more convenient way to get even better behavior:
function y = sinewave(t,A,T)
if ~exists('T','var') || isempty(T)
T = 1; % default period is 1
end
if ~exists('A','var') || isempty(A)
A = 1; % default amplitude 1
end
y = A*sin(2*pi*t/T);
This has the benefits that it is more clear what is happening and you could omit A but still specify T (the same can be done for the previous example, but that gets complicated quite easily when you have a lot of parameters). You can do such things by calling sinewave(1:10,[],4) where A will retain it's default value. If an empty input should be valid, you should use another invalid input (e.g. NaN, inf or a negative value for a parameter that is known to be positive, ...).
Using the function above, all the following calls are equivalent:
t = rand(1,10);
y1 = sinewave(t,1,1);
y2 = sinewave(t,1);
y3 = sinewave(t);
If the parameters don't have default values, you could wrap the function into a function handle which fills in those parameters. This is something you might need to do when you are using some toolboxes that impose constraints onto the functions that are to be used. This is the case in the Optimization Toolbox.
I will consider the sinewave function again, but this time I use the first definition (i.e. without a variable number of parameters). Then you could work with a function handle:
f = #(x)(sinewave(x,1,1));
You can work with f as you would with an other function:
e.g. f(10) will evaluate sinewave(10,1,1).
That way you can write a general function (i.e. sinewave that is as general and simple as possible) but you create a function (handle) on the fly with the constants substituted. This allows you to work with that function, but also prevents global storage of data.
You can of course combine different solutions: e.g. create function handle to a function with a variable number of parameters that sets a certain global variable.
The easiest way to address this is via global variable:
http://www.mathworks.com/help/techdoc/ref/global.html
You can also get the values in other workspaces, including the base or parent workspace, but this is ill-advised, as you do not necessarily know what wraps a given function.
If you want to go that route, take a look at the evalin function:
http://www.mathworks.com/help/techdoc/ref/evalin.html
Still, the standard method is to pass all of the variables you need. You can put these into a struct, if you wish, and only pass the one struct.