2627.sagews

# Requirements
from numpy import linspace

# Constant in interval function generator
CI = lambda min, max, value : lambda x : (lambda : 0, lambda : value)[x >= min and x <= max]()

# Constant in interval with definite integration for all reals equal to one function
CI1 = lambda min, max: CI(min, max, 1 / (max - min))

# Kernel density estimation
KDE = lambda data, kernel, bandwidth : lambda x : sum(map(lambda value : kernel((x - value) / bandwidth), data)) / (len(data) * bandwidth)

# Gaussian function generator
G = lambda a, b, c : (lambda x : a * exp(-(x-b)**2 / (2 * c**2)))

# Normal distribution function generator
N = lambda avg, stdev : G(1/sqrt(2 * pi * stdev**2), avg, stdev)

# Standard normal distribution function
SN = N(0, 1)

# Inherited values
num = 5
Plot_hmin = 0
Plot_hmax = 10
Plot_vmin = 0
Plot_palpha = 0.25

# (Length 1)

# PDF
L1_min = 1
L1_max = 2
L1_num = num * (L1_max - L1_min)
L1_PDF = CI1(L1_min, L1_max)
L1_PDFx = linspace(L1_min, L1_max, L1_num)
#L1_PDFp = map(lambda x : (x, L1_PDF(x)), L1_PDFx)

# Stats
L1_PDFx_avg = mean(L1_PDFx)
L1_PDFx_stdev = std(L1_PDFx)
L1_low = L1_min
L1_high = L1_max

# Print stats
print("Average: " + str(L1_PDFx_avg))
print("Standard deviation: " + str(L1_PDFx_stdev))
print("Low: " + str(L1_low))
print("High: " + str(L1_high))

# Displaying the plot
L1_Plot_hmin = Plot_hmin
L1_Plot_hmax = Plot_hmax
L1_Plot_vmin = Plot_vmin
L1_Plot = plot(L1_PDF, (L1_Plot_hmin, L1_Plot_hmax), color = "blue")
L1_Plot += line([(L1_low, 0), (L1_low, L1_PDF(L1_low))], color = "red")
L1_Plot += line([(L1_high, 0), (L1_high, L1_PDF(L1_high))], color = "red")
L1_Plot += point(map(lambda x : (x, 0), L1_PDFx), color = "blue", alpha = Plot_palpha)
L1_Plot.show(xmin = L1_Plot_hmin, xmax = L1_Plot_hmax, ymin = L1_Plot_vmin)

Average: 1.5 Standard deviation: 0.395284707521 Low: 1 High: 2

# (Length 2)

# PDF
L2_min = 2
L2_max = 4
L2_num = num * (L2_max - L2_min)
L2_PDF = CI1(L2_min, L2_max)
L2_PDFx = linspace(L2_min, L2_max, L2_num)
#L2_PDFp = map(lambda x : (x, L2_PDF(x)), L2_PDFx)

# Stats
L2_PDFx_avg = mean(L2_PDFx)
L2_PDFx_stdev = std(L2_PDFx)
L2_low = L2_min
L2_high = L2_max

# Print stats
print("Average: " + str(L2_PDFx_avg))
print("Standard deviation: " + str(L2_PDFx_stdev))
print("Low: " + str(L2_low))
print("High: " + str(L2_high))

# Displaying the plot
L2_Plot_hmin = Plot_hmin
L2_Plot_hmax = Plot_hmax
L2_Plot_vmin = Plot_vmin
L2_plot = plot(L2_PDF, (L2_Plot_hmin, L2_Plot_hmax))
L2_plot += line([(L2_low, 0), (L2_low, L2_PDF(L2_low))], color = "red")
L2_plot += line([(L2_high, 0), (L2_high, L2_PDF(L2_high))], color = "red")
L2_plot += point(map(lambda x : (x, 0), L2_PDFx), alpha = Plot_palpha)
L2_plot.show(xmin = L2_Plot_hmin, xmax = L2_Plot_hmax, ymin = L2_Plot_vmin)

Average: 3.0 Standard deviation: 0.672811189799 Low: 2 High: 4

# (Sum Length) = (Length 1) * (Length 2)

L3_f = lambda L1, L2 : L1 * L2

# PDF
L3_num = L1_num * L2_num
L3_PDFx = []
for L1_val in L1_PDFx:
    for L2_val in L2_PDFx:
        L3_PDFx.append(L3_f(L1_val, L2_val))
L3_PDF = KDE(L3_PDFx, SN, 0.5)
#L3_PDFp = map(lambda x : (x, 0.5), L3_PDFx)

# Stats
L3_PDFx_avg = mean(L3_PDFx)
L3_PDFx_stdev = std(L3_PDFx)
L3_low = min([L3_f(L1_min, L2_min),L3_f(L1_max, L2_max)])
L3_high = max([L3_f(L1_min, L2_min), L3_f(L1_max, L2_max)])

# Print stats
print("Average: " + str(L3_PDFx_avg))
print("Standard deviation: " + str(L3_PDFx_stdev))
print("Low: " + str(L3_low))
print("High: " + str(L3_high))

# Displaying the plot
L3_Plot_hmin = Plot_hmin
L3_Plot_hmax = Plot_hmax
L3_Plot_vmin = Plot_vmin
L3_plot = plot(L3_PDF, (L3_Plot_hmin, L3_Plot_hmax))
#L3_plot = plot(L3_PDF, (L3_Plot_hmin, L3_Plot_hmax), plot_points = 20)
L3_plot += line([(L3_low, 0), (L3_low, L3_PDF(L3_low))], color = "red")
L3_plot += line([(L3_high, 0), (L3_high, L3_PDF(L3_high))], color = "red")
L3_plot += point(map(lambda x : (x, 0), L3_PDFx), alpha = Plot_palpha)
L3_plot.show(xmin = L3_Plot_hmin, xmax = L3_Plot_hmax, ymin = L3_Plot_vmin)

Average: 4.5 Standard deviation: 1.4612660825 Low: 2 High: 8