def build_data(nx, ny, nz):
input = StencilGrid([nx, ny, nz])
input.set_neighborhood(2, input.moore_neighborhood(include_origin=True))
# input.set_neighborhood(2, [
# (0, 0, 0),
# (1, 0, 0), (0, 1, 0), (0, 0, 1),
# (-1, -1, 0), (-1, 1, 0), (-1, 0, -1), (-1, 0, 1),
# (0, -1, -1), (0, -1, 1), (0, 1, -1), (0, 1, 1),
# (-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1),
# (1, -1, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1),
# ])
for x in input.interior_points():
input[x] = random.random()
coefficients = StencilGrid([4])
coefficients[0] = 1.0
coefficients[1] = 0.5
coefficients[2] = 0.25
coefficients[3] = 0.125
for n in input.neighbor_definition:
print(n)
output = StencilGrid([nx,ny,nz])
return input, coefficients, output
def test_von_neuman_neighborhood(self):
stencil_grid = StencilGrid([2, 2])
neighborhood = stencil_grid.von_neuman_neighborhood()
self._are_lists_equal(
neighborhood,
[(-1, 0), (0, -1), (0, 1), (1, 0)]
)
self._are_lists_unequal(
neighborhood,
[(-1, 0), (0, -1), (0, 0), (0, 1), (1, 0)]
)
stencil_grid = StencilGrid([2, 2, 2])
neighborhood = stencil_grid.von_neuman_neighborhood()
self._are_lists_equal(
neighborhood,
[
(-1, 0, 0), (0, -1, 0), (0, 0, -1), (0, 0, 1), (0, 1, 0), (1, 0, 0),
]
)
def build_data(nx, ny, nz):
input = StencilGrid([nx, ny, nz])
input.set_neighborhood(2, input.moore_neighborhood(include_origin=True))
# input.set_neighborhood(2, [
# (0, 0, 0),
# (1, 0, 0), (0, 1, 0), (0, 0, 1),
# (-1, -1, 0), (-1, 1, 0), (-1, 0, -1), (-1, 0, 1),
# (0, -1, -1), (0, -1, 1), (0, 1, -1), (0, 1, 1),
# (-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1),
# (1, -1, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1),
# ])
for x in input.interior_points():
input[x] = random.random()
coefficients = StencilGrid([4])
coefficients[0] = 1.0
coefficients[1] = 0.5
coefficients[2] = 0.25
coefficients[3] = 0.125
for n in input.neighbor_definition:
print(n)
output = StencilGrid([nx, ny, nz])
return input, coefficients, output
def test_border_points(self):
stencil_grid = StencilGrid([3, 3])
border = [x for x in stencil_grid.border_points()]
# self._are_lists_equal(border, [(0, 1), (2, 1), (1, 0), (1, 2), (0, 0), (0, 2), (2, 0), (2, 2)])
# print "border"
# for point in stencil_grid.border_points():
# print(point)
stencil_grid = StencilGrid([3, 3, 3])
border = sorted(list(stencil_grid.border_points()))
# print "corners %s" % sorted(list(stencil_grid.corner_points()))
# print "edges %s" % sorted(list(stencil_grid.edge_points()))
border2 = sorted(list(stencil_grid.boundary_points()))
# print border2
# print("len border %d len border2 %d" % (len(border), len(border2)))
# print("len border %d len border2 %d" % (len(set(border)), len(set(border2))))
# print("sorted border %s" % border)
# print("sorted border2 %s" % border2)
self._are_lists_equal(border, border2)
stencil_grid = StencilGrid([100, 99, 8, 7, 6])
border1 = sorted(list(stencil_grid.border_points()))
border2 = sorted(list(stencil_grid.boundary_points()))
# print("len border1 %d len border2 %d" % (len(border1), len(border2)))
# print("len border1 %d len border2 %d" % (len(set(border1)), len(set(border2))))
# print("sorted border1 %s" % border1)
# print("sorted border2 %s" % border2)
self._are_lists_equal(list(set(border1)), border2)
def gaussian(stdev, length):
result = StencilGrid([length])
scale = 1.0/(stdev*math.sqrt(2.0*math.pi))
divisor = -1.0 / (2.0 * stdev * stdev)
for x in range(length):
result[x] = scale * math.exp(float(x) * float(x) * divisor)
return result
def test_corner_points(self):
stencil_grid = StencilGrid([3, 3])
corners = [x for x in stencil_grid.corner_points()]
self._are_lists_equal(corners, [(0, 0), (0, 2), (2, 0), (2, 2)])
# print "corners"
# for point in stencil_grid.corner_points():
# print(point)
import itertools
stencil_grid = StencilGrid([10, 9, 8, 7, 6])
corners = [x for x in stencil_grid.corner_points()]
ends = [[0, 9], [0, 8], [0, 7], [0, 6], [0, 5]]
self._are_lists_equal(corners, itertools.product(*ends))
def test_moore_neighborhood(self):
stencil_grid = StencilGrid([2, 2])
neighborhood = stencil_grid.moore_neighborhood()
self._are_lists_equal(neighborhood, [(-1, -1), (-1, 0), (-1, 1),
(0, -1), (0, 1), (1, -1), (1, 0),
(1, 1)])
self._are_lists_unequal(neighborhood, [(-1, -1), (-1, 0), (-1, 1),
(0, -1), (0, 0), (0, 1),
(1, -1), (1, 0), (1, 1)])
neighborhood = stencil_grid.moore_neighborhood(include_origin=True)
self._are_lists_equal(neighborhood, [(-1, -1), (-1, 0), (-1, 1),
(0, -1), (0, 0), (0, 1), (1, -1),
(1, 0), (1, 1)])
stencil_grid = StencilGrid([2, 2, 2])
neighborhood = stencil_grid.moore_neighborhood()
self._are_lists_equal(neighborhood,
[(-1, -1, -1), (-1, -1, 0), (-1, -1, 1),
(-1, 0, -1), (-1, 0, 0),
(-1, 0, 1), (-1, 1, -1), (-1, 1, 0), (-1, 1, 1),
(0, -1, -1), (0, -1, 0), (0, -1, 1), (0, 0, -1),
(0, 0, 1), (0, 1, -1), (0, 1, 0), (0, 1, 1),
(1, -1, -1), (1, -1, 0), (1, -1, 1), (1, 0, -1),
(1, 0, 0), (1, 0, 1), (1, 1, -1), (1, 1, 0),
(1, 1, 1)])
neighborhood = stencil_grid.moore_neighborhood(include_origin=True)
self._are_lists_equal(neighborhood,
[(-1, -1, -1), (-1, -1, 0), (-1, -1, 1),
(-1, 0, -1), (-1, 0, 0),
(-1, 0, 1), (-1, 1, -1), (-1, 1, 0), (-1, 1, 1),
(0, -1, -1), (0, -1, 0), (0, -1, 1), (0, 0, -1),
(0, 0, 0), (0, 0, 1), (0, 1, -1), (0, 1, 0),
(0, 1, 1), (1, -1, -1), (1, -1, 0), (1, -1, 1),
(1, 0, -1), (1, 0, 0), (1, 0, 1), (1, 1, -1),
(1, 1, 0), (1, 1, 1)])
def test_corner_points(self):
stencil_grid = StencilGrid([3, 3])
corners = [x for x in stencil_grid.corner_points()]
self._are_lists_equal(corners, [(0, 0), (0, 2), (2, 0), (2, 2)])
# print "corners"
# for point in stencil_grid.corner_points():
# print(point)
import itertools
stencil_grid = StencilGrid([10, 9, 8, 7, 6])
corners = [x for x in stencil_grid.corner_points()]
ends = [[0, 9], [0, 8], [0, 7], [0, 6], [0, 5]]
self._are_lists_equal(corners, itertools.product(*ends))
def test_moore_neighborhood(self):
stencil_grid = StencilGrid([2, 2])
neighborhood = stencil_grid.moore_neighborhood()
self._are_lists_equal(
neighborhood,
[(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)]
)
self._are_lists_unequal(
neighborhood,
[(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1)]
)
neighborhood = stencil_grid.moore_neighborhood(include_origin=True)
self._are_lists_equal(
neighborhood,
[(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1)]
)
stencil_grid = StencilGrid([2, 2, 2])
neighborhood = stencil_grid.moore_neighborhood()
self._are_lists_equal(
neighborhood,
[
(-1, -1, -1), (-1, -1, 0), (-1, -1, 1), (-1, 0, -1), (-1, 0, 0), (-1, 0, 1), (-1, 1, -1), (-1, 1, 0), (-1, 1, 1),
(0, -1, -1), (0, -1, 0), (0, -1, 1), (0, 0, -1), (0, 0, 1), (0, 1, -1), (0, 1, 0), (0, 1, 1),
(1, -1, -1), (1, -1, 0), (1, -1, 1), (1, 0, -1), (1, 0, 0), (1, 0, 1), (1, 1, -1), (1, 1, 0), (1, 1, 1)
]
)
neighborhood = stencil_grid.moore_neighborhood(include_origin=True)
self._are_lists_equal(
neighborhood,
[
(-1, -1, -1), (-1, -1, 0), (-1, -1, 1), (-1, 0, -1), (-1, 0, 0), (-1, 0, 1), (-1, 1, -1), (-1, 1, 0), (-1, 1, 1),
(0, -1, -1), (0, -1, 0), (0, -1, 1), (0, 0, -1), (0, 0, 0), (0, 0, 1), (0, 1, -1), (0, 1, 0), (0, 1, 1),
(1, -1, -1), (1, -1, 0), (1, -1, 1), (1, 0, -1), (1, 0, 0), (1, 0, 1), (1, 1, -1), (1, 1, 0), (1, 1, 1)
]
)
def test_von_neuman_neighborhood(self):
stencil_grid = StencilGrid([2, 2])
neighborhood = stencil_grid.von_neuman_neighborhood()
self._are_lists_equal(neighborhood, [(-1, 0), (0, -1), (0, 1), (1, 0)])
self._are_lists_unequal(neighborhood, [(-1, 0), (0, -1), (0, 0),
(0, 1), (1, 0)])
stencil_grid = StencilGrid([2, 2, 2])
neighborhood = stencil_grid.von_neuman_neighborhood()
self._are_lists_equal(neighborhood, [
(-1, 0, 0),
(0, -1, 0),
(0, 0, -1),
(0, 0, 1),
(0, 1, 0),
(1, 0, 0),
])
def test_edge_points(self):
stencil_grid = StencilGrid([3, 3])
edges = [x for x in stencil_grid.edge_points()]
self._are_lists_equal(edges, [(0, 1), (2, 1), (1, 0), (1, 2)])
height = width
image = np.random.rand(width, height)
# print("Print numpy image: ", image)
stencil = np.array([[0, 1, 0], [1, -4, 1], [0, 1, 0]])
class Kernel(StencilKernel):
def kernel(self, in_grid, out_grid):
for x in in_grid.interior_points():
out_grid[x] = -4 * in_grid[x]
for y in in_grid.neighbors(x, 1):
out_grid[x] += in_grid[y]
in_grid = StencilGrid([width, height])
for i in range(width):
for j in range(height):
in_grid[(i, j)] = image[(i, j)]
# print("StencilGrid in_grid:", in_grid)
iterations = 10
total = 0.0
for _ in range(iterations):
with Timer() as t:
out_image = convolve(image, stencil, mode='constant', cval=0.0)
total += t.interval
print("Numpy convolve avg: {0}".format(total / iterations))
total = 0.0
for _ in range(iterations):
time_steps = 18
class Kernel(StencilKernel):
def kernel(self, in_img, out_img):
for x in out_img.interior_points():
out_img[x] = in_img[x]
for y in in_img.neighbors(x, 0):
out_img[x] += 0.125 * in_img[y]
for z in in_img.neighbors(x, 1):
out_img[x] -= 0.125 * 2.0 * in_img[z]
kernel = Kernel(backend='ocl')
kernel.should_unroll = False
out_grid = StencilGrid([time_steps, width, height])
out_grid.ghost_depth = 1
in_grid = StencilGrid([time_steps, width, height])
in_grid.ghost_depth = 1
base = 1024
r = random.seed()
for i in range(width):
for j in range(height):
in_grid.data[(0, i, j)] = random.randrange(1024) * 1.0
in_grid.neighbor_definition[0] = [(-1, 1, 0), (-1, -1, 0), (-1, 0, 1),
(-1, 0, -1)]
in_grid.neighbor_definition[1] = [(-1, 0, 0), (-1, 0, 0)]
height = 130
time_steps = 18
class Kernel(StencilKernel):
def kernel(self, in_img, out_img):
for x in out_img.interior_points():
out_img[x] = in_img[x]
for y in in_img.neighbors(x, 0):
out_img[x] += 0.125 * in_img[y]
for z in in_img.neighbors(x, 1):
out_img[x] -= 0.125 * 2.0 * in_img[z]
kernel = Kernel(backend='ocl')
kernel.should_unroll = False
out_grid = StencilGrid([time_steps, width, height])
out_grid.ghost_depth = 1
in_grid = StencilGrid([time_steps, width, height])
in_grid.ghost_depth = 1
base = 1024
r = random.seed()
for i in range(width):
for j in range(height):
in_grid.data[(0, i, j)] = random.randrange(1024) * 1.0
in_grid.neighbor_definition[0] = [(-1, 1, 0), (-1, -1, 0),
(-1, 0, 1), (-1, 0, -1)]
in_grid.neighbor_definition[1] = [(-1, 0, 0), (-1, 0, 0)]
def test_edge_points(self):
stencil_grid = StencilGrid([3, 3])
edges = [x for x in stencil_grid.edge_points()]
self._are_lists_equal(edges, [(0, 1), (2, 1), (1, 0), (1, 2)])
stdev_d = 3
stdev_s = 70
radius = 1
width = 64 + radius * 2
class Kernel(StencilKernel):
def kernel(self, in_grid, out_grid):
for x in out_grid.interior_points():
for y in in_grid.neighbors(x, 1):
out_grid[x] += in_grid[y]
kernel = Kernel()
kernel.should_unroll = False
out_grid1 = StencilGrid([width, width])
out_grid1.ghost_depth = radius
out_grid2 = StencilGrid([width, width])
out_grid2.ghost_depth = radius
in_grid = StencilGrid([width, width])
in_grid.ghost_depth = radius
for x in range(0, width):
for y in range(0, width):
in_grid.data[(x, y)] = 1.0
# for x in range(-radius, radius+1):
# for y in range(-radius, radius+1):
# in_grid.neighbor_definition[1].append((x, y))
scale = 1.0/(stdev*math.sqrt(2.0*math.pi))
divisor = -1.0 / (2.0 * stdev * stdev)
for x in range(length):
result[x] = scale * math.exp(float(x) * float(x) * divisor)
return result
def distance(x, y):
return math.sqrt(sum([(x[i]-y[i])**2 for i in range(0, len(x))]))
pixels = map(ord, list(image_in.read(width * height))) # Read in grayscale values
intensity = float(sum(pixels))/len(pixels)
kernel = Kernel()
kernel.should_unroll = False
out_grid = StencilGrid([width, height])
out_grid.ghost_depth = radius
in_grid = StencilGrid([width, height])
in_grid.ghost_depth = radius
for x in range(-radius, radius+1):
for y in range(-radius, radius+1):
in_grid.neighbor_definition[1].append((x, y))
for x in range(0, width):
for y in range(0, height):
in_grid.data[(x, y)] = pixels[y * width + x]
gaussian1 = gaussian(stdev_d, radius*2)
gaussian2 = gaussian(stdev_s, 256)
kernel.kernel(in_grid, gaussian1, gaussian2, out_grid)
height = 50
stdev_d = 3
stdev_s = 70
radius = 1
width = 64 + radius*2
class Kernel(StencilKernel):
def kernel(self, in_grid, out_grid):
for x in out_grid.interior_points():
for y in in_grid.neighbors(x, 1):
out_grid[x] += in_grid[y]
kernel = Kernel()
kernel.should_unroll = False
out_grid1 = StencilGrid([width, width])
out_grid1.ghost_depth = radius
out_grid2 = StencilGrid([width, width])
out_grid2.ghost_depth = radius
in_grid = StencilGrid([width, width])
in_grid.ghost_depth = radius
for x in range(0, width):
for y in range(0, width):
in_grid.data[(x, y)] = 1.0
# for x in range(-radius, radius+1):
# for y in range(-radius, radius+1):
# in_grid.neighbor_definition[1].append((x, y))
for x in in_grid.interior_points():
out_grid[x] = -4 * in_grid[x]
for y in in_grid.neighbors(x, 1):
out_grid[x] += in_grid[y]
x = []
iterations = 10
results = [[] for _ in range(7)]
totals = [0.0 for _ in range(7)]
for width in (2**x + 4 for x in range(10, 14)):
height = width
image = np.random.rand(width, height)
in_grid = StencilGrid([width, height])
for i in range(width):
for j in range(height):
in_grid[(i, j)] = image[(i, j)]
in_grid.neighbor_definition[1] = [
(-2, 2), (-1, 2), (0, 2), (1, 2), (2, 2),
(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 1),
(-2, 0), (-1, 0), (1, 0), (2, 0),
(-2, -1), (-1, -1), (0, -1), (1, -1), (2, -1),
(-2, -2), (-1, -2), (0, -2), (1, -2), (2, -2)
]
in_grid.ghost_depth = 2
out_grid = StencilGrid([width, height])
out_grid.ghost_depth = 2
out_grid[x] = -4 * in_grid[x]
for y in in_grid.neighbors(x, 1):
out_grid[x] += in_grid[y]
x = []
iterations = 10
results = [[] for _ in range(7)]
totals = [0.0 for _ in range(7)]
for width in (2**x + 4 for x in range(10, 14)):
height = width
image = np.random.rand(width, height)
in_grid = StencilGrid([width, height])
for i in range(width):
for j in range(height):
in_grid[(i, j)] = image[(i, j)]
in_grid.neighbor_definition[1] = [(-2, 2), (-1, 2), (0, 2), (1, 2), (2, 2),
(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 1),
(-2, 0), (-1, 0), (1, 0), (2, 0),
(-2, -1), (-1, -1), (0, -1), (1, -1),
(2, -1), (-2, -2), (-1, -2), (0, -2),
(1, -2), (2, -2)]
in_grid.ghost_depth = 2
out_grid = StencilGrid([width, height])
out_grid.ghost_depth = 2
# print("StencilGrid in_grid:", in_grid)
def __init__(self, alpha, beta):
super(LaplacianKernel, self).__init__(backend='c')
self.constants = {'alpha': alpha, 'beta': beta}
def kernel(self, in_grid, out_grid):
for x in in_grid.interior_points():
out_grid[x] = alpha * in_grid[x]
for y in in_grid.neighbors(x, 1):
out_grid[x] += beta * in_grid[y]
# nx = int(sys.argv[1])
# ny = int(sys.argv[2])
# nz = int(sys.argv[3])
nx = 1026
ny = 1026
nz = 34
input_grid = StencilGrid([nx, ny, nz])
output_grid = StencilGrid([nx, ny, nz])
# input_grid.data = ones([nx, ny, nz], dtype=float32)
# for x in input_grid.interior_points():
# input_grid[x] = random.randint(nx * ny * nz)
laplacian = LaplacianKernel(alpha, beta)
laplacian.kernel(input_grid, output_grid)
# for i in range(50):
# for x in input_grid.interior_points():
# input_grid[x] = random.randint(nx * ny * nz)
# laplacian.kernel(input_grid, output_grid)
def test_border_points(self):
stencil_grid = StencilGrid([3, 3])
border = [x for x in stencil_grid.border_points()]
# self._are_lists_equal(border, [(0, 1), (2, 1), (1, 0), (1, 2), (0, 0), (0, 2), (2, 0), (2, 2)])
# print "border"
# for point in stencil_grid.border_points():
# print(point)
stencil_grid = StencilGrid([3, 3, 3])
border = sorted(list(stencil_grid.border_points()))
# print "corners %s" % sorted(list(stencil_grid.corner_points()))
# print "edges %s" % sorted(list(stencil_grid.edge_points()))
border2 = sorted(list(stencil_grid.boundary_points()))
# print border2
# print("len border %d len border2 %d" % (len(border), len(border2)))
# print("len border %d len border2 %d" % (len(set(border)), len(set(border2))))
# print("sorted border %s" % border)
# print("sorted border2 %s" % border2)
self._are_lists_equal(border, border2)
stencil_grid = StencilGrid([100, 99, 8, 7, 6])
border1 = sorted(list(stencil_grid.border_points()))
border2 = sorted(list(stencil_grid.boundary_points()))
# print("len border1 %d len border2 %d" % (len(border1), len(border2)))
# print("len border1 %d len border2 %d" % (len(set(border1)), len(set(border2))))
# print("sorted border1 %s" % border1)
# print("sorted border2 %s" % border2)
self._are_lists_equal(list(set(border1)), border2)