#!/usr/bin/env python
# coding: utf-8

# In[9]:


import bqplot as bq


# In[10]:


import sympy
from sympy import sympify, latex
sympy.init_printing(use_latex='mathjax')

from IPython.display import display
import ipywidgets as widgets
from ipywidgets import interact, fixed
import numbers


# In[11]:


def explore(f, x, prms=None, x_min=-10, x_max=10):
    # construct the arguments for @interact
    interact_args = {}
    for symbol, value in (prms or {}).items():
        if isinstance(value, numbers.Number):
            interact_args[symbol] = widgets.fixed(value)
        else:
            interact_args[symbol] = value
    dx = x_max - x_min
    interact_args['x_range'] = widgets.FloatRangeSlider(
        value=(x_min, x_max),
        min=x_min - 2 * dx,
        max=x_max + 2 * dx,
        description=x,
    )
    
    # make the figure:
    x_sc = bq.LinearScale()
    y_sc = bq.LinearScale()
    ax_x = bq.Axis(label='x', scale=x_sc, grid_lines='solid')
    ax_y = bq.Axis(label='y', scale=y_sc, orientation='vertical', grid_lines='solid')
    line = bq.Lines(x=[], y=[], scales={'x': x_sc, 'y': y_sc})
    fig = bq.Figure(axes=[ax_x, ax_y], marks=[line])

    display(fig)
    
    # also display the latex expression
    expression = widgets.Label('$%s$' % latex(f), description='f')
    display(expression)



    @widgets.interact(**interact_args)
    def foo(**kwargs):
        # evaluate the expression for each parameter
        g = f
        for symbol in sorted(prms):
            g = g.subs(symbol, kwargs[symbol])
        # update the expression
        expression.value = '${} = {}$'.format(latex(f), latex(g))
        
        # update the plot
        x_min, x_max = kwargs['x_range']
        X = np.linspace(x_min, x_max, 100)
        Y = sympy.lambdify(x, g, 'numpy')(X)
        line.x = X
        line.y = Y


# In[13]:


f = sympify('q*x**2 + p*x + r')

explore(f, 'x', prms={
    'p': (0., 10),
    'q': (-1., 1),
    'r': 5,
})