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import matplotlib.pyplot as plt
%matplotlib inline

import numpy as np

from IPython.html.widgets import interactive
from IPython.display import display


    

In [8]:

    

def amdhals_law(B, n):
    """
    Calculates Amdhals law.
    
    :param B: float, fraction of program that is strictly serial.
    :param n: integer, the number of threads.
    """
    
    return 1. / (B + ((1 / n)*(1-B)))


    

In [9]:

    

def amdhals_law2(B, n, c=1e-6):
    """
    Calculates Amdhals law.
    
    :param B: float, fraction of program that is strictly serial.
    :param n: integer, the number of threads.
    """
    
    return 1. / (B + (c*n**2) + ((1 / n)*(1-B)))


    

In [10]:

    

def speedup_plot(speedup_fn=amdhals_law):
    """
    Plot the response of amdhals law to changes in variables.
  
    :param B: float, fraction of program that is strictly serial.
    :param n: integer, the number of threads.
    """
    
    processes = np.array([2**(x-1) for x in range(1, 12)])
    
    strictly_serial = np.linspace(0.1, 1.0, 4)
    
    fig, ax = plt.subplots(figsize=(10, 5))
    ax.grid()
    for _b in strictly_serial:
        ax.plot(speedup_fn(_b, processes), linewidth=2.0, linestyle='-')
    
    plt.legend(strictly_serial, loc='upper left', frameon=False)
    ax.set_xticks(range(1,len(processes)))
    ax.set_xticklabels(processes)
    
    
    ax.set_ylim(0., 11.)
    
    ax.set_xlabel('Number of processes (n)', weight='bold')
    ax.set_ylabel('Theoretical speedup (x times faster)', weight='bold')
    return ax


    

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speedup_plot(amdhals_law);


    

In [12]:

    

speedup_plot(amdhals_law2);


    

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