Is there a way to use numpy.linalg.det or numpy.linalg.inv on an nx3x3 array (a line in a multiband image), for example? Right now I am doing something like:
det = numpy.array([numpy.linalg.det(i) for i in X])
but surely there is a more efficient way. Of course, I could use map:
det = numpy.array(map(numpy.linalg.det, X))
Any other more direct way?
I'm pretty sure there is no substantially more efficient way than what you have. You can save some memory by first creating an empty array for the results and writing all results directly to that array:
res = numpy.empty_like(X)
for i, A in enumerate(X):
res[i] = numpy.linalg.inv(A)
This won't be any faster, though -- it will only use less memory.
a "normal" determinant is only defined for a matrix (dimension=2), so if that's what you want i don't see another way.
if you really want to compute the determinant of a cube then you could try to implement one of the ways described here:
http://en.wikipedia.org/wiki/Hyperdeterminant
notice that it is not necessarily the same value as the one you're currently computing.
New answer to an old question: Since version 1.8.0, numpy supports evaluating a batch of 2D matrices. For a batch of MxM matrices, the input and output now looks like:
linalg.det(a)
Compute the determinant of an array.
Parameters a(…, M, M) array_like
Input array to compute determinants for.
Returns det(…) array_like
Determinant of a.
Note the ellipsis. There can be multiple "batch dimensions", where for example you can evaluate a determinants on a meshgrid.
https://numpy.org/doc/stable/reference/generated/numpy.linalg.det.html
https://numpy.org/doc/stable/reference/generated/numpy.linalg.inv.html
Related
From my understanding, when we want to define a numpy array, we have to define its size.
However, in my case, I want to define a numpy array and then extend it based on my values in the for loop. The shape of values might differ in each run. So I cannot define the numpy array shape in advance.
Is there any way to overcome this?
I would like to avoid using lists.
Thanks
import numpy as np
myArrayShape = 2
myArray = np.empty(shape=2)
Note that this generates random values for each element in the array.
I think numpy array is just like array in clang or c++, I mean when you make numpy array you allocate memory depend on your request(size and dtype).
So it is better to make array after the size of array is determinated.
Or you can try numpy.append
https://numpy.org/doc/stable/reference/generated/numpy.append.html
But I don't think it is preferable way because it keeps generate new arrays.
From the Octave (free-MATLAB) docs, https://octave.org/doc/v6.3.0/Advanced-Indexing.html
In cases where a loop cannot be avoided, or a number of values must be combined to form a larger matrix, it is generally faster to set the size of the matrix first (pre-allocate storage), and then insert elements using indexing commands. For example, given a matrix a,
[nr, nc] = size (a);
x = zeros (nr, n * nc);
for i = 1:n
x(:,(i-1)*nc+1:i*nc) = a;
endfor
is considerably faster than
x = a;
for i = 1:n-1
x = [x, a];
endfor
because Octave does not have to repeatedly resize the intermediate result.
The same idea applies in numpy. While you can start with a (0,n) shaped array, and grow by concatenating (1,n) arrays, that is a lot slower than starting with a (m,n) array, and assigning values.
There's a deleted answer that illustrates how to create an array by list append. That is highly recommended.
I'm using cupy and I want to know if there is any way to make the following calculation faster
import cupy as cp
cp.sum([cp.dot(var, cp.matmul(M, var)).item() for var in x])
Could parallelize with python built-in libraries but I don't know if it's the best (efficient) way to do it. My need arises from the fact that the above sum is done many times in another cycle for, moving through x
EDIT:
here x is an array with shape (m, n), so each var is a 1D array of length n, by other hand M is a matrix with shape (n,n).
I am generating a series of Gaussian arrays given a x vector of length (1400), and arrays for the sigma, center, amplitude (amp), all with length (100). I thought the best way to speed this up would be to use numpy and list comprehension:
g = np.sum([(amp[i]*np.exp(-0.5*(x - (center[i]))**2/(sigma[i])**2)) for i in range(len(center))],axis=0)
Each row is a gaussian along a vector x, and then I sum the columns into a single array of length x.
But this doesn't seem to speed things up at all. I think there is a faster way to do this while avoiding the for loop but I can't quite figure out how.
You should use vectorized computation instead of comprehension so the loops are all performed at c speed.
In order to do so you have to reshape x to be a column vector. For example you could do x = x.reshape((1400,1)).
Then you can operate directly on the arrays, like this:
v=(amp*np.exp(-0.5*(x - (center))**2/(sigma)**2
Then you obtain an array of shape (1400,100) which you can sum up to a vector by np.sum(v, axe=1)
You should try to vectorize all the operations. IMHO the most efficient to first converts your input data to numpy arrays (if they were plain Python lists) and then let numpy process the computations:
np_amp = np.array(amp)
np_center = np.array(center)
np_sigma = np.array(sigma)
g = np.sum((np_amp*np.exp(-0.5*(x - (np_center))**2/(np_sigma)**2)),axis=0)
I have a matrix thing that looks like this:
thing.shape
(8070829, 2)
and I want to scale all elements by some scalingfactor = np.iinfo(np.int16).max/thing.max() to normalize the values. Right now I am iterating over all elements which works, but is really slow:
for j, sample in enumerate(thing):
thing[j] = [int(sample[0] * scalingfactor), int(sample[1] * scalingfactor)]
I thought I could do the following, but the results are not the same:
np.multiply(thing, scalingfactor)
Is there are more efficient way to normalize a matrix?
Use vectorized elementwise multiplication and then change dtype (that does the floor-ing) -
(thing*scalingfactor).astype(int) # for thing as array type
Or use np.floor on the scaled version -
np.floor(thing*scalingfactor)
Using the posted code from the question : np.multiply(thing, scalingfactor) would work too, just needs the additional floor-ing step, as suggested earlier.
I have an array of shape (l,m,n). I'm trying to calculate a distance matrix of shape (l,m,n) where entry (i,j,k) is the coefficient between vectors (i,j,:) and (i,:,k). I haven't found anything in numpy or scipy that fits the bill.
I tried using a for loop and iterating along axis 0, then feeding that to scipy.spatial.distance.pdist, but that takes a long time as pdist itself uses a nested for loop. In essence, what I would like to do would be to perform pdist down axis 0, but ideally make it so pdist doesn't use for loops either....
Any thoughts?
I would personally write a little Cython function to do this ( http://cython.org). Write and test an iterative pure Python version (with for loops), move it to a .pyx Cython file, add type declarations and follow the NumPy integration guide:
http://docs.cython.org/src/tutorial/numpy.html
Might seem like work but if you're doing computing in Python, some basic Cython skills are well worth cultivating as it makes writing C extensions much easier.
Any thoughts?
First thought is that you cannot compute such distances as long as m != n
Second thought is that internal loops of pdist should not bother you if those are written in C, so the probable reason is not in implementation, but in the amount of computations needed
Final thought is that your problem may be solved by numpy.einsum and linear algebra:
Code (which I assume to be optimal):
products = numpy.einsum('ijl, ilk -> ijk')
distances = numpy.einsum('ijj -> ij', products)
distances = distances[:, :, None] + distances[:, None, :] - 2 * product