%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
"""


t=np.linspace(0,4*np.pi,250)
def plot_sine1(a, b):
    plt.figure(figsize=(6+a,6))
    plt.plot(t, np.sin(t*a+b))
    plt.xticks([0,np.pi,2*np.pi,3*np.pi,4*np.pi], [0,r'$\pi$',r'$2\pi$',r'$3\pi$',r'$4\pi$'])
    plt.tight_layout
    plt.ylabel('sin(ax+b)')
    plt.xlabel('x')
    plt.title('Sin(ax+b) vs x')
    plt.ylim(-1.25,1.25)
    plt.yticks([-1.0,0,1.0], [-1,0,1])

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):
    plt.figure(figsize=(6+a,6))
    plt.plot(t, np.sin(t*a+b), style)
    plt.xticks([0,np.pi,2*np.pi,3*np.pi,4*np.pi], [0,r'$\pi$',r'$2\pi$',r'$3\pi$',r'$4\pi$'])
    plt.tight_layout
    plt.ylabel('sin(ax+b)')
    plt.xlabel('x')
    plt.title('Sin(ax+b) vs x')
    plt.ylim(-1.25,1.25)
    plt.yticks([-1.0,0,1.0], [-1,0,1])

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=('b','ko','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
"""


