I have two matrices S and T which have n columns and a row vector v of length n. By my construction, I know that S does not have any duplicates. What I'm looking for is a fast way to find out whether or not the row vector v appears as one of the rows of S. Currently I'm using the test
if min([sum(abs(S - repmat(f,size(S,1),1)),2);sum(abs(T - repmat(v,size(dS_new,1),1)),2)]) ~= 0 ....
When I first wrote it, I had a for loop testing each (I knew this would be slow, I was just making sure the whole thing worked first). I then changed this to defining a matrix diff by the two components above and then summing, but this was slightly slower than the above.
All the stuff I've found online says to use the function unique. However, this is very slow as it orders my matrix after. I don't need this, and it's a massively waste of time (it makes the process really slow). This is a bottleneck in my code -- taking nearly 90% of the run time. If anyone has any advice as how to speed this up, I'd be most appreciative!
I imagine there's a fairly straightforward way, but I'm not that experienced with Matlab (fairly, just not lots). I know how to use basic stuff, but not some of the more specialist functions.
Thanks!
To clarify following Sardar_Usama's comment, I want this to work for a matrix with any number of rows and a single vector. I'd forgotten to mention that the elements are all in the set {0,1,...,q-1}. I don't know whether that helps or not to make it faster!
You may want this:
ismember(v,S,'rows')
and replace arguments S and v to get indices of duplicates
ismember(S,v,'rows')
Or
for test if v is member of S:
any(all(bsxfun(#eq,S,v,2))
this returns logical indices of all duplicates
all(bsxfun(#eq,S,v),2)
There is a [Q,R] = qr(A,0) function in Matlab, which, according to documentation, returns an "economy" version of qr-decomposition of A. norm(A-Q*R) returns ~1e-12 for my data set. Also Q'*Q should theoretically return I. In practice there are small nonzero elements above and below the diagonal (of the order of 1e-6 or so), as well as diagonal elements that are slightly greater than 1 (again, by 1e-6 or so). Is anyone aware of a way to control precision of qr(.,0), or quality(orthogonality) of resulting Q, either by specifying epsilon, or via the number of iterations ? The size of the data set makes qr(A) run out of memory so I have to use qr(A,0).
When I try the non- economy setting, I actually get comparable results for A-Q*R. Even for a tiny matrix containing small numbers as shown here:
A = magic(20);
[Q, R] = qr(A); %Result does not change when using qr(A,0)
norm(A-Q*R)
As such I don't believe the 'economy' is the problem as confirmed by #horchler in the comments, but that you have just ran into the limits of how accurate calculations can be done with data of type 'double'.
Even if you change the accuracy somehow, you will always be dealing with an approximation, so perhaps the first thing to consider here is whether you really need greater accuracy than you already have. If you need more accuracy there may always be a way, but I doubt whether it will be a straightforward one.
We have a problem formulation as shown in this link.
Considering that the first call of bintprog gives a solution x that after some post processing does not adequately addresses the physical problem, is it possible to recall bintprog and exclude the prior solution x?
You need a nogood cut.
Suppose you find a solution \hat{x} that you then decide is infeasible (through some sort of post-processing). Let x and \hat{x} be indexed by i.
You can add a constraint of the following form:
\sum_{i : \hat{x}_i = 0} x_i + \sum_{i : \hat{x} = 1} (1-x_i) \geq 1
This constraint is an example of a no-good cut: the solution must differ from \hat{x} by at least one index i, otherwise it is infeasible. If your variables are not binary no-goods can be a little more complex.
You can add a no-good to your solution by appending the constraint as a row to your constraint matrix and re-solving with the bintprog() function. I'll leave it to you to you rewrite it in the MATLAB notation.
You didn't say what your post-processing does, but it would be even better if the post-processing could infer from your solution \hat{x} that other solutions are also infeasible, and you can add more than one row per iteration. This is a form of logic-based Benders decomposition, and the inference of other infeasible solutions is called solving an inference dual (as opposed to standard Benders decomposition, where you're solving the linear programming dual). More on logic based Benders decomposition from the man who coined the term, John Hooker of CMU.
Sorry for the formatting. I need to go but I'll figure out a way to display equations more nicely later.
I have 2 sets of data of float numbers, set A and set B. Both of them are matrices of size 40*40. I would like to find out which set is closer to the normal distribution. I know how to use probplot() in matlab to plot the probability of one set. However, I do not know how to find out the level of the fitness of the distribution is.
In python, when people use problot, a parameter ,R^2, shows how good the distribution of the data is against to the normal distribution. The closer the R^2 value to value 1, the better the fitness is. Thus, I can simply use the function to compare two set of data by their R^2 value. However, because of some machine problem, I can not use the python in my current machine. Is there such parameter or function similar to the R^2 value in matlab ?
Thank you very much,
Fitting a curve or surface to data and obtaining the goodness of fit, i.e., sse, rsquare, dfe, adjrsquare, rmse, can be done using the function fit. More info here...
The approach of #nate (+1) is definitely one possible way of going about this problem. However, the statistician in me is compelled to suggest the following alternative (that does, alas, require the statistics toolbox - but you have this if you have the student version):
Given that your data is Normal (not Multivariate normal), consider using the Jarque-Bera test.
Jarque-Bera tests the null hypothesis that a given dataset is generated by a Normal distribution, versus the alternative that it is generated by some other distribution. If the Jarque-Bera test statistic is less than some critical value, then we fail to reject the null hypothesis.
So how does this help with the goodness-of-fit problem? Well, the larger the test statistic, the more "non-Normal" the data is. The smaller the test statistic, the more "Normal" the data is.
So, assuming you have converted your matrices into two vectors, A and B (each should be 1600 by 1 based on the dimensions you provide in the question), you could do the following:
%# Build sample data
A = randn(1600, 1);
B = rand(1600, 1);
%# Perform JB test
[ANormal, ~, AStat] = jbtest(A);
[BNormal, ~, BStat] = jbtest(B);
%# Display result
if AStat < BStat
disp('A is closer to normal');
else
disp('B is closer to normal');
end
As a little bonus of doing things this way, ANormal and BNormal tell you whether you can reject or fail to reject the null hypothesis that the sample in A or B comes from a normal distribution! Specifically, if ANormal is 1, then you fail to reject the null (ie the test statistic indicates that A is probably drawn from a Normal). If ANormal is 0, then the data in A is probably not generated from a Normal distribution.
CAUTION: The approach I've advocated here is only valid if A and B are the same size, but you've indicated in the question that they are :-)
I programmed in MATLAB for many years, but switched to using R exclusively in the past few years so I'm a little out of practice. I'm interviewing a candidate today who describes himself as a MATLAB expert.
What MATLAB interview questions should I ask?
Some other sites with resources for this:
"Matlab interview questions" on Wilmott
"MATLAB Questions and Answers" on GlobaleGuildLine
"Matlab Interview Questions" on CoolInterview
This is a bit subjective, but I'll bite... ;)
For someone who is a self-professed MATLAB expert, here are some of the things that I would personally expect them to be able to illustrate in an interview:
How to use the arithmetic operators for matrix or element-wise operations.
A familiarity with all the basic data types and how to convert effortlessly between them.
A complete understanding of matrix indexing and assignment, be it logical, linear, or subscripted indexing (basically, everything on this page of the documentation).
An ability to manipulate multi-dimensional arrays.
The understanding and regular usage of optimizations like preallocation and vectorization.
An understanding of how to handle file I/O for a number of different situations.
A familiarity with handle graphics and all of the basic plotting capabilities.
An intimate knowledge of the types of functions in MATLAB, in particular nested functions. Specifically, given the following function:
function fcnHandle = counter
value = 0;
function currentValue = increment
value = value+1;
currentValue = value;
end
fcnHandle = #increment;
end
They should be able to tell you what the contents of the variable output will be in the following code, without running it in MATLAB:
>> f1 = counter();
>> f2 = counter();
>> output = [f1() f1() f2() f1() f2()]; %# WHAT IS IT?!
We get several new people in the technical support department here at MathWorks. This is all post-hiring (I am not involved in the hiring), but I like to get to know people, so I give them the "Impossible and adaptive MATLAB programming challenge"
I start out with them at MATLAB and give them some .MAT file with data in it. I ask them to analyze it, without further instruction. I can very quickly get a feel for their actual experience.
http://blogs.mathworks.com/videos/2008/07/02/puzzler-data-exploration/
The actual challenge does not mean much of anything, I learn more from watching them attempt it.
Are they making scripts, functions, command line or GUI based? Do they seem to have a clear idea where they are going with it? What level of confidence do they have with what they are doing?
Are they computer scientists or an engineer that learned to program. CS majors tend to do things like close their parenthesis immediately, and other small optimizations like that. People that have been using MATLAB a while tend to capture the handles from plotting commands for later use.
How quickly do they navigate the documentation? Once I see they are going down the 'right' path then I will just change the challenge to see how quickly they can do plots, pull out submatrices etc...
I will throw out some old stuff from Project Euler. Mostly just ramp up the questions until one of us is stumped.
Floating Point Questions
Given that Matlab's main (only?) data type is the double precision floating point matrix, and that most people use floating point arithmetic -- whether they know it or not -- I'm astonished that nobody has suggested asking basic floating point questions. Here are some floating point questions of variable difficulty:
What is the range of |x|, an IEEE dp fpn?
Approximately how many IEEE dp fpns are there?
What is machine epsilon?
x = 10^22 is exactly representable as a dp fpn. What are the fpns xp
and xs just below and just above x ?
How many dp fpns are in [1,2)? How many atoms are on an edge of a
1-inch sugar cube?
Explain why sin(pi) ~= 0, but cos(pi) = -1.
Why is if abs(x1-x2) < 1e-10 then a bad convergence test?
Why is if f(a)*f(b) < 0 then a bad sign check test?
The midpoint c of the interval [a,b] may be calculated as:
c1 = (a+b)/2, or
c2 = a + (b-a)/2, or
c3 = a/2 + b/2.
Which do you prefer? Explain.
Calculate in Matlab: a = 4/3; b = a-1; c = b+b+b; e = 1-c;
Mathematically, e should be zero but Matlab gives e = 2.220446049250313e-016 = 2^(-52), machine epsilon (eps). Explain.
Given that realmin = 2.225073858507201e-308, and Matlab's u = rand gives a dp fpn uniformly distributed over the open interval (0,1):
Are the floating point numbers [2^(-400), 2^(-100), 2^(-1)]
= 3.872591914849318e-121, 7.888609052210118e-031, 5.000000000000000e-001
equally likely to be output by rand ?
Matlab's rand uses the Mersenne Twister rng which has a period of
(2^19937-1)/2, yet there are only about 2^64 dp fpns. Explain.
Find the smallest IEEE double precision fpn x, 1 < x < 2, such that x*(1/x) ~= 1.
Write a short Matlab function to search for such a number.
Answer: Alan Edelman, MIT
Would you fly in a plane whose software was written by you?
Colin K would not hire me (and probably fire me) for saying "that
Matlab's main (only?) data type is the double precision floating
point matrix".
When Matlab started that was all the user saw, but over the years
they have added what they coyly call 'storage classes': single,
(u)int8,16,32,64, and others. But these are not really types
because you cannot do USEFUL arithmetic on them. Arithmetic on
these storage classes is so slow that they are useless as types.
Yes, they do save storage but what is the point if you can't do
anything worthwhile with them?
See my post (No. 13) here, where I show that arithmetic on int32s is 12 times slower than
double arithmetic and where MathWorkser Loren Shure says "By
default, MATLAB variables are double precision arrays. In the olden
days, these were the ONLY kind of arrays in MATLAB. Back then even
character arrays were stored as double values."
For me the biggest flaw in Matlab is its lack of proper types,
such as those available in C and Fortran.
By the way Colin, what was your answer to Question 14?
Ask questions about his expertise and experience in applying MATLAB in your domain.
Ask questions about how he would approach designing an application for implementation in MATLAB. If he refers to recent features of MATLAB, ask him to explain them, and how they are different from the older features they replace or supplement, and why they are preferable (or not).
Ask questions about his expertise with MATLAB data structures. Many of the MATLAB 'experts' I've come across are very good at writing code, but very poor at determining what are the best data structures for the job in hand. This is often a direct consequence of their being domain experts who've picked up MATLAB rather than having been trained in computerism. The result is often good code which has to compensate for the wrong data structures.
Ask questions about his experience, if any, with other languages/systems and invite him to expand upon his observations about the relative strengths and weaknesses of MATLAB.
Ask for top tips on optimising MATLAB programs. Expect the answers: vectorisation, pre-allocation, clearing unused variables, etc.
Ask about his familiarity with the MATLAB profiler, debugger and lint tools. I've recently discovered that the MATLAB 'expert' over in the corner here had never, in 10 years using the tool, found the profiler.
That should get you started.
I. I think this recent SO question
on indexing is a very good question
for an "expert".
I have a 2D array, call it 'A'. I have
two other 2D arrays, call them 'ix'
and 'iy'. I would like to create an
output array whose elements are the
elements of A at the index pairs
provided by x_idx and y_idx. I can do
this with a loop as follows:
for i=1:nx
for j=1:ny
output(i,j) = A(ix(i,j),iy(i,j));
end
end
How can I do this without the loop? If
I do output = A(ix,iy), I get the
value of A over the whole range of
(ix)X(iy).
II. Basic knowledge of operators like element-wise multiplication between two matrices (.*).
III. Logical indexing - generate a random symmetric matrix with values from 0-1 and set all values above T to 0.
IV. Read a file with some properly formatted data into a matrix (importdata)
V. Here's another sweet SO question
I have three 1-d arrays where elements
are some values and I want to compare
every element in one array to all
elements in other two.
For example:
a=[2,4,6,8,12]
b=[1,3,5,9,10]
c=[3,5,8,11,15]
I want to know if there are same
values in different arrays (in this
case there are 3,5,8)
Btw, there's an excellent chance your interviewee will Google "MATLAB interview questions" and see this post :)
Possible question:
I have an array A of n R,G,B triplets. It is a 3xn matrix. I have another array B in the form 1xn which stores an index value (association to a cluster) for each triplet.
How do I plot the triplets of A in 3D space (using plot3 function), coloring each triplet according to its index in B? (The goal is to qualitatively evaluate my clustering)
Really, really good programmers who are MATLAB novices won't be able to give you an efficient (== MATLAB style) solution. However, it is a very simple problem if you do know your MATLAB.
Depends a bit what you want to test.
To test MATLAB fluency, there are several nice Stack Overflow questions that you could use to test e.g. array manipulations (example 1, example 2), or you could use fix-this problems like this question (I admit, I'm rather fond of that one), or look into this list for some highly MATLAB-specific stuff. If you want to be a bit mean, throw in a question like this one, where the best solution is a loop, and the typical MATLAB-way-of-thinking solution would just fill up the memory.
However, it may be more useful to ask more general programming questions that are related to your area of work and see whether they get the problem solved with MATLAB.
For example, since I do image analysis, I may ask them to design a class for loading images of different formats (a MATLAB expert should know how to do OOP, after all, it has been out for two years now), and then ask follow-ups as to how to deal with large images (I want to see a check on how much memory would be used - or maybe they know memory.m - and to hear about how MATLAB usually works with doubles), etc.