sgolay2.py

# -*- coding: utf-8 -*-

"""
Two-dimensional Savitzky-Golay filter

"""

import collections
import typing as t

import numpy as np
import numpy.linalg as la

import scipy.ndimage as ndim


Param2 = collections.namedtuple('Param2', ('row', 'column'))
Polynom2 = collections.namedtuple('Polynom2', ('row_pows', 'column_pows', 'num_coeffs'))

_Param2Type = t.Union[Param2, t.Tuple[int, int]]
_ParamType = t.Union[int, _Param2Type]

_DIM = 2


class SGolayKernel2:
    """Computes two-dimensional kernel (weights) for Savitzky-Golay filter
    """

    def __init__(self, window_size: _Param2Type, poly_order: _Param2Type):
        self._window_size = Param2(*window_size)
        self._poly_order = Param2(*poly_order)

        self._kernel = None  # type: np.ndarray
        self.computed = False

    def __call__(self):
        self.compute()

    def compute(self):
        if self.computed:
            return

        polynom = self._make_polynom(self._poly_order)
        basis_matrix = self._make_basis_matrix(self._window_size, polynom)

        self._kernel = self._compute_kernel(self._window_size, basis_matrix)

        self.computed = True

    @property
    def kernel(self) -> np.ndarray:
        """Returns 2D Savitzky-Golay kernel
        """
        self.compute()
        return self._kernel

    @staticmethod
    def _make_polynom(poly_order: Param2) -> Polynom2:
        """
        Creates 2-D polynom model (for example poly33):
            p = a00 + a10x + a01y + a20x^2 + a11xy + a02y^2 + a30x^3 + a21x^2y \
                + a12xy^2 + a03y^3
        """
        row_pows = []
        column_pows = []
        num_coeffs = 0

        for row in range(poly_order.row + 1):
            for column in range(poly_order.column + 1):
                if (row + column) > max(*poly_order):
                    continue

                row_pows.append(row)
                column_pows.append(column)

                num_coeffs += 1

        return Polynom2(row_pows, column_pows, num_coeffs)

    @staticmethod
    def _make_basis_matrix(window_size: Param2, poly: Polynom2) -> np.ndarray:
        """Creates basis polynomial matrix
        """
        basis_rows = window_size.row * window_size.column
        basis_columns = poly.num_coeffs

        basis_matrix = np.zeros((basis_rows, basis_columns))

        radius_row = (window_size.row - 1) // 2
        radius_column = (window_size.column - 1) // 2

        row_pows = np.array(poly.row_pows)
        column_pows = np.array(poly.column_pows)

        k = 0

        for row in range(-radius_row, radius_row + 1):
            for column in range(-radius_column, radius_column + 1):
                basis_matrix[k, :] = column ** column_pows * row ** row_pows
                k += 1

        return basis_matrix

    @staticmethod
    def _compute_kernel(window_size: Param2,
                        basis_matrix: np.ndarray) -> np.ndarray:
        """Computes filter 2D kernel via solving least squares problem
        """
        q, _ = la.qr(basis_matrix)

        iq = (window_size.row * window_size.column - 1) // 2
        kernel = q @ np.array(q[iq, :], ndmin=2).T
        kernel = np.fliplr(kernel.reshape(*window_size, order='F'))

        return kernel


class SGolayFilter2:
    """Two-dimensional Savitzky-Golay filter
    """

    def __init__(self, window_size: _ParamType, poly_order: _ParamType):
        self._window_size = self._canonize_param(
            'window_size', window_size, self._validate_window_size)
        self._poly_order = self._canonize_param(
            'poly_order', poly_order, self._validate_poly_order)

        self._kernel = SGolayKernel2(self._window_size, self._poly_order)

    def __call__(self, data: np.ndarray,
                 mode: str = 'reflect', cval: float = 0.0):
        return self._filtrate(data, mode=mode, cval=cval)

    @property
    def window_size(self) -> Param2:
        return self._window_size

    @property
    def poly_order(self) -> Param2:
        return self._poly_order

    @property
    def kernel(self) -> SGolayKernel2:
        """Returns filter 2D kernel
        """
        return self._kernel

    @staticmethod
    def _canonize_param(name, value: _ParamType, validator) -> Param2:
        err = TypeError(
            'The parameter "{}" must be int scalar or Tuple[int, int]'.format(
                name))

        if isinstance(value, int):
            value = (value, value)

        if not isinstance(value, (list, tuple)):
            raise err
        if len(value) != _DIM:
            raise err
        if not all(isinstance(v, int) for v in value):
            raise err

        validator(value)

        return Param2(*value)

    @staticmethod
    def _validate_window_size(value):
        if not all(v >= 3 and bool(v % 2) for v in value):
            raise ValueError(
                'Window size values must be odd and >= 3 (Given: {})'.format(
                    value))

    @staticmethod
    def _validate_poly_order(value):
        if not all(v >= 1 for v in value):
            raise ValueError(
                'Polynom order values must be >= 1 (Given: {})'.format(value))

    def _filtrate(self, data: np.ndarray, *args, **kwargs):
        self._kernel.compute()
        return ndim.correlate(data, self._kernel.kernel, *args, **kwargs)