pydata2015 berlin bokeh taylor server

14 February 2016

code

  1. taylor_server

    1. original

       from __future__ import print_function

 import numpy as np
 import sympy as sy

 from bokeh.browserlib import view
 from bokeh.document import Document
 from bokeh.models.glyphs import Line
 from bokeh.models import Plot, DataRange1d, LinearAxis, ColumnDataSource, Grid, Legend
 from bokeh.session import Session
 from bokeh.models.widgets import Slider, TextInput, HBox, VBox, Dialog

 document = Document()
 session = Session()
 session.use_doc('taylor_server')
 session.load_document(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

     session.store_document(document)

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

 xdr = DataRange1d()
 ydr = DataRange1d()

 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(orientation="bottom_left")
 plot.add_layout(legend)

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

 def on_text_value_change(obj, 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
         session.store_objects(dialog)
     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])

 document.add(layout)
 update_data()

 if __name__ == "__main__":
     link = session.object_link(document.context)
     print("Please visit %s to see the plots" % link)
     view(link)
     print("\npress ctrl-C to exit")
     session.poll_document(document)

    2. convert to bokeh 0.11

       import numpy as np
 import sympy as sy

 from bokeh.io import curdoc
 from bokeh.client import push_session
 from bokeh.models import Plot, DataRange1d, LinearAxis, ColumnDataSource, Grid, Legend
 from bokeh.models.glyphs import Line
 from bokeh.models.widgets import Slider, TextInput, HBox, VBox, Dialog

 document = curdoc()
 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 = DataRange1d()
 ydr = DataRange1d()

 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="bottom_left")
 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])

 document.add_root(layout)
 update_data()

 if __name__ == "__main__":
     # open the doc in browser
     session.show()
     # run forever
     session.loop_until_closed()

class LinearAxis(**kwargs)

  1. base bokeh.models.axes.ContinuousAxis

  2. description

    1. an axis that picks nice numbers for tick locations on a linear scale

    2. configured with a BasicTickFormatter by default

class Grid(**kwargs)

  1. base bokeh.models.renderers.GuideRenderer

  2. description

    1. display horizontal or vertical grid lines at locations given by a supplied Ticker

  3. attr

    1. dimension which dimension the axis grid lines will intersect

       the x-axis is dimension 0 (vertical grid lines)
 the y-axis is dimension 1 (horizontal grid lines)

    2. ticker the ticker to use for computing locations for the grid lines

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