def compareCompleteVSIncomplete():
size = 100
nbOfPoints = 50
nbValuesForAverage = 4
x, yComplete, yIncomplete = [], [], []
for i in numpy.linspace(0, size*(size-1), nbOfPoints):
# Computes matrix density
x.append((size*size-i)/(size*size))
# Computes average execution times on 3 calls on different matrix
completeTime, incompleteTime = 0, 0
for j in range(nbValuesForAverage):
M = matgen.symmetricSparsePositiveDefinite(size, i)
wrapped1 = wrapper(cholesky.completeCholesky, M)
completeTime += timeit.timeit(wrapped1, number=1)
wrapped2 = wrapper(cholesky.incompleteCholesky, M)
incompleteTime += timeit.timeit(wrapped2, number=1)
yComplete.append(completeTime/nbValuesForAverage)
yIncomplete.append(incompleteTime/nbValuesForAverage)
p1 = plt.plot(x, yComplete, 'b', marker='o')
p2 = plt.plot(x, yIncomplete, 'g', marker='o')
plt.title("Average execution time for the Cholesky factorization in function of matrix density\n")
plt.legend(["New custom Complete factorization", "Custom incomplete factorization"], loc=4)
plt.ylabel("Execution time (s)")
plt.xlabel("density of the initial 100*100 matrix")
plt.show()
def testIncompleteCholeskyPrecision():
size = 100
nbOfPoints = 100
x, y = [], []
for i in numpy.linspace(0, size*(size-1), nbOfPoints):
x.append(i/(size*size))
M = matgen.symmetricSparsePositiveDefinite(size, i)
complete = cholesky.completeCholesky(M)
incomplete = cholesky.incompleteCholesky(M)
y.append(numpy.linalg.norm(complete-incomplete)/numpy.linalg.norm(complete))
plt.plot(x, y, marker='o')
plt.title("Relative error made by Cholesky incomplete factorization, in function of matrix density\n")
plt.ylabel("relative error on the norm of the matrix obtained")
plt.xlabel("density of the initial 100*100 matrix")
plt.show()