I have this code:
from itertools import product
from numpy import zeros
Ysys = zeros((2*n_bus, 2*n_bus))
for a, b in product(range(n_bus), range(n_bus)):
Ysys[2*a, 2*b] = Yseries[a, b].real
Ysys[2*a, 2*b+1] = -Yseries[a, b].imag
Ysys[2*a+1, 2*b] = Yseries[a, b].imag
Ysys[2*a+1, 2*b+1] = Yseries[a, b].real
Yseries is a square sparse matrix of n_bus by n_bus dimensions that contains complex numbers. Essentially I want to "explode" the complex matrix into a float matrix.
My for loop is inefficient since I should know in advance which are the row, column coordinates of every data entry. Ideally a would be an array with all the row coordinates of every entry, and b should be an array with all the column coordinates of every entry.
My problem is that I don't understand the arrays indices and indptr contained in my CSR matrx Yseries.
Regardless of all that I've said, I'd appreciate indications of how to vectorize the for loop.
I solved it by passing the matrix to COO sparse type:
m = Yseries.tocoo()
a = m.row
b = m.col
Ysys[2 * a, 2 * b] = m.data.real
Ysys[2 * a, 2 * b + 1] = -m.data.imag
Ysys[2 * a + 1, 2 * b] = m.data.imag
Ysys[2 * a + 1, 2 * b + 1] = m.data.real
After measuring the execution time, for dimension = 30 I get:
For loop (original question): 0.06154400000000004 s
Vectorized (this answer): 0.00011099999999997223 s
Related
I have three vectors in a function, each of size 2. I want to get the sum of the top 2 numbers at each index. What I mean is this:
A = [4,4];
B = [3,5];
C = [5,6];
Sum = [9,11];
I would like to skip if-else statements if possible.
A simple way is to
concatenate the row vectors into a matrix: [A; B; C]
apply maxk along the first dimension: maxk(..., 2, 1), where 2 is the desired number of elements
then apply sum along the first dimension: sum(..., 1.
Thus:
result = sum(maxk([A; B; C], 2, 1), 1);
First, you concatenate your three vectors through
vectors = [A; B; C];
Then, you sort it through
s = sort(vectors, 'descent');
Finally, you sum the two bigger element of each column through
SUM = s(1, :) + s(2, :)
I wish to fill a N x M x W matrix ‘S’ with the data from matrices ‘P’ and ‘Q’. They are defined below and illustrated in the attached image. Also, we know for sure that n_1 + n_2 = N, m < M, so all the data may fit in the ‘S’ matrix.
S = zeros(M,N,W);
P = rand(m,n_1,W);
Q = rand(m,n_2,W);
I wish to combine ‘P’ and ‘Q’ in a manner specified by 3 other matrices, ‘Line_num’, ‘P_col’ and ‘Q_col’, described below and in the middle part of the attached image.
P_col = randperm(N); P_col = P_col(1:n_1); % 1 x n_1 matrix
Q_col = setxor(P_col, 1:1:N); % 1 x n_2 matrix
Line_num is a matrix composed of W vectors of the form aa:1:bb, where bb-aa = m and aa is chosen at random for each vector.
The important thing is that in this case the data along the 3rd dimension in all these matrixes represent W different test cases, with the data being different and not to be mixed between each other.
To fill ‘S’ one may proceed in two logical steps (although if it can be done in one I shall be glad)
combine Q and P into an intermediate matrix Y of shape m x N x W by
interweaving their columns. The columns specified in ‘Q_col’ are
taken from Q (using the vector index) and put in the matrix Y (using
the vector value). The same goes for P.
For each of the W vectors composing Line_num and arrays composing S,
use the values in the vector Line_num to spread out Y to the
corresponding rows in S, meanwhile maintaining their top to bottom
order.
I wish to achieve this without for-loops as I am looking to ‘vectorize’ my code and thus improve its running speed.
I have had a look at this post and this post, which are similar to what I desire. However they are simpler as the numbers to be extracted are constant. Maybe something similar would be appropriate?
Thank you for your help :)
Link to the image aforementioned
EDIT: here is an example code with a for-loop of what I want (my problem is that I want to get rid of the loop)
W = 4;
N = 10; n_1 = 4; n_2 = 6;
M = 20; m = 5;
P_col = [1,3,5,8]; % 1 x n_1 matrix
Q_col = setxor(P_col, 1:1:N); % 1 x n_2 matrix
line_num(:,:,1) = [1,5,10,15,18];
line_num(:,:,2) = [2,3,8,11,12];
line_num(:,:,3) = [4,7,8,14,19];
line_num(:,:,4) = [2,6,13,15,16];
S = zeros(M,N,W);
P = rand(m,n_1,W);
Q = rand(m,n_2,W);
for w=1:W
line_num_I = line_num(:,:,w);
S(line_num_I,Q_col,w) = Q(:,:,w);
S(line_num_I,P_col,w) = P(:,:,w);
end
Here is a vectorized solution. I'm not sure if it is more efficient than loop version specially when the size of data is large.
S ( reshape(line_num,[],1,W) ...
+ ([Q_col-1 P_col-1]) * M ...
+ (reshape(0:W-1,1,1,[]))*M*N ...
) ...
= ...
[reshape(Q,[],W);reshape(P,[],W)];
Here implicit expansion is used to convert subscripts to indices. Equivalently bsxfun can be used to compute linear indices:
S ( ...
bsxfun(#plus, ...
reshape(line_num,[],1,W), ...
bsxfun (#plus, ...
([Q_col-1 P_col-1]) * M, ...
(reshape(0:W-1,1,1,[]))*M*N ...
) ...
) ...
) ...
= ...
[reshape(Q,[],W);reshape(P,[],W)];
*Here You can find how to convert 3D index to lindex.
So I ended up finding the answer. For those of you that it may interest, the above for-loop may be replaced by
% 1. Combine columns
mixed_col = zeros(m,N,W);
mixed_col(:,Q_col,:) = Q(:,:,:);
mixed_col(:,P_col,:) = P(:,:,:);
mixed_col = permute(mixed_col,[2,1,3]); % turn 3D matrix into 2D [1]
mixed_col = reshape(mixed_col,N,[],1)';
% 2. Combine lines
S = reshape(S,M*w,N,1); % turn 3D matrix into 2D [2]
line_num_v = permute(line_num + reshape((0:1:(W-1)).*M,1,1,W),[2,1,3]); % turn 3D matrix into 2D [3]
line_num_v = reshape(line_num_v,[],1,1);
S(line_num_v,:) = mixed_col(:,:); % combine using three 2D matrices
S = permute(reshape(S',N,M,W),[2,1,3]);
This involves lots of reshaping but I don't have a simpler answer.
Thanks again for your help.
I have two matrices A and B. A(:,1) corresponds to an x-coordinate, A(:,2) corresponds to a y-coordinate, and A(:,3) corresponds to a certain radius. All three values in a row describe the same circle. Now let's say...
A =
[1,4,3]
[8,8,7]
[3,6,3]
B =
[1,3,3]
[1, 92,3]
[4,57,8]
[5,62,1]
[3,4,6]
[9,8,7]
What I need is to be able to loop through matrix A and determine if there are any rows in matrix B that are "similar" as in the x value is within a range (-2,2) of the x value of A (Likewise with the y-coordinate and radius).If it satisfies all three of these conditions, it will be added to a new matrix with the values that were in A. So for example I would need the above data to return...
ans =
[1,4,3]
[8,8,7]
Please help and thank you in advance to anyone willing to take the time!
You can use ismembertol.
result = A(ismembertol(A,B,2,'ByRows',1,'DataScale',1),:)
Manual method
A = [1,4,3;
8,8,7;
3,6,3];
B = [1,3,3;
1,92,3;
4,57,8;
5,62,1;
3,4,6;
9,8,7]; % example matrices
t = 2; % desired threshold
m = any(all(abs(bsxfun(#minus, A, permute(B, [3 2 1])))<=t, 2), 3);
result = A(m,:);
The key is using permute to move the first dimension of B to the third dimension. Then bsxfun computes the element-wise differences for all pairs of rows in the original matrices. A row of A should be selected if all the absolute differences with respect to any column of B are less than the desired threshold t. The resulting variable m is a logical index which is used for selecting those rows.
Using pdist2 (Statistics and Machine Learning Toolbox)
m = any(pdist2(A, B, 'chebychev')<=t, 2);
result = A(m,:);
Ths pdist2 function with the chebychev option computes the maximum coordinate difference (Chebychev distance, or L∞ metric) between pairs of rows.
With for loop
It should work:
A = [1,4,3;
8,8,7;
3,6,3]
B = [1,3,3;
1,92,3;
4,57,8;
5,62,1;
3,4,6;
9,8,7]
index = 1;
for i = 1:size(A,1)
C = abs(B - A(i,:));
if any(max(C,[],2)<=2)
out(index,:) = A(i,:);
index = index + 1
end
end
For each row of A, computes the absolute difference between B and that row, then checks if there exists a row in which the maximum is less than 2.
Without for loop
ind = any(max(abs(B - permute(A,[3 2 1])),[],2)<=2);
out = A(ind(:),:);
I have a Matrix of 100 sub matrix . Each of this sub matrix have 6 elements (1*6),
I need to compute the mean of the first element of each sub matrix then the
second, etc
Example:
B=[4,**3**,2,1,1,2]
C=[4,**3**,5,1,1,2]
D=[6,**3**,2,1,1,2]
A={B,C,D}
...etc
So I want the mean of the surlined numbers, then the next etc
How can I do that ???
Thanks by advance,
i think what you need here is the command cell2mat. here a small script of how to compute means automatically without knowing the size of the data. let me know if that was what you were looking for.
% Problem
vec1 = [4,3,2,1,1,2];
vec2 = [4,3,5,1,1,2];
vec3 = [6,3,2,1,1,2];
A = {vec1,vec2,vec3};
% get dimensions
cols = numel(cell2mat(A(1)));
rows = numel(A);
% convert list of vectors to matrix
M = cell2mat(A);
M = reshape(M,[cols,rows]);
M = M';
means = mean(M)
I have a vector whose elements identify the indices (per column) that I need to set in a different matrix. Specifically, I have:
A = 7
1
2
and I need to create a matrix B with some number of rows of zeros, except for the elements identified by A. In other words, I want B:
B = zeros(10, 3); % number of rows is known; num columns = size(A)
B(A(1), 1) = 1
B(A(2), 2) = 1
B(A(3), 3) = 1
I would like to do this without having to write a loop.
Any pointers would be appreciated.
Thanks.
Use linear indexing:
B = zeros(10, 3);
B(A(:).'+ (0:numel(A)-1)*size(B,1)) = 1;
The second line can be written equivalently with sub2ind (may be a little slower):
B(sub2ind(size(B), A(:).', 1:numel(A))) = 1;