import pandas as pd
import numpy as np
import datetime
import calendar
from math import e
from brightwind.analyse import plot as plt
# noinspection PyProtectedMember
from brightwind.analyse.analyse import dist_by_dir_sector, dist_12x24, coverage, _convert_df_to_series
from ipywidgets import FloatProgress
from IPython.display import display
from IPython.display import clear_output
import re
import warnings

pd.options.mode.chained_assignment = None

__all__ = ['Shear']


class Shear:

    class TimeSeries:

        def __init__(self, wspds, heights, min_speed=3, calc_method='power_law', max_plot_height=None,
                     maximise_data=False):
            """
            Calculates alpha, using the power law, or the roughness coefficient, using the log law, for each timestamp
            of a wind series.

           :param wspds: pandas DataFrame, list of pandas.Series or list of wind speeds to be used for calculating shear.
           :type wspds:  pandas.DataFrame, list of pandas.Series or list.
           :param heights: List of anemometer heights.
           :type heights: list
           :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.
           :type min_speed: float
           :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                              (returns the roughness coefficient).
           :type calc_method: str
           :param max_plot_height: height to which the wind profile plot is extended.
           :type max_plot_height: float
           :param maximise_data: If maximise_data is True, calculations will be carried out on all data where two or
                                 more anemometers readings exist for a timestamp. If False, calculations will only be
                                 carried out on timestamps where readings exist for all anemometers.
           :type maximise_data: Boolean
           :return TimeSeries object containing calculated alpha/roughness coefficient values, a plot
                   and other data.
           :rtype TimeSeries object

           **Example usage**
           ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Using with a DataFrame of wind speeds
                timeseries_power_law = bw.Shear.TimeSeries(anemometers, heights, maximise_data=True)
                timeseries_log_law = bw.Shear.TimeSeries(anemometers, heights, calc_method='log_law',
                                                         max_plot_height=120)

                # Get the alpha or roughness values calculated
                timeseries_power_law.alpha
                timeseries_log_law.roughness

                # View plot
                timeseries_power_law.plot
                timeseries_log_law.plot

                # View input anemometer data
                timeseries_power_law.wspds
                timeseries_log_law.wspds

                # View other information
                pprint.pprint(timeseries_power_law.info)
                pprint.pprint(timeseries_log_law.info)

           """
            print('This may take a while...')

            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed, maximise_data=maximise_data)

            if calc_method == 'power_law':
                alpha_c = (wspds[(wspds > min_speed).all(axis=1)].apply(Shear._calc_power_law, heights=heights,
                                                                        return_coeff=True,
                                                                        maximise_data=maximise_data, axis=1))
                alpha = pd.Series(alpha_c.iloc[:, 0], name='alpha')
                self._alpha = alpha

            elif calc_method == 'log_law':
                slope_intercept = (wspds[(wspds > min_speed).all(axis=1)].apply(Shear._calc_log_law, heights=heights,
                                                                                return_coeff=True,
                                                                                maximise_data=maximise_data, axis=1))
                slope = slope_intercept.iloc[:, 0]
                intercept = slope_intercept.iloc[:, 1]
                roughness_coefficient = pd.Series(Shear._calc_roughness(slope=slope, intercept=intercept),
                                                  name='roughness_coefficient')
                self._roughness = roughness_coefficient

            clear_output()
            avg_plot = Shear.Average(wspds=wspds, heights=heights, calc_method=calc_method,
                                     max_plot_height=max_plot_height)

            self.origin = 'TimeSeries'
            self.calc_method = calc_method
            self.wspds = wspds
            self.plot = avg_plot.plot
            self.info = Shear._create_info(self, heights=heights, cvg=cvg, min_speed=min_speed)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, height, shear_to):
            """"
            Applies shear calculated to a wind speed time series and scales wind speed from one height to
            another for each matching timestamp.

           :param self: TimeSeries object to use when applying shear to the data.
           :type self: TimeSeries object
           :param wspds: Wind speed time series to apply shear to.
           :type wspds: pandas.Series
           :param height: height of above wspds.
           :type height: float
           :param shear_to: height to which wspds should be scaled to.
           :type shear_to: float
           :return: a pandas.Series of the scaled wind speeds.
           :rtype: pandas.Series

            **Example Usage**
            ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Get power law object
                timeseries_power_law = bw.Shear.TimeSeries(anemometers, heights)
                timeseries_log_law = bw.Shear.TimeSeries(anemometers, heights, calc_method='log_law')

                # Scale wind speeds using calculated exponents
                timeseries_power_law.apply(data['Spd40mN'], height=40, shear_to=70)
                timeseries_log_law.apply(data['Spd40mN'], height=40, shear_to=70)
               """

            return Shear._apply(self, wspds, height, shear_to)

    class TimeOfDay:

        def __init__(self, wspds, heights, min_speed=3, calc_method='power_law', by_month=True, segment_start_time=7,
                     segments_per_day=24, plot_type='line'):
            """
            Calculates alpha, using the power law, or the roughness coefficient, using the log law, for a wind series
            binned by time of the day and (optionally by) month, depending on the user's inputs. The alpha/roughness
            coefficient values are calculated based on the average wind speeds at each measurement height in each bin.

            :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating
             shear.
            :type wspds:  pandas.DataFrame, list of pandas.Series or list.
            :param heights: List of anemometer heights..
            :type heights: list
            :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3
            :type min_speed: float
            :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                                (returns the roughness coefficient).
            :type calc_method: str
            :param by_month: If True, calculate alpha or roughness coefficient values for each daily segment and month.
                             If False, average alpha or roughness coefficient values are calculated for each daily
                             segment across all months.
            :type by_month: Boolean
            :param segment_start_time: Starting time for first segment.
            :type segment_start_time: int
            :param segments_per_day: Number of segments into which each 24 period is split. Must be a divisor of 24.
            :type segments_per_day: int
            :param plot_type: Type of plot to be generated. Options include 'line', 'step' and '12x24'.
            :type plot_type: str
            :return: TimeOfDay object containing calculated alpha/roughness coefficient values, a plot
                     and other data.
            :rtype: TimeOfDay object

            **Example usage**
            ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Using with a DataFrame of wind speeds
                timeofday_power_law = bw.Shear.TimeOfDay(anemometers, heights, daily_segments=2, segment_start_time=7)
                timeofday_log_law = bw.Shear.TimeOfDay(anemometers, heights, calc_method='log_law', by_month=False)

                # Get alpha or roughness values calculated
                timeofday_power_law.alpha
                timeofday_log_law.roughness

                # View plot
                timeofday_power_law.plot
                timeofday_log_law.plot

                # View input data
                timeofday_power_law.wspds
                timeofday_log_law.wspds

                # View other information
                pprint.pprint(timeofday_power_law.info)
                pprint.pprint(timeofday_log_law.info)

            """

            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed)

            # initialise empty series for later use
            start_times = pd.Series([])
            time_wspds = pd.Series([])
            mean_time_wspds = pd.Series([])
            c = pd.Series([])
            slope = pd.Series([])
            intercept = pd.Series([])
            alpha = pd.Series([])
            roughness = pd.Series([])
            slope_df = pd.DataFrame([])
            intercept_df = pd.DataFrame([])
            roughness_df = pd.DataFrame([])
            alpha_df = pd.DataFrame([])

            # time of day shear calculations
            interval = int(24 / segments_per_day)

            if by_month is False and plot_type == '12x24':
                raise ValueError("12x24 plot is only possible when 'by_month=True'")

            if not int(segment_start_time) % 1 == 0:
                raise ValueError("'segment_start_time' must be an integer between 0 and 24'")

            if not (24 % segments_per_day == 0) | (segments_per_day == 1):
                raise ValueError("'segments_per_day' must be a divisor of 24'")

            segment_start_time = str(segment_start_time)
            start_times[0] = datetime.datetime.strptime(segment_start_time, '%H')
            dt = datetime.timedelta(hours=interval)

            # extract wind speeds for each daily segment
            for i in range(1, segments_per_day):
                start_times[i] = start_times[i - 1] + dt

            # extract wind speeds for each month
            months_tot = pd.unique(wspds.index.month.values)
            for j in months_tot:

                anemometers_df = wspds[wspds.index.month == j]
                for i in range(0, segments_per_day):

                    if segments_per_day == 1:
                        mean_time_wspds[i] = anemometers_df.mean().dropna()

                    elif i == segments_per_day - 1:
                        start_times[i] = start_times[i].strftime("%H:%M:%S")
                        start = str(start_times[i].time())
                        end = str(start_times[0].time())
                        time_wspds[i] = pd.DataFrame(anemometers_df).between_time(start, end, include_end=False)
                        mean_time_wspds[i] = time_wspds[i][(time_wspds[i] > min_speed).all(axis=1)].mean().dropna()

                    else:
                        start_times[i] = start_times[i].strftime("%H:%M:%S")
                        start = str(start_times[i].time())
                        end = str(start_times[i + 1].time())
                        time_wspds[i] = pd.DataFrame(anemometers_df).between_time(start, end, include_end=False)
                        mean_time_wspds[i] = time_wspds[i][(time_wspds[i] > min_speed).all(axis=1)].mean().dropna()

                # calculate shear
                if calc_method == 'power_law':
                    for i in range(0, len(mean_time_wspds)):
                        alpha[i], c[i] = Shear._calc_power_law(mean_time_wspds[i].values, heights, return_coeff=True)
                    alpha_df = pd.concat([alpha_df, alpha], axis=1)

                if calc_method == 'log_law':
                    for i in range(0, len(mean_time_wspds)):
                        slope[i], intercept[i] = Shear._calc_log_law(mean_time_wspds[i].values, heights,
                                                                     return_coeff=True)
                        roughness[i] = Shear._calc_roughness(slope=slope[i], intercept=intercept[i])
                    roughness_df = pd.concat([roughness_df, roughness], axis=1)
                    slope_df = pd.concat([slope_df, slope], axis=1)
                    intercept_df = pd.concat([intercept_df, intercept], axis=1)

            # error check
            if mean_time_wspds.shape[0] == 0:
                raise ValueError('None of the input wind speeds are greater than the min_speed, cannot calculate shear')

            if calc_method == 'power_law':
                alpha_df.index = start_times
                alpha_df.index = alpha_df.index.time
                alpha_df.sort_index(inplace=True)

                if by_month is True:
                    alpha_df.columns = [calendar.month_abbr[month] for month in months_tot]
                    self.plot = plt.plot_shear_time_of_day(Shear._fill_df_12x24(alpha_df), calc_method=calc_method,
                                                           plot_type=plot_type)

                else:
                    n_months = len(alpha_df.columns.values)
                    alpha_df = pd.DataFrame(alpha_df.mean(axis=1))
                    alpha_df.columns = [str(n_months) + ' Month Average']
                    df_in = pd.DataFrame((Shear._fill_df_12x24(alpha_df)).iloc[:, 0])
                    df_in.columns = [str(n_months) + ' Month Average']
                    self.plot = plt.plot_shear_time_of_day(df_in, calc_method=calc_method, plot_type=plot_type)

                alpha_df.index.name = 'segment_start_time'
                self._alpha = alpha_df

            if calc_method == 'log_law':
                roughness_df.index = slope_df.index = intercept_df.index = start_times
                roughness_df.index = slope_df.index = intercept_df.index = roughness_df.index.time
                roughness_df.sort_index(inplace=True)

                slope_df.sort_index(inplace=True)
                intercept_df.sort_index(inplace=True)

                if by_month is True:
                    roughness_df.columns = slope_df.columns = intercept_df.columns = \
                                                                    [calendar.month_abbr[month] for month in months_tot]
                    self.plot = plt.plot_shear_time_of_day(Shear._fill_df_12x24(roughness_df),
                                                           calc_method=calc_method, plot_type=plot_type)
                else:
                    n_months = len(slope_df.columns.values)
                    slope_df = pd.DataFrame(slope_df.mean(axis=1))
                    intercept_df = pd.DataFrame(intercept_df.mean(axis=1))
                    roughness_df = pd.DataFrame(roughness_df.mean(axis=1))
                    roughness_df.columns = slope_df.columns = intercept_df.columns = \
                                                                            [str(len(months_tot)) + '_month_average']
                    df_in = pd.DataFrame(Shear._fill_df_12x24(roughness_df).iloc[:, 0])
                    df_in.columns = [str(n_months) + ' Month Average']
                    self.plot = plt.plot_shear_time_of_day(df_in, calc_method=calc_method, plot_type=plot_type)

                roughness_df.index.name = 'segment_start_time'
                self._roughness = roughness_df

            self.calc_method = calc_method
            self.wspds = wspds
            self.origin = 'TimeOfDay'
            self.info = Shear._create_info(self, heights=heights, cvg=cvg, min_speed=min_speed,
                                           segment_start_time=segment_start_time, segments_per_day=segments_per_day)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, height, shear_to):
            """
            Applies shear calculated to a wind speed time series by time of day (and optionally by month) to scale
            wind speed from one height to another.

           :param self: TimeOfDay object to use when applying shear to the data.
           :type self: TimeOfDay object
           :param wspds: Wind speed time series to apply shear to.
           :type wspds: pandas.Series
           :param height: height of above wspds.
           :type height: float
           :param shear_to: height to which wspds should be scaled.
           :type shear_to: float
           :return: a pandas.Series of the scaled wind speeds.
           :rtype: pandas.Series

            **Example Usage**
            ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Get power law object
                timeofday_power_law = bw.Shear.TimeOfDay(anemometers, heights)
                timeofday_log_law = bw.Shear.TimeOfDay(anemometers, heights, calc_method='log_law')

                # Scale wind speeds using calculated exponents
                timeofday_power_law.apply(data['Spd40mN'], height=40, shear_to=70)
                timeofday_log_law.apply(data['Spd40mN'], height=40, shear_to=70)

            """

            return Shear._apply(self, wspds, height, shear_to)

    class Average:

        def __init__(self, wspds, heights, min_speed=3, calc_method='power_law', plot_both=False, max_plot_height=None):
            """
             Calculates alpha, using the power law, or the roughness coefficient, using the log law, based on the
             average wind speeds of each supplied time series.

            :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating
             shear.
            :type wspds:  pandas.DataFrame, list of pandas.Series or list.
            :param heights: List of anemometer heights
            :type heights: list
            :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.
            :type min_speed: float
            :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                                      (returns the roughness coefficient).
            :type calc_method: str
            :param max_plot_height: height to which the wind profile plot is extended.
            :type max_plot_height: float
            :return:  Average object containing calculated alpha/roughness coefficient values, a plot and other data.
            :rtype: Average object

            **Example usage**
            ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Using with a DataFrame of wind speeds
                average_power_law = bw.Shear.Average(anemometers, heights)
                average_log_law = bw.Shear.Average(anemometers, heights, calc_method='log_law', max_plot_height=120)

                # Get the alpha or roughness values calculated
                average_power_law.alpha
                average_log_law.roughness

                # View plot
                average_power_law.plot
                average_log_law.plot

                # View input data
                average_power_law.wspds
                average_log_law.wspds

                # View other information
                pprint.pprint(average_power_law.info)
                pprint.pprint(average_log_law.info)

            """

            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed)

            mean_wspds = wspds.mean(axis=0)

            if mean_wspds.shape[0] == 0:
                raise ValueError('None of the input wind speeds are greater than the min_speed, cannot calculate shear')

            if calc_method == 'power_law':
                alpha, c = Shear._calc_power_law(mean_wspds.values, heights, return_coeff=True)
                if plot_both is True:
                    slope, intercept = Shear._calc_log_law(mean_wspds.values, heights, return_coeff=True)
                    self.plot = plt.plot_power_law(plot_both=True, avg_alpha=alpha, avg_c=c, avg_slope=slope,
                                                   avg_intercept=intercept,
                                                   wspds=mean_wspds.values, heights=heights,
                                                   max_plot_height=max_plot_height)
                else:
                    self.plot = plt.plot_power_law(alpha, c, mean_wspds.values, heights,
                                                   max_plot_height=max_plot_height)
                self._alpha = alpha

            elif calc_method == 'log_law':
                slope, intercept = Shear._calc_log_law(mean_wspds.values, heights, return_coeff=True)
                roughness = Shear._calc_roughness(slope=slope, intercept=intercept)
                self._roughness = roughness
                if plot_both is True:
                    alpha, c = Shear._calc_power_law(mean_wspds.values, heights, return_coeff=True)
                    self.plot = plt.plot_power_law(avg_alpha=alpha, avg_c=c, avg_slope=slope, avg_intercept=intercept,
                                                   wspds=mean_wspds.values, heights=heights,
                                                   max_plot_height=max_plot_height)
                else:
                    self.plot = plt.plot_log_law(slope, intercept, mean_wspds.values, heights,
                                                 max_plot_height=max_plot_height)

            else:
                raise ValueError("Please enter a valid calculation method, either 'power_law' or 'log_law'.")

            self.wspds = wspds
            self.origin = 'Average'
            self.calc_method = calc_method
            self.info = Shear._create_info(self, heights=heights, min_speed=min_speed, cvg=cvg)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, height, shear_to):
            """
            Applies average shear calculated to a wind speed time series to scale wind speed from one height to another.

           :param self: Average object to use when applying shear to the data.
           :type self: Average object
           :param wspds: Wind speed time series to apply shear to.
           :type wspds: pandas.Series
           :param height: height of above wspds.
           :type height: float
           :param shear_to: height to which wspds should be scaled to.
           :type shear_to: float
           :return: a pandas.Series of the scaled wind speeds.
           :rtype: pandas.Series

            **Example Usage**
            ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Get power law object
                average_power_law = bw.Shear.Average(anemometers, heights)
                average_log_law = bw.Shear.Average(anemometers, heights, calc_method='log_law', max_plot_height=120)

               # Scale wind speeds using exponents
               average_power_law.apply(data['Spd40mN'], height=40, shear_to=70)
               average_log_law.apply(data['Spd40mN'], height=40, shear_to=70)

               """
            return Shear._apply(self, wspds, height, shear_to)

    class BySector:

        def __init__(self, wspds, heights, wdir, min_speed=3, calc_method='power_law', sectors=12,
                     direction_bin_array=None, direction_bin_labels=None):
            """
            Calculates alpha, using the power law, or the roughness coefficient, using the log law, for a wind series
            binned by direction. The alpha/roughness coefficient values are calculated based on the average wind speeds
            at each measurement height in each bin.


            :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating
            shear.
            :type wspds: pandas.DataFrame, list of pandas.Series or list.
            :param heights: List of anemometer heights
            :type heights: list
            :param wdir: Wind direction measurements
            :type wdir: pandas.DataFrame or Series
            :param: min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.
            :type: min_speed: float
            :param calc_method: Method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                                (returns the roughness coefficient).
            :type calc_method: str
            :param sectors: Number of sectors for the shear to be calculated for.
            :type sectors: int
            :param direction_bin_array: Specific array of directional bins to be used. If None, bins are calculated
                                        by 360/sectors.
            :type direction_bin_array: list or array
            :param direction_bin_labels: Labels to be given to the above direction_bin array.
            :type direction_bin_labels: list or array
            :return: BySector object containing calculated alpha/roughness coefficient values, a plot and other data.
            :rtype: BySector object

             **Example usage**
            ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]
                directions = data['Dir78mS']

                # Calculate shear exponents using default bins ([345,15,45,75,105,135,165,195,225,255,285,315,345])
                by_sector_power_law= bw.Shear.BySector(anemometers, heights, directions)
                by_sector_log_law= bw.Shear.BySector(anemometers, heights, directions, calc_method='log_law')

                # Calculate shear exponents using custom bins
                custom_bins = [0,30,60,90,120,150,180,210,240,270,300,330,360]
                by_sector_power_law_custom_bins = bw.Shear.BySector(anemometers, heights, directions,
                direction_bin_array=custom_bins)

                # Get alpha or roughness values calculated
                by_sector_power_law.alpha
                by_sector_log_law.roughness

                # View plot
                by_sector_power_law.plot
                by_sector_log_law.plot

                # View input data
                by_sector_power_law.wspds
                by_sector_log_law.wspds

                # View other information
                pprint.pprint(by_sector_power_law.info)
                pprint.pprint(by_sector_log_law.info)

            """
            print('This may take a while...')
            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed)

            if direction_bin_array is not None:
                sectors = len(direction_bin_array) - 1

            wdir = _convert_df_to_series(wdir)
            mean_wspds = pd.Series([])
            mean_wspds_df = pd.DataFrame([])
            count_df = pd.DataFrame([])
            count = pd.Series([])

            for i in range(len(wspds.columns)):

                w = wspds.iloc[:, i]
                plot, mean_wspds[i] = dist_by_dir_sector(w, wdir, direction_bin_array=direction_bin_array,
                                                         sectors=sectors,
                                                         aggregation_method='mean', return_data=True)

                plot, count[i] = dist_by_dir_sector(w, wdir, direction_bin_array=direction_bin_array,
                                                    sectors=sectors,
                                                    aggregation_method='count', return_data=True)

                if i == 0:
                    mean_wspds_df = mean_wspds[i].copy()
                    count_df = count[i].copy()
                else:
                    mean_wspds_df = pd.concat([mean_wspds_df, mean_wspds[i]], axis=1)
                    count_df = pd.concat([count_df, count[i]], axis=1)

            count_df = count_df.mean(axis=1)
            wind_rose_plot, wind_rose_dist = dist_by_dir_sector(wspds.iloc[:, 0], wdir,
                                                                direction_bin_array=direction_bin_array,
                                                                sectors=sectors,
                                                                direction_bin_labels=direction_bin_labels,
                                                                return_data=True)
            if calc_method == 'power_law':

                alpha = mean_wspds_df.apply(Shear._calc_power_law, heights=heights, return_coeff=False, axis=1)

                wind_rose_plot, wind_rose_dist = dist_by_dir_sector(wspds.iloc[:, 0], wdir,
                                                                    direction_bin_array=direction_bin_array,
                                                                    sectors=sectors,
                                                                    direction_bin_labels=direction_bin_labels,
                                                                    return_data=True)

                self.alpha_count = count_df
                self._alpha = pd.Series(alpha, name='alpha')
                clear_output()
                self.plot = plt.plot_shear_by_sector(scale_variable=alpha, wind_rose_data=wind_rose_dist,
                                                     calc_method=calc_method)

            elif calc_method == 'log_law':

                slope_intercept = mean_wspds_df.apply(Shear._calc_log_law, heights=heights, return_coeff=True, axis=1)

                slope = slope_intercept.iloc[:, 0]
                intercept = slope_intercept.iloc[:, 1]
                roughness = Shear._calc_roughness(slope=slope, intercept=intercept)
                self.roughness_count = count_df
                self._roughness = pd.Series(roughness, name='roughness_coefficient')
                clear_output()
                self.plot = plt.plot_shear_by_sector(scale_variable=roughness, wind_rose_data=wind_rose_dist,
                                                     calc_method=calc_method)

            else:
                raise ValueError("Please enter a valid calculation method, either 'power_law' or 'log_law'.")

            self.wspds = wspds
            self.wdir = wdir
            self.origin = 'BySector'
            self.sectors = sectors
            self.calc_method = calc_method
            self.info = Shear._create_info(self, heights=heights, cvg=cvg, min_speed=min_speed,
                                           direction_bin_array=direction_bin_array)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, wdir, height, shear_to):
            """
            Applies shear calculated to a wind speed time series by wind direction to scale
            wind speed from one height to another.

            :param self: BySector object to use when applying shear to the data
            :type self: BySector object
            :param wspds: Wind speed time series to apply shear to.
            :type wspds: pandas.Series
            :param wdir: Wind direction measurements of wspds, only required if shear is to be applied by direction
            sector.
            :type wdir: pandas.Series
            :param height: Height of wspds.
            :type height: float
            :param shear_to: Height to which wspds should be scaled to.
            :type shear_to: float
            :return: A pandas.Series of the scaled wind speeds.
            :rtype: pandas.Series

             **Example Usage**
             ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS']]
                heights = [80, 60]
                directions = data[['Dir78mS']]

                # Calculate shear exponents
                by_sector_power_law = bw.Shear.BySector(anemometers, heights, directions)
                by_sector_log_law = bw.Shear.BySector(anemometers, heights, directions, calc_method='log_law')

                # Calculate shear exponents using default bins ([345,15,45,75,105,135,165,195,225,255,285,315,345])
                by_sector_power_law= bw.Shear.BySector(anemometers, heights, directions)

                # Scale wind speeds using exponents
                by_sector_power_law.apply(data['Spd40mN'], data['Dir38mS'], height=40, shear_to=70)
                by_sector_log_law.apply(data['Spd40mN'], data['Dir38mS'], height=40, shear_to=70)

            """

            return Shear._apply(self, wspds=wspds, height=height, shear_to=shear_to, wdir=wdir)

    @staticmethod
    def _log_roughness_scale(wspds, height, shear_to, roughness):
        """
        Scale wind speeds using the logarithmic wind shear law.

        :param wspds: wind speeds at height z1, U1
        :param height: z1
        :param shear_to: z2
        :param roughness: z0
        :return: Scaled wind speeds, U2
        :rtype: pandas.Series or float

        METHODOLOGY:

                                            U2 = (ln(z2/z0)/ln(z1/z0))U1
            Where:
                    - U2 is the wind speed at height z2
                    - U1 is the wind speed at height z1
                    - z1 is the lower height
                    - z2 is the upper height
                    - zo is the roughness coefficient
        """
        scale_factor = np.log(shear_to / roughness) / (np.log(height / roughness))
        scaled_wspds = wspds * scale_factor

        return scaled_wspds

    @staticmethod
    def _calc_log_law(wspds, heights, return_coeff=False, maximise_data=False) -> (np.array, float):
        """
        Derive the best fit logarithmic law line from a given time-step of speed data at 2 or more elevations

        :param wspds: List of wind speeds [m/s]
        :param heights: List of heights [m above ground]. The position of the height in the list must be the same
            position in the list as its corresponding wind speed value.
        :return: The slope and intercept of the best fit line, as defined above
        :rtype: pandas.Series and float

        METHODOLOGY:
            Derive natural log of elevation data sets
            Derive coefficients of linear best fit along ln(heights)- wspds distribution
            Characterise new distribution of speed values based on linear best fit
            Return the slope and the intercept of this linear best fit.
            The slope and intercept can then be used to find the corresponding roughness coefficient, using the
            equivilant laws:

                                                1)  $U(z) = (v/k)*ln(z/zo)$
            which can be rewritten as:
                                                $U(z) = (v/k)*ln(z) - (v/k)ln(zo)$
                                                where zo = e ** (-c/m) of this line

            Where:

                - U(z) is the wind speed at height z
                - v is the friction velocity at the location
                - k is the Von Karmen constant, taken aa .4
                - z is the height
                - zo is the roughness coefficient

                                                2)  $U2 = (ln(z2/z0)/ln(z1/z0))U1$

            """

        if maximise_data:
            log_heights = np.log(
                pd.Series(heights).drop(wspds[wspds == 0].index.values.astype(int)))  # take log of elevations
            wspds = wspds.drop(wspds[wspds == 0].index.values.astype(int))

        else:
            log_heights = np.log(heights)  # take log of elevations

        coeffs = np.polyfit(log_heights, wspds, deg=1)
        if return_coeff:
            return pd.Series([coeffs[0], coeffs[1]])
        return coeffs[0]

    @staticmethod
    def _calc_power_law(wspds, heights, return_coeff=False, maximise_data=False) -> (np.array, float):
        """
        Derive the best fit power law exponent (as 1/alpha) from a given time-step of speed data at 2 or more elevations

        :param wspds: pandas.Series or list of wind speeds [m/s]
        :param heights: List of heights [m above ground]. The position of the height in the list must be the same
            position in the list as its corresponding wind speed value.
        :return: The shear value (alpha), as the inverse exponent of the best fit power law, based on the form:
            $(v1/v2) = (z1/z2)^(1/alpha)$
        :rtype: pandas.Series and float

        METHODOLOGY:
            Derive natural log of elevation and speed data sets
            Derive coefficients of linear best fit along log-log distribution
            Characterise new distribution of speed values based on linear best fit
            Derive 'alpha' based on gradient of first and last best fit points (function works for 2 or more points)
            Return alpha value

        """
        if maximise_data:
            log_heights = np.log(pd.Series(heights).drop(wspds[wspds == 0].index.values.astype(int)))
            log_wspds = np.log(wspds.drop(wspds[wspds == 0].index.values.astype(int)))

        else:
            log_heights = np.log(heights)  # take log of elevations
            log_wspds = np.log(wspds)  # take log of speeds

        coeffs = np.polyfit(log_heights, log_wspds, deg=1)  # get coefficients of linear best fit to log distribution
        if return_coeff:
            return pd.Series([coeffs[0], np.exp(coeffs[1])])
        return coeffs[0]

    @staticmethod
    def _calc_roughness(slope, intercept):
        return e**(-intercept/slope)

    @staticmethod
    def _by_12x24(wspds, heights, min_speed=3, return_data=False, var_name='Shear'):
        tab_12x24 = dist_12x24(wspds[(wspds > min_speed).all(axis=1)].apply(Shear._calc_power_law, heights=heights,
                                                                            axis=1), return_data=True)[1]
        if return_data:
            return plt.plot_12x24_contours(tab_12x24, label=(var_name, 'mean')), tab_12x24
        return plt.plot_12x24_contours(tab_12x24, label=(var_name, 'mean'))

    @staticmethod
    def scale(wspd,  height, shear_to, alpha=None, roughness=None, calc_method='power_law'):
        """
        Scales wind speeds from one height to another given a value of alpha or roughness coefficient (zo)

        :param wspd: Wind speed time series to apply shear to.
        :type wspd: pandas.Series
        :param height: height of above wspds.
        :type height: float
        :param shear_to: Height to which wspd should be scaled to.
        :type shear_to: float
        :param alpha: Shear exponent to be used when scaling wind speeds.
        :type alpha: Float
        :param roughness: Roughness coefficient to be used when scaling wind speeds.
        :type roughness: float
        :param calc_method: calculation method used to scale the wind speed.
                Using either:   1) 'power_law' :    $(v1/v2) = (z1/z2)^(1/alpha)$
                                2) 'log_law':       $v2 = (ln(z2/z0)/ln(z1/z0))v1$
        :type calc_method: string
        :return: a pandas series of the scaled wind speed
        :return: pandas.Series or float

        **Example Usage**
        ::

           # Scale wind speeds using exponents

           # Specify alpha to use
           alpha_value = .2

           # Specify roughness coefficient to use
           zo = .03

           height = 40
           shear_to = 80

           scaled_by_power_law = bw.Shear.scale(data['Spd40mN'], height, shear_to, alpha=alpha_value)
           scaled_by_log_law = bw.Shear.scale(data['Spd40mN'], height, shear_to, roughness=zo, calc_method='log_law')

        """
        return Shear._scale(wspds=wspd, height=height, shear_to=shear_to, calc_method=calc_method,
                            alpha=alpha, roughness=roughness)

    @staticmethod
    def _scale(wspds, height, shear_to, calc_method='power_law', alpha=None, roughness=None, origin=None):
        """
        Private function for execution of scale()
        """
        if not isinstance(wspds, pd.Series):
            wspds = pd.Series(wspds)

        if calc_method == 'power_law':
            scale_factor = (shear_to / height) ** alpha
            scaled_wspds = wspds * scale_factor

        elif calc_method == 'log_law':
            if origin == 'TimeSeries':
                scaled_wspds = Shear._log_roughness_scale(wspds=wspds, height=height,
                                                          shear_to=shear_to, roughness=roughness)
            else:
                scaled_wspds = wspds.apply(Shear._log_roughness_scale, args=(height, shear_to, roughness))
        else:
            raise ValueError("Please enter a valid calculation method, either 'power_law' or 'log_law'.")

        return scaled_wspds

    @staticmethod
    def _apply(self, wspds, height, shear_to, wdir=None):
        scaled_wspds = pd.Series([])
        result = pd.Series([])

        if self.origin == 'TimeSeries':

            if self.calc_method == 'power_law':
                df = pd.concat([wspds, self.alpha], axis=1).dropna()
                scaled_wspds = Shear._scale(wspds=df.iloc[:, 0], height=height, shear_to=shear_to,
                                            calc_method='power_law', alpha=df.iloc[:, 1])

            else:
                df = pd.concat([wspds, self.roughness], axis=1).dropna()
                scaled_wspds = Shear._scale(wspds=df.iloc[:, 0], height=height, shear_to=shear_to,
                                            calc_method=self.calc_method,
                                            roughness=self._roughness, origin=self.origin)

            result = scaled_wspds.dropna()

        if self.origin == 'TimeOfDay':

            if self.calc_method == 'power_law':
                filled_alpha = Shear._fill_df_12x24(self.alpha)

            else:
                filled_roughness = Shear._fill_df_12x24(self._roughness)
                filled_alpha = filled_roughness

            df_wspds = [[None for y in range(12)] for x in range(24)]
            f = FloatProgress(min=0, max=24 * 12, description='Calculating', bar_style='success')
            display(f)

            for i in range(0, 24):

                for j in range(0, 12):

                    if i == 23:
                        df_wspds[i][j] = wspds[
                            (wspds.index.time >= filled_alpha.index[i]) & (wspds.index.month == j + 1)]
                    else:
                        df_wspds[i][j] = wspds[
                            (wspds.index.time >= filled_alpha.index[i]) & (wspds.index.time < filled_alpha.index[i + 1])
                            & (wspds.index.month == j + 1)]

                    if self.calc_method == 'power_law':
                        df_wspds[i][j] = Shear._scale(df_wspds[i][j], shear_to=shear_to, height=height,
                                                      alpha=filled_alpha.iloc[i, j], calc_method=self.calc_method)

                    else:
                        df_wspds[i][j] = Shear._scale(df_wspds[i][j], shear_to=shear_to, height=height,
                                                      roughness=filled_roughness.iloc[i, j],
                                                      calc_method=self.calc_method)

                    scaled_wspds = pd.concat([scaled_wspds, df_wspds[i][j]], axis=0)
                    f.value += 1

            result = scaled_wspds.sort_index()
            f.close()

        if self.origin == 'BySector':

            # initialise series for later use
            bin_edges = pd.Series([])
            by_sector = pd.Series([])

            if self.calc_method == 'power_law':
                direction_bins = self.alpha
            else:
                direction_bins = self._roughness

            # join wind speeds and directions together in DataFrame
            df = pd.concat([wspds, wdir], axis=1)
            df.columns = ['Unscaled_Wind_Speeds', 'Wind_Direction']

            # get directional bin edges from Shear.by_sector output
            for i in range(self.sectors):
                bin_edges[i] = float(re.findall(r"[-+]?\d*\.\d+|\d+", direction_bins.index[i])[0])
                if i == self.sectors - 1:
                    bin_edges[i + 1] = -float(re.findall(r"[-+]?\d*\.\d+|\d+", direction_bins.index[i])[1])

            for i in range(0, self.sectors):
                if bin_edges[i] > bin_edges[i + 1]:
                    by_sector[i] = df[
                        (df['Wind_Direction'] >= bin_edges[i]) | (df['Wind_Direction'] < bin_edges[i + 1])]

                elif bin_edges[i + 1] == 360:
                    by_sector[i] = df[(df['Wind_Direction'] >= bin_edges[i])]

                else:
                    by_sector[i] = df[
                        (df['Wind_Direction'] >= bin_edges[i]) & (df['Wind_Direction'] < bin_edges[i + 1])]

                by_sector[i].columns = ['Unscaled_Wind_Speeds', 'Wind_Direction']

                if self.calc_method == 'power_law':
                    scaled_wspds[i] = Shear._scale(wspds=by_sector[i]['Unscaled_Wind_Speeds'], height=height,
                                                   shear_to=shear_to,
                                                   calc_method=self.calc_method, alpha=self.alpha[i])

                elif self.calc_method == 'log_law':
                    scaled_wspds[i] = Shear._scale(wspds=by_sector[i]['Unscaled_Wind_Speeds'], height=height,
                                                   shear_to=shear_to,
                                                   calc_method=self.calc_method,
                                                   roughness=self._roughness[i])

                if i == 0:
                    result = scaled_wspds[i]
                else:
                    result = pd.concat([result, scaled_wspds[i]], axis=0)

            result.sort_index(axis='index', inplace=True)

        if self.origin == 'Average':

            if wdir is not None:
                warnings.warn('Warning: Wind direction will not be accounted for when calculating scaled wind speeds.'
                              ' The shear exponents for this object were not calculated by sector. '
                              'Check the origin of the object using ".origin". ')

            if self.calc_method == 'power_law':
                result = Shear._scale(wspds=wspds, height=height, shear_to=shear_to,
                                      calc_method=self.calc_method, alpha=self.alpha)

            elif self.calc_method == 'log_law':
                result = Shear._scale(wspds=wspds, height=height, shear_to=shear_to,
                                      calc_method=self.calc_method, roughness=self._roughness)

        new_name = wspds.name + '_scaled_to_' + str(shear_to) + 'm'
        result.rename(new_name, inplace=True)
        return result

    @staticmethod
    def _fill_df_12x24(data):
        """
        Fills a pandas.DataFrame or Series to be a 12 month x 24 hour pandas.DataFrame by duplicating entries.
        Used for plotting TimeOfDay shear.

        :param data: pandas.DataFrame or Series to be turned into a 12x24 dataframe
        :type data: pandas.Series or pandas.DataFrame.
        :return: 12x24 pandas.DataFrame

        """
        # create copy for later use
        df_copy = data.copy()
        interval = int(24 / len(data))
        # set index for new data frame to deal with less than 24 sectors
        idx = pd.date_range('2017-01-01 00:00', '2017-01-01 23:00', freq='1H')

        # create new dataframe with 24 rows only interval number of unique values
        df = pd.DataFrame(index=pd.DatetimeIndex(idx).time, columns=df_copy.columns)
        df = pd.concat(
            [(df[df_copy.index[0].hour:]), (df[:df_copy.index[0].hour])],
            axis=0)

        for i in range(0, len(df_copy)):
            df.iloc[i * interval:(i + 1) * interval, :] = pd.DataFrame(df_copy.iloc[i, :]).values.T

        df.sort_index(inplace=True)
        df_copy.sort_index(inplace=True)

        if len(df.columns) == 1:
            df_12x24 = pd.DataFrame([[None for y in range(12)] for x in range(24)])
            df_12x24.index = df.index
            for i in range(12):
                df_12x24.iloc[:, i] = df.iloc[:, 0]
            df = df_12x24

        return df

    @staticmethod
    def _data_prep(wspds, heights, min_speed, maximise_data=False):

        if not isinstance(wspds, pd.DataFrame):
            wspds = pd.DataFrame(wspds).T

        if len(wspds.columns) != len(heights):
            Shear._unequal_wspd_heights_error_msg(wspds, heights)

        cvg = None
        if isinstance(wspds.index, pd.DatetimeIndex):
            if maximise_data is False:
                cvg = coverage(wspds[wspds > min_speed].dropna(), period='1AS').sum()[1]
            else:
                _wspds = wspds[wspds > min_speed]
                count = _wspds.count(axis=1)
                count = count[count >= 2]
                count.rename('count', inplace=True)
                cvg = coverage(count, period='1AS').sum()

        wspds = wspds[wspds > min_speed].dropna()

        return wspds, cvg

    @staticmethod
    def _unequal_wspd_heights_error_msg(wspds, heights):
        raise ValueError('An equal number of wind speed data series and heights is required. ' +
                         str(len(wspds.columns)) + ' wind speed(s) and ' +
                         str(len(heights)) + ' height(s) were given.')

    @staticmethod
    def _create_info(self, heights, min_speed, cvg, direction_bin_array=None, segments_per_day=None,
                     segment_start_time=None):
        """
        Create the info dict that is returned to the user.

        :param self:
        :param heights:
        :param min_speed:
        :param cvg:
        :param direction_bin_array:
        :param segments_per_day:
        :param segment_start_time:
        :return:
        """

        info = {}
        input_data = {}
        output_data = {}
        input_wind_speeds = {'heights': heights, 'column_names': list(self.wspds.columns.values),
                             'min_spd': min_speed}
        input_data['input_wind_speeds'] = input_wind_speeds
        input_data['calculation_method'] = self.calc_method
        if cvg is not None:
            output_data['concurrent_period'] = float("{:.3f}".format(cvg))

        if self.origin == 'TimeOfDay':
            input_data['segments_per_day'] = int(segments_per_day)
            input_data['segment_start_time'] = int(segment_start_time)

        if self.origin == 'BySector':
            input_wind_dir = {'heights': None,
                              'column_names': str(self.wdir.name)}
            input_data['input_wind_dir'] = input_wind_dir
            input_data['sectors'] = self.sectors
            input_data['direction_bins'] = direction_bin_array

            if self.calc_method == 'power_law':
                output_data['alpha'] = self.alpha
                output_data['alpha_count'] = self.alpha_count
            if self.calc_method == 'log_law':
                output_data['roughness'] = self.roughness
                output_data['roughness_count'] = self.roughness_count

        if self.calc_method == 'power_law':
            output_data['alpha'] = self.alpha
        if self.calc_method == 'log_law':
            output_data['roughness'] = self.roughness
            
        info['input data'] = input_data
        info['output data'] = output_data

        return info

import pandas as pd
import numpy as np
import datetime
import calendar
from math import e
from brightwind.analyse import plot as plt
# noinspection PyProtectedMember
from brightwind.analyse.analyse import dist_by_dir_sector, dist_12x24, coverage, _convert_df_to_series
from ipywidgets import FloatProgress
from IPython.display import display
from IPython.display import clear_output
import re
import warnings

pd.options.mode.chained_assignment = None

__all__ = ['Shear']


class Shear:

    class TimeSeries:

        def __init__(self, wspds, heights, min_speed=3, calc_method='power_law', max_plot_height=None,
                     maximise_data=False):
            """
            Calculates alpha, using the power law, or the roughness coefficient, using the log law, for each timestamp
            of a wind series.

           :param wspds: pandas DataFrame, list of pandas.Series or list of wind speeds to be used for calculating shear.
           :type wspds:  pandas.DataFrame, list of pandas.Series or list.
           :param heights: List of anemometer heights.
           :type heights: list
           :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.
           :type min_speed: float
           :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                              (returns the roughness coefficient).
           :type calc_method: str
           :param max_plot_height: height to which the wind profile plot is extended.
           :type max_plot_height: float
           :param maximise_data: If maximise_data is True, calculations will be carried out on all data where two or
                                 more anemometers readings exist for a timestamp. If False, calculations will only be
                                 carried out on timestamps where readings exist for all anemometers.
           :type maximise_data: Boolean
           :return TimeSeries object containing calculated alpha/roughness coefficient values, a plot
                   and other data.
           :rtype TimeSeries object

           **Example usage**
           ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Using with a DataFrame of wind speeds
                timeseries_power_law = bw.Shear.TimeSeries(anemometers, heights, maximise_data=True)
                timeseries_log_law = bw.Shear.TimeSeries(anemometers, heights, calc_method='log_law',
                                                         max_plot_height=120)

                # Get the alpha or roughness values calculated
                timeseries_power_law.alpha
                timeseries_log_law.roughness

                # View plot
                timeseries_power_law.plot
                timeseries_log_law.plot

                # View input anemometer data
                timeseries_power_law.wspds
                timeseries_log_law.wspds

                # View other information
                pprint.pprint(timeseries_power_law.info)
                pprint.pprint(timeseries_log_law.info)

           """
            print('This may take a while...')

            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed, maximise_data=maximise_data)

            if calc_method == 'power_law':
                alpha_c = (wspds[(wspds > min_speed).all(axis=1)].apply(Shear._calc_power_law, heights=heights,
                                                                        return_coeff=True,
                                                                        maximise_data=maximise_data, axis=1))
                alpha = pd.Series(alpha_c.iloc[:, 0], name='alpha')
                self._alpha = alpha

            elif calc_method == 'log_law':
                slope_intercept = (wspds[(wspds > min_speed).all(axis=1)].apply(Shear._calc_log_law, heights=heights,
                                                                                return_coeff=True,
                                                                                maximise_data=maximise_data, axis=1))
                slope = slope_intercept.iloc[:, 0]
                intercept = slope_intercept.iloc[:, 1]
                roughness_coefficient = pd.Series(Shear._calc_roughness(slope=slope, intercept=intercept),
                                                  name='roughness_coefficient')
                self._roughness = roughness_coefficient

            clear_output()
            avg_plot = Shear.Average(wspds=wspds, heights=heights, calc_method=calc_method,
                                     max_plot_height=max_plot_height)

            self.origin = 'TimeSeries'
            self.calc_method = calc_method
            self.wspds = wspds
            self.plot = avg_plot.plot
            self.info = Shear._create_info(self, heights=heights, cvg=cvg, min_speed=min_speed)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, height, shear_to):
            """"
            Applies shear calculated to a wind speed time series and scales wind speed from one height to
            another for each matching timestamp.

           :param self: TimeSeries object to use when applying shear to the data.
           :type self: TimeSeries object
           :param wspds: Wind speed time series to apply shear to.
           :type wspds: pandas.Series
           :param height: height of above wspds.
           :type height: float
           :param shear_to: height to which wspds should be scaled to.
           :type shear_to: float
           :return: a pandas.Series of the scaled wind speeds.
           :rtype: pandas.Series

            **Example Usage**
            ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Get power law object
                timeseries_power_law = bw.Shear.TimeSeries(anemometers, heights)
                timeseries_log_law = bw.Shear.TimeSeries(anemometers, heights, calc_method='log_law')

                # Scale wind speeds using calculated exponents
                timeseries_power_law.apply(data['Spd40mN'], height=40, shear_to=70)
                timeseries_log_law.apply(data['Spd40mN'], height=40, shear_to=70)
               """

            return Shear._apply(self, wspds, height, shear_to)

    class TimeOfDay:

        def __init__(self, wspds, heights, min_speed=3, calc_method='power_law', by_month=True, segment_start_time=7,
                     segments_per_day=24, plot_type='line'):
            """
            Calculates alpha, using the power law, or the roughness coefficient, using the log law, for a wind series
            binned by time of the day and (optionally by) month, depending on the user's inputs. The alpha/roughness
            coefficient values are calculated based on the average wind speeds at each measurement height in each bin.

            :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating
             shear.
            :type wspds:  pandas.DataFrame, list of pandas.Series or list.
            :param heights: List of anemometer heights..
            :type heights: list
            :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3
            :type min_speed: float
            :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                                (returns the roughness coefficient).
            :type calc_method: str
            :param by_month: If True, calculate alpha or roughness coefficient values for each daily segment and month.
                             If False, average alpha or roughness coefficient values are calculated for each daily
                             segment across all months.
            :type by_month: Boolean
            :param segment_start_time: Starting time for first segment.
            :type segment_start_time: int
            :param segments_per_day: Number of segments into which each 24 period is split. Must be a divisor of 24.
            :type segments_per_day: int
            :param plot_type: Type of plot to be generated. Options include 'line', 'step' and '12x24'.
            :type plot_type: str
            :return: TimeOfDay object containing calculated alpha/roughness coefficient values, a plot
                     and other data.
            :rtype: TimeOfDay object

            **Example usage**
            ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Using with a DataFrame of wind speeds
                timeofday_power_law = bw.Shear.TimeOfDay(anemometers, heights, daily_segments=2, segment_start_time=7)
                timeofday_log_law = bw.Shear.TimeOfDay(anemometers, heights, calc_method='log_law', by_month=False)

                # Get alpha or roughness values calculated
                timeofday_power_law.alpha
                timeofday_log_law.roughness

                # View plot
                timeofday_power_law.plot
                timeofday_log_law.plot

                # View input data
                timeofday_power_law.wspds
                timeofday_log_law.wspds

                # View other information
                pprint.pprint(timeofday_power_law.info)
                pprint.pprint(timeofday_log_law.info)

            """

            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed)

            # initialise empty series for later use
            start_times = pd.Series([])
            time_wspds = pd.Series([])
            mean_time_wspds = pd.Series([])
            c = pd.Series([])
            slope = pd.Series([])
            intercept = pd.Series([])
            alpha = pd.Series([])
            roughness = pd.Series([])
            slope_df = pd.DataFrame([])
            intercept_df = pd.DataFrame([])
            roughness_df = pd.DataFrame([])
            alpha_df = pd.DataFrame([])

            # time of day shear calculations
            interval = int(24 / segments_per_day)

            if by_month is False and plot_type == '12x24':
                raise ValueError("12x24 plot is only possible when 'by_month=True'")

            if not int(segment_start_time) % 1 == 0:
                raise ValueError("'segment_start_time' must be an integer between 0 and 24'")

            if not (24 % segments_per_day == 0) | (segments_per_day == 1):
                raise ValueError("'segments_per_day' must be a divisor of 24'")

            segment_start_time = str(segment_start_time)
            start_times[0] = datetime.datetime.strptime(segment_start_time, '%H')
            dt = datetime.timedelta(hours=interval)

            # extract wind speeds for each daily segment
            for i in range(1, segments_per_day):
                start_times[i] = start_times[i - 1] + dt

            # extract wind speeds for each month
            months_tot = pd.unique(wspds.index.month.values)
            for j in months_tot:

                anemometers_df = wspds[wspds.index.month == j]
                for i in range(0, segments_per_day):

                    if segments_per_day == 1:
                        mean_time_wspds[i] = anemometers_df.mean().dropna()

                    elif i == segments_per_day - 1:
                        start_times[i] = start_times[i].strftime("%H:%M:%S")
                        start = str(start_times[i].time())
                        end = str(start_times[0].time())
                        time_wspds[i] = pd.DataFrame(anemometers_df).between_time(start, end, include_end=False)
                        mean_time_wspds[i] = time_wspds[i][(time_wspds[i] > min_speed).all(axis=1)].mean().dropna()

                    else:
                        start_times[i] = start_times[i].strftime("%H:%M:%S")
                        start = str(start_times[i].time())
                        end = str(start_times[i + 1].time())
                        time_wspds[i] = pd.DataFrame(anemometers_df).between_time(start, end, include_end=False)
                        mean_time_wspds[i] = time_wspds[i][(time_wspds[i] > min_speed).all(axis=1)].mean().dropna()

                # calculate shear
                if calc_method == 'power_law':
                    for i in range(0, len(mean_time_wspds)):
                        alpha[i], c[i] = Shear._calc_power_law(mean_time_wspds[i].values, heights, return_coeff=True)
                    alpha_df = pd.concat([alpha_df, alpha], axis=1)

                if calc_method == 'log_law':
                    for i in range(0, len(mean_time_wspds)):
                        slope[i], intercept[i] = Shear._calc_log_law(mean_time_wspds[i].values, heights,
                                                                     return_coeff=True)
                        roughness[i] = Shear._calc_roughness(slope=slope[i], intercept=intercept[i])
                    roughness_df = pd.concat([roughness_df, roughness], axis=1)
                    slope_df = pd.concat([slope_df, slope], axis=1)
                    intercept_df = pd.concat([intercept_df, intercept], axis=1)

            # error check
            if mean_time_wspds.shape[0] == 0:
                raise ValueError('None of the input wind speeds are greater than the min_speed, cannot calculate shear')

            if calc_method == 'power_law':
                alpha_df.index = start_times
                alpha_df.index = alpha_df.index.time
                alpha_df.sort_index(inplace=True)

                if by_month is True:
                    alpha_df.columns = [calendar.month_abbr[month] for month in months_tot]
                    self.plot = plt.plot_shear_time_of_day(Shear._fill_df_12x24(alpha_df), calc_method=calc_method,
                                                           plot_type=plot_type)

                else:
                    n_months = len(alpha_df.columns.values)
                    alpha_df = pd.DataFrame(alpha_df.mean(axis=1))
                    alpha_df.columns = [str(n_months) + ' Month Average']
                    df_in = pd.DataFrame((Shear._fill_df_12x24(alpha_df)).iloc[:, 0])
                    df_in.columns = [str(n_months) + ' Month Average']
                    self.plot = plt.plot_shear_time_of_day(df_in, calc_method=calc_method, plot_type=plot_type)

                alpha_df.index.name = 'segment_start_time'
                self._alpha = alpha_df

            if calc_method == 'log_law':
                roughness_df.index = slope_df.index = intercept_df.index = start_times
                roughness_df.index = slope_df.index = intercept_df.index = roughness_df.index.time
                roughness_df.sort_index(inplace=True)

                slope_df.sort_index(inplace=True)
                intercept_df.sort_index(inplace=True)

                if by_month is True:
                    roughness_df.columns = slope_df.columns = intercept_df.columns = \
                                                                    [calendar.month_abbr[month] for month in months_tot]
                    self.plot = plt.plot_shear_time_of_day(Shear._fill_df_12x24(roughness_df),
                                                           calc_method=calc_method, plot_type=plot_type)
                else:
                    n_months = len(slope_df.columns.values)
                    slope_df = pd.DataFrame(slope_df.mean(axis=1))
                    intercept_df = pd.DataFrame(intercept_df.mean(axis=1))
                    roughness_df = pd.DataFrame(roughness_df.mean(axis=1))
                    roughness_df.columns = slope_df.columns = intercept_df.columns = \
                                                                            [str(len(months_tot)) + '_month_average']
                    df_in = pd.DataFrame(Shear._fill_df_12x24(roughness_df).iloc[:, 0])
                    df_in.columns = [str(n_months) + ' Month Average']
                    self.plot = plt.plot_shear_time_of_day(df_in, calc_method=calc_method, plot_type=plot_type)

                roughness_df.index.name = 'segment_start_time'
                self._roughness = roughness_df

            self.calc_method = calc_method
            self.wspds = wspds
            self.origin = 'TimeOfDay'
            self.info = Shear._create_info(self, heights=heights, cvg=cvg, min_speed=min_speed,
                                           segment_start_time=segment_start_time, segments_per_day=segments_per_day)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, height, shear_to):
            """
            Applies shear calculated to a wind speed time series by time of day (and optionally by month) to scale
            wind speed from one height to another.

           :param self: TimeOfDay object to use when applying shear to the data.
           :type self: TimeOfDay object
           :param wspds: Wind speed time series to apply shear to.
           :type wspds: pandas.Series
           :param height: height of above wspds.
           :type height: float
           :param shear_to: height to which wspds should be scaled.
           :type shear_to: float
           :return: a pandas.Series of the scaled wind speeds.
           :rtype: pandas.Series

            **Example Usage**
            ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Get power law object
                timeofday_power_law = bw.Shear.TimeOfDay(anemometers, heights)
                timeofday_log_law = bw.Shear.TimeOfDay(anemometers, heights, calc_method='log_law')

                # Scale wind speeds using calculated exponents
                timeofday_power_law.apply(data['Spd40mN'], height=40, shear_to=70)
                timeofday_log_law.apply(data['Spd40mN'], height=40, shear_to=70)

            """

            return Shear._apply(self, wspds, height, shear_to)

    class Average:

        def __init__(self, wspds, heights, min_speed=3, calc_method='power_law', plot_both=False, max_plot_height=None):
            """
             Calculates alpha, using the power law, or the roughness coefficient, using the log law, based on the
             average wind speeds of each supplied time series.

            :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating
             shear.
            :type wspds:  pandas.DataFrame, list of pandas.Series or list.
            :param heights: List of anemometer heights
            :type heights: list
            :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.
            :type min_speed: float
            :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                                      (returns the roughness coefficient).
            :type calc_method: str
            :param max_plot_height: height to which the wind profile plot is extended.
            :type max_plot_height: float
            :return:  Average object containing calculated alpha/roughness coefficient values, a plot and other data.
            :rtype: Average object

            **Example usage**
            ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Using with a DataFrame of wind speeds
                average_power_law = bw.Shear.Average(anemometers, heights)
                average_log_law = bw.Shear.Average(anemometers, heights, calc_method='log_law', max_plot_height=120)

                # Get the alpha or roughness values calculated
                average_power_law.alpha
                average_log_law.roughness

                # View plot
                average_power_law.plot
                average_log_law.plot

                # View input data
                average_power_law.wspds
                average_log_law.wspds

                # View other information
                pprint.pprint(average_power_law.info)
                pprint.pprint(average_log_law.info)

            """

            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed)

            mean_wspds = wspds.mean(axis=0)

            if mean_wspds.shape[0] == 0:
                raise ValueError('None of the input wind speeds are greater than the min_speed, cannot calculate shear')

            if calc_method == 'power_law':
                alpha, c = Shear._calc_power_law(mean_wspds.values, heights, return_coeff=True)
                if plot_both is True:
                    slope, intercept = Shear._calc_log_law(mean_wspds.values, heights, return_coeff=True)
                    self.plot = plt.plot_power_law(plot_both=True, avg_alpha=alpha, avg_c=c, avg_slope=slope,
                                                   avg_intercept=intercept,
                                                   wspds=mean_wspds.values, heights=heights,
                                                   max_plot_height=max_plot_height)
                else:
                    self.plot = plt.plot_power_law(alpha, c, mean_wspds.values, heights,
                                                   max_plot_height=max_plot_height)
                self._alpha = alpha

            elif calc_method == 'log_law':
                slope, intercept = Shear._calc_log_law(mean_wspds.values, heights, return_coeff=True)
                roughness = Shear._calc_roughness(slope=slope, intercept=intercept)
                self._roughness = roughness
                if plot_both is True:
                    alpha, c = Shear._calc_power_law(mean_wspds.values, heights, return_coeff=True)
                    self.plot = plt.plot_power_law(avg_alpha=alpha, avg_c=c, avg_slope=slope, avg_intercept=intercept,
                                                   wspds=mean_wspds.values, heights=heights,
                                                   max_plot_height=max_plot_height)
                else:
                    self.plot = plt.plot_log_law(slope, intercept, mean_wspds.values, heights,
                                                 max_plot_height=max_plot_height)

            else:
                raise ValueError("Please enter a valid calculation method, either 'power_law' or 'log_law'.")

            self.wspds = wspds
            self.origin = 'Average'
            self.calc_method = calc_method
            self.info = Shear._create_info(self, heights=heights, min_speed=min_speed, cvg=cvg)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, height, shear_to):
            """
            Applies average shear calculated to a wind speed time series to scale wind speed from one height to another.

           :param self: Average object to use when applying shear to the data.
           :type self: Average object
           :param wspds: Wind speed time series to apply shear to.
           :type wspds: pandas.Series
           :param height: height of above wspds.
           :type height: float
           :param shear_to: height to which wspds should be scaled to.
           :type shear_to: float
           :return: a pandas.Series of the scaled wind speeds.
           :rtype: pandas.Series

            **Example Usage**
            ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]

                # Get power law object
                average_power_law = bw.Shear.Average(anemometers, heights)
                average_log_law = bw.Shear.Average(anemometers, heights, calc_method='log_law', max_plot_height=120)

               # Scale wind speeds using exponents
               average_power_law.apply(data['Spd40mN'], height=40, shear_to=70)
               average_log_law.apply(data['Spd40mN'], height=40, shear_to=70)

               """
            return Shear._apply(self, wspds, height, shear_to)

    class BySector:

        def __init__(self, wspds, heights, wdir, min_speed=3, calc_method='power_law', sectors=12,
                     direction_bin_array=None, direction_bin_labels=None):
            """
            Calculates alpha, using the power law, or the roughness coefficient, using the log law, for a wind series
            binned by direction. The alpha/roughness coefficient values are calculated based on the average wind speeds
            at each measurement height in each bin.


            :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating
            shear.
            :type wspds: pandas.DataFrame, list of pandas.Series or list.
            :param heights: List of anemometer heights
            :type heights: list
            :param wdir: Wind direction measurements
            :type wdir: pandas.DataFrame or Series
            :param: min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.
            :type: min_speed: float
            :param calc_method: Method to use for calculation, either 'power_law' (returns alpha) or 'log_law'
                                (returns the roughness coefficient).
            :type calc_method: str
            :param sectors: Number of sectors for the shear to be calculated for.
            :type sectors: int
            :param direction_bin_array: Specific array of directional bins to be used. If None, bins are calculated
                                        by 360/sectors.
            :type direction_bin_array: list or array
            :param direction_bin_labels: Labels to be given to the above direction_bin array.
            :type direction_bin_labels: list or array
            :return: BySector object containing calculated alpha/roughness coefficient values, a plot and other data.
            :rtype: BySector object

             **Example usage**
            ::
                import brightwind as bw
                import pprint

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]
                heights = [80, 60, 40]
                directions = data['Dir78mS']

                # Calculate shear exponents using default bins ([345,15,45,75,105,135,165,195,225,255,285,315,345])
                by_sector_power_law= bw.Shear.BySector(anemometers, heights, directions)
                by_sector_log_law= bw.Shear.BySector(anemometers, heights, directions, calc_method='log_law')

                # Calculate shear exponents using custom bins
                custom_bins = [0,30,60,90,120,150,180,210,240,270,300,330,360]
                by_sector_power_law_custom_bins = bw.Shear.BySector(anemometers, heights, directions,
                direction_bin_array=custom_bins)

                # Get alpha or roughness values calculated
                by_sector_power_law.alpha
                by_sector_log_law.roughness

                # View plot
                by_sector_power_law.plot
                by_sector_log_law.plot

                # View input data
                by_sector_power_law.wspds
                by_sector_log_law.wspds

                # View other information
                pprint.pprint(by_sector_power_law.info)
                pprint.pprint(by_sector_log_law.info)

            """
            print('This may take a while...')
            wspds, cvg = Shear._data_prep(wspds=wspds, heights=heights, min_speed=min_speed)

            if direction_bin_array is not None:
                sectors = len(direction_bin_array) - 1

            wdir = _convert_df_to_series(wdir)
            mean_wspds = pd.Series([])
            mean_wspds_df = pd.DataFrame([])
            count_df = pd.DataFrame([])
            count = pd.Series([])

            for i in range(len(wspds.columns)):

                w = wspds.iloc[:, i]
                plot, mean_wspds[i] = dist_by_dir_sector(w, wdir, direction_bin_array=direction_bin_array,
                                                         sectors=sectors,
                                                         aggregation_method='mean', return_data=True)

                plot, count[i] = dist_by_dir_sector(w, wdir, direction_bin_array=direction_bin_array,
                                                    sectors=sectors,
                                                    aggregation_method='count', return_data=True)

                if i == 0:
                    mean_wspds_df = mean_wspds[i].copy()
                    count_df = count[i].copy()
                else:
                    mean_wspds_df = pd.concat([mean_wspds_df, mean_wspds[i]], axis=1)
                    count_df = pd.concat([count_df, count[i]], axis=1)

            count_df = count_df.mean(axis=1)
            wind_rose_plot, wind_rose_dist = dist_by_dir_sector(wspds.iloc[:, 0], wdir,
                                                                direction_bin_array=direction_bin_array,
                                                                sectors=sectors,
                                                                direction_bin_labels=direction_bin_labels,
                                                                return_data=True)
            if calc_method == 'power_law':

                alpha = mean_wspds_df.apply(Shear._calc_power_law, heights=heights, return_coeff=False, axis=1)

                wind_rose_plot, wind_rose_dist = dist_by_dir_sector(wspds.iloc[:, 0], wdir,
                                                                    direction_bin_array=direction_bin_array,
                                                                    sectors=sectors,
                                                                    direction_bin_labels=direction_bin_labels,
                                                                    return_data=True)

                self.alpha_count = count_df
                self._alpha = pd.Series(alpha, name='alpha')
                clear_output()
                self.plot = plt.plot_shear_by_sector(scale_variable=alpha, wind_rose_data=wind_rose_dist,
                                                     calc_method=calc_method)

            elif calc_method == 'log_law':

                slope_intercept = mean_wspds_df.apply(Shear._calc_log_law, heights=heights, return_coeff=True, axis=1)

                slope = slope_intercept.iloc[:, 0]
                intercept = slope_intercept.iloc[:, 1]
                roughness = Shear._calc_roughness(slope=slope, intercept=intercept)
                self.roughness_count = count_df
                self._roughness = pd.Series(roughness, name='roughness_coefficient')
                clear_output()
                self.plot = plt.plot_shear_by_sector(scale_variable=roughness, wind_rose_data=wind_rose_dist,
                                                     calc_method=calc_method)

            else:
                raise ValueError("Please enter a valid calculation method, either 'power_law' or 'log_law'.")

            self.wspds = wspds
            self.wdir = wdir
            self.origin = 'BySector'
            self.sectors = sectors
            self.calc_method = calc_method
            self.info = Shear._create_info(self, heights=heights, cvg=cvg, min_speed=min_speed,
                                           direction_bin_array=direction_bin_array)

        @property
        def alpha(self):
            return self._alpha

        @property
        def roughness(self):
            return self._roughness

        def apply(self, wspds, wdir, height, shear_to):
            """
            Applies shear calculated to a wind speed time series by wind direction to scale
            wind speed from one height to another.

            :param self: BySector object to use when applying shear to the data
            :type self: BySector object
            :param wspds: Wind speed time series to apply shear to.
            :type wspds: pandas.Series
            :param wdir: Wind direction measurements of wspds, only required if shear is to be applied by direction
            sector.
            :type wdir: pandas.Series
            :param height: Height of wspds.
            :type height: float
            :param shear_to: Height to which wspds should be scaled to.
            :type shear_to: float
            :return: A pandas.Series of the scaled wind speeds.
            :rtype: pandas.Series

             **Example Usage**
             ::
                import brightwind as bw

                # Load anemometer data to calculate exponents
                data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)
                anemometers = data[['Spd80mS', 'Spd60mS']]
                heights = [80, 60]
                directions = data[['Dir78mS']]

                # Calculate shear exponents
                by_sector_power_law = bw.Shear.BySector(anemometers, heights, directions)
                by_sector_log_law = bw.Shear.BySector(anemometers, heights, directions, calc_method='log_law')

                # Calculate shear exponents using default bins ([345,15,45,75,105,135,165,195,225,255,285,315,345])
                by_sector_power_law= bw.Shear.BySector(anemometers, heights, directions)

                # Scale wind speeds using exponents
                by_sector_power_law.apply(data['Spd40mN'], data['Dir38mS'], height=40, shear_to=70)
                by_sector_log_law.apply(data['Spd40mN'], data['Dir38mS'], height=40, shear_to=70)

            """

            return Shear._apply(self, wspds=wspds, height=height, shear_to=shear_to, wdir=wdir)

    @staticmethod
    def _log_roughness_scale(wspds, height, shear_to, roughness):
        """
        Scale wind speeds using the logarithmic wind shear law.

        :param wspds: wind speeds at height z1, U1
        :param height: z1
        :param shear_to: z2
        :param roughness: z0
        :return: Scaled wind speeds, U2
        :rtype: pandas.Series or float

        METHODOLOGY:

                                            U2 = (ln(z2/z0)/ln(z1/z0))U1
            Where:
                    - U2 is the wind speed at height z2
                    - U1 is the wind speed at height z1
                    - z1 is the lower height
                    - z2 is the upper height
                    - zo is the roughness coefficient
        """
        scale_factor = np.log(shear_to / roughness) / (np.log(height / roughness))
        scaled_wspds = wspds * scale_factor

        return scaled_wspds

    @staticmethod
    def _calc_log_law(wspds, heights, return_coeff=False, maximise_data=False) -> (np.array, float):
        """
        Derive the best fit logarithmic law line from a given time-step of speed data at 2 or more elevations

        :param wspds: List of wind speeds [m/s]
        :param heights: List of heights [m above ground]. The position of the height in the list must be the same
            position in the list as its corresponding wind speed value.
        :return: The slope and intercept of the best fit line, as defined above
        :rtype: pandas.Series and float

        METHODOLOGY:
            Derive natural log of elevation data sets
            Derive coefficients of linear best fit along ln(heights)- wspds distribution
            Characterise new distribution of speed values based on linear best fit
            Return the slope and the intercept of this linear best fit.
            The slope and intercept can then be used to find the corresponding roughness coefficient, using the
            equivilant laws:

                                                1)  $U(z) = (v/k)*ln(z/zo)$
            which can be rewritten as:
                                                $U(z) = (v/k)*ln(z) - (v/k)ln(zo)$
                                                where zo = e ** (-c/m) of this line

            Where:

                - U(z) is the wind speed at height z
                - v is the friction velocity at the location
                - k is the Von Karmen constant, taken aa .4
                - z is the height
                - zo is the roughness coefficient

                                                2)  $U2 = (ln(z2/z0)/ln(z1/z0))U1$

            """

        if maximise_data:
            log_heights = np.log(
                pd.Series(heights).drop(wspds[wspds == 0].index.values.astype(int)))  # take log of elevations
            wspds = wspds.drop(wspds[wspds == 0].index.values.astype(int))

        else:
            log_heights = np.log(heights)  # take log of elevations

        coeffs = np.polyfit(log_heights, wspds, deg=1)
        if return_coeff:
            return pd.Series([coeffs[0], coeffs[1]])
        return coeffs[0]

    @staticmethod
    def _calc_power_law(wspds, heights, return_coeff=False, maximise_data=False) -> (np.array, float):
        """
        Derive the best fit power law exponent (as 1/alpha) from a given time-step of speed data at 2 or more elevations

        :param wspds: pandas.Series or list of wind speeds [m/s]
        :param heights: List of heights [m above ground]. The position of the height in the list must be the same
            position in the list as its corresponding wind speed value.
        :return: The shear value (alpha), as the inverse exponent of the best fit power law, based on the form:
            $(v1/v2) = (z1/z2)^(1/alpha)$
        :rtype: pandas.Series and float

        METHODOLOGY:
            Derive natural log of elevation and speed data sets
            Derive coefficients of linear best fit along log-log distribution
            Characterise new distribution of speed values based on linear best fit
            Derive 'alpha' based on gradient of first and last best fit points (function works for 2 or more points)
            Return alpha value

        """
        if maximise_data:
            log_heights = np.log(pd.Series(heights).drop(wspds[wspds == 0].index.values.astype(int)))
            log_wspds = np.log(wspds.drop(wspds[wspds == 0].index.values.astype(int)))

        else:
            log_heights = np.log(heights)  # take log of elevations
            log_wspds = np.log(wspds)  # take log of speeds

        coeffs = np.polyfit(log_heights, log_wspds, deg=1)  # get coefficients of linear best fit to log distribution
        if return_coeff:
            return pd.Series([coeffs[0], np.exp(coeffs[1])])
        return coeffs[0]

    @staticmethod
    def _calc_roughness(slope, intercept):
        return e**(-intercept/slope)

    @staticmethod
    def _by_12x24(wspds, heights, min_speed=3, return_data=False, var_name='Shear'):
        tab_12x24 = dist_12x24(wspds[(wspds > min_speed).all(axis=1)].apply(Shear._calc_power_law, heights=heights,
                                                                            axis=1), return_data=True)[1]
        if return_data:
            return plt.plot_12x24_contours(tab_12x24, label=(var_name, 'mean')), tab_12x24
        return plt.plot_12x24_contours(tab_12x24, label=(var_name, 'mean'))

    @staticmethod
    def scale(wspd,  height, shear_to, alpha=None, roughness=None, calc_method='power_law'):
        """
        Scales wind speeds from one height to another given a value of alpha or roughness coefficient (zo)

        :param wspd: Wind speed time series to apply shear to.
        :type wspd: pandas.Series
        :param height: height of above wspds.
        :type height: float
        :param shear_to: Height to which wspd should be scaled to.
        :type shear_to: float
        :param alpha: Shear exponent to be used when scaling wind speeds.
        :type alpha: Float
        :param roughness: Roughness coefficient to be used when scaling wind speeds.
        :type roughness: float
        :param calc_method: calculation method used to scale the wind speed.
                Using either:   1) 'power_law' :    $(v1/v2) = (z1/z2)^(1/alpha)$
                                2) 'log_law':       $v2 = (ln(z2/z0)/ln(z1/z0))v1$
        :type calc_method: string
        :return: a pandas series of the scaled wind speed
        :return: pandas.Series or float

        **Example Usage**
        ::

           # Scale wind speeds using exponents

           # Specify alpha to use
           alpha_value = .2

           # Specify roughness coefficient to use
           zo = .03

           height = 40
           shear_to = 80

           scaled_by_power_law = bw.Shear.scale(data['Spd40mN'], height, shear_to, alpha=alpha_value)
           scaled_by_log_law = bw.Shear.scale(data['Spd40mN'], height, shear_to, roughness=zo, calc_method='log_law')

        """
        return Shear._scale(wspds=wspd, height=height, shear_to=shear_to, calc_method=calc_method,
                            alpha=alpha, roughness=roughness)

    @staticmethod
    def _scale(wspds, height, shear_to, calc_method='power_law', alpha=None, roughness=None, origin=None):
        """
        Private function for execution of scale()
        """
        if not isinstance(wspds, pd.Series):
            wspds = pd.Series(wspds)

        if calc_method == 'power_law':
            scale_factor = (shear_to / height) ** alpha
            scaled_wspds = wspds * scale_factor

        elif calc_method == 'log_law':
            if origin == 'TimeSeries':
                scaled_wspds = Shear._log_roughness_scale(wspds=wspds, height=height,
                                                          shear_to=shear_to, roughness=roughness)
            else:
                scaled_wspds = wspds.apply(Shear._log_roughness_scale, args=(height, shear_to, roughness))
        else:
            raise ValueError("Please enter a valid calculation method, either 'power_law' or 'log_law'.")

        return scaled_wspds

    @staticmethod
    def _apply(self, wspds, height, shear_to, wdir=None):
        scaled_wspds = pd.Series([])
        result = pd.Series([])

        if self.origin == 'TimeSeries':

            if self.calc_method == 'power_law':
                df = pd.concat([wspds, self.alpha], axis=1).dropna()
                scaled_wspds = Shear._scale(wspds=df.iloc[:, 0], height=height, shear_to=shear_to,
                                            calc_method='power_law', alpha=df.iloc[:, 1])

            else:
                df = pd.concat([wspds, self.roughness], axis=1).dropna()
                scaled_wspds = Shear._scale(wspds=df.iloc[:, 0], height=height, shear_to=shear_to,
                                            calc_method=self.calc_method,
                                            roughness=self._roughness, origin=self.origin)

            result = scaled_wspds.dropna()

        if self.origin == 'TimeOfDay':

            if self.calc_method == 'power_law':
                filled_alpha = Shear._fill_df_12x24(self.alpha)

            else:
                filled_roughness = Shear._fill_df_12x24(self._roughness)
                filled_alpha = filled_roughness

            df_wspds = [[None for y in range(12)] for x in range(24)]
            f = FloatProgress(min=0, max=24 * 12, description='Calculating', bar_style='success')
            display(f)

            for i in range(0, 24):

                for j in range(0, 12):

                    if i == 23:
                        df_wspds[i][j] = wspds[
                            (wspds.index.time >= filled_alpha.index[i]) & (wspds.index.month == j + 1)]
                    else:
                        df_wspds[i][j] = wspds[
                            (wspds.index.time >= filled_alpha.index[i]) & (wspds.index.time < filled_alpha.index[i + 1])
                            & (wspds.index.month == j + 1)]

                    if self.calc_method == 'power_law':
                        df_wspds[i][j] = Shear._scale(df_wspds[i][j], shear_to=shear_to, height=height,
                                                      alpha=filled_alpha.iloc[i, j], calc_method=self.calc_method)

                    else:
                        df_wspds[i][j] = Shear._scale(df_wspds[i][j], shear_to=shear_to, height=height,
                                                      roughness=filled_roughness.iloc[i, j],
                                                      calc_method=self.calc_method)

                    scaled_wspds = pd.concat([scaled_wspds, df_wspds[i][j]], axis=0)
                    f.value += 1

            result = scaled_wspds.sort_index()
            f.close()

        if self.origin == 'BySector':

            # initialise series for later use
            bin_edges = pd.Series([])
            by_sector = pd.Series([])

            if self.calc_method == 'power_law':
                direction_bins = self.alpha
            else:
                direction_bins = self._roughness

            # join wind speeds and directions together in DataFrame
            df = pd.concat([wspds, wdir], axis=1)
            df.columns = ['Unscaled_Wind_Speeds', 'Wind_Direction']

            # get directional bin edges from Shear.by_sector output
            for i in range(self.sectors):
                bin_edges[i] = float(re.findall(r"[-+]?\d*\.\d+|\d+", direction_bins.index[i])[0])
                if i == self.sectors - 1:
                    bin_edges[i + 1] = -float(re.findall(r"[-+]?\d*\.\d+|\d+", direction_bins.index[i])[1])

            for i in range(0, self.sectors):
                if bin_edges[i] > bin_edges[i + 1]:
                    by_sector[i] = df[
                        (df['Wind_Direction'] >= bin_edges[i]) | (df['Wind_Direction'] < bin_edges[i + 1])]

                elif bin_edges[i + 1] == 360:
                    by_sector[i] = df[(df['Wind_Direction'] >= bin_edges[i])]

                else:
                    by_sector[i] = df[
                        (df['Wind_Direction'] >= bin_edges[i]) & (df['Wind_Direction'] < bin_edges[i + 1])]

                by_sector[i].columns = ['Unscaled_Wind_Speeds', 'Wind_Direction']

                if self.calc_method == 'power_law':
                    scaled_wspds[i] = Shear._scale(wspds=by_sector[i]['Unscaled_Wind_Speeds'], height=height,
                                                   shear_to=shear_to,
                                                   calc_method=self.calc_method, alpha=self.alpha[i])

                elif self.calc_method == 'log_law':
                    scaled_wspds[i] = Shear._scale(wspds=by_sector[i]['Unscaled_Wind_Speeds'], height=height,
                                                   shear_to=shear_to,
                                                   calc_method=self.calc_method,
                                                   roughness=self._roughness[i])

                if i == 0:
                    result = scaled_wspds[i]
                else:
                    result = pd.concat([result, scaled_wspds[i]], axis=0)

            result.sort_index(axis='index', inplace=True)

        if self.origin == 'Average':

            if wdir is not None:
                warnings.warn('Warning: Wind direction will not be accounted for when calculating scaled wind speeds.'
                              ' The shear exponents for this object were not calculated by sector. '
                              'Check the origin of the object using ".origin". ')

            if self.calc_method == 'power_law':
                result = Shear._scale(wspds=wspds, height=height, shear_to=shear_to,
                                      calc_method=self.calc_method, alpha=self.alpha)

            elif self.calc_method == 'log_law':
                result = Shear._scale(wspds=wspds, height=height, shear_to=shear_to,
                                      calc_method=self.calc_method, roughness=self._roughness)

        new_name = wspds.name + '_scaled_to_' + str(shear_to) + 'm'
        result.rename(new_name, inplace=True)
        return result

    @staticmethod
    def _fill_df_12x24(data):
        """
        Fills a pandas.DataFrame or Series to be a 12 month x 24 hour pandas.DataFrame by duplicating entries.
        Used for plotting TimeOfDay shear.

        :param data: pandas.DataFrame or Series to be turned into a 12x24 dataframe
        :type data: pandas.Series or pandas.DataFrame.
        :return: 12x24 pandas.DataFrame

        """
        # create copy for later use
        df_copy = data.copy()
        interval = int(24 / len(data))
        # set index for new data frame to deal with less than 24 sectors
        idx = pd.date_range('2017-01-01 00:00', '2017-01-01 23:00', freq='1H')

        # create new dataframe with 24 rows only interval number of unique values
        df = pd.DataFrame(index=pd.DatetimeIndex(idx).time, columns=df_copy.columns)
        df = pd.concat(
            [(df[df_copy.index[0].hour:]), (df[:df_copy.index[0].hour])],
            axis=0)

        for i in range(0, len(df_copy)):
            df.iloc[i * interval:(i + 1) * interval, :] = pd.DataFrame(df_copy.iloc[i, :]).values.T

        df.sort_index(inplace=True)
        df_copy.sort_index(inplace=True)

        if len(df.columns) == 1:
            df_12x24 = pd.DataFrame([[None for y in range(12)] for x in range(24)])
            df_12x24.index = df.index
            for i in range(12):
                df_12x24.iloc[:, i] = df.iloc[:, 0]
            df = df_12x24

        return df

    @staticmethod
    def _data_prep(wspds, heights, min_speed, maximise_data=False):

        if not isinstance(wspds, pd.DataFrame):
            wspds = pd.DataFrame(wspds).T

        if len(wspds.columns) != len(heights):
            Shear._unequal_wspd_heights_error_msg(wspds, heights)

        cvg = None
        if isinstance(wspds.index, pd.DatetimeIndex):
            if maximise_data is False:
                cvg = coverage(wspds[wspds > min_speed].dropna(), period='1AS').sum()[1]
            else:
                _wspds = wspds[wspds > min_speed]
                count = _wspds.count(axis=1)
                count = count[count >= 2]
                count.rename('count', inplace=True)
                cvg = coverage(count, period='1AS').sum()

        wspds = wspds[wspds > min_speed].dropna()

        return wspds, cvg

    @staticmethod
    def _unequal_wspd_heights_error_msg(wspds, heights):
        raise ValueError('An equal number of wind speed data series and heights is required. ' +
                         str(len(wspds.columns)) + ' wind speed(s) and ' +
                         str(len(heights)) + ' height(s) were given.')

    @staticmethod
    def _create_info(self, heights, min_speed, cvg, direction_bin_array=None, segments_per_day=None,
                     segment_start_time=None):
        """
        Create the info dict that is returned to the user.

        :param self:
        :param heights:
        :param min_speed:
        :param cvg:
        :param direction_bin_array:
        :param segments_per_day:
        :param segment_start_time:
        :return:
        """

        info = {}
        input_data = {}
        output_data = {}
        input_wind_speeds = {'heights': heights, 'column_names': list(self.wspds.columns.values),
                             'min_spd': min_speed}
        input_data['input_wind_speeds'] = input_wind_speeds
        input_data['calculation_method'] = self.calc_method
        if cvg is not None:
            output_data['concurrent_period'] = float("{:.3f}".format(cvg))

        if self.origin == 'TimeOfDay':
            input_data['segments_per_day'] = int(segments_per_day)
            input_data['segment_start_time'] = int(segment_start_time)

        if self.origin == 'BySector':
            input_wind_dir = {'heights': None,
                              'column_names': str(self.wdir.name)}
            input_data['input_wind_dir'] = input_wind_dir
            input_data['sectors'] = self.sectors
            input_data['direction_bins'] = direction_bin_array

            if self.calc_method == 'power_law':
                output_data['alpha'] = self.alpha
                output_data['alpha_count'] = self.alpha_count
            if self.calc_method == 'log_law':
                output_data['roughness'] = self.roughness
                output_data['roughness_count'] = self.roughness_count

        if self.calc_method == 'power_law':
            output_data['alpha'] = self.alpha
        if self.calc_method == 'log_law':
            output_data['roughness'] = self.roughness
            
        info['input data'] = input_data
        info['output data'] = output_data

        return info

# noinspection PyProtectedMember Calculates alpha, using the power law, or the roughness coefficient, using the log law, for each timestamp             of a wind series.             :param wspds: pandas DataFrame, list of pandas.Series or list of wind speeds to be used for calculating shear.            :type wspds:  pandas.DataFrame, list of pandas.Series or list.            :param heights: List of anemometer heights.            :type heights: list            :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.            :type min_speed: float            :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'                               (returns the roughness coefficient).            :type calc_method: str            :param max_plot_height: height to which the wind profile plot is extended.            :type max_plot_height: float            :param maximise_data: If maximise_data is True, calculations will be carried out on all data where two or                                  more anemometers readings exist for a timestamp. If False, calculations will only be                                  carried out on timestamps where readings exist for all anemometers.            :type maximise_data: Boolean            :return TimeSeries object containing calculated alpha/roughness coefficient values, a plot                    and other data.            :rtype TimeSeries object             **Example usage**            ::                 import brightwind as bw                 import pprint                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]                 heights = [80, 60, 40]                  # Using with a DataFrame of wind speeds                 timeseries_power_law = bw.Shear.TimeSeries(anemometers, heights, maximise_data=True)                 timeseries_log_law = bw.Shear.TimeSeries(anemometers, heights, calc_method='log_law',                                                          max_plot_height=120)                  # Get the alpha or roughness values calculated                 timeseries_power_law.alpha                 timeseries_log_law.roughness                  # View plot                 timeseries_power_law.plot                 timeseries_log_law.plot                  # View input anemometer data                 timeseries_power_law.wspds                 timeseries_log_law.wspds                  # View other information                 pprint.pprint(timeseries_power_law.info)                 pprint.pprint(timeseries_log_law.info) "             Applies shear calculated to a wind speed time series and scales wind speed from one height to             another for each matching timestamp.             :param self: TimeSeries object to use when applying shear to the data.            :type self: TimeSeries object            :param wspds: Wind speed time series to apply shear to.            :type wspds: pandas.Series            :param height: height of above wspds.            :type height: float            :param shear_to: height to which wspds should be scaled to.            :type shear_to: float            :return: a pandas.Series of the scaled wind speeds.            :rtype: pandas.Series              **Example Usage**             ::                 import brightwind as bw                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]                 heights = [80, 60, 40]                  # Get power law object                 timeseries_power_law = bw.Shear.TimeSeries(anemometers, heights)                 timeseries_log_law = bw.Shear.TimeSeries(anemometers, heights, calc_method='log_law')                  # Scale wind speeds using calculated exponents                 timeseries_power_law.apply(data['Spd40mN'], height=40, shear_to=70)                 timeseries_log_law.apply(data['Spd40mN'], height=40, shear_to=70) Calculates alpha, using the power law, or the roughness coefficient, using the log law, for a wind series             binned by time of the day and (optionally by) month, depending on the user's inputs. The alpha/roughness             coefficient values are calculated based on the average wind speeds at each measurement height in each bin.              :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating              shear.             :type wspds:  pandas.DataFrame, list of pandas.Series or list.             :param heights: List of anemometer heights..             :type heights: list             :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3             :type min_speed: float             :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'                                 (returns the roughness coefficient).             :type calc_method: str             :param by_month: If True, calculate alpha or roughness coefficient values for each daily segment and month.                              If False, average alpha or roughness coefficient values are calculated for each daily                              segment across all months.             :type by_month: Boolean             :param segment_start_time: Starting time for first segment.             :type segment_start_time: int             :param segments_per_day: Number of segments into which each 24 period is split. Must be a divisor of 24.             :type segments_per_day: int             :param plot_type: Type of plot to be generated. Options include 'line', 'step' and '12x24'.             :type plot_type: str             :return: TimeOfDay object containing calculated alpha/roughness coefficient values, a plot                      and other data.             :rtype: TimeOfDay object              **Example usage**             ::                 import brightwind as bw                 import pprint                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]                 heights = [80, 60, 40]                  # Using with a DataFrame of wind speeds                 timeofday_power_law = bw.Shear.TimeOfDay(anemometers, heights, daily_segments=2, segment_start_time=7)                 timeofday_log_law = bw.Shear.TimeOfDay(anemometers, heights, calc_method='log_law', by_month=False)                  # Get alpha or roughness values calculated                 timeofday_power_law.alpha                 timeofday_log_law.roughness                  # View plot                 timeofday_power_law.plot                 timeofday_log_law.plot                  # View input data                 timeofday_power_law.wspds                 timeofday_log_law.wspds                  # View other information                 pprint.pprint(timeofday_power_law.info)                 pprint.pprint(timeofday_log_law.info) # initialise empty series for later use # time of day shear calculations # extract wind speeds for each daily segment # extract wind speeds for each month # calculate shear # error check Applies shear calculated to a wind speed time series by time of day (and optionally by month) to scale             wind speed from one height to another.             :param self: TimeOfDay object to use when applying shear to the data.            :type self: TimeOfDay object            :param wspds: Wind speed time series to apply shear to.            :type wspds: pandas.Series            :param height: height of above wspds.            :type height: float            :param shear_to: height to which wspds should be scaled.            :type shear_to: float            :return: a pandas.Series of the scaled wind speeds.            :rtype: pandas.Series              **Example Usage**             ::                 import brightwind as bw                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]                 heights = [80, 60, 40]                  # Get power law object                 timeofday_power_law = bw.Shear.TimeOfDay(anemometers, heights)                 timeofday_log_law = bw.Shear.TimeOfDay(anemometers, heights, calc_method='log_law')                  # Scale wind speeds using calculated exponents                 timeofday_power_law.apply(data['Spd40mN'], height=40, shear_to=70)                 timeofday_log_law.apply(data['Spd40mN'], height=40, shear_to=70) Calculates alpha, using the power law, or the roughness coefficient, using the log law, based on the              average wind speeds of each supplied time series.              :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating              shear.             :type wspds:  pandas.DataFrame, list of pandas.Series or list.             :param heights: List of anemometer heights             :type heights: list             :param min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.             :type min_speed: float             :param calc_method: method to use for calculation, either 'power_law' (returns alpha) or 'log_law'                                       (returns the roughness coefficient).             :type calc_method: str             :param max_plot_height: height to which the wind profile plot is extended.             :type max_plot_height: float             :return:  Average object containing calculated alpha/roughness coefficient values, a plot and other data.             :rtype: Average object              **Example usage**             ::                 import brightwind as bw                 import pprint                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]                 heights = [80, 60, 40]                  # Using with a DataFrame of wind speeds                 average_power_law = bw.Shear.Average(anemometers, heights)                 average_log_law = bw.Shear.Average(anemometers, heights, calc_method='log_law', max_plot_height=120)                  # Get the alpha or roughness values calculated                 average_power_law.alpha                 average_log_law.roughness                  # View plot                 average_power_law.plot                 average_log_law.plot                  # View input data                 average_power_law.wspds                 average_log_law.wspds                  # View other information                 pprint.pprint(average_power_law.info)                 pprint.pprint(average_log_law.info) Applies average shear calculated to a wind speed time series to scale wind speed from one height to another.             :param self: Average object to use when applying shear to the data.            :type self: Average object            :param wspds: Wind speed time series to apply shear to.            :type wspds: pandas.Series            :param height: height of above wspds.            :type height: float            :param shear_to: height to which wspds should be scaled to.            :type shear_to: float            :return: a pandas.Series of the scaled wind speeds.            :rtype: pandas.Series              **Example Usage**             ::                 import brightwind as bw                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]                 heights = [80, 60, 40]                  # Get power law object                 average_power_law = bw.Shear.Average(anemometers, heights)                 average_log_law = bw.Shear.Average(anemometers, heights, calc_method='log_law', max_plot_height=120)                 # Scale wind speeds using exponents                average_power_law.apply(data['Spd40mN'], height=40, shear_to=70)                average_log_law.apply(data['Spd40mN'], height=40, shear_to=70) Calculates alpha, using the power law, or the roughness coefficient, using the log law, for a wind series             binned by direction. The alpha/roughness coefficient values are calculated based on the average wind speeds             at each measurement height in each bin.               :param wspds: pandas.DataFrame, list of pandas.Series or list of wind speeds to be used for calculating             shear.             :type wspds: pandas.DataFrame, list of pandas.Series or list.             :param heights: List of anemometer heights             :type heights: list             :param wdir: Wind direction measurements             :type wdir: pandas.DataFrame or Series             :param: min_speed: Only speeds higher than this would be considered for calculating shear, default is 3.             :type: min_speed: float             :param calc_method: Method to use for calculation, either 'power_law' (returns alpha) or 'log_law'                                 (returns the roughness coefficient).             :type calc_method: str             :param sectors: Number of sectors for the shear to be calculated for.             :type sectors: int             :param direction_bin_array: Specific array of directional bins to be used. If None, bins are calculated                                         by 360/sectors.             :type direction_bin_array: list or array             :param direction_bin_labels: Labels to be given to the above direction_bin array.             :type direction_bin_labels: list or array             :return: BySector object containing calculated alpha/roughness coefficient values, a plot and other data.             :rtype: BySector object               **Example usage**             ::                 import brightwind as bw                 import pprint                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS','Spd40mS']]                 heights = [80, 60, 40]                 directions = data['Dir78mS']                  # Calculate shear exponents using default bins ([345,15,45,75,105,135,165,195,225,255,285,315,345])                 by_sector_power_law= bw.Shear.BySector(anemometers, heights, directions)                 by_sector_log_law= bw.Shear.BySector(anemometers, heights, directions, calc_method='log_law')                  # Calculate shear exponents using custom bins                 custom_bins = [0,30,60,90,120,150,180,210,240,270,300,330,360]                 by_sector_power_law_custom_bins = bw.Shear.BySector(anemometers, heights, directions,                 direction_bin_array=custom_bins)                  # Get alpha or roughness values calculated                 by_sector_power_law.alpha                 by_sector_log_law.roughness                  # View plot                 by_sector_power_law.plot                 by_sector_log_law.plot                  # View input data                 by_sector_power_law.wspds                 by_sector_log_law.wspds                  # View other information                 pprint.pprint(by_sector_power_law.info)                 pprint.pprint(by_sector_log_law.info) Applies shear calculated to a wind speed time series by wind direction to scale             wind speed from one height to another.              :param self: BySector object to use when applying shear to the data             :type self: BySector object             :param wspds: Wind speed time series to apply shear to.             :type wspds: pandas.Series             :param wdir: Wind direction measurements of wspds, only required if shear is to be applied by direction             sector.             :type wdir: pandas.Series             :param height: Height of wspds.             :type height: float             :param shear_to: Height to which wspds should be scaled to.             :type shear_to: float             :return: A pandas.Series of the scaled wind speeds.             :rtype: pandas.Series               **Example Usage**              ::                 import brightwind as bw                  # Load anemometer data to calculate exponents                 data = bw.load_csv(C:\\Users\\Stephen\\Documents\\Analysis\\demo_data)                 anemometers = data[['Spd80mS', 'Spd60mS']]                 heights = [80, 60]                 directions = data[['Dir78mS']]                  # Calculate shear exponents                 by_sector_power_law = bw.Shear.BySector(anemometers, heights, directions)                 by_sector_log_law = bw.Shear.BySector(anemometers, heights, directions, calc_method='log_law')                  # Calculate shear exponents using default bins ([345,15,45,75,105,135,165,195,225,255,285,315,345])                 by_sector_power_law= bw.Shear.BySector(anemometers, heights, directions)                  # Scale wind speeds using exponents                 by_sector_power_law.apply(data['Spd40mN'], data['Dir38mS'], height=40, shear_to=70)                 by_sector_log_law.apply(data['Spd40mN'], data['Dir38mS'], height=40, shear_to=70) Scale wind speeds using the logarithmic wind shear law.          :param wspds: wind speeds at height z1, U1         :param height: z1         :param shear_to: z2         :param roughness: z0         :return: Scaled wind speeds, U2         :rtype: pandas.Series or float          METHODOLOGY:                                              U2 = (ln(z2/z0)/ln(z1/z0))U1             Where:                     - U2 is the wind speed at height z2                     - U1 is the wind speed at height z1                     - z1 is the lower height                     - z2 is the upper height                     - zo is the roughness coefficient Derive the best fit logarithmic law line from a given time-step of speed data at 2 or more elevations          :param wspds: List of wind speeds [m/s]         :param heights: List of heights [m above ground]. The position of the height in the list must be the same             position in the list as its corresponding wind speed value.         :return: The slope and intercept of the best fit line, as defined above         :rtype: pandas.Series and float          METHODOLOGY:             Derive natural log of elevation data sets             Derive coefficients of linear best fit along ln(heights)- wspds distribution             Characterise new distribution of speed values based on linear best fit             Return the slope and the intercept of this linear best fit.             The slope and intercept can then be used to find the corresponding roughness coefficient, using the             equivilant laws:                                                  1)  $U(z) = (v/k)*ln(z/zo)$             which can be rewritten as:                                                 $U(z) = (v/k)*ln(z) - (v/k)ln(zo)$                                                 where zo = e ** (-c/m) of this line              Where:                  - U(z) is the wind speed at height z                 - v is the friction velocity at the location                 - k is the Von Karmen constant, taken aa .4                 - z is the height                 - zo is the roughness coefficient                                                  2)  $U2 = (ln(z2/z0)/ln(z1/z0))U1$ # take log of elevations # take log of elevations Derive the best fit power law exponent (as 1/alpha) from a given time-step of speed data at 2 or more elevations          :param wspds: pandas.Series or list of wind speeds [m/s]         :param heights: List of heights [m above ground]. The position of the height in the list must be the same             position in the list as its corresponding wind speed value.         :return: The shear value (alpha), as the inverse exponent of the best fit power law, based on the form:             $(v1/v2) = (z1/z2)^(1/alpha)$         :rtype: pandas.Series and float          METHODOLOGY:             Derive natural log of elevation and speed data sets             Derive coefficients of linear best fit along log-log distribution             Characterise new distribution of speed values based on linear best fit             Derive 'alpha' based on gradient of first and last best fit points (function works for 2 or more points)             Return alpha value # take log of elevations # take log of speeds # get coefficients of linear best fit to log distribution Scales wind speeds from one height to another given a value of alpha or roughness coefficient (zo)          :param wspd: Wind speed time series to apply shear to.         :type wspd: pandas.Series         :param height: height of above wspds.         :type height: float         :param shear_to: Height to which wspd should be scaled to.         :type shear_to: float         :param alpha: Shear exponent to be used when scaling wind speeds.         :type alpha: Float         :param roughness: Roughness coefficient to be used when scaling wind speeds.         :type roughness: float         :param calc_method: calculation method used to scale the wind speed.                 Using either:   1) 'power_law' :    $(v1/v2) = (z1/z2)^(1/alpha)$                                 2) 'log_law':       $v2 = (ln(z2/z0)/ln(z1/z0))v1$         :type calc_method: string         :return: a pandas series of the scaled wind speed         :return: pandas.Series or float          **Example Usage**         ::             # Scale wind speeds using exponents             # Specify alpha to use            alpha_value = .2             # Specify roughness coefficient to use            zo = .03             height = 40            shear_to = 80             scaled_by_power_law = bw.Shear.scale(data['Spd40mN'], height, shear_to, alpha=alpha_value)            scaled_by_log_law = bw.Shear.scale(data['Spd40mN'], height, shear_to, roughness=zo, calc_method='log_law') Private function for execution of scale() # initialise series for later use # join wind speeds and directions together in DataFrame # get directional bin edges from Shear.by_sector output Fills a pandas.DataFrame or Series to be a 12 month x 24 hour pandas.DataFrame by duplicating entries.         Used for plotting TimeOfDay shear.          :param data: pandas.DataFrame or Series to be turned into a 12x24 dataframe         :type data: pandas.Series or pandas.DataFrame.         :return: 12x24 pandas.DataFrame # create copy for later use # set index for new data frame to deal with less than 24 sectors # create new dataframe with 24 rows only interval number of unique values Create the info dict that is returned to the user.          :param self:         :param heights:         :param min_speed:         :param cvg:         :param direction_bin_array:         :param segments_per_day:         :param segment_start_time:         :return: