Here is the attachment of the python code:
from scipy.stats import norm
import matplotlib.pyplot as plt
import numpy as np
import math
def V(S0):
# nx = norm.cdf(x)
K = 1.5
T = 1
sigma = 0.1
rd = 0.03
ry = 0.02
e = math.e
d1 = (math.log((S0 * e ** ((rd - ry) * T)) / K) + (sigma ** 2 * T) / 2) / (sigma * math.sqrt(T))
d2 = (math.log((S0 * e ** ((rd - ry) * T)) / K) - (sigma ** 2 * T) / 2) / (sigma * math.sqrt(T))
nd1 = norm.cdf(d1)
nd2 = norm.cdf(d2)
V = e ** (-rd * T) * (S0 * e ** ((rd - ry) * T) * nd1 - K * nd2)
V2 = np.vectorize(V)
S0 = np.arange(1, 1000, 1)
plt.title('V as a function of S0')
plt.xlabel('S0')
plt.ylabel('V')
plt.plot(S0, V2(S0))
plt.show()
And the code with such a result:
How can I fix it?
There are two issues
math.log only accepts size-1 arrays
Removed the math module and switched to numpy methods
Nothing is returned by the function V
Added return V
from scipy.stats import norm
import matplotlib.pyplot as plt
import numpy as np
def V(S0):
# nx = norm.cdf(x)
K = 1.5
T = 1
sigma = 0.1
rd = 0.03
ry = 0.02
e = np.e
d1 = (np.log((S0 * e ** ((rd - ry) * T)) / K) + (sigma ** 2 * T) / 2) / (sigma * np.sqrt(T))
d2 = (np.log((S0 * e ** ((rd - ry) * T)) / K) - (sigma ** 2 * T) / 2) / (sigma * np.sqrt(T))
nd1 = norm.cdf(d1)
nd2 = norm.cdf(d2)
V = e ** (-rd * T) * (S0 * e ** ((rd - ry) * T) * nd1 - K * nd2)
return V # return V added
V2 = np.vectorize(V)
S0 = np.arange(1, 1000, 1)
plt.title('V as a function of S0')
plt.xlabel('S0')
plt.ylabel('V')
plt.plot(S0, V2(S0))
plt.show()
Related
I've got a code that runs as follows:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import pyXSteam.XSteam
from pyXSteam.XSteam import XSteam
steamTable = XSteam(XSteam.UNIT_SYSTEM_MKS) # m/kg/sec/°C/bar/W
A = 3000 #define the heat exchange area
d_in = 20 #define the inner diameter of HE tubes
CF = 0.85 #define the cleanliness factor of SC.
w = 2.26 #define the water velocity within the tubes
Dk=np.arange(27.418,301.598,27.418) #define the range of steam loads
dk = (Dk * 1000 / (A * 3.600)) #calculate the relative steam load
Tcwin=20
def Cp():
return steamTable.CpL_t(Tcwin)
Gw = 13000 #define the flow of CW, t/hr
e = 2.718281828
f_velocity = w * 1.1 / (20 ** 0.25)
f_w=0.12 * CF * (1 + 0.15 * Tcwin)
Ф_в = f_velocity ** f_w
K = CF * 4070 * ((1.1 * w / (d_in ** 0.25)) ** (0.12 * CF * (1 + 0.15 * Tcwin))) * (1 - (((35 - Tcwin) ** 2) * (0.52 - 0.0072 * dk) * (CF ** 0.5)) / 1000)
n = (K * A) / (Cp() * Gw * 1000)
Tcwout_theor = Tcwin + (Dk * 2225 / (Cp() * Gw))
Subcooling_theor = (Tcwout_theor - Tcwin) / (e ** (K * A / (Cp() * (Gw * 1000 / 3600) * 1000)))
TR_theor = (Tcwout_theor - Tcwin)
Tsat_theor = (Tcwout_theor + Subcooling_theor)
def Ts():
return np.vectorize(Tsat_theor)
def Psat_theor():
return steamTable.psat_t(Tsat_theor)
print(Dk)
print(Tsat_theor)
print(Psat_theor)
While it does calculate Tsat_theor, it fails to print Psat_theor.
The output goes like this:
<function Psat_theor at 0x000002A7C29F0D30>
How can I obtain the actual value of Psat_theor?
You need to call mentioned function, change
print(Psat_theor)
to
print(Psat_theor())
I am trying to solve the double integral of this complicated function. The function contains 3 symbolic variables which are defined with sympy.symbols. My goal is to integrate the function with respect to only two of the variables. sym.integrate run for 2 hours with no results to show. I tried numerical integration with scipy.integrate.dblquad. But I am having troubles which I suspect is due to the third symbolic variable. Is there a way to do this.
Problem summarized.
sym.symbols('x y z')
My_function(x,y,z)
Integrate My_function with respect to x and y (Both from 0 to inf i.e. definite integral).
Thank you in advance
h, t, w, r, q = sym.symbols('h t w r q') # Define symbols
wn = 2.0
alpha = 1.76
beta = 1.59
a0 = 0.7
a1 = 0.282
a2 = 0.167
b0 = 0.07
b1 = 0.3449
b2 = -0.2073
psi = 0.05
F_H = 1.0 - sym.exp(-(h / alpha) ** beta)
mu_h = a0 + a1 * h ** a2
sig_h = b0 + b1 * sym.exp(b2 * h)
F_TIH = (1 / 2) * (1 + sym.erf((sym.log(t) - mu_h) / (sig_h * sym.sqrt(2))))
f_h = sym.diff(F_H, h)
f_tzIhs = sym.diff(F_TIH, t)
f_S = f_h * f_tzIhs
H = (1.0 - (w / wn) ** 2.0 + 1.0j * 2.0 * psi * w / wn) ** (-1.0)
S_eta_h_t = h ** 2.0 * t / (8.0 * pi ** 2.0) * (w * t / (2.0 * pi)) ** (-5.0) * sym.exp(-1.0 / pi * (w * t / (2.0 * pi)) ** (-4.0))
S_RIS_hu_tu = abs(H) ** 2.0 * S_eta_h_t
m0_s = sym.integrate((w ** 0 * S_RIS_hu_tu), (w, 0, np.inf))
m0_s.doit()
m2_s = sym.integrate((w ** 2 * S_RIS_hu_tu), (w, 0, np.inf))
m2_s.doit()
v_rIs = 1 / (2 * pi) * sym.sqrt(m2_s / m0_s) * sym.exp(-r ** 2 / (2 * m0_s))
fun = v_rIs * f_S
# The integral I am trying to solve is a function of h,t and r.
integ_ht = sym.integrate(fun,(h,0,np.inf),(t,0,np.inf))
I am trying to build a code for chemical reactor design which is able to solve for the pressure drop, conversion, and temperature of a reactor. All these parameters have differential equations, so i tried to define them inside a function to be able to integrate them using ODEINT. However it seems that the function i've built has an error which i can't figure out which held me back from integration it.
the error that i'm encountering:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-32-63c706e84be5> in <module>
1 X0=[0.05,1200,2]
----> 2 y=func(X0,0)
<ipython-input-27-6cfd4fef5ee2> in func(x, W)
8 kp=np.exp(((42311)/(R*T))-11.24)
9 deltah=-42471-1.563*(T-1260)+0.00136*(T**2 -1260**2)- 2,459*10e-7*(T**3-1260**3)
---> 10 ra=k*np.sqrt((1-X)/X)*((0.2-0.11*X)/(1-0.055*X)*(P/P0)-(x/(kp*(1-x)))**2)
11 summ = 57.23+0.014*T-1.94*10e-6*T**2
12 dcp=-1.5625+2.72*10e-3*T-7.38*10e-7*T**2
TypeError: unsupported operand type(s) for -: 'int' and 'list'
and here is the full code:
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
fi = 0.45
gas_density = 0.054 #density
Pres0 = 2 #pressure
visc = 0.09
U = 10
Ac = 0.0422
T0 = 1400 #and 1200 also
gc = 4.17 * 10**8
bed_density = 33.8
Ta = 1264.6 #wall temp
fa0 = 0.188
def func(x,W):
X = x[0]
T = x[1]
P = x[2]
P0 = 2
R = 0.7302413
k = np.exp((-176008 / T) - (110.1 * np.log(T) + 912.8))
kp = np.exp(((42311) / (R * T)) - 11.24)
deltah = -42471 - 1.563 * (T - 1260) + 0.00136 * (T**2 - 1260**2) - 2,459 * 10e-7 * (T**3 - 1260**3)
ra = k * np.sqrt((1 - X) / X) * ((0.2 - 0.11 * X) / (1 - 0.055 * X) * (P / P0) - (x / (kp * (1 - x)))**2)
summ = 57.23 + 0.014 * T - 1.94 * 10e-6 * T**2
dcp = -1.5625 + 2.72 * 10e-3 * T - 7.38 * 10e-7 * T**2
dxdw = 5.31 * k * np.sqrt((1 - X) / X) * ((0.2 - 0.11 * X) / (1 - 0.055 * X) * (P / P0) - (x / (kp * (1 - x)))**2)
dpdw = (((-1.12 * 10**-8) * (1 - 0.55 * X) * T) / P) * (5500 * visc + 2288)
dtdw = (5.11 * (Ta - T) + (-ra) * deltah) / (fa0 * (summ + x * dcp))
return [dxdw, dpdw, dtdw]
X0 = [0.05, 1200, 2]
y = func(X0, 0)
thanks in advance
Inside line
ra=k*np.sqrt((1-X)/X)*((0.2-0.11*X)/(1-0.055*X)*(P/P0)-(x/(kp*(1-x)))**2)
you probably want to use ...X/(kp*(1-X))... instead of ...x/(kp*(1-x))... (i.e. use upper X), lower x is list type.
If you want to use some list variable l as multiple values somewhere then convert it to numpy array la = np.array(l) and use la in numpy vectorized expression.
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 have no idea about how to plot fourier series graph from equation like this
I try to use matplotlib to plot this but there are so many values. Here are code that I used. Not sure about algorithm.
import numpy as np
import matplotlib.pyplot as plt
x_ = np.linspace(0, 30, 10000)
a0 = 3/5
##an = 1/n * np.pi * (np.sin(0.4 * n * np.pi) + np.sin(0.8 * n * np.pi))
##bn = 1/n * np.pi * (2 - np.cos(0.4 * n * np.pi) - np.cos(0.8 * n * np.pi))
f0 = 5
def a(n):
return 1/n * np.pi * (np.sin(0.4 * n * np.pi) + np.sin(0.8 * n * np.pi))
def b(n):
return 1/n * np.pi * (2 - np.cos(0.4 * n * np.pi) - np.cos(0.8 * n * np.pi))
def s(t, n):
temp = 0
for i in range (1, n + 1):
temp = temp + (a(i) * np.cos(2 * np.pi * i * f0 * t) \
+ b(i) * np.sin(2 * np.pi * n * f0 * t))
temp += a0
return temp
st = []
for i in range (1, 6):
st.append(s(1, 6))
plt.title("Test")
plt.plot(x_, st, color="red")
plt.show()
Tried this then got this error
ValueError: x and y must have same first dimension, but have shapes (10000,) and (5,)
thanks for any help