I'm going beyond my previous question because of speed problems. I have an array of Lat/Lon coordinates of points, and I would like to assign them to an index code derived from a 2D square grid of equal size cells. This is an example of how it would be. Let's called points my first array containing coordinates (called them [x y] pairs) of six points:
points = [[ 1.5 1.5]
[ 1.1 1.1]
[ 2.2 2.2]
[ 1.3 1.3]
[ 3.4 1.4]
[ 2. 1.5]]
Then I have another array containing the coordinates of the vertices of a grid of two cells in the form [minx,miny,maxx,maxy]; let's call it bounds:
bounds = [[ 0. 0. 2. 2.]
[ 2. 2. 3. 3.]]
I would like to find which points are in which boundary, and then assign a code derived from the bounds array index (in this case the first cell has code 0, the second 1 and so on...). Since the cells are squares, the easiest way to compute if each point is in each cell is to evaluate:
x > minx & x < maxx & y > miny & y < maxy
So that the resulting array would appear as:
results = [0 0 1 0 NaN NaN]
where NaN means that the point is outside cells. The number of elements in my real case is of the order of finding 10^6 points into 10^4 cells. Is there a way to do this kind of things in a fast way using numpy arrays?
EDIT: to clarify, the results array expected means that the first points is inside the first cell (0 index of the bounds array) so the second, and the first is inside the second cell of the bounds array and so on...
Here is a vectorized approach to your problem. It should speed things up significantly.
import numpy as np
def findCells(points, bounds):
# make sure points is n by 2 (pool.map might send us 1D arrays)
points = points.reshape((-1,2))
# check for each point if all coordinates are in bounds
# dimension 0 is bound
# dimension 1 is is point
allInBounds = (points[:,0] > bounds[:,None,0])
allInBounds &= (points[:,1] > bounds[:,None,1])
allInBounds &= (points[:,0] < bounds[:,None,2])
allInBounds &= (points[:,1] < bounds[:,None,3])
# now find out the positions of all nonzero (i.e. true) values
# nz[0] contains the indices along dim 0 (bound)
# nz[1] contains the indices along dim 1 (point)
nz = np.nonzero(allInBounds)
# initialize the result with all nan
r = np.full(points.shape[0], np.nan)
# now use nz[1] to index point position and nz[0] to tell which cell the
# point belongs to
r[nz[1]] = nz[0]
return r
def findCellsParallel(points, bounds, chunksize=100):
import multiprocessing as mp
from functools import partial
func = partial(findCells, bounds=bounds)
# using python3 you could also do 'with mp.Pool() as p:'
p = mp.Pool()
try:
return np.hstack(p.map(func, points, chunksize))
finally:
p.close()
def main():
nPoints = 1e6
nBounds = 1e4
# points = np.array([[ 1.5, 1.5],
# [ 1.1, 1.1],
# [ 2.2, 2.2],
# [ 1.3, 1.3],
# [ 3.4, 1.4],
# [ 2. , 1.5]])
points = np.random.random([nPoints, 2])
# bounds = np.array([[0,0,2,2],
# [2,2,3,3]])
# bounds = np.array([[0,0,1.4,1.4],
# [1.4,1.4,2,2],
# [2,2,3,3]])
bounds = np.sort(np.random.random([nBounds, 2, 2]), 1).reshape(nBounds, 4)
r = findCellsParallel(points, bounds)
print(points[:10])
for bIdx in np.unique(r[:10]):
if np.isnan(bIdx):
continue
print("{}: {}".format(bIdx, bounds[bIdx]))
print(r[:10])
if __name__ == "__main__":
main()
Edit:
Trying it with your amount of data gave me a MemoryError. You can avoid that and even speed things up a little more if you use multiprocessing.Pool with its map function, see updated code.
Result:
>time python test.py
[[ 0.69083585 0.19840985]
[ 0.31732711 0.80462512]
[ 0.30542996 0.08569184]
[ 0.72582609 0.46687164]
[ 0.50534322 0.35530554]
[ 0.93581095 0.36375539]
[ 0.66226118 0.62573407]
[ 0.08941219 0.05944215]
[ 0.43015872 0.95306899]
[ 0.43171644 0.74393729]]
9935.0: [ 0.31584562 0.18404152 0.98215445 0.83625487]
9963.0: [ 0.00526106 0.017255 0.33177741 0.9894455 ]
9989.0: [ 0.17328876 0.08181912 0.33170444 0.23493507]
9992.0: [ 0.34548987 0.15906761 0.92277442 0.9972481 ]
9993.0: [ 0.12448765 0.5404578 0.33981119 0.906822 ]
9996.0: [ 0.41198261 0.50958195 0.62843379 0.82677092]
9999.0: [ 0.437169 0.17833114 0.91096133 0.70713434]
[ 9999. 9993. 9989. 9999. 9999. 9935. 9999. 9963. 9992. 9996.]
real 0m 24.352s
user 3m 4.919s
sys 0m 1.464s
You can use a nested loop with to check the condition and yield the result as a generator :
points = [[ 1.5 1.5]
[ 1.1 1.1]
[ 2.2 2.2]
[ 1.3 1.3]
[ 3.4 1.4]
[ 2. 1.5]]
bounds = [[ 0. ,0. , 2., 2.],
[ 2. ,2. ,3., 3.]]
import numpy as np
def pos(p,b):
for x,y in p:
flag=False
for index,dis in enumerate(b):
minx,miny,maxx,maxy=dis
if x > minx and x < maxx and y > miny and y < maxy :
flag=True
yield index
if not flag:
yield 'NaN'
print list(pos(points,bounds))
result :
[0, 0, 1, 0, 'NaN', 'NaN']
I would do it like this:
import numpy as np
points = np.random.rand(10,2)
xmin = [0.25,0.5]
ymin = [0.25,0.5]
results = np.zeros(len(points))
for i in range(len(xmin)):
bool_index_array = np.greater(points, [xmin[i],ymin[i]])
print "boolean index of (x,y) greater (xmin, ymin): ", bool_index_array
indicies_of_true_true = np.where(bool_index_array[:,0]*bool_index_array[:,1]==1)[0]
print "indices of [True,True]: ", indicies_of_true_true
results[indicies_of_true_true] += 1
print "results: ", results
[out]: [ 1. 1. 1. 2. 0. 0. 1. 1. 1. 1.]
This uses the lower boundaries to catagorize your points into the groups:
1 (if xmin[0] < x <= xmin[1] & ymin[0] < y <= ymin[1])
2 (if x > xmin[1] & y > ymin[1])
0 if none of the conditions above are fullfilled
Related
I want to apply a transformation matrix to a set of points. So the set of points:
points = np.array([[0 ,20], [0, 575], [0, 460]])
And I want to use the matrix I calculated with cv2.getPerspectiveTransform() which is a 3x3 matrix.
matrix = np.array([
[ -4. , -3. , 1920. ],
[ -2.25 , -1.6875 , 1080. ],
[ -0.0020833, -0.0015625, 1. ]])
Then I pass the array and a matrix to the following function:
def poly_points_transform(poly_points, matrix):
poly_points_transformed = np.empty_like(poly_points)
for i in range(len(poly_points)):
point = np.array([[poly_points[i]]])
transformed_point = cv2.perspectiveTransform(point, matrix)
np.append(poly_points_transformed, transformed_point)
return poly_points_transformed
Now It doesn't throw an error, but it just copies the src array to the poly_points_transformed. It might be something really rudimentary and stupid. If it is the case, I am sorry, but could someone give me a hint on what is wrong? Thanks in advance
We may solve it with one line of code:
transformed_point = cv2.perspectiveTransform(np.array([points], np.float64), matrix)[0]
As Micka commented cv2.perspectiveTransform takes a list of points (and returns a list of points as output).
np.array([points]) is used because cv2.perspectiveTransform expects 3D array.
For details see trouble getting cv.transform to work.
np.float64 is used in case the dtype of points is int32 (the method accepts float64 and float32 types).
[0] is used for removing the redundant dimension (convert from 3D to 2D).
For fixing the loop, replace np.append(poly_points_transformed, transformed_point) with:
poly_points_transformed[i] = transformed_point[0].
Since the array is initialized to poly_points_transformed = np.empty_like(poly_points), we can't use np.append().
Code sample:
import cv2
import numpy as np
points = np.array([[0.0 ,20.0], [0.0, 575.0], [0.0, 460.0]])
matrix = np.array([
[ -4. , -3. , 1920. ],
[ -2.25 , -1.6875 , 1080. ],
[ -0.0020833, -0.0015625, 1. ]])
# transformed_point = cv2.perspectiveTransform(np.array([points], np.float64), matrix)[0]
def poly_points_transform(poly_points, matrix):
poly_points_transformed = np.empty_like(poly_points)
for i in range(len(poly_points)):
point = np.array([[poly_points[i]]])
transformed_point = cv2.perspectiveTransform(point, matrix)
poly_points_transformed[i] = transformed_point[0] #np.append(poly_points_transformed, transformed_point)
return poly_points_transformed
poly_points_transformed = poly_points_transform(points, matrix)
The result is:
poly_points_transformed =
array([[1920., 1080.],
[1920., 1080.],
[1920., 1080.]])
Why are we getting [1920.0, 1080.0] value for all the transformed points?
Lets transform the middle point mathematically:
Multiply matrix by point (with 1 in the third index)
[ -4. , -3. , 1920. ] [ 0]
[ -2.25 , -1.6875 , 1080. ] * [575] =
[ -0.0020833, -0.0015625, 1. ] [ 1]
p = matrix # np.array([[0.0], [575.0], [1.0]]) =
[1.950000e+02]
[1.096875e+02]
[1.015625e-01]
Now divide the coordinates by the last element (converting homogeneous coordinates to Euclidian coordinates):
[1.950000e+02/1.015625e-01] [1920]
[1.096875e+02/1.015625e-01] = p / p[2] = [1080]
[1.015625e-01/1.015625e-01] [ 1]
The equivalent Euclidian point is [1920, 1080].
The transformation matrix may be wrong, because it transforms all the input points (with x coordinate equals 0) to the same output point...
I'm trying to scale the following NumPy array based on its minimum and maximum values.
array = [[17405.051 17442.4 17199.6 17245.65 ]
[17094.949 17291.75 17091.15 17222.75 ]
[17289. 17294.9 17076.551 17153. ]
[17181.85 17235.1 17003.9 17222. ]]
Formula used is:
m=(x-xmin)/(xmax-xmin)
wherein m is an individually scaled item, x is an individual item, xmax is the highest value and xmin is the smallest value of the array.
My question is how do I print the scaled array?
P.S. - I can't use MinMaxScaler as I need to scale a given number (outside the array) by plugging it in the mentioned formula with xmin & xmax of the given array.
I tried scaling the individual items by iterating over the array but I'm unable to put together the scaled array.
I'm new to NumPy, any suggestions would be welcome.
Thank you.
Use method ndarray.min(), ndarray.max() or ndarray.ptp()(gets the range of the values in the array):
>>> ar = np.array([[17405.051, 17442.4, 17199.6, 17245.65 ],
... [17094.949, 17291.75, 17091.15, 17222.75 ],
... [17289., 17294.9, 17076.551, 17153. ],
... [17181.85, 17235.1, 17003.9, 17222. ]])
>>> min_val = ar.min()
>>> range_val = ar.ptp()
>>> (ar - min_val) / range_val
array([[0.91482554, 1. , 0.44629418, 0.55131129],
[0.2076374 , 0.65644242, 0.19897377, 0.4990878 ],
[0.65017104, 0.663626 , 0.16568073, 0.34002281],
[0.40581528, 0.527252 , 0. , 0.49737742]])
I think you should learn more about the basic operation of numpy.
import numpy as np
array_list = [[17405.051, 17442.4, 17199.6, 17245.65 ],
[17094.949, 17291.75, 17091.15, 17222.75 ],
[17289., 17294.9, 17076.551, 17153., ],
[17181.85, 17235.1, 17003.9, 17222. ]]
# Convert list into numpy array
array = np.array(array_list)
# Create empty list
scaled_array_list=[]
for x in array:
m = (x - np.min(array))/(np.max(array)-np.min(array))
scaled_array_list.append(m)
# Convert list into numpy array
scaled_array = np.array(scaled_array_list)
scaled_array
My version is by iterating over the array as you said.
You can also put everything in a function and use it in future:
def scaler(array_to_scale):
# Create empty list
scaled_array_list=[]
for x in array:
m = (x - np.min(array))/(np.max(array)-np.min(array))
scaled_array_list.append(m)
# Convert list into numpy array
scaled_array = np.array(scaled_array_list)
return scaled_array
# Here it is our input
array_list = [[17405.051, 17442.4, 17199.6, 17245.65 ],
[17094.949, 17291.75, 17091.15, 17222.75 ],
[17289., 17294.9, 17076.551, 17153., ],
[17181.85, 17235.1, 17003.9, 17222. ]]
# Convert list into numpy array
array = np.array(array_list)
scaler(array)
Output:
Out:
array([[0.91482554, 1. , 0.44629418, 0.55131129],
[0.2076374 , 0.65644242, 0.19897377, 0.4990878 ],
[0.65017104, 0.663626 , 0.16568073, 0.34002281],
[0.40581528, 0.527252 , 0. , 0.49737742]])
I'm implementing the Nearest Centroid Classification algorithm and I'm kind of blocked on how to use numpy.mean in my case.
So suppose I have some spherical datasets X:
[[ 0.39151059 3.48203037]
[-0.68677876 1.45377717]
[ 2.30803493 4.19341503]
[ 0.50395297 2.87076658]
[ 0.06677012 3.23265678]
[-0.24135103 3.78044279]
[-0.05660036 2.37695381]
[ 0.74210998 -3.2654815 ]
[ 0.05815341 -2.41905942]
[ 0.72126958 -1.71081388]
[ 1.03581142 -4.09666955]
[ 0.23209714 -1.86675298]
[-0.49136284 -1.55736028]
[ 0.00654881 -2.22505305]]]
and the labeled vector Y:
[0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1.]
An example with 100 2D data points gives the following result:
The NCC algorithm consists of first calculating the class mean of each class (0 and 1: that's blue and red) and then calculating the nearest class centroid for the next data point.
This is my current function:
def mean_ncc(X,Y):
# find unique classes
m_cids = np.unique(Y) #[0. 1.]
# compute class means
mu = np.zeros((len(cids), X.shape[1])) #[[0. 0.] [0. 0.]] (in the case where Y has 2 unique points (0 and 1)
for class_idx, class_label in enumerate(cids):
mu[class_idx, :] = #problem here
return mu
So here I want an array containing the class means of '0' (blue) points and '1' (red) points:
How can I specify the number of elements of X whose mean I want to calculate?
I would like to do something like this:
for class_idx, class_label in enumerate(m_cids):
mu[class_idx, :] = np.mean(X[only the elements,that contains the same class_label], axis=0)
Is it possible or is there another way to implement this?
You could use something like this:
import numpy as np
tags = [0, 0, 1, 1, 0, 1]
values = [5, 4, 2, 5, 9, 8]
tags_np = np.array(tags)
values_np = np.array(values)
print(values_np[tags_np == 1].mean())
EDIT: You will surely need to look more into the axis parameter for the mean function:
import numpy as np
values = [[5, 4],
[5, 4],
[4, 3],
[4, 3]]
values_np = np.array(values)
tags_np = np.array([0, 0, 1, 1])
print(values_np[tags_np == 0].mean(axis=0))
I want to split a numpy array into three different arrays based on a logical comparison. The numpy array I want to split is called x. It's shape looks as follows, but it's entries vary: (In response to Saullo Castro's comment I included a slightly different array x.)
array([[ 0.46006547, 0.5580928 , 0.70164242, 0.84519205, 1.4 ],
[ 0.00912908, 0.00912908, 0.05 , 0.05 , 0.05 ]])
This values of this array are monotonically increasing along columns. I also have two other arrays called lowest_gridpoints and highest_gridpoints. The entries of these arrays also vary, but the shape is always identical to the following:
array([ 0.633, 0.01 ]), array([ 1.325, 0.99 ])
The selection procedure I want to apply is as follows:
All columns containing values lower than any value in lowest_gridpoints should be removed from x and constitute the array temp1.
All columns containing values higher than any value in highest_gridpoints should be removed from x and constitute the array temp2.
All columns of x that are included in neither temp1 or temp2 constitute the array x_new.
The following code I wrote achieves the task.
if np.any( x[:,-1] > highest_gridpoints ) or np.any( x[:,0] < lowest_gridpoints ):
for idx, sample, in enumerate(x.T):
if np.any( sample > highest_gridpoints):
max_idx = idx
break
elif np.any( sample < lowest_gridpoints ):
min_idx = idx
temp1, temp2 = np.array([[],[]]), np.array([[],[]])
if 'min_idx' in locals():
temp1 = x[:,0:min_idx+1]
if 'max_idx' in locals():
temp2 = x[:,max_idx:]
if 'min_idx' in locals() or 'max_idx' in locals():
if 'min_idx' not in locals():
min_idx = -1
if 'max_idx' not in locals():
max_idx = x.shape[1]
x_new = x[:,min_idx+1:max_idx]
However, I suspect that this code is very inefficient because of the heavy use of loops. Additionally, I think the syntax is bloated.
Does someone have an idea for a code which achieve the task outlined above more efficiently or looks concise?
Only the first part of your question
from numpy import *
x = array([[ 0.46006547, 0.5580928 , 0.70164242, 0.84519205, 1.4 ],
[ 0.00912908, 0.00912908, 0.05 , 0.05 , 0.05 ]])
low, high = array([ 0.633, 0.01 ]), array([ 1.325, 0.99 ])
# construct an array of two rows of bools expressing your conditions
indices1 = array((x[0,:]<low[0], x[1,:]<low[1]))
print indices1
# do an or of the values along the first axis
indices1 = any(indices1, axis=0)
# now it's a single row array
print indices1
# use the indices1 to extract what you want,
# the double transposition because the elements
# of a 2d array are the rows
tmp1 = x.T[indices1].T
print tmp1
# [[ True True False False False]
# [ True True False False False]]
# [ True True False False False]
# [[ 0.46006547 0.5580928 ]
# [ 0.00912908 0.00912908]]
next construct similarly indices2 and tmp2, the indices of the remnant are the negation of the oring of the first two indices. (i.e., numpy.logical_not(numpy.logical_or(i1,i2))).
Addendum
Another approach, possibly faster if you have thousands of entries, implies numpy.searchsorted
from numpy import *
x = array([[ 0.46006547, 0.5580928 , 0.70164242, 0.84519205, 1.4 ],
[ 0.00912908, 0.00912908, 0.05 , 0.05 , 0.05 ]])
low, high = array([ 0.633, 0.01 ]), array([ 1.325, 0.99 ])
l0r = searchsorted(x[0,:], low[0], side='right')
l1r = searchsorted(x[1,:], low[1], side='right')
h0l = searchsorted(x[0,:], high[0], side='left')
h1l = searchsorted(x[1,:], high[1], side='left')
lr = max(l0r, l1r)
hl = min(h0l, h1l)
print lr, hl
print x[:,:lr]
print x[:,lr:hl]
print x[:,hl]
# 2 4
# [[ 0.46006547 0.5580928 ]
# [ 0.00912908 0.00912908]]
# [[ 0.70164242 0.84519205]
# [ 0.05 0.05 ]]
# [ 1.4 0.05]
Excluding overlaps can be obtained by hl = max(lr, hl). NB in previuos approach the array slices are copied to new objects, here you get views on x and you have to be explicit if you want new objects.
Edit An unnecessary optimization
If we use only the upper part of x in the second couple of sortedsearches (if you look at the code you'll see what I mean...) we get two benefits, 1) a very small speedup of the searches (sortedsearch is always fast enough) and 2) the case of overlap is automatically managed.
As a bonus, code for copying the segments of x in the new arrays. NB x was changed to force overlap
from numpy import *
# I changed x to force overlap
x = array([[ 0.46006547, 1.4 , 1.4, 1.4, 1.4 ],
[ 0.00912908, 0.00912908, 0.05, 0.05, 0.05 ]])
low, high = array([ 0.633, 0.01 ]), array([ 1.325, 0.99 ])
l0r = searchsorted(x[0,:], low[0], side='right')
l1r = searchsorted(x[1,:], low[1], side='right')
lr = max(l0r, l1r)
h0l = searchsorted(x[0,lr:], high[0], side='left')
h1l = searchsorted(x[1,lr:], high[1], side='left')
hl = min(h0l, h1l) + lr
t1 = x[:,range(lr)]
xn = x[:,range(lr,hl)]
ncol = shape(x)[1]
t2 = x[:,range(hl,ncol)]
print x
del(x)
print
print t1
print
# note that xn is a void array
print xn
print
print t2
# [[ 0.46006547 1.4 1.4 1.4 1.4 ]
# [ 0.00912908 0.00912908 0.05 0.05 0.05 ]]
#
# [[ 0.46006547 1.4 ]
# [ 0.00912908 0.00912908]]
#
# []
#
# [[ 1.4 1.4 1.4 ]
# [ 0.05 0.05 0.05]]
EDIT: Paul has solved this one below. Thanks!
I'm trying to resample (upscale) a 3x3 matrix to 5x5, filling in the intermediate points with either interpolate.interp2d or interpolate.RectBivariateSpline (or whatever works).
If there's a simple, existing function to do this, I'd like to use it, but I haven't found it yet. For example, a function that would work like:
# upscale 2x2 to 4x4
matrixSmall = ([[-1,8],[3,5]])
matrixBig = matrixSmall.resample(4,4,cubic)
So, if I start with a 3x3 matrix / array:
0,-2,0
-2,11,-2
0,-2,0
I want to compute a new 5x5 matrix ("I" meaning interpolated value):
0, I[1,0], -2, I[3,0], 0
I[0,1], I[1,1], I[2,1], I[3,1], I[4,1]
-2, I[1,2], 11, I[3,2], -2
I[0,3], I[1,3], I[2,3], I[3,3], I[4,3]
0, I[1,4], -2, I[3,4], 0
I've been searching and reading up and trying various different test code, but I haven't quite figured out the correct syntax for what I'm trying to do. I'm also not sure if I need to be using meshgrid, mgrid or linspace in certain lines.
EDIT: Fixed and working Thanks to Paul
import numpy, scipy
from scipy import interpolate
kernelIn = numpy.array([[0,-2,0],
[-2,11,-2],
[0,-2,0]])
inKSize = len(kernelIn)
outKSize = 5
kernelOut = numpy.zeros((outKSize,outKSize),numpy.uint8)
x = numpy.array([0,1,2])
y = numpy.array([0,1,2])
z = kernelIn
xx = numpy.linspace(x.min(),x.max(),outKSize)
yy = numpy.linspace(y.min(),y.max(),outKSize)
newKernel = interpolate.RectBivariateSpline(x,y,z, kx=2,ky=2)
kernelOut = newKernel(xx,yy)
print kernelOut
Only two small problems:
1) Your xx,yy is outside the bounds of x,y (you can extrapolate, but I'm guessing you don't want to.)
2) Your sample size is too small for a kx and ky of 3 (default). Lower it to 2 and get a quadratic fit instead of cubic.
import numpy, scipy
from scipy import interpolate
kernelIn = numpy.array([
[0,-2,0],
[-2,11,-2],
[0,-2,0]])
inKSize = len(kernelIn)
outKSize = 5
kernelOut = numpy.zeros((outKSize),numpy.uint8)
x = numpy.array([0,1,2])
y = numpy.array([0,1,2])
z = kernelIn
xx = numpy.linspace(x.min(),x.max(),outKSize)
yy = numpy.linspace(y.min(),y.max(),outKSize)
newKernel = interpolate.RectBivariateSpline(x,y,z, kx=2,ky=2)
kernelOut = newKernel(xx,yy)
print kernelOut
##[[ 0. -1.5 -2. -1.5 0. ]
## [ -1.5 5.4375 7.75 5.4375 -1.5 ]
## [ -2. 7.75 11. 7.75 -2. ]
## [ -1.5 5.4375 7.75 5.4375 -1.5 ]
## [ 0. -1.5 -2. -1.5 0. ]]
If you are using scipy already, I think scipy.ndimage.interpolate.zoom can do what you need:
import numpy
import scipy.ndimage
a = numpy.array([[0.,-2.,0.], [-2.,11.,-2.], [0.,-2.,0.]])
out = numpy.round(scipy.ndimage.interpolation.zoom(input=a, zoom=(5./3), order = 2),1)
print out
#[[ 0. -1. -2. -1. 0. ]
# [ -1. 1.8 4.5 1.8 -1. ]
# [ -2. 4.5 11. 4.5 -2. ]
# [ -1. 1.8 4.5 1.8 -1. ]
# [ 0. -1. -2. -1. 0. ]]
Here the "zoom factor" is 5./3 because we are going from a 3x3 array to a 5x5 array. If you read the docs, it says that you can also specify the zoom factor independently for the two axes, which means you can upscale non-square matrices as well. By default, it uses third order spline interpolation, which I am not sure is best.
I tried it on some images and it works nicely.