path: root/contrib/python/matplotlib/py3/mpl_toolkits/axisartist/grid_helper_curvelinear.py

"""
An experimental support for curvilinear grid.
"""

import functools
from itertools import chain

import numpy as np

import matplotlib as mpl
from matplotlib.path import Path
from matplotlib.transforms import Affine2D, IdentityTransform
from .axislines import (
    _FixedAxisArtistHelperBase, _FloatingAxisArtistHelperBase, GridHelperBase)
from .axis_artist import AxisArtist
from .grid_finder import GridFinder


def _value_and_jacobian(func, xs, ys, xlims, ylims):
    """
    Compute *func* and its derivatives along x and y at positions *xs*, *ys*,
    while ensuring that finite difference calculations don't try to evaluate
    values outside of *xlims*, *ylims*.
    """
    eps = np.finfo(float).eps ** (1/2)  # see e.g. scipy.optimize.approx_fprime
    val = func(xs, ys)
    # Take the finite difference step in the direction where the bound is the
    # furthest; the step size is min of epsilon and distance to that bound.
    xlo, xhi = sorted(xlims)
    dxlo = xs - xlo
    dxhi = xhi - xs
    xeps = (np.take([-1, 1], dxhi >= dxlo)
            * np.minimum(eps, np.maximum(dxlo, dxhi)))
    val_dx = func(xs + xeps, ys)
    ylo, yhi = sorted(ylims)
    dylo = ys - ylo
    dyhi = yhi - ys
    yeps = (np.take([-1, 1], dyhi >= dylo)
            * np.minimum(eps, np.maximum(dylo, dyhi)))
    val_dy = func(xs, ys + yeps)
    return (val, (val_dx - val) / xeps, (val_dy - val) / yeps)


class FixedAxisArtistHelper(_FixedAxisArtistHelperBase):
    """
    Helper class for a fixed axis.
    """

    def __init__(self, grid_helper, side, nth_coord_ticks=None):
        """
        nth_coord = along which coordinate value varies.
         nth_coord = 0 ->  x axis, nth_coord = 1 -> y axis
        """

        super().__init__(loc=side)

        self.grid_helper = grid_helper
        if nth_coord_ticks is None:
            nth_coord_ticks = self.nth_coord
        self.nth_coord_ticks = nth_coord_ticks

        self.side = side

    def update_lim(self, axes):
        self.grid_helper.update_lim(axes)

    def get_tick_transform(self, axes):
        return axes.transData

    def get_tick_iterators(self, axes):
        """tick_loc, tick_angle, tick_label"""
        v1, v2 = axes.get_ylim() if self.nth_coord == 0 else axes.get_xlim()
        if v1 > v2:  # Inverted limits.
            side = {"left": "right", "right": "left",
                    "top": "bottom", "bottom": "top"}[self.side]
        else:
            side = self.side
        g = self.grid_helper
        ti1 = g.get_tick_iterator(self.nth_coord_ticks, side)
        ti2 = g.get_tick_iterator(1-self.nth_coord_ticks, side, minor=True)
        return chain(ti1, ti2), iter([])


class FloatingAxisArtistHelper(_FloatingAxisArtistHelperBase):

    def __init__(self, grid_helper, nth_coord, value, axis_direction=None):
        """
        nth_coord = along which coordinate value varies.
         nth_coord = 0 ->  x axis, nth_coord = 1 -> y axis
        """
        super().__init__(nth_coord, value)
        self.value = value
        self.grid_helper = grid_helper
        self._extremes = -np.inf, np.inf
        self._line_num_points = 100  # number of points to create a line

    def set_extremes(self, e1, e2):
        if e1 is None:
            e1 = -np.inf
        if e2 is None:
            e2 = np.inf
        self._extremes = e1, e2

    def update_lim(self, axes):
        self.grid_helper.update_lim(axes)

        x1, x2 = axes.get_xlim()
        y1, y2 = axes.get_ylim()
        grid_finder = self.grid_helper.grid_finder
        extremes = grid_finder.extreme_finder(grid_finder.inv_transform_xy,
                                              x1, y1, x2, y2)

        lon_min, lon_max, lat_min, lat_max = extremes
        e_min, e_max = self._extremes  # ranges of other coordinates
        if self.nth_coord == 0:
            lat_min = max(e_min, lat_min)
            lat_max = min(e_max, lat_max)
        elif self.nth_coord == 1:
            lon_min = max(e_min, lon_min)
            lon_max = min(e_max, lon_max)

        lon_levs, lon_n, lon_factor = \
            grid_finder.grid_locator1(lon_min, lon_max)
        lat_levs, lat_n, lat_factor = \
            grid_finder.grid_locator2(lat_min, lat_max)

        if self.nth_coord == 0:
            xx0 = np.full(self._line_num_points, self.value)
            yy0 = np.linspace(lat_min, lat_max, self._line_num_points)
            xx, yy = grid_finder.transform_xy(xx0, yy0)
        elif self.nth_coord == 1:
            xx0 = np.linspace(lon_min, lon_max, self._line_num_points)
            yy0 = np.full(self._line_num_points, self.value)
            xx, yy = grid_finder.transform_xy(xx0, yy0)

        self._grid_info = {
            "extremes": (lon_min, lon_max, lat_min, lat_max),
            "lon_info": (lon_levs, lon_n, np.asarray(lon_factor)),
            "lat_info": (lat_levs, lat_n, np.asarray(lat_factor)),
            "lon_labels": grid_finder.tick_formatter1(
                "bottom", lon_factor, lon_levs),
            "lat_labels": grid_finder.tick_formatter2(
                "bottom", lat_factor, lat_levs),
            "line_xy": (xx, yy),
        }

    def get_axislabel_transform(self, axes):
        return Affine2D()  # axes.transData

    def get_axislabel_pos_angle(self, axes):
        def trf_xy(x, y):
            trf = self.grid_helper.grid_finder.get_transform() + axes.transData
            return trf.transform([x, y]).T

        xmin, xmax, ymin, ymax = self._grid_info["extremes"]
        if self.nth_coord == 0:
            xx0 = self.value
            yy0 = (ymin + ymax) / 2
        elif self.nth_coord == 1:
            xx0 = (xmin + xmax) / 2
            yy0 = self.value
        xy1, dxy1_dx, dxy1_dy = _value_and_jacobian(
            trf_xy, xx0, yy0, (xmin, xmax), (ymin, ymax))
        p = axes.transAxes.inverted().transform(xy1)
        if 0 <= p[0] <= 1 and 0 <= p[1] <= 1:
            d = [dxy1_dy, dxy1_dx][self.nth_coord]
            return xy1, np.rad2deg(np.arctan2(*d[::-1]))
        else:
            return None, None

    def get_tick_transform(self, axes):
        return IdentityTransform()  # axes.transData

    def get_tick_iterators(self, axes):
        """tick_loc, tick_angle, tick_label, (optionally) tick_label"""

        lat_levs, lat_n, lat_factor = self._grid_info["lat_info"]
        yy0 = lat_levs / lat_factor

        lon_levs, lon_n, lon_factor = self._grid_info["lon_info"]
        xx0 = lon_levs / lon_factor

        e0, e1 = self._extremes

        def trf_xy(x, y):
            trf = self.grid_helper.grid_finder.get_transform() + axes.transData
            return trf.transform(np.column_stack(np.broadcast_arrays(x, y))).T

        # find angles
        if self.nth_coord == 0:
            mask = (e0 <= yy0) & (yy0 <= e1)
            (xx1, yy1), (dxx1, dyy1), (dxx2, dyy2) = _value_and_jacobian(
                trf_xy, self.value, yy0[mask], (-np.inf, np.inf), (e0, e1))
            labels = self._grid_info["lat_labels"]

        elif self.nth_coord == 1:
            mask = (e0 <= xx0) & (xx0 <= e1)
            (xx1, yy1), (dxx2, dyy2), (dxx1, dyy1) = _value_and_jacobian(
                trf_xy, xx0[mask], self.value, (-np.inf, np.inf), (e0, e1))
            labels = self._grid_info["lon_labels"]

        labels = [l for l, m in zip(labels, mask) if m]

        angle_normal = np.arctan2(dyy1, dxx1)
        angle_tangent = np.arctan2(dyy2, dxx2)
        mm = (dyy1 == 0) & (dxx1 == 0)  # points with degenerate normal
        angle_normal[mm] = angle_tangent[mm] + np.pi / 2

        tick_to_axes = self.get_tick_transform(axes) - axes.transAxes
        in_01 = functools.partial(
            mpl.transforms._interval_contains_close, (0, 1))

        def f1():
            for x, y, normal, tangent, lab \
                    in zip(xx1, yy1, angle_normal, angle_tangent, labels):
                c2 = tick_to_axes.transform((x, y))
                if in_01(c2[0]) and in_01(c2[1]):
                    yield [x, y], *np.rad2deg([normal, tangent]), lab

        return f1(), iter([])

    def get_line_transform(self, axes):
        return axes.transData

    def get_line(self, axes):
        self.update_lim(axes)
        x, y = self._grid_info["line_xy"]
        return Path(np.column_stack([x, y]))


class GridHelperCurveLinear(GridHelperBase):
    def __init__(self, aux_trans,
                 extreme_finder=None,
                 grid_locator1=None,
                 grid_locator2=None,
                 tick_formatter1=None,
                 tick_formatter2=None):
        """
        Parameters
        ----------
        aux_trans : `.Transform` or tuple[Callable, Callable]
            The transform from curved coordinates to rectilinear coordinate:
            either a `.Transform` instance (which provides also its inverse),
            or a pair of callables ``(trans, inv_trans)`` that define the
            transform and its inverse.  The callables should have signature::

                x_rect, y_rect = trans(x_curved, y_curved)
                x_curved, y_curved = inv_trans(x_rect, y_rect)

        extreme_finder

        grid_locator1, grid_locator2
            Grid locators for each axis.

        tick_formatter1, tick_formatter2
            Tick formatters for each axis.
        """
        super().__init__()
        self._grid_info = None
        self.grid_finder = GridFinder(aux_trans,
                                      extreme_finder,
                                      grid_locator1,
                                      grid_locator2,
                                      tick_formatter1,
                                      tick_formatter2)

    def update_grid_finder(self, aux_trans=None, **kwargs):
        if aux_trans is not None:
            self.grid_finder.update_transform(aux_trans)
        self.grid_finder.update(**kwargs)
        self._old_limits = None  # Force revalidation.

    def new_fixed_axis(self, loc,
                       nth_coord=None,
                       axis_direction=None,
                       offset=None,
                       axes=None):
        if axes is None:
            axes = self.axes
        if axis_direction is None:
            axis_direction = loc
        helper = FixedAxisArtistHelper(self, loc, nth_coord_ticks=nth_coord)
        axisline = AxisArtist(axes, helper, axis_direction=axis_direction)
        # Why is clip not set on axisline, unlike in new_floating_axis or in
        # the floating_axig.GridHelperCurveLinear subclass?
        return axisline

    def new_floating_axis(self, nth_coord,
                          value,
                          axes=None,
                          axis_direction="bottom"
                          ):
        if axes is None:
            axes = self.axes
        helper = FloatingAxisArtistHelper(
            self, nth_coord, value, axis_direction)
        axisline = AxisArtist(axes, helper)
        axisline.line.set_clip_on(True)
        axisline.line.set_clip_box(axisline.axes.bbox)
        # axisline.major_ticklabels.set_visible(True)
        # axisline.minor_ticklabels.set_visible(False)
        return axisline

    def _update_grid(self, x1, y1, x2, y2):
        self._grid_info = self.grid_finder.get_grid_info(x1, y1, x2, y2)

    def get_gridlines(self, which="major", axis="both"):
        grid_lines = []
        if axis in ["both", "x"]:
            for gl in self._grid_info["lon"]["lines"]:
                grid_lines.extend(gl)
        if axis in ["both", "y"]:
            for gl in self._grid_info["lat"]["lines"]:
                grid_lines.extend(gl)
        return grid_lines

    def get_tick_iterator(self, nth_coord, axis_side, minor=False):

        # axisnr = dict(left=0, bottom=1, right=2, top=3)[axis_side]
        angle_tangent = dict(left=90, right=90, bottom=0, top=0)[axis_side]
        # angle = [0, 90, 180, 270][axisnr]
        lon_or_lat = ["lon", "lat"][nth_coord]
        if not minor:  # major ticks
            for (xy, a), l in zip(
                    self._grid_info[lon_or_lat]["tick_locs"][axis_side],
                    self._grid_info[lon_or_lat]["tick_labels"][axis_side]):
                angle_normal = a
                yield xy, angle_normal, angle_tangent, l
        else:
            for (xy, a), l in zip(
                    self._grid_info[lon_or_lat]["tick_locs"][axis_side],
                    self._grid_info[lon_or_lat]["tick_labels"][axis_side]):
                angle_normal = a
                yield xy, angle_normal, angle_tangent, ""
            # for xy, a, l in self._grid_info[lon_or_lat]["ticks"][axis_side]:
            #     yield xy, a, ""