I am currently using a nested 'for' loop to calculate an average value. This is an image with 3527*256 pixels, each pixel containing 448 values. I wish to multiply these 448 values with the array called 'modis_rsr'(448*8), then sum only the zero and positive values. After that, I wish to divide this sum by the sum of the values of 'modis_rsr' corresponding to only those with positive values in hyp_1nm.
As you would expect, this sequence is taking too long, and I wish to use a matrix multiplication to speed things up. The only thing I don't know how to do is to include the conditional sum for 'modis_rsr'. I was thinking of creating a reference array to store the indices of those which were negative. But that also seems computationally intensive.
for j = 1:8
for k = 1:256
for i = 1:3527
RLs = 0;
for jj = 1:448
if hyp_1nm(i,jj,k)>= 0
RLi = hyp_1nm(i,jj,k)*modis_rsr(jj,j);
RLs = RLs + RLi;
temp_rsr(jj,j) = modis_rsr(jj,j);
else
temp_rsr(jj,j) = 0;
end
end
Rs = sum(temp_rsr(1:448,j));
% Write basr
basr(i,j,k) = RLs/Rs;
end
end
end
You can't multiply arrays along one particular dimension with matlab, so you can't avoid using loop in this case. But you can reduce the number of loop by using the logical indexing and the element-wise multiplication.
for j = 1:8
for k = 1:256
for i = 1:3527
RLs = 0;
ind = hyp_1nm(i,:,k) >= 0; %by using the logical indexing you can avoid 1 loop.
RLs = sum(hyp_1nm(i,ind,k).*modis_rsr(ind,j)'); % .* = element-wise multiplication
temp_rsr(ind,j) = modis_rsr(ind,j);
temp_rsr(~ind,j) = 0;
Rs = sum(temp_rsr(1:448,j));
basr(i,j,k) = RLs/Rs;
end
end
end
If really you want to avoid for loop, you can use the function bsxfun, but bsxfunonly hide the foor loop, it don't linearize your code.
Related
My code needs to in a loop modify the elements of a sparse matrix. Doing this matlab warns me that This sparse indexing expression is likely to be slow. I am preallocating the sparse arrays using the Spalloc function but am still getting this warning. What is the optimal approach for assembling of sparse matrices? This is what I am currently doing.
K=spalloc(n,n,100); f=spalloc(n,1,100);
for i = 1:Nel
[Ke,fe] = myFunction(Ex(i),Ey(i));
inds = data(i,2:end);
K(inds,inds) = K(inds,inds) + Ke;
f(inds) = f(inds)+fe;
end
the indices in inds may be appear several times in the loop, meaning an element in K or f may receive multiple contributions. The last two lines within the loop are where I'm getting warnings.
A common approach is to use the triplet form of the sparse constructor:
S = sparse(i,j,v,m,n)
i and j are row and column index vectors and v is the corresponding data vector. Values corresponding to repeated indices are summed like your code does. So you could instead build up row and column index vectors along with a data vector and then just call sparse with those.
For example something like:
nout = Nel*(size(data,2)-1);
% Data vector for K
Kdata = zeros(1,nout);
% Data vector for f
fdata = zeros(1,nout);
% Index vector for K and f
sparseIdxvec = ones(1,nout);
outIdx = 1;
for i = 1:Nel
[Ke,fe] = myFunction(Ex(i),Ey(i));
inds = data(i,2:end);
nidx = numel(inds);
outIdxvec = outIdx:outIdx+nidx-1;
sparseIdxvec(outIdxvec) = inds;
Kdata(outIdxvec) = Ke;
fdata(outIdxvec) = fe;
outIdx = outIdx + nidx;
end
K = sparse(sparseIdxvec,sparseIdxvec,Kdata,n,n);
f = sparse(sparseIdxvec,1,fdata,n,1);
Depending on your application, that may or may not actually be faster.
I've written a function that generates a sparse matrix of size nxd
and puts in each column 2 non-zero values.
function [M] = generateSparse(n,d)
M = sparse(d,n);
sz = size(M);
nnzs = 2;
val = ceil(rand(nnzs,n));
inds = zeros(nnzs,d);
for i=1:n
ind = randperm(d,nnzs);
inds(:,i) = ind;
end
points = (1:n);
nnzInds = zeros(nnzs,d);
for i=1:nnzs
nnzInd = sub2ind(sz, inds(i,:), points);
nnzInds(i,:) = nnzInd;
end
M(nnzInds) = val;
end
However, I'd like to be able to give the function another parameter num-nnz which will make it choose randomly num-nnz cells and put there 1.
I can't use sprand as it requires density and I need the number of non-zero entries to be in-dependable from the matrix size. And giving a density is basically dependable of the matrix size.
I am a bit confused on how to pick the indices and fill them... I did with a loop which is extremely costly and would appreciate help.
EDIT:
Everything has to be sparse. A big enough matrix will crash in memory if I don't do it in a sparse way.
You seem close!
You could pick num_nnz random (unique) integers between 1 and the number of elements in the matrix, then assign the value 1 to the indices in those elements.
To pick the random unique integers, use randperm. To get the number of elements in the matrix use numel.
M = sparse(d, n); % create dxn sparse matrix
num_nnz = 10; % number of non-zero elements
idx = randperm(numel(M), num_nnz); % get unique random indices
M(idx) = 1; % Assign 1 to those indices
I want to convert a sparse matrix in matlab to single precision, however it appears that matlab doesn't have single sparse implemented.
Instead of that, I am just planning on checking it the values are outside of the single precision range and rounding them off to the highest and lowest values of the single precision range.
I'd like to do something like this:
for i = 1:rows
for j = 1:cols
if (abs(A(i,j) < 2^-126))
A(i,j) == 0;
end
end
end
However, ths is extremely slow. Is there another command I can use that will work on sparse matrix class type in MATLAB? I notice most commands don't work for the sparse data type.
EDIT 1:
I also tried the following, but as you can see I run out of memory (the matrix is sparse and is 200K x 200K with ~3 million nonzeros):
A(A < 2^-126) = 0
Error using <
Out of memory. Type HELP MEMORY for your options.
EDIT 2:
Current solution I developed based on input from #rahnema1:
% Convert entries that aren't in single precision
idx = find(A); % find locations of nonzeros
idx2 = find(abs(A(idx)) < double(realmin('single')));
A(idx(idx2)) = sign(A(idx(idx2)))*double(realmin('single'));
idx3 = find(abs(Problem.A(idx)) > double(realmax('single')));
A(idx(idx3)) = sign(A(idx(idx3)))*double(realmax('single'));
You can find indices of non zero elements and use that to change the matrix;
idx = find(A);
Anz = A(idx);
idx = idx(Anz < 2^-126);
A(idx) = 0;
Or more compact:
idx = find(A);
A(idx(A(idx) < 2^-126)) = 0;
However if you want to convert from double to single you can use single function:
idx = find(A);
A(idx) = double(single(full(A(idx))));
or
A(find(A)) = double(single(nonzeros(A)));
To convert Inf to realmax you can write:
A(find(A)) = double(max(-realmax('single'),min(realmax('single'),single(nonzeros(A)))));
If you only want to convert Inf to realmax you can do:
Anz = nonzeros(A);
AInf = isinf(A);
Anz(AInf) = double(realmax('single')) * sign(Anz(AInf));
A(find(A)) = Anz;
As one still reaches this thread when interested in how to convert sparse to single: an easy answer is to use full(). However, this can be problematic if you rely on the memory savings that sparse gives you, as it basically converts to double first.
sparseMatrix = sparse(ones(2, 'double'));
single(full(sparseMatrix)) % works
% ans =
% 2×2 single matrix
% 1 1
% 1 1
single(sparseMatrix) % doesn't work
% Error using single
% Attempt to convert to unimplemented sparse type
Let's say we have three m-by-n matrices of equal size: A, B, C.
Every column in C represents a time series.
A is the running maximum (over a fixed window length) of each time series in C.
B is the running minimum (over a fixed window length) of each time series in C.
Is there a way to determine T in a vectorized way?
[nrows, ncols] = size(A);
T = zeros(nrows, ncols);
for row = 2:nrows %loop over the rows (except row #1).
for col = 1:ncols %loop over the columns.
if C(row, col) > A(row-1, col)
T(row, col) = 1;
elseif C(row, col) < B(row-1, col)
T(row, col) = -1;
else
T(row, col) = T(row-1, col);
end
end
end
This is what I've come up with so far:
T = zeros(m, n);
T(C > circshift(A,1)) = 1;
T(C < circshift(B,1)) = -1;
Well, the trouble was the dependency with the ELSE part of the conditional statement. So, after a long mental work-out, here's a way I summed up to vectorize the hell-outta everything.
Now, this approach is based on mapping. We get column-wise runs or islands of 1s corresponding to the 2D mask for the ELSE part and assign them the same tags. Then, we go to the start-1 along each column of each such run and store that value. Finally, indexing into each such start-1 with those tagged numbers, which would work as mapping indices would give us all the elements that are to be set in the new output.
Here's the implementation to fulfill all those aspirations -
%// Store sizes
[m1,n1] = size(A);
%// Masks corresponding to three conditions
mask1 = C(2:nrows,:) > A(1:nrows-1,:);
mask2 = C(2:nrows,:) < B(1:nrows-1,:);
mask3 = ~(mask1 | mask2);
%// All but mask3 set values as output
out = [zeros(1,n1) ; mask1 + (-1*(~mask1 & mask2))];
%// Proceed if any element in mask3 is set
if any(mask3(:))
%// Row vectors for appending onto matrices for matching up sizes
mask_appd = false(1,n1);
row_appd = zeros(1,n1);
%// Get 2D mapped indices
df = diff([mask_appd ; mask3],[],1)==1;
cdf = cumsum(df,1);
offset = cumsum([0 max(cdf(:,1:end-1),[],1)]);
map_idx = bsxfun(#plus,cdf,offset);
map_idx(map_idx==0) = 1;
%// Extract the values to be used for setting into new places
A1 = out([df ; false(1,n1)]);
%// Map with the indices obtained earlier and set at places from mask3
newval = [row_appd ; A1(map_idx)];
mask3_appd = [mask_appd ; mask3];
out(mask3_appd) = newval(mask3_appd);
end
Doing this vectorized is rather difficult because the current row's output depends on the previous row's output. Doing vectorized operations usually means that each element should stand out on its own using some relationship that is independent of the other elements that surround it.
I don't have any input on how you would achieve this without a for loop but I can help you reduce your operations down to one instead of two. You can do the assignment vectorized per row, but I can't see how you'd do it all in one shot.
As such, try something like this instead:
[nrows, ncols] = size(A);
T = zeros(nrows, ncols);
for row = 2:nrows
out = T(row-1,:); %// Change - Make a copy of the previous row
out(C(row,:) > A(row-1,:)) = 1; %// Set those elements of C
%// in the current row that are larger
%// than the previous row of A to 1
out(C(row,:) < B(row-1,:)) = -1; %// Same logic but for B now and it's
%// less than and the value is -1 instead
T(row,:) = out; %// Assign to the output
end
I'm currently figuring out how to do this with any loops whatsoever. I'll keep you posted.
Suppose I want to find the size of a matrix, but can't use any functions such as size, numel, and length. Are there any neat ways to do this? I can think of a few versions using loops, such as the one below, but is it possible to do this without loops?
function sz = find_size(m)
sz = [0, 0]
for ii = m' %' or m(1,:) (probably faster)
sz(1) = sz(1) + 1;
end
for ii = m %' or m(:,1)'
sz(2) = sz(2) + 1;
end
end
And for the record: This is not a homework, it's out of curiosity. Although the solutions to this question would never be useful in this context, it is possible that they provide new knowledge in terms of how certain functions/techniques can be used.
Here is a more generic solution
function sz = find_size(m)
sz = [];
m(f(end), f(end));
function r = f(e)
r=[];
sz=[sz e];
end
end
Which
Works for arrays, cell arrays and arrays of objects
Its time complexity is constant and independent of matrix size
Does not use any MATLAB functions
Is easy to adapt to higher dimensions
For non-empty matrices you can use:
sz = [sum(m(:,1)|1) sum(m(1,:)|1)];
But to cover empty matrices we need more function calls
sz = sqrt([sum(sum(m*m'|1)) sum(sum(m'*m|1))]);
or more lines
n=m&0;
n(end+1,end+1)=1;
[I,J]=find(n);
sz=[I,J]-1;
Which both work fine for m=zeros(0,0), m=zeros(0,10) and m=zeros(10,0).
Incremental indexing and a try-catch statement works:
function sz = find_size(m)
sz = [0 0];
isError = false;
while ~isError
try
b = m(sz(1) + 1, :);
sz(1) = sz(1) + 1;
catch
isError = true;
end
end
isError = false;
while ~isError
try
b = m(:, sz(2) + 1);
sz(2) = sz(2) + 1;
catch
isError = true;
end
end
end
A quite general solution is:
[ sum(~sum(m(:,[]),2)) sum(~sum(m([],:),1)) ]
It accepts empty matrices (with 0 columns, 0 rows, or both), as well as complex, NaN or inf values.
It is also very fast: for a 1000 × 1000 matrix it takes about 22 microseconds in my old laptop (a for loop with 1e5 repetitions takes 2.2 seconds, measured with tic, toc).
How this works:
The keys to handling empty matrices in a unified way are:
empty indexing (that is, indexing with []);
the fact that summing along an empty dimension gives zeros.
Let r and c be the (possibly zero) numbers of rows and columns of m. m(:,[]) is an r × 0 empty vector. This holds even if r or c are zero. In addition, this empty indexing automatically provides insensitivity to NaN, inf or complex values in m (and probably accounts for the small computation time as well).
Summing that r × 0 vector along its second dimension (sum(m(:,[]),2)) produces a vector of r × 1 zeros. Negating and summing this vector gives r.
The same procedure is applied for the number of columns, c, by empty-indexing in the first dimension and summing along that dimension.
The find command has a neat option to get the last K elements:
I = find(X,K,'last') returns at most the last K indices corresponding to the nonzero entries of the arrayX`.
To get the size, ask for the last k=1 elements. For example,
>> x=zeros(256,4);
>> [numRows,numCols] = find(x|x==0, 1, 'last')
numRows =
256
numCols =
4
>> numRows0 = size(x,1), numCols0 = size(x,2)
numRows0 =
256
numCols0 =
4
You can use find with the single output argument syntax, which will give you numel:
>> numEl = find(x|x==0, 1, 'last')
numEl =
1024
>> numEl0 = numel(x)
numEl0 =
1024
Another straightforward, but less interesting solution uses whos (thanks for the reminder Navan):
s=whos('x'); s.size
Finally, there is format debug.