""" **Description**
        A Finite Impulse Response ( FIR ) filter realizes a discrete difference
        equation as a function of a forward coefficient array and a state array
        of a specified order, consuming an incident signal and producing a
        reference signal.

        .. math::
            y_{n} = \sum_{i = 0}^{N} b_{i,n} x_{n-i} = \sum_{i = 1}^{N} b_{i,n} s_{i,n} + b_{0,n} x_{n}

        .. math::
            s_{1,n+1} = x_{n}\qquad\quad s_{i,n+1} = s_{i-1,n}

        A reset may minimize edge effects at a discontinuity by assuming
        persistent operation at a specified incident signal condition.

        .. math::
            s_{i,n} = x_{n}

        A frequency response is expressed as a function of a forward
        coefficient array.

        .. math::
            H_{z,n} = \sum_{i = 0}^{N} b_{i,n} z^{-i}

        A forward coefficient array and state array of a specified order are
        defined to realize specified constraints.  A style, frequency,
        order, count, complement, and gain are electively specified.
        Alternatively, a forward coefficient array and state array may be explicitly
        defined to ignore constraints.

        Frequency corresponds to a -3 dB frequency response normalized relative
        to Nyquist.

        Style is in ( 'Blackman', 'Hamming', 'Hann', 'Kaiser' ).

        * | 'Blackman' filters demonstrate low resolution and spectral leakage
          | with improved rate of attenuation.

        * | 'Hamming' filters demonstrate minimal nearest side lobe magnitude
          | response.

        * | 'Hann' filters demonstrate high resolution and spectral leakage.

        * | 'Kaiser' filters demonstrate flexible resolution and spectral
          | leakage dependent upon a beta value of a Bessel function of the
          | first kind, with beta equal to 7.0.

        Order must even to ensure a Type I form linear phase solution.

        Count is a quantity of filters of a specified order concatenated to
        form an aggregate frequency response in cascade form.

        Complement effectively constructs a mirror image of a specified
        frequency response.

    **Example**
        
        ::
        
            from diamondback import FirFilter
            import numpy

            # Create an instance with constraints.

            obj = FirFilter( style = 'Kaiser', frequency = 0.1, order = 32, count = 1 )

            # Create an instance with coefficients.

            obj = FirFilter( b = obj.b )

            # Estimate frequency response, group delay, and roots.

            y, f = obj.response( length = 8192, count = 1 )
            y, f = obj.delay( length = 8192, count = 1 )
            p, z = obj.roots( count = 1 )

            # Filter an incident signal.

            x = numpy.random.rand( 128 ) * 2.0 - 1.0
            obj.reset( x[ 0 ] )
            y = obj.filter( x )

    **License**
        `BSD-3C.  <https://github.com/larryturner/diamondback/blob/master/license>`_
        © 2018 - 2022 Larry Turner, Schneider Electric Industries SAS. All rights reserved.

    **Author**
        Larry Turner, Schneider Electric, Analytics & AI, 2018-01-23.
"""

from typing import List, Tuple, Union
import math
import numpy
import scipy.signal
import warnings

class FirFilter( object ) :

    """ Finite Impulse Response ( FIR ) filter.
    """

    __style = ( 'Blackman', 'Hamming', 'Hann', 'Kaiser' )

    @property
    def b( self ) :

        """ b : Union[ List, numpy.ndarray ] - forward coefficient.
        """

        return self._b

    @b.setter
    def b( self, b : Union[ List, numpy.ndarray ] ) :

        self._b = b

    @property
    def s( self ) :

        """ s : Union[ List, numpy.ndarray ] - state.
        """

        return self._s

    @s.setter
    def s( self, s : Union[ List, numpy.ndarray ] ) :

        self._s = s

    def __init__( self, style : str = '', frequency : float = 0.0, order : int = 0, count : int = 1, complement : bool = False, gain : float = 1.0,
                  b : Union[ List, numpy.ndarray ] = [ ], s : Union[ List, numpy.ndarray ] = [ ] ) -> None :

        """ Initialize.

            Specify constraints including style, frequency, and order.
            Alternatively, a forward coefficient array may be explicitly defined
            to ignore constraints.

            Labels should be used to avoid ambiguity between constraints and
            coefficients.

            Arguments :
                style : str - in ( 'Blackman', 'Hamming', 'Hann', 'Kaiser' ).
                frequency : float - relative to Nyquist in ( 0.0, 1.0 ).
                order : int.
                count : int.
                complement : bool.
                gain : float.
                b : Union[ List, numpy.ndarray ].
                s : Union[ List, numpy.ndarray ].
        """

        if ( not len( b ) ) :
            if ( ( not style ) or ( style not in FirFilter.__style ) ) :
                raise ValueError( f'style = {style}' )
            if ( ( frequency <= 0.0 ) or ( frequency >= 1.0 ) ) :
                raise ValueError( f'Frequency = {frequency}' )
            if ( order < 0 ) :
                raise ValueError( f'Order = {order}' )
            if ( count <= 0 ) :
                raise ValueError( f'Count = {count}' )
            if ( complement ) :
                frequency = 1.0 - frequency
            if ( style == 'Kaiser' ) :
                window = ( style.lower( ), 7.0 )
            else :
                window = style.lower( )
            beta, eps, error = 10.0, numpy.finfo( float ).eps, float( 'inf' )
            index, mu, zeta = 500 * ( 1 + ( count > 2 ) ), 2.5e-2, 1.0
            for _ in range( 0, index ) :
                with warnings.catch_warnings( ) :
                    warnings.simplefilter( 'ignore' )
                    v = scipy.signal.firwin( order + 1, zeta * frequency, None, window, True, True, 1.0 )
                    if ( numpy.isnan( v ).any( ) ) :
                        raise ValueError( f'V = {v}' )
                    x = numpy.exp( 1j * math.pi * frequency )
                    e = ( 2.0 ** ( -0.5 ) ) - ( abs( numpy.polyval( v, x ) ) ** count )
                    if ( abs( e ) < error ) :
                        b, error = v, abs( e )
                        if ( error < ( 10.0 * eps ) ) :
                            break
                    zeta = numpy.maximum( zeta + mu * math.tanh( beta * e ), eps )
            if ( complement ) :
                b *= numpy.array( [ ( ( -1.0 ) ** x ) for x in range( 0, len( b ) ) ] )
                b /= sum( b * numpy.array( [ ( ( -1.0 ) ** x ) for x in range( 0, len( b ) ) ] ) )
            b *= gain
        if ( ( not numpy.isscalar( b ) ) and ( not isinstance( b, numpy.ndarray ) ) ) :
            b = numpy.array( list( b ) )
        if ( not len( b ) ) :
            raise ValueError( f'B = {b}' )
        if ( ( not numpy.isscalar( s ) ) and ( not isinstance( s, numpy.ndarray ) ) ) :
            s = numpy.array( list( s ) )
        if ( len( b ) < len( s ) ) :
            b = numpy.concatenate( ( b, numpy.zeros( len( s ) - len( b ) ) ) )
        if ( len( s ) < len( b ) ) :
            s = numpy.concatenate( ( s, numpy.zeros( len( b ) - len( s ) ) ) )
        super( ).__init__( )
        self._b, self._s = numpy.array( b ), numpy.array( s, type( b[ 0 ] ) )

    def delay( self, length : int = 8192, count : int = 1 ) -> Tuple[ numpy.ndarray, numpy.ndarray ] :

        """ Estimates group delay and produces a reference signal.

            Arguments :
                length : int.
                count : int.

            Returns :
                y : numpy.ndarray - reference signal.
                f : numpy.ndarray - relative to Nyquist in [ -1.0, 1.0 ).
        """

        if ( length <= 0 ) :
            raise ValueError( f'Length = {length}' )
        if ( count <= 0 ) :
            raise ValueError( f'Count = {count}' )
        with warnings.catch_warnings( ) :
            warnings.simplefilter( 'ignore' )
            y, f = scipy.signal.group_delay( ( self.b, [ 1.0 ] ), length, True )[ 1 ], numpy.linspace( -1.0, 1.0 - 2.0 / length, length )
            y = numpy.concatenate( ( y[ len( y ) // 2 : ], y[ : len( y ) // 2 ] ) )
        if ( length > 2 ) :
            y[ 0 ] = y[ 1 ] * 2.0 - y[ 2 ]
        return y, f

    def filter( self, x : Union[ List, numpy.ndarray ] ) -> numpy.ndarray :

        """ Filters an incident signal and produces a reference signal.

            Arguments :
                x : Union[ List, numpy.ndarray ] - incident signal.

            Returns :
                y : numpy.ndarray - reference signal.
        """

        if ( ( not numpy.isscalar( x ) ) and ( not isinstance( x, numpy.ndarray ) ) ) :
            x = numpy.array( list( x ) )
        if ( not len( x ) ) :
            raise ValueError( f'X = {x}' )
        y = numpy.zeros( len( x ), type( self.b[ 0 ] ) )
        for ii in range( 0, len( x ) ) :
            self.s[ 0 ] = x[ ii ]
            y[ ii ] = self.b.dot( self.s )
            if ( len( self.s ) > 1 ) :
                self.s[ 1 : ] = self.s[ : -1 ]
        return y

    def reset( self, x : Union[ complex, float ] ) -> None :

        """ Modifies a state to minimize edge effects by assuming persistent
            operation at a specified incident signal condition.

            Arguments :
                x : Union[ complex, float ] - incident signal.
        """

        if ( not numpy.isscalar( x ) ) :
            raise ValueError( f'X = {x}' )
        self.s.fill( x )

    def response( self, length = 8192, count = 1 ) -> Tuple[ numpy.ndarray, numpy.ndarray ] :

        """ Estimates frequency response and produces a reference signal.

            Arguments :
                length : int.
                count : int.

            Returns :
                y : numpy.ndarray - reference signal.
                f : numpy.ndarray - relative to Nyquist in [ -1.0, 1.0 ).
        """

        if ( length <= 0 ) :
            raise ValueError( f'Length = {length}' )
        if ( count <= 0 ) :
            raise ValueError( f'Count = {count}' )
        y, f = scipy.signal.freqz( self.b, [ 1.0, 0.0 ], length, True )[ 1 ], numpy.linspace( -1.0, 1.0 - 2.0 / length, length )
        y = numpy.concatenate( ( y[ len( y ) // 2 : ], y[ : len( y ) // 2 ] ) ) ** count
        return y, f

    def roots( self, count = 1 ) -> Tuple[ numpy.ndarray, numpy.ndarray ] :

        """ Estimates roots of a frequency response in poles and zeros.

            Arguments :
                count : int.
            Returns :
                p : numpy.ndarray - poles.
                z : numpy.ndarray - zeros.
        """

        z = numpy.tile( numpy.roots( self.b ), count )
        return numpy.zeros( count * ( len( self.b ) - 1 ) ), z[ numpy.argsort( abs( z ) ) ]
