def cg(A, b, x=None, tol=1e-5, force_niter=None):
"""
Conjugate Gradient (CG) solver
Implemented as example MATLAB code from <https://en.wikipedia.org/wiki/Conjugate_gradient_method>
"""
# If no guess is given, set an empty guess
if x is None:
x = array_create.zeros_like(b)
r = b - dot(A, x)
p = r.copy()
r_squared = r * r
rsold = np.sum(r_squared)
tol_squared = tol * tol
i = 0
while np.max(r_squared) > tol_squared or force_niter is not None:
Ap = dot(A, p)
alpha = rsold / dot(p, Ap)
x = x + alpha * p
r = r - alpha * Ap
r_squared = r * r
rsnew = np.sum(r_squared)
p = r + (rsnew / rsold) * p
rsold = rsnew
if force_niter is not None and i >= force_niter:
break
i += 1
return x
def cg(A, b, x=None, tol=1e-5, force_niter=None):
"""
Conjugate Gradient (CG) solver
Implemented as example MATLAB code from <https://en.wikipedia.org/wiki/Conjugate_gradient_method>
"""
# If no guess is given, set an empty guess
if x is None:
x = array_create.zeros_like(b)
r = b - dot(A, x)
p = r.copy()
r_squared = r * r
rsold = np.sum(r_squared)
tol_squared = tol * tol
i = 0
while np.max(r_squared) > tol_squared or force_niter is not None:
Ap = dot(A, p)
alpha = rsold / dot(p, Ap)
x = x + alpha * p
r = r - alpha * Ap
r_squared = r * r
rsnew = np.sum(r_squared)
p = r + (rsnew / rsold) * p
rsold = rsnew
if force_niter is not None and i >= force_niter:
break
i += 1
return x
def cg(A, b, x=None, tol=1e-5):
# If no guess is given, set an empty guess
if x is None:
x = np.zeros(shape=b.shape, dtype=b.dtype)
# Initialize arrays
alpha = np.zeros(shape=(1, 1), dtype=b.dtype)
rsold = np.zeros(shape=(1, 1), dtype=b.dtype)
rsnew = np.zeros(shape=(1, 1), dtype=b.dtype)
r = b - np.dot(A, x)
p = r.copy()
r_squared = r * r
rsold = np.sum(r_squared)
tol_squared = tol * tol
while np.max(r_squared) > tol_squared:
Ap = np.dot(A, p)
alpha = rsold / np.dot(p, Ap)
x = x + alpha * p
r = r - alpha * Ap
r_squared = r * r
rsnew = np.sum(r_squared)
p = r + (rsnew / rsold) * p
rsold = rsnew
return x
def bestBounds(image, size, regionOfInterest=None):
"""
utility determine the best bounds for a given size
if regionOfInterest is None, then will center the crop
:param image: any supported image type
:param size: can be anything that getSize() supports
:param regionOfInterest: a black and white mask used to liquid resize images
(if =True, then auto-calculate as necessary)
:return (x,y,x2,y2):
"""
imsize = getSize(image)
size = getSize(size)
dx = max(int(imsize[0] - size[0]), 0)
dy = max(int(imsize[1] - size[1]), 0)
if regionOfInterest is None:
return (dx / 2, dy / 2, imsize[0] - dx / 2, imsize[1] - dy / 2)
if regionOfInterest is True: # auto-calculate
from . import autoInterest
regionOfInterest = autoInterest.interest(image)
# determine bounds
n, s, e, w = 0, imsize[0] - 1, imsize[1] - 1, 0
if dy > 0:
col_roi = np.sum(regionOfInterest, axis=1)
ff = False # when there's a tie, alternate sides
for _ in range(dy):
if col_roi[e] > col_roi[w]:
w += 1
ff = True
elif col_roi[e] < col_roi[w] or ff:
e -= 1
ff = False
else:
w += 1
ff = True
if dx > 0:
col_roi = np.sum(regionOfInterest, axis=0)
ff = False # when there's a tie, alternate sides
for _ in range(dx):
if col_roi[s] > col_roi[n]:
n += 1
ff = True
elif col_roi[s] < col_roi[n] or ff:
s -= 1
ff = False
else:
n += 1
ff = True
return (n, w, s, e)
def smartsize(self, size: Tuple[int, int], useGolden: bool = False):
"""
returns an image smartly cropped to the given size
:param size: the size to change to
:param useGolden: TODO: try to position regions of interest on golden mean
"""
image = self.image
if image is None:
return image
if image.size[0] < 1 or image.size[1] < 1:
raise Exception("Image is busted. ", image.size)
roi = self.roi
resize = 1.0 # percent
if size[0] != image.size[0]:
resize = size[0] / max(image.size[0], 1)
if size[1] != image.size[1]:
resize = max(resize, size[1] / max(image.size[1], 1))
# TODO: do I want to scale up the image directly,
# or get smart about oversizing and using region of interest??
if resize != 1.0:
newsize = (int(round(image.size[0] * resize)),
int(round(image.size[1] * resize)))
image = image.resize(newsize)
roi = roi.resize(newsize)
# crop in on region of interest
# for now, simply find the best place in the lingering dimension to crop
if newsize[0] == size[0]:
if newsize[1] != size[1]:
# width matches, crop height
d = int(size[1])
a = np.sum(roi, axis=1) # or use mean
for u in range(len(a) - d):
a[u] = np.sum(a[u:u + d])
a = a[0:-d]
idx = np.argmax(a)
cropTo = (0, idx, size[0], idx + size[1])
image = image.crop(cropTo)
else:
# height matches, crop width
d = int(size[0])
a = np.sum(roi, axis=0) # or use mean
for u in range(len(a) - d):
a[u] = np.sum(a[u:u + d])
a = a[0:-d]
idx = np.argmax(a)
cropTo = (idx, 0, idx + size[0], size[1])
image = image.crop(cropTo)
return image
def avalanche(x, A, f, N):
count = 0
degree = np.sum(A, 0, dtype=np.int32)
#print(degree.shape)
xc = degree + (degree == 0)
spikes = x >= xc
ava = spikes.copy()
while np.dot(degree, spikes) > 0:
ava = (ava + spikes) > 0
spikes = x >= xc
add_particles = np.dot(A, spikes)
#subtract=np.multiply(np.random.rand(N),spikes)>f
nonzero = add_particles.nonzero()[0]
add_particles[nonzero] = np.random.rand(
len(nonzero)) > f #leak of avalanching particles
x = x + add_particles
x = x - np.multiply(spikes, degree)
#x = x - (np.random.rand(N)>f)
#x = np.multiply(x,(x>0))
count = count + 1
return [x, ava]
def avalanche(x, A, f, N):
count = 0
degree = np.sum(A, 0, dtype=np.int32)
#print(degree.shape)
xc = degree + (degree == 0)
spikes = x >= xc
ava = spikes.copy()
while np.sum(np.multiply(degree, spikes)) > 0:
ava = (ava + spikes) > 0
spikes = x >= xc
x = x + np.dot(A, spikes)
x = x - np.multiply(spikes, degree)
x = x - (np.random.rand(N) > f)
x = np.multiply(x, (x > 0))
count = count + 1
return [x, ava]
def move(galaxy, dt):
"""Move the bodies
first find forces and change velocity and then move positions
"""
n = len(galaxy['x'])
# Calculate all dictances component wise (with sign)
dx = galaxy['x'][np.newaxis, :].T - galaxy['x']
dy = galaxy['y'][np.newaxis, :].T - galaxy['y']
dz = galaxy['z'][np.newaxis, :].T - galaxy['z']
# Euclidian distances (all bodys)
r = np.sqrt(dx**2 + dy**2 + dz**2)
diagonal(r)[:] = 1.0
# prevent collition
mask = r < 1.0
r = r * ~mask + 1.0 * mask
m = galaxy['m'][np.newaxis, :].T
# Calculate the acceleration component wise
Fx = G * m * dx / r**3
Fy = G * m * dy / r**3
Fz = G * m * dz / r**3
# Set the force (acceleration) a body exerts on it self to zero
diagonal(Fx)[:] = 0.0
diagonal(Fy)[:] = 0.0
diagonal(Fz)[:] = 0.0
galaxy['vx'] += dt * np.sum(Fx, axis=0)
galaxy['vy'] += dt * np.sum(Fy, axis=0)
galaxy['vz'] += dt * np.sum(Fz, axis=0)
galaxy['x'] += dt * galaxy['vx']
galaxy['y'] += dt * galaxy['vy']
galaxy['z'] += dt * galaxy['vz']
def norm(x, ord=None, axis=None):
"""
This version of norm is not fully compliant with the NumPy version,
it only supports computing 2-norm of a vector.
"""
if ord != None:
raise NotImplementedError("Unsupported value param ord=%s" % ord)
if axis != None:
raise NotImplementedError("Unsupported value of param ord=%s" % axis)
r = np.sum(x*x)
if issubclass(np.dtype(r.dtype).type, np.integer):
r_f32 = np.empty(r.shape, dtype=np.float32)
r_f32[:] = r
r = r_f32
return np.sqrt(r)
def norm(x, ord=None, axis=None):
"""
This version of norm is not fully compliant with the NumPy version,
it only supports computing 2-norm of a vector.
"""
if ord != None:
raise NotImplementedError("Unsupported value param ord=%s" % ord)
if axis != None:
raise NotImplementedError("Unsupported value of param ord=%s" % axis)
r = np.sum(x * x)
if issubclass(np.dtype(r.dtype).type, np.integer):
r_f32 = np.empty(r.shape, dtype=np.float32)
r_f32[:] = r
r = r_f32
return np.sqrt(r)
stripes = 37 # number of stripes per wave
N = 512 # image size in pixels
ite = 30 # iterations
phases = np.arange(0, 2 * pi, 2 * pi / ite)
image = np.empty((N, N))
d = np.arange(-N / 2, N / 2, dtype=np.float64)
xv, yv = np.meshgrid(d, d)
theta = np.arctan2(yv, xv)
r = np.log(np.sqrt(xv * xv + yv * yv))
r[np.isinf(r) == True] = 0
tcos = theta * np.cos(np.arange(0, pi, pi / k))[:, np.newaxis, np.newaxis]
rsin = r * np.sin(np.arange(0, pi, pi / k))[:, np.newaxis, np.newaxis]
inner = (tcos - rsin) * stripes
cinner = np.cos(inner)
sinner = np.sin(inner)
i = 0
for phase in phases:
image[:] = np.sum(cinner * np.cos(phase) - sinner * np.sin(phase),
axis=0) + k
plt.imshow(image.copy2numpy(), cmap="RdGy")
fig.savefig("quasi-{:03d}.png".format(i),
bbox_inches='tight',
pad_inches=0)
i += 1
#!/usr/bin/dython2 import bohrium as bh a = bh.array(range(9 * 100000)) a = bh.sum(a) print(a)
#storex = np.zeros((N,steps))
#storex_noava = np.zeros((N,steps))
temp = np.arange(0, int(2 * G_undir.number_of_edges()))
R = [(temp[2 * i], temp[2 * i + 1]) for i in range(G_undir.number_of_edges())]
recency = {}
for edge, rec in zip(G_dir.edges(), R):
recency[edge] = {'recency': rec}
nx.set_edge_attributes(G_dir, recency)
#print()
#print(G_dir.edges(data=True))
print(G_dir.edges(data=True))
degree = np.array(np.sum(A, 0), dtype=np.int32)
G_undir.clear()
del (R)
del (temp)
del (recency)
#Initial State
x = np.zeros(N, dtype=np.int32)
for i in range(N):
if degree[i] > 0:
#np.random.seed(1)
x[i] = np.random.randint(0, degree[i])
else:
x[i] = 0
def test_reduce(np, bohrium, shape):
return np.sum(np.ones(shape))
if __name__ == "__main__":
"""
print("NUMPY")
import numpy as np
print test_reduce(np, False, (10, 10, 10))
print test_reduce(np, False, (10, 10, 10))
"""
print("BOHRIUM")
import bohrium as np
shape = (10,10,10)
a = np.sum(np.ones(shape))
b = np.sum(np.ones(shape))
c = np.add.reduce(np.add.reduce(np.add.reduce(np.ones(shape))))
d = np.sum(np.ones(shape))
print a,b,c,d
#print np.add.reduce(np.add.reduce(np.add.reduce(np.ones(shape))))
#t1 = np.add.reduce(np.ones(shape))
#t2 = np.add.reduce(t1)
#t3 = np.add.reduce(t2)
#del t1, t2
#print t3
def selectByColor(img,
color,
tolerance=0,
soften=10,
smartSoften=True,
colorspace='RGB'):
"""
Select all pixels of a given color
:param img: can be a pil image, numpy array, etc
:param color: (in colorspace units) can be anything that pickColor returns:
a color int array
a color string to decode
a color range (colorLow,colorHigh)
an array of any of these
:param tolerance: how close the selection must be
:param soften: apply a soften radius to the edges of the selection
:param smartSoften: multiply the soften radius by how near the pixel is to the selection color
:param colorspace: change the given img (assumed to be RGB) into another corlorspace before matching
:returns: black and white image in a numpy array (usable as a selection or a mask)
"""
from . import colorSpaces
img = numpyArray(img)
img = colorSpaces.changeColorspace(img, colorspace)
if (isinstance(color, list)
and isinstance(color[0], list)) or (isinstance(color, np.ndarray)
and len(color.shape) > 1):
# there are multiple colors, so select them all one at a time
# TODO: this could possibly be made faster with array operations??
ret = None
for c in color:
if ret is None:
ret = selectByColor(img, c, tolerance, soften, smartSoften)
else:
ret = ret + selectByColor(img, c, tolerance, soften,
smartSoften)
ret = clampImage(ret)
elif isinstance(color, tuple):
# color range - select all colors "between" these two in the given color space
color = (matchColorToImage(color[0],
img), matchColorToImage(color[1], img))
matches = np.logical_and(img >= color[0], img <= color[1])
ret = np.where(matches.all(axis=2), 1.0, 0.0)
else:
# a single color (or a series of colors that have been averaged down to one)
color = matchColorToImage(color, img)
if isFloat(color):
imax = 1.0
imin = 0.0
else:
imax = 255
imin = 0
numColors = img.shape[-1]
avgDelta = np.sum(np.abs(img[:, :] - color), axis=-1) / numColors
ret = np.where(avgDelta <= tolerance, imax, imin)
if soften > 0:
ret = gaussianBlur(ret, soften)
if smartSoften:
ret = np.minimum(imax, ret / avgDelta)
return ret
#plt.show()
#storex = np.zeros((N,steps))
#storex_noava = np.zeros((N,steps))
temp = np.arange(0, int(2 * G_undir.number_of_edges()))
R = [(temp[2 * i], temp[2 * i + 1]) for i in range(G_undir.number_of_edges())]
recency = {}
for edge, rec in zip(G_dir.edges(), R):
recency[edge] = {'recency': rec}
nx.set_edge_attributes(G_dir, recency)
#print()
#print(G_dir.edges(data=True))
degree = np.array(np.sum(A, 0), dtype=np.int32)
G_undir.clear()
del (R)
del (temp)
del (recency)
#Initial State
x = np.zeros(N, dtype=np.int32)
for i in range(N):
if degree[i] > 0:
#np.random.seed(1)
x[i] = np.random.randint(0, degree[i])
else:
x[i] = 0