12.1.10.2.2. Fit data

This demo shows how data fitting can be performed using the itom.dataObject and itom.algorithms.

import numpy as np
from itom import dataObject
from itom import algorithms

Polynomial of order 2 in x- and y-direction

def polyFuncOrder2x2(x: float, y: float) -> float:
    return 2.5 * x**2 + -1.7 * y**2 + 1.3 * x * y + 0.7 * x - 0.3 * y + 3.2

Vectorize this function to be evaluated over an array of x and y-coordinates

f = np.vectorize(polyFuncOrder2x2)

[X, Y] = np.meshgrid(np.arange(-10, 10.5, 0.5), np.arange(-10, 10.5, 0.5))
Z = f(X, Y)
total = np.prod(Z.shape)

First create a 2d polynomial fit with order x = 2 and order y = 2. Z_ must be a regular grid where the x- and y- values are defined by its axisScales and axisOffsets attributes.

Z_ = dataObject(Z)
Z_.axisScales = (0.5, 0.5)
Z_.axisOffsets = (20, 20)

coeffs = algorithms.polyfitWeighted2D(Z_, 2, 2)
print("coefficients: ", coeffs)

# Reconstruct the fitted sphere using the determined coefficients.
# First, create a ``dataObject`` with the desired size, scaling and offset for the
# the grid of x- and y- values. The z-values are then calculated.
Z_reconstruction = Z_.copy()
Z_reconstruction[:, :] = float("nan")

algorithms.polyval2D(Z_reconstruction, coeffs, 2, 2)

coefficients:  (3.200000000000888, -0.3000000000000551, -1.7000000000000066, 0.6999999999999961, 1.2999999999999994, 2.5)

Randomly select a number of samples unique values in the range [0,total).

samples = 100
randomUniqueValues = np.random.choice(total, samples)
X2 = dataObject([1, samples], "float64")
Y2 = dataObject([1, samples], "float64")
Z2 = dataObject([1, samples], "float64")
c = Z.shape[1]

for i in range(samples):
    idx = randomUniqueValues[i]
    X2[0, i] = X[int(idx / c), idx % c]
    Y2[0, i] = Y[int(idx / c), idx % c]
    Z2[0, i] = Z[int(idx / c), idx % c]

Determine the polyonimal coefficients only using the random samples.

coeffs2 = algorithms.polyfitWeighted2DSinglePoints(X2, Y2, Z2, 2, 2)
# coeffs and coeffs2 must be the same!
print("fitted coefficient: ", coeffs2)

fitted coefficient:  (3.2000000000000166, -0.30000000000000165, -1.699999999999999, 0.6999999999999973, 1.3000000000000007, 2.5000000000000004)

And reconstruct the entire surface for X and Y values.

reconstruction = dataObject()
algorithms.polyval2DSinglePoints(
    dataObject(X),
    dataObject(Y),
    reconstruction,
    coeffs2,
    2,
    2,
)

sample_reconstruction = dataObject()
algorithms.polyval2DSinglePoints(X2, Y2, sample_reconstruction, coeffs2, 2, 2)