I'm trying to simulate an exoplanet transit and to determine its orbital characteristics with curve fitting. However, the intersection area between two circles needs to distinguish two cases: if the center of the smallest circle is in the biggest or not. This is a problem for scipy with the function curve_fit, calling an array in my function cacl_aire. The function transit simulates the smallest disc's evolution with time.
Here's my code:
import numpy as np
from matplotlib import pyplot as plt
from scipy.optimize import curve_fit
import xlrd
dt = 0.1
Vx = 0.08
Vy = 0
X0 = -5
Y0 = 0
R = 2
r = 0.7
X = X0
Y = Y0
doc = xlrd.open_workbook("transit data.xlsx")
feuille_1 = doc.sheet_by_index(0)
mag = [feuille_1.cell_value(rowx=k, colx=4) for k in range(115)]
T = [feuille_1.cell_value(rowx=k, colx=3) for k in range(115)]
def calc_aire(r, x, y):
D2 = x * x + y * y
if D2 >= (r + R)**2:
return 0
d = (r**2 - R**2 + D2) / (2 * (D2**0.5))
d2 = D2**0.5 - d
if abs(d) >= r:
return min([r * r * np.pi, R * R * np.pi])
H = (r * r - d * d)**0.5
As = np.arccos(d / r) * r * r - d * H
As2 = R * R * np.arccos(d2 / R) - d2 * H
return As + As2
def transit(t, r, X0, Y0, Vx, Vy):
return -calc_aire(r, X0 + Vx * t, Y0 + Vy * t)
best_vals = curve_fit(transit, T, mag)[0]
print('best_vals: {}'.format(best_vals))
plt.figure()
plt.plot(T, mag)
plt.draw()
I have the following error :
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all() with the line 28 :
if D2 >= (r + R)**2:
Here is my database:
https://drive.google.com/file/d/1SP12rrHGjjpHfKBQ0l3nVMJDIRCPlkuf/view?usp=sharing
I don't see any trick to solve my problem.
Related
Can anyone tell me what is wrong with this code? It is from https://jakevdp.github.io/blog/2012/09/05/quantum-python/ .
Everything in it worked out except the title of the plot.I can't figure it out.
It should look like this
but when the code is run, it polts this
Here is the code given:-
"""
General Numerical Solver for the 1D Time-Dependent Schrodinger's equation.
author: Jake Vanderplas
email: vanderplas#astro.washington.edu
website: http://jakevdp.github.com
license: BSD
Please feel free to use and modify this, but keep the above information. Thanks!
"""
import numpy as np
from matplotlib import pyplot as pl
from matplotlib import animation
from scipy.fftpack import fft,ifft
class Schrodinger(object):
"""
Class which implements a numerical solution of the time-dependent
Schrodinger equation for an arbitrary potential
"""
def __init__(self, x, psi_x0, V_x,
k0 = None, hbar=1, m=1, t0=0.0):
"""
Parameters
----------
x : array_like, float
length-N array of evenly spaced spatial coordinates
psi_x0 : array_like, complex
length-N array of the initial wave function at time t0
V_x : array_like, float
length-N array giving the potential at each x
k0 : float
the minimum value of k. Note that, because of the workings of the
fast fourier transform, the momentum wave-number will be defined
in the range
k0 < k < 2*pi / dx
where dx = x[1]-x[0]. If you expect nonzero momentum outside this
range, you must modify the inputs accordingly. If not specified,
k0 will be calculated such that the range is [-k0,k0]
hbar : float
value of planck's constant (default = 1)
m : float
particle mass (default = 1)
t0 : float
initial tile (default = 0)
"""
# Validation of array inputs
self.x, psi_x0, self.V_x = map(np.asarray, (x, psi_x0, V_x))
N = self.x.size
assert self.x.shape == (N,)
assert psi_x0.shape == (N,)
assert self.V_x.shape == (N,)
# Set internal parameters
self.hbar = hbar
self.m = m
self.t = t0
self.dt_ = None
self.N = len(x)
self.dx = self.x[1] - self.x[0]
self.dk = 2 * np.pi / (self.N * self.dx)
# set momentum scale
if k0 == None:
self.k0 = -0.5 * self.N * self.dk
else:
self.k0 = k0
self.k = self.k0 + self.dk * np.arange(self.N)
self.psi_x = psi_x0
self.compute_k_from_x()
# variables which hold steps in evolution of the
self.x_evolve_half = None
self.x_evolve = None
self.k_evolve = None
# attributes used for dynamic plotting
self.psi_x_line = None
self.psi_k_line = None
self.V_x_line = None
def _set_psi_x(self, psi_x):
self.psi_mod_x = (psi_x * np.exp(-1j * self.k[0] * self.x)
* self.dx / np.sqrt(2 * np.pi))
def _get_psi_x(self):
return (self.psi_mod_x * np.exp(1j * self.k[0] * self.x)
* np.sqrt(2 * np.pi) / self.dx)
def _set_psi_k(self, psi_k):
self.psi_mod_k = psi_k * np.exp(1j * self.x[0]
* self.dk * np.arange(self.N))
def _get_psi_k(self):
return self.psi_mod_k * np.exp(-1j * self.x[0] *
self.dk * np.arange(self.N))
def _get_dt(self):
return self.dt_
def _set_dt(self, dt):
if dt != self.dt_:
self.dt_ = dt
self.x_evolve_half = np.exp(-0.5 * 1j * self.V_x
/ self.hbar * dt )
self.x_evolve = self.x_evolve_half * self.x_evolve_half
self.k_evolve = np.exp(-0.5 * 1j * self.hbar /
self.m * (self.k * self.k) * dt)
psi_x = property(_get_psi_x, _set_psi_x)
psi_k = property(_get_psi_k, _set_psi_k)
dt = property(_get_dt, _set_dt)
def compute_k_from_x(self):
self.psi_mod_k = fft(self.psi_mod_x)
def compute_x_from_k(self):
self.psi_mod_x = ifft(self.psi_mod_k)
def time_step(self, dt, Nsteps = 1):
"""
Perform a series of time-steps via the time-dependent
Schrodinger Equation.
Parameters
----------
dt : float
the small time interval over which to integrate
Nsteps : float, optional
the number of intervals to compute. The total change
in time at the end of this method will be dt * Nsteps.
default is N = 1
"""
self.dt = dt
if Nsteps > 0:
self.psi_mod_x *= self.x_evolve_half
for i in xrange(Nsteps - 1):
self.compute_k_from_x()
self.psi_mod_k *= self.k_evolve
self.compute_x_from_k()
self.psi_mod_x *= self.x_evolve
self.compute_k_from_x()
self.psi_mod_k *= self.k_evolve
self.compute_x_from_k()
self.psi_mod_x *= self.x_evolve_half
self.compute_k_from_x()
self.t += dt * Nsteps
######################################################################
# Helper functions for gaussian wave-packets
def gauss_x(x, a, x0, k0):
"""
a gaussian wave packet of width a, centered at x0, with momentum k0
"""
return ((a * np.sqrt(np.pi)) ** (-0.5)
* np.exp(-0.5 * ((x - x0) * 1. / a) ** 2 + 1j * x * k0))
def gauss_k(k,a,x0,k0):
"""
analytical fourier transform of gauss_x(x), above
"""
return ((a / np.sqrt(np.pi))**0.5
* np.exp(-0.5 * (a * (k - k0)) ** 2 - 1j * (k - k0) * x0))
######################################################################
# Utility functions for running the animation
def theta(x):
"""
theta function :
returns 0 if x<=0, and 1 if x>0
"""
x = np.asarray(x)
y = np.zeros(x.shape)
y[x > 0] = 1.0
return y
def square_barrier(x, width, height):
return height * (theta(x) - theta(x - width))
######################################################################
# Create the animation
# specify time steps and duration
dt = 0.01
N_steps = 50
t_max = 120
frames = int(t_max / float(N_steps * dt))
# specify constants
hbar = 1.0 # planck's constant
m = 1.9 # particle mass
# specify range in x coordinate
N = 2 ** 11
dx = 0.1
x = dx * (np.arange(N) - 0.5 * N)
# specify potential
V0 = 1.5
L = hbar / np.sqrt(2 * m * V0)
a = 3 * L
x0 = -60 * L
V_x = square_barrier(x, a, V0)
V_x[x < -98] = 1E6
V_x[x > 98] = 1E6
# specify initial momentum and quantities derived from it
p0 = np.sqrt(2 * m * 0.2 * V0)
dp2 = p0 * p0 * 1./80
d = hbar / np.sqrt(2 * dp2)
k0 = p0 / hbar
v0 = p0 / m
psi_x0 = gauss_x(x, d, x0, k0)
# define the Schrodinger object which performs the calculations
S = Schrodinger(x=x,
psi_x0=psi_x0,
V_x=V_x,
hbar=hbar,
m=m,
k0=-28)
######################################################################
# Set up plot
fig = pl.figure()
# plotting limits
xlim = (-100, 100)
klim = (-5, 5)
# top axes show the x-space data
ymin = 0
ymax = V0
ax1 = fig.add_subplot(211, xlim=xlim,
ylim=(ymin - 0.2 * (ymax - ymin),
ymax + 0.2 * (ymax - ymin)))
psi_x_line, = ax1.plot([], [], c='r', label=r'$|\psi(x)|$')
V_x_line, = ax1.plot([], [], c='k', label=r'$V(x)$')
center_line = ax1.axvline(0, c='k', ls=':',
label = r"$x_0 + v_0t$")
title = ax1.set_title("")
ax1.legend(prop=dict(size=12))
ax1.set_xlabel('$x$')
ax1.set_ylabel(r'$|\psi(x)|$')
# bottom axes show the k-space data
ymin = abs(S.psi_k).min()
ymax = abs(S.psi_k).max()
ax2 = fig.add_subplot(212, xlim=klim,
ylim=(ymin - 0.2 * (ymax - ymin),
ymax + 0.2 * (ymax - ymin)))
psi_k_line, = ax2.plot([], [], c='r', label=r'$|\psi(k)|$')
p0_line1 = ax2.axvline(-p0 / hbar, c='k', ls=':', label=r'$\pm p_0$')
p0_line2 = ax2.axvline(p0 / hbar, c='k', ls=':')
mV_line = ax2.axvline(np.sqrt(2 * V0) / hbar, c='k', ls='--',
label=r'$\sqrt{2mV_0}$')
ax2.legend(prop=dict(size=12))
ax2.set_xlabel('$k$')
ax2.set_ylabel(r'$|\psi(k)|$')
V_x_line.set_data(S.x, S.V_x)
######################################################################
# Animate plot
def init():
psi_x_line.set_data([], [])
V_x_line.set_data([], [])
center_line.set_data([], [])
psi_k_line.set_data([], [])
title.set_text("")
return (psi_x_line, V_x_line, center_line, psi_k_line, title)
def animate(i):
S.time_step(dt, N_steps)
psi_x_line.set_data(S.x, 4 * abs(S.psi_x))
V_x_line.set_data(S.x, S.V_x)
center_line.set_data(2 * [x0 + S.t * p0 / m], [0, 1])
psi_k_line.set_data(S.k, abs(S.psi_k))
title.set_text("t = %.2f" % S.t)
return (psi_x_line, V_x_line, center_line, psi_k_line, title)
# call the animator. blit=True means only re-draw the parts that have changed.
anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=frames, interval=30, blit=True)
# uncomment the following line to save the video in mp4 format. This
# requires either mencoder or ffmpeg to be installed on your system
#anim.save('schrodinger_barrier.mp4', fps=15, extra_args=['-vcodec', 'libx264'])
pl.show()
For your ease I mention the lines of this code which I do suspect for the error are line number 238,247,255,286,287,296,297
Thanks in advance
The problem is resolved when blit=False, though it may slow down your animation.
Just quoting from a previous answer:
"Possible solutions are:
Put the title inside the axes.
Don't use blitting"
See: How to update plot title with matplotlib using animation?
You also need ffmpeg installed. There are other answers on stackoverflow that help you through that installation. But for this script, here are my recommended new lines you need to add, assuming you're using Windows:
pl.rcParams['animation.ffmpeg_path'] = r"PUT_YOUR_FULL_PATH_TO_FFMPEG_HERE\ffmpeg.exe"
Writer = animation.writers['ffmpeg']
Then adjust the anim.save() line to:
anim.save('schrodinger_barrier.mp4', writer=Writer(fps=15, codec='libx264'))
I solve the motion in gravitational field around the sun with scipy and mathplotlib and have a problem. My solution is not correct. It is not like in example. Formulas that I used.
from scipy.integrate import odeint
import scipy.constants as constants
import numpy as np
import matplotlib.pyplot as plt
M = 1.989 * (10 ** 30)
G = constants.G
alpha = 30
alpha0 = (alpha / 180) * np.pi
v00 = 0.7
v0 = v00 * 1000
def dqdt(q, t):
x = q[0]
y = q[2]
ax = - G * M * (x / ((x ** 2 + y ** 2) ** 1.5))
ay = - G * M * (y / ((x ** 2 + y ** 2) ** 1.5))
return [q[1], ax, q[3], ay]
vx0 = v0 * np.cos(alpha0)
vy0 = v0 * np.sin(alpha0)
x0 = -150 * (10 ** 11)
y0 = 0 * (10 ** 11)
q0 = [x0, vx0, y0, vy0]
N = 1000000
t = np.linspace(0.0, 100000000000.0, N)
pos = odeint(dqdt, q0, t)
x1 = pos[:, 0]
y1 = pos[:, 2]
plt.plot(x1, y1, 0, 0, 'ro')
plt.ylabel('y')
plt.xlabel('x')
plt.grid(True)
plt.show()
How can I fix this?
Maybe you can tell me solution with another method for example with Euler's formula or with using other library.
I will be very greatful if you help me.
Below is my code, I'm supposed to use the electric field equation and the given variables to create a density plot and surface plot of the equation. I'm getting "invalid dimensions for image data" probably because the function E takes multiple variables and is trying to display them all as multiple dimensions. I know the issue is that I have to turn E into an array so that the density plot can be displayed, but I cannot figure out how to do so. Please help.
import numpy as np
from numpy import array,empty,linspace,exp,cos,sqrt,pi
import matplotlib.pyplot as plt
lam = 500 #Nanometers
x = linspace(-10*lam,10*lam,10)
z = linspace(-20*lam,20*lam,10)
w0 = lam
E0 = 5
def E(E0,w0,x,z,lam):
E = np.zeros((len(x),len(z)))
for i in z:
for j in x:
E = ((E0 * w0) / w(z,w0,zR(w0,lam)))
E = E * exp((-r(x)**2) / (w(z,w0,zR(w0,lam)))**2)
E = E * cos((2 * pi / lam) * (z + (r(x)**2 / (2 * Rz(z,zR,lam)))))
return E
def r(x):
r = sqrt(x**2)
return r
def w(z,w0,lam):
w = w0 * sqrt(1 + (z / zR(w0,lam))**2)
return w
def Rz(z,w0,lam):
Rz = z * (1 + (zR(w0,lam) / z)**2)
return Rz
def zR(w0,lam):
zR = pi * lam
return zR
p = E(E0,w0,x,z,lam)
plt.imshow(p)
It took me way too much time and thinking but I finally figured it out after searching for similar examples of codes for similar problems. The correct code looks like:
import numpy as np
from numpy import array,empty,linspace,exp,cos,sqrt,pi
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
lam = 500*10**-9 #Nanometers
x1 = linspace(-10*lam,10*lam,100)
z1 = linspace(-20*lam,20*lam,100)
[x,y] = np.meshgrid(x1,z1)
w0 = lam
E0 = 5
r = sqrt(x**2)
zR = pi * lam
w = w0 * sqrt(1 + (y / zR)**2)
Rz = y * (1 + (zR / y)**2)
E = (E0 * w0) / w
E = E * exp((-r**2 / w**2))
E = E * cos((2 * pi / lam) * (y + (r**2 / (2 * Rz))))
def field(x,y):
lam = 500*10**-9
k = (5 * lam) / lam * sqrt(1 + (y / (pi*lam))**2)
k *= exp(((-sqrt(x**2)**2 / (lam * sqrt(1 + (y / pi * lam)**2))**2)))
k *= cos((2 / lam) * (y + ((sqrt(x**2)**2 / (2 * y * (1 + (pi * lam / y)**2))))))
return k
#Density Plot
f = field(x,y)
plt.imshow(f)
plt.show()
#Surface Plot
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(x,y,E,rstride=1,cstride=1)
plt.show
I am writing a code to solve coupled harmonic oscillator equations using odeint from scipy. I want to add a random number to one of the equations at every time step of the ODESolver. To do this, I have written two time dependent constants, and used them. However, this gives me the following error.
ODEintWarning: Excess work done on this call (perhaps wrong Dfun type). Run
with full_output = 1 to get quantitative information.
warnings.warn(warning_msg, ODEintWarning)
My code is given below.
import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import odeint
import scipy.stats as stats
from scipy.stats import beta
m1 = 1.1
m2 = 1.0
k1 = 1000.0
k2 = 1000.0
k12 = 100
g = 0.0
global Steps
Steps = 0
x10 = 1
x20 = 0
alpha = 1
a = 2
b = 3
v10 = 0
v20 = 0
#A = np.random.beta(a,b, 10) * alpha
#B = np.random.beta(a,b, 10) * alpha
def c(t):
return np.random.beta(a,b) * alpha
def d(t):
return np.random.beta(a,b) * alpha
def f(x, t, c, d):
y = []
y.append(x[1] - c(t) * x[0])
#print(c(t))
y.append(-(k1 + k12) / m1 * x[0] + k12 / m1 * x[2] - 2 * g * x[1] - c(t) * x[1])
y.append(x[3] - d(t) * x[2])
y.append(-(k2 + k12) / m2 * x[2] + k12 / m2 * x[0] - 2 * g * x[3] - d(t) * x[3])
return y
b0 = [x10, v10, x20, v20]
b0 = np.array(b0)
args = (c, d)
t = np.linspace(0, 1, 1000 )
t = np.array(t)
X1, infodict = odeint(f, b0, t, args, full_output = 1)
X1 = X1.T
Q1 = X1[0]
Q2 = X1[2]
plt.plot(t, Q1, 'g-')
plt.plot(t, Q2, 'b-')
plt.show()
a = m1*m2
b = -(m1*(k2 + k12) + m2*(k1 + k12))
c = k1*k2 + k12*(k1 + k2)
wp = np.sqrt((-b + np.sqrt(b**2 - 4*a*c))/(2*a))
wm = np.sqrt((-b - np.sqrt(b**2 - 4*a*c))/(2*a))
print(wp)
print(wm)
f = open('simdata.csv', mode='w')
for i in range(len(t)):
p = str(t[i]) + ',' + str(Q1[i]) + ',' + str(Q2[i]) + '\n'
f.write(p)
f.close()
I am trying to use the Python interpolation function to get the value y for a given x but I am getting the error "raise ValueError("x and y arrays must be equal in length along along interpolation axis" even though my arrays have both equal size and shape (according to what I get when I use .shape in my code). I am quite new to programming so I don't know how to check what else could be different in my arrays. Here is my code:
s = []
def slowroll(y, t):
phi, dphi, a = y
h = np.sqrt(1/3. * (1/2. * dphi**2 + 1/2.*phi**2))
da = h*a
ddphi = -3.*h*dphi - phi
return [dphi,ddphi,da]
phi_ini = 18.
dphi_ini = -0.1
init_y = [phi_ini,dphi_ini,1.]
h_ini =np.sqrt(1/3. * (1/2. * dphi_ini**2. + 1/2.*phi_ini**2.))
t=np.linspace(0.,20.,100.)
from scipy.integrate import odeint
sol = odeint(slowroll, init_y, t)
phi = sol[:,0]
dphi = sol[:,1]
a=sol[:,2]
n=np.log(a)
h = np.sqrt(1/3. * (1/2. * dphi**2 + 1/2.*phi**2))
s.extend(a*h)
x = np.asarray(s)
y = np.asarray(t)
F = interp1d(y, x, kind='cubic')
print F(7.34858263)
After adding in the required imports, I've been unable to duplicate your error with version 2.7.12. What python version are you running?
import numpy as np
from scipy.interpolate import interp1d
s = []
def slowroll(y, t):
phi, dphi, a = y
h = np.sqrt(1/3. * (1/2. * dphi**2 + 1/2.*phi**2))
da = h*a
ddphi = -3.*h*dphi - phi
return [dphi,ddphi,da]
phi_ini = 18.
dphi_ini = -0.1
init_y = [phi_ini,dphi_ini,1.]
h_ini =np.sqrt(1/3. * (1/2. * dphi_ini**2. + 1/2.*phi_ini**2.))
t=np.linspace(0.,20.,100.)
from scipy.integrate import odeint
sol = odeint(slowroll, init_y, t)
phi = sol[:,0]
dphi = sol[:,1]
a=sol[:,2]
n=np.log(a)
h = np.sqrt(1/3. * (1/2. * dphi**2 + 1/2.*phi**2))
s.extend(a*h)
x = np.asarray(s)
y = np.asarray(t)
F = interp1d(y, x, kind='cubic')
print F(7.34858263)
Output:
2.11688518961e+20