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# tag: numpy | ||
# You can ignore the previous line. | ||
# It's for internal testing of the cython documentation. | ||
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from __future__ import division | ||
import numpy as np | ||
# "cimport" is used to import special compile-time information | ||
# about the numpy module (this is stored in a file numpy.pxd which is | ||
# currently part of the Cython distribution). | ||
cimport numpy as np | ||
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# We now need to fix a datatype for our arrays. I've used the variable | ||
# DTYPE for this, which is assigned to the usual NumPy runtime | ||
# type info object. | ||
DTYPE = np.int | ||
# "ctypedef" assigns a corresponding compile-time type to DTYPE_t. For | ||
# every type in the numpy module there's a corresponding compile-time | ||
# type with a _t-suffix. | ||
ctypedef np.int_t DTYPE_t | ||
# "def" can type its arguments but not have a return type. The type of the | ||
# arguments for a "def" function is checked at run-time when entering the | ||
# function. | ||
# | ||
# The arrays f, g and h is typed as "np.ndarray" instances. The only effect | ||
# this has is to a) insert checks that the function arguments really are | ||
# NumPy arrays, and b) make some attribute access like f.shape[0] much | ||
# more efficient. (In this example this doesn't matter though.) | ||
def naive_convolve(np.ndarray f, np.ndarray g): | ||
if g.shape[0] % 2 != 1 or g.shape[1] % 2 != 1: | ||
raise ValueError("Only odd dimensions on filter supported") | ||
assert f.dtype == DTYPE and g.dtype == DTYPE | ||
# The "cdef" keyword is also used within functions to type variables. It | ||
# can only be used at the top indentation level (there are non-trivial | ||
# problems with allowing them in other places, though we'd love to see | ||
# good and thought out proposals for it). | ||
# | ||
# For the indices, the "int" type is used. This corresponds to a C int, | ||
# other C types (like "unsigned int") could have been used instead. | ||
# Purists could use "Py_ssize_t" which is the proper Python type for | ||
# array indices. | ||
cdef int vmax = f.shape[0] | ||
cdef int wmax = f.shape[1] | ||
cdef int smax = g.shape[0] | ||
cdef int tmax = g.shape[1] | ||
cdef int smid = smax // 2 | ||
cdef int tmid = tmax // 2 | ||
cdef int xmax = vmax + 2 * smid | ||
cdef int ymax = wmax + 2 * tmid | ||
cdef np.ndarray h = np.zeros([xmax, ymax], dtype=DTYPE) | ||
cdef int x, y, s, t, v, w | ||
# It is very important to type ALL your variables. You do not get any | ||
# warnings if not, only much slower code (they are implicitly typed as | ||
# Python objects). | ||
cdef int s_from, s_to, t_from, t_to | ||
# For the value variable, we want to use the same data type as is | ||
# stored in the array, so we use "DTYPE_t" as defined above. | ||
# NB! An important side-effect of this is that if "value" overflows its | ||
# datatype size, it will simply wrap around like in C, rather than raise | ||
# an error like in Python. | ||
cdef DTYPE_t value | ||
for x in range(xmax): | ||
for y in range(ymax): | ||
s_from = max(smid - x, -smid) | ||
s_to = min((xmax - x) - smid, smid + 1) | ||
t_from = max(tmid - y, -tmid) | ||
t_to = min((ymax - y) - tmid, tmid + 1) | ||
value = 0 | ||
for s in range(s_from, s_to): | ||
for t in range(t_from, t_to): | ||
v = x - smid + s | ||
w = y - tmid + t | ||
value += g[smid - s, tmid - t] * f[v, w] | ||
h[x, y] = value | ||
return h |
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from __future__ import division | ||
import numpy as np | ||
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def naive_convolve(f, g): | ||
# f is an image and is indexed by (v, w) | ||
# g is a filter kernel and is indexed by (s, t), | ||
# it needs odd dimensions | ||
# h is the output image and is indexed by (x, y), | ||
# it is not cropped | ||
if g.shape[0] % 2 != 1 or g.shape[1] % 2 != 1: | ||
raise ValueError("Only odd dimensions on filter supported") | ||
# smid and tmid are number of pixels between the center pixel | ||
# and the edge, ie for a 5x5 filter they will be 2. | ||
# | ||
# The output size is calculated by adding smid, tmid to each | ||
# side of the dimensions of the input image. | ||
vmax = f.shape[0] | ||
wmax = f.shape[1] | ||
smax = g.shape[0] | ||
tmax = g.shape[1] | ||
smid = smax // 2 | ||
tmid = tmax // 2 | ||
xmax = vmax + 2 * smid | ||
ymax = wmax + 2 * tmid | ||
# Allocate result image. | ||
h = np.zeros([xmax, ymax], dtype=f.dtype) | ||
# Do convolution | ||
for x in range(xmax): | ||
for y in range(ymax): | ||
# Calculate pixel value for h at (x,y). Sum one component | ||
# for each pixel (s, t) of the filter g. | ||
s_from = max(smid - x, -smid) | ||
s_to = min((xmax - x) - smid, smid + 1) | ||
t_from = max(tmid - y, -tmid) | ||
t_to = min((ymax - y) - tmid, tmid + 1) | ||
value = 0 | ||
for s in range(s_from, s_to): | ||
for t in range(t_from, t_to): | ||
v = x - smid + s | ||
w = y - tmid + t | ||
value += g[smid - s, tmid - t] * f[v, w] | ||
h[x, y] = value | ||
return h |
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