def solve(A, b, pivoting):
# No pivoting
if pivoting == 0:
L, U = lu.lu_out_of_place(A)
z = forward_substitution(L, b)
x = back_substitution(U, z)
return x
# Partial pivoting
if pivoting == 1:
P, L, U = lu.lu_partial_pivot(A)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = back_substitution(U, z)
return x
# Complete pivoting
if pivoting == 2:
P, Q, L, U = lu.lu_complete_pivot(A)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = np.dot(Q.transpose(), back_substitution(U, z))
return x
# Rook pivoting
if pivoting == 3:
P, Q, L, U = lu.lu_rook_pivot(A)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = np.dot(Q.transpose(), back_substitution(U, z))
return x
# Blok PP
if pivoting == 4:
P, L, U = lu_block.lu_partial_block(A, 32)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = back_substitution(U, z)
return x
def inverse(A, pivoting):
(m, n) = A.shape
A_inverse = np.zeros((m, m))
b = np.identity(m)
# No pivot
if pivoting == 0:
L, U = lu.lu_out_of_place(A)
for k in range(m):
z = forward_substitution(L, b[:, k])
x = back_substitution(U, z)
A_inverse[:, k, np.newaxis] = x
return A_inverse
# Partial pivot
if pivoting == 1:
P, L, U = lu.lu_partial_pivot(A)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = back_substitution(U, z)
A_inverse[:, k, np.newaxis] = x
return A_inverse
# Complete pivot
if pivoting == 2:
P, Q, L, U = lu.lu_complete_pivot(A)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = np.dot(Q.transpose(), back_substitution(U, z))
A_inverse[:, k, np.newaxis] = x
return A_inverse
# Rook pivot
if pivoting == 3:
P, Q, L, U = lu.lu_rook_pivot(A)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = np.dot(Q.transpose(), back_substitution(U, z))
A_inverse[:, k, np.newaxis] = x
return A_inverse
# PP block
if pivoting == 4:
P, L, U = lu_block.lu_partial_block(A, 32)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = back_substitution(U, z)
A_inverse[:, k, np.newaxis] = x
return A_inverse
def precision_test(minsize, maxsize, step, repeat):
plot_data = []
y_sp = []
y_partial = []
y_complete = []
y_rook = []
y_block = []
for index, i in enumerate(range(minsize, maxsize, step)):
test_sp = []
test_my = []
test_lu = []
test_partial = []
test_complete = []
test_rook = []
test_block = []
for j in range(repeat):
# A = np.random.rand(i, i)
# Ab = np.random.rand(i, 1)
# pos_def = tests.generate_pos_dif(i, 1, 1000)
A = np.random.randint(-1000, 1000, size=(i, i)) # change
# Ab = np.random.randint(-1000, 1000, size=(i, 1)) # change
# x = sp.solve(A, Ab)
# Anew = np.dot(A, x)
# test_sp += [norm_2(Ab, Anew)]
#
# x = solve.solve(A, Ab, 2)
# Anew = np.dot(A, x)
# test_block += [norm_2(Ab, Anew)]
# invers = sp.inv(A)
# Asp = np.dot(A, invers)
# dif_matrix = Asp - np.identity(Asp.shape[0])
# test_sp += [np.sum(np.abs(dif_matrix))]
# invers = solve.inverse(A, 2)
# Asp = np.dot(A, invers)
# dif_matrix = Asp - np.identity(Asp.shape[0])
# test_my += [np.sum(np.abs(dif_matrix))]
# x = sp.inv(A)
# Amy = np.dot(A, x)
# test_sp += [norm_2(np.identity(i), Amy)]
#
# # x = lu.lu_partial_pivot(A, Ab, 1)
# # Amy = np.dot(A, x)
# # test_partial += [norm_2(Ab, Amy)]
#
# x = solve.inverse(A, 4)
# Amy = np.dot(A, x)
# test_block += [norm_2(np.identity(i), Amy)]
#
# x = solve.solve(A, Ab, 3)
# Amy = np.dot(A, x)
# test_rook += [norm_2(Ab, Amy)]
#
# x = solve.solve(A, Ab, 4)
# Amy = np.dot(A, x)
# test_block += [norm_2(Ab, Amy)]
P, L, U = sp.lu(A)
Amy = np.dot(P, np.dot(L, U))
test_sp += [norm_1(A, Amy)]
P, L, U = lu.lu_partial_pivot(A)
Amy = np.dot(P, np.dot(L, U))
test_partial += [norm_1(A, Amy)]
P, Q, L, U = lu.lu_complete_pivot(A)
Amy = np.dot(np.dot(P, np.dot(L, U)), Q)
test_complete += [norm_1(A, Amy)]
P, Q, L, U = lu.lu_rook_pivot(A)
Amy = np.dot(np.dot(P, np.dot(L, U)), Q)
test_rook += [norm_1(A, Amy)]
P, L, U = lu_block.lu_partial_block(A, 32)
Amy = np.dot(P, np.dot(L, U))
test_block += [norm_1(A, Amy)]
# U = sp.cholesky(pos_def)
# Amy = np.dot(U.transpose(), U)
# test_sp += [norm_2(pos_def, Amy)]
#
# U = cholesky.cholesky_block(pos_def, 32)
# Amy = np.dot(U.transpose(), U)
# test_partial += [norm_2(pos_def, Amy)]
# L2, U2 = lu_square.lu_in_place(A)
# lu = np.dot(L2, U2)
# dif_matrix = lu - A
# test_lu += [np.sum(np.abs(dif_matrix))]
# P3, L3, U3 = lu_square.lu_partial_pivot(A)
# partial = np.dot(P3, np.dot(L3, U3))
# dif_matrix = partial - A
# test_partial += [np.sum(np.abs(dif_matrix))]
#
# P4, Q4, L4, U4 = lu_square.lu_complete_pivot(A)
# complete = np.dot(np.dot(P4, np.dot(L4, U4)), Q4)
# dif_matrix = complete - A
# test_complete += [np.sum(np.abs(dif_matrix))]
# P5, Q5, L5, U5 = lu_square.lu_rook_pivot(A)
# rook = np.dot(np.dot(P5, np.dot(L5, U5)), Q5)
# dif_matrix = rook - A
# test_rook += [np.sum(np.abs(dif_matrix))]
#
print i, j
plot_data += [{
'y': test_sp,
'type':'box',
'marker':{'color': 'black'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_partial,
'type':'box',
'marker':{'color': 'blue'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_complete,
'type':'box',
'marker':{'color': 'red'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_rook,
'type':'box',
'marker':{'color': 'green'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_block,
'type':'box',
'marker':{'color': 'purple'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
# sp_avg = [np.sum(test_sp) / len(test_sp)]
# y += [sp_avg][0]
# plot_data += [{
# 'y': sp_avg,
# 'type':'box',
# 'marker':{'color': 'green'},
# 'name': str(i) + 'x' + str(i)
# }]
# print plot_data
# xi = np.arange(len(avg))
y_sp += [np.sum(test_sp) / len(test_sp)]
y_partial += [np.sum(test_partial) / len(test_partial)]
y_complete += [np.sum(test_complete) / len(test_complete)]
y_rook += [np.sum(test_rook) / len(test_rook)]
y_block += [np.sum(test_block) / len(test_block)]
print np.polyfit(range(len(y_sp)), y_sp, 1, full=True)
print np.polyfit(range(len(y_sp)), y_sp, 2, full=True)
print np.polyfit(range(len(y_partial)), y_partial, 1, full=True)
print np.polyfit(range(len(y_partial)), y_partial, 2, full=True)
print np.polyfit(range(len(y_complete)), y_complete, 1, full=True)
print np.polyfit(range(len(y_complete)), y_complete, 2, full=True)
print np.polyfit(range(len(y_rook)), y_rook, 1, full=True)
print np.polyfit(range(len(y_rook)), y_rook, 2, full=True)
print np.polyfit(range(len(y_block)), y_block, 1, full=True)
print np.polyfit(range(len(y_block)), y_block, 2, full=True)
url = py.plot(plot_data, filename='precision')
def benchmark_test(minsize, maxsize, step, repeat):
plot_data = []
y_sp = []
y_block = []
y_no = []
for i in range(minsize, maxsize, step):
test_sp = []
test_no = []
test_partial = []
test_complete = []
test_rook = []
test_block = []
for j in range(repeat):
# pos_def = tests.generate_pos_dif(i, 1, 1000)
A = np.random.randint(-1000, 1000, size=(i, i)) # change
# Ab = np.random.randint(-1000, 1000, size=(i, 1)) # change
time_start = time.clock()
sp.lu(A)
test_sp += [time.clock() - time_start]
time_start = time.clock()
lu.lu_in_place(A)
test_no += [time.clock() - time_start]
time_start = time.clock()
lu.lu_partial_pivot(A)
test_partial += [time.clock() - time_start]
time_start = time.clock()
lu.lu_complete_pivot(A)
test_complete += [time.clock() - time_start]
time_start = time.clock()
lu.lu_rook_pivot(A)
test_rook += [time.clock() - time_start]
time_start = time.clock()
lu_block.lu_partial_block(A, 32)
test_block += [time.clock() - time_start]
# time_start = time.clock()
# lu.lu_partial_pivot(A)
# test_no += [time.clock() - time_start]
print i, j
plot_data += [{
'y': test_sp,
'type':'box',
'marker':{'color': 'black'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_no,
'type':'box',
'marker':{'color': 'grey'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_partial,
'type':'box',
'marker':{'color': 'blue'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_complete,
'type':'box',
'marker':{'color': 'red'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_rook,
'type':'box',
'marker':{'color': 'green'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
plot_data += [{
'y': test_block,
'type':'box',
'marker':{'color': 'purple'},
'name': str(i) + 'x' + str(i),
'boxpoints': False
}]
# plot_data += [{
# 'y': test_no,
# 'type':'box',
# 'marker':{'color': 'blue'},
# 'name': str(i) + 'x' + str(i),
# 'boxpoints': False
# }]
#
# y_sp += [np.sum(test_sp) / len(test_sp)]
# y_block += [np.sum(test_block) / len(test_block)]
# y_no += [np.sum(test_no) / len(test_no)]
# print np.polyfit(range(len(y_sp)), y_sp, 1, full=True)
# print np.polyfit(range(len(y_sp)), y_sp, 2, full=True)
# print np.polyfit(range(len(y_block)), y_block, 1, full=True)
# print np.polyfit(range(len(y_block)), y_block, 2, full=True)
# print np.polyfit(range(len(y_no)), y_no, 1, full=True)
# print np.polyfit(range(len(y_no)), y_no, 2, full=True)
url = py.plot(plot_data, filename='Benchmark')
def test_lu_partial(self):
rand_int_matrix = np.random.randint(-1000, 1000, size=(1000, 1000))
np.array_equal(lu.lu_partial_pivot(rand_int_matrix)[0].transpose(), sp.lu(rand_int_matrix)[0])