Matlab plot requires the data to be of the same dimension. Meaning, you cannot plot a 1x10 vector with a 1x1x10 vector. This is sometimes necessary. For those purposes, you can use the squeeze function to get rid of the singleton dimensions.
However, this is kind of a hassle. For the plot function specifically, it would be useful to have the argument always squeezed. How would one go about creating a new function, lets call it splot which squeezes every input and passes it onto plot. Here is an attempt (that doesn't work)
function splot(varargin)
for i=1:length(varargin)
varargin{i}=squeeze(varargin{i});
end
plot(varargin)
end
plot(varargin) part fails, because that is simply not how matlab syntax works. But is there any way to achieve what I want? I guess I could write a long if elseif chain where I manually write the case with every possible number of input arguments like:
if length(varargin)==2
plot(varargin{1},varargin{2})
if length(varargin)==3
plot(varargin{1},varargin{2},varargin{3})
But this is going to be very annoying. Any better ideas.
This question is similar to Is there any mechanism to auto squeeze in Matlab / Octave , however, not similar enough, because the other question is for squeezing every vector, which is a bad idea. Here I am asking a way to squeeze only the inputs to the plot function and requiring syntax help.
From the docs there are several ways to call plot. Generally
Just numeric arrays, these can be on their own, or one or more pairs
plot(Y), plot(X,Y) or plot(X1,Y1,...,Xn,Yn)
Numeric arrays as before, with a char array giving the line spec
plot(X,Y,LineSpec) or plot(Y,LineSpec)
Either of the previous two, plus name-value pair options
plot(___,Name,Value)
In any of these cases, you want to squeeze the first N inputs which are numeric, since either of the optional additions have the first non-plottable input as a char.
We can achieve that with the following code, see the comments for details:
function h = splot( varargin )
% Check if there are any optional inputs, which will either be
% LineSpec (which is a char) or name-value pairs (which the
% first of will be a char)
bNumericArg = cellfun( #isnumeric, varargin );
% By default, assume all inputs are arrays to plot
lastArrayArg = numel(varargin);
if ~all(bNumericArg)
% In this case, there are some optional inputs, get last array index
lastArrayArg = find( ~bNumericArg, 1 ) - 1;
end
% Squeeze the arrays
for ii = 1:lastArrayArg
varargin{ii} = squeeze(varargin{ii});
end
% Plot with all inputs, optional output
if nargout > 0
h = plot( varargin{:} );
else
plot( varargin{:} );
end
end
There are two possible cases I've not handled here which the plot function can handle,
Having the first input as the target axes i.e. plot(ax,___), could be achieved by altering the loop slightly to start from 1 or 2 depending if the first input is an axes object
Having pairs of arrays each with their own line spec argument i.e. plot(X1,Y1,LineSpec1,...,Xn,Yn,LineSpecn). The later pairs will be ignored. This would be trickier to handle since you'd likely have to parse all inputs and check whether a char is just a line spec or if you're messing with name-value pairs. Maybe a heuristic to do with "two arrays then a char, repeated". I've never used this syntax so omitting the over-complication for now.
This works (plots an "empty" figure):
function testme
plot(1)
This works (returns 1):
function testme
plot = #(x)x;
plot(1)
This does not (Error: "Undefined function or variable 'plot'."):
function testme
if 0
plot = #(x)x;
end
plot(1)
What's going on here? Why does rewriting but not redefining an already defined function render the function undefined?
Note 1: this is not specific for builtin functions; the following code returns the same error:
function testme
if 0
myfun = #(x)x;
end
myfun(1)
function x=myfun(x)
x=x*2;
Note 2: the error occurs in a function environment, not in a script; the following code does not return an error (and plots the same empty figure as in the first example):
if 0
plot = #(x)x;
end
plot(1)
Update: For the interested reader, here is some background information
on my original problem. The above examples are just minimum working
samples to illustrate the main issue (which indeed feature dead end if
statements). In practice, I was trying to make a function useable for
colleagues who did not have certain library/toolbox functions
available, by overwriting those functions for simplified custom ones
if they did not exist, as a quick fix. In particular, it concerned
imdilate (and imerode). The function looked something like the
following:
function [myoutputs] = myfunction(myinputs)
% if the images toolbox is not available, use the following simplified
% replacement function
if ~exist('imdilate','file')
imdilate = #(IM,SE)vecdilate(IM,SE);
end
%% The original function goes here, which uses a lot of imdilate(IM,SE).
%% local functions
function M = vecdilate(IM,SE)
% simplified version of imdilate (can only process 1-D vertical arrays)
nSE = size(SE);
nIM = size(IM);
SE = logical(SE); % make logical if it isn't yet
% copy and shift xth column x down. new border entries are 0:
M = repmat([IM;zeros(nSE)],nSE);
M = M(1:end-nSE(1));
M = reshape(M,[size(M,1)/nSE(1) nSE(1)]);
% shrink back to column by taking max of every row:
M = max(M(:,SE),[],2);
M = M(ceil(nSE(1)/2)-1+(1:nIM(1))); % clip to obtain correct size
You might see that the replacement function covers some
functionality of imdilate, but not all, and it might not be as
efficient. The purpose simply was to use function A if it was available, and
function B if it was not. To my surprise however, the former case
returned an error, which eventually resulted in this question. For your interest, I solved the practical problem by renaming the function in the
original code, and by using an if/else statement:
function [myoutputs] = myfunction(myinputs)
% if the images toolbox is not available, use the following simplified
% replacement function
if ~exist('imdilate','file')
mydilate = #(IM,SE)vecdilate(IM,SE);
else
mydilate = #(IM,SE)imdilate(IM,SE);
end
%% The original function goes here, which uses a lot of mydilate(IM,SE).
%% local functions
function M = vecdilate(IM,SE)
etc. etc. etc.
Just-in-time-compilation (JIT) does not mean that there is no compilation and that every line is interpreted separately, so you can still mess with the code;)
The error would also appear if you use a not-defined function, where you woun't even expect the code to run, like
function [] = test()
if false
a = #(x)x;
end
a(1)
end
Scripts are stored command line entries, i.e. the compiler has no choice but to handle every line separately (you may want to think of it as a keyboard macro).
Functions in contrast are encapsulated pieces of code. The compiler (in general) does not expect anything unknown + it thinks that this encapsulated piece of code might be reused. Therefore, it makes sure to do a proper job compile all code once beforehand (if the compile would do this all the time, it is called ahead-of-time compilation).
This becomes in particular obvious when your clear the variables in between:
function [] = test()
if false
plot = #(x)x;
else
clear all % clear vs clear all
end
plot(1)
end
(Note that clear clears all variables but clear all would also clear excising code (see MATLAB Execution Engine))
Have a look at this interesting blog post from Loren
MATLAB provides the best of both worlds by compiling MATLAB code on-the-fly, or just-in-time. MATLAB code is compiled whether it be in classes, functions, scripts, or simply at the command line. There is no explicit compile step for the user to initiate and MATLAB code can be executed in blocks as small as one line at a time. The MATLAB JIT compiler generates native machine level code that is optimized for the MATLAB code being executed and for the specific hardware platform.
Anyway, you should not write dead ends in your code or overwrite (native) functions. It is good to use function handles to overcome this problem, but make sure that you define it for all cases
function [] = test()
if false % dead end definition
fnc = #(x)x;
else
fnc = #plot;
end
fnc(1)
end
Can somebody explain to me the meaning of the # (function handle) operator and why to use it?
The function handle operator in MATLAB acts essentially like a pointer to a specific instance of a function. Some of the other answers have discussed a few of its uses, but I'll add another use here that I often have for it: maintaining access to functions that are no longer "in scope".
For example, the following function initializes a value count, and then returns a function handle to a nested function increment:
function fHandle = start_counting(count)
disp(count);
fHandle = #increment;
function increment
count = count+1;
disp(count);
end
end
Since the function increment is a nested function, it can only be used within the function start_counting (i.e. the workspace of start_counting is its "scope"). However, by returning a handle to the function increment, I can still use it outside of start_counting, and it still retains access to the variables in the workspace of start_counting! That allows me to do this:
>> fh = start_counting(3); % Initialize count to 3 and return handle
3
>> fh(); % Invoke increment function using its handle
4
>> fh();
5
Notice how we can keep incrementing count even though we are outside of the function start_counting. But you can do something even more interesting by calling start_counting again with a different number and storing the function handle in another variable:
>> fh2 = start_counting(-4);
-4
>> fh2();
-3
>> fh2();
-2
>> fh(); % Invoke the first handle to increment
6
>> fh2(); % Invoke the second handle to increment
-1
Notice that these two different counters operate independently. The function handles fh and fh2 point to different instances of the function increment with different workspaces containing unique values for count.
In addition to the above, using function handles in conjunction with nested functions can also help streamline GUI design, as I illustrate in this other SO post.
Function handles are an extremely powerful tool in matlab. A good start is to read the online help, which will give you far more than I can. At the command prompt, type
doc function_handle
A function handle is a simple way to create a function in one line. For example, suppose I wished to numerically integrate the function sin(k*x), where k has some fixed, external value. I could use an inline function, but a function handle is much neater. Define a function
k = 2;
fofx = #(x) sin(x*k);
See that I can now evaluate the function fofx at the command line. MATLAB knows what k is, so we can use fofx as a function now.
fofx(0.3)
ans =
0.564642473395035
In fact, we can pass fofx around, effectively as a variable. For example, lets call quad to do the numerical integration. I'll pick the interval [0,pi/2].
quad(fofx,0,pi/2)
ans =
0.999999998199215
As you can see, quad did the numerical integration. (By the way, an inline function would have been at least an order of magitude slower, and far less easy to work with.)
x = linspace(0,pi,1000);
tic,y = fofx(x);toc
Elapsed time is 0.000493 seconds.
By way of comparison, try an inline function.
finline = inline('sin(x*k)','x','k');
tic,y = finline(x,2);toc
Elapsed time is 0.002546 seconds.
A neat thing about a function handle is you can define it on the fly. Minimize the function cos(x), over the interval [0,2*pi]?
xmin = fminbnd(#(x) cos(x),0,2*pi)
xmin =
3.14159265358979
There are many, many other uses for function handles in MATLAB. I've only scratched the surface here.
Disclaimer: code not tested...
The function handle operator allows you to create a reference to a function and pass it around just like any other variable:
% function to add two numbers
function total = add(first, second)
total = first + second;
end
% this variable now points to the add function
operation = #add;
Once you've got a function handle, you can invoke it just like a regular function:
operation(10, 20); % returns 30
One nice thing about function handles is that you can pass them around just like any other data, so you can write functions that act on other functions. This often allows you to easily separate out business logic:
% prints hello
function sayHello
disp('hello world!');
end
% does something five times
function doFiveTimes(thingToDo)
for idx = 1 : 5
thingToDo();
end
end
% now I can say hello five times easily:
doFiveTimes(#sayHello);
% if there's something else I want to do five times, I don't have to write
% the five times logic again, only the operation itself:
function sayCheese
disp('Cheese');
end
doFiveTimes(#sayCheese);
% I don't even need to explicitly declare a function - this is an
% anonymous function:
doFiveTimes(#() disp('do something else'));
The Matlab documentation has a fuller description of the Matlab syntax, and describes some other uses for function handles like graphics callbacks.
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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!