I'm trying to find/write a function that would perform the same operation as imlincomb(). However, I am having trouble finding such functions in C++ without using any Matlab API functions other than Intel Performance Primitiives library, and I don't really want to purchase a license for it unless my application really has to take advantage of it. What would be any easy method of implementing it, or perhaps if there are any standard functions that make the job a lot easier?
Thanks in advance.
There's definitely nothing of the sort in any standard C++ package. You might be able to use something in LAPACK, but I think you'd be better off writing your own. It's a fairly simple function: each output pixel is independent and depends only on the input pixels at the same coordinates. In pseudocode:
for each row y in [0, height-1]
for each column x in [0, width-1]
for each color channel c in (R, G, B)
output[y][x][c] = 0
for each input i
output[y][x][c] += weight[i] * input[i][y][x][c]
Of course, the exact formulation depends on how exactly your images are stored (3D array, 2D array, or 1D array, and be careful about the order of your dimensions!).
Related
I have n points in a 2D plane. I want to calculate the distance between each two points in c++. Position of m'th point in the plan is (x(m),y(m)). This points changes during passing time. The number of time steps is equal to 10^5.
I wrote below code, but as n is a big number(5000) and I want to find the distance between points 10^5 times, I'm searching for the most optimized way to do that. Could anyone tell me what is the least time-consuming way to do that?
for(i=1;n;++)
for(j=1;n;++)
if (i>j)
r(i,j)= r(j,i);
else
r(i,j)=sqrt((x(i)-x(j))^2+(y(i)-y(j))^2);
end
end
end
I know that, in Matlab, I can find this by using bsxfun function. I want also to know which one could calculate distances faster? Matlab or c++?
Regarding Matlab, you have also pdist which does exactly that (but is not so fast), and you should also read this.
About comparing Matlab and C first read this and this. Also keep in mind that Matlab, as a desktop program, requires knowing not only a general efficient way to implement your code but also the right way to do this in Matlab. One example is the difference between functions. Built-in functions are written in FORTRAN or C and run much faster then non-built-in functions. To know if a function is built-in, type:
which function_name
and check if you see "built-in" at the start of the output:
built-in (C:\Program Files\MATLAB\...)
I'm new to C++ and I think a good way for me to jump in is to build some basic models that I've built in other languages. I want to start with just Linear Regression solved using first order methods. So here's how I want things to be organized (in pseudocode).
class LinearRegression
LinearRegression:
tol = <a supplied tolerance or defaulted to 1e-5>
max_ite = <a supplied max iter or default to 1k>
fit(X, y):
// model learns weights specific to this data set
_gradient(X, y):
// compute the gradient
score(X,y):
// model uses weights learned from fit to compute accuracy of
// y_predicted to actual y
My question is when I use fit, score and gradient methods I don't actually need to pass around the arrays (X and y) or even store them anywhere so I want to use a reference or a pointer to those structures. My problem is that if the method accepts a pointer to a 2D array I need to supply the second dimension size ahead of time or use templating. If I use templating I now have something like this for every method that accepts a 2D array
template<std::size_t rows, std::size_t cols>
void fit(double (&X)[rows][cols], double &y){...}
It seems there likely a better way. I want my regression class to work with any size input. How is this done in industry? I know in some situations the array is just flattened into row or column major format where just a pointer to the first element is passed but I don't have enough experience to know what people use in C++.
You wrote a quite a few points in your question, so here are some points addressing them:
Contemporary C++ discourages working directly with heap-allocated data that you need to manually allocate or deallocate. You can use, e.g., std::vector<double> to represent vectors, and std::vector<std::vector<double>> to represent matrices. Even better would be to use a matrix class, preferably one that is already in mainstream use.
Once you use such a class, you can easily get the dimension at runtime. With std::vector, for example, you can use the size() method. Other classes have other methods. Check the documentation for the one you choose.
You probably really don't want to use templates for the dimensions.
a. If you do so, you will need to recompile each time you get a different input. Your code will be duplicated (by the compiler) to the number of different dimensions you simultaneously use. Lots of bad stuff, with little gain (in this case). There's no real drawback to getting the dimension at runtime from the class.
b. Templates (in your setting) are fitting for the type of the matrix (e.g., is it a matrix of doubles or floats), or possibly the number of dimesions (e.g., for specifying tensors).
Your regressor doesn't need to store the matrix and/or vector. Pass them by const reference. Your interface looks like that of sklearn. If you like, check the source code there. The result of calling fit just causes the class object to store the parameter corresponding to the prediction vector β. It doesn't copy or store the input matrix and/or vector.
I have been looking for an answer to this for quite a while, but I am not able to find one.
The problem:
I have a n-dimensional (e.g. n = 9) function which is extremely computationally burdensome to evaluate, but for which I need a huge amount of evaluations. I want to use interpolation for this case.
However k < n dimensions (e.g. k = 7) are discrete (mostly binary) and therefore I need not to interpolate over these, which leaves me with m-dimensions (e.g. 2) over which I want to interpolate. I am mostly interested in basic linear interpolation, similar to http://rncarpio.github.io/linterp/.
The question:
(Option A) Should I invoke d1 x d2 x ... x dk interpolation functions (e.g. 2^7= 128) which then only interpolate over the two dimensions I need, but I need to look for the right interpolation function every time I need a value, ...
... (Option B) or should I invoke one interpolation function which could possible interpolate between all dimensions, but which I then will only use to interpolate across the two dimensions I need (for all others I fully provide the grid with function values)?
I think it is important to emphasize that I am really interested in linear interpolation and that the answer will most likely differ in other cases. Furthermore, in the application I want to use this, I need not 128 functions but rather over 10,000 functions.
Additionally, should option A be the answer, how should I store the interpolation functions in c++, i.e. should I use a map with a tuple as a key (drawing on the boost library), or a multidimensional array (again, drawing on the boost library) or is there an easier way?
I'd likely choose Option A, but not maps. If you have binary data, just use an array of size 2 (this is one of the rare cases when using an array is right); if you have a small domain consider having two vectors, one for keys, one for values. This is because vector search can be made extremely efficient on at least on x86 / x64 architectures. Be sure to hide this implementation detail by providing an accessor function (i.e., const value& T::lookup(const key&)). I'd vote against using a tuple as a map key as it makes it both slower and more complicated. If you need to extremely optimize and your domains are so small that the product of their cardinality fits within 64 bits, you might just manually create an index key (like: (1<<3) * key4bits + (1<<2) * keyBinary + key2bits), in this case you'll use a map (or two vectors).
I have a dataset from custom abstract objects and a custom distance function. Is there any good SVM libraries that allows me to train on my custom objects (not 2d points) and my custom distance function?
I searched the answers in this similar stackoverflow question, but none of them allows me to use custom objects and distance functions.
First things first.
SVM does not work on distance functions, it only accepts dot products. So your distance function (actually similarity, but usually 1-distance is similarity) has to:
be symmetric s(a,b)=s(b,a)
be positive definite s(a,a)>=0, s(a,a)=0 <=> a=0
be linear in first argument s(ka, b) = k s(a,b) and s(a+b,c) = s(a,c) + s(b,c)
This can be tricky to check, as you actually ask "is there a function from my objects to some vector space, phi such that s(phi(x), phi(y))" is a dot-product, thus leading to definition of so called kernel, K(x,y)=s(phi(x), phi(y)). If your objects are themselves elements of vector space, then sometimes it is enough to put phi(x)=x thus K=s, but it is not true in general.
Once you have this kind of similarity nearly any SVM library (for example libSVM) works with providing Gram matrix. Which is simply defined as
G_ij = K(x_i, x_j)
Thus requiring O(N^2) memory and time. Consequently it does not matter what are your objects, as SVM only works on pairwise dot-products, nothing more.
If you look appropriate mathematical tools to show this property, what can be done is to look for kernel learning from similarity. These methods are able to create valid kernel which behaves similarly to your similarity.
Check out the following:
MLPack: a lightweight library that provides lots of functionality.
DLib: a very popular toolkit that is used both in industry and academia.
Apart from these, you can also use Python packages, but import them from C++.
In OpenCV 2.0, they switched from having separate image and matrix classes to a unified class called cv::Mat. What was the design decision there? To me, who works with both images and matrices on a daily basis, they are very different objects that just happen to have a commonality: they are both accessed in a grid. However, the thing that makes a matrix a matrix in my mind is you can do y = A*x, where A is m by n, x is n by 1, and y is m by 1. This makes almost no sense when A is an image why you would want to do this operation.
Merging the classes also had the nasty side effect of needing templating and odd matrix types (like CV_32FC3 for a 3-channel floating-point matrix/image). Since I know the guys working on OpenCV aren't crazy, what was the design decision that made them merge image and matrix classes? Was it code reuse? Was it efficiency somehow?
Main drawback is that you can't overload ' * ' to do a multiplcation, but I don't think you should overload ' * ' for anything more complex than builtin types anyway.
What is a convolution kernel - an image or a matrix?
You only have to learn all the handler/ctor functions once - instead of two sets of them