I am trying to reimplement in python an IDL function:
http://star.pst.qub.ac.uk/idl/REBIN.html
which downsizes by an integer factor a 2d array by averaging.
For example:
>>> a=np.arange(24).reshape((4,6))
>>> a
array([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23]])
I would like to resize it to (2,3) by taking the mean of the relevant samples, the expected output would be:
>>> b = rebin(a, (2, 3))
>>> b
array([[ 3.5, 5.5, 7.5],
[ 15.5, 17.5, 19.5]])
i.e. b[0,0] = np.mean(a[:2,:2]), b[0,1] = np.mean(a[:2,2:4]) and so on.
I believe I should reshape to a 4 dimensional array and then take the mean on the correct slice, but could not figure out the algorithm. Would you have any hint?
Here's an example based on the answer you've linked (for clarity):
>>> import numpy as np
>>> a = np.arange(24).reshape((4,6))
>>> a
array([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23]])
>>> a.reshape((2,a.shape[0]//2,3,-1)).mean(axis=3).mean(1)
array([[ 3.5, 5.5, 7.5],
[ 15.5, 17.5, 19.5]])
As a function:
def rebin(a, shape):
sh = shape[0],a.shape[0]//shape[0],shape[1],a.shape[1]//shape[1]
return a.reshape(sh).mean(-1).mean(1)
J.F. Sebastian has a great answer for 2D binning. Here is a version of his "rebin" function that works for N dimensions:
def bin_ndarray(ndarray, new_shape, operation='sum'):
"""
Bins an ndarray in all axes based on the target shape, by summing or
averaging.
Number of output dimensions must match number of input dimensions and
new axes must divide old ones.
Example
-------
>>> m = np.arange(0,100,1).reshape((10,10))
>>> n = bin_ndarray(m, new_shape=(5,5), operation='sum')
>>> print(n)
[[ 22 30 38 46 54]
[102 110 118 126 134]
[182 190 198 206 214]
[262 270 278 286 294]
[342 350 358 366 374]]
"""
operation = operation.lower()
if not operation in ['sum', 'mean']:
raise ValueError("Operation not supported.")
if ndarray.ndim != len(new_shape):
raise ValueError("Shape mismatch: {} -> {}".format(ndarray.shape,
new_shape))
compression_pairs = [(d, c//d) for d,c in zip(new_shape,
ndarray.shape)]
flattened = [l for p in compression_pairs for l in p]
ndarray = ndarray.reshape(flattened)
for i in range(len(new_shape)):
op = getattr(ndarray, operation)
ndarray = op(-1*(i+1))
return ndarray
Here's a way of doing what you ask using matrix multiplication that doesn't require the new array dimensions to divide the old.
First we generate a row compressor matrix and a column compressor matrix (I'm sure there's a cleaner way of doing this, maybe even using numpy operations alone):
def get_row_compressor(old_dimension, new_dimension):
dim_compressor = np.zeros((new_dimension, old_dimension))
bin_size = float(old_dimension) / new_dimension
next_bin_break = bin_size
which_row = 0
which_column = 0
while which_row < dim_compressor.shape[0] and which_column < dim_compressor.shape[1]:
if round(next_bin_break - which_column, 10) >= 1:
dim_compressor[which_row, which_column] = 1
which_column += 1
elif next_bin_break == which_column:
which_row += 1
next_bin_break += bin_size
else:
partial_credit = next_bin_break - which_column
dim_compressor[which_row, which_column] = partial_credit
which_row += 1
dim_compressor[which_row, which_column] = 1 - partial_credit
which_column += 1
next_bin_break += bin_size
dim_compressor /= bin_size
return dim_compressor
def get_column_compressor(old_dimension, new_dimension):
return get_row_compressor(old_dimension, new_dimension).transpose()
... so, for instance, get_row_compressor(5, 3) gives you:
[[ 0.6 0.4 0. 0. 0. ]
[ 0. 0.2 0.6 0.2 0. ]
[ 0. 0. 0. 0.4 0.6]]
and get_column_compressor(3, 2) gives you:
[[ 0.66666667 0. ]
[ 0.33333333 0.33333333]
[ 0. 0.66666667]]
Then simply premultiply by the row compressor and postmultiply by the column compressor to get the compressed matrix:
def compress_and_average(array, new_shape):
# Note: new shape should be smaller in both dimensions than old shape
return np.mat(get_row_compressor(array.shape[0], new_shape[0])) * \
np.mat(array) * \
np.mat(get_column_compressor(array.shape[1], new_shape[1]))
Using this technique,
compress_and_average(np.array([[50, 7, 2, 0, 1],
[0, 0, 2, 8, 4],
[4, 1, 1, 0, 0]]), (2, 3))
yields:
[[ 21.86666667 2.66666667 2.26666667]
[ 1.86666667 1.46666667 1.86666667]]
I was trying to downscale a raster -- take a roughly 6000 by 2000 size raster and turn it into an arbitrarily sized smaller raster that averaged the values properly across the previous bins sizes. I found a solution using SciPy, but then I couldn't get SciPy to install on the shared hosting service I was using, so I just wrote this function instead. There is likely a better ways to do this that doesn't involve looping through the rows and columns, but this does seem to work.
The nice part about this is that the old number of rows and columns don't have to be divisible by the new number of rows and columns.
def resize_array(a, new_rows, new_cols):
'''
This function takes an 2D numpy array a and produces a smaller array
of size new_rows, new_cols. new_rows and new_cols must be less than
or equal to the number of rows and columns in a.
'''
rows = len(a)
cols = len(a[0])
yscale = float(rows) / new_rows
xscale = float(cols) / new_cols
# first average across the cols to shorten rows
new_a = np.zeros((rows, new_cols))
for j in range(new_cols):
# get the indices of the original array we are going to average across
the_x_range = (j*xscale, (j+1)*xscale)
firstx = int(the_x_range[0])
lastx = int(the_x_range[1])
# figure out the portion of the first and last index that overlap
# with the new index, and thus the portion of those cells that
# we need to include in our average
x0_scale = 1 - (the_x_range[0]-int(the_x_range[0]))
xEnd_scale = (the_x_range[1]-int(the_x_range[1]))
# scale_line is a 1d array that corresponds to the portion of each old
# index in the_x_range that should be included in the new average
scale_line = np.ones((lastx-firstx+1))
scale_line[0] = x0_scale
scale_line[-1] = xEnd_scale
# Make sure you don't screw up and include an index that is too large
# for the array. This isn't great, as there could be some floating
# point errors that mess up this comparison.
if scale_line[-1] == 0:
scale_line = scale_line[:-1]
lastx = lastx - 1
# Now it's linear algebra time. Take the dot product of a slice of
# the original array and the scale_line
new_a[:,j] = np.dot(a[:,firstx:lastx+1], scale_line)/scale_line.sum()
# Then average across the rows to shorten the cols. Same method as above.
# It is probably possible to simplify this code, as this is more or less
# the same procedure as the block of code above, but transposed.
# Here I'm reusing the variable a. Sorry if that's confusing.
a = np.zeros((new_rows, new_cols))
for i in range(new_rows):
the_y_range = (i*yscale, (i+1)*yscale)
firsty = int(the_y_range[0])
lasty = int(the_y_range[1])
y0_scale = 1 - (the_y_range[0]-int(the_y_range[0]))
yEnd_scale = (the_y_range[1]-int(the_y_range[1]))
scale_line = np.ones((lasty-firsty+1))
scale_line[0] = y0_scale
scale_line[-1] = yEnd_scale
if scale_line[-1] == 0:
scale_line = scale_line[:-1]
lasty = lasty - 1
a[i:,] = np.dot(scale_line, new_a[firsty:lasty+1,])/scale_line.sum()
return a
来源：https://stackoverflow.com/questions/8090229/resize-with-averaging-or-rebin-a-numpy-2d-array