def polyFit(xData, yData, m):
"""
Returns coefficients of the polynomial
p(x) = c[0] + c[1]x + c[2]x^2 +...+ c[m]x^m
that fits the specified data in the least
squares sense.
USAGE:
c = polyFit(xData,yData,m)
INPUT:
xData,yData : numpy arrays
data to be fitted
m : int
degree of p(x)
OUTPUT:
c : numpy array
coefficients of p(x)
"""
import numpy as np
from ps12 import gaussElimin
def SUM1(j, k, x):
s = 0
for i in range(len(x)):
s = x[i] ** (j + k) + s
return s
def SUM2(k, x, y):
s = 0
for i in range(len(y)):
s = x[i] ** k * y[i] + s
return s
a = np.zeros([m + 1, m + 1])
for j in range(m + 1):
for k in range(m + 1):
a[k, j] = SUM1(j, k, xData)
b = np.zeros([m + 1, 1])
for k in range(m + 1):
b[k, 0] = SUM2(k, xData, yData)
x = gaussElimin(a, b)
return x
def main():
a = np.array([[2, 1, -1], [-3, -1, 2], [-2, 1, 2]])
b = np.array([[8], [-11], [-3]])
x = ps12.gaussElimin(a, b)
x = ps12.LUdecomp(a)
y = ps12.LUsolve(x, b)