Source code for pylops.basicoperators.Regression

import logging

import numpy as np

from pylops import LinearOperator
from pylops.utils.backend import get_array_module

logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)

[docs]class Regression(LinearOperator): r"""Polynomial regression. Creates an operator that applies polynomial regression to a set of points. Values along the :math:`t`-axis must be provided while initializing the operator. The coefficients of the polynomial regression form the model vector to be provided in forward mode, while the values of the regression curve shall be provided in adjoint mode. Parameters ---------- taxis : :obj:`numpy.ndarray` Elements along the :math:`t`-axis. order : :obj:`int` Order of the regressed polynomial. dtype : :obj:`str`, optional Type of elements in input array. Attributes ---------- shape : :obj:`tuple` Operator shape explicit : :obj:`bool` Operator contains a matrix that can be solved explicitly (``True``) or not (``False``) Raises ------ TypeError If ``taxis`` is not :obj:`numpy.ndarray`. See Also -------- LinearRegression: Linear regression Notes ----- The Regression operator solves the following problem: .. math:: y_i = \sum_{n=0}^\text{order} x_n t_i^n \qquad \forall i=0,1,\ldots,N-1 where :math:`N` represents the number of points in ``taxis``. We can express this problem in a matrix form .. math:: \mathbf{y}= \mathbf{A} \mathbf{x} where .. math:: \mathbf{y}= [y_0, y_1,\ldots,y_{N-1}]^T, \qquad \mathbf{x}= [x_0, x_1,\ldots,x_\text{order}]^T and .. math:: \mathbf{A} = \begin{bmatrix} 1 & t_{0} & t_{0}^2 & \ldots & t_{0}^\text{order} \\ 1 & t_{1} & t_{1}^2 & \ldots & t_{1}^\text{order} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & t_{N-1} & t_{N-1}^2 & \ldots & t_{N-1}^\text{order} \end{bmatrix}_{N\times \text{order}+1} """ def __init__(self, taxis, order, dtype="float64"): ncp = get_array_module(taxis) if not isinstance(taxis, ncp.ndarray): logging.error("t must be numpy.ndarray...") raise TypeError("t must be numpy.ndarray...") else: self.taxis = taxis self.order = order self.shape = (len(self.taxis), self.order + 1) self.dtype = np.dtype(dtype) self.explicit = False def _matvec(self, x): ncp = get_array_module(x) y = ncp.zeros_like(self.taxis) for i in range(self.order + 1): y += x[i] * self.taxis ** i return y def _rmatvec(self, x): ncp = get_array_module(x) return ncp.vstack([ ** i, x) for i in range(self.order + 1)])
[docs] def apply(self, t, x): """Return values along y-axis given certain ``t`` location(s) along t-axis and regression coefficients ``x`` Parameters ---------- taxis : :obj:`numpy.ndarray` Elements along the t-axis. x : :obj:`numpy.ndarray` Regression coefficients dtype : :obj:`str`, optional Returns ---------- y : :obj:`numpy.ndarray` Values along y-axis """ torig = self.taxis.copy() self.taxis = t y = self._matvec(x) self.taxis = torig return y