Merge branch 'master' into latex
This commit is contained in:
Paul ALNET
commit
ad8d300348
1 changed files with 270 additions and 74 deletions
344
Probas.py
Normal file → Executable file
344
Probas.py
Normal file → Executable file
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@ -1,11 +1,16 @@
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#!/usr/bin/python3
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from random import random
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from math import floor, sqrt
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from math import floor, sqrt, factorial
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from statistics import mean, variance
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# from matplotlib import pyplot
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from matplotlib import pyplot as plt
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from pylab import *
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import numpy as np
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import matplotlib.pyplot as pt
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def simulate_NFBP(N):
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"""
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Tries to simulate T_i, V_i and H_n for N boxes of random size.
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Tries to simulate T_i, V_i and H_n for N items of random size.
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"""
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i = 0 # Nombre de boites
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R = [0] # Remplissage de la i-eme boite
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@ -16,7 +21,7 @@ def simulate_NFBP(N):
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size = random()
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if R[i] + size >= 1:
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# Il y n'y a plus de la place dans la boite pour le paquet.
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# On passe à la boite suivante (qu'on initialise)
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# On passe a la boite suivante (qu'on initialise)
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i += 1
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R.append(0)
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T.append(0)
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@ -28,20 +33,15 @@ def simulate_NFBP(N):
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V[i] = size
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H.append(i)
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return {
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"i": i,
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"R": R,
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"T": T,
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"V": V,
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"H": H
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}
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return {"i": i, "R": R, "T": T, "V": V, "H": H}
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# unused
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def stats_NFBP(R, N):
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"""
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Runs R runs of NFBP (for N packages) and studies distribution, variance, mean...
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Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
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"""
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print("Running {} NFBP simulations with {} packages".format(R, N))
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print("Running {} NFBP simulations with {} items".format(R, N))
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I = []
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H = [[] for _ in range(N)] # List of empty lists
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@ -51,42 +51,136 @@ def stats_NFBP(R, N):
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for n in range(N):
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H[n].append(sim["H"][n])
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print("Mean number of boxes : {} (variance {})".format(mean(I), variance(I)))
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print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
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for n in range(N):
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print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
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def stats_NFBP_iter(R, N):
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"""
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Runs R runs of NFBP (for N packages) and studies distribution, variance, mean...
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Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
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Calculates stats during runtime instead of after to avoid excessive memory usage.
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"""
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print("Running {} NFBP simulations with {} packages".format(R, N))
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P = R * N # Total number of items
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print("## Running {} NFBP simulations with {} items".format(R, N))
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# number of bins
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ISum = 0
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IVarianceSum = 0
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# index of the bin containing the n-th item
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HSum = [0 for _ in range(N)]
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HSumVariance = [0 for _ in range(N)]
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# number of items in the i-th bin
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Sum_T = [0 for _ in range(N)]
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# size of the first item in the i-th bin
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Sum_V = [0 for _ in range(N)]
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for i in range(R):
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sim = simulate_NFBP(N)
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ISum += sim["i"]
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IVarianceSum += sim["i"]**2
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IVarianceSum += sim["i"] ** 2
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for n in range(N):
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HSum[n] += sim["H"][n]
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HSumVariance[n] += sim["H"][n]**2
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HSumVariance[n] += sim["H"][n] ** 2
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T = sim["T"]
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V = sim["V"]
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# ensure that T, V have the same length as Sum_T, Sum_V
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for i in range(N - sim["i"]):
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T.append(0)
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V.append(0)
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Sum_T = [x + y for x, y in zip(Sum_T, T)]
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Sum_V = [x + y for x, y in zip(Sum_V, V)]
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I = ISum/R
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IVariance = sqrt(IVarianceSum/(R-1) - I**2)
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Sum_T = [x / R for x in Sum_T]
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Sum_V = [round(x / R, 2) for x in Sum_V]
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# print(Sum_V)
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I = ISum / R
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IVariance = sqrt(IVarianceSum / (R - 1) - I**2)
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print("Mean number of bins : {} (variance {})".format(I, IVariance), "\n")
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# TODO clarify line below
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print(" {} * {} iterations of T".format(R, N), "\n")
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for n in range(min(N, 10)):
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Hn = HSum[n] / R # moyenne
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HVariance = sqrt(HSumVariance[n] / (R - 1) - Hn**2) # Variance
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print(
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"Index of bin containing the {}th item (H_{}) : {} (variance {})".format(
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n, n, Hn, HVariance
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)
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)
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HSum = [x / R for x in HSum]
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# print(HSum)
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# Plotting
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fig = plt.figure()
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# T plot
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x = np.arange(N)
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# print(x)
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ax = fig.add_subplot(221)
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ax.bar(
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x,
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Sum_T,
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width=1,
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label="Empirical values",
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edgecolor="blue",
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linewidth=0.7,
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color="red",
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)
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ax.set(
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xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 3), yticks=np.linspace(0, 3, 5)
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)
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ax.set_ylabel("Items")
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ax.set_xlabel("Bins (1-{})".format(N))
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ax.set_title("T histogram for {} items (Number of items in each bin)".format(P))
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ax.legend(loc="upper left", title="Legend")
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# V plot
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bx = fig.add_subplot(222)
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bx.bar(
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x,
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Sum_V,
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width=1,
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label="Empirical values",
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edgecolor="blue",
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linewidth=0.7,
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color="orange",
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)
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bx.set(
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xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 1), yticks=np.linspace(0, 1, 10)
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)
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bx.set_ylabel("First item size")
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bx.set_xlabel("Bins (1-{})".format(N))
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bx.set_title("V histogram for {} items (first item size of each bin)".format(P))
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bx.legend(loc="upper left", title="Legend")
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# H plot
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# We will simulate this part for a asymptotic study
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cx = fig.add_subplot(223)
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cx.bar(
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x,
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HSum,
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width=1,
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label="Empirical values",
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edgecolor="blue",
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linewidth=0.7,
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color="green",
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)
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cx.set(
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xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 10), yticks=np.linspace(0, N, 5)
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)
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cx.set_ylabel("Bin ranking of n-item")
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cx.set_xlabel("n-item (1-{})".format(N))
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cx.set_title("H histogram for {} items".format(P))
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xb = linspace(0, N, 10)
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yb = Hn * xb / 10
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wb = HVariance * xb / 10
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cx.plot(xb, yb, label="Theoretical E(Hn)", color="brown")
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cx.plot(xb, wb, label="Theoretical V(Hn)", color="purple")
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cx.legend(loc="upper left", title="Legend")
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plt.show()
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print("Mean number of boxes : {} (variance {})".format(I, IVariance))
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for n in range(n):
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Hn = HSum[n]/R
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HVariance = sqrt(HSumVariance[n]/(R-1) - Hn**2)
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print("Index of box containing the {}th package (H_{}) : {} (variance {})".format(n, n, Hn, HVariance))
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def simulate_NFDBP(N):
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"""
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Tries to simulate T_i, V_i and H_n for N boxes of random size.
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Tries to simulate T_i, V_i and H_n for N items of random size.
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Next Fit Dual Bin Packing : bins should overflow
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"""
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i = 0 # Nombre de boites
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R = [0] # Remplissage de la i-eme boite
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@ -95,83 +189,185 @@ def simulate_NFDBP(N):
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H = [] # Rang de la boite contenant le n-ieme paquet
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for n in range(N):
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size = random()
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R[i] += size
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T[i] += 1
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if R[i] + size >= 1:
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if R[i] >= 1:
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# Il y n'y a plus de la place dans la boite pour le paquet.
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# On passe à la boite suivante (qu'on initialise)
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# On passe a la boite suivante (qu'on initialise).
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i += 1
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R.append(0)
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T.append(0)
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V.append(0)
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if V[i] == 0:
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# C'est le premier paquet de la boite
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V[i] = size
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H.append(i)
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R[i] += size
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T[i] += 1
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return {
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"i": i,
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"R": R,
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"T": T,
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"V": V,
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"H": H
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}
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return {"i": i, "R": R, "T": T, "V": V, "H": H}
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def stats_NFDBP(R, N):
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def stats_NFDBP(R, N, t_i):
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"""
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Runs R runs of NFDBP (for N packages) and studies distribution, variance, mean...
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Runs R runs of NFDBP (for N items) and studies distribution, variance, mean...
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"""
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print("Running {} NFDBP simulations with {} packages".format(R, N))
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print("## Running {} NFDBP simulations with {} items".format(R, N))
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# TODO comment this function
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P = N * R # Total number of items
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I = []
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H = [[] for _ in range(N)] # List of empty lists
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Tmean=[]
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T = []
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Tk = [[] for _ in range(N)]
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Ti = []
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T_maths = []
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# First iteration to use zip after
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sim = simulate_NFDBP(N)
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Sum_T = [0 for _ in range(N)]
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for i in range(R):
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sim = simulate_NFDBP(N)
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I.append(sim["i"])
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for k in range(N):
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T.append(0)
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T = sim["T"]
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for n in range(N):
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H[n].append(sim["H"][n])
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Tk[n].append(sim["T"][n])
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Ti.append(sim["T"])
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Sum_T = [x + y for x, y in zip(Sum_T, T)]
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Sum_T = [x / R for x in Sum_T] # Experimental [Ti=k]
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Sum_T = [
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x * 100 / (sum(Sum_T)) for x in Sum_T
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] # Pourcentage de la repartition des items
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for k in range(sim["i"]):
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# for o in range(sim["i"]):
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Tmean+=sim["T"]
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print("Mean number of boxes : {} (variance {})".format(mean(I), variance(I)))
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print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
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for n in range(N):
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print("Mean H_{} : {} (variance {})".format(n, mean(H[n]), variance(H[n])))
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for k in range(int(mean(I))+1):
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print(Tmean[7])
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# print("Mean T_{} : {} (variance {})".format(k, mean(Tmean[k]), variance(Tmean[k])))
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# TODO variance for T_k doesn't see right
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print("Mean T_{} : {} (variance {})".format(k, mean(Sum_T), variance(Sum_T)))
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# Loi math
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for u in range(N):
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u = u + 2
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T_maths.append(1 / (factorial(u - 1)) - 1 / factorial(u))
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E = 0
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sigma2 = 0
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# print(T_maths)
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for p in range(len(T_maths)):
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E = E + (p + 1) * T_maths[p]
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sigma2 = ((T_maths[p] - E) ** 2) / (len(T_maths) - 1)
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print(
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"Mathematical values : Empiric mean T_{} : {} Variance {})".format(
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t_i, E, sqrt(sigma2)
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)
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)
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T_maths = [x * 100 for x in T_maths]
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# Plotting
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fig = plt.figure()
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# T plot
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x = np.arange(N)
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print(x)
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print(Sum_T)
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ax = fig.add_subplot(221)
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ax.bar(
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x,
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Sum_T,
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width=1,
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label="Empirical values",
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edgecolor="blue",
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linewidth=0.7,
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color="red",
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)
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ax.set(
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xlim=(0, N), xticks=np.arange(0, N), ylim=(0, 20), yticks=np.linspace(0, 20, 2)
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)
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ax.set_ylabel("Items(n) in %")
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ax.set_xlabel("Bins (1-{})".format(N))
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ax.set_title(
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"Items percentage for each bin and {} items (Number of items in each bin)".format(
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P
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)
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)
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ax.legend(loc="upper right", title="Legend")
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N = 10 ** 1
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sim = simulate_NFBP(N)
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# TODO fix the graph below
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# Mathematical P(Ti=k) plot. It shows the Ti(t_i) law with the probability of each number of items.
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print(len(Tk[t_i]))
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bx = fig.add_subplot(222)
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bx.hist(
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Tk[t_i],
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bins=10,
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width=1,
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label="Empirical values",
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edgecolor="blue",
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linewidth=0.7,
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color="red",
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)
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bx.set(
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xlim=(0, N),
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xticks=np.arange(0, N),
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ylim=(0, len(Tk[t_i])),
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yticks=np.linspace(0, 1, 1),
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)
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bx.set_ylabel("P(T{}=i)".format(t_i))
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bx.set_xlabel("Bins i=(1-{}) in %".format(N))
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bx.set_title(
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"T{} histogram for {} items (Number of items in each bin)".format(t_i, P)
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)
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bx.legend(loc="upper right", title="Legend")
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print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N))
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for j in range(sim["i"] + 1):
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remplissage = floor(sim["R"][j] * 100)
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print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage, sim["T"][j],
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sim["V"][j]))
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# Loi mathematique
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print(T_maths)
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cx = fig.add_subplot(224)
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cx.bar(
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x,
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T_maths,
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width=1,
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label="Theoretical values",
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edgecolor="blue",
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linewidth=0.7,
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color="red",
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)
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cx.set(
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xlim=(0, N),
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xticks=np.arange(0, N),
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ylim=(0, 100),
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yticks=np.linspace(0, 100, 10),
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)
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cx.set_ylabel("P(T{}=i)".format(t_i))
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cx.set_xlabel("Bins i=(1-{})".format(N))
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cx.set_title("Theoretical T{} values in %".format(t_i))
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cx.legend(loc="upper right", title="Legend")
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plt.show()
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print()
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stats_NFBP(10 ** 4, 10)
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N = 10 ** 1
|
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sim = simulate_NFDBP(N)
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print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N))
|
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for j in range(sim["i"] + 1):
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remplissage = floor(sim["R"][j] * 100)
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print("Boite {} : Rempli à {} % avec {} paquets. Taille du premier paquet : {}".format(j, remplissage,
|
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sim["T"][j],
|
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sim["V"][j]))
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# unused
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def basic_demo():
|
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N = 10**1
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sim = simulate_NFBP(N)
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|
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print()
|
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stats_NFDBP(10 ** 4, 10)
|
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stats_NFBP_iter(10**6, 10)
|
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print("Simulation NFBP pour {} packaets. Contenu des boites :".format(N))
|
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for j in range(sim["i"] + 1):
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remplissage = floor(sim["R"][j] * 100)
|
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print(
|
||||
"Boite {} : Rempli a {} % avec {} paquets. Taille du premier paquet : {}".format(
|
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j, remplissage, sim["T"][j], sim["V"][j]
|
||||
)
|
||||
)
|
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|
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#
|
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# pyplot.plot([1, 2, 4, 4, 2, 1], color = 'red', linestyle = 'dashed', linewidth = 2,
|
||||
# markerfacecolor = 'blue', markersize = 5)
|
||||
# pyplot.ylim(0, 5)
|
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# pyplot.title('Un exemple')
|
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print()
|
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stats_NFBP(10**3, 10)
|
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|
||||
N = 10**1
|
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sim = simulate_NFDBP(N)
|
||||
print("Simulation NFDBP pour {} packaets. Contenu des boites :".format(N))
|
||||
for j in range(sim["i"] + 1):
|
||||
remplissage = floor(sim["R"][j] * 100)
|
||||
print(
|
||||
"Boite {} : Rempli a {} % avec {} paquets. Taille du premier paquet : {}".format(
|
||||
j, remplissage, sim["T"][j], sim["V"][j]
|
||||
)
|
||||
)
|
||||
|
||||
|
||||
stats_NFBP_iter(10**3, 10)
|
||||
print("\n\n")
|
||||
stats_NFDBP(10**3, 10, 1)
|
||||
|
|
|
|||
Loading…
Reference in a new issue