def IC_condition(Nx, Np, u, v, u_hat, v_hat, ICchoice, omega, omega_hat, X, Y):
#todo this initial condition function does not work for any amount of processes
# I need to discretize the initial condition amongst the processes after setting IC.
if ICchoice == 'randomVel':
u = random.rand(Np, Ny)
v = random.rand(Np, Ny)
# u = u / npmax(u)
# v = v / npmax(v)
u_hat = fftn_mpi(u, u_hat)
v_hat = fftn_mpi(v, v_hat)
omega_hat = 1j * (Kx * v_hat - Ky * u_hat)
if ICchoice == 'TaylorGreen':
u = sin(3 * X) * cos(3 * Y)
v = -cos(3 * X) * sin(3 * Y)
# u = u / npmax(u)
# v = v / npmax(v)
u_hat = fftn_mpi(u, u_hat)
v_hat = fftn_mpi(v, v_hat)
omega_hat = 1j * (Kx * v_hat - Ky * u_hat)
if ICchoice == 'Vel1':
if rank == 0:
# u =
## v =
# u = u/npmax(u)
# v = v/npmax(v)
# u_hat = fftn_mpi(u, u_hat)
# v_hat = fftn_mpi(v, v_hat)
u_hat[2, 2] = 5 + 10j
v_hat[2, 2] = 5 + 10j
u_hat[5, 2] = 5 + 10j
v_hat[5, 2] = 5 + 10j
u_hat[2, 3] = 5 + 10j
v_hat[2, 3] = 5 + 10j
u = ifftn_mpi(u_hat, u)
v = ifftn_mpi(v_hat, v)
u = u / npmax(u)
v = v / npmax(v)
u_hat = fftn_mpi(u, u_hat)
v_hat = fftn_mpi(v, v_hat)
omega_hat = 1j * (Kx * v_hat - Ky * u_hat)
if ICchoice == 'omegahat1':
if rank == 0:
random.seed(1969)
omega_hat[0, 4] = random.uniform() + 1j * random.uniform()
omega_hat[1, 1] = random.uniform() + 1j * random.uniform()
omega_hat[3, 0] = random.uniform() + 1j * random.uniform()
omega_hat[2, 3] = random.uniform() + 1j * random.uniform()
omega_hat[5, 3] = random.uniform() + 1j * random.uniform()
omega = abs(ifftn_mpi(omega_hat, omega))
omega = omega / npmax(omega)
omega_hat = fftn_mpi(omega, omega_hat)
if ICchoice == 'omega1':
omega = sin(X) * cos(Y)
omega_hat = fftn_mpi(omega, omega_hat)
if ICchoice == 'omegahatrandom':
omega_hat = random.rand(N, Np) * 1j + random.rand(N, Np)
binary = random.choice([0, 1], size=(N, Np), p=[7. / 10, 3. / 10])
omega_hat = omega_hat * binary
if ICchoice == 'omega3':
H = exp(-((2*X - pi + pi / 5) ** 2 + (4*Y - pi + pi / 5) ** 2) / 0.3) - exp(
-((2*X - pi - pi / 5) ** 2 + (3*Y - pi + pi / 5) ** 2) / 0.2) + exp(
-((3*X - pi - pi / 5) ** 2 + (2*Y - pi - pi / 5) ** 2) / 0.4)+exp(-((2*X - pi + pi / 5)**2 + (Y - pi + pi / 5) ** 2) / 0.3) - exp(
-((X - pi - pi / 5)**2 + (Y - pi + pi / 5) ** 2) /0.2) + exp(-((X - pi - pi / 5)**2 + (3*Y - pi - pi / 5)**2)/0.4)+\
exp(-((X - pi + pi / 5)**2 + (Y - pi + pi / 5) ** 2) / 0.3) + exp(
-((X - pi - pi / 5)**2 + (3*Y - pi + pi / 5) ** 2) /0.3) - exp(-((X - pi - pi / 5)**2 + (Y - pi - pi / 5)**2)/0.4)
epsilon = 0.4
Noise = random.rand(Np, Ny)
omega = H + Noise * epsilon
omega_hat = (fftn_mpi(omega, omega_hat))
omega = real(ifftn_mpi(omega_hat, omega))
if ICchoice == 'omega4':
H = exp(-((2*X - pi + pi / 5) ** 2 + (4*Y - pi + pi / 5) ** 2) / 0.3) - exp(
-((2*X - pi - pi / 5) ** 2 + (3*Y - pi + pi / 5) ** 2) / 0.2) + exp(
-((X + pi - pi / 5) ** 2 + (2*Y - pi - pi / 5) ** 2) / 0.4)+exp(-((2*X - pi + pi / 5)**2 + (Y - pi + pi / 5) ** 2) / 0.3) - exp(
-((X - pi - pi / 5)**2 + (Y - pi + pi / 5) ** 2) /0.2) + exp(-((X - pi - pi / 5)**2 + (3*Y - pi - pi / 5)**2)/0.4)+\
exp(-((X - pi + pi / 5)**2 + (Y - pi + pi / 5) ** 2) / 0.3) + exp(
-((X - pi - pi / 5)**2 + (3*Y - pi + pi / 5) ** 2) /0.3) + exp(-((X + pi - pi / 5)**2 + (Y + pi - pi / 5)**2)/0.4)-\
exp(-((X - pi + pi / 5) ** 2 + (Y - pi + pi / 5) ** 2) / 0.3) + exp(
-((2*X - pi - pi / 5) ** 2 + (3*Y - pi + pi / 5) ** 2) / 0.2) + exp(
-((X - pi - pi / 5) ** 2 + (Y - pi - pi / 5) ** 2) / 0.4)
epsilon = 0.7
Noise = random.rand(Np, Ny)
omega = H + Noise * epsilon
omega_hat = (fftn_mpi(omega, omega_hat))
omega = real(ifftn_mpi(omega_hat, omega))
if ICchoice == 'omega2':
H = exp(-((X - pi + pi / 5)**2 + (Y - pi + pi / 5)**2) / 0.3) - exp(-(
(X - pi - pi / 5)**2 +
(Y - pi + pi / 5)**2) / 0.2) + exp(-((X - pi - pi / 5)**2 +
(Y - pi - pi / 5)**2) / 0.4)
#epsilon = 0.1;
#Noise = random.rand(Np, Ny)
omega = H
omega_hat = (fftn_mpi(omega, omega_hat))
omega = real(ifftn_mpi(omega_hat, omega))
return omega_hat
imgx = 20
imgy = 0
def pltshow(plt, dpi=300):
global imgx, imgy
temppath = tempimage()
plt.savefig(temppath, dpi=dpi)
dx,dy = imagesize(temppath)
w = min(W,dx)
image(temppath,imgx,imgy,width=w)
imgy = imgy + dy + 20
os.remove(temppath)
size(W, HEIGHT+dy+40)
else:
def pltshow(mplpyplot):
mplpyplot.show()
# nodebox section end
x = [val*radians for val in np.arange(0, 15, 0.01)]
fig = plt.figure()
fig.subplots_adjust(hspace=0.3)
ax = fig.add_subplot(211)
line1, = ax.plot(x, cos(x), xunits=radians)
ax = fig.add_subplot(212)
line2, = ax.plot(x, cos(x), xunits=degrees)
pltshow(plt)
""" Plot with radians from the basic_units mockup example package This example shows how the unit class can determine the tick locating, formatting and axis labeling. """ import numpy as np from basic_units import radians, degrees, cos from pylab import figure, show from matplotlib.cbook import iterable import math x = np.arange(0, 15, 0.01) * radians fig = figure() ax = fig.add_subplot(211) ax.plot(x, cos(x), xunits=radians) ax = fig.add_subplot(212) ax.plot(x, cos(x), xunits=degrees) show()
""" Plot with radians from the basic_units mockup example package This example shows how the unit class can determine the tick locating, formatting and axis labeling. """ import numpy as np from basic_units import radians, degrees, cos from matplotlib.pyplot import figure, show x = [val * radians for val in np.arange(0, 15, 0.01)] fig = figure() fig.subplots_adjust(hspace=0.3) ax = fig.add_subplot(211) line1, = ax.plot(x, cos(x), xunits=radians) ax = fig.add_subplot(212) line2, = ax.plot(x, cos(x), xunits=degrees) show()
import numpy as np from basic_units import radians, degrees, cos from pylab import figure, show x = np.arange(0, 15, 0.01) * radians fig = figure() fig.subplots_adjust(hspace=0.3) ax = fig.add_subplot(211) ax.plot(x, cos(x), xunits=radians) ax = fig.add_subplot(212) ax.plot(x, cos(x), xunits=degrees) show()
plt.style.use(astropy_mpl_style)
from matplotlib import rc
rc('font', **{'family': 'serif', 'serif': ['Palatino']})
rc('text', usetex=True)
rc('text.latex',
preamble=r'''\usepackage{amsmath}
\usepackage{physics}
\usepackage{siunitx}
''')
from basic_units import cos, sin, radians
theta_r = np.linspace(0, 2 * np.pi, num=1000)
theta = np.array([x * radians for x in theta_r])
a = (1 - cos(theta)) / 2
t = (theta_r - sin(theta)) / 2
plt.plot(theta, a, label='Scale factor $a$')
plt.plot(theta, t, label='Time $t$')
plt.xlabel('Angle parameter $\\theta$')
plt.ylabel(
'Normalized scale factor $a / \\widetilde{a}_0$ or time $t / \\widetilde{t}_0$'
)
plt.legend()
plt.savefig('positive_curvature_a.pdf', format='pdf')
# plt.show()
plt.close()
plt.plot(t, a)
plt.xlabel("Time $t / \\widetilde{t}_0$")
""" ============ Radian ticks ============ Plot with radians from the basic_units mockup example package. This example shows how the unit class can determine the tick locating, formatting and axis labeling. .. only:: builder_html This example requires :download:`basic_units.py <basic_units.py>` """ import matplotlib.pyplot as plt import numpy as np from basic_units import radians, degrees, cos x = [val*radians for val in np.arange(0, 15, 0.01)] fig, axs = plt.subplots(2) axs[0].plot(x, cos(x), xunits=radians) axs[1].plot(x, cos(x), xunits=degrees) fig.tight_layout() plt.show()