%matplotlib inline
from matplotlib import pyplot as plt
import numpy as np

from IPython.html.widgets import interact, interactive, fixed
from IPython.display import display

"""
Explanation: Interact Exercise 2
Imports
End of explanation
"""


def plot_sine1(a,b):
    x=np.linspace(0,4*np.pi,1000)
    f=plt.figure(figsize=(10,5))
    plt.plot(x, np.sin(a*x+b))
    plt.xlim(right=4*np.pi)
    plt.box(False)
    plt.grid(True)
    plt.xticks([0,1*np.pi,2*np.pi,3*np.pi,4*np.pi],['$0\pi$','$1\pi$','$2\pi$','$3\pi$','$4\pi$'])
    plt.tick_params(axis='x', top='off', direction='out')
    plt.tick_params(axis='y', right='off', direction='out')
    plt.title('Sine Wave'), plt.xlabel('Input'), plt.ylabel('Output')

plot_sine1(5, 3.4)

"""
Explanation: Plotting with parameters
Write a plot_sin1(a, b) function that plots $sin(ax+b)$ over the interval $[0,4\pi]$.

Customize your visualization to make it effective and beautiful.
Customize the box, grid, spines and ticks to match the requirements of this data.
Use enough points along the x-axis to get a smooth plot.
For the x-axis tick locations use integer multiples of $\pi$.
For the x-axis tick labels use multiples of pi using LaTeX: $3\pi$.
End of explanation
"""


interact(plot_sine1, a=(0.0,5.0,0.1), b=(-5.0,5.0,0.1));

assert True # leave this for grading the plot_sine1 exercise

"""
Explanation: Then use interact to create a user interface for exploring your function:

a should be a floating point slider over the interval $[0.0,5.0]$ with steps of $0.1$.
b should be a floating point slider over the interval $[-5.0,5.0]$ with steps of $0.1$.
End of explanation
"""


def plot_sine2(a,b,style):
    x=np.linspace(0,4*np.pi,1000)
    f=plt.figure(figsize=(9,6))
    plt.plot(x,np.sin(a*x+b),style)
    plt.xlim(right=max(x))
    plt.box(False)
    plt.grid(True)
    plt.xticks([0,1*np.pi,2*np.pi,3*np.pi,4*np.pi],['$0\pi$','$1\pi$','$2\pi$','$3\pi$','$4\pi$'])
    plt.tick_params(axis='x', top='off', direction='out')
    plt.tick_params(axis='y', right='off', direction='out')
    plt.title('Sine Wave with Different Styles'), plt.xlabel('Input'), plt.ylabel('Output')

plot_sine2(4.0, -1.0, 'r--')

"""
Explanation: In matplotlib, the line style and color can be set with a third argument to plot. Examples of this argument:

dashed red: r--
blue circles: bo
dotted black: k.

Write a plot_sine2(a, b, style) function that has a third style argument that allows you to set the line style of the plot. The style should default to a blue line.
End of explanation
"""


interact(plot_sine2, a=(0.0,5.0,0.1), b=(-5.0,5.0,0.1), style={'dotted blue line':'b--', 'black circles':'ko','red trianges':'r^'});

assert True # leave this for grading the plot_sine2 exercise

"""
Explanation: Use interact to create a UI for plot_sine2.

Use a slider for a and b as above.
Use a drop down menu for selecting the line style between a dotted blue line line, black circles and red triangles.
End of explanation
"""


