I am trying to write a function in MATLAB that takes 1x3 vectors as input. My code looks something like this:
function myFunction=([x1, x2, x3], [y1, y2, y3], [z1, z2, z3])
where all inputs are numbers, and then in the body of the function I perform some calculations indexing through the numerical values in the vectors. i want the vectors to be user input, so the user will enter the vectors and their components (x1, x2, etc.) into the function argument. However, I am getting an error saying "Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters." Therefore I believe I either have the syntax or something else wrong. I know MATLAB is supposed to be able to take vector input in functions, so please let me know what I am doing wrong. Thanks!
What you need to do is declare your function like this:
function myFunction(x,y,z)
% your function code here
end
Then within your function you can access the individual elements of the vectors using x(1), y(2), etc.
To call the function, including whatever number you like, you can enter on the Matlab command window (for example),
myFunction([1 2 3],[4 5 6],[7 8 9]) and the code in your function will be called with the x variable set to the vector [1,2,3], the y variable set to [4,5,6] and z to [7,8,9]. The use of commas to delineate values is optional. If your function then accesses y(2) it will get the second value of the y vector which will be 5 - it is important to note that indexing in Matlab is 1-based so the 1st element of x is obtained with x(1).
If you need to return values you can use:
function [a,b,c] = myFunction(x,y,z)
Then just assign the a, b or c in your code before the end statement.
See the offical Matlab documentation for more info.
I would add that much of the advantage of matlab is dealing with data in a vectorised form, so if you can avoid splitting out into separate elements I would do so. For example, if you need to add two vecors, you could do z = [x(1)+y(1), x(2)+y(2), x(3)+y(3)], but much better (more readable, more maintainable, faster) is z=x+y.
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.
As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.
Closed 11 years ago.
Locked. This question and its answers are locked because the question is off-topic but has historical significance. It is not currently accepting new answers or interactions.
I think everyone would agree that the MATLAB language is not pretty, or particularly consistent. But nevermind! We still have to use it to get things done.
What are your favourite tricks for making things easier? Let's have one per answer so people can vote them up if they agree. Also, try to illustrate your answer with an example.
Using the built-in profiler to see where the hot parts of my code are:
profile on
% some lines of code
profile off
profile viewer
or just using the built in tic and toc to get quick timings:
tic;
% some lines of code
toc;
Directly extracting the elements of a matrix that satisfy a particular condition, using logical arrays:
x = rand(1,50) .* 100;
xpart = x( x > 20 & x < 35);
Now xpart contains only those elements of x which lie in the specified range.
Provide quick access to other function documentation by adding a "SEE ALSO" line to the help comments. First, you must include the name of the function in all caps as the first comment line. Do your usual comment header stuff, then put SEE ALSO with a comma separated list of other related functions.
function y = transmog(x)
%TRANSMOG Transmogrifies a matrix X using reverse orthogonal eigenvectors
%
% Usage:
% y = transmog(x)
%
% SEE ALSO
% UNTRANSMOG, TRANSMOG2
When you type "help transmog" at the command line, you will see all the comments in this comment header, with hyperlinks to the comment headers for the other functions listed.
Turn a matrix into a vector using a single colon.
x = rand(4,4);
x(:)
Vectorizing loops. There are lots of ways to do this, and it is entertaining to look for loops in your code and see how they can be vectorized. The performance is astonishingly faster with vector operations!
Anonymous functions, for a few reasons:
to make a quick function for one-off uses, like 3x^2+2x+7. (see listing below) This is useful for functions like quad and fminbnd that take functions as arguments. It's also convenient in scripts (.m files that don't start with a function header) since unlike true functions you can't include subfunctions.
for closures -- although anonymous functions are a little limiting as there doesn't seem to be a way to have assignment within them to mutate state.
.
% quick functions
f = #(x) 3*x.^2 + 2*x + 7;
t = (0:0.001:1);
plot(t,f(t),t,f(2*t),t,f(3*t));
% closures (linfunc below is a function that returns a function,
% and the outer functions arguments are held for the lifetime
% of the returned function.
linfunc = #(m,b) #(x) m*x+b;
C2F = linfunc(9/5, 32);
F2C = linfunc(5/9, -32*5/9);
Matlab's bsxfun, arrayfun, cellfun, and structfun are quite interesting and often save a loop.
M = rand(1000, 1000);
v = rand(1000, 1);
c = bsxfun(#plus, M, v);
This code, for instance, adds column-vector v to each column of matrix M.
Though, in performance critical parts of your application you should benchmark these functions versus the trivial for-loop because often loops are still faster.
LaTeX mode for formulas in graphs: In one of the recent releases (R2006?) you add the additional arguments ,'Interpreter','latex' at the end of a function call and it will use LaTeX rendering. Here's an example:
t=(0:0.001:1);
plot(t,sin(2*pi*[t ; t+0.25]));
xlabel('t');
ylabel('$\hat{y}_k=sin 2\pi (t+{k \over 4})$','Interpreter','latex');
legend({'$\hat{y}_0$','$\hat{y}_1$'},'Interpreter','latex');
Not sure when they added it, but it works with R2006b in the text(), title(), xlabel(), ylabel(), zlabel(), and even legend() functions. Just make sure the syntax you are using is not ambiguous (so with legend() you need to specify the strings as a cell array).
Using xlim and ylim to draw vertical and horizontal lines. Examples:
Draw a horizontal line at y=10:
line(xlim, [10 10])
Draw vertical line at x=5:
line([5 5], ylim)
Here's a quick example:
I find the comma separated list syntax quite useful for building function calls:
% Build a list of args, like so:
args = {'a', 1, 'b', 2};
% Then expand this into arguments:
output = func(args{:})
Here's a bunch of nonobvious functions that are useful from time to time:
mfilename (returns the name of the currently running MATLAB script)
dbstack (gives you access to the names & line numbers of the matlab function stack)
keyboard (stops execution and yields control to the debugging prompt; this is why there's a K in the debug prompt K>>
dbstop error (automatically puts you in debug mode stopped at the line that triggers an error)
I like using function handles for lots of reasons. For one, they are the closest thing I've found in MATLAB to pointers, so you can create reference-like behavior for objects. There are a few neat (and simpler) things you can do with them, too. For example, replacing a switch statement:
switch number,
case 1,
outargs = fcn1(inargs);
case 2,
outargs = fcn2(inargs);
...
end
%
%can be turned into
%
fcnArray = {#fcn1, #fcn2, ...};
outargs = fcnArray{number}(inargs);
I just think little things like that are cool.
Using nargin to set default values for optional arguments and using nargout to set optional output arguments. Quick example
function hLine=myplot(x,y,plotColor,markerType)
% set defaults for optional paramters
if nargin<4, markerType='none'; end
if nargin<3, plotColor='k'; end
hL = plot(x,y,'linetype','-', ...
'color',plotColor, ...
'marker',markerType, ...
'markerFaceColor',plotColor,'markerEdgeColor',plotColor);
% return handle of plot object if required
if nargout>0, hLine = hL; end
Invoking Java code from Matlab
cellfun and arrayfun for automated for loops.
Oh, and reverse an array
v = 1:10;
v_reverse = v(length(v):-1:1);
conditional arguments in the left-hand side of an assignment:
t = (0:0.005:10)';
x = sin(2*pi*t);
x(x>0.5 & t<5) = 0.5;
% This limits all values of x to a maximum of 0.5, where t<5
plot(t,x);
Know your axis properties! There are all sorts of things you can set to tweak the default plotting properties to do what you want:
set(gca,'fontsize',8,'linestyleorder','-','linewidth',0.3,'xtick',1:2:9);
(as an example, sets the fontsize to 8pt, linestyles of all new lines to all be solid and their width 0.3pt, and the xtick points to be [1 3 5 7 9])
Line and figure properties are also useful, but I find myself using axis properties the most.
Be strict with specifying dimensions when using aggregation functions like min, max, mean, diff, sum, any, all,...
For instance the line:
reldiff = diff(a) ./ a(1:end-1)
might work well to compute relative differences of elements in a vector, however in case the vector degenerates to just one element the computation fails:
>> a=rand(1,7);
>> diff(a) ./ a(1:end-1)
ans =
-0.5822 -0.9935 224.2015 0.2708 -0.3328 0.0458
>> a=1;
>> diff(a) ./ a(1:end-1)
??? Error using ==> rdivide
Matrix dimensions must agree.
If you specify the correct dimensions to your functions, this line returns an empty 1-by-0 matrix, which is correct:
>> diff(a, [], 2) ./ a(1, 1:end-1)
ans =
Empty matrix: 1-by-0
>>
The same goes for a min-function which usually computes minimums over columns on a matrix, until the matrix only consists of one row. - Then it will return the minimum over the row unless the dimension parameter states otherwise, and probably break your application.
I can almost guarantee you that consequently setting the dimensions of these aggregation functions will save you quite some debugging work later on.
At least that would have been the case for me. :)
The colon operator for the manipulation of arrays.
#ScottieT812, mentions one: flattening an array, but there's all the other variants of selecting bits of an array:
x=rand(10,10);
flattened=x(:);
Acolumn=x(:,10);
Arow=x(10,:);
y=rand(100);
firstSix=y(1:6);
lastSix=y(end-5:end);
alternate=y(1:2:end);
In order to be able to quickly test a function, I use nargin like so:
function result = multiply(a, b)
if nargin == 0 %no inputs provided, run using defaults for a and b
clc;
disp('RUNNING IN TEST MODE')
a = 1;
b = 2;
end
result = a*b;
Later on, I add a unit test script to test the function for different input conditions.
Using ismember() to merge data organized by text identfiers. Useful when you are analyzing differing periods when entries, in my case company symbols, come and go.
%Merge B into A based on Text identifiers
UniverseA = {'A','B','C','D'};
UniverseB = {'A','C','D'};
DataA = [20 40 60 80];
DataB = [30 50 70];
MergeData = NaN(length(UniverseA),2);
MergeData(:,1) = DataA;
[tf, loc] = ismember(UniverseA, UniverseB);
MergeData(tf,2) = DataB(loc(tf));
MergeData =
20 30
40 NaN
60 50
80 70
Asking 'why' (useful for jarring me out of a Matlab runtime-fail debugging trance at 3am...)
Executing a Simulink model directly from a script (rather than interactively) using the sim command. You can do things like take parameters from a workspace variable, and repeatedly run sim in a loop to simulate something while varying the parameter to see how the behavior changes, and graph the results with whatever graphical commands you like. Much easier than trying to do this interactively, and it gives you much more flexibility than the Simulink "oscilloscope" blocks when visualizing the results. (although you can't use it to see what's going on in realtime while the simulation is running)
A really important thing to know is the DstWorkspace and SrcWorkspace options of the simset command. These control where the "To Workspace" and "From Workspace" blocks get and put their results. Dstworkspace defaults to the current workspace (e.g. if you call sim from inside a function the "To Workspace" blocks will show up as variables accessible from within that same function) but SrcWorkspace defaults to the base workspace and if you want to encapsulate your call to sim you'll want to set SrcWorkspace to current so there is a clean interface to providing/retrieving simulation input parameters and outputs. For example:
function Y=run_my_sim(t,input1,params)
% runs "my_sim.mdl"
% with a From Workspace block referencing I1 as an input signal
% and parameters referenced as fields of the "params" structure
% and output retrieved from a To Workspace block with name O1.
opt = simset('SrcWorkspace','current','DstWorkspace','current');
I1 = struct('time',t,'signals',struct('values',input1,'dimensions',1));
Y = struct;
Y.t = sim('my_sim',t,opt);
Y.output1 = O1.signals.values;
Contour plots with [c,h]=contour and clabel(c,h,'fontsize',fontsize). I usually use the fontsize parameter to reduce the font size so the numbers don't run into each other. This is great for viewing the value of 2-D functions without having to muck around with 3D graphs.
Vectorization:
function iNeedle = findClosest(hay,needle)
%FINDCLOSEST find the indicies of the closest elements in an array.
% Given two vectors [A,B], findClosest will find the indicies of the values
% in vector A closest to the values in vector B.
[hay iOrgHay] = sort(hay(:)'); %#ok must have row vector
% Use histogram to find indices of elements in hay closest to elements in
% needle. The bins are centered on values in hay, with the edges on the
% midpoint between elements.
[iNeedle iNeedle] = histc(needle,[-inf hay+[diff(hay)/2 inf]]); %#ok
% Reversing the sorting.
iNeedle = iOrgHay(iNeedle);
Using persistent (static) variables when running an online algorithm. It may speed up the code in areas like Bayesian machine learning where the model is trained iteratively for the new samples. For example, for computing the independent loglikelihoods, I compute the loglikelihood initially from scratch and update it by summing this previously computed loglikelihood and the additional loglikelihood.
Instead of giving a more specialized machine learning problem, let me give a general online averaging code which I took from here:
function av = runningAverage(x)
% The number of values entered so far - declared persistent.
persistent n;
% The sum of values entered so far - declared persistent.
persistent sumOfX;
if x == 'reset' % Initialise the persistent variables.
n = 0;
sumOfX = 0;
av = 0;
else % A data value has been added.
n = n + 1;
sumOfX = sumOfX + x;
av = sumOfX / n; % Update the running average.
end
Then, the calls will give the following results
runningAverage('reset')
ans = 0
>> runningAverage(5)
ans = 5
>> runningAverage(10)
ans = 7.5000
>> runningAverage(3)
ans = 6
>> runningAverage('reset')
ans = 0
>> runningAverage(8)
ans = 8
I'm surprised that while people mentioned the logical array approach of indexing an array, nobody mentioned the find command.
e.g. if x is an NxMxO array
x(x>20) works by generating an NxMxO logical array and using it to index x (which can be bad if you have large arrays and are looking for a small subset
x(find(x>20)) works by generating list (i.e. 1xwhatever) of indices of x that satisfy x>20, and indexing x by it. "find" should be used more than it is, in my experience.
More what I would call 'tricks'
you can grow/append to arrays and cell arrays if you don't know the size you'll need, by using end + 1 (works with higher dimensions too, so long as the dimensions of the slice match -- so you'll have to initialize x to something other than [] in that case). Not good for numerics but for small dynamic lists of things (or cell arrays), e.g. parsing files.
e.g.
>> x=[1,2,3]
x = 1 2 3
>> x(end+1)=4
x = 1 2 3 4
Another think many people don't know is that for works on any dim 1 array, so to continue the example
>> for n = x;disp(n);end
1
2
3
4
Which means if all you need is the members of x you don't need to index them.
This also works with cell arrays but it's a bit annoying because as it walks them the element is still wrapped in a cell:
>> for el = {1,2,3,4};disp(el);end
[1]
[2]
[3]
[4]
So to get at the elements you have to subscript them
>> for el = {1,2,3,4};disp(el{1});end
1
2
3
4
I can't remember if there is a nicer way around that.
-You can make a Matlab shortcut to an initialization file called startup.m. Here, I define formatting, precision of the output, and plot parameters for my Matlab session (for example, I use a larger plot axis/font size so that .fig's can be seen plainly when I put them in presentations.) See a good blog post from one of the developers about it http://blogs.mathworks.com/loren/2009/03/03/whats-in-your-startupm/ .
-You can load an entire numerical ascii file using the "load" function. This isn't particularly fast, but gets the job done quickly for prototyping (shouldn't that be the Matlab motto?)
-As mentioned, the colon operator and vectorization are lifesavers. Screw loops.
x=repmat([1:10],3,1); % say, x is an example array of data
l=x>=3; % l is a logical vector (1s/0s) to highlight those elements in the array that would meet a certain condition.
N=sum(sum(l));% N is the number of elements that meet that given condition.
cheers -- happy scripting!