parseccoef.py

# Import libraries
from math import sqrt, tan, pi
import numpy as np

# User function pcoef
def pcoef(
        xte,yte,rle,
        x_cre,y_cre,d2ydx2_cre,th_cre,
        surface):
    

    # Docstrings
    """evaluate the PARSEC coefficients"""


    # Initialize coefficients
    coef = np.zeros(6)


    # 1st coefficient depends on surface (pressure or suction)
    if surface.startswith('p'):
        coef[0] = -sqrt(2*rle)
    else:
        coef[0] = sqrt(2*rle)
 
    # Form system of equations
    A = np.array([
                 [xte**1.5, xte**2.5, xte**3.5, xte**4.5, xte**5.5],
                 [x_cre**1.5, x_cre**2.5, x_cre**3.5, x_cre**4.5, 
                  x_cre**5.5],
                 [1.5*sqrt(xte), 2.5*xte**1.5, 3.5*xte**2.5, 
                  4.5*xte**3.5, 5.5*xte**4.5],
                 [1.5*sqrt(x_cre), 2.5*x_cre**1.5, 3.5*x_cre**2.5, 
                  4.5*x_cre**3.5, 5.5*x_cre**4.5],
                 [0.75*(1/sqrt(x_cre)), 3.75*sqrt(x_cre), 8.75*x_cre**1.5, 
                  15.75*x_cre**2.5, 24.75*x_cre**3.5]
                 ]) 

    B = np.array([
                 [yte - coef[0]*sqrt(xte)],
                 [y_cre - coef[0]*sqrt(x_cre)],
                 [tan(th_cre*pi/180) - 0.5*coef[0]*(1/sqrt(xte))],
                 [-0.5*coef[0]*(1/sqrt(x_cre))],
                 [d2ydx2_cre + 0.25*coef[0]*x_cre**(-1.5)]
                 ])
    

    # Solve system of linear equations
    X = np.linalg.solve(A,B) 


    # Gather all coefficients
    coef[1:6] = X[0:5,0]


    # Return coefficients
    return coef