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 normalMapFromHeightMap(heightmap):
"""
Create a normal map from a height map (sometimes called a bumpmap)
:param heightmap: height map to convert
Comes from:
http://www.juhanalankinen.com/calculating-normalmaps-with-python-and-numpy/
"""
heightmap = numpyArray(heightmap)
heightmap = normalize(heightmap)
matI = np.identity(heightmap.shape[0] + 1)
matNeg = -1 * matI[0:-1, 1:]
matNeg[0, -1] = -1
matI = matI[1:, 0:-1]
matI[-1, 0] = 1
matI += matNeg
matGradX = (matI.dot(heightmap.T)).T
matGradY = matI.dot(heightmap)
matNormal = np.zeros([heightmap.shape[0], heightmap.shape[1], 3])
matNormal[:, :, 0] = -matGradX
matNormal[:, :, 1] = matGradY
matNormal[:, :, 2] = 1.0
fNormMax = np.max(np.abs(matNormal))
matNormal = ((matNormal / fNormMax) + 1.0) / 2.0
return matNormal
def random_galaxy(N):
""" Generate a galaxy of random bodies """
m = np.array((numpy.arange(0.0, 1.0, step=1.0 / N) + np.float64(10)) *
np.float64(m_sol / 10))
x = np.array((numpy.arange(0.0, 1.0, step=1.0 / N) - np.float64(0.5)) *
np.float64(r_ly / 100))
y = np.array((numpy.arange(0.0, 1.0, step=1.0 / N) - np.float64(0.5)) *
np.float64(r_ly / 100))
z = np.array((numpy.arange(0.0, 1.0, step=1.0 / N) - np.float64(0.5)) *
np.float64(r_ly / 100))
vx = np.zeros(N, dtype=np.float64)
vy = np.zeros(N, dtype=np.float64)
vz = np.zeros(N, dtype=np.float64)
assert len(m) == N
return m, x, y, z, vx, vy, vz
def sor_setup(W, H, dtype=np.float32, bohrium=False):
if W % 2 > 0 or H % 2 > 0:
raise Exception("Each dimension must have an even size.")
full = np.zeros((H + 2, W + 2), dtype=dtype, bohrium=bohrium)
full[:, 0] += -273.15
full[:, -1] += -273.15
full[0, :] += 40.0
full[-1, :] += -273.13
return full
def sor_setup(W,H,dtype=np.float32,bohrium=False):
if W%2 > 0 or H%2 > 0:
raise Exception("Each dimension must have an even size.")
full = np.zeros((H+2,W+2), dtype=dtype,bohrium=bohrium)
full[:,0] += -273.15
full[:,-1] += -273.15
full[0,:] += 40.0
full[-1,:] += -273.13
return full
def simulate(galaxy, timesteps, visualize=False):
for i in range(timesteps):
move(galaxy, dt)
util.Benchmark().flush()
if visualize: #NB: this is only for experiments
T = np.zeros((3, len(galaxy['x'])), dtype=np.float32)
T[0, :] = galaxy['x']
T[1, :] = galaxy['y']
T[2, :] = galaxy['z']
np.visualize(T, "3d", 0, 0.0, 10)
def iexpand(image):
"""
expand image by factor of 2
Comes from:
https://compvisionlab.wordpress.com/2013/05/13/image-blending-using-pyramid/
"""
out = None
kernel = generating_kernel(0.4)
outimage = np.zeros((image.shape[0]*2, image.shape[1]*2), dtype=np.float64)
outimage[::2,::2]=image[:,:]
out = 4*scipy.signal.convolve2d(outimage,kernel,'same')
return out
def random_galaxy(N, B, dtype=np.float64):
"""Generate a galaxy of random bodies"""
galaxy = { # We let all bodies stand still initially
'm': (B.random_array(
(N, ), dtype=dtype) + dtype(10)) * dtype(m_sol / 10),
'x': (B.random_array(
(N, ), dtype=dtype) - dtype(0.5)) * dtype(r_ly / 100),
'y': (B.random_array(
(N, ), dtype=dtype) - dtype(0.5)) * dtype(r_ly / 100),
'z': (B.random_array(
(N, ), dtype=dtype) - dtype(0.5)) * dtype(r_ly / 100),
'vx': np.zeros(N, dtype=dtype),
'vy': np.zeros(N, dtype=dtype),
'vz': np.zeros(N, dtype=dtype)
}
if dtype == np.float32:
galaxy['m'] /= 1e10
galaxy['x'] /= 1e5
galaxy['y'] /= 1e5
galaxy['z'] /= 1e5
return galaxy
def monte_carlo_pi(samples, iterations):
s = np.zeros(1)
for i in xrange(0, iterations): # sample
x = np.random.random((samples), dtype=np.float64, bohrium=True)
y = np.random.random((samples), dtype=np.float64, bohrium=True)
m = np.sqrt(x*x + y*y) # model
c = np.add.reduce((m<1.0).astype('float')) # count
s += c*4.0 / samples # approximate
return s / (iterations)
def directionalBlur(img, size=15):
"""
blur in a given direction
https://www.packtpub.com/mapt/book/application_development/9781785283932/2/ch02lvl1sec21/motion-blur#!
"""
oSize = img.shape
kernel = np.zeros((size, size))
kernel[int((size - 1) / 2), :] = np.ones(size)
kernel = kernel / size
img = scipy.signal.convolve(img, kernel)
d = (img.shape[0] - oSize[0]) / 2, (img.shape[1] - oSize[1]) / 2
img = img[d[0]:-d[0], d[1]:-d[1]]
return img
def perlinNoise(size=(256,256),octaves=None,seed=None):
"""
generate perlin noise
"""
if octaves is None:
octaves=math.log(max(size),2.0)
ret=np.zeros(size)
for n in range(1,int(octaves)):
k=n
amp=1.0#/octaves/float(n)
px=randomNoise((size[0]/k,size[1]/k),seed)
px=scipy.ndimage.zoom(px,(float(ret.shape[0])/px.shape[0],float(ret.shape[1])/px.shape[1]),order=2)
px=np.clip(px,0.0,1.0) # unfortunately zoom function can cause values to go out of bounds :(
ret=(ret+px*amp)/2.0 # average with existing
ret=np.clip(ret,0.0,1.0)
return ret
def waveImage(size=(256,256),repeats=2,angle=0,wave='sine',radial=False):
"""
create an image based on a sine, saw, or triangle wave function
"""
ret=np.zeros(size)
if radial:
raise NotImplementedError() # TODO: Implement radial wave images
else:
twopi=2*pi
thetas=np.arange(size[0])*float(repeats)/size[0]*twopi
if wave=='sine':
ret[:,:]=0.5+0.5*np.sin(thetas)
elif wave=='saw':
n=np.round(thetas/twopi)
thetas-=n*twopi
ret[:,:]=np.where(thetas<0,thetas+twopi,thetas)/twopi
elif wave=='triangle':
ret[:,:]=1.0-2.0*np.abs(np.floor((thetas*(1.0/twopi))+0.5)-(thetas*(1.0/twopi)))
return ret
def collapse(lapl_pyr):
"""
Reconstruct the image based on its laplacian pyramid.
Comes from:
https://compvisionlab.wordpress.com/2013/05/13/image-blending-using-pyramid/
"""
output = None
output = np.zeros((lapl_pyr[0].shape[0],lapl_pyr[0].shape[1]), dtype=np.float64)
for i in range(len(lapl_pyr)-1,0,-1):
lap = iexpand(lapl_pyr[i])
lapb = lapl_pyr[i-1]
if lap.shape[0] > lapb.shape[0]:
lap = np.delete(lap,(-1),axis=0)
if lap.shape[1] > lapb.shape[1]:
lap = np.delete(lap,(-1),axis=1)
tmp = lap + lapb
lapl_pyr.pop()
lapl_pyr.pop()
lapl_pyr.append(tmp)
output = tmp
return output
def interest(image):
"""
get regions of interest in the image
returns b&w image where white=interesting, black=uninteresting
"""
program = [] # (weight, function)
if not has_opencv:
print('WARN: Attempting auto-detection of regions of interest.')
print('\t This works A LOT better with OpenCV installed.')
print('\t try: pip install opencv-contrib-python')
print(
'\t or go here: https://sourceforge.net/projects/opencvlibrary/files/'
)
program = [(0.5, selectSkin), (0.1, selectHighContrast),
(0.1, selectHighSaturation), (0.05, selectSobel)]
else:
program = [(0.8, selectEyes), (0.8, selectFaces), (0.5, selectSkin),
(0.3, selectHighContrast), (0.5, selectHighSaturation),
(0.3, selectSobel)]
image = imageRepr.numpyArray(image)
outImage = np.zeros(image.shape[0:2])
totalWeight = 0
for weight, _ in program:
totalWeight += weight
for weight, fn in program:
weight = weight / totalWeight
if weight < 0.001:
#print("skipping",fn.__name__,weight)
continue
#print("calculating",fn.__name__,weight)
im = fn(image)
if weight != 1.0:
im = im * weight
outImage = outImage + im
return normalize(outImage)
def getChannel(img, channel):
"""
get a channel as a new image.
:param img: the image to extract a color channel from
:param channel: name of the channel to extract - supports R,G,B,A,H,S,V
Returns a grayscale image, or None
"""
img = numpyArray(img)
if channel == 'R':
if len(img.shape) == 2:
img = img[:, :]
else:
img = img[:, :, 0]
elif channel == 'G':
if len(img.shape) == 2:
img = img[:, :]
else:
img = img[:, :, 1]
elif channel == 'B':
if len(img.shape) == 2:
img = img[:, :]
else:
img = img[:, :, 2]
elif channel == 'A':
if len(img.shape) == 2 or len(img[0, 0]) < 4:
img = np.ones(img.shape)
else:
img = img[:, :, 3]
elif channel == 'H':
if len(img.shape) == 2:
img = np.zeros(img.shape)
else:
img = rgb2hsvArray(img)[:, :, 0]
elif channel == 'S':
if len(img.shape) == 2:
img = np.zeros(img.shape)
else:
img = rgb2hsvArray(img)[:, :, 1]
elif channel == 'V':
if len(img.shape) == 2:
pass
else:
img = rgb2hsvArray(img)[:, :, 2]
elif channel == 'C':
if len(img.shape) == 2:
img = np.zeros(img.shape)
else:
img = rgb2cmykArray(img)[:, :, 0]
elif channel == 'M':
if len(img.shape) == 2:
img = np.zeros(img.shape)
else:
img = rgb2cmykArray(img)[:, :, 1]
elif channel == 'Y':
if len(img.shape) == 2:
img = np.zeros(img.shape)
else:
img = rgb2cmykArray(img)[:, :, 2]
elif channel == 'K':
if len(img.shape) == 2:
pass
else:
img = rgb2cmykArray(img)[:, :, 3]
else:
raise Exception('Unknown channel: ' + channel)
return img
def pad_z_edges(arr):
arr_shape = list(arr.shape)
arr_shape[2] += 2
out = bh.zeros(arr_shape, arr.dtype)
out[:, :, 1:-1] = arr
return out
def integrate_tke(u, v, w, maskU, maskV, maskW, dxt, dxu, dyt, dyu, dzt, dzw, cost, cosu, kbot, kappaM, mxl, forc, forc_tke_surface, tke, dtke):
tau = 0
taup1 = 1
taum1 = 2
dt_tracer = 1
dt_mom = 1
AB_eps = 0.1
alpha_tke = 1.
c_eps = 0.7
K_h_tke = 2000.
flux_east = bh.zeros_like(maskU)
flux_north = bh.zeros_like(maskU)
flux_top = bh.zeros_like(maskU)
sqrttke = bh.sqrt(bh.maximum(0., tke[:, :, :, tau]))
"""
integrate Tke equation on W grid with surface flux boundary condition
"""
dt_tke = dt_mom # use momentum time step to prevent spurious oscillations
"""
vertical mixing and dissipation of TKE
"""
ks = kbot[2:-2, 2:-2] - 1
a_tri = bh.zeros_like(maskU[2:-2, 2:-2])
b_tri = bh.zeros_like(maskU[2:-2, 2:-2])
c_tri = bh.zeros_like(maskU[2:-2, 2:-2])
d_tri = bh.zeros_like(maskU[2:-2, 2:-2])
delta = bh.zeros_like(maskU[2:-2, 2:-2])
delta[:, :, :-1] = dt_tke / dzt[bh.newaxis, bh.newaxis, 1:] * alpha_tke * 0.5 \
* (kappaM[2:-2, 2:-2, :-1] + kappaM[2:-2, 2:-2, 1:])
a_tri[:, :, 1:-1] = -delta[:, :, :-2] / \
dzw[bh.newaxis, bh.newaxis, 1:-1]
a_tri[:, :, -1] = -delta[:, :, -2] / (0.5 * dzw[-1])
b_tri[:, :, 1:-1] = 1 + (delta[:, :, 1:-1] + delta[:, :, :-2]) / dzw[bh.newaxis, bh.newaxis, 1:-1] \
+ dt_tke * c_eps \
* sqrttke[2:-2, 2:-2, 1:-1] / mxl[2:-2, 2:-2, 1:-1]
b_tri[:, :, -1] = 1 + delta[:, :, -2] / (0.5 * dzw[-1]) \
+ dt_tke * c_eps / mxl[2:-2, 2:-
2, -1] * sqrttke[2:-2, 2:-2, -1]
b_tri_edge = 1 + delta / dzw[bh.newaxis, bh.newaxis, :] \
+ dt_tke * c_eps / mxl[2:-2, 2:-2, :] * sqrttke[2:-2, 2:-2, :]
c_tri[:, :, :-1] = -delta[:, :, :-1] / dzw[bh.newaxis, bh.newaxis, :-1]
d_tri[...] = tke[2:-2, 2:-2, :, tau] + dt_tke * forc[2:-2, 2:-2, :]
d_tri[:, :, -1] += dt_tke * forc_tke_surface[2:-2, 2:-2] / (0.5 * dzw[-1])
sol, water_mask = solve_implicit(ks, a_tri, b_tri, c_tri, d_tri, b_edge=b_tri_edge)
tke[2:-2, 2:-2, :, taup1] = where(water_mask, sol, tke[2:-2, 2:-2, :, taup1])
"""
Add TKE if surface density flux drains TKE in uppermost box
"""
tke_surf_corr = bh.zeros(maskU.shape[:2])
mask = tke[2:-2, 2:-2, -1, taup1] < 0.0
tke_surf_corr[2:-2, 2:-2] = where(
mask,
-tke[2:-2, 2:-2, -1, taup1] * 0.5 * dzw[-1] / dt_tke,
0.
)
tke[2:-2, 2:-2, -1, taup1] = bh.maximum(0., tke[2:-2, 2:-2, -1, taup1])
"""
add tendency due to lateral diffusion
"""
flux_east[:-1, :, :] = K_h_tke * (tke[1:, :, :, tau] - tke[:-1, :, :, tau]) \
/ (cost[bh.newaxis, :, bh.newaxis] * dxu[:-1, bh.newaxis, bh.newaxis]) * maskU[:-1, :, :]
flux_east[-1, :, :] = 0.
flux_north[:, :-1, :] = K_h_tke * (tke[:, 1:, :, tau] - tke[:, :-1, :, tau]) \
/ dyu[bh.newaxis, :-1, bh.newaxis] * maskV[:, :-1, :] * cosu[bh.newaxis, :-1, bh.newaxis]
flux_north[:, -1, :] = 0.
tke[2:-2, 2:-2, :, taup1] += dt_tke * maskW[2:-2, 2:-2, :] * \
((flux_east[2:-2, 2:-2, :] - flux_east[1:-3, 2:-2, :])
/ (cost[bh.newaxis, 2:-2, bh.newaxis] * dxt[2:-2, bh.newaxis, bh.newaxis])
+ (flux_north[2:-2, 2:-2, :] - flux_north[2:-2, 1:-3, :])
/ (cost[bh.newaxis, 2:-2, bh.newaxis] * dyt[bh.newaxis, 2:-2, bh.newaxis]))
"""
add tendency due to advection
"""
adv_flux_superbee_wgrid(
flux_east, flux_north, flux_top, tke[:, :, :, tau],
u[..., tau], v[..., tau], w[..., tau], maskW, dxt, dyt, dzw,
cost, cosu, dt_tracer
)
dtke[2:-2, 2:-2, :, tau] = maskW[2:-2, 2:-2, :] * (-(flux_east[2:-2, 2:-2, :] - flux_east[1:-3, 2:-2, :])
/ (cost[bh.newaxis, 2:-2, bh.newaxis] * dxt[2:-2, bh.newaxis, bh.newaxis])
- (flux_north[2:-2, 2:-2, :] - flux_north[2:-2, 1:-3, :])
/ (cost[bh.newaxis, 2:-2, bh.newaxis] * dyt[bh.newaxis, 2:-2, bh.newaxis]))
dtke[:, :, 0, tau] += -flux_top[:, :, 0] / dzw[0]
dtke[:, :, 1:-1, tau] += - \
(flux_top[:, :, 1:-1] - flux_top[:, :, :-2]) / dzw[1:-1]
dtke[:, :, -1, tau] += - \
(flux_top[:, :, -1] - flux_top[:, :, -2]) / \
(0.5 * dzw[-1])
"""
Adam Bashforth time stepping
"""
tke[:, :, :, taup1] += dt_tracer * ((1.5 + AB_eps) * dtke[:, :, :, tau] - (0.5 + AB_eps) * dtke[:, :, :, taum1])
return tke, dtke, tke_surf_corr
def main():
B = util.Benchmark()
nx = B.size[0]
ny = B.size[1]
nz = B.size[2]
ITER = B.size[3]
NO_OBST = 1
omega = 1.0
density = 1.0
deltaU = 1e-7
t1 = 1/3.0
t2 = 1/18.0
t3 = 1/36.0
B.start()
F = np.ones((19, nx, ny, nz), dtype=np.float64)
F[:] = density/19.0
FEQ = np.ones((19, nx, ny, nz), dtype=np.float64)
FEQ[:] = density/19.0
T = np.zeros((19, nx, ny, nz), dtype=np.float64)
#Create the scenery.
BOUND = np.zeros((nx, ny, nz), dtype=np.float64)
BOUNDi = np.ones((nx, ny, nz), dtype=np.float64)
"""
if not NO_OBST:
for i in xrange(nx):
for j in xrange(ny):
for k in xrange(nz):
if ((i-4)**2+(j-5)**2+(k-6)**2) < 6:
BOUND[i,j,k] += 1.0
BOUNDi[i,j,k] += 0.0
BOUND[:,0,:] += 1.0
BOUNDi[:,0,:] *= 0.0
"""
if util.Benchmark().bohrium:
np.flush()
for ts in xrange(0, ITER):
##Propagate / Streaming step
T[:] = F
#nearest-neighbours
F[1,:,:,0] = T[1,:,:,-1]
F[1,:,:,1:] = T[1,:,:,:-1]
F[2,:,:,:-1] = T[2,:,:,1:]
F[2,:,:,-1] = T[2,:,:,0]
F[3,:,0,:] = T[3,:,-1,:]
F[3,:,1:,:] = T[3,:,:-1,:]
F[4,:,:-1,:] = T[4,:,1:,:]
F[4,:,-1,:] = T[4,:,0,:]
F[5,0,:,:] = T[5,-1,:,:]
F[5,1:,:,:] = T[5,:-1,:,:]
F[6,:-1,:,:] = T[6,1:,:,:]
F[6,-1,:,:] = T[6,0,:,:]
#next-nearest neighbours
F[7,0 ,0 ,:] = T[7,-1 , -1,:]
F[7,0 ,1:,:] = T[7,-1 ,:-1,:]
F[7,1:,0 ,:] = T[7,:-1, -1,:]
F[7,1:,1:,:] = T[7,:-1,:-1,:]
F[8,0 ,:-1,:] = T[8,-1 ,1:,:]
F[8,0 , -1,:] = T[8,-1 ,0 ,:]
F[8,1:,:-1,:] = T[8,:-1,1:,:]
F[8,1:, -1,:] = T[8,:-1,0 ,:]
F[9,:-1,0 ,:] = T[9,1:, -1,:]
F[9,:-1,1:,:] = T[9,1:,:-1,:]
F[9,-1 ,0 ,:] = T[9,0 , 0,:]
F[9,-1 ,1:,:] = T[9,0 ,:-1,:]
F[10,:-1,:-1,:] = T[10,1:,1:,:]
F[10,:-1, -1,:] = T[10,1:,0 ,:]
F[10,-1 ,:-1,:] = T[10,0 ,1:,:]
F[10,-1 , -1,:] = T[10,0 ,0 ,:]
F[11,0 ,:,0 ] = T[11,0 ,:, -1]
F[11,0 ,:,1:] = T[11,0 ,:,:-1]
F[11,1:,:,0 ] = T[11,:-1,:, -1]
F[11,1:,:,1:] = T[11,:-1,:,:-1]
F[12,0 ,:,:-1] = T[12, -1,:,1:]
F[12,0 ,:, -1] = T[12, -1,:,0 ]
F[12,1:,:,:-1] = T[12,:-1,:,1:]
F[12,1:,:, -1] = T[12,:-1,:,0 ]
F[13,:-1,:,0 ] = T[13,1:,:, -1]
F[13,:-1,:,1:] = T[13,1:,:,:-1]
F[13, -1,:,0 ] = T[13,0 ,:, -1]
F[13, -1,:,1:] = T[13,0 ,:,:-1]
F[14,:-1,:,:-1] = T[14,1:,:,1:]
F[14,:-1,:, -1] = T[14,1:,:,0 ]
F[14,-1 ,:,:-1] = T[14,0 ,:,1:]
F[14,-1 ,:, -1] = T[14,0 ,:,0 ]
F[15,:,0 ,0 ] = T[15,:, -1, -1]
F[15,:,0 ,1:] = T[15,:, -1,:-1]
F[15,:,1:,0 ] = T[15,:,:-1, -1]
F[15,:,1:,1:] = T[15,:,:-1,:-1]
F[16,:,0 ,:-1] = T[16,:, -1,1:]
F[16,:,0 , -1] = T[16,:, -1,0 ]
F[16,:,1:,:-1] = T[16,:,:-1,1:]
F[16,:,1:, -1] = T[16,:,:-1,0 ]
F[17,:,:-1,0 ] = T[17,:,1:, -1]
F[17,:,:-1,1:] = T[17,:,1:,:-1]
F[17,:, -1,0 ] = T[17,:,0 , -1]
F[17,:, -1,1:] = T[17,:,0 ,:-1]
F[18,:,:-1,:-1] = T[18,:,1:,1:]
F[18,:,:-1, -1] = T[18,:,1:,0 ]
F[18,:,-1 ,:-1] = T[18,:,0 ,1:]
F[18,:,-1 , -1] = T[18,:,0 ,0 ]
#Densities bouncing back at next timestep
BB = np.empty(F.shape)
T[:] = F
T[1:,:,:,:] *= BOUND[np.newaxis,:,:,:]
BB[2 ,:,:,:] += T[1 ,:,:,:]
BB[1 ,:,:,:] += T[2 ,:,:,:]
BB[4 ,:,:,:] += T[3 ,:,:,:]
BB[3 ,:,:,:] += T[4 ,:,:,:]
BB[6 ,:,:,:] += T[5 ,:,:,:]
BB[5 ,:,:,:] += T[6 ,:,:,:]
BB[10,:,:,:] += T[7 ,:,:,:]
BB[9 ,:,:,:] += T[8 ,:,:,:]
BB[8 ,:,:,:] += T[9 ,:,:,:]
BB[7 ,:,:,:] += T[10,:,:,:]
BB[14,:,:,:] += T[11,:,:,:]
BB[13,:,:,:] += T[12,:,:,:]
BB[12,:,:,:] += T[13,:,:,:]
BB[11,:,:,:] += T[14,:,:,:]
BB[18,:,:,:] += T[15,:,:,:]
BB[17,:,:,:] += T[16,:,:,:]
BB[16,:,:,:] += T[17,:,:,:]
BB[15,:,:,:] += T[18,:,:,:]
# Relax calculate equilibrium state (FEQ) with equivalent speed and density to F
DENSITY = np.add.reduce(F)
#UX = F[5,:,:,:].copy()
UX = np.ones(F[5,:,:,:].shape, dtype=np.float64)
UX[:,:,:] = F[5,:,:,:]
UX += F[7,:,:,:]
UX += F[8,:,:,:]
UX += F[11,:,:,:]
UX += F[12,:,:,:]
UX -= F[6,:,:,:]
UX -= F[9,:,:,:]
UX -= F[10,:,:,:]
UX -= F[13,:,:,:]
UX -= F[14,:,:,:]
UX /=DENSITY
#UY = F[3,:,:,:].copy()
UY = np.ones(F[3,:,:,:].shape, dtype=np.float64)
UY[:,:,:] = F[3,:,:,:]
UY += F[7,:,:,:]
UY += F[9,:,:,:]
UY += F[15,:,:,:]
UY += F[16,:,:,:]
UY -= F[4,:,:,:]
UY -= F[8,:,:,:]
UY -= F[10,:,:,:]
UY -= F[17,:,:,:]
UY -= F[18,:,:,:]
UY /=DENSITY
#UZ = F[1,:,:,:].copy()
UZ = np.ones(F[1,:,:,:].shape, dtype=np.float64)
UZ[:,:,:] = F[1,:,:,:]
UZ += F[11,:,:,:]
UZ += F[13,:,:,:]
UZ += F[15,:,:,:]
UZ += F[17,:,:,:]
UZ -= F[2,:,:,:]
UZ -= F[12,:,:,:]
UZ -= F[14,:,:,:]
UZ -= F[16,:,:,:]
UZ -= F[18,:,:,:]
UZ /=DENSITY
UX[0,:,:] += deltaU #Increase inlet pressure
#Set bourderies to zero.
UX[:,:,:] *= BOUNDi
UY[:,:,:] *= BOUNDi
UZ[:,:,:] *= BOUNDi
DENSITY[:,:,:] *= BOUNDi
U_SQU = UX**2 + UY**2 + UZ**2
# Calculate equilibrium distribution: stationary
FEQ[0,:,:,:] = (t1*DENSITY)*(1.0-3.0*U_SQU/2.0)
# nearest-neighbours
T1 = 3.0/2.0*U_SQU
tDENSITY = t2*DENSITY
FEQ[1,:,:,:]=tDENSITY*(1.0 + 3.0*UZ + 9.0/2.0*UZ**2 - T1)
FEQ[2,:,:,:]=tDENSITY*(1.0 - 3.0*UZ + 9.0/2.0*UZ**2 - T1)
FEQ[3,:,:,:]=tDENSITY*(1.0 + 3.0*UY + 9.0/2.0*UY**2 - T1)
FEQ[4,:,:,:]=tDENSITY*(1.0 - 3.0*UY + 9.0/2.0*UY**2 - T1)
FEQ[5,:,:,:]=tDENSITY*(1.0 + 3.0*UX + 9.0/2.0*UX**2 - T1)
FEQ[6,:,:,:]=tDENSITY*(1.0 - 3.0*UX + 9.0/2.0*UX**2 - T1)
# next-nearest neighbours
T1 = 3.0*U_SQU/2.0
tDENSITY = t3*DENSITY
U8 = UX+UY
FEQ[7,:,:,:] =tDENSITY*(1.0 + 3.0*U8 + 9.0/2.0*(U8)**2 - T1)
U9 = UX-UY
FEQ[8,:,:,:] =tDENSITY*(1.0 + 3.0*U9 + 9.0/2.0*(U9)**2 - T1)
U10 = -UX+UY
FEQ[9,:,:,:] =tDENSITY*(1.0 + 3.0*U10 + 9.0/2.0*(U10)**2 - T1)
U8 *= -1.0
FEQ[10,:,:,:]=tDENSITY*(1.0 + 3.0*U8 + 9.0/2.0*(U8)**2 - T1)
U12 = UX+UZ
FEQ[11,:,:,:]=tDENSITY*(1.0 + 3.0*U12 + 9.0/2.0*(U12)**2 - T1)
U12 *= 1.0
FEQ[14,:,:,:]=tDENSITY*(1.0 + 3.0*U12 + 9.0/2.0*(U12)**2 - T1)
U13 = UX-UZ
FEQ[12,:,:,:]=tDENSITY*(1.0 + 3.0*U13 + 9.0/2.0*(U13)**2 - T1)
U13 *= -1.0
FEQ[13,:,:,:]=tDENSITY*(1.0 + 3.0*U13 + 9.0/2.0*(U13)**2 - T1)
U16 = UY+UZ
FEQ[15,:,:,:]=tDENSITY*(1.0 + 3.0*U16 + 9.0/2.0*(U16)**2 - T1)
U17 = UY-UZ
FEQ[16,:,:,:]=tDENSITY*(1.0 + 3.0*U17 + 9.0/2.0*(U17)**2 - T1)
U17 *= -1.0
FEQ[17,:,:,:]=tDENSITY*(1.0 + 3.0*U17 + 9.0/2.0*(U17)**2 - T1)
U16 *= -1.0
FEQ[18,:,:,:]=tDENSITY*(1.0 + 3.0*U16 + 9.0/2.0*(U16)**2 - T1)
F *= (1.0-omega)
F += omega * FEQ
#Densities bouncing back at next timestep
F[1:,:,:,:] *= BOUNDi[np.newaxis,:,:,:]
F[1:,:,:,:] += BB[1:,:,:,:]
del BB
del T1
del UX, UY, UZ
del U_SQU
del DENSITY, tDENSITY
del U8, U9, U10, U12, U13, U16, U17
if util.Benchmark().bohrium:
np.flush()
B.stop()
B.pprint()
if B.outputfn:
B.tofile(B.outputfn, {'res': UX})
"""
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
xb = x
count = 0
#xsave = [0]*steps
#save_As=[]
#save_distribution = []
WRITE("Starting simulation")