HW1 Done

HW1_Stones/env/lib/python3.7/site-packages/matplotlib/projections/__init__.py

@@ -0,0 +1,72 @@
+from .. import axes, cbook
+from .geo import AitoffAxes, HammerAxes, LambertAxes, MollweideAxes
+from .polar import PolarAxes
+
+
+class ProjectionRegistry:
+    """
+    Manages the set of projections available to the system.
+    """
+    def __init__(self):
+        self._all_projection_types = {}
+
+    def register(self, *projections):
+        """
+        Register a new set of projections.
+        """
+        for projection in projections:
+            name = projection.name
+            self._all_projection_types[name] = projection
+
+    def get_projection_class(self, name):
+        """
+        Get a projection class from its *name*.
+        """
+        return self._all_projection_types[name]
+
+    def get_projection_names(self):
+        """
+        Get a list of the names of all projections currently registered.
+        """
+        return sorted(self._all_projection_types)
+
+
+projection_registry = ProjectionRegistry()
+projection_registry.register(
+    axes.Axes,
+    PolarAxes,
+    AitoffAxes,
+    HammerAxes,
+    LambertAxes,
+    MollweideAxes)
+
+
+def register_projection(cls):
+    projection_registry.register(cls)
+
+
+def get_projection_class(projection=None):
+    """
+    Get a projection class from its name.
+
+    If *projection* is None, a standard rectilinear projection is returned.
+    """
+    if projection is None:
+        projection = 'rectilinear'
+
+    try:
+        return projection_registry.get_projection_class(projection)
+    except KeyError:
+        raise ValueError("Unknown projection %r" % projection)
+
+
+@cbook.deprecated("3.1")
+def process_projection_requirements(figure, *args, **kwargs):
+    return figure._process_projection_requirements(*args, **kwargs)
+
+
+def get_projection_names():
+    """
+    Get a list of acceptable projection names.
+    """
+    return projection_registry.get_projection_names()

HW1_Stones/env/lib/python3.7/site-packages/matplotlib/projections/geo.py

@@ -0,0 +1,530 @@
+import numpy as np
+
+from matplotlib import cbook, rcParams
+from matplotlib.axes import Axes
+import matplotlib.axis as maxis
+from matplotlib.patches import Circle
+from matplotlib.path import Path
+import matplotlib.spines as mspines
+from matplotlib.ticker import (
+    Formatter, NullLocator, FixedLocator, NullFormatter)
+from matplotlib.transforms import Affine2D, BboxTransformTo, Transform
+
+
+class GeoAxes(Axes):
+    """An abstract base class for geographic projections."""
+    class ThetaFormatter(Formatter):
+        """
+        Used to format the theta tick labels.  Converts the native
+        unit of radians into degrees and adds a degree symbol.
+        """
+        def __init__(self, round_to=1.0):
+            self._round_to = round_to
+
+        def __call__(self, x, pos=None):
+            degrees = (x / np.pi) * 180.0
+            degrees = np.round(degrees / self._round_to) * self._round_to
+            if rcParams['text.usetex'] and not rcParams['text.latex.unicode']:
+                return r"$%0.0f^\circ$" % degrees
+            else:
+                return "%0.0f\N{DEGREE SIGN}" % degrees
+
+    RESOLUTION = 75
+
+    def _init_axis(self):
+        self.xaxis = maxis.XAxis(self)
+        self.yaxis = maxis.YAxis(self)
+        # Do not register xaxis or yaxis with spines -- as done in
+        # Axes._init_axis() -- until GeoAxes.xaxis.cla() works.
+        # self.spines['geo'].register_axis(self.yaxis)
+        self._update_transScale()
+
+    def cla(self):
+        Axes.cla(self)
+
+        self.set_longitude_grid(30)
+        self.set_latitude_grid(15)
+        self.set_longitude_grid_ends(75)
+        self.xaxis.set_minor_locator(NullLocator())
+        self.yaxis.set_minor_locator(NullLocator())
+        self.xaxis.set_ticks_position('none')
+        self.yaxis.set_ticks_position('none')
+        self.yaxis.set_tick_params(label1On=True)
+        # Why do we need to turn on yaxis tick labels, but
+        # xaxis tick labels are already on?
+
+        self.grid(rcParams['axes.grid'])
+
+        Axes.set_xlim(self, -np.pi, np.pi)
+        Axes.set_ylim(self, -np.pi / 2.0, np.pi / 2.0)
+
+    def _set_lim_and_transforms(self):
+        # A (possibly non-linear) projection on the (already scaled) data
+        self.transProjection = self._get_core_transform(self.RESOLUTION)
+
+        self.transAffine = self._get_affine_transform()
+
+        self.transAxes = BboxTransformTo(self.bbox)
+
+        # The complete data transformation stack -- from data all the
+        # way to display coordinates
+        self.transData = \
+            self.transProjection + \
+            self.transAffine + \
+            self.transAxes
+
+        # This is the transform for longitude ticks.
+        self._xaxis_pretransform = \
+            Affine2D() \
+            .scale(1, self._longitude_cap * 2) \
+            .translate(0, -self._longitude_cap)
+        self._xaxis_transform = \
+            self._xaxis_pretransform + \
+            self.transData
+        self._xaxis_text1_transform = \
+            Affine2D().scale(1, 0) + \
+            self.transData + \
+            Affine2D().translate(0, 4)
+        self._xaxis_text2_transform = \
+            Affine2D().scale(1, 0) + \
+            self.transData + \
+            Affine2D().translate(0, -4)
+
+        # This is the transform for latitude ticks.
+        yaxis_stretch = Affine2D().scale(np.pi * 2, 1).translate(-np.pi, 0)
+        yaxis_space = Affine2D().scale(1, 1.1)
+        self._yaxis_transform = \
+            yaxis_stretch + \
+            self.transData
+        yaxis_text_base = \
+            yaxis_stretch + \
+            self.transProjection + \
+            (yaxis_space + \
+             self.transAffine + \
+             self.transAxes)
+        self._yaxis_text1_transform = \
+            yaxis_text_base + \
+            Affine2D().translate(-8, 0)
+        self._yaxis_text2_transform = \
+            yaxis_text_base + \
+            Affine2D().translate(8, 0)
+
+    def _get_affine_transform(self):
+        transform = self._get_core_transform(1)
+        xscale, _ = transform.transform_point((np.pi, 0))
+        _, yscale = transform.transform_point((0, np.pi / 2))
+        return Affine2D() \
+            .scale(0.5 / xscale, 0.5 / yscale) \
+            .translate(0.5, 0.5)
+
+    def get_xaxis_transform(self, which='grid'):
+        cbook._check_in_list(['tick1', 'tick2', 'grid'], which=which)
+        return self._xaxis_transform
+
+    def get_xaxis_text1_transform(self, pad):
+        return self._xaxis_text1_transform, 'bottom', 'center'
+
+    def get_xaxis_text2_transform(self, pad):
+        return self._xaxis_text2_transform, 'top', 'center'
+
+    def get_yaxis_transform(self, which='grid'):
+        cbook._check_in_list(['tick1', 'tick2', 'grid'], which=which)
+        return self._yaxis_transform
+
+    def get_yaxis_text1_transform(self, pad):
+        return self._yaxis_text1_transform, 'center', 'right'
+
+    def get_yaxis_text2_transform(self, pad):
+        return self._yaxis_text2_transform, 'center', 'left'
+
+    def _gen_axes_patch(self):
+        return Circle((0.5, 0.5), 0.5)
+
+    def _gen_axes_spines(self):
+        return {'geo': mspines.Spine.circular_spine(self, (0.5, 0.5), 0.5)}
+
+    def set_yscale(self, *args, **kwargs):
+        if args[0] != 'linear':
+            raise NotImplementedError
+
+    set_xscale = set_yscale
+
+    def set_xlim(self, *args, **kwargs):
+        raise TypeError("It is not possible to change axes limits "
+                        "for geographic projections. Please consider "
+                        "using Basemap or Cartopy.")
+
+    set_ylim = set_xlim
+
+    def format_coord(self, lon, lat):
+        'return a format string formatting the coordinate'
+        lon, lat = np.rad2deg([lon, lat])
+        if lat >= 0.0:
+            ns = 'N'
+        else:
+            ns = 'S'
+        if lon >= 0.0:
+            ew = 'E'
+        else:
+            ew = 'W'
+        return ('%f\N{DEGREE SIGN}%s, %f\N{DEGREE SIGN}%s'
+                % (abs(lat), ns, abs(lon), ew))
+
+    def set_longitude_grid(self, degrees):
+        """
+        Set the number of degrees between each longitude grid.
+        """
+        # Skip -180 and 180, which are the fixed limits.
+        grid = np.arange(-180 + degrees, 180, degrees)
+        self.xaxis.set_major_locator(FixedLocator(np.deg2rad(grid)))
+        self.xaxis.set_major_formatter(self.ThetaFormatter(degrees))
+
+    def set_latitude_grid(self, degrees):
+        """
+        Set the number of degrees between each latitude grid.
+        """
+        # Skip -90 and 90, which are the fixed limits.
+        grid = np.arange(-90 + degrees, 90, degrees)
+        self.yaxis.set_major_locator(FixedLocator(np.deg2rad(grid)))
+        self.yaxis.set_major_formatter(self.ThetaFormatter(degrees))
+
+    def set_longitude_grid_ends(self, degrees):
+        """
+        Set the latitude(s) at which to stop drawing the longitude grids.
+        """
+        self._longitude_cap = np.deg2rad(degrees)
+        self._xaxis_pretransform \
+            .clear() \
+            .scale(1.0, self._longitude_cap * 2.0) \
+            .translate(0.0, -self._longitude_cap)
+
+    def get_data_ratio(self):
+        '''
+        Return the aspect ratio of the data itself.
+        '''
+        return 1.0
+
+    ### Interactive panning
+
+    def can_zoom(self):
+        """
+        Return *True* if this axes supports the zoom box button functionality.
+
+        This axes object does not support interactive zoom box.
+        """
+        return False
+
+    def can_pan(self) :
+        """
+        Return *True* if this axes supports the pan/zoom button functionality.
+
+        This axes object does not support interactive pan/zoom.
+        """
+        return False
+
+    def start_pan(self, x, y, button):
+        pass
+
+    def end_pan(self):
+        pass
+
+    def drag_pan(self, button, key, x, y):
+        pass
+
+
+class _GeoTransform(Transform):
+    # Factoring out some common functionality.
+    input_dims = 2
+    output_dims = 2
+    is_separable = False
+
+    def __init__(self, resolution):
+        """
+        Create a new geographical transform.
+
+        Resolution is the number of steps to interpolate between each input
+        line segment to approximate its path in curved space.
+        """
+        Transform.__init__(self)
+        self._resolution = resolution
+
+    def __str__(self):
+        return "{}({})".format(type(self).__name__, self._resolution)
+
+    def transform_path_non_affine(self, path):
+        # docstring inherited
+        ipath = path.interpolated(self._resolution)
+        return Path(self.transform(ipath.vertices), ipath.codes)
+
+
+class AitoffAxes(GeoAxes):
+    name = 'aitoff'
+
+    class AitoffTransform(_GeoTransform):
+        """The base Aitoff transform."""
+
+        def transform_non_affine(self, ll):
+            # docstring inherited
+            longitude = ll[:, 0]
+            latitude = ll[:, 1]
+
+            # Pre-compute some values
+            half_long = longitude / 2.0
+            cos_latitude = np.cos(latitude)
+
+            alpha = np.arccos(cos_latitude * np.cos(half_long))
+            # Avoid divide-by-zero errors using same method as NumPy.
+            alpha[alpha == 0.0] = 1e-20
+            # We want unnormalized sinc.  numpy.sinc gives us normalized
+            sinc_alpha = np.sin(alpha) / alpha
+
+            xy = np.empty_like(ll, float)
+            xy[:, 0] = (cos_latitude * np.sin(half_long)) / sinc_alpha
+            xy[:, 1] = np.sin(latitude) / sinc_alpha
+            return xy
+
+        def inverted(self):
+            # docstring inherited
+            return AitoffAxes.InvertedAitoffTransform(self._resolution)
+
+    class InvertedAitoffTransform(_GeoTransform):
+
+        def transform_non_affine(self, xy):
+            # docstring inherited
+            # MGDTODO: Math is hard ;(
+            return xy
+
+        def inverted(self):
+            # docstring inherited
+            return AitoffAxes.AitoffTransform(self._resolution)
+
+    def __init__(self, *args, **kwargs):
+        self._longitude_cap = np.pi / 2.0
+        GeoAxes.__init__(self, *args, **kwargs)
+        self.set_aspect(0.5, adjustable='box', anchor='C')
+        self.cla()
+
+    def _get_core_transform(self, resolution):
+        return self.AitoffTransform(resolution)
+
+
+class HammerAxes(GeoAxes):
+    name = 'hammer'
+
+    class HammerTransform(_GeoTransform):
+        """The base Hammer transform."""
+
+        def transform_non_affine(self, ll):
+            # docstring inherited
+            longitude = ll[:, 0:1]
+            latitude  = ll[:, 1:2]
+
+            # Pre-compute some values
+            half_long = longitude / 2.0
+            cos_latitude = np.cos(latitude)
+            sqrt2 = np.sqrt(2.0)
+
+            alpha = np.sqrt(1.0 + cos_latitude * np.cos(half_long))
+            x = (2.0 * sqrt2) * (cos_latitude * np.sin(half_long)) / alpha
+            y = (sqrt2 * np.sin(latitude)) / alpha
+            return np.concatenate((x, y), 1)
+
+        def inverted(self):
+            # docstring inherited
+            return HammerAxes.InvertedHammerTransform(self._resolution)
+
+    class InvertedHammerTransform(_GeoTransform):
+
+        def transform_non_affine(self, xy):
+            # docstring inherited
+            x, y = xy.T
+            z = np.sqrt(1 - (x / 4) ** 2 - (y / 2) ** 2)
+            longitude = 2 * np.arctan((z * x) / (2 * (2 * z ** 2 - 1)))
+            latitude = np.arcsin(y*z)
+            return np.column_stack([longitude, latitude])
+
+        def inverted(self):
+            # docstring inherited
+            return HammerAxes.HammerTransform(self._resolution)
+
+    def __init__(self, *args, **kwargs):
+        self._longitude_cap = np.pi / 2.0
+        GeoAxes.__init__(self, *args, **kwargs)
+        self.set_aspect(0.5, adjustable='box', anchor='C')
+        self.cla()
+
+    def _get_core_transform(self, resolution):
+        return self.HammerTransform(resolution)
+
+
+class MollweideAxes(GeoAxes):
+    name = 'mollweide'
+
+    class MollweideTransform(_GeoTransform):
+        """The base Mollweide transform."""
+
+        def transform_non_affine(self, ll):
+            # docstring inherited
+            def d(theta):
+                delta = (-(theta + np.sin(theta) - pi_sin_l)
+                         / (1 + np.cos(theta)))
+                return delta, np.abs(delta) > 0.001
+
+            longitude = ll[:, 0]
+            latitude  = ll[:, 1]
+
+            clat = np.pi/2 - np.abs(latitude)
+            ihigh = clat < 0.087  # within 5 degrees of the poles
+            ilow = ~ihigh
+            aux = np.empty(latitude.shape, dtype=float)
+
+            if ilow.any():  # Newton-Raphson iteration
+                pi_sin_l = np.pi * np.sin(latitude[ilow])
+                theta = 2.0 * latitude[ilow]
+                delta, large_delta = d(theta)
+                while np.any(large_delta):
+                    theta[large_delta] += delta[large_delta]
+                    delta, large_delta = d(theta)
+                aux[ilow] = theta / 2
+
+            if ihigh.any():  # Taylor series-based approx. solution
+                e = clat[ihigh]
+                d = 0.5 * (3 * np.pi * e**2) ** (1.0/3)
+                aux[ihigh] = (np.pi/2 - d) * np.sign(latitude[ihigh])
+
+            xy = np.empty(ll.shape, dtype=float)
+            xy[:, 0] = (2.0 * np.sqrt(2.0) / np.pi) * longitude * np.cos(aux)
+            xy[:, 1] = np.sqrt(2.0) * np.sin(aux)
+
+            return xy
+
+        def inverted(self):
+            # docstring inherited
+            return MollweideAxes.InvertedMollweideTransform(self._resolution)
+
+    class InvertedMollweideTransform(_GeoTransform):
+
+        def transform_non_affine(self, xy):
+            # docstring inherited
+            x = xy[:, 0:1]
+            y = xy[:, 1:2]
+
+            # from Equations (7, 8) of
+            # http://mathworld.wolfram.com/MollweideProjection.html
+            theta = np.arcsin(y / np.sqrt(2))
+            lon = (np.pi / (2 * np.sqrt(2))) * x / np.cos(theta)
+            lat = np.arcsin((2 * theta + np.sin(2 * theta)) / np.pi)
+
+            return np.concatenate((lon, lat), 1)
+
+        def inverted(self):
+            # docstring inherited
+            return MollweideAxes.MollweideTransform(self._resolution)
+
+    def __init__(self, *args, **kwargs):
+        self._longitude_cap = np.pi / 2.0
+        GeoAxes.__init__(self, *args, **kwargs)
+        self.set_aspect(0.5, adjustable='box', anchor='C')
+        self.cla()
+
+    def _get_core_transform(self, resolution):
+        return self.MollweideTransform(resolution)
+
+
+class LambertAxes(GeoAxes):
+    name = 'lambert'
+
+    class LambertTransform(_GeoTransform):
+        """The base Lambert transform."""
+
+        def __init__(self, center_longitude, center_latitude, resolution):
+            """
+            Create a new Lambert transform.  Resolution is the number of steps
+            to interpolate between each input line segment to approximate its
+            path in curved Lambert space.
+            """
+            _GeoTransform.__init__(self, resolution)
+            self._center_longitude = center_longitude
+            self._center_latitude = center_latitude
+
+        def transform_non_affine(self, ll):
+            # docstring inherited
+            longitude = ll[:, 0:1]
+            latitude  = ll[:, 1:2]
+            clong = self._center_longitude
+            clat = self._center_latitude
+            cos_lat = np.cos(latitude)
+            sin_lat = np.sin(latitude)
+            diff_long = longitude - clong
+            cos_diff_long = np.cos(diff_long)
+
+            inner_k = np.maximum(  # Prevent divide-by-zero problems
+                1 + np.sin(clat)*sin_lat + np.cos(clat)*cos_lat*cos_diff_long,
+                1e-15)
+            k = np.sqrt(2 / inner_k)
+            x = k * cos_lat*np.sin(diff_long)
+            y = k * (np.cos(clat)*sin_lat - np.sin(clat)*cos_lat*cos_diff_long)
+
+            return np.concatenate((x, y), 1)
+
+        def inverted(self):
+            # docstring inherited
+            return LambertAxes.InvertedLambertTransform(
+                self._center_longitude,
+                self._center_latitude,
+                self._resolution)
+
+    class InvertedLambertTransform(_GeoTransform):
+
+        def __init__(self, center_longitude, center_latitude, resolution):
+            _GeoTransform.__init__(self, resolution)
+            self._center_longitude = center_longitude
+            self._center_latitude = center_latitude
+
+        def transform_non_affine(self, xy):
+            # docstring inherited
+            x = xy[:, 0:1]
+            y = xy[:, 1:2]
+            clong = self._center_longitude
+            clat = self._center_latitude
+            p = np.maximum(np.hypot(x, y), 1e-9)
+            c = 2 * np.arcsin(0.5 * p)
+            sin_c = np.sin(c)
+            cos_c = np.cos(c)
+
+            lat = np.arcsin(cos_c*np.sin(clat) +
+                             ((y*sin_c*np.cos(clat)) / p))
+            lon = clong + np.arctan(
+                (x*sin_c) / (p*np.cos(clat)*cos_c - y*np.sin(clat)*sin_c))
+
+            return np.concatenate((lon, lat), 1)
+
+        def inverted(self):
+            # docstring inherited
+            return LambertAxes.LambertTransform(
+                self._center_longitude,
+                self._center_latitude,
+                self._resolution)
+
+    def __init__(self, *args, center_longitude=0, center_latitude=0, **kwargs):
+        self._longitude_cap = np.pi / 2
+        self._center_longitude = center_longitude
+        self._center_latitude = center_latitude
+        GeoAxes.__init__(self, *args, **kwargs)
+        self.set_aspect('equal', adjustable='box', anchor='C')
+        self.cla()
+
+    def cla(self):
+        GeoAxes.cla(self)
+        self.yaxis.set_major_formatter(NullFormatter())
+
+    def _get_core_transform(self, resolution):
+        return self.LambertTransform(
+            self._center_longitude,
+            self._center_latitude,
+            resolution)
+
+    def _get_affine_transform(self):
+        return Affine2D() \
+            .scale(0.25) \
+            .translate(0.5, 0.5)