kadereub/numba_polyfit.py

## numba_polyfit.py
# Load relevant libraries
import numpy as np
import numba as nb
import matplotlib.pyplot as plt

# Goal is to implement a numba compatible polyfit (note does not include error handling)

# Define Functions Using Numba
# Idea here is to solve ax = b, using least squares, where a represents our coefficients e.g. x**2, x, constants
@nb.njit
def _coeff_mat(x, deg):
    mat_ = np.zeros(shape=(x.shape[0],deg + 1))
    const = np.ones_like(x)
    mat_[:,0] = const
    mat_[:, 1] = x
    if deg > 1:
        for n in range(2, deg + 1):
            mat_[:, n] = x**n
    return mat_

@nb.jit
def _fit_x(a, b):
    # linalg solves ax = b
    det_ = np.linalg.lstsq(a, b)[0]
    return det_

 @nb.jit
def fit_poly(x, y, deg):
    a = _coeff_mat(x, deg)
    p = _fit_x(a, y)
    # Reverse order so p[0] is coefficient of highest order
    return p[::-1]

@nb.jit
def eval_polynomial(P, x):
    '''
    Compute polynomial P(x) where P is a vector of coefficients, highest
    order coefficient at P[0].  Uses Horner's Method.
    '''
    result = 0
    for coeff in P:
        result = x * result + coeff
    return result

# Create Dummy Data and use existing numpy polyfit as test
x = np.linspace(0, 2, 20)
y = np.cos(x) + 0.3*np.random.rand(20)
p = np.poly1d(np.polyfit(x, y, 3))

t = np.linspace(0, 2, 200)
plt.plot(x, y, 'o', t, p(t), '-')

# Now plot using the Numba (amazing) functions
p_coeffs = fit_poly(x, y, deg=3)
plt.plot(x, y, 'o', t, eval_polynomial(p_coeffs, t), '-')

# Great Success...

# References
# 1. Numpy least squares docs -> https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html#numpy.linalg.lstsq
# 2. Numba linear alegbra supported funcs -> https://numba.pydata.org/numba-doc/dev/reference/numpysupported.html#linear-algebra
# 3. SO Post -> https://stackoverflow.com/questions/56181712/fitting-a-quadratic-function-in-python-without-numpy-polyfit
	# Load relevant libraries
	import numpy as np
	import numba as nb
	import matplotlib.pyplot as plt

	# Goal is to implement a numba compatible polyfit (note does not include error handling)

	# Define Functions Using Numba
	# Idea here is to solve ax = b, using least squares, where a represents our coefficients e.g. x**2, x, constants
	@nb.njit
	def _coeff_mat(x, deg):
	mat_ = np.zeros(shape=(x.shape[0],deg + 1))
	const = np.ones_like(x)
	mat_[:,0] = const
	mat_[:, 1] = x
	if deg > 1:
	for n in range(2, deg + 1):
	mat_[:, n] = x**n
	return mat_

	@nb.jit
	def _fit_x(a, b):
	# linalg solves ax = b
	det_ = np.linalg.lstsq(a, b)[0]
	return det_

	@nb.jit
	def fit_poly(x, y, deg):
	a = _coeff_mat(x, deg)
	p = _fit_x(a, y)
	# Reverse order so p[0] is coefficient of highest order
	return p[::-1]

	@nb.jit
	def eval_polynomial(P, x):
	'''
	Compute polynomial P(x) where P is a vector of coefficients, highest
	order coefficient at P[0]. Uses Horner's Method.
	'''
	result = 0
	for coeff in P:
	result = x * result + coeff
	return result

	# Create Dummy Data and use existing numpy polyfit as test
	x = np.linspace(0, 2, 20)
	y = np.cos(x) + 0.3*np.random.rand(20)
	p = np.poly1d(np.polyfit(x, y, 3))

	t = np.linspace(0, 2, 200)
	plt.plot(x, y, 'o', t, p(t), '-')

	# Now plot using the Numba (amazing) functions
	p_coeffs = fit_poly(x, y, deg=3)
	plt.plot(x, y, 'o', t, eval_polynomial(p_coeffs, t), '-')

	# Great Success...

	# References
	# 1. Numpy least squares docs -> https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html#numpy.linalg.lstsq
	# 2. Numba linear alegbra supported funcs -> https://numba.pydata.org/numba-doc/dev/reference/numpysupported.html#linear-algebra
	# 3. SO Post -> https://stackoverflow.com/questions/56181712/fitting-a-quadratic-function-in-python-without-numpy-polyfit