efficient parallel(vector) matrix-times matlab - arrays

Does anyone know how to do array matrix multiplication in matlab? i.e. I have two 3 dimensional arrays consisting of sets of matrices in the first 2 dimensions and I would like to multiply each matrix in the first array with the corresponding one in the second array. So, i.e. if
A=randn(3,3);
B=cat(3,A,A);
I would like [[operation]] such that
B[[operation]]B = cat(3,A*A, A*A)
done in efficient vector form.
Many thanks in advance.

I have used MULTIPROD from the Mathworks FileExchange for N-D array multiplication before. It is basically an extension of bsxfun to N-D arrays, and works quite nicely (and fast) - although the interface is a bit cumbersome.

Related

Reshaping array by horizontal slices (Matlab)

I am working with pretty big arrays of data, but here I'll consider a toy example.
Suppose a is 6x3 array:
a=[1,2,3;4,5,6;7,8,9;10,11,12;13,14,15;16,17,18]
I want to reshape it to the array of size (3,3,2) by horizontal slices, so that the resulting array b would be:
b(:,:,1)= [1,2,3;4,5,6;7,8,9]
b(:,:,2)= [10,11,12;13,14,15;16,17,18]
I was trying to do it with the reshape function: b=reshape(a,[3,3,2]), however, the resulting array is different (in goes though columns first).
I didn't really find the appropriate options for the reshape function.
Is there a nice solution to this issue? I know how to do it with a single for loop.
Thanks
One approach is to reshape the transposed a matrix, then transpose back using permute.
b = permute(reshape(a.',3,3,2), [2,1,3]);
This solution requires a permute and a cheap reshape:
b = permute(reshape(a,3,2,3),[1,3,2]);

Mathematical representation of a multidimensional array

This might me a ridiculous question.
I created mathematical model using Python and I know that I started this from the end, but I need write mathematical equations for the documentation.
The equation has multidimensional array in it.
So my question is how to present multidimensional array in mathematical way?
If the number of dimensions in your array is one, you can represent it as a vector, or perhaps a tuple. But this almost certainly is not what you mean by "multidimensional."
If the number of dimensions is two, you can use a matrix.
If the number of dimensions is greater than two, you can use a tensor. Here is a Wikipedia link explaining a little how tensors and multidimensional arrays are related. A search will give you many more such pages. Tensors include vectors and matrices, so this is the most general solution, though vectors and matrices are much more well known.

Matlab: multiply subset of three dimensional array with two dimensional array

I have a AxBxC array where AXB are pointing to individual grids of a field that i sampled (like coordinates) and C corresponds to the layers underneath. Now I want to calculate the impact of certain activities on these individual points by multiplying it with a 2D matrix.
E.g.
x=5; %x-Dimensions of the sampled area
y=5; %y-Dimensions of the sampled area
z=3; %z-number of layers sampled
Area= zeros(x,y,z);
AreaN= zeros(x,y,z);
now I want to multiply every layer of a given point in X*Y with:
AppA=[0.4,0.4,0.2;0.4,0.5,0.1;0.1,0.2,0.7];
I tried:
for i=1:x
for j=1:y
AreaN(i,j,:)= AppA*Area(i,j,:);
end
end
Unfotunately I get the error:
Error using *
Inputs must be 2-D, or at least one input must be scalar.
To compute elementwise TIMES, use TIMES (.*) instead.
Any help to this is appreciated since I am not yet really familiar with matlab.
Correct Approach
I think, to correct your code, you need to convert that Area(i,j,:) to a column vector, which you can do with squeeze. Thus, the correct loop-based code would look something like this -
AreaN= zeros(x,y,z);
for i=1:x
for j=1:y
AreaN(i,j,:)= AppA*squeeze(Area(i,j,:));
end
end
Now, there are efficient no-loop/vectorized approaches that can be suggested here to get to the output.
Vectorized Approach #1
First approach could be with matrix multiplication and has to be pretty efficient one -
AreaN = reshape(reshape(Area,x*y,z)*AppA.',x,y,z)
Vectorized Approach #2
Second one with bsxfun -
AreaN = squeeze(sum(bsxfun(#times,Area,permute(AppA,[3 4 2 1])),3))
Vectorized Approach #2 Rev 1
If you would like to get rid of the squeeze in the bsxfun code, you need to use an extra permute in there -
AreaN = sum(bsxfun(#times,permute(Area,[1 2 4 3]),permute(AppA,[4 3 1 2])),4)
This would solve the matrix multiplication problem:
AreaN(i,j,:)= AppA*reshape(Area(i,j,:),3,[]);
You might want to consider using bsxfun to aviod loops.

How to indicate specific slice of a 3D array in MATLAB using GPUs?

I have a 4x4x1250 matrix in MATLAB. I want to find a way to move through the 4x4 matrices slice by slice in order to find the condition of the 4x4 matrices individually.
I don't want to do it in a loop because I want to do this on the GPU and would like it to be indexed.
I saw "squeeze", but I don't think it works for 3D arrays...
I kind of want to use arrayfun, but I don't know how to indicate the specific dimension that I'm interested in.
Any ideas?
Edit: I thought the details I gave are sufficient, nevertheless:
I have a matrix A, size 4x4x1250.
I am interested in the conditions of the 1250 4x4 matrices that make up A. So lets say B = A(:,:,1).
I want to calculate cond(B), but in reality I want 1250 of these calculations.
If I do arrayfun, I don't know how to specify the specific dimension of A along which to slice.
ARRAYFUN disregards the shape of the input, and operates in a purely element-wise fashion. There's also PAGEFUN on the GPU which operates on pages of an array - however, PAGEFUN only really offers an advantage if you're using one of the functions explicitly supported - otherwise it operates in an element-wise fashion.

Matlab Arrays of 2x2 matrices and element by element matrix/vector multiplication

I want to have a time series of 2x2 complex matrices,Ot, and I then want to have 1-line commands to multiply an array of complex vectors Vt, by the array Ot where the position in the array is understood as the time instant. I will want Vtprime(i) = Ot(i)*Vt(i). Can anyone suggest a simple way to implement this?
Suppose I have a matrix, M(t), where the elements m(j,k) are functions of t and t is an element of some series (t = 0:0.1:3). Can I create an array of matrices very easily?
I understand how to have an array in Matlab, and even a two dimensional array, where each "i" index holds two complex numbers (j=0,1). That would be a way to have a "time series of complex 2-d vectors". A way to have a time series of complex matrices would be a three dimensional array. (i,j,k) denotes the "ith" matrix and j=0,1 and k=0,1 give the elements of that matrix.
If I go a head and treat matlab like a programming language with no special packages, then I end up having to write the matrix multiplications in terms of loops etc. This then goes towards all the matrix operations. I would prefer to use commands that will make all this very easy if I can.
This could be solved with Matlab array iterations like
vtprime(:) = Ot(:)*Vt(:)
if I understand your problem correctly.
Since Ot and Vt are both changing with time index, I think the best way to do this is in a loop. (If only one of Ot or Vt was changing with time, you could set it up in one big matrix multiplication.)
Here's how I would set it up: Ot is a complex 2x2xI 3D matrix, so that
Ot(:,:,i)
references the matrix at time instant i.
Vt is a complex 2xI matrix, so that
Vt(:,i)
references the vector at time instant i.
To do the multiplication:
for i = 1:I
Vtprime(:,i) = Ot(:,:,i) * Vt(:,i);
end
The resulting Vtprime is a 2xI matrix set up so that Vtprime(:,i) is the output at time instant i.

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