from __future__ import print_function

import numpy as np
import sympy as sy

from bokeh.client import push_session
from bokeh.document import Document
from bokeh.models.glyphs import Line
from bokeh.models import Plot, Range1d, LinearAxis, ColumnDataSource, Grid, Legend
from bokeh.models.widgets import Slider, TextInput, HBox, VBox, Dialog

document = Document()
session = push_session(document)

xs = sy.Symbol('x')
expr = sy.exp(-xs)*sy.sin(xs)
order = 1

def taylor(fx, xs, order, x_range=(0, 1), n=200):
    x0, x1 = x_range
    x = np.linspace(float(x0), float(x1), n)

    fy = sy.lambdify(xs, fx, modules=['numpy'])(x)
    tx = fx.series(xs, n=order).removeO()

    if tx.is_Number:
        ty = np.zeros_like(x)
        ty.fill(float(tx))
    else:
        ty = sy.lambdify(xs, tx, modules=['numpy'])(x)

    return x, fy, ty

def update_data():
    x, fy, ty = taylor(expr, xs, order, (-2*sy.pi, 2*sy.pi), 200)

    plot.title = "%s vs. taylor(%s, n=%d)" % (expr, expr, order)
    legend.legends = [
        ("%s"         % expr, [line_f_glyph]),
        ("taylor(%s)" % expr, [line_t_glyph]),
    ]
    source.data = dict(x=x, fy=fy, ty=ty)
    slider.value = order

source = ColumnDataSource(data=dict(x=[], fy=[], ty=[]))

xdr = Range1d(-7, 7)
ydr = Range1d(-20, 200)

plot = Plot(x_range=xdr, y_range=ydr, plot_width=800, plot_height=400)

line_f = Line(x="x", y="fy", line_color="blue", line_width=2)
line_f_glyph = plot.add_glyph(source, line_f)
plot.add_layout(line_f_glyph)

line_t = Line(x="x", y="ty", line_color="red", line_width=2)
line_t_glyph = plot.add_glyph(source, line_t)
plot.add_layout(line_t_glyph)

xaxis = LinearAxis()
plot.add_layout(xaxis, 'below')

yaxis = LinearAxis()
plot.add_layout(yaxis, 'left')

xgrid = Grid(dimension=0, ticker=xaxis.ticker)
ygrid = Grid(dimension=1, ticker=yaxis.ticker)

legend = Legend(location="top_right")
plot.add_layout(legend)

def on_slider_value_change(attr, old, new):
    global order
    order = int(new)
    update_data()

def on_text_value_change(attr, old, new):
    try:
        global expr
        expr = sy.sympify(new, dict(x=xs))
    except (sy.SympifyError, TypeError, ValueError) as exception:
        dialog.content = str(exception)
        dialog.visible = True
    else:
        update_data()

dialog = Dialog(title="Invalid expression")

slider = Slider(start=1, end=20, value=order, step=1, title="Order:")
slider.on_change('value', on_slider_value_change)

text = TextInput(value=str(expr), title="Expression:")
text.on_change('value', on_text_value_change)

inputs = HBox(children=[slider, text])
layout = VBox(children=[inputs, plot, dialog])
update_data()
document.add_root(layout)
session.show(layout)

if __name__ == "__main__":
    print("\npress ctrl-C to exit")
    session.loop_until_closed()
