# Import plotting modules
import matplotlib.pyplot as plt
import seaborn as sns
# Import numpy
import numpy as np

# Set default Seaborn style
sns.set()


# Compute number of data points: n_data
n_data = len(versicolor_petal_length)

# Number of bins is the square root of number of data points: n_bins
n_bins = np.sqrt(n_data)

# Convert number of bins to integer: n_bins
n_bins = int(n_bins)

# Plot the histogram
plt.hist(versicolor_petal_length, bins = n_bins)

# Label axes
_ = plt.xlabel('petal length (cm)')
_ = plt.ylabel('count')

# Show histogram
plt.show()

# Create bee swarm plot with Seaborn's default settings
_ = sns.swarmplot(x='species', y='petal length (cm)',data =df)

# Label the axes
_ = plt.xlabel('species')
_ = plt.ylabel('petal length')
# Show the plot
plt.show()

def ecdf(data):
    """Compute ECDF for a one-dimensional array of measurements."""
    # Number of data points: n
    n = len(data)

    # x-data for the ECDF: x
    x = np.sort(data)

    # y-data for the ECDF: y
    y = np.arange(1, n+1) / n

    return x, y

# Compute Empirical Cumulative Distribution Function for versicolor data: x_vers, y_vers
x_vers, y_vers = ecdf(versicolor_petal_length)

# Generate plot
_ = plt.plot(x_vers, y_vers, marker='.', linestyle='none')

# Label the axes
_ = plt.xlabel('petal lengths')
_ = plt.ylabel('ECDF')

# Display the plot
plt.show()

# plot ECDFs for the petal lengths of all three iris species
x_set, y_set = ecdf(setosa_petal_length)
x_vers, y_vers = ecdf(versicolor_petal_length)
x_virg, y_virg = ecdf(virginica_petal_length)

# Plot all ECDFs on the same plot
_ = plt.plot(x_set, y_set, marker='.', linestyle='none')
_ = plt.plot(x_vers, y_vers, marker='.', linestyle='none')
_ = plt.plot(x_virg, y_virg, marker='.', linestyle='none')

# Annotate the plot
plt.legend(('setosa', 'versicolor', 'virginica'), loc='lower right')
_ = plt.xlabel('petal length (cm)')
_ = plt.ylabel('ECDF')

# Display the plot
plt.show()

# Compute the mean: mean_length_vers
mean_length_vers = np.mean(versicolor_petal_length)
# Print the result with some nice formatting
print('I. versicolor:', mean_length_vers, 'cm')

# Specify array of percentiles: percentiles
percentiles = np.array([2.5, 25, 50, 75, 97.5])

# Compute percentiles: ptiles_vers
ptiles_vers = np.percentile(versicolor_petal_length, percentiles)

# Print the result
print('Versicolor length percentiles:', ptiles_vers,)

# To see how the percentiles relate to the ECDF

# Plot the ECDF
_ = plt.plot(x_vers, y_vers, '.')
_ = plt.xlabel('petal length (cm)')
_ = plt.ylabel('ECDF')

# Overlay percentiles as red diamonds.
_ = plt.plot(ptiles_vers, percentiles/100, marker='D', color='red',
         linestyle='none')

# Show the plot
plt.show()

# Create box plot with Seaborn's default settings
_ = sns.boxplot(x='species', y='petal length (cm)', data =df)

# Label the axes
_ = plt.xlabel('species')
_ = plt.ylabel('petal length (cm)')

# Show the plot
plt.show()

# Array of differences to mean: differences
differences = versicolor_petal_length - np.mean(versicolor_petal_length)

# Square the differences: diff_sq
diff_sq = differences**2

# Compute the mean square difference: variance_explicit
variance_explicit = np.mean(diff_sq)

# Compute the variance using NumPy: variance_np
variance_np = np.var(versicolor_petal_length)

# Print the results
print(variance_np, variance_explicit)

# Make a scatter plot
_ = plt.plot(versicolor_petal_length, versicolor_petal_width, marker='.', linestyle='none')


# Label the axes
_ = plt.xlabel('Petal length')
_ = plt.ylabel('Petal Width')

# Show the result
plt.show()

# Compute the covariance matrix: covariance_matrix
covariance_matrix = np.cov(versicolor_petal_length, versicolor_petal_width)

# Print covariance matrix
print(covariance_matrix)

# Extract covariance of length and width of petals: petal_cov
petal_cov = covariance_matrix[[0],[1]]

# Print the length/width covariance
print(petal_cov)

def pearson_r(x, y):
    """Compute Pearson correlation coefficient between two arrays."""
    # Compute correlation matrix: corr_mat
    corr_mat = np.corrcoef(x,y)

    # Return entry [0,1]
    return corr_mat[0,1]

# Compute Pearson correlation coefficient for I. versicolor: r
r = pearson_r(versicolor_petal_length, versicolor_petal_width)

# Print the result
print(r)