Support for Python 3.10

[nickyg543]

This is by far the best smith chart plotting solution. Please add support for Python 3.10

Python 3.10 deprecated Iterable from collections (they moved it to collection.abc)

replacing collections with collection.abc is doesn't quite fix it though - it results in a different error

[mskomek]

try this `# -- coding: utf-8 --

last edit: 11.04.2018

''' Library for plotting fully automatic a Smith Chart with various customizable parameters and well selected default values. It also provides the following modifications and features:

- circle shaped drawing area with labels placed around
- :meth:`plot` accepts single real and complex numbers and numpy.ndarray's
- plotted lines can be interpolated
- start/end markers of lines can be modified and rotate tangential
- gridlines are 3-point arcs to improve space efficiency of exported plots
- 'fancy' option for adaptive grid generation
- own tick locators for nice axis labels

For making a Smith Chart plot it is sufficient to import :mod:smithplot and create a new subplot with projection set to 'smith'. Parameters can be set either with keyword arguments or :meth:update_Params.

Example:

# creating a new plot and modify parameters afterwards
import smithplot
from smithplot import SmithAxes
from matplotlib import pyplot as pp
ax = pp.subplot('111', projection='smith')
SmithAxes.update_scParams(ax, reset=True, grid_major_enable=False)
## or in short form direct
#ax = pp.subplot('111', projection='smith', grid_major_enable=False)
pp.plot([25, 50 + 50j, 100 - 50j], datatype=SmithAxes.Z_PARAMETER)
pp.show()

Note: Supplying parameters to :meth:subplot may not always work as expected, because subplot uses an index for the axes with a key created of all given parameters. This does not work always, especially if the parameters are array-like types (e.g. numpy.ndarray). '''

from collections.abc import Iterable from numbers import Number from types import MethodType, FunctionType

import matplotlib as mp import numpy as np import scipy.interpolate from matplotlib.axes import Axes from matplotlib.axis import XAxis from matplotlib.cbook import simple_linear_interpolation as linear_interpolation from matplotlib.legend_handler import HandlerLine2D, HandlerLine2DCompound from matplotlib.lines import Line2D from matplotlib.markers import MarkerStyle from matplotlib.patches import Circle, Arc from matplotlib.path import Path from matplotlib.spines import Spine from matplotlib.ticker import Formatter, AutoMinorLocator, Locator from matplotlib.transforms import Affine2D, BboxTransformTo, Transform from scipy.interpolate import fitpack

from . import smithhelper

from .smithhelper import EPSILON, TWO_PI, ang_to_c, z_to_xy

INF = 1e9 EPSILON = 1e-7 TWO_PI = 2 * np.pi

class SmithAxes1(Axes): ''' The :class:SmithAxes provides an implementation of :class:matplotlib.axes.Axes for drawing a full automatic Smith Chart it also provides own implementations for

    - :class:`matplotlib.transforms.Transform`
        -> :class:`MoebiusTransform`
        -> :class:`InvertedMoebiusTransform`
        -> :class:`PolarTranslate`
    - :class:`matplotlib.ticker.Locator`
        -> :class:`RealMaxNLocator`
        -> :class:`ImagMaxNLocator`
        -> :class:`SmithAutoMinorLocator`
    - :class:`matplotlib.ticker.Formatter`
        -> :class:`RealFormatter`
        -> :class:`ImagFormatter`
'''

name = 'smith'

# data types
S_PARAMETER = "S"
Z_PARAMETER = "Z"
Y_PARAMETER = "Y"
_datatypes = [S_PARAMETER, Z_PARAMETER, Y_PARAMETER]

# constants used for indicating values near infinity, which are all transformed into one point
_inf = INF
_near_inf = 0.9 * INF
_ax_lim_x = 2 * _inf  # prevents missing labels in special cases
_ax_lim_y = 2 * _inf  # prevents missing labels in special cases

# default parameter, see update_scParams for description
scDefaultParams = {"plot.zorder": 4,
                   "plot.marker.hack": True,
                   "plot.marker.rotate": True,
                   "plot.marker.start": "s",
                   "plot.marker.default": "o",
                   "plot.marker.end": "^",
                   "plot.default.interpolation": 5,
                   "plot.default.datatype": S_PARAMETER,
                   "grid.zorder": 1,
                   "grid.locator.precision": 2,
                   "grid.major.enable": True,
                   "grid.major.linestyle": '-',
                   "grid.major.linewidth": 1,
                   "grid.major.color": "0.2",
                   "grid.major.xmaxn": 10,
                   "grid.major.ymaxn": 16,
                   "grid.major.fancy": True,
                   "grid.major.fancy.threshold": (100, 50),
                   "grid.minor.enable": True,
                   "grid.minor.capstyle": "round",
                   "grid.minor.dashes": [0.2, 2],
                   "grid.minor.linewidth": 0.75,
                   "grid.minor.color": "0.4",
                   "grid.minor.xauto": 4,
                   "grid.minor.yauto": 4,
                   "grid.minor.fancy": True,
                   "grid.minor.fancy.dividers": [0, 1, 2, 3, 5, 10, 20],
                   "grid.minor.fancy.threshold": 35,
                   "axes.xlabel.rotation": 90,
                   "axes.xlabel.fancybox": {"boxstyle": "round,pad=0.2,rounding_size=0.2",
                                            "facecolor": 'w',
                                            "edgecolor": "w",
                                            "mutation_aspect": 0.75,
                                            "alpha": 1},
                   "axes.ylabel.correction": (-1, 0, 0),
                   "axes.radius": 0.44,
                   "axes.impedance": 50,
                   "axes.normalize": True,
                   "axes.normalize.label": True,
                   "symbol.infinity": "∞ ",  # BUG: symbol gets cut off without end-space
                   "symbol.infinity.correction": 8,
                   "symbol.ohm": "Ω"}

@staticmethod
def update_scParams(sc_dict=None, instance=None, filter_dict=False, reset=True, **kwargs):
    '''
    Method for updating the parameters of a SmithAxes instance. If no instance
    is given, the changes are global, but affect only instances created
    afterwards. Parameter can be passed as dictionary or keyword arguments.
    If passed as keyword, the seperator '.' must be  replaced with '_'.

    Note: Parameter changes are not always immediate (e.g. changes to the
    grid). It is not recommended to modify parameter after adding anything to
    the plot. For a reset call :meth:`cla`.

    Example:
        update_scParams({grid.major: True})
        update_scParams(grid_major=True)

    Valid parameters with default values and description:

        plot.zorder: 5
            Zorder of plotted lines.
            Accepts: integer

        plot.marker.hack: True
            Enables the replacement of start and endmarkers.
            Accepts: boolean
            Note: Uses ugly code injection and may causes unexpected behavior.

        plot.marker.rotate: True
            Rotates the endmarker in the direction of its line.
            Accepts: boolean
            Note: needs plot.marker.hack=True

        plot.marker.start: 's',
            Marker for the first point of a line, if it has more than 1 point.
            Accepts: None or see matplotlib.markers.MarkerStyle()
            Note: needs plot.marker.hack=True

        plot.marker.default: 'o'
            Marker used for linepoints.
            Accepts: None or see matplotlib.markers.MarkerStyle()

        plot.marker.end: '^',
            Marker for the last point of a line, if it has more than 1 point.
            Accepts: None or see matplotlib.markers.MarkerStyle()
            Note: needs plot.marker.hack=True

        plot.default.interpolation: 5
            Default number of interpolated steps between two points of a
            line, if interpolation is used.
            Accepts: integer

        plot.default.datatype: SmithAxes.S_PARAMETER
            Default datatype for plots.
            Accepts: SmithAxes.[S_PARAMETER,Z_PARAMETER,Y_PARAMETER]

        grid.zorder : 1
            Zorder of the gridlines.
            Accepts: integer
            Note: may not work as expected

        grid.locator.precision: 2
            Sets the number of significant decimals per decade for the
            Real and Imag MaxNLocators. Example with precision 2:
                1.12 -> 1.1, 22.5 -> 22, 135 -> 130, ...
            Accepts: integer
            Note: value is an orientation, several exceptions are implemented

        grid.major.enable: True
            Enables the major grid.
            Accepts: boolean

        grid.major.linestyle: 'solid'
            Major gridline style.
            Accepts: see matplotlib.patches.Patch.set_linestyle()

        grid.major.linewidth: 1
            Major gridline width.
            Accepts: float

        grid.major.color: '0.2'
            Major gridline color.
            Accepts: matplotlib color

        grid.major.xmaxn: 10
            Maximum number of spacing steps for the real axis.
            Accepts: integer

        grid.major.ymaxn: 16
            Maximum number of spacing steps for the imaginary axis.
            Accepts: integer

        grid.major.fancy: True
            Draws a fancy major grid instead of the standard one.
            Accepts: boolean

        grid.major.fancy.threshold: (100, 50)
            Minimum distance times 1000 between two gridlines relative to
            total plot size 2x2. Either tuple for individual real and
            imaginary distances or single value for both.
            Accepts: (float, float) or float

        grid.minor.enable: True
            Enables the minor grid.
            Accepts: boolean

        grid.minor.capstyle: 'round'
            Minor dashes capstyle
            Accepts: 'round', 'butt', 'miter', 'projecting'

        grid.minor.dashes: (0.2, 2)
            Minor gridline dash style.
            Accepts: tuple

        grid.minor.linewidth: 0.75
            Minor gridline width.
            Accepts: float

        grid.minor.color: 0.4
            Minor gridline color.
            Accepts: matplotlib color

        grid.minor.xauto: 4
            Maximum number of spacing steps for the real axis.
            Accepts: integer

        grid.minor.yauto: 4
            Maximum number of spacing steps for the imaginary axis.
            Accepts: integer

        grid.minor.fancy: True
            Draws a fancy minor grid instead the standard one.
            Accepts: boolean

        grid.minor.fancy.dividers: [1, 2, 3, 5, 10, 20]
            Divisions for the fancy minor grid, which are selected by
            comparing the distance of gridlines with the threshold value.
            Accepts: list of integers

        grid.minor.fancy.threshold: 25
            Minimum distance for using the next bigger divider. Value times
            1000 relative to total plot size 2.
            Accepts: float

        axes.xlabel.rotation: 90
           Rotation of the real axis labels in degree.
           Accepts: float

        axes.xlabel.fancybox: {"boxstyle": "round4,pad=0.3,rounding_size=0.2",
                                           "facecolor": 'w',
                                           "edgecolor": "w",
                                           "mutation_aspect": 0.75,
                                           "alpha": 1},
            FancyBboxPatch parameters for the x-label background box.
            Accepts: dictionary with rectprops

        axes.ylabel.correction: (-1, 0, 0)
            Correction in x, y, and radial direction for the labels of the imaginary axis.
            Usually needs to be adapted when fontsize changes 'font.size'.
            Accepts: (float, float, float)

        axes.radius: 0.44
            Radius of the plotting area. Usually needs to be adapted to
            the size of the figure.
            Accepts: float

        axes.impedance: 50
            Defines the reference impedance for normalisation.
            Accepts: float

        axes.normalize: True
            If True, the Smith Chart is normalized to the reference impedance.
            Accepts: boolean

        axes.normalize.label: True
            If 'axes.normalize' and True, a textbox with 'Z_0: ... Ohm' is put in
            the lower left corner.
            Accepts: boolean

        symbol.infinity: "∞ "
            Symbol string for infinity.
            Accepts: string

            Note: Without the trailing space the label might get cut off.

        symbol.infinity.correction: 8
            Correction of size for the infinity symbol, because normal symbol
            seems smaller than other letters.
            Accepts: float

        symbol.ohm "Ω"
            Symbol string for the resistance unit (usually a large Omega).
            Accepts: string

    Note: The keywords are processed after the dictionary and override
    possible double entries.
    '''
    scParams = SmithAxes.scDefaultParams if instance is None else instance.scParams

    if sc_dict is not None:
        for key, value in sc_dict.items():
            if key in scParams:
                scParams[key] = value
            else:
                raise KeyError("key '%s' is not in scParams" % key)

    remaining = kwargs.copy()
    for key in kwargs:
        key_dot = key.replace("_", ".")
        if key_dot in scParams:
            scParams[key_dot] = remaining.pop(key)

    if not filter_dict and len(remaining) > 0:
        raise KeyError("Following keys are invalid SmithAxes parameters: '%s'" % ",".join(remaining.keys()))

    if reset and instance is not None:
        instance.cla()

    if filter_dict:
        return remaining

def __init__(self, *args, **kwargs):
    '''
    Builds a new :class:`SmithAxes` instance. For futher details see:

        :meth:`update_scParams`
        :class:`matplotlib.axes.Axes`
    '''
    # define new class attributes
    self._majorarcs = None
    self._minorarcs = None
    self._impedance = None
    self._normalize = None
    self._current_zorder = None
    self.scParams = self.scDefaultParams.copy()

    # seperate Axes parameter
    Axes.__init__(self, *args, **SmithAxes.update_scParams(instance=self, filter_dict=True, reset=False, **kwargs))
    self.set_aspect(1, adjustable='box', anchor='C')

    # remove all ticks
    self.tick_params(axis="both", which="both", bottom=False, top=False, left=False, right=False)

def _get_key(self, key):
    '''
    Get a key from the local parameter dictionary or from global
    matplotlib rcParams.

    Keyword arguments:

        *key*:
            Key to get from scParams or matplotlib.rcParams
            Accepts: string

    Returns:

        *value*:
            Value got from scParams or rcParams with key
    '''
    if key in self.scParams:
        return self.scParams[key]
    elif key in mp.rcParams:
        return mp.rcParams[key]
    else:
        raise KeyError("%s is not a valid key" % key)

def _init_axis(self):
    self.xaxis = mp.axis.XAxis(self)
    self.yaxis = mp.axis.YAxis(self)
    self._update_transScale()

def cla(self):
    self._majorarcs = []
    self._minorarcs = []

    # deactivate grid function when calling base class
    tgrid = self.grid

    def dummy(*args, **kwargs):
        pass

    self.grid = dummy
    # Don't forget to call the base class
    Axes.cla(self)
    self.grid = tgrid

    self._normbox = None
    self._impedance = self._get_key("axes.impedance")
    self._normalize = self._get_key("axes.normalize")
    self._current_zorder = self._get_key("plot.zorder")

    self.xaxis.set_major_locator(self.RealMaxNLocator(self, self._get_key("grid.major.xmaxn")))
    self.yaxis.set_major_locator(self.ImagMaxNLocator(self, self._get_key("grid.major.ymaxn")))

    self.xaxis.set_minor_locator(self.SmithAutoMinorLocator(self._get_key("grid.minor.xauto")))
    self.yaxis.set_minor_locator(self.SmithAutoMinorLocator(self._get_key("grid.minor.yauto")))

    self.xaxis.set_ticks_position('none')
    self.yaxis.set_ticks_position('none')

    Axes.set_xlim(self, 0, self._ax_lim_x)
    Axes.set_ylim(self, -self._ax_lim_y, self._ax_lim_y)

    for label in self.get_xticklabels():
        label.set_verticalalignment("center")
        label.set_horizontalalignment('center')
        label.set_rotation_mode("anchor")
        label.set_rotation(self._get_key("axes.xlabel.rotation"))
        label.set_bbox(self._get_key("axes.xlabel.fancybox"))
        self.add_artist(label)  # if not readded, labels are drawn behind grid

    for tick, loc in zip(self.yaxis.get_major_ticks(),
                         self.yaxis.get_majorticklocs()):
        # workaround for fixing to small infinity symbol
        if abs(loc) > self._near_inf:
            # tick.label.set_size(tick.label.get_size() +
            #                     self._get_key("symbol.infinity.correction"))
            tick.label1.set_fontsize(tick.label1.get_fontsize() +
                                self._get_key("symbol.infinity.correction"))

        # tick.label.set_verticalalignment('center')
        tick.label1.set_verticalalignment('center')

        x = np.real(self._moebius_z(loc * 1j))
        if x < -0.1:
            tick.label1.set_horizontalalignment('right')
        elif x > 0.1:
            tick.label1.set_horizontalalignment('left')
        else:
            tick.label1.set_horizontalalignment('center')

    self.yaxis.set_major_formatter(self.ImagFormatter(self))
    self.xaxis.set_major_formatter(self.RealFormatter(self))

    if self._get_key("axes.normalize") and self._get_key("axes.normalize.label"):
        x, y = z_to_xy(self._moebius_inv_z(-1 - 1j))
        box = self.text(x, y, "Z$_\mathrm{0}$ = %d$\,$%s" % (self._impedance, self._get_key("symbol.ohm")),
                        ha="left", va="bottom")

        px = self._get_key("ytick.major.pad")
        py = px + 0.5 * box.get_size()
        box.set_transform(self._yaxis_correction + Affine2D().translate(-px, -py))

    for grid in ['major', "minor"]:
        self.grid(b=self._get_key("grid.%s.enable" % grid), which=grid)

def _set_lim_and_transforms(self):
    r = self._get_key("axes.radius")
    self.transProjection = self.MoebiusTransform(self)  # data space  -> moebius space
    self.transAffine = Affine2D().scale(r, r).translate(0.5, 0.5)  # moebius space -> axes space
    self.transDataToAxes = self.transProjection + self.transAffine
    self.transAxes = BboxTransformTo(self.bbox)  # axes space -> drawing space
    self.transMoebius = self.transAffine + self.transAxes
    self.transData = self.transProjection + self.transMoebius

    self._xaxis_pretransform = Affine2D().scale(1, 2 * self._ax_lim_y).translate(0, -self._ax_lim_y)
    self._xaxis_transform = self._xaxis_pretransform + self.transData
    self._xaxis_text1_transform = Affine2D().scale(1.0, 0.0) + self.transData

    self._yaxis_stretch = Affine2D().scale(self._ax_lim_x, 1.0)
    self._yaxis_correction = self.transData + Affine2D().translate(*self._get_key("axes.ylabel.correction")[:2])
    self._yaxis_transform = self._yaxis_stretch + self.transData
    self._yaxis_text1_transform = self._yaxis_stretch + self._yaxis_correction

def get_xaxis_transform(self, which='grid'):
    assert which in ['tick1', 'tick2', 'grid']
    return self._xaxis_transform

def get_xaxis_text1_transform(self, pixelPad):
    return self._xaxis_text1_transform, 'center', 'center'

def get_yaxis_transform(self, which='grid'):
    assert which in ['tick1', 'tick2', 'grid']
    return self._yaxis_transform

def get_yaxis_text1_transform(self, pixelPad):
    if hasattr(self, 'yaxis') and len(self.yaxis.majorTicks) > 0:
        # font_size = self.yaxis.majorTicks[0].label.get_size()
        font_size = self.yaxis.majorTicks[0].label1.get_fontsize()
    else:
        font_size = self._get_key("font.size")

    offset = self._get_key("axes.ylabel.correction")[2]
    return self._yaxis_text1_transform + self.PolarTranslate(self, pad=pixelPad + offset,
                                                             font_size=font_size), 'center', 'center'

def _gen_axes_patch(self):
    return Circle((0.5, 0.5), self._get_key("axes.radius") + 0.015)

def _gen_axes_spines(self, locations=None, offset=0.0, units='inches'):
    return {SmithAxes.name: Spine.circular_spine(self, (0.5, 0.5), self._get_key("axes.radius"))}

def set_xscale(self, *args, **kwargs):
    if args[0] != 'linear':
        raise NotImplementedError()
    Axes.set_xscale(self, *args, **kwargs)

def set_yscale(self, *args, **kwargs):
    if args[0] != 'linear':
        raise NotImplementedError()
    Axes.set_yscale(self, *args, **kwargs)

def set_xlim(self, *args, **kwargs):
    '''xlim is immutable and always set to (0, infinity)'''
    Axes.set_xlim(self, 0, self._ax_lim_x)

def set_ylim(self, *args, **kwargs):
    '''ylim is immutable and always set to (-infinity, infinity)'''
    Axes.set_ylim(self, -self._ax_lim_y, self._ax_lim_y)

def format_coord(self, re, im):
    sgn = "+" if im > 0 else "-"
    return "%.5f %s %.5fj" % (re, sgn, abs(im)) if re > 0 else ""

def get_data_ratio(self):
    return 1.0

# disable panning and zoom in matplotlib figure viewer
def can_zoom(self):
    return False

def start_pan(self, x, y, button):
    pass

def end_pan(self):
    pass

def drag_pan(self, button, key, x, y):
    pass

def _moebius_z(self, *args, normalize=None):
    '''
    Basic transformation.

    Arguments:

        *z*:
            Complex number or numpy.ndarray with dtype=complex

        *x, y*:
            Float numbers or numpy.ndarray's with dtype not complex

        *normalize*:
            If True, the values are normalized to self._impedance.
            If None, self._normalize determines behaviour.
            Accepts: boolean or None

    Returns:

        *w*:
            Performs w = (z - k) / (z + k) with k = 'axes.scale'
            Type: Complex number or numpy.ndarray with dtype=complex
    '''
    normalize = self._normalize if normalize is None else normalize
    norm = 1 if normalize else self._impedance
    return moebius_z(*args, norm=norm)

def _moebius_inv_z(self, *args, normalize=None):
    '''
    Basic inverse transformation.

    Arguments:

        *z*:
            Complex number or numpy.ndarray with dtype=complex

        *x, y*:
            Float numbers or numpy.ndarray's with dtype not complex

        *normalize*:
            If True, the values are normalized to self._impedance.
            If None, self._normalize determines behaviour.
            Accepts: boolean or None

    Returns:

        *w*:
            Performs w = k * (1 - z) / (1 + z) with k = 'axes.scale'
            Type: Complex number or numpy.ndarray with dtype=complex
    '''
    normalize = self._normalize if normalize is None else normalize
    norm = 1 if normalize else self._impedance
    return moebius_inv_z(*args, norm=norm)

def real_interp1d(self, x, steps):
    '''
    Interpolates the given vector as real numbers in the way, that they
    are evenly spaced after a transformation with imaginary part 0.

    Keyword Arguments

        *x*:
            Real values to interpolate.
            Accepts: 1D iterable (e.g. list or numpy.ndarray)

        *steps*:
            Number of steps between two points.
            Accepts: integer
    '''
    return self._moebius_inv_z(linear_interpolation(self._moebius_z(np.array(x)), steps))

def imag_interp1d(self, y, steps):
    '''
    Interpolates the given vector as imaginary numbers in the way, that
    they are evenly spaced after a transformation with real part 0.

    Keyword Arguments

        *y*:
            Imaginary values to interpolate.
            Accepts: 1D iterable (e.g. list or numpy.ndarray)

        *steps*:
            Number of steps between two points.
            Accepts: integer
    '''
    angs = np.angle(self._moebius_z(np.array(y) * 1j)) % TWO_PI
    i_angs = linear_interpolation(angs, steps)
    return np.imag(self._moebius_inv_z(ang_to_c(i_angs)))

def legend(self, *args, **kwargs):
    this_axes = self

    class SmithHandlerLine2D(HandlerLine2DCompound):
        def create_artists(self, legend, orig_handle,
                           xdescent, ydescent, width, height, fontsize,
                           trans):

            legline, legline_marker = HandlerLine2DCompound.create_artists(self, legend, orig_handle, xdescent, ydescent,
                                                                   width, height, fontsize, trans)

            if hasattr(orig_handle, "_markerhacked"):
                this_axes._hack_linedraw(legline_marker, True)
            return legline, legline_marker

    return Axes.legend(self, *args, handler_map={Line2D: SmithHandlerLine2D()}, **kwargs)

def plot(self, *args, **kwargs):
    '''
    Plot the given data into the Smith Chart. Behavior similar to basic
    :meth:`matplotlib.axes.Axes.plot`, but with some extensions:

        - Additional support for real and complex data. Complex values must be
        either of type 'complex' or a numpy.ndarray with dtype=complex.
        - If 'zorder' is not provided, the current default value is used.
        - If 'marker' is not providet, the default value is used.
        - Extra keywords are added.

    Extra keyword arguments:

        *datatype*:
            Specifies the input data format. Must be either 'S', 'Z' or 'Y'.
            Accepts: SmithAxes.[S_PARAMETER,Z_PARAMETER,Y_PARAMETER]
            Default: 'plot.default.datatype'

        *markerhack*:
            If set, activates the manipulation of start and end markern
            of the created line.
            Accepts: boolean
            Default: 'plot.marker.hack'

        *rotate_marker*:
            If *markerhack* is active, rotates the endmarker in direction
            of the corresponding path.
            Accepts: boolean
            Default: 'plot.rotatemarker'

        *interpolate*:
            If 'value' >0 the given data is interpolated linearly by 'value'
            steps in SmithAxes cooardinate space. 'markevery', if specified,
            will be modified accordingly. If 'True' the 'plot.default_intperpolation'
            value is used.
            Accepts: boolean or integer
            Default: False

        *equipoints*:
            If 'value' >0 the given data is interpolated linearly by equidistant
            steps in SmithAxes cooardinate space. Cannot be used with 'interpolate'
            enabled.
            Accepts: boolean
            Default: False

    See :meth:`matplotlib.axes.Axes.plot` for mor details
    '''
    # split input into real and imaginary part if complex
    new_args = ()
    for arg in args:
        # check if argument is a string or already an ndarray
        # if not, try to convert to an ndarray
        if not (isinstance(arg, str) or isinstance(arg, np.ndarray)):
            try:
                if isinstance(arg, Iterable):
                    arg = np.array(arg)
                elif isinstance(arg, Number):
                    arg = np.array([arg])
            except TypeError:
                pass

        # if (converted) arg is an ndarray of complex type, split it
        if isinstance(arg, np.ndarray) and arg.dtype in [np.complex64, np.complex128]:
            new_args += z_to_xy(arg)
        else:
            new_args += (arg,)

    # ensure newer plots are above older ones
    if 'zorder' not in kwargs:
        kwargs['zorder'] = self._current_zorder
        self._current_zorder += 0.001

    # extract or load non-matplotlib keyword arguments from parameters
    kwargs.setdefault("marker", self._get_key("plot.marker.default"))
    interpolate = kwargs.pop("interpolate", False)
    equipoints = kwargs.pop("equipoints", False)
    datatype = kwargs.pop("datatype", self._get_key("plot.default.datatype"))
    markerhack = kwargs.pop("markerhack", self._get_key("plot.marker.hack"))
    rotate_marker = kwargs.pop("rotate_marker", self._get_key("plot.marker.rotate"))

    if datatype not in self._datatypes:
        raise ValueError("'datatype' must be either '%s'" % ",".join(self._datatypes))

    if interpolate is not False:
        if equipoints > 0:
            raise ValueError("Interpolation is not available with equidistant markers")

        if interpolate is True:
            interpolate = self._get_key("plot.default.interpolation")
        elif interpolate < 0:
            raise ValueError("Interpolation is only for positive values possible!")

        if "markevery" in kwargs:
            mark = kwargs["markevery"]
            if isinstance(mark, Iterable):
                mark = np.asarray(mark) * (interpolate + 1)
            else:
                mark *= interpolate + 1
            kwargs["markevery"] = mark

    lines = Axes.plot(self, *new_args, **kwargs)
    for line in lines:
        cdata = xy_to_z(line.get_data())

        if datatype == SmithAxes.S_PARAMETER:
            z = self._moebius_inv_z(cdata)
        elif datatype == SmithAxes.Y_PARAMETER:
            z = 1 / cdata
        elif datatype == SmithAxes.Z_PARAMETER:
            z = cdata
        else:
            raise ValueError("'datatype' must be '%s', '%s' or '%s'" % (
            SmithAxes.S_PARAMETER, SmithAxes.Z_PARAMETER, SmithAxes.Y_PARAMETER))

        if self._normalize and datatype != SmithAxes.S_PARAMETER:
            z /= self._impedance

        line.set_data(z_to_xy(z))

        if interpolate or equipoints:
            z = self._moebius_z(*line.get_data())
            if len(z) > 1:
                spline, t0 = fitpack.splprep(z_to_xy(z), s=0)
                ilen = (interpolate + 1) * (len(t0) - 1) + 1
                if equipoints == 1:
                    t = np.linspace(0, 1, ilen)
                elif equipoints > 1:
                    t = np.linspace(0, 1, equipoints)
                else:
                    t = np.zeros(ilen)
                    t[0], t[1:] = t0[0], np.concatenate(
                        [np.linspace(i0, i1, interpolate + 2)[1:] for i0, i1 in zip(t0[:-1], t0[1:])])

                z = self._moebius_inv_z(*fitpack.splev(t, spline))
                line.set_data(z_to_xy(z))

        if markerhack:
            self._hack_linedraw(line, rotate_marker)

    return lines

def grid(self,
         b=None,
         which='major',
         fancy=None,
         dividers=None,
         threshold=None,
         **kwargs):
    '''
    Complete rewritten grid function. Gridlines are replaced with Arcs,
    which reduces the amount of points to store and increases speed. The
    grid consist of a minor and major part, which can be drawn either as
    standard with lines from axis to axis, or fancy with dynamic spacing
    and length adaption.

    Keyword arguments:

        *b*:
            Enables or disables the selected grid.
            Accepts: boolean

        *which*:
            The grid to be drawn.
            Accepts: ['major', 'minor', 'both']

        *axis*:
            The axis to be drawn. x=real and y=imaginary
            Accepts: ['x', 'y', 'both']
            Note: if fancy is set, only 'both' is valid

        *fancy*:
            If set to 'True', draws the grid on the fancy way.
            Accepts: boolean

        *dividers*:
            Adaptive divisions for the minor fancy grid.
            Accepts: array with integers
            Note: has no effect on major and non-fancy grid

        *threshold*:
            Threshold for dynamic adaption of spacing and line length. Can
            be specified for both axis together or each seperatly.
            Accepts: float or (float, float)

        **kwargs*:
            Keyword arguments passed to the gridline creator.
            Note: Gridlines are :class:`matplotlib.patches.Patch` and does
            not accept all arguments :class:`matplotlib.lines.Line2D`
            accepts.
    '''
    assert which in ["both", "major", "minor"]
    assert fancy in [None, False, True]

    def get_kwargs(grid):
        kw = kwargs.copy()
        kw.setdefault('zorder', self._get_key("grid.zorder"))
        kw.setdefault("alpha", self._get_key("grid.alpha"))

        for key in ["linestyle", "linewidth", "color"]:
            if grid == "minor" and key == "linestyle":
                if "linestyle" not in kw:
                    kw.setdefault("dash_capstyle", self._get_key("grid.minor.capstyle"))
                    kw.setdefault("dashes", self._get_key("grid.minor.dashes"))
            else:
                kw.setdefault(key, self._get_key("grid.%s.%s" % (grid, key)))

        return kw

    def check_fancy(yticks):
        # checks if the imaginary axis is symetric
        len_y = (len(yticks) - 1) // 2
        if not (len(yticks) % 2 == 1 and (yticks[len_y:] + yticks[len_y::-1] < EPSILON).all()):
            raise ValueError(
                "fancy minor grid is only supported for zero-symetric imaginary grid - e.g. ImagMaxNLocator")
        return yticks[len_y:]

    def split_threshold(threshold):
        if isinstance(threshold, tuple):
            thr_x, thr_y = threshold
        else:
            thr_x = thr_y = threshold

        assert thr_x > 0 and thr_y > 0

        return thr_x / 1000, thr_y / 1000

    def add_arc(ps, p0, p1, grid, type):
        assert grid in ["major", "minor"]
        assert type in ["real", "imag"]
        assert p0 != p1
        arcs = self._majorarcs if grid == "major" else self._minorarcs
        if grid == "minor":
            param["zorder"] -= 1e-9
        arcs.append((type, (ps, p0, p1), self._add_gridline(ps, p0, p1, type, **param)))

    def draw_nonfancy(grid):
        if grid == "major":
            xticks = self.xaxis.get_majorticklocs()
            yticks = self.yaxis.get_majorticklocs()
        else:
            xticks = self.xaxis.get_minorticklocs()
            yticks = self.yaxis.get_minorticklocs()

        xticks = np.round(xticks, 7)
        yticks = np.round(yticks, 7)

        for xs in xticks:
            if xs < self._near_inf:
                add_arc(xs, -self._near_inf, self._inf, grid, "real")

        for ys in yticks:
            if abs(ys) < self._near_inf:
                add_arc(ys, 0, self._inf, grid, "imag")

    # set fancy parameters
    if fancy is None:
        fancy_major = self._get_key("grid.major.fancy")
        fancy_minor = self._get_key("grid.minor.fancy")
    else:
        fancy_major = fancy_minor = fancy

    # check parameters
    if "axis" in kwargs and kwargs["axis"] != "both":
        raise ValueError("Only 'both' is a supported value for 'axis'")

    # plot major grid
    if which in ['both', 'major']:
        for _, _, arc in self._majorarcs:
            arc.remove()
        self._majorarcs = []

        if b:
            param = get_kwargs('major')
            if fancy_major:
                xticks = np.sort(self.xaxis.get_majorticklocs())
                yticks = np.sort(self.yaxis.get_majorticklocs())
                assert len(xticks) > 0 and len(yticks) > 0
                yticks = check_fancy(yticks)

                if threshold is None:
                    threshold = self._get_key("grid.major.fancy.threshold")

                thr_x, thr_y = split_threshold(threshold)

                # draw the 0 line
                add_arc(yticks[0], 0, self._inf, "major", "imag")

                tmp_yticks = yticks.copy()
                for xs in xticks:
                    k = 1
                    while k < len(tmp_yticks):
                        y0, y1 = tmp_yticks[k - 1:k + 1]
                        if abs(self._moebius_z(xs, y0) - self._moebius_z(xs, y1)) < thr_x:
                            add_arc(y1, 0, xs, "major", "imag")
                            add_arc(-y1, 0, xs, "major", "imag")
                            tmp_yticks = np.delete(tmp_yticks, k)
                        else:
                            k += 1

                for i in range(1, len(yticks)):
                    y0, y1 = yticks[i - 1:i + 1]
                    k = 1
                    while k < len(xticks):
                        x0, x1 = xticks[k - 1:k + 1]
                        if abs(self._moebius_z(x0, y1) - self._moebius_z(x1, y1)) < thr_y:
                            add_arc(x1, -y0, y0, "major", "real")
                            xticks = np.delete(xticks, k)
                        else:
                            k += 1
            else:
                draw_nonfancy("major")

    # plot minor grid
    if which in ['both', 'minor']:
        # remove the old grid
        for _, _, arc in self._minorarcs:
            arc.remove()
        self._minorarcs = []

        if b:
            param = get_kwargs("minor")

            if fancy_minor:
                # 1. Step: get x/y grid data
                xticks = np.sort(self.xaxis.get_majorticklocs())
                yticks = np.sort(self.yaxis.get_majorticklocs())
                assert len(xticks) > 0 and len(yticks) > 0
                yticks = check_fancy(yticks)

                if dividers is None:
                    dividers = self._get_key("grid.minor.fancy.dividers")
                assert len(dividers) > 0
                dividers = np.sort(dividers)

                if threshold is None:
                    threshold = self._get_key("grid.minor.fancy.threshold")

                thr_x, thr_y = split_threshold(threshold)
                len_x, len_y = len(xticks) - 1, len(yticks) - 1

                # 2. Step: calculate optimal gridspacing for each quadrant
                d_mat = np.ones((len_x, len_y, 2))

                # TODO: optimize spacing algorithm
                for i in range(len_x):
                    for k in range(len_y):
                        x0, x1 = xticks[i:i + 2]
                        y0, y1 = yticks[k:k + 2]

                        xm = self.real_interp1d([x0, x1], 2)[1]
                        ym = self.imag_interp1d([y0, y1], 2)[1]

                        x_div = y_div = dividers[0]

                        for div in dividers[1:]:
                            if abs(self._moebius_z(x1 - (x1 - x0) / div, ym) - self._moebius_z(x1, ym)) > thr_x:
                                x_div = div
                            else:
                                break

                        for div in dividers[1:]:
                            if abs(self._moebius_z(xm, y1) - self._moebius_z(xm, y1 - (y1 - y0) / div)) > thr_y:
                                y_div = div
                            else:
                                break

                        d_mat[i, k] = [x_div, y_div]

                # 3. Steps: optimize spacing
                # ensure the x-spacing declines towards infinity
                d_mat[:-1, 0, 0] = list(map(np.max, zip(d_mat[:-1, 0, 0], d_mat[1:, 0, 0])))

                # find the values which are near (0, 0.5) on the plot
                idx = np.searchsorted(xticks, self._moebius_inv_z(0)) + 1
                idy = np.searchsorted(yticks, self._moebius_inv_z(1j).imag)

                # extend the values around the center towards the border
                if idx > idy:
                    for d in range(idy):
                        delta = idx - idy + d
                        d_mat[delta, :d + 1] = d_mat[:delta, d] = d_mat[delta, 0]
                else:
                    for d in range(idx):
                        delta = idy - idx + d
                        d_mat[:d + 1, delta] = d_mat[d, :delta] = d_mat[d, 0]

                # 4. Step: gather and optimize the lines
                x_lines, y_lines = [], []

                for i in range(len_x):
                    x0, x1 = xticks[i:i + 2]

                    for k in range(len_y):
                        y0, y1 = yticks[k:k + 2]

                        x_div, y_div = d_mat[i, k]

                        for xs in np.linspace(np.int32(x0), x1, np.int32(x_div + 1))[1:]:
                            x_lines.append([xs, y0, y1])
                            x_lines.append([xs, -y1, -y0])

                        for ys in np.linspace(np.int32(y0), y1, np.int32(y_div + 1))[1:]:
                            y_lines.append([ys, x0, x1])
                            y_lines.append([-ys, x0, x1])

                # round values to prevent float inaccuarcy
                x_lines = np.round(np.array(x_lines), 7)
                y_lines = np.round(np.array(y_lines), 7)

                # remove lines which overlap with the major grid
                for tp, lines in [("real", x_lines), ("imag", y_lines)]:
                    for i in range(len(lines)):
                        ps, p0, p1 = lines[i]
                        if p0 > p1:
                            p0, p1 = p1, p0

                        for tq, (qs, q0, q1), _ in self._majorarcs:
                            if tp == tq and abs(ps - qs) < EPSILON and p1 > q0 and p0 < q1:
                                lines[i, :] = np.nan
                                break

                    lines = lines[~np.isnan(lines[:, 0])]
                    lines = lines[np.lexsort(lines[:, 1::-1].transpose())]

                    ps, p0, p1 = lines[0]
                    for qs, q0, q1 in lines[1:]:
                        if ps != qs or p1 != q0:
                            add_arc(ps, p0, p1, "minor", tp)
                            ps, p0, p1 = qs, q0, q1
                        else:
                            p1 = q1

            else:
                draw_nonfancy("minor")

def _hack_linedraw(self, line, rotate_marker=None):
    '''
    Modifies the draw method of a :class:`matplotlib.lines.Line2D` object
    to draw different stard and end marker.

    Keyword arguments:

        *line*:
            Line to be modified
            Accepts: Line2D

        *rotate_marker*:
            If set, the end marker will be rotated in direction of their
            corresponding path.
            Accepts: boolean
    '''
    assert isinstance(line, Line2D)

    def new_draw(self_line, renderer):
        def new_draw_markers(self_renderer, gc, marker_path, marker_trans, path, trans, rgbFace=None):
            # get the drawn path for determining the rotation angle
            line_vertices = self_line._get_transformed_path().get_fully_transformed_path().vertices
            vertices = path.vertices

            if len(vertices) == 1:
                line_set = [[default_marker, vertices]]
            else:
                if rotate_marker:
                    dx, dy = np.array(line_vertices[-1]) - np.array(line_vertices[-2])
                    end_rot = MarkerStyle(end.get_marker())
                    end_rot._transform += Affine2D().rotate(np.arctan2(dy, dx) - np.pi / 2)
                else:
                    end_rot = end

                if len(vertices) == 2:
                    line_set = [[start, vertices[0:1]], [end_rot, vertices[1:2]]]
                else:
                    line_set = [[start, vertices[0:1]], [default_marker, vertices[1:-1]], [end_rot, vertices[-1:]]]

            for marker, points in line_set:
                transform = marker.get_transform() + Affine2D().scale(self_line._markersize)
                old_draw_markers(gc, marker.get_path(), transform, Path(points), trans, rgbFace)

        old_draw_markers = renderer.draw_markers
        renderer.draw_markers = MethodType(new_draw_markers, renderer)
        old_draw(renderer)
        renderer.draw_markers = old_draw_markers

    default_marker = line._marker
    # check if marker is set and visible
    if default_marker:
        start = MarkerStyle(self._get_key("plot.marker.start"))
        if start.get_marker() is None:
            start = default_marker

        end = MarkerStyle(self._get_key("plot.marker.end"))
        if end.get_marker() is None:
            end = default_marker

        if rotate_marker is None:
            rotate_marker = self._get_key("plot.marker.rotate")

        old_draw = line.draw
        line.draw = MethodType(new_draw, line)
        line._markerhacked = True

def _add_gridline(self, ps, p0, p1, type, **kwargs):
    '''
    Add a gridline for a real axis circle.

    Keyword arguments:

        *ps*:
            Axis value
            Accepts: float

        *p0*:
            Start point
            Accepts: float

        *p1*:
            End Point
            Accepts: float

        **kwargs*:
            Keywords passed to the arc creator
    '''
    assert type in ["real", "imag"]

    if type == "real":
        assert ps >= 0

        line = Line2D(2 * [ps], [p0, p1], **kwargs)
        line.get_path()._interpolation_steps = "x_gridline"
    else:
        assert 0 <= p0 < p1

        line = Line2D([p0, p1], 2 * [ps], **kwargs)

        if abs(ps) > EPSILON:
            line.get_path()._interpolation_steps = "y_gridline"

    return self.add_artist(line)

class MoebiusTransform(Transform):
    '''
    Class for transforming points and paths to Smith Chart data space.
    '''
    input_dims = 2
    output_dims = 2
    is_separable = False

    def __init__(self, axes):
        assert isinstance(axes, SmithAxes)
        Transform.__init__(self)
        self._axes = axes

    def transform_non_affine(self, data):
        def _moebius_xy(_xy):
            return z_to_xy(self._axes._moebius_z(*_xy))

        if isinstance(data[0], Iterable):
            return list(map(_moebius_xy, data))
        else:
            return _moebius_xy(data)

    def transform_path_non_affine(self, path):
        vertices = path.vertices
        codes = path.codes

        linetype = path._interpolation_steps
        if linetype in ["x_gridline", "y_gridline"]:
            assert len(vertices) == 2

            x, y = np.array(list(zip(*vertices)))
            z = self._axes._moebius_z(x, y)

            if linetype == "x_gridline":
                assert x[0] == x[1]
                zm = 0.5 * (1 + self._axes._moebius_z(x[0]))
            else:
                assert y[0] == y[1]
                scale = 1j * (1 if self._axes._normalize else self._axes._impedance)
                zm = 1 + scale / y[0]

            d = 2 * abs(zm - 1)
            ang0, ang1 = np.angle(z - zm, deg=True) % 360

            reverse = ang0 > ang1
            if reverse:
                ang0, ang1 = ang1, ang0

            arc = Arc(z_to_xy(zm), d, d, theta1=ang0, theta2=ang1, transform=self._axes.transMoebius)
            arc._path = Path.arc(ang0, ang1)  # fix for Matplotlib 2.1+
            arc_path = arc.get_patch_transform().transform_path(arc.get_path())

            if reverse:
                new_vertices = arc_path.vertices[::-1]
            else:
                new_vertices = arc_path.vertices

            new_codes = arc_path.codes
        elif linetype == 1:
            new_vertices = self.transform_non_affine(vertices)
            new_codes = codes
        else:
            raise NotImplementedError("Value for 'path_interpolation' cannot be interpreted.")

        return Path(new_vertices, new_codes)

    def inverted(self):
        return SmithAxes.InvertedMoebiusTransform(self._axes)

class InvertedMoebiusTransform(Transform):
    '''
    Inverse transformation for points and paths in Smith Chart data space.
    '''
    input_dims = 2
    output_dims = 2
    is_separable = False

    def __init__(self, axes):
        assert isinstance(axes, SmithAxes)
        Transform.__init__(self)
        self._axes = axes

    def transform_non_affine(self, data):
        def _moebius_inv_xy(_xy):
            return z_to_xy(self._axes._moebius_inv_z(*_xy))

        return list(map(_moebius_inv_xy, data))

    def inverted(self):
        return SmithAxes.MoebiusTransform(self._axes)

class PolarTranslate(Transform):
    '''
    Transformation for translating points away from the center by a given
    padding.

    Keyword arguments:

        *axes*:
            Parent :class:`SmithAxes`
            Accepts: SmithAxes instance

        *pad*:
            Distance to translate away from center for x and y values.

        *font_size*:
            y values are shiftet 0.5 * font_size further away.
    '''
    input_dims = 2
    output_dims = 2
    is_separable = False

    def __init__(self, axes, pad, font_size):
        Transform.__init__(self, shorthand_name=None)
        self.axes = axes
        self.pad = pad
        self.font_size = font_size

    def transform_non_affine(self, xy):
        def _translate(_xy):
            x, y = _xy
            ang = np.angle(complex(x - x0, y - y0))
            return x + np.cos(ang) * self.pad, y + np.sin(ang) * (self.pad + 0.5 * self.font_size)

        x0, y0 = self.axes.transAxes.transform([0.5, 0.5])
        if isinstance(xy[0], Iterable):
            return list(map(_translate, xy))
        else:
            return _translate(xy)

class RealMaxNLocator(Locator):
    '''
    Locator for the real axis of a SmithAxes. Creates a nicely rounded
    spacing with maximum n values. The transformed center value is
    always included.

    Keyword arguments:

        *axes*:
            Parent SmithAxes
            Accepts: SmithAxes instance

        *n*:
            Maximum number of divisions
            Accepts: integer

        *precision*:
            Maximum number of significant decimals
            Accepts: integer
    '''

    def __init__(self, axes, n, precision=None):
        assert isinstance(axes, SmithAxes)
        assert n > 0

        Locator.__init__(self)
        self.steps = n
        if precision is None:
            self.precision = axes._get_key("grid.locator.precision")
        else:
            self.precision = precision
        assert self.precision > 0

        self.ticks = None
        self.axes = axes

    def __call__(self):
        if self.ticks is None:
            self.ticks = self.tick_values(0, self.axes._inf)
        return self.ticks

    def nice_round(self, num, down=True):
        # normalize to 'precision' decimals befor comma
        exp = np.ceil(np.log10(np.abs(num) + EPSILON))
        if exp < 1:  # fix for leading 0
            exp += 1
        norm = 10 ** -(exp - self.precision)

        num_normed = num * norm
        # increase precision by 0.5, if normed value is smaller than 1/3
        # of its decade range
        if num_normed < 3.3:
            norm *= 2
        # decrease precision by 1, if normed value is bigger than 1/2
        elif num_normed > 50:
            norm /= 10

        # select rounding function
        if not 1 < num_normed % 10 < 9:
            # round to nearest value, if last digit is 1 or 9
            if abs(num_normed % 10 - 1) < EPSILON:
                num -= 0.5 / norm
            f_round = np.round
        else:
            f_round = np.floor if down else np.ceil

        return f_round(np.round(num * norm, 1)) / norm

    def tick_values(self, vmin, vmax):
        tmin, tmax = self.transform(vmin), self.transform(vmax)
        mean = self.transform(self.nice_round(self.invert(0.5 * (tmin + tmax))))

        result = [tmin, tmax, mean]
        d0 = abs(tmin - tmax) / (self.steps + 1)
        # calculate values above and below mean, adapt delta
        for sgn, side, end in [[1, False, tmax], [-1, True, tmin]]:
            d, d0 = d0, None
            last = mean
            while True:
                new = last + d * sgn
                if self.out_of_range(new) or abs(end - new) < d / 2:
                    break

                # round new value to the next nice display value
                new = self.transform(self.nice_round(self.invert(new), side))
                d = abs(new - last)
                if d0 is None:
                    d0 = d

                last = new
                result.append(last)

        return np.sort(self.invert(np.array(result)))

    def out_of_range(self, x):
        return abs(x) > 1

    def transform(self, x):
        return self.axes._moebius_z(x)

    def invert(self, x):
        return self.axes._moebius_inv_z(x)

class ImagMaxNLocator(RealMaxNLocator):
    def __init__(self, axes, n, precision=None):
        SmithAxes.RealMaxNLocator.__init__(self, axes, n // 2, precision)

    def __call__(self):
        if self.ticks is None:
            tmp = self.tick_values(0, self.axes._inf)
            self.ticks = np.concatenate((-tmp[:0:-1], tmp))
        return self.ticks

    def out_of_range(self, x):
        return not 0 <= x <= np.pi

    def transform(self, x):
        return np.pi - np.angle(self.axes._moebius_z(x * 1j))

    def invert(self, x):
        return np.imag(-self.axes._moebius_inv_z(ang_to_c(np.pi + np.array(x))))

class SmithAutoMinorLocator(AutoMinorLocator):
    '''
    AutoLocator for SmithAxes. Returns linear spaced intermediate ticks
    depending on the major tickvalues.

    Keyword arguments:

        *n*:
            Number of intermediate ticks
            Accepts: positive integer
    '''

    def __init__(self, n=4):
        assert isinstance(n, int) and n > 0
        AutoMinorLocator.__init__(self, n=n)
        self._ticks = None

    def __call__(self):
        if self._ticks is None:
            locs = self.axis.get_majorticklocs()
            self._ticks = np.concatenate(
                [np.linspace(p0, p1, self.ndivs + 1)[1:-1] for (p0, p1) in zip(locs[:-1], locs[1:])])
        return self._ticks

class RealFormatter(Formatter):
    '''
    Formatter for the real axis of a SmithAxes. Prints the numbers as
    float and removes trailing zeros and commata. Special returns:
        '' for 0.

    Keyword arguments:

        *axes*:
            Parent axes
            Accepts: SmithAxes instance
    '''

    def __init__(self, axes, *args, **kwargs):
        assert isinstance(axes, SmithAxes)
        Formatter.__init__(self, *args, **kwargs)
        self._axes = axes

    def __call__(self, x, pos=None):
        if x < EPSILON or x > self._axes._near_inf:
            return ""
        else:
            return ('%f' % x).rstrip('0').rstrip('.')

class ImagFormatter(RealFormatter):
    '''
    Formatter for the imaginary axis of a SmithAxes. Prints the numbers
    as  float and removes trailing zeros and commata. Special returns:
        - '' for minus infinity
        - 'symbol.infinity' from scParams for plus infinity
        - '0' for value near zero (prevents -0)

    Keyword arguments:

        *axes*:
            Parent axes
            Accepts: SmithAxes instance
    '''

    def __call__(self, x, pos=None):
        if x < -self._axes._near_inf:
            return ""
        elif x > self._axes._near_inf:
            return self._axes._get_key("symbol.infinity")  # utf8 infinity symbol
        elif abs(x) < EPSILON:
            return "0"
        else:
            return ("%f" % x).rstrip('0').rstrip('.') + "j"

# update docstrings for all methode not set
for key, value in locals().copy().items():
    if isinstance(value, FunctionType):
        if value.__doc__ is None and hasattr(Axes, key):
            value.__doc__ = getattr(Axes, key).__doc__

class SmithAxes(Axes): ''' The :class:SmithAxes provides an implementation of :class:matplotlib.axes.Axes for drawing a full automatic Smith Chart it also provides own implementations for

    - :class:`matplotlib.transforms.Transform`
        -> :class:`MoebiusTransform`
        -> :class:`InvertedMoebiusTransform`
        -> :class:`PolarTranslate`
    - :class:`matplotlib.ticker.Locator`
        -> :class:`RealMaxNLocator`
        -> :class:`ImagMaxNLocator`
        -> :class:`SmithAutoMinorLocator`
    - :class:`matplotlib.ticker.Formatter`
        -> :class:`RealFormatter`
        -> :class:`ImagFormatter`
'''

name = 'smith'

# data types
S_PARAMETER = "S"
Z_PARAMETER = "Z"
Y_PARAMETER = "Y"
_datatypes = [S_PARAMETER, Z_PARAMETER, Y_PARAMETER]

# constants used for indicating values near infinity, which are all transformed into one point
_inf = INF
_near_inf = 0.9 * INF
_ax_lim_x = 2 * _inf  # prevents missing labels in special cases
_ax_lim_y = 2 * _inf  # prevents missing labels in special cases

# default parameter, see update_scParams for description
scDefaultParams = {"plot.zorder": 4,
                   "plot.marker.hack": True,
                   "plot.marker.rotate": True,
                   "plot.marker.start": "s",
                   "plot.marker.default": "o",
                   "plot.marker.end": "^",
                   "plot.default.interpolation": 5,
                   "plot.default.datatype": S_PARAMETER,
                   "grid.zorder": 1,
                   "grid.locator.precision": 2,
                   "grid.major.enable": True,
                   "grid.major.linestyle": '-',
                   "grid.major.linewidth": 1,
                   "grid.major.color": "0.2",
                   "grid.major.xmaxn": 10,
                   "grid.major.ymaxn": 16,
                   "grid.major.fancy": True,
                   "grid.major.fancy.threshold": (100, 50),
                   "grid.minor.enable": True,
                   "grid.minor.capstyle": "round",
                   "grid.minor.dashes": [0.2, 2],
                   "grid.minor.linewidth": 0.75,
                   "grid.minor.color": "0.4",
                   "grid.minor.xauto": 4,
                   "grid.minor.yauto": 4,
                   "grid.minor.fancy": True,
                   "grid.minor.fancy.dividers": [0, 1, 2, 3, 5, 10, 20],
                   "grid.minor.fancy.threshold": 35,
                   "axes.xlabel.rotation": 90,
                   "axes.xlabel.fancybox": {"boxstyle": "round,pad=0.2,rounding_size=0.2",
                                            "facecolor": 'w',
                                            "edgecolor": "w",
                                            "mutation_aspect": 0.75,
                                            "alpha": 1},
                   "axes.ylabel.correction": (-1, 0, 0),
                   "axes.radius": 0.44,
                   "axes.impedance": 50,
                   "axes.normalize": True,
                   "axes.normalize.label": True,
                   "symbol.infinity": "∞ ",  # BUG: symbol gets cut off without end-space
                   "symbol.infinity.correction": 8,
                   "symbol.ohm": "Ω"}

@staticmethod
def update_scParams(sc_dict=None, instance=None, filter_dict=False, reset=True, **kwargs):
    '''
    Method for updating the parameters of a SmithAxes instance. If no instance
    is given, the changes are global, but affect only instances created
    afterwards. Parameter can be passed as dictionary or keyword arguments.
    If passed as keyword, the seperator '.' must be  replaced with '_'.

    Note: Parameter changes are not always immediate (e.g. changes to the
    grid). It is not recommended to modify parameter after adding anything to
    the plot. For a reset call :meth:`cla`.

    Example:
        update_scParams({grid.major: True})
        update_scParams(grid_major=True)

    Valid parameters with default values and description:

        plot.zorder: 5
            Zorder of plotted lines.
            Accepts: integer

        plot.marker.hack: True
            Enables the replacement of start and endmarkers.
            Accepts: boolean
            Note: Uses ugly code injection and may causes unexpected behavior.

        plot.marker.rotate: True
            Rotates the endmarker in the direction of its line.
            Accepts: boolean
            Note: needs plot.marker.hack=True

        plot.marker.start: 's',
            Marker for the first point of a line, if it has more than 1 point.
            Accepts: None or see matplotlib.markers.MarkerStyle()
            Note: needs plot.marker.hack=True

        plot.marker.default: 'o'
            Marker used for linepoints.
            Accepts: None or see matplotlib.markers.MarkerStyle()

        plot.marker.end: '^',
            Marker for the last point of a line, if it has more than 1 point.
            Accepts: None or see matplotlib.markers.MarkerStyle()
            Note: needs plot.marker.hack=True

        plot.default.interpolation: 5
            Default number of interpolated steps between two points of a
            line, if interpolation is used.
            Accepts: integer

        plot.default.datatype: SmithAxes.S_PARAMETER
            Default datatype for plots.
            Accepts: SmithAxes.[S_PARAMETER,Z_PARAMETER,Y_PARAMETER]

        grid.zorder : 1
            Zorder of the gridlines.
            Accepts: integer
            Note: may not work as expected

        grid.locator.precision: 2
            Sets the number of significant decimals per decade for the
            Real and Imag MaxNLocators. Example with precision 2:
                1.12 -> 1.1, 22.5 -> 22, 135 -> 130, ...
            Accepts: integer
            Note: value is an orientation, several exceptions are implemented

        grid.major.enable: True
            Enables the major grid.
            Accepts: boolean

        grid.major.linestyle: 'solid'
            Major gridline style.
            Accepts: see matplotlib.patches.Patch.set_linestyle()

        grid.major.linewidth: 1
            Major gridline width.
            Accepts: float

        grid.major.color: '0.2'
            Major gridline color.
            Accepts: matplotlib color

        grid.major.xmaxn: 10
            Maximum number of spacing steps for the real axis.
            Accepts: integer

        grid.major.ymaxn: 16
            Maximum number of spacing steps for the imaginary axis.
            Accepts: integer

        grid.major.fancy: True
            Draws a fancy major grid instead of the standard one.
            Accepts: boolean

        grid.major.fancy.threshold: (100, 50)
            Minimum distance times 1000 between two gridlines relative to
            total plot size 2x2. Either tuple for individual real and
            imaginary distances or single value for both.
            Accepts: (float, float) or float

        grid.minor.enable: True
            Enables the minor grid.
            Accepts: boolean

        grid.minor.capstyle: 'round'
            Minor dashes capstyle
            Accepts: 'round', 'butt', 'miter', 'projecting'

        grid.minor.dashes: (0.2, 2)
            Minor gridline dash style.
            Accepts: tuple

        grid.minor.linewidth: 0.75
            Minor gridline width.
            Accepts: float

        grid.minor.color: 0.4
            Minor gridline color.
            Accepts: matplotlib color

        grid.minor.xauto: 4
            Maximum number of spacing steps for the real axis.
            Accepts: integer

        grid.minor.yauto: 4
            Maximum number of spacing steps for the imaginary axis.
            Accepts: integer

        grid.minor.fancy: True
            Draws a fancy minor grid instead the standard one.
            Accepts: boolean

        grid.minor.fancy.dividers: [1, 2, 3, 5, 10, 20]
            Divisions for the fancy minor grid, which are selected by
            comparing the distance of gridlines with the threshold value.
            Accepts: list of integers

        grid.minor.fancy.threshold: 25
            Minimum distance for using the next bigger divider. Value times
            1000 relative to total plot size 2.
            Accepts: float

        axes.xlabel.rotation: 90
           Rotation of the real axis labels in degree.
           Accepts: float

        axes.xlabel.fancybox: {"boxstyle": "round4,pad=0.3,rounding_size=0.2",
                                           "facecolor": 'w',
                                           "edgecolor": "w",
                                           "mutation_aspect": 0.75,
                                           "alpha": 1},
            FancyBboxPatch parameters for the x-label background box.
            Accepts: dictionary with rectprops

        axes.ylabel.correction: (-1, 0, 0)
            Correction in x, y, and radial direction for the labels of the imaginary axis.
            Usually needs to be adapted when fontsize changes 'font.size'.
            Accepts: (float, float, float)

        axes.radius: 0.44
            Radius of the plotting area. Usually needs to be adapted to
            the size of the figure.
            Accepts: float

        axes.impedance: 50
            Defines the reference impedance for normalisation.
            Accepts: float

        axes.normalize: True
            If True, the Smith Chart is normalized to the reference impedance.
            Accepts: boolean

        axes.normalize.label: True
            If 'axes.normalize' and True, a textbox with 'Z_0: ... Ohm' is put in
            the lower left corner.
            Accepts: boolean

        symbol.infinity: "∞ "
            Symbol string for infinity.
            Accepts: string

            Note: Without the trailing space the label might get cut off.

        symbol.infinity.correction: 8
            Correction of size for the infinity symbol, because normal symbol
            seems smaller than other letters.
            Accepts: float

        symbol.ohm "Ω"
            Symbol string for the resistance unit (usually a large Omega).
            Accepts: string

    Note: The keywords are processed after the dictionary and override
    possible double entries.
    '''
    scParams = SmithAxes.scDefaultParams if instance is None else instance.scParams

    if sc_dict is not None:
        for key, value in sc_dict.items():
            if key in scParams:
                scParams[key] = value
            else:
                raise KeyError("key '%s' is not in scParams" % key)

    remaining = kwargs.copy()
    for key in kwargs:
        key_dot = key.replace("_", ".")
        if key_dot in scParams:
            scParams[key_dot] = remaining.pop(key)

    if not filter_dict and len(remaining) > 0:
        raise KeyError("Following keys are invalid SmithAxes parameters: '%s'" % ",".join(remaining.keys()))

    if reset and instance is not None:
        instance.cla()

    if filter_dict:
        return remaining

def __init__(self, *args, **kwargs):
    '''
    Builds a new :class:`SmithAxes` instance. For futher details see:

        :meth:`update_scParams`
        :class:`matplotlib.axes.Axes`
    '''
    # define new class attributes
    self._majorarcs = None
    self._minorarcs = None
    self._impedance = None
    self._normalize = None
    self._current_zorder = None
    self.scParams = self.scDefaultParams.copy()

    # seperate Axes parameter
    Axes.__init__(self, *args, **SmithAxes.update_scParams(instance=self, filter_dict=True, reset=False, **kwargs))
    self.set_aspect(1, adjustable='box', anchor='C')

    # remove all ticks
    self.tick_params(axis="both", which="both", bottom=False, top=False, left=False, right=False)

def _get_key(self, key):
    '''
    Get a key from the local parameter dictionary or from global
    matplotlib rcParams.

    Keyword arguments:

        *key*:
            Key to get from scParams or matplotlib.rcParams
            Accepts: string

    Returns:

        *value*:
            Value got from scParams or rcParams with key
    '''
    if key in self.scParams:
        return self.scParams[key]
    elif key in mp.rcParams:
        return mp.rcParams[key]
    else:
        raise KeyError("%s is not a valid key" % key)

def _init_axis(self):
    self.xaxis = mp.axis.XAxis(self)
    self.yaxis = mp.axis.YAxis(self)
    self._update_transScale()

def cla(self):
    self._majorarcs = []
    self._minorarcs = []

    # deactivate grid function when calling base class
    tgrid = self.grid

    def dummy(*args, **kwargs):
        pass

    self.grid = dummy
    # Don't forget to call the base class
    Axes.cla(self)
    self.grid = tgrid

    self._normbox = None
    self._impedance = self._get_key("axes.impedance")
    self._normalize = self._get_key("axes.normalize")
    self._current_zorder = self._get_key("plot.zorder")

    self.xaxis.set_major_locator(self.RealMaxNLocator(self, self._get_key("grid.major.xmaxn")))
    self.yaxis.set_major_locator(self.ImagMaxNLocator(self, self._get_key("grid.major.ymaxn")))

    self.xaxis.set_minor_locator(self.SmithAutoMinorLocator(self._get_key("grid.minor.xauto")))
    self.yaxis.set_minor_locator(self.SmithAutoMinorLocator(self._get_key("grid.minor.yauto")))

    self.xaxis.set_ticks_position('none')
    self.yaxis.set_ticks_position('none')

    Axes.set_xlim(self, 0, self._ax_lim_x)
    Axes.set_ylim(self, -self._ax_lim_y, self._ax_lim_y)

    for label in self.get_xticklabels():
        label.set_verticalalignment("center")
        label.set_horizontalalignment('center')
        label.set_rotation_mode("anchor")
        label.set_rotation(self._get_key("axes.xlabel.rotation"))
        label.set_bbox(self._get_key("axes.xlabel.fancybox"))
        self.add_artist(label)  # if not readded, labels are drawn behind grid

    for tick, loc in zip(self.yaxis.get_major_ticks(),
                         self.yaxis.get_majorticklocs()):
        # workaround for fixing to small infinity symbol
        if abs(loc) > self._near_inf:
            tick.label1.set_size(tick.label1.get_size() +
                                self._get_key("symbol.infinity.correction"))

        tick.label1.set_verticalalignment('center')

        x = np.real(self._moebius_z(loc * 1j))
        if x < -0.1:
            tick.label1.set_horizontalalignment('right')
        elif x > 0.1:
            tick.label1.set_horizontalalignment('left')
        else:
            tick.label1.set_horizontalalignment('center')

    self.yaxis.set_major_formatter(self.ImagFormatter(self))
    self.xaxis.set_major_formatter(self.RealFormatter(self))

    if self._get_key("axes.normalize") and self._get_key("axes.normalize.label"):
        x, y = z_to_xy(self._moebius_inv_z(-1 - 1j))
        box = self.text(x, y, "Z$_\mathrm{0}$ = %d$\,$%s" % (self._impedance, self._get_key("symbol.ohm")),
                        ha="left", va="bottom")

        px = self._get_key("ytick.major.pad")
        py = px + 0.5 * box.get_size()
        box.set_transform(self._yaxis_correction + Affine2D().translate(-px, -py))

    for grid in ['major', "minor"]:
        self.grid(b=self._get_key("grid.%s.enable" % grid), which=grid)

def _set_lim_and_transforms(self):
    r = self._get_key("axes.radius")
    self.transProjection = self.MoebiusTransform(self)  # data space  -> moebius space
    self.transAffine = Affine2D().scale(r, r).translate(0.5, 0.5)  # moebius space -> axes space
    self.transDataToAxes = self.transProjection + self.transAffine
    self.transAxes = BboxTransformTo(self.bbox)  # axes space -> drawing space
    self.transMoebius = self.transAffine + self.transAxes
    self.transData = self.transProjection + self.transMoebius

    self._xaxis_pretransform = Affine2D().scale(1, 2 * self._ax_lim_y).translate(0, -self._ax_lim_y)
    self._xaxis_transform = self._xaxis_pretransform + self.transData
    self._xaxis_text1_transform = Affine2D().scale(1.0, 0.0) + self.transData

    self._yaxis_stretch = Affine2D().scale(self._ax_lim_x, 1.0)
    self._yaxis_correction = self.transData + Affine2D().translate(*self._get_key("axes.ylabel.correction")[:2])
    self._yaxis_transform = self._yaxis_stretch + self.transData
    self._yaxis_text1_transform = self._yaxis_stretch + self._yaxis_correction

def get_xaxis_transform(self, which='grid'):
    assert which in ['tick1', 'tick2', 'grid']
    return self._xaxis_transform

def get_xaxis_text1_transform(self, pixelPad):
    return self._xaxis_text1_transform, 'center', 'center'

def get_yaxis_transform(self, which='grid'):
    assert which in ['tick1', 'tick2', 'grid']
    return self._yaxis_transform

def get_yaxis_text1_transform(self, pixelPad):
    if hasattr(self, 'yaxis') and len(self.yaxis.majorTicks) > 0:
        font_size = self.yaxis.majorTicks[0].label1.get_size()
    else:
        font_size = self._get_key("font.size")

    offset = self._get_key("axes.ylabel.correction")[2]
    return self._yaxis_text1_transform + self.PolarTranslate(self, pad=pixelPad + offset,
                                                             font_size=font_size), 'center', 'center'

def _gen_axes_patch(self):
    return Circle((0.5, 0.5), self._get_key("axes.radius") + 0.015)

def _gen_axes_spines(self, locations=None, offset=0.0, units='inches'):
    return {SmithAxes.name: Spine.circular_spine(self, (0.5, 0.5), self._get_key("axes.radius"))}

def set_xscale(self, *args, **kwargs):
    if args[0] != 'linear':
        raise NotImplementedError()
    Axes.set_xscale(self, *args, **kwargs)

def set_yscale(self, *args, **kwargs):
    if args[0] != 'linear':
        raise NotImplementedError()
    Axes.set_yscale(self, *args, **kwargs)

def set_xlim(self, *args, **kwargs):
    '''xlim is immutable and always set to (0, infinity)'''
    Axes.set_xlim(self, 0, self._ax_lim_x)

def set_ylim(self, *args, **kwargs):
    '''ylim is immutable and always set to (-infinity, infinity)'''
    Axes.set_ylim(self, -self._ax_lim_y, self._ax_lim_y)

def format_coord(self, re, im):
    sgn = "+" if im > 0 else "-"
    return "%.5f %s %.5fj" % (re, sgn, abs(im)) if re > 0 else ""

def get_data_ratio(self):
    return 1.0

# disable panning and zoom in matplotlib figure viewer
def can_zoom(self):
    return False

def start_pan(self, x, y, button):
    pass

def end_pan(self):
    pass

def drag_pan(self, button, key, x, y):
    pass

def _moebius_z(self, *args, normalize=None):
    '''
    Basic transformation.

    Arguments:

        *z*:
            Complex number or numpy.ndarray with dtype=complex

        *x, y*:
            Float numbers or numpy.ndarray's with dtype not complex

        *normalize*:
            If True, the values are normalized to self._impedance.
            If None, self._normalize determines behaviour.
            Accepts: boolean or None

    Returns:

        *w*:
            Performs w = (z - k) / (z + k) with k = 'axes.scale'
            Type: Complex number or numpy.ndarray with dtype=complex
    '''
    normalize = self._normalize if normalize is None else normalize
    norm = 1 if normalize else self._impedance
    return moebius_z(*args, norm=norm)

def _moebius_inv_z(self, *args, normalize=None):
    '''
    Basic inverse transformation.

    Arguments:

        *z*:
            Complex number or numpy.ndarray with dtype=complex

        *x, y*:
            Float numbers or numpy.ndarray's with dtype not complex

        *normalize*:
            If True, the values are normalized to self._impedance.
            If None, self._normalize determines behaviour.
            Accepts: boolean or None

    Returns:

        *w*:
            Performs w = k * (1 - z) / (1 + z) with k = 'axes.scale'
            Type: Complex number or numpy.ndarray with dtype=complex
    '''
    normalize = self._normalize if normalize is None else normalize
    norm = 1 if normalize else self._impedance
    return moebius_inv_z(*args, norm=norm)

def real_interp1d(self, x, steps):
    '''
    Interpolates the given vector as real numbers in the way, that they
    are evenly spaced after a transformation with imaginary part 0.

    Keyword Arguments

        *x*:
            Real values to interpolate.
            Accepts: 1D iterable (e.g. list or numpy.ndarray)

        *steps*:
            Number of steps between two points.
            Accepts: integer
    '''
    return self._moebius_inv_z(linear_interpolation(self._moebius_z(np.array(x)), steps))

def imag_interp1d(self, y, steps):
    '''
    Interpolates the given vector as imaginary numbers in the way, that
    they are evenly spaced after a transformation with real part 0.

    Keyword Arguments

        *y*:
            Imaginary values to interpolate.
            Accepts: 1D iterable (e.g. list or numpy.ndarray)

        *steps*:
            Number of steps between two points.
            Accepts: integer
    '''
    angs = np.angle(self._moebius_z(np.array(y) * 1j)) % TWO_PI
    i_angs = linear_interpolation(angs, steps)
    return np.imag(self._moebius_inv_z(ang_to_c(i_angs)))

def legend(self, *args, **kwargs):
    this_axes = self

    class SmithHandlerLine2D(HandlerLine2DCompound):
        def create_artists(self, legend, orig_handle,
                           xdescent, ydescent, width, height, fontsize,
                           trans):
            legline, legline_marker = HandlerLine2DCompound.create_artists(self, legend, orig_handle, xdescent, ydescent,
                                                                   width, height, fontsize, trans)

            if hasattr(orig_handle, "_markerhacked"):
                this_axes._hack_linedraw(legline_marker, True)
            return legline, legline_marker

    return Axes.legend(self, *args, handler_map={Line2D: SmithHandlerLine2D()}, **kwargs)

def plot(self, *args, **kwargs):
    '''
    Plot the given data into the Smith Chart. Behavior similar to basic
    :meth:`matplotlib.axes.Axes.plot`, but with some extensions:

        - Additional support for real and complex data. Complex values must be
        either of type 'complex' or a numpy.ndarray with dtype=complex.
        - If 'zorder' is not provided, the current default value is used.
        - If 'marker' is not providet, the default value is used.
        - Extra keywords are added.

    Extra keyword arguments:

        *datatype*:
            Specifies the input data format. Must be either 'S', 'Z' or 'Y'.
            Accepts: SmithAxes.[S_PARAMETER,Z_PARAMETER,Y_PARAMETER]
            Default: 'plot.default.datatype'

        *markerhack*:
            If set, activates the manipulation of start and end markern
            of the created line.
            Accepts: boolean
            Default: 'plot.marker.hack'

        *rotate_marker*:
            If *markerhack* is active, rotates the endmarker in direction
            of the corresponding path.
            Accepts: boolean
            Default: 'plot.rotatemarker'

        *interpolate*:
            If 'value' >0 the given data is interpolated linearly by 'value'
            steps in SmithAxes cooardinate space. 'markevery', if specified,
            will be modified accordingly. If 'True' the 'plot.default_intperpolation'
            value is used.
            Accepts: boolean or integer
            Default: False

        *equipoints*:
            If 'value' >0 the given data is interpolated linearly by equidistant
            steps in SmithAxes cooardinate space. Cannot be used with 'interpolate'
            enabled.
            Accepts: boolean
            Default: False

    See :meth:`matplotlib.axes.Axes.plot` for mor details
    '''
    # split input into real and imaginary part if complex
    new_args = ()
    for arg in args:
        # check if argument is a string or already an ndarray
        # if not, try to convert to an ndarray
        if not (isinstance(arg, str) or isinstance(arg, np.ndarray)):
            try:
                if isinstance(arg, Iterable):
                    arg = np.array(arg)
                elif isinstance(arg, Number):
                    arg = np.array([arg])
            except TypeError:
                pass

        # if (converted) arg is an ndarray of complex type, split it
        if isinstance(arg, np.ndarray) and arg.dtype in [np.complex64, np.complex128]:
            new_args += z_to_xy(arg)
        else:
            new_args += (arg,)

    # ensure newer plots are above older ones
    if 'zorder' not in kwargs:
        kwargs['zorder'] = self._current_zorder
        self._current_zorder += 0.001

    # extract or load non-matplotlib keyword arguments from parameters
    kwargs.setdefault("marker", self._get_key("plot.marker.default"))
    interpolate = kwargs.pop("interpolate", False)
    equipoints = kwargs.pop("equipoints", False)
    datatype = kwargs.pop("datatype", self._get_key("plot.default.datatype"))
    markerhack = kwargs.pop("markerhack", self._get_key("plot.marker.hack"))
    rotate_marker = kwargs.pop("rotate_marker", self._get_key("plot.marker.rotate"))

    if datatype not in self._datatypes:
        raise ValueError("'datatype' must be either '%s'" % ",".join(self._datatypes))

    if interpolate is not False:
        if equipoints > 0:
            raise ValueError("Interpolation is not available with equidistant markers")

        if interpolate is True:
            interpolate = self._get_key("plot.default.interpolation")
        elif interpolate < 0:
            raise ValueError("Interpolation is only for positive values possible!")

        if "markevery" in kwargs:
            mark = kwargs["markevery"]
            if isinstance(mark, Iterable):
                mark = np.asarray(mark) * (interpolate + 1)
            else:
                mark *= interpolate + 1
            kwargs["markevery"] = mark

    lines = Axes.plot(self, *new_args, **kwargs)
    for line in lines:
        cdata = xy_to_z(line.get_data())

        if datatype == SmithAxes.S_PARAMETER:
            z = self._moebius_inv_z(cdata)
        elif datatype == SmithAxes.Y_PARAMETER:
            z = 1 / cdata
        elif datatype == SmithAxes.Z_PARAMETER:
            z = cdata
        else:
            raise ValueError("'datatype' must be '%s', '%s' or '%s'" % (
            SmithAxes.S_PARAMETER, SmithAxes.Z_PARAMETER, SmithAxes.Y_PARAMETER))

        if self._normalize and datatype != SmithAxes.S_PARAMETER:
            z /= self._impedance

        line.set_data(z_to_xy(z))

        if interpolate or equipoints:
            z = self._moebius_z(*line.get_data())
            if len(z) > 1:
                spline, t0 = fitpack.splprep(z_to_xy(z), s=0)
                ilen = (interpolate + 1) * (len(t0) - 1) + 1
                if equipoints == 1:
                    t = np.linspace(0, 1, ilen)
                elif equipoints > 1:
                    t = np.linspace(0, 1, equipoints)
                else:
                    t = np.zeros(ilen)
                    t[0], t[1:] = t0[0], np.concatenate(
                        [np.linspace(i0, i1, interpolate + 2)[1:] for i0, i1 in zip(t0[:-1], t0[1:])])

                z = self._moebius_inv_z(*fitpack.splev(t, spline))
                line.set_data(z_to_xy(z))

        if markerhack:
            self._hack_linedraw(line, rotate_marker)

    return lines

def grid(self,
         b=None,
         which='major',
         fancy=None,
         dividers=None,
         threshold=None,
         **kwargs):
    '''
    Complete rewritten grid function. Gridlines are replaced with Arcs,
    which reduces the amount of points to store and increases speed. The
    grid consist of a minor and major part, which can be drawn either as
    standard with lines from axis to axis, or fancy with dynamic spacing
    and length adaption.

    Keyword arguments:

        *b*:
            Enables or disables the selected grid.
            Accepts: boolean

        *which*:
            The grid to be drawn.
            Accepts: ['major', 'minor', 'both']

        *axis*:
            The axis to be drawn. x=real and y=imaginary
            Accepts: ['x', 'y', 'both']
            Note: if fancy is set, only 'both' is valid

        *fancy*:
            If set to 'True', draws the grid on the fancy way.
            Accepts: boolean

        *dividers*:
            Adaptive divisions for the minor fancy grid.
            Accepts: array with integers
            Note: has no effect on major and non-fancy grid

        *threshold*:
            Threshold for dynamic adaption of spacing and line length. Can
            be specified for both axis together or each seperatly.
            Accepts: float or (float, float)

        **kwargs*:
            Keyword arguments passed to the gridline creator.
            Note: Gridlines are :class:`matplotlib.patches.Patch` and does
            not accept all arguments :class:`matplotlib.lines.Line2D`
            accepts.
    '''
    assert which in ["both", "major", "minor"]
    assert fancy in [None, False, True]

    def get_kwargs(grid):
        kw = kwargs.copy()
        kw.setdefault('zorder', self._get_key("grid.zorder"))
        kw.setdefault("alpha", self._get_key("grid.alpha"))

        for key in ["linestyle", "linewidth", "color"]:
            if grid == "minor" and key == "linestyle":
                if "linestyle" not in kw:
                    kw.setdefault("dash_capstyle", self._get_key("grid.minor.capstyle"))
                    kw.setdefault("dashes", self._get_key("grid.minor.dashes"))
            else:
                kw.setdefault(key, self._get_key("grid.%s.%s" % (grid, key)))

        return kw

    def check_fancy(yticks):
        # checks if the imaginary axis is symetric
        len_y = (len(yticks) - 1) // 2
        if not (len(yticks) % 2 == 1 and (yticks[len_y:] + yticks[len_y::-1] < EPSILON).all()):
            raise ValueError(
                "fancy minor grid is only supported for zero-symetric imaginary grid - e.g. ImagMaxNLocator")
        return yticks[len_y:]

    def split_threshold(threshold):
        if isinstance(threshold, tuple):
            thr_x, thr_y = threshold
        else:
            thr_x = thr_y = threshold

        assert thr_x > 0 and thr_y > 0

        return thr_x / 1000, thr_y / 1000

    def add_arc(ps, p0, p1, grid, type):
        assert grid in ["major", "minor"]
        assert type in ["real", "imag"]
        assert p0 != p1
        arcs = self._majorarcs if grid == "major" else self._minorarcs
        if grid == "minor":
            param["zorder"] -= 1e-9
        arcs.append((type, (ps, p0, p1), self._add_gridline(ps, p0, p1, type, **param)))

    def draw_nonfancy(grid):
        if grid == "major":
            xticks = self.xaxis.get_majorticklocs()
            yticks = self.yaxis.get_majorticklocs()
        else:
            xticks = self.xaxis.get_minorticklocs()
            yticks = self.yaxis.get_minorticklocs()

        xticks = np.round(xticks, 7)
        yticks = np.round(yticks, 7)

        for xs in xticks:
            if xs < self._near_inf:
                add_arc(xs, -self._near_inf, self._inf, grid, "real")

        for ys in yticks:
            if abs(ys) < self._near_inf:
                add_arc(ys, 0, self._inf, grid, "imag")

    # set fancy parameters
    if fancy is None:
        fancy_major = self._get_key("grid.major.fancy")
        fancy_minor = self._get_key("grid.minor.fancy")
    else:
        fancy_major = fancy_minor = fancy

    # check parameters
    if "axis" in kwargs and kwargs["axis"] != "both":
        raise ValueError("Only 'both' is a supported value for 'axis'")

    # plot major grid
    if which in ['both', 'major']:
        for _, _, arc in self._majorarcs:
            arc.remove()
        self._majorarcs = []

        if b:
            param = get_kwargs('major')
            if fancy_major:
                xticks = np.sort(self.xaxis.get_majorticklocs())
                yticks = np.sort(self.yaxis.get_majorticklocs())
                assert len(xticks) > 0 and len(yticks) > 0
                yticks = check_fancy(yticks)

                if threshold is None:
                    threshold = self._get_key("grid.major.fancy.threshold")

                thr_x, thr_y = split_threshold(threshold)

                # draw the 0 line
                add_arc(yticks[0], 0, self._inf, "major", "imag")

                tmp_yticks = yticks.copy()
                for xs in xticks:
                    k = 1
                    while k < len(tmp_yticks):
                        y0, y1 = tmp_yticks[k - 1:k + 1]
                        if abs(self._moebius_z(xs, y0) - self._moebius_z(xs, y1)) < thr_x:
                            add_arc(y1, 0, xs, "major", "imag")
                            add_arc(-y1, 0, xs, "major", "imag")
                            tmp_yticks = np.delete(tmp_yticks, k)
                        else:
                            k += 1

                for i in range(1, len(yticks)):
                    y0, y1 = yticks[i - 1:i + 1]
                    k = 1
                    while k < len(xticks):
                        x0, x1 = xticks[k - 1:k + 1]
                        if abs(self._moebius_z(x0, y1) - self._moebius_z(x1, y1)) < thr_y:
                            add_arc(x1, -y0, y0, "major", "real")
                            xticks = np.delete(xticks, k)
                        else:
                            k += 1
            else:
                draw_nonfancy("major")

    # plot minor grid
    if which in ['both', 'minor']:
        # remove the old grid
        for _, _, arc in self._minorarcs:
            arc.remove()
        self._minorarcs = []

        if b:
            param = get_kwargs("minor")

            if fancy_minor:
                # 1. Step: get x/y grid data
                xticks = np.sort(self.xaxis.get_majorticklocs())
                yticks = np.sort(self.yaxis.get_majorticklocs())
                assert len(xticks) > 0 and len(yticks) > 0
                yticks = check_fancy(yticks)

                if dividers is None:
                    dividers = self._get_key("grid.minor.fancy.dividers")
                assert len(dividers) > 0
                dividers = np.sort(dividers)

                if threshold is None:
                    threshold = self._get_key("grid.minor.fancy.threshold")

                thr_x, thr_y = split_threshold(threshold)
                len_x, len_y = len(xticks) - 1, len(yticks) - 1

                # 2. Step: calculate optimal gridspacing for each quadrant
                d_mat = np.ones((len_x, len_y, 2))

                # TODO: optimize spacing algorithm
                for i in range(len_x):
                    for k in range(len_y):
                        x0, x1 = xticks[i:i + 2]
                        y0, y1 = yticks[k:k + 2]

                        xm = self.real_interp1d([x0, x1], 2)[1]
                        ym = self.imag_interp1d([y0, y1], 2)[1]

                        x_div = y_div = dividers[0]

                        for div in dividers[1:]:
                            if abs(self._moebius_z(x1 - (x1 - x0) / div, ym) - self._moebius_z(x1, ym)) > thr_x:
                                x_div = div
                            else:
                                break

                        for div in dividers[1:]:
                            if abs(self._moebius_z(xm, y1) - self._moebius_z(xm, y1 - (y1 - y0) / div)) > thr_y:
                                y_div = div
                            else:
                                break

                        d_mat[i, k] = [x_div, y_div]

                # 3. Steps: optimize spacing
                # ensure the x-spacing declines towards infinity
                d_mat[:-1, 0, 0] = list(map(np.max, zip(d_mat[:-1, 0, 0], d_mat[1:, 0, 0])))

                # find the values which are near (0, 0.5) on the plot
                idx = np.searchsorted(xticks, self._moebius_inv_z(0)) + 1
                idy = np.searchsorted(yticks, self._moebius_inv_z(1j).imag)

                # extend the values around the center towards the border
                if idx > idy:
                    for d in range(idy):
                        delta = idx - idy + d
                        d_mat[delta, :d + 1] = d_mat[:delta, d] = d_mat[delta, 0]
                else:
                    for d in range(idx):
                        delta = idy - idx + d
                        d_mat[:d + 1, delta] = d_mat[d, :delta] = d_mat[d, 0]

                # 4. Step: gather and optimize the lines
                x_lines, y_lines = [], []

                for i in range(len_x):
                    x0, x1 = xticks[i:i + 2]

                    for k in range(len_y):
                        y0, y1 = yticks[k:k + 2]

                        x_div, y_div = d_mat[i, k]

                        for xs in np.linspace(np.int32(x0), np.int32(x1), np.int32(x_div) + 1)[1:]:
                            x_lines.append([xs, y0, y1])
                            x_lines.append([xs, -y1, -y0])

                        for ys in np.linspace(np.int32(y0), np.int32(y1), np.int32(y_div) + 1)[1:]:
                            y_lines.append([ys, x0, x1])
                            y_lines.append([-ys, x0, x1])

                # round values to prevent float inaccuarcy
                x_lines = np.round(np.array(x_lines), 7)
                y_lines = np.round(np.array(y_lines), 7)

                # remove lines which overlap with the major grid
                for tp, lines in [("real", x_lines), ("imag", y_lines)]:
                    for i in range(len(lines)):
                        ps, p0, p1 = lines[i]
                        if p0 > p1:
                            p0, p1 = p1, p0

                        for tq, (qs, q0, q1), _ in self._majorarcs:
                            if tp == tq and abs(ps - qs) < EPSILON and p1 > q0 and p0 < q1:
                                lines[i, :] = np.nan
                                break

                    lines = lines[~np.isnan(lines[:, 0])]
                    lines = lines[np.lexsort(lines[:, 1::-1].transpose())]

                    ps, p0, p1 = lines[0]
                    for qs, q0, q1 in lines[1:]:
                        if ps != qs or p1 != q0:
                            add_arc(ps, p0, p1, "minor", tp)
                            ps, p0, p1 = qs, q0, q1
                        else:
                            p1 = q1

            else:
                draw_nonfancy("minor")

def _hack_linedraw(self, line, rotate_marker=None):
    '''
    Modifies the draw method of a :class:`matplotlib.lines.Line2D` object
    to draw different stard and end marker.

    Keyword arguments:

        *line*:
            Line to be modified
            Accepts: Line2D

        *rotate_marker*:
            If set, the end marker will be rotated in direction of their
            corresponding path.
            Accepts: boolean
    '''
    assert isinstance(line, Line2D)

    def new_draw(self_line, renderer):
        def new_draw_markers(self_renderer, gc, marker_path, marker_trans, path, trans, rgbFace=None):
            # get the drawn path for determining the rotation angle
            line_vertices = self_line._get_transformed_path().get_fully_transformed_path().vertices
            vertices = path.vertices

            if len(vertices) == 1:
                line_set = [[default_marker, vertices]]
            else:
                if rotate_marker:
                    dx, dy = np.array(line_vertices[-1]) - np.array(line_vertices[-2])
                    end_rot = MarkerStyle(end.get_marker())
                    end_rot._transform += Affine2D().rotate(np.arctan2(dy, dx) - np.pi / 2)
                else:
                    end_rot = end

                if len(vertices) == 2:
                    line_set = [[start, vertices[0:1]], [end_rot, vertices[1:2]]]
                else:
                    line_set = [[start, vertices[0:1]], [default_marker, vertices[1:-1]], [end_rot, vertices[-1:]]]

            for marker, points in line_set:
                transform = marker.get_transform() + Affine2D().scale(self_line._markersize)
                old_draw_markers(gc, marker.get_path(), transform, Path(points), trans, rgbFace)

        old_draw_markers = renderer.draw_markers
        renderer.draw_markers = MethodType(new_draw_markers, renderer)
        old_draw(renderer)
        renderer.draw_markers = old_draw_markers

    default_marker = line._marker
    # check if marker is set and visible
    if default_marker:
        start = MarkerStyle(self._get_key("plot.marker.start"))
        if start.get_marker() is None:
            start = default_marker

        end = MarkerStyle(self._get_key("plot.marker.end"))
        if end.get_marker() is None:
            end = default_marker

        if rotate_marker is None:
            rotate_marker = self._get_key("plot.marker.rotate")

        old_draw = line.draw
        line.draw = MethodType(new_draw, line)
        line._markerhacked = True

def _add_gridline(self, ps, p0, p1, type, **kwargs):
    '''
    Add a gridline for a real axis circle.

    Keyword arguments:

        *ps*:
            Axis value
            Accepts: float

        *p0*:
            Start point
            Accepts: float

        *p1*:
            End Point
            Accepts: float

        **kwargs*:
            Keywords passed to the arc creator
    '''
    assert type in ["real", "imag"]

    if type == "real":
        assert ps >= 0

        line = Line2D(2 * [ps], [p0, p1], **kwargs)
        line.get_path()._interpolation_steps = "x_gridline"
    else:
        assert 0 <= p0 < p1

        line = Line2D([p0, p1], 2 * [ps], **kwargs)

        if abs(ps) > EPSILON:
            line.get_path()._interpolation_steps = "y_gridline"

    return self.add_artist(line)

class MoebiusTransform(Transform):
    '''
    Class for transforming points and paths to Smith Chart data space.
    '''
    input_dims = 2
    output_dims = 2
    is_separable = False

    def __init__(self, axes):
        assert isinstance(axes, SmithAxes)
        Transform.__init__(self)
        self._axes = axes

    def transform_non_affine(self, data):
        def _moebius_xy(_xy):
            return z_to_xy(self._axes._moebius_z(*_xy))

        if isinstance(data[0], Iterable):
            return list(map(_moebius_xy, data))
        else:
            return _moebius_xy(data)

    def transform_path_non_affine(self, path):
        vertices = path.vertices
        codes = path.codes

        linetype = path._interpolation_steps
        if linetype in ["x_gridline", "y_gridline"]:
            assert len(vertices) == 2

            x, y = np.array(list(zip(*vertices)))
            z = self._axes._moebius_z(x, y)

            if linetype == "x_gridline":
                assert x[0] == x[1]
                zm = 0.5 * (1 + self._axes._moebius_z(x[0]))
            else:
                assert y[0] == y[1]
                scale = 1j * (1 if self._axes._normalize else self._axes._impedance)
                zm = 1 + scale / y[0]

            d = 2 * abs(zm - 1)
            ang0, ang1 = np.angle(z - zm, deg=True) % 360

            reverse = ang0 > ang1
            if reverse:
                ang0, ang1 = ang1, ang0

            arc = Arc(z_to_xy(zm), d, d, theta1=ang0, theta2=ang1, transform=self._axes.transMoebius)
            arc._path = Path.arc(ang0, ang1)  # fix for Matplotlib 2.1+
            arc_path = arc.get_patch_transform().transform_path(arc.get_path())

            if reverse:
                new_vertices = arc_path.vertices[::-1]
            else:
                new_vertices = arc_path.vertices

            new_codes = arc_path.codes
        elif linetype == 1:
            new_vertices = self.transform_non_affine(vertices)
            new_codes = codes
        else:
            raise NotImplementedError("Value for 'path_interpolation' cannot be interpreted.")

        return Path(new_vertices, new_codes)

    def inverted(self):
        return SmithAxes.InvertedMoebiusTransform(self._axes)

class InvertedMoebiusTransform(Transform):
    '''
    Inverse transformation for points and paths in Smith Chart data space.
    '''
    input_dims = 2
    output_dims = 2
    is_separable = False

    def __init__(self, axes):
        assert isinstance(axes, SmithAxes)
        Transform.__init__(self)
        self._axes = axes

    def transform_non_affine(self, data):
        def _moebius_inv_xy(_xy):
            return z_to_xy(self._axes._moebius_inv_z(*_xy))

        return list(map(_moebius_inv_xy, data))

    def inverted(self):
        return SmithAxes.MoebiusTransform(self._axes)

class PolarTranslate(Transform):
    '''
    Transformation for translating points away from the center by a given
    padding.

    Keyword arguments:

        *axes*:
            Parent :class:`SmithAxes`
            Accepts: SmithAxes instance

        *pad*:
            Distance to translate away from center for x and y values.

        *font_size*:
            y values are shiftet 0.5 * font_size further away.
    '''
    input_dims = 2
    output_dims = 2
    is_separable = False

    def __init__(self, axes, pad, font_size):
        Transform.__init__(self, shorthand_name=None)
        self.axes = axes
        self.pad = pad
        self.font_size = font_size

    def transform_non_affine(self, xy):
        def _translate(_xy):
            x, y = _xy
            ang = np.angle(complex(x - x0, y - y0))
            return x + np.cos(ang) * self.pad, y + np.sin(ang) * (self.pad + 0.5 * self.font_size)

        x0, y0 = self.axes.transAxes.transform([0.5, 0.5])
        if isinstance(xy[0], Iterable):
            return list(map(_translate, xy))
        else:
            return _translate(xy)

class RealMaxNLocator(Locator):
    '''
    Locator for the real axis of a SmithAxes. Creates a nicely rounded
    spacing with maximum n values. The transformed center value is
    always included.

    Keyword arguments:

        *axes*:
            Parent SmithAxes
            Accepts: SmithAxes instance

        *n*:
            Maximum number of divisions
            Accepts: integer

        *precision*:
            Maximum number of significant decimals
            Accepts: integer
    '''

    def __init__(self, axes, n, precision=None):
        assert isinstance(axes, SmithAxes)
        assert n > 0

        Locator.__init__(self)
        self.steps = n
        if precision is None:
            self.precision = axes._get_key("grid.locator.precision")
        else:
            self.precision = precision
        assert self.precision > 0

        self.ticks = None
        self.axes = axes

    def __call__(self):
        if self.ticks is None:
            self.ticks = self.tick_values(0, self.axes._inf)
        return self.ticks

    def nice_round(self, num, down=True):
        # normalize to 'precision' decimals befor comma
        exp = np.ceil(np.log10(np.abs(num) + EPSILON))
        if exp < 1:  # fix for leading 0
            exp += 1
        norm = 10 ** -(exp - self.precision)

        num_normed = num * norm
        # increase precision by 0.5, if normed value is smaller than 1/3
        # of its decade range
        if num_normed < 3.3:
            norm *= 2
        # decrease precision by 1, if normed value is bigger than 1/2
        elif num_normed > 50:
            norm /= 10

        # select rounding function
        if not 1 < num_normed % 10 < 9:
            # round to nearest value, if last digit is 1 or 9
            if abs(num_normed % 10 - 1) < EPSILON:
                num -= 0.5 / norm
            f_round = np.round
        else:
            f_round = np.floor if down else np.ceil

        return f_round(np.round(num * norm, 1)) / norm

    def tick_values(self, vmin, vmax):
        tmin, tmax = self.transform(vmin), self.transform(vmax)
        mean = self.transform(self.nice_round(self.invert(0.5 * (tmin + tmax))))

        result = [tmin, tmax, mean]
        d0 = abs(tmin - tmax) / (self.steps + 1)
        # calculate values above and below mean, adapt delta
        for sgn, side, end in [[1, False, tmax], [-1, True, tmin]]:
            d, d0 = d0, None
            last = mean
            while True:
                new = last + d * sgn
                if self.out_of_range(new) or abs(end - new) < d / 2:
                    break

                # round new value to the next nice display value
                new = self.transform(self.nice_round(self.invert(new), side))
                d = abs(new - last)
                if d0 is None:
                    d0 = d

                last = new
                result.append(last)

        return np.sort(self.invert(np.array(result)))

    def out_of_range(self, x):
        return abs(x) > 1

    def transform(self, x):
        return self.axes._moebius_z(x)

    def invert(self, x):
        return self.axes._moebius_inv_z(x)

class ImagMaxNLocator(RealMaxNLocator):
    def __init__(self, axes, n, precision=None):
        SmithAxes.RealMaxNLocator.__init__(self, axes, n // 2, precision)

    def __call__(self):
        if self.ticks is None:
            tmp = self.tick_values(0, self.axes._inf)
            self.ticks = np.concatenate((-tmp[:0:-1], tmp))
        return self.ticks

    def out_of_range(self, x):
        return not 0 <= x <= np.pi

    def transform(self, x):
        return np.pi - np.angle(self.axes._moebius_z(x * 1j))

    def invert(self, x):
        return np.imag(-self.axes._moebius_inv_z(ang_to_c(np.pi + np.array(x))))

class SmithAutoMinorLocator(AutoMinorLocator):
    '''
    AutoLocator for SmithAxes. Returns linear spaced intermediate ticks
    depending on the major tickvalues.

    Keyword arguments:

        *n*:
            Number of intermediate ticks
            Accepts: positive integer
    '''

    def __init__(self, n=4):
        assert isinstance(n, int) and n > 0
        AutoMinorLocator.__init__(self, n=n)
        self._ticks = None

    def __call__(self):
        if self._ticks is None:
            locs = self.axis.get_majorticklocs()
            self._ticks = np.concatenate(
                [np.linspace(p0, p1, self.ndivs + 1)[1:-1] for (p0, p1) in zip(locs[:-1], locs[1:])])
        return self._ticks

class RealFormatter(Formatter):
    '''
    Formatter for the real axis of a SmithAxes. Prints the numbers as
    float and removes trailing zeros and commata. Special returns:
        '' for 0.

    Keyword arguments:

        *axes*:
            Parent axes
            Accepts: SmithAxes instance
    '''

    def __init__(self, axes, *args, **kwargs):
        assert isinstance(axes, SmithAxes)
        Formatter.__init__(self, *args, **kwargs)
        self._axes = axes

    def __call__(self, x, pos=None):
        if x < EPSILON or x > self._axes._near_inf:
            return ""
        else:
            return ('%f' % x).rstrip('0').rstrip('.')

class ImagFormatter(RealFormatter):
    '''
    Formatter for the imaginary axis of a SmithAxes. Prints the numbers
    as  float and removes trailing zeros and commata. Special returns:
        - '' for minus infinity
        - 'symbol.infinity' from scParams for plus infinity
        - '0' for value near zero (prevents -0)

    Keyword arguments:

        *axes*:
            Parent axes
            Accepts: SmithAxes instance
    '''

    def __call__(self, x, pos=None):
        if x < -self._axes._near_inf:
            return ""
        elif x > self._axes._near_inf:
            return self._axes._get_key("symbol.infinity")  # utf8 infinity symbol
        elif abs(x) < EPSILON:
            return "0"
        else:
            return ("%f" % x).rstrip('0').rstrip('.') + "j"

# update docstrings for all methode not set
for key, value in locals().copy().items():
    if isinstance(value, FunctionType):
        if value.__doc__ is None and hasattr(Axes, key):
            value.__doc__ = getattr(Axes, key).__doc__

author = "Paul Staerke" copyright = "Copyright 2018, Paul Staerke" license = "BSD" version = "0.3" maintainer = "Paul Staerke" email = "paul.staerke@gmail.com" status = "Prototype"

def xy_to_z(xy): if len(xy) == 1: z = xy[0] if isinstance(z, Iterable): z = np.array(z) if len(z.shape) == 2: z = z[0] + 1j z[1] elif len(z.shape) > 2: raise ValueError("Something went wrong!") elif len(xy) == 2: x, y = xy if isinstance(x, Iterable): if isinstance(y, Iterable) and len(x) == len(y): z = np.array(x) + 1j np.array(y) else: raise ValueError("x and y vectors dont match in type and/or size") else: z = x + 1j y else: raise ValueError("Arguments are not valid - specify either complex number/vector z or real and imaginary number/vector x, y")

return z

def z_to_xy(z): return z.real, z.imag

def moebius_z(args, norm): z = xy_to_z(args) return 1 - 2 * norm / (z + norm)

def moebius_inv_z(args, norm): z = xy_to_z(args) return norm * (1 + z) / (1 - z)

def ang_to_c(ang, radius=1): return radius (np.cos(ang) + np.sin(ang) 1j)

def lambda_to_rad(lmb): return lmb 4 np.pi

def rad_to_lambda(rad): return rad * 0.25 / np.pi

import sys

import numpy as np from matplotlib import rcParams, pyplot as pp from matplotlib.projections import register_projection register_projection(SmithAxes) rcParams.update({"legend.numpoints": 3})

sys.path.append("..")

sample data

data = np.loadtxt("data/s11.csv", delimiter=",", skiprows=1)[::100] val1 = data[:, 1] + data[:, 2] * 1j

data = np.loadtxt("data/s22.csv", delimiter=",", skiprows=1)[::100] val2 = data[:, 1] + data[:, 2] * 1j

plot data

pp.figure(figsize=(6, 6))

ax = pp.subplot(1, 1, 1, projection='smith') pp.plot([10, 100], markevery=1)

pp.plot(200 + 100j, datatype=SmithAxes.Z_PARAMETER) pp.plot(50 val1, label="default", datatype=SmithAxes.Z_PARAMETER) pp.plot(50 val2, markevery=1, label="interpolate=3", interpolate=3, datatype=SmithAxes.Z_PARAMETER) pp.plot(val1, markevery=1, label="equipoints=22", equipoints=22, datatype=SmithAxes.S_PARAMETER) pp.plot(val2, markevery=3, label="equipoints=22, \nmarkevery=3", equipoints=22, datatype=SmithAxes.S_PARAMETER)

leg = pp.legend(loc="lower right", fontsize=12) pp.title("Matplotlib Smith Chart Projection")

pp.savefig("export.pdf", format="pdf", bbox_inches="tight") pp.show() `