def mouseReleaseEvent(self, event):
self.clear()
self.inputting = False
self.fourier = Fourier(self.view, self.path, path_offset=self.start_at,
closed=False)
self.addItem(self.fourier)
self.go()
def fourier():
if request.args.get('function') is None:
return render_template('fourier.html')
else:
fourier_in = cv2.imread('web/lena.jpg', 0)
fourier_out = Fourier(fourier_in)
cv2.imwrite('web/static/fourier.jpg', fourier_out)
return send_file('static/fourier.jpg', mimetype='image/jpeg')
def initScene(self):
self.scene = QGraphicsScene(self)
self.setScene(self.scene)
self.setSceneRect(-self.WIDTH/2, -self.HEIGHT/2,
self.WIDTH, self.HEIGHT)
# Pick a random .svg file in svg folder.
self.fileName = 'svg/' + random.choice(os.listdir('svg/'))
# Get QPainterPath from said file.
path, closed = svgToPath(self.fileName)
scale = getScale(path, 1000, 600, 500, 300)
self.fourier = Fourier(self, path, scale=scale, closed=closed)
self.scene.addItem(self.fourier)
def rankFeaturesFourier(self, X, y, d=1):
compare = lambda x, y: cmp(abs(x), abs(y))
sorted_coeffs = sorted(Fourier(X, y, self.logger).coeff(d).items(),
key=operator.itemgetter(1),
reverse=True,
cmp=compare)
featureIndices = []
for ranking in sorted_coeffs:
for index in ranking[0]:
if index not in featureIndices:
featureIndices.append(index)
return featureIndices
def run(Ns, save_anim=False):
# --- user input ---
fig, ax = plt.subplots()
ax.set_xlim([0, 1])
ax.set_ylim([0, 1])
draw = Drawer(fig, ax)
plt.show()
# --- find Fourier series for drawn shape ---
fouriers = [Fourier(draw.points, N) for N in Ns]
# --- plot drawn shape against Fourier approximation ---
fig, axs = plt.subplots(1, len(Ns))
ps = draw.points
t_start, t_end = ps[0, 0].real, ps[-1, 0].real
ts = np.linspace(t_start, t_end, 100)
fs = [f(ts) for f in fouriers]
for ax, f in zip(axs, fs):
ax.plot(ps[:, 1].real, ps[:, 1].imag)
ax.plot(f.real, f.imag)
plt.legend(("User Input", "Fourier Approximation"))
plt.show()
# --- animate Fourier drawing ---
anim_fig, anim_axs = plt.subplots(1, len(Ns))
anim_fig.suptitle(f"Fourier approximations of orders {Ns}")
anims = []
for anim_ax, fourier in zip(anim_axs, fouriers):
anim_ax.set_xlim([0, 1])
anim_ax.set_ylim([0, 1])
anim_ax.set_title(f"N = {len(fourier.n) // 2}")
anims.append(Animator(anim_ax, fourier))
group_anim = GroupAnimator(anim_fig, anims, ts[-1])
if save_anim:
fig.savefig('images\comparison.png')
group_anim.save('images\drawing.gif', writer='imagemagick', fps=30)
plt.show()
class Operators(Param):
def __init__(self, param, grid):
self.list_param = [
'varname_list', 'tracer_list', 'whosetspsi', 'mpi', 'npx', 'npy',
'nh', 'gravity', 'f0', 'beta', 'Rd', 'qgoperator', 'order',
'Kdiff', 'diffusion', 'enforce_momentum', 'isisland', 'aparab',
'flux_splitting_method', 'hydroepsilon', 'myrank', 'geometry',
'sqgoperator'
]
param.copy(self, self.list_param)
self.list_grid = [
'msk', 'nxl', 'nyl', 'dx', 'dy', 'bcarea', 'mpitools', 'msknoslip',
'mskbc', 'domain_integration', 'nh', 'xr0', 'yr0', 'i0', 'j0',
'area'
]
grid.copy(self, self.list_grid)
self.first_time = True
# internal work array for the inversion
self.work = zeros((self.nyl, self.nxl))
self.work2 = zeros((self.nyl, self.nxl))
pp = {
'np': param.npx,
'mp': param.npy,
'nh': param.nh,
'n': param.nx // param.npx,
'm': param.ny // param.npy,
'omega': 8. / 9.,
'npmpmax': 1,
'verbose': False,
'dx': grid.dx,
'dy': grid.dy,
'n1': 32,
'n0': 4,
'method': 'deep',
'nagglo': 2,
'hydroepsilon': param.hydroepsilon,
'relaxation': param.relaxation
}
# load the multigrid solver
#
# WARNING: the multigrid needs the mask at cell corners!!!
# not at cell centers
mskr = self.msk * 1.
# this piece is a bit awkward: to initialize gmg, we need
# a mask with a halo properly filled but the fill_halo method
# belongs to gmg. We have a circular definition.
# the trick: define a dummy gmg first a msk=1 everywhere
# then grab the fill_halo method and redefine once again the
# multigrid, this time with the proper mask
# self.gmg = Gmg(pp,mskr)
# borrow the fill_halo from the multigrid
# self.fill_halo = self.gmg.grid[0].halo.fill
fo.celltocorner(mskr, self.work)
# self.fill_halo(self.work)
# del self.gmg
# del self.fill_halo
self.work[self.work < 1.] = 0.
self.mskp = self.msk * 0
self.mskp[self.work == 1.] = 1
pp['verbose'] = True
if self.myrank == 0:
print('-' * 50)
print(' Multigrid hierarchy')
print('-' * 50)
if hasattr(self, 'qgoperator'):
pp['qgoperator'] = True
pp['Rd'] = self.Rd
self.gmg = Gmg(pp, self.work)
else:
self.gmg = Gmg(pp, self.work)
if hasattr(self, 'sqgoperator'):
self.fourier = Fourier(param, grid)
# borrow the fill_halo from the multigrid
self.fill_halo = self.gmg.grid[0].halo.fill
grid.fill_halo = self.gmg.grid[0].halo.fill
self.blwidth = param.Lx * 0.05
# tentative for a regularized no-slip source term
coef = 0. * zeros_like(self.mskp)
coef[1:, 1:] = (self.mskp[:-1, 1:] + self.mskp[:-1, :-1] +
self.mskp[1:, 1:] + self.mskp[1:, :-1])
# nbpsibc is the number of land psi-points surrounding a fluid cell
self.nbpsibc = (4. - coef) * self.msk
self.nbpsibc[self.nbpsibc > 0] = 1.
self.set_boundary_msk()
self.cst = zeros(5, )
# select the proper flux discretization
if self.order % 2 == 0:
self.fortran_adv = fa.adv_centered
self.cst[0] = grid.dx
self.cst[1] = grid.dy
self.cst[2] = 0.05
self.cst[3] = 0 # umax
self.cst[4] = 0 # unused
# should be updated at each timestep
# self.cst[3]=param.umax
else:
self.fortran_adv = fa.adv_upwind
self.cst[0] = grid.dx
self.cst[1] = grid.dy
self.cst[2] = 0.05
self.cst[3] = 0 # umax
self.cst[4] = self.aparab
# should be updated at each timestep
# self.cst[3]=param.umax
# controls the flux splitting method
# 0 = min/max
# 1 = parabolic
list_fs_method = ['minmax', 'parabolic']
if self.flux_splitting_method in list_fs_method:
self.fs_method = list_fs_method.index(self.flux_splitting_method)
else:
print('Warning: %s does not exist' % self.flux_splitting_method)
print('replaced with the default: parabolic')
self.fs_method = list_fs_method.index('parabolic')
# these coefficients below are used for the thermalwind model
coef = 0. * zeros_like(self.msk)
coef[1:-1, 1:-1] = self.msk[1:-1, 2:] + self.msk[1:-1, 0:-2]
coef[coef < 2] = 0.
coef[coef == 2] = 0.5
self.fill_halo(coef)
self.coefb = coef * 1.
coef = 0. * zeros_like(self.msk)
coef[1:-1, 1:-1] = self.msk[2:, 1:-1] + self.msk[0:-2, 1:-1]
coef[coef < 2] = 0.
coef[coef == 2] = 0.5
self.fill_halo(coef)
self.coefV = coef * 1.
if type(self.Kdiff) != dict:
K = self.Kdiff
self.Kdiff = {}
for trac in self.tracer_list:
self.Kdiff[trac] = K
if self.diffusion:
print('diffusion coefficients')
print(' => ', self.Kdiff)
def set_boundary_msk(self):
""" for the no slip boundary source term """
# nh = self.nh
msk = self.msknoslip
z = (roll(msk, -1, axis=1) + roll(msk, -1, axis=0) +
roll(msk, +1, axis=1) + roll(msk, +1, axis=0) - 4 * msk)
z = z * msk
self.mskbc = self.msk * 0
self.mskbc[z < 0] = 1
# the halo will be filled later in operator.py
# when fill_halo will become available
# we can now fix the boundary mask
# to go with the new definition for the source term
# self.mskbc = self.nbpsibc.copy()
self.mskbc *= self.msknoslip
self.fill_halo(self.mskbc)
# idx in the 2D array where boundary terms are computed
# used for storage and i/o
# self.idxbc = where(self.mskbc==1)
self.bcarea = self.domain_integration(self.mskbc)
self.x2bc = self.domain_integration(
(self.xr0)**2 * self.mskbc * self.msknoslip)
self.y2bc = self.domain_integration(
(self.yr0)**2 * self.mskbc * self.msknoslip)
return
def smooth(msk, msk0, k):
y = (+roll(msk, -1, axis=1) + roll(msk, -1, axis=0) +
roll(msk, +1, axis=1) + roll(msk, +1, axis=0))
z = msk * 1.
z[y > 0] = k + 1
z[msk > 0] = msk[msk > 0]
z[msk0 == 0] = 0
self.fill_halo(z)
return z
z0 = 1 - msk * 1.
nk = int(round((self.blwidth / self.dx)))
nk = 1
for k in range(nk):
z = z0 * 1.
z0 = smooth(z, msk, k)
z0[z0 == 0] = nk
z0 = z0 / nk
z0 *= msk
z0 = (1. - z0)**(nk / 2.)
z0[msk == 0] = 1
self.cv = (roll(z0, -1, axis=1) + z0) * .5
self.cu = (roll(z0, -1, axis=0) + z0) * .5
# self.mskbc = z0
# self.bcarea = self.domain_integration(z0)
def rhs_adv(self, x, t, dxdt):
""" compute -div(u*tracer) using finite volume flux discretization
the flux is computed at edge cells using p-th order interpolation
for p even, the flux is centered
for p odd, the flux is upwinded (more points on the upwind side) """
iu = self.varname_list.index('u')
iv = self.varname_list.index('v')
u = x[iu]
v = x[iv]
for trac in self.tracer_list:
ik = self.varname_list.index(trac)
y = dxdt[ik]
self.fortran_adv(self.msk, x[ik], y, u, v, self.cst, self.nh,
self.fs_method, self.order)
self.fill_halo(y)
# for an unknown reason dxdt[ik] is
# not updated by the Fortran routine
# it should be done manually
# (this yields an excessive data movement)
dxdt[ik][:, :] = y
def wallshear(self, x, shear):
# ip = self.varname_list.index('psi')
# meansource = fo.computewallshear(self.msk, x[ip],
# shear, self.dx, self.nh)
return
def rhs_noslip(self, x, source):
""" add the vorticity source term along the boundary to enforce
zero tangential velocity (=no-slip) """
ip = self.varname_list.index('psi')
# iu = self.varname_list.index('u')
# iv = self.varname_list.index('v')
iw = self.varname_list.index(self.whosetspsi)
fo.cornertocell(x[ip], self.work)
meansource = fo.computenoslipsourceterm(self.msknoslip, x[ip],
self.work, self.dx, self.dy,
self.nh)
# K = self.dx*self.dy * 0.25
# self.work2[:, :] = self.work[:, :]
# for kt in range(2):
# fo.add_diffusion(self.msk, self.work, self.dx,
# self.nh, K, self.work2)
# self.fill_halo(self.work2)
# fo.add_diffusion(self.msk, self.work2, self.dx,
# self.nh, K, self.work)
# self.fill_halo(self.work)
# # self.work = self.work/(self.dx**2)*self.mskbc
source[:, :] = self.work
# this step is SUPER important to ensure GLOBAL vorticity conservation
meansource = self.domain_integration(source) / self.bcarea
source -= meansource * self.mskbc
if self.enforce_momentum:
xr = self.xr0
yr = self.yr0
# this step ensures the zero momentum
px = fd.computedotprod(self.msk, source, xr, self.nh)
py = fd.computedotprod(self.msk, source, yr, self.nh)
cst = self.mpitools.local_to_global([(px, 'sum'), (py, 'sum')])
px, py = cst[0] / self.x2bc, cst[1] / self.y2bc
source -= (px * xr + py * yr) * self.mskbc
self.fill_halo(source)
x[iw] -= source
def rhs_diffusion(self, x, t, dxdt, coef=1.):
""" add a diffusion term on the tracer variables """
for trac in self.tracer_list:
ik = self.varname_list.index(trac)
y = dxdt[ik]
fo.add_diffusion(self.msk, x[ik], self.dx, self.nh,
coef * self.Kdiff[trac], y)
self.fill_halo(y)
dxdt[ik] = y
def rhs_torque(self, x, t, dxdt):
""" compute g*db/dx for the Boussinesq model """
ib = self.varname_list.index('buoyancy')
iw = self.varname_list.index('vorticity')
y = dxdt[iw]
b = x[ib]
#y[1:-1, 1:-1] += self.gravity*self.diffx(b)
y *= self.msk
fo.add_torque(self.msk, b, self.dx, self.nh, self.gravity, y)
self.fill_halo(y)
dxdt[iw][:, :] = y
def rhs_torque_density(self, x, t, dxdt):
""" compute g*db/dx for the Boussinesq model """
ib = self.varname_list.index('density')
iw = self.varname_list.index('vorticity')
y = dxdt[iw]
b = x[ib]
#y[1:-1, 1:-1] += self.gravity*self.diffx(b)
# y *= self.msk
# trick: use -gravity to account that density is opposite to buoyancy
fo.add_torque(self.msk, b, self.dx, self.nh, -self.gravity, y)
self.fill_halo(y)
dxdt[iw][:, :] = y
def diffx(self, x):
nh = self.nh
if self.i0 == self.npx - 1:
x[:, -nh] = 2 * x[:, -nh - 1] - x[:, -nh - 2]
if self.i0 == 0:
x[:, nh - 1] = 2 * x[:, nh] - x[:, nh + 1]
return 0.5 * (x[1:-1, 2:] - x[1:-1, :-2]) / self.dx
def diff1x(self, x):
nh = self.nh
if self.i0 == self.npx - 1:
x[:, -nh] = 2 * x[:, -nh - 1] - x[:, -nh - 2]
if self.i0 == 0:
x[:, nh - 1] = 2 * x[:, nh] - x[:, nh + 1]
return (x[:, 1:] - x[:, :-1]) / self.dx
def diffz(self, x):
nh = self.nh
if self.j0 == self.npy - 1:
x[-nh, :] = 2 * x[-nh - 1, :] - x[-nh - 2, :]
if self.j0 == 0:
x[nh - 1, :] = 2 * x[nh, :] - x[nh + 1, :]
return 0.5 * (x[2:, 1:-1] - x[:-2, 1:-1]) / self.dy
def jacobian(self, x, y):
return self.diffx(x) * self.diffz(y) - self.diffz(x) * self.diffx(y)
def rhs_thermalwind(self, x, t, dxdt):
iu = self.varname_list.index('u')
ib = self.varname_list.index('buoyancy')
iw = self.varname_list.index('vorticity')
iV = self.varname_list.index('V')
nh = self.nh
# add the themal wind balance
# g*db/dx + f0*dV/dz
# to domega/dt
b = x[ib]
V = x[iV]
dw = dxdt[iw]
y = self.work
# dw[1:-1, 1:-1] += self.diffx(b)*self.gravity
# dw[1:-1, 1:-1] -= self.diffz(V)*self.f0
y[1:-1, 1:-1] = self.diffx(b) * self.gravity
y[1:-1, 1:-1] -= self.diffz(V) * self.f0
# dw[1:-1, 1:-1] += self.coefb[1:-1, 1:-1]*self.diffx(b)*self.gravity
# dw[1:-1, 1:-1] -= self.coefV[1:-1, 1:-1]*self.diffz(V)*self.f0
# dw[:, :nh+1] = 0
# dw[:, -nh-1:] = 0
y *= self.msk
self.fill_halo(y)
dw[:, :] += y
u = x[iu]
# dxdt[iV][:, 1:] -= 0.5*self.f0*(u[:, :-1]+u[:, 1:])
# dxdt[iV] *= self.msk
# self.fill_halo(dxdt[iV])
y[:, 1:] = -0.5 * self.f0 * (u[:, :-1] + u[:, 1:])
y *= self.msk
self.fill_halo(y)
dxdt[iV][:, :] += y
def fourier_invert_vorticity(self, x, flag='full'):
""" invert using Fourier transform """
iu = self.varname_list.index('u')
iv = self.varname_list.index('v')
ip = self.varname_list.index('psi')
ivor = self.varname_list.index('vorticity')
ipv = self.varname_list.index('pv')
u = x[iu]
v = x[iv]
psi = x[ip]
pv = x[ipv]
vor = x[ivor]
self.fourier.invert(pv, psi, vor)
self.fill_halo(psi)
self.fill_halo(vor)
self.first_time = False
# compute (u,v) @ U,V points from psi @ cell corner
fo.computeorthogradient(self.msk, psi, self.dx, self.dy, self.nh, u, v)
x[iu] = u
x[iv] = v
def invert_vorticity(self, x, flag='full', island=False):
""" compute psi from vorticity (or 'whosetspsi' in general)
this routine interpolates the vorticity from cell centers to
cell corners (where psi is defined)
it then solves div*grad psi = omega with psi=0 along the boundary
(Dirichlet condition) using a multigrid
the non-divergent velocity is computed from psi"""
iu = self.varname_list.index('u')
iv = self.varname_list.index('v')
ip = self.varname_list.index('psi')
iw = self.varname_list.index(self.whosetspsi)
u = x[iu]
v = x[iv]
psi = x[ip]
fo.celltocorner(x[iw], self.work)
#fo.celltocornerbicubic(x[iw], self.work)
if island:
# correcting RHS for islands
self.work[:, :] -= self.rhsp
if flag == 'fast':
ite, res = self.gmg.twoVcycle(psi, self.work, {
'maxite': 1,
'tol': 1e-6,
'verbose': True
})
# ite, res = self.gmg.solve(psi, self.work,
# {'maxite': 2,
# 'tol': 1e-8,
# 'verbose': False})
else:
# compute to machine accuracy
if self.first_time:
verbose = True
else:
verbose = False
if (self.myrank == 0) and verbose:
print('-' * 50)
print(' Convergence of the vorticity inversion')
print(' the residual should decrease by several orders')
print(' of magnitude otherwise something is wrong')
print('-' * 50)
ite, res = self.gmg.solve(psi, self.work, {
'maxite': 4,
'tol': 1e-11,
'verbose': verbose
})
if self.geometry == 'perio':
# make sure psi has zero mean (to avoid the drift)
psim = self.domain_integration(psi) / self.area
psi -= psim
# don't apply the fill_halo on it
# [because fill_halo, as it is, is applying periodic BC]
psi = psi * self.mskp
if island:
# we set psi on the boundary values by adding
# self.psi (defined in island module)
# before that line, psi=0 along all boundaries
psi += self.psi
# it should be added only if we invert for the total psi
# it should not be added if we compute the increment of psi
self.first_time = False
# compute (u,v) @ U,V points from psi @ cell corner
fo.computeorthogradient(self.msk, psi, self.dx, self.dy, self.nh, u, v)
# self.fill_halo(u)
# self.fill_halo(v)
x[iu] = u
x[iv] = v
x[ip] = psi
def __init__(self, param, grid):
self.list_param = [
'varname_list', 'tracer_list', 'whosetspsi', 'mpi', 'npx', 'npy',
'nh', 'gravity', 'f0', 'beta', 'Rd', 'qgoperator', 'order',
'Kdiff', 'diffusion', 'enforce_momentum', 'isisland', 'aparab',
'flux_splitting_method', 'hydroepsilon', 'myrank', 'geometry',
'sqgoperator'
]
param.copy(self, self.list_param)
self.list_grid = [
'msk', 'nxl', 'nyl', 'dx', 'dy', 'bcarea', 'mpitools', 'msknoslip',
'mskbc', 'domain_integration', 'nh', 'xr0', 'yr0', 'i0', 'j0',
'area'
]
grid.copy(self, self.list_grid)
self.first_time = True
# internal work array for the inversion
self.work = zeros((self.nyl, self.nxl))
self.work2 = zeros((self.nyl, self.nxl))
pp = {
'np': param.npx,
'mp': param.npy,
'nh': param.nh,
'n': param.nx // param.npx,
'm': param.ny // param.npy,
'omega': 8. / 9.,
'npmpmax': 1,
'verbose': False,
'dx': grid.dx,
'dy': grid.dy,
'n1': 32,
'n0': 4,
'method': 'deep',
'nagglo': 2,
'hydroepsilon': param.hydroepsilon,
'relaxation': param.relaxation
}
# load the multigrid solver
#
# WARNING: the multigrid needs the mask at cell corners!!!
# not at cell centers
mskr = self.msk * 1.
# this piece is a bit awkward: to initialize gmg, we need
# a mask with a halo properly filled but the fill_halo method
# belongs to gmg. We have a circular definition.
# the trick: define a dummy gmg first a msk=1 everywhere
# then grab the fill_halo method and redefine once again the
# multigrid, this time with the proper mask
# self.gmg = Gmg(pp,mskr)
# borrow the fill_halo from the multigrid
# self.fill_halo = self.gmg.grid[0].halo.fill
fo.celltocorner(mskr, self.work)
# self.fill_halo(self.work)
# del self.gmg
# del self.fill_halo
self.work[self.work < 1.] = 0.
self.mskp = self.msk * 0
self.mskp[self.work == 1.] = 1
pp['verbose'] = True
if self.myrank == 0:
print('-' * 50)
print(' Multigrid hierarchy')
print('-' * 50)
if hasattr(self, 'qgoperator'):
pp['qgoperator'] = True
pp['Rd'] = self.Rd
self.gmg = Gmg(pp, self.work)
else:
self.gmg = Gmg(pp, self.work)
if hasattr(self, 'sqgoperator'):
self.fourier = Fourier(param, grid)
# borrow the fill_halo from the multigrid
self.fill_halo = self.gmg.grid[0].halo.fill
grid.fill_halo = self.gmg.grid[0].halo.fill
self.blwidth = param.Lx * 0.05
# tentative for a regularized no-slip source term
coef = 0. * zeros_like(self.mskp)
coef[1:, 1:] = (self.mskp[:-1, 1:] + self.mskp[:-1, :-1] +
self.mskp[1:, 1:] + self.mskp[1:, :-1])
# nbpsibc is the number of land psi-points surrounding a fluid cell
self.nbpsibc = (4. - coef) * self.msk
self.nbpsibc[self.nbpsibc > 0] = 1.
self.set_boundary_msk()
self.cst = zeros(5, )
# select the proper flux discretization
if self.order % 2 == 0:
self.fortran_adv = fa.adv_centered
self.cst[0] = grid.dx
self.cst[1] = grid.dy
self.cst[2] = 0.05
self.cst[3] = 0 # umax
self.cst[4] = 0 # unused
# should be updated at each timestep
# self.cst[3]=param.umax
else:
self.fortran_adv = fa.adv_upwind
self.cst[0] = grid.dx
self.cst[1] = grid.dy
self.cst[2] = 0.05
self.cst[3] = 0 # umax
self.cst[4] = self.aparab
# should be updated at each timestep
# self.cst[3]=param.umax
# controls the flux splitting method
# 0 = min/max
# 1 = parabolic
list_fs_method = ['minmax', 'parabolic']
if self.flux_splitting_method in list_fs_method:
self.fs_method = list_fs_method.index(self.flux_splitting_method)
else:
print('Warning: %s does not exist' % self.flux_splitting_method)
print('replaced with the default: parabolic')
self.fs_method = list_fs_method.index('parabolic')
# these coefficients below are used for the thermalwind model
coef = 0. * zeros_like(self.msk)
coef[1:-1, 1:-1] = self.msk[1:-1, 2:] + self.msk[1:-1, 0:-2]
coef[coef < 2] = 0.
coef[coef == 2] = 0.5
self.fill_halo(coef)
self.coefb = coef * 1.
coef = 0. * zeros_like(self.msk)
coef[1:-1, 1:-1] = self.msk[2:, 1:-1] + self.msk[0:-2, 1:-1]
coef[coef < 2] = 0.
coef[coef == 2] = 0.5
self.fill_halo(coef)
self.coefV = coef * 1.
if type(self.Kdiff) != dict:
K = self.Kdiff
self.Kdiff = {}
for trac in self.tracer_list:
self.Kdiff[trac] = K
if self.diffusion:
print('diffusion coefficients')
print(' => ', self.Kdiff)
from image import Image
from fourier import Fourier
from plot import Plot
im = Image("house.jpg", (200, 200))
path = im.sort()
period, tup_circle_rads, tup_circle_locs = Fourier(n_approx=1000,
coord_1=path).get_circles()
Plot(period, tup_circle_rads, tup_circle_locs, speed=80).plot()
date_parser=dateparse)
vt = df[df.Category == 'VEHICLE THEFT'] # Vehicle Theft Data
mydate = vt['Dates']
nd = len(mydate)
print "%d crimes in total" % nd
tw = np.zeros(nd) # array of times in weeks
ni = np.linspace(0, nd - 1, nd, dtype=np.int)
mydate.index = ni
for i in range(0, nd):
tw[i] = (mydate[i] - t0).total_seconds()
tw[i] /= swk
# Now get Fourier curve
nw = 323
t = np.linspace(0.5, 644.5, nw)
#MyF = Fourier(645.0, 20, 52.1775, 12, 1.0, 6, 1.0/7.0, 6, df)
MyF = Fourier(645.0, 16, 52.1775, 12, 1.0, 0, 1.0 / 7.0, 0, df, t0)
MyF.compute()
fv = np.empty(nw)
#fv.fill(2700.0)
for i in range(0, nw):
fv[i] = MyF.f(t[i], 'VEHICLE THEFT')
fv[i] *= nd + 0.0
fv[i] /= 322.0
# Got Fourier curve
plt.hist(tw, bins=322) # 645 weeks but we only have alternating weeks
plt.plot(t, fv, linewidth=2.5)
plt.title("Vehicle Theft History")
plt.xlabel("Weeks")
plt.ylabel("Thefts per week")
plt.savefig('time-3.png')
mytimes, mygroups = run.getTimeGroups(time)
#
ds = float(run.dl)
dt = float(mytimes[1] - mytimes[0])
#
numoftimes = mytimes.__len__()
numofcells = int(run.ncells) + 1
#
data = np.empty([numoftimes, numofcells], dtype=complex, order='C')
#
# then fill the data for input fft
for it in range(mytimes.__len__()):
data[it, :].real = run.GetB(mytimes[it])[..., 2]
data[it, :].imag = 0.0
#
f = Fourier(data, field=field, domain=domain)
#
#
# .. draw the plot
plo = Colp(colordata=[
f.xdata / float(run.dl), f.ydata / float(mytimes[1] - mytimes[0]), f.zdata
],
bounds=bounds,
colormap=colormap,
contourdata=None,
flines=None,
arrowdata=None,
labels=['$k$', '$\omega$'],
ticks=ticks,
subticks=subticks,
figsize=figsize,
import matplotlib.pyplot as pt from fourier import Fourier import numpy as np t = np.arange(0.0, 8, 0.01) print(t.shape[0]) s1 = np.sin(2 * np.pi * t) s2 = np.cos(4 * np.pi * t) + s1 s3 = np.random.random(128) jf = Fourier() #f_s1 = jf.Fast(s1) #f_s2 = jf.Fast(s2) #f_s3 = jf.Fast(s3) f_s1 = np.fft.fft(s1) #f_s2 = np.fft.fft(s2) f_s2 = jf.Fast(s2, vect=False) f_s3 = np.fft.fft(s3) m_s1 = jf.complex_to_linear(f_s1) m_s2 = jf.complex_to_linear(f_s2) m_s3 = jf.complex_to_linear(f_s3) fig, ax = pt.subplots(3, 3) ax[0, 0].plot(t, s1) ax[0, 1].plot(t, s2)
import math
from datetime import datetime
from fourier import Fourier
twopi = 2.0 * math.pi
t0 = np.datetime64("2003-01-01")
## read training file
z = zipfile.ZipFile('../train.csv.zip')
dateparse = lambda x: pd.datetime.strptime(x, '%Y-%m-%d %H:%M:%S')
df = pd.read_csv(z.open('train.csv'), parse_dates=['Dates'], date_parser=dateparse)
#crime_category = df['Category'] # list of crime types
#group = df.groupby('Category')
#freq = group.size() # histogram of crime types
#cr_index = freq.index.values
#Nc = len(cr_index) # number of crime types
#cr_a_index = pd.DataFrame(data = np.arange(Nc, dtype=np.int), index = cr_index)
#cr_a_index = cr_a_index[0] # this now holds the index for each crime type
MyF = Fourier(645.0, 20, 52.1775, 12, 1.0, 6, 1.0/7.0, 6, df)
MyF.compute()
MyF.graph()
## read testing file
#z = zipfile.ZipFile('../test.csv.zip')
#df = pd.read_csv(z.open('train.csv'), parse_dates=['Dates'], date_parser=dateparse)
type=str,
help="directory to embeddings")
parser.add_argument('--pca', action='store_true', help="apply pca or not")
parser.add_argument('--pca_path', type=str, help="path to pca file")
parser.add_argument('--periods',
type=int,
nargs='+',
help="list of periods")
parser.add_argument('--mean',
action='store_true',
help="use mean descriptor or not")
parser.add_argument('--events',
type=int,
nargs='+',
default=range(1, 14),
help="list of events")
args = parser.parse_args()
if not os.path.exists(args.embed_dir):
os.makedirs(args.embed_dir)
apply_pca = args.pca
use_mean = args.mean
if apply_pca:
assert os.path.exists(args.pca_path)
pca = utils.load(args.pca_path)
if not use_mean:
periods = args.periods
fourier = Fourier(periods)
timestamps_dict = fourier.get_timestamps()
embed = Embed(args.infos_dir, args.embed_dir)
embed(args.events)
df = pd.read_csv(z.open('train.csv'), parse_dates=['Dates'], date_parser=dateparse)
vt = df[df.Category == 'VEHICLE THEFT'] # Vehicle Theft Data
mydate = vt['Dates']
nd = len(mydate)
print "%d crimes in total" % nd
tw = np.zeros(nd) # array of times in weeks
ni = np.linspace(0, nd-1, nd, dtype=np.int)
mydate.index = ni
for i in range (0, nd):
tw[i] = (mydate[i]-t0).total_seconds()
tw[i] /= swk
# Now get Fourier curve
nw = 323
t = np.linspace(0.5, 644.5, nw)
#MyF = Fourier(645.0, 20, 52.1775, 12, 1.0, 6, 1.0/7.0, 6, df)
MyF = Fourier(645.0, 16, 52.1775, 12, 1.0, 0, 1.0/7.0, 0, df, t0)
MyF.compute()
fv = np.empty(nw)
#fv.fill(2700.0)
for i in range(0, nw):
fv[i] = MyF.f(t[i], 'VEHICLE THEFT')
fv[i] *= nd + 0.0
fv[i] /= 322.0
# Got Fourier curve
plt.hist(tw, bins=322) # 645 weeks but we only have alternating weeks
plt.plot(t, fv, linewidth=2.5)
plt.title("Vehicle Theft History")
plt.xlabel("Weeks")
plt.ylabel("Thefts per week")
plt.savefig('time-3.png')
print "%d crimes in total" % nd
tw = np.zeros(nd) # array of times in weeks
ni = np.linspace(0, nd-1, nd, dtype=np.int)
mydate.index = ni
for i in range (0, nd):
tw[i] = (mydate[i]-t0).total_seconds()
tw[i] /= swk
tw = tw[tw <= 100.0] # only times in the first 100 weeks
tw = tw % 1
tw = tw * 7
nc = len(tw)
# Now get Fourier curve
nw = 336
nb = 84
t = np.linspace(0.0, 1.0, nw)
MyF = Fourier(645.0, 16, 52.1775, 12, 1.0, 6, 1.0/7.0, 8, df, t0)
MyF.compute()
fv = np.empty(nw)
#fv.fill(2700.0)
for i in range(0, nw):
fv[i] = 0.0
for j in range(0, 50):
#fv[i] = MyF.f(t[i], 'DRUNKENNESS')
fv[i] += MyF.f(t[i] + j * 2.0, 'LARCENY/THEFT')
fv[i] *= nc + 0.0 # nc - number of crimes
fv[i] /= 50.0 * nb # nb - number of histogram bins
# Got Fourier curve
t = t * 7
plt.hist(tw, bins=nb) # 645 weeks but we only have alternating weeks
plt.plot(t, fv, linewidth=2.5)
import csv
import math
from datetime import datetime
from fourier import Fourier
twopi = 2.0 * math.pi
t0 = np.datetime64("2003-01-01")
## read training file
z = zipfile.ZipFile('../train.csv.zip')
dateparse = lambda x: pd.datetime.strptime(x, '%Y-%m-%d %H:%M:%S')
df = pd.read_csv(z.open('train.csv'),
parse_dates=['Dates'],
date_parser=dateparse)
#crime_category = df['Category'] # list of crime types
#group = df.groupby('Category')
#freq = group.size() # histogram of crime types
#cr_index = freq.index.values
#Nc = len(cr_index) # number of crime types
#cr_a_index = pd.DataFrame(data = np.arange(Nc, dtype=np.int), index = cr_index)
#cr_a_index = cr_a_index[0] # this now holds the index for each crime type
MyF = Fourier(645.0, 20, 52.1775, 12, 1.0, 6, 1.0 / 7.0, 6, df)
MyF.compute()
MyF.graph()
## read testing file
#z = zipfile.ZipFile('../test.csv.zip')
#df = pd.read_csv(z.open('train.csv'), parse_dates=['Dates'], date_parser=dateparse)
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('--embed_dir',
type=str,
help="directory to embeddings")
parser.add_argument('--results_dir', type=str, help="directory to results")
parser.add_argument('--periods',
type=int,
nargs='+',
help="list of periods")
parser.add_argument('--mean',
action='store_true',
help="use mean descriptor or not")
parser.add_argument('--events',
type=int,
nargs='+',
default=range(1, 14),
help="list of events")
args = parser.parse_args()
use_mean = args.mean
if not os.path.exists(args.results_dir):
os.makedirs(args.results_dir)
if not use_mean:
periods = args.periods
fourier = Fourier(periods)
fourier_coefs = fourier.get_fourier_coefs()
offset_mat_dicts = fourier.get_offset_mats()
retrieve = Retrieve(args.embed_dir, args.results_dir)
retrieve()
print "%d crimes in total" % nd
tw = np.zeros(nd) # array of times in weeks
ni = np.linspace(0, nd-1, nd, dtype=np.int)
mydate.index = ni
for i in range (0, nd):
tw[i] = (mydate[i]-t0).total_seconds()
tw[i] /= swk
tw = tw[tw <= 100.0] # only times in the first 100 weeks
tw = tw % 1
tw = tw * 7
nc = len(tw)
# Now get Fourier curve
nw = 336
nb = 84
t = np.linspace(0.0, 1.0, nw)
MyF = Fourier(645.0, 16, 52.1775, 12, 1.0, 6, 1.0/7.0, 8, df, t0)
MyF.compute()
fv = np.empty(nw)
#fv.fill(2700.0)
for i in range(0, nw):
fv[i] = 0.0
for j in range(0, 50):
fv[i] += MyF.f(t[i] + j * 2.0, 'DRUNKENNESS')
fv[i] *= nc + 0.0 # nc - number of crimes
fv[i] /= 50.0 * nb # nb - number of histogram bins
# Got Fourier curve
t = t * 7
plt.hist(tw, bins=nb) # 645 weeks but we only have alternating weeks
plt.plot(t, fv, linewidth=2.5)
plt.title("Drunkenness")
df = pd.read_csv(z.open('train.csv'), parse_dates=['Dates'], date_parser=dateparse)
#vt = df[df.Category == 'VEHICLE THEFT'] # Vehicle Theft Data
mydate = df['Dates']
#print df.ix['VEHICLE THEFT']
nd = len(mydate)
print "%d crimes in total" % nd
tw = np.zeros(nd) # array of times in weeks
for i in range(0, nd):
tw[i] = (mydate[i]-t0).total_seconds()
tw[i] /= swk
# Now get Fourier curve
nw = 323
t = np.linspace(0.5, 644.5, nw)
#MyF = Fourier(645.0, 20, 52.1775, 12, 1.0, 6, 1.0/7.0, 6, df)
MyF = Fourier(645.0, 16, 52.1775, 12, 1.0, 0, 1.0/7.0, 0, df, t0)
MyF.compute()
fv = np.empty(nw)
#fv.fill(2700.0)
for i in range(0, nw):
fv[i] = MyF.fa(t[i])
fv[i] *= nd + 0.0
fv[i] /= 322.0
# Got Fourier curve
plt.hist(tw, bins=322) # 645 weeks but we only have alternating weeks
plt.plot(t, fv, linewidth=2.5)
plt.title("Crime History")
plt.xlabel("Weeks")
plt.ylabel("Crimes per week")
plt.savefig('time-1.png')
mydate = df['Dates']
nd = len(mydate)
print "%d crimes in total" % nd
tw = np.zeros(nd) # array of times in weeks
for i in range(0, nd):
tw[i] = (mydate[i]-t0).total_seconds()
tw[i] /= swk
tw = tw[tw <= 1.0] # only times in the first week
tw = tw * 7
nc = len(tw)
# Now get Fourier curve
nw = 336
nb = 84
t = np.linspace(0.0, 1.0, nw)
MyF = Fourier(645.0, 16, 52.1775, 12, 1.0, 6, 1.0/7.0, 8, df, t0)
MyF.compute()
fv = np.empty(nw)
#fv.fill(2700.0)
for i in range(0, nw):
fv[i] = MyF.fa(t[i])
fv[i] *= nc + 0.0
fv[i] /= nb + 0.0
# Got Fourier curve
t = t * 7
plt.hist(tw, bins=nb) # 645 weeks but we only have alternating weeks
plt.plot(t, fv, linewidth=2.5)
plt.title("Crimes History")
plt.xlabel("Days")
plt.ylabel("Crimes per 2 hours")
def create_arrows(ax, fourier): """Create arrows from the coefficients of a Fourier series""" p = 0 + 0j arrows = [] for c, n in zip(fourier.c, fourier.n): arrow = Arrow(ax, p.real, p.imag, n, c, fourier.L) arrows.append(arrow) p += c return arrows if __name__ == "__main__": fig, axes = plt.subplots(1, 2) fig.set_size_inches(14, 7) ts = np.linspace(0, 6.28, 100) xs = 0.5 * np.cos(ts) + 0.5 * np.cos(2 * ts) ys = np.sin(ts) + 0.25 points = np.array([ts, xs + 1j * ys]).T anims = [] for n, ax in enumerate(axes): f = Fourier(points, N=n+1) anims.append(Animator(ax, f)) ax.set_xlim((-2, 2)) ax.set_ylim((-2, 2)) group_anims = GroupAnimator(fig, anims, 6.28) plt.show()
print "%d crimes in total" % nd
tw = np.zeros(nd) # array of times in weeks
ni = np.linspace(0, nd - 1, nd, dtype=np.int)
mydate.index = ni
for i in range(0, nd):
tw[i] = (mydate[i] - t0).total_seconds()
tw[i] /= swk
tw = tw[tw <= 100.0] # only times in the first 100 weeks
tw = tw % 1
tw = tw * 7
nc = len(tw)
# Now get Fourier curve
nw = 336
nb = 84
t = np.linspace(0.0, 1.0, nw)
MyF = Fourier(645.0, 16, 52.1775, 12, 1.0, 6, 1.0 / 7.0, 8, df, t0)
MyF.compute()
fv = np.empty(nw)
#fv.fill(2700.0)
for i in range(0, nw):
fv[i] = 0.0
for j in range(0, 50):
fv[i] += MyF.f(t[i] + j * 2.0, 'DRUNKENNESS')
fv[i] *= nc + 0.0 # nc - number of crimes
fv[i] /= 50.0 * nb # nb - number of histogram bins
# Got Fourier curve
t = t * 7
plt.hist(tw, bins=nb) # 645 weeks but we only have alternating weeks
plt.plot(t, fv, linewidth=2.5)
plt.title("Drunkenness")
