lab_coffee_utils.py

import numpy as np
import matplotlib.pyplot as plt
plt.style.use('./deeplearning.mplstyle')
import tensorflow as tf
from tensorflow.keras.activations import sigmoid
from matplotlib import cm
import matplotlib.colors as colors
from lab_utils_common import dlc

def load_coffee_data():
    """ Creates a coffee roasting data set.
        roasting duration: 12-15 minutes is best
        temperature range: 175-260C is best
    """
    rng = np.random.default_rng(2)
    X = rng.random(400).reshape(-1,2)
    X[:,1] = X[:,1] * 4 + 11.5          # 12-15 min is best
    X[:,0] = X[:,0] * (285-150) + 150  # 350-500 F (175-260 C) is best
    Y = np.zeros(len(X))
    
    i=0
    for t,d in X:
        y = -3/(260-175)*t + 21
        if (t > 175 and t < 260 and d > 12 and d < 15 and d<=y ):
            Y[i] = 1
        else:
            Y[i] = 0
        i += 1

    return (X, Y.reshape(-1,1))

def plt_roast(X,Y):
    Y = Y.reshape(-1,)
    colormap = np.array(['r', 'b'])
    fig, ax = plt.subplots(1,1,)
    ax.scatter(X[Y==1,0],X[Y==1,1], s=70, marker='x', c='red', label="Good Roast" )
    ax.scatter(X[Y==0,0],X[Y==0,1], s=100, marker='o', facecolors='none', 
               edgecolors=dlc["dldarkblue"],linewidth=1,  label="Bad Roast")
    tr = np.linspace(175,260,50)
    ax.plot(tr, (-3/85) * tr + 21, color=dlc["dlpurple"],linewidth=1)
    ax.axhline(y=12,color=dlc["dlpurple"],linewidth=1)
    ax.axvline(x=175,color=dlc["dlpurple"],linewidth=1)
    ax.set_title(f"Coffee Roasting", size=16)
    ax.set_xlabel("Temperature \n(Celsius)",size=12)
    ax.set_ylabel("Duration \n(minutes)",size=12)
    ax.legend(loc='upper right')
    plt.show()

def plt_prob(ax,fwb):
    """ plots a decision boundary but include shading to indicate the probability """
    #setup useful ranges and common linspaces
    x0_space  = np.linspace(150, 285 , 40)
    x1_space  = np.linspace(11.5, 15.5 , 40)

    # get probability for x0,x1 ranges
    tmp_x0,tmp_x1 = np.meshgrid(x0_space,x1_space)
    z = np.zeros_like(tmp_x0)
    for i in range(tmp_x0.shape[0]):
        for j in range(tmp_x1.shape[1]):
            x = np.array([[tmp_x0[i,j],tmp_x1[i,j]]])
            z[i,j] = fwb(x)


    cmap = plt.get_cmap('Blues')
    new_cmap = truncate_colormap(cmap, 0.0, 0.5)
    pcm = ax.pcolormesh(tmp_x0, tmp_x1, z,
                   norm=cm.colors.Normalize(vmin=0, vmax=1),
                   cmap=new_cmap, shading='nearest', alpha = 0.9)
    ax.figure.colorbar(pcm, ax=ax)

def truncate_colormap(cmap, minval=0.0, maxval=1.0, n=100):
    """ truncates color map """
    new_cmap = colors.LinearSegmentedColormap.from_list(
        'trunc({n},{a:.2f},{b:.2f})'.format(n=cmap.name, a=minval, b=maxval),
        cmap(np.linspace(minval, maxval, n)))
    return new_cmap

def plt_layer(X,Y,W1,b1,norm_l):
    Y = Y.reshape(-1,)
    fig,ax = plt.subplots(1,W1.shape[1], figsize=(16,4))
    for i in range(W1.shape[1]):
        layerf= lambda x : sigmoid(np.dot(norm_l(x),W1[:,i]) + b1[i])
        plt_prob(ax[i], layerf)
        ax[i].scatter(X[Y==1,0],X[Y==1,1], s=70, marker='x', c='red', label="Good Roast" )
        ax[i].scatter(X[Y==0,0],X[Y==0,1], s=100, marker='o', facecolors='none', 
                   edgecolors=dlc["dldarkblue"],linewidth=1,  label="Bad Roast")
        tr = np.linspace(175,260,50)
        ax[i].plot(tr, (-3/85) * tr + 21, color=dlc["dlpurple"],linewidth=2)
        ax[i].axhline(y= 12, color=dlc["dlpurple"], linewidth=2)
        ax[i].axvline(x=175, color=dlc["dlpurple"], linewidth=2)
        ax[i].set_title(f"Layer 1, unit {i}")
        ax[i].set_xlabel("Temperature \n(Celsius)",size=12)
    ax[0].set_ylabel("Duration \n(minutes)",size=12)
    plt.show()
        
def plt_network(X,Y,netf):
    fig, ax = plt.subplots(1,2,figsize=(16,4))
    Y = Y.reshape(-1,)
    plt_prob(ax[0], netf)
    ax[0].scatter(X[Y==1,0],X[Y==1,1], s=70, marker='x', c='red', label="Good Roast" )
    ax[0].scatter(X[Y==0,0],X[Y==0,1], s=100, marker='o', facecolors='none', 
                   edgecolors=dlc["dldarkblue"],linewidth=1,  label="Bad Roast")
    ax[0].plot(X[:,0], (-3/85) * X[:,0] + 21, color=dlc["dlpurple"],linewidth=1)
    ax[0].axhline(y= 12, color=dlc["dlpurple"], linewidth=1)
    ax[0].axvline(x=175, color=dlc["dlpurple"], linewidth=1)
    ax[0].set_xlabel("Temperature \n(Celsius)",size=12)
    ax[0].set_ylabel("Duration \n(minutes)",size=12)
    ax[0].legend(loc='upper right')
    ax[0].set_title(f"network probability")

    ax[1].plot(X[:,0], (-3/85) * X[:,0] + 21, color=dlc["dlpurple"],linewidth=1)
    ax[1].axhline(y= 12, color=dlc["dlpurple"], linewidth=1)
    ax[1].axvline(x=175, color=dlc["dlpurple"], linewidth=1)
    fwb = netf(X)
    yhat = (fwb > 0.5).astype(int)
    ax[1].scatter(X[yhat[:,0]==1,0],X[yhat[:,0]==1,1], s=70, marker='x', c='orange', label="Predicted Good Roast" )
    ax[1].scatter(X[yhat[:,0]==0,0],X[yhat[:,0]==0,1], s=100, marker='o', facecolors='none', 
                   edgecolors=dlc["dldarkblue"],linewidth=1,  label="Bad Roast")
    ax[1].set_title(f"network decision")
    ax[1].set_xlabel("Temperature \n(Celsius)",size=12)
    ax[1].set_ylabel("Duration \n(minutes)",size=12)
    ax[1].legend(loc='upper right')


def plt_output_unit(W,b):
    """ plots a single unit function with 3 inputs """
    steps = 10
    fig = plt.figure()
    ax = fig.add_subplot(projection='3d')
    x_ = np.linspace(0., 1., steps)
    y_ = np.linspace(0., 1., steps)
    z_ = np.linspace(0., 1., steps)
    x, y, z = np.meshgrid(x_, y_, z_, indexing='ij')
    d = np.zeros((steps,steps,steps))
    cmap = plt.get_cmap('Blues')
    for i in range(steps):
        for j in range(steps):
            for k in range(steps):
                v = np.array([x[i,j,k],y[i,j,k],z[i,j,k]])
                d[i,j,k] = tf.keras.activations.sigmoid(np.dot(v,W[:,0])+b).numpy()
    pcm = ax.scatter(x, y, z, c=d, cmap=cmap, alpha = 1 )
    ax.set_xlabel("unit 0"); 
    ax.set_ylabel("unit 1"); 
    ax.set_zlabel("unit 2"); 
    ax.view_init(30, -120)
    ax.figure.colorbar(pcm, ax=ax)
    ax.set_title(f"Layer 2, output unit")

    plt.show()