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Equations.py
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Equations.py
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"""
Every function below must accept a numpy array inputs of shape (no_samples, no_vars) and return a target array of shape (no_samples, )
It is highly recommended to use vector operations instead of looping through rows as numpy is faster with vectorization
Use the get_column function for this easily
----------------------------------------------
-----------------------------------------------
At the bottom is a dictionary that must be updated in order for the equations to work
"""
import numpy as np
e = np.e
pi = np.pi
sqrt = np.sqrt
exp = np.exp
sin = np.sin
cos = np.cos
tan = np.tan
arcsin = np.arcsin
ln = np.log
def get_column(inputs, col):
try:
return inputs[:, col]
except:
print(f"inputs had shape {inputs.shape} but was asked for column {col}")
def I62a(inputs):
return exp(-get_column(inputs, 0)**2/2)/sqrt(2*pi)
def I62(inputs):
return exp(-(get_column(inputs, 0)/get_column(inputs, 1))**2/2)/(sqrt(2*pi)*get_column(inputs, 1))
def I62b(inputs):
theta = get_column(inputs, 0)
theta1 = get_column(inputs, 1)
sigma = get_column(inputs, 2)
return exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma)
def I814(inputs):
return np.sqrt((get_column(inputs, 1)-get_column(inputs, 0))**2+(get_column(inputs, 3)-get_column(inputs, 2))**2)
def I918(inputs):
G = 6.67259 * 10**(-11)
m1 = get_column(inputs, 0)
m2 = get_column(inputs, 1)
x1 = get_column(inputs, 2)
x2 = get_column(inputs, 3)
y1 = get_column(inputs, 4)
y2 = get_column(inputs, 5)
z1 = get_column(inputs, 6)
z2 = get_column(inputs, 7)
return G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2)
def I107(inputs):
m_0 = get_column(inputs, 0)
v = get_column(inputs, 1)
c = get_column(inputs, 2)
return m_0/sqrt(1-v**2/c**2)
def I1119(inputs):
x1 = get_column(inputs, 0)
x2 = get_column(inputs, 1)
x3 = get_column(inputs, 2)
y1 = get_column(inputs, 3)
y2 = get_column(inputs, 4)
y3 = get_column(inputs, 5)
return x1*y1+x2*y2+x3*y3
def I121(inputs):
return get_column(inputs, 0)*get_column(inputs, 1)
def I122(inputs):
q1 = get_column(inputs, 0)
q2 = get_column(inputs, 1)
r = get_column(inputs, 2)
epsilon = get_column(inputs, 3)
return q1*q2*r/(4*pi*epsilon*r**3)
def I124(inputs):
q1 = get_column(inputs, 0)
r = get_column(inputs, 1)
epsilon = get_column(inputs, 2)
return q1*r/(4*pi*epsilon*r**3)
def I125(inputs):
q2 = get_column(inputs, 0)
Ef = get_column(inputs, 1)
return q2*Ef
def I1211(inputs):
q = get_column(inputs, 0)
Ef = get_column(inputs, 1)
B = get_column(inputs, 2)
v = get_column(inputs, 3)
theta = get_column(inputs, 4)
return q*(Ef+B*v*sin(theta))
def I134(inputs):
m = get_column(inputs, 0)
v = get_column(inputs, 1)
u = get_column(inputs, 2)
w = get_column(inputs, 3)
return 1/2*m*(v**2+u**2+w**2)
def I1312(inputs):
G = 1#6.67259 * 10**(-11)
m1 = get_column(inputs, 0)
m2 = get_column(inputs, 1)
r2 = get_column(inputs, 3)
r1 = get_column(inputs, 2)
return G*m1*m2*(1/r2-1/r1)
def I143(inputs):
m = get_column(inputs, 0)
g = get_column(inputs, 1)
z = get_column(inputs, 2)
return m*g*z
def I144(inputs):
k_spring = get_column(inputs, 0)
x = get_column(inputs, 1)
return 1/2*k_spring*x**2
def I153x(inputs):
x = get_column(inputs, 0)
u = get_column(inputs, 1)
t = get_column(inputs, 2)
c = get_column(inputs, 3)
return (x-u*t)/sqrt(1-u**2/c**2)
def I153t(inputs):
x = get_column(inputs, 0)
u = get_column(inputs, 1)
t = get_column(inputs, 2)
c = get_column(inputs, 3)
return (t-u*x/c**2)/sqrt(1-u**2/c**2)
def I151(inputs):
m_0 = get_column(inputs, 0)
v = get_column(inputs, 1)
c = get_column(inputs, 2)
return m_0*v/sqrt(1-v**2/c**2)
def I166(inputs):
u = get_column(inputs, 0)
v = get_column(inputs, 1)
c = get_column(inputs, 2)
return (u+v)/(1+u*v/c**2)
def I184(inputs):
m1 = get_column(inputs, 0)
m2 = get_column(inputs, 1)
r1 = get_column(inputs, 2)
r2 = get_column(inputs, 3)
return (m1*r1+m2*r2)/(m1+m2)
def I1812(inputs):
r = get_column(inputs, 0)
F = get_column(inputs, 1)
theta = get_column(inputs, 2)
return r*F*sin(theta)
def I1814(inputs):
m = get_column(inputs, 0)
r = get_column(inputs, 1)
v = get_column(inputs, 2)
theta = get_column(inputs, 3)
return m*r*v*sin(theta)
def I246(inputs):
m = get_column(inputs, 0)
omega = get_column(inputs, 1)
omega_0 = get_column(inputs, 2)
x = get_column(inputs, 3)
return 1/2*m*(omega**2+omega_0**2)*1/2*x**2
def I2513(inputs):
q = get_column(inputs, 0)
C = get_column(inputs, 1)
return q/C
def I262(inputs):
# Can only take inputs within a certain range
n = get_column(inputs, 0)
theta2 = get_column(inputs, 1)
return arcsin(n*sin(theta2))
def I276(inputs):
d1 = get_column(inputs, 0)
d2 = get_column(inputs, 1)
n = get_column(inputs, 2)
return 1/(1/d1+n/d2)
def I294(inputs):
omega = get_column(inputs, 0)
c = get_column(inputs, 0)
return omega/c
def I2916(inputs):
x1 = get_column(inputs, 0)
x2 = get_column(inputs, 1)
theta1 = get_column(inputs, 2)
theta2 = get_column(inputs, 3)
return sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2))
def I303(inputs):
Int_0 = get_column(inputs, 0)
n = get_column(inputs, 1)
theta = get_column(inputs, 2)
return Int_0*sin(n*theta/2)**2/sin(theta/2)**2
def I305(inputs):
lambd = get_column(inputs, 0)
n = get_column(inputs, 1)
d = get_column(inputs, 2)
return arcsin(lambd/(n*d))
def I325(inputs):
q = get_column(inputs, 0)
a = get_column(inputs, 1)
epsilon = get_column(inputs, 2)
c = get_column(inputs, 3)
return q**2*a**2/(6*pi*epsilon*c**3)
def I3217(inputs):
epsilon = get_column(inputs, 0)
c = get_column(inputs, 1)
Ef = get_column(inputs, 2)
r = get_column(inputs, 3)
omega = get_column(inputs, 4)
omega_0 = get_column(inputs, 5)
return (1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2)
def I348(inputs):
q = get_column(inputs, 0)
v = get_column(inputs, 1)
B = get_column(inputs, 2)
p = get_column(inputs, 3)
return q*v*B/p
def I341(inputs):
omega_0 = get_column(inputs, 0)
v = get_column(inputs, 1)
c = get_column(inputs, 2)
return omega_0/(1-v/c)
def I3414(inputs):
v = get_column(inputs, 0)
c = get_column(inputs, 1)
omega_0 = get_column(inputs, 2)
return (1+v/c)/sqrt(1-v**2/c**2)*omega_0
def I3427(inputs):
h = get_column(inputs, 0)
omega = get_column(inputs, 1)
return (h/(2*pi))*omega
def I374(inputs):
I1 = get_column(inputs, 0)
l1 = I1
I2 = get_column(inputs, 1)
l2 = I2
delta = get_column(inputs, 2)
return I1+I2+2*sqrt(I1*I2)*cos(delta)
def I3812(inputs):
epsilon = get_column(inputs, 0)
h = get_column(inputs, 1)
m = get_column(inputs, 2)
q = get_column(inputs, 3)
return 4*pi*epsilon*(h/(2*pi))**2/(m*q**2)
def I391(inputs):
pr = get_column(inputs, 0)
V = get_column(inputs, 1)
return 3/2*pr*V
def I3911(inputs):
gamma = get_column(inputs, 0)
pr = get_column(inputs, 1)
V= get_column(inputs, 2)
return 1/(gamma-1)*pr*V
def I3922(inputs):
n = get_column(inputs, 0)
kb = get_column(inputs, 1)
T = get_column(inputs, 2)
V = get_column(inputs, 3)
return n*kb*T/V
def I401(inputs):
n_0 = get_column(inputs, 0)
m = get_column(inputs, 1)
g = get_column(inputs, 2)
x = get_column(inputs, 3)
T = get_column(inputs, 4)
kb = 1.38*(10**-23)
return n_0*exp(-m*g*x/(kb*T))
def I4116(inputs):
h = get_column(inputs, 0)
omega = get_column(inputs, 1)
c = get_column(inputs, 2)
kb = get_column(inputs, 3)
T = get_column(inputs, 4)
return h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1))
def I4316(inputs):
mu_drift = get_column(inputs, 0)
q = get_column(inputs, 1)
Volt = get_column(inputs, 2)
d = get_column(inputs, 3)
return mu_drift*q*Volt/d
def I4331(inputs):
mob= get_column(inputs, 0)
kb = get_column(inputs, 1)
T = get_column(inputs, 2)
return mob*kb*T
def I4343(inputs):
gamma = get_column(inputs, 0)
kb = get_column(inputs, 1)
v = get_column(inputs, 2)
A = get_column(inputs, 3)
return 1/(gamma-1)*kb*v/A
def I444(inputs):
n = get_column(inputs, 0)
kb = get_column(inputs, 1)
T = get_column(inputs, 2)
V2 = get_column(inputs, 3)
V1 = get_column(inputs, 4)
return n*kb*T*ln(V2/V1)
def I4723(inputs):
gamma = get_column(inputs, 0)
pr = get_column(inputs, 1)
rho = get_column(inputs, 2)
return sqrt(gamma*pr/rho)
def I482(inputs):
m = get_column(inputs, 0)
c = get_column(inputs, 1)
v = get_column(inputs, 2)
return m*c**2/sqrt(1-v**2/c**2)
def II3411(inputs):
g = get_column(inputs, 0)
q = get_column(inputs, 1)
b = get_column(inputs, 2)
m = get_column(inputs, 3)
return g*q*b/(2*m)
######################################################################################################################
# Self Defined Equations
######################################################################################################################
def sine(inputs):
x = get_column(inputs, 0)
return sin(x)
equation_dict = {
"sine" : sine,
"I.6.2a" : I62a,
"I.6.2" : I62,
"I.6.2b" : I62b,
"I.8.14" : I814,
"I.9.18" : I918,
"I.10.7" : I107,
"I.11.19": I1119,
"I.12.1" : I121,
"I.12.2" : I122,
"I.12.4" : I124,
"I.12.5" : I125,
"I.12.11": I1211,
"I.13.4" : I134,
"I.13.12":I1312,
"I.14.3" : I143,
"I.14.4" : I144,
"I.15.3x": I153x,
"I.15.3t": I153t,
"I.15.1" : I151,
"I.16.6" : I166,
"I.18.4" : I184,
"I.18.12": I1812,
"I.18.14": I1814,
"I.24.6" : I246,
"I.25.13": I2513,
"I.26.2" : I262,
"I.27.6" : I276,
"I.29.4" : I294,
"I.29.16": I2916,
"I.30.3" : I303,
"I.30.5" : I305,
"I.32.5" : I325,
"I.32.17": I3217,
"I.34.8" : I348,
"I.34.1" : I341,
"I.34.14": I3414,
"I.34.27": I3427,
"I.37.4" : I374,
"I.38.12": I3812,
"I.39.1" : I391,
"I.39.11": I3911,
"I.40.1" : I401,
"I.41.16": I4116,
"I.43.16": I4316,
"I.43.31": I4331,
"I.43.43": I4343,
"I.44.4" : I444,
"I.47.23": I4723,
"I.48.2" : I482,
"II.34.11": II3411
}