def smagorinsky(particle, fieldset, time):
dx = 0.01
dudx = (fieldset.U[time, particle.depth, particle.lat, particle.lon + dx] -
fieldset.U[time, particle.depth, particle.lat,
particle.lon - dx]) / (2 * dx)
dudy = (fieldset.U[time, particle.depth, particle.lat + dx, particle.lon] -
fieldset.U[time, particle.depth, particle.lat - dx,
particle.lon]) / (2 * dx)
dvdx = (fieldset.V[time, particle.depth, particle.lat, particle.lon + dx] -
fieldset.V[time, particle.depth, particle.lat,
particle.lon - dx]) / (2 * dx)
dvdy = (fieldset.V[time, particle.depth, particle.lat + dx, particle.lon] -
fieldset.V[time, particle.depth, particle.lat - dx,
particle.lon]) / (2 * dx)
A = fieldset.cell_areas[time, 0, particle.lat, particle.lon]
deg_to_m = (1852 * 60)**2 * math.cos(particle.lat * math.pi / 180)
A = A / deg_to_m
Vh = fieldset.Cs * A * math.sqrt(dudx**2 + 0.5 *
(dudy + dvdx)**2 + dvdy**2)
xres = 1 # [degrees]
yres = 1
hitBoundary = True
tries = 0
while hitBoundary and tries < 5:
dlat = yres * random.normalvariate(0., 1.) * math.sqrt(
2 * math.fabs(particle.dt) * Vh) #/ dy_cell
dlon = xres * random.normalvariate(0., 1.) * math.sqrt(
2 * math.fabs(particle.dt) * Vh) #/ dx_cell
if (fieldset.U[time, particle.depth, particle.lat + dlat,
particle.lon + dlon] > 0):
if (fieldset.V[time, particle.depth, particle.lat + dlat,
particle.lon + dlon] > 0):
hitBoundary = False
elif (fieldset.V[time, particle.depth, particle.lat + dlat,
particle.lon + dlon] < 0):
hitBoundary = False
elif (fieldset.U[time, particle.depth, particle.lat + dlat,
particle.lon + dlon] < 0):
if (fieldset.V[time, particle.depth, particle.lat + dlat,
particle.lon + dlon] > 0):
hitBoundary = False
elif (fieldset.V[time, particle.depth, particle.lat + dlat,
particle.lon + dlon] < 0):
hitBoundary = False
tries += 1
if tries == 5:
particle.beached = 1
dlat = 0
dlon = 0
particle.lat += dlat
particle.lon += dlon
def sample(self):
s = [None] * self.p
s[0] = random.normalvariate(self.mu[0], self.sigma[0])
for i in range(1, self.p):
pid = self.parents[i]
assert s[pid] != None # XXX assumes that the features are in topological order
shift_mu = self.mu[i] - (self.w[i] * self.mu[pid])
s[i] = random.normalvariate(shift_mu + (self.w[i] * s[pid]), self.sigma[i])
return s
def sample(self):
s = [None] * self.p
s[0] = random.normalvariate(self.mu[0], self.sigma[0])
for i in range(1, self.p):
pid = self.parents[i]
assert s[
pid] != None # XXX assumes that the features are in topological order
shift_mu = self.mu[i] - (self.w[i] * self.mu[pid])
s[i] = random.normalvariate(shift_mu + (self.w[i] * s[pid]),
self.sigma[i])
return s
def randProjectPts(pts, cluDim):
d = len(pts[0])
r = 1.0 / float(len(pts[0])**.5)
M = ([[random.normalvariate(0, 1) * r for a in range(cluDim)]
for b in range(d)])
return mult(pts, M)
def default(particle, fieldset, time):
"""Smagorinski parametrization kernel.
"""
dx = 0.01;
dudx = (fieldset.U[time, particle.depth, particle.lat, particle.lon+dx]-fieldset.U[time, particle.depth, particle.lat, particle.lon-dx]) / (2*dx)
dudy = (fieldset.U[time, particle.depth, particle.lat+dx, particle.lon]-fieldset.U[time, particle.depth, particle.lat-dx, particle.lon]) / (2*dx)
dvdx = (fieldset.V[time, particle.depth, particle.lat, particle.lon+dx]-fieldset.V[time, particle.depth, particle.lat, particle.lon-dx]) / (2*dx)
dvdy = (fieldset.V[time, particle.depth, particle.lat+dx, particle.lon]-fieldset.V[time, particle.depth, particle.lat-dx, particle.lon]) / (2*dx)
A = fieldset.cell_areas[time, 0, particle.lat, particle.lon]
Vh = fieldset.Cs * A * math.sqrt(dudx**2 + 0.5*(dudy + dvdx)**2 + dvdy**2)
xres = fieldset.resolutionx # [degrees]
yres = fieldset.resolutiony
dx_cell = fieldset.cell_edge_sizes_x[0, 0, particle.lat, particle.lon] # [meters]
dy_cell = fieldset.cell_edge_sizes_y[0, 0, particle.lat, particle.lon]
hitBoundary = True
tries = 0
while hitBoundary and tries <15:
dlat = yres * random.normalvariate(0,1) * math.sqrt(2*math.fabs(particle.dt)* Vh) / dy_cell
dlon = xres * random.normalvariate(0,1) * math.sqrt(2*math.fabs(particle.dt)* Vh) / dx_cell
if(fieldset.U[time, particle.depth, particle.lat+dlat, particle.lon+dlon] > 0):
if(fieldset.V[time, particle.depth, particle.lat+dlat, particle.lon+dlon] > 0):
hitBoundary = False
elif(fieldset.V[time, particle.depth, particle.lat+dlat, particle.lon+dlon] < 0):
hitBoundary = False
elif(fieldset.U[time, particle.depth, particle.lat+dlat, particle.lon+dlon] < 0):
if(fieldset.V[time, particle.depth, particle.lat+dlat, particle.lon+dlon] > 0):
hitBoundary = False
elif(fieldset.V[time, particle.depth, particle.lat+dlat, particle.lon+dlon] < 0):
hitBoundary = False
tries += 1
if tries == 15:
dlat = 0
dlon = 0
particle.lat += dlat
particle.lon += dlon
def test_upsample():
before_num = 500
after_num = 1000
xs = [random.normalvariate(0,1) for i in range(before_num)]
ps = [1/float(before_num) for i in range(before_num)]
states = zip(xs,ps)
mu0 = sum([x*p for x,p in states])
sigma0 = sum([(x**2)*p for x,p in states])
new_states = upsample(states,after_num)
mu1 = sum([x*p for x,p in new_states])
sigma1 = sum([(x**2)*p for x,p in new_states])
print mu0,sigma0
print mu1,sigma1
def randProjectPts(pts,cluDim):
d = len(pts[0])
r = 1.0/float(len(pts[0])**.5)
M= ([[random.normalvariate(0,1)*r for a in range(cluDim)] for b in range(d)])
return mult(pts,M)
