Radical Edward - 3 months ago 16

Python Question

I'm trying to solve for the intersection of the two equations:

`y=Rx^1.75`

`y=ax^2+bx+c`

`R,a,b,c`

`fsolve()`

Here is an example dataframe with coefficients

`R a b c`

0 0.5 -0.01 -0.50 32.42

1 0.6 0.00 0.07 14.12

2 0.7 -0.01 -0.50 32.42

And here is the working example code that I'm using to test methods:

`import numpy as np`

import pandas as pd

from scipy.optimize import *

# The fSolve function

def myFunction(zGuess,*Params):

# Get the coefficients

R,a,b,c = Params

# Get the initial guess

x,y = zGuess

F = np.empty((2))

F[0] = R*x**1.75-y

F[1] = a*x**2+b*x+c-y

return F

# Example Dataframe that is 10K rows of different coefficients

df = pd.DataFrame({"R":[0.500, 0.600,0.700],

"a":[-0.01, 0.000,-0.01],

"b":[-0.50, 0.070,-0.50],

"c":[32.42, 14.12,32.42]})

# Initial guess

zGuess = np.array([50,50])

# Make a place to store the answers

df["x"] = None

df["y"] = None

# Loop through the rows?

for index, coeffs in df.iterrows():

# Get the coefficients

Params = (coeffs["R"],coeffs["a"],coeffs["b"],coeffs["c"])

# fSolve

z = fsolve(myFunction,zGuess,args=Params)

# Set the answers

df.loc[index,"x"] = z[0]

df.loc[index,"y"] = z[1]

print df

============================================

I got two answers below that both gave mathematically correct answers. So at this point, it's all who's calculation is faster! The test dataframe will be 3K rows.

`# Solution 1`

import numpy as np

import pandas as pd

Count = 1000

df = pd.DataFrame({"R":[0.500, 0.600,0.700]*Count,

"a":[-0.01, 0.000,-0.01]*Count,

"b":[-0.50, 0.070,-0.50]*Count,

"c":[32.42, 14.12,32.42]*Count})

from datetime import datetime

t_start = datetime.now()

#---------------------------------

InitialGuess = 50.0

Iterations = 20

x = np.full(df["a"].shape, InitialGuess)

for i in range(Iterations):

x = x - (-df["R"]*x**1.75 + df["a"]*x**2 + df["b"]*x + df["c"])/(-1.75*df["R"]*x**0.75 + 2*df["a"]*x + df["b"])

df["x"] = x

df["y"] = df["R"]*x**1.75

df["x Error"] = df["a"]*x**2 + df["b"]*x + df["c"] - df["R"]*x**1.75

#---------------------------------

t_end = datetime.now()

print ('\n\n\nTime spent running this was:')

print(t_end - t_start)

print df

And the time spent was:

`Time spent running this was:`

0:00:00.015000

`# Solution 2`

import numpy as np

import pandas as pd

from scipy.optimize import *

Count = 1000

df = pd.DataFrame({"R":[0.500, 0.600,0.700]*Count,

"a":[-0.01, 0.000,-0.01]*Count,

"b":[-0.50, 0.070,-0.50]*Count,

"c":[32.42, 14.12,32.42]*Count})

from datetime import datetime

t_start = datetime.now()

#---------------------------------

coefs = df.values[:, 0:4]

def mfun(x, *args):

args = np.array(args[0], dtype=np.float64)

return args[:,1] * x**2 + args[:,2] * x + args[:,3] - args[:,0] * x**1.75

nrows = coefs.shape[0]

df["x"] = fsolve(mfun, np.ones(nrows) * 50, args=coefs)

df["y"] = coefs[:, 0] * df["x"]**1.75

#---------------------------------

t_end = datetime.now()

print ('\n\n\nTime spent running this was:')

print(t_end - t_start)

print df

And the time spent was:

`Time spent running this was:`

0:00:35.786000

For this particular case, Newtons method was much faster (I can run 300K rows in

`0:00:01.139000`

Answer

Maybe you can use Newton's method:

```
import numpy as np
data = np.array(
[[0.5, -0.01, -0.50, 32.42],
[0.6, 0.00, 0.07, 14.12],
[0.7, -0.01, -0.50, 32.42]])
R, a, b, c = data.T
x = np.full(a.shape, 10.0)
m = 1.0
for i in range(20):
x = x - m * (-R*x**1.75 + a*x**2 + b*x + c)/(-1.75*R*x**0.75 + 2*a*x + b)
print(a*x**2 + b*x + c - R * x**1.75)
```

output:

```
[ 0.00000000e+00 1.77635684e-15 3.55271368e-15]
```

be careful to choose the iteration count and initial value of x.