Source code for openmdao.test_suite.components.polynomial_fit

Component to demonstrate using an ImplicitComponent to perform a polynomial curve fit.
import openmdao.api as om
import numpy as np

[docs]class PolynomialFit(om.ImplicitComponent):
[docs] def initialize(self): self.options.declare('N_cp', types=int) self.options.declare('N_predict', types=int)
[docs] def setup(self): # data to fit, which can also be thought of as the "control points" # of the fit function self.add_input('x_cp', shape=self.options['N_cp']) self.add_input('y_cp', shape=self.options['N_cp']) # location of the points you want to evaluate the final fit function at self.add_input('x', shape=self.options['N_predict']) # computed value of the fitted polynomial at the x points self.add_output('y', shape=self.options['N_predict']) # these are the coefficients of the polynomial function you are fitting self.add_output('A', np.zeros(6)) # assuming a 5th order polynomial # analytic derivatives are left as an exercise # using CS here will give accurate partials, but will miss the sparsity pattern self.declare_partials('*', '*', method='cs')
[docs] def apply_nonlinear(self, inputs, outputs, residuals): a0, a1, a2, a3, a4, a5 = outputs['A'] X_cp = inputs['x_cp'] Y_cp = inputs['y_cp'] Y_computed = a0 + a1*X_cp + a2*X_cp**2 + a3*X_cp**3 + a4*X_cp**4 + a5*X_cp**5 # error = np.sum((Y_computed-Y_cp)**2) # note that derivatives are showing up in the apply_nonlinear method because # this is the formulation we use to form the residual. # We are minimizing the sum of the square of the error: np.sum((Y_computed-Y_cp)**2) w.r.t A # hence we differentiate the objective w.r.t A and set the resulting system of equations to 0 d_error__d_Y_computed = 2*(Y_computed-Y_cp) d_Y_computed__d_a0 = np.ones(self.options['N_cp']) d_Y_computed__d_a1 = X_cp d_Y_computed__d_a2 = X_cp**2 d_Y_computed__d_a3 = X_cp**3 d_Y_computed__d_a4 = X_cp**4 d_Y_computed__d_a5 = X_cp**5 residuals['A'][0] = np.sum(d_error__d_Y_computed * d_Y_computed__d_a0) residuals['A'][1] = np.sum(d_error__d_Y_computed * d_Y_computed__d_a1) residuals['A'][2] = np.sum(d_error__d_Y_computed * d_Y_computed__d_a2) residuals['A'][3] = np.sum(d_error__d_Y_computed * d_Y_computed__d_a3) residuals['A'][4] = np.sum(d_error__d_Y_computed * d_Y_computed__d_a4) residuals['A'][5] = np.sum(d_error__d_Y_computed * d_Y_computed__d_a5) X = inputs['x'] Y = a0 + a1*X + a2*X**2 + a3*X**3 + a4*X**4 + a5*X**5 residuals['y'] = Y - outputs['y']