def test_matrix_basic():
A1 = matrix(3)
for i in xrange(3):
A1[i,i] = 1
assert A1 == eye(3)
assert A1 == matrix(A1)
A2 = matrix(3, 2)
assert not A2._matrix__data
A3 = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert list(A3) == range(1, 10)
A3[1,1] = 0
assert not (1, 1) in A3._matrix__data
A4 = matrix([[1, 2, 3], [4, 5, 6]])
A5 = matrix([[6, -1], [3, 2], [0, -3]])
assert A4 * A5 == matrix([[12, -6], [39, -12]])
assert A1 * A3 == A3 * A1 == A3
try:
A2 * A2
assert False
except ValueError:
pass
l = [[10, 20, 30], [40, 0, 60], [70, 80, 90]]
A6 = matrix(l)
assert A6.tolist() == l
assert A6 == eval(repr(A6))
A6 = matrix(A6, force_type=float)
assert A6 == eval(repr(A6))
assert A6*1j == eval(repr(A6*1j))
assert A3 * 10 == 10 * A3 == A6
assert A2.rows == 3
assert A2.cols == 2
A3.rows = 2
A3.cols = 2
assert len(A3._matrix__data) == 3
assert A4 + A4 == 2*A4
try:
A4 + A2
except ValueError:
pass
assert sum(A1 - A1) == 0
A7 = matrix([[1, 2], [3, 4], [5, 6], [7, 8]])
x = matrix([10, -10])
assert A7*x == matrix([-10, -10, -10, -10])
A8 = ones(5)
assert sum((A8 + 1) - (2 - zeros(5))) == 0
assert (1 + ones(4)) / 2 - 1 == zeros(4)
assert eye(3)**10 == eye(3)
try:
A7**2
assert False
except ValueError:
pass
A9 = randmatrix(3)
A10 = matrix(A9)
A9[0,0] = -100
assert A9 != A10
A11 = matrix(randmatrix(2, 3), force_type=mpi)
for a in A11:
assert isinstance(a, mpi)
assert nstr(A9)
def test_matrix_basic():
A1 = matrix(3)
for i in xrange(3):
A1[i, i] = 1
assert A1 == eye(3)
assert A1 == matrix(A1)
A2 = matrix(3, 2)
assert not A2._matrix__data
A3 = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert list(A3) == range(1, 10)
A3[1, 1] = 0
assert not (1, 1) in A3._matrix__data
A4 = matrix([[1, 2, 3], [4, 5, 6]])
A5 = matrix([[6, -1], [3, 2], [0, -3]])
assert A4 * A5 == matrix([[12, -6], [39, -12]])
assert A1 * A3 == A3 * A1 == A3
try:
A2 * A2
assert False
except ValueError:
pass
l = [[10, 20, 30], [40, 0, 60], [70, 80, 90]]
A6 = matrix(l)
assert A6.tolist() == l
assert A6 == eval(repr(A6))
A6 = matrix(A6, force_type=float)
assert A6 == eval(repr(A6))
assert A3 * 10 == 10 * A3 == A6
assert A2.rows == 3
assert A2.cols == 2
A3.rows = 2
A3.cols = 2
assert len(A3._matrix__data) == 3
assert A4 + A4 == 2 * A4
try:
A4 + A2
except ValueError:
pass
assert sum(A1 - A1) == 0
A7 = matrix([[1, 2], [3, 4], [5, 6], [7, 8]])
x = matrix([10, -10])
assert A7 * x == matrix([-10, -10, -10, -10])
A8 = ones(5)
assert sum((A8 + 1) - (2 - zeros(5))) == 0
assert (1 + ones(4)) / 2 - 1 == zeros(4)
assert eye(3)**10 == eye(3)
try:
A7**2
assert False
except ValueError:
pass
A9 = randmatrix(3)
A10 = matrix(A9)
A9[0, 0] = -100
assert A9 != A10
A11 = matrix(randmatrix(2, 3), force_type=mpi)
for a in A11:
assert isinstance(a, mpi)
def test_matrix_creation():
assert diag([1, 2, 3]) == matrix([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
A1 = ones(2, 3)
assert A1.rows == 2 and A1.cols == 3
for a in A1:
assert a == 1
A2 = zeros(3, 2)
assert A2.rows == 3 and A2.cols == 2
for a in A2:
assert a == 0
assert randmatrix(10) != randmatrix(10)
def test_matrix_creation():
assert diag([1, 2, 3]) == matrix([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
A1 = ones(2, 3)
assert A1.rows == 2 and A1.cols == 3
for a in A1:
assert a == 1
A2 = zeros(3, 2)
assert A2.rows == 3 and A2.cols == 2
for a in A2:
assert a == 0
assert randmatrix(10) != randmatrix(10)
def test_matrix_creation():
assert diag([1, 2, 3]) == matrix([[1, 0, 0], [0, 2, 0], [0, 0, 3]])
A1 = ones(2, 3)
assert A1.rows == 2 and A1.cols == 3
for a in A1:
assert a == 1
A2 = zeros(3, 2)
assert A2.rows == 3 and A2.cols == 2
for a in A2:
assert a == 0
assert randmatrix(10) != randmatrix(10)
one = mpf(1)
assert hilbert(3) == matrix([[one, one / 2, one / 3], [one / 2, one / 3, one / 4], [one / 3, one / 4, one / 5]])
def test_LU_decomp():
A = A3.copy()
b = b3
A, p = LU_decomp(A)
y = L_solve(A, b, p)
x = U_solve(A, y)
assert p == [2, 1, 2, 3]
assert [round(i, 14) for i in x] == [
3.78953107960742, 2.9989094874591098, -0.081788440567070006,
3.8713195201744801, 2.9171210468920399
]
A = A4.copy()
b = b4
A, p = LU_decomp(A)
y = L_solve(A, b, p)
x = U_solve(A, y)
assert p == [0, 3, 4, 3]
assert [round(i, 14) for i in x] == [
2.6383625899619201, 2.6643834462368399, 0.79208015947958998,
-2.5088376454101899, -1.0567657691375001
]
A = randmatrix(3)
bak = A.copy()
LU_decomp(A, overwrite=1)
assert A != bak
def test_exp_pade():
for i in range(3):
dps = 15
extra = 5
mp.dps = dps + extra
dm = 0
while not dm:
m = randmatrix(3)
dm = det(m)
m = m/dm
a = diag([1,2,3])
a1 = m**-1 * a * m
mp.dps = dps
e1 = exp_pade(a1)
mp.dps = dps + extra
e2 = m * a1 * m**-1
d = e2 - a
#print d
mp.dps = dps
assert norm_p(d, inf).ae(0)
mp.dps = 15
def test_LU_decomp():
A = A3.copy()
b = b3
A, p = LU_decomp(A)
y = L_solve(A, b, p)
x = U_solve(A, y)
assert p == [2, 1, 2, 3]
assert [round(i, 14) for i in x] == [3.78953107960742, 2.9989094874591098,
-0.081788440567070006, 3.8713195201744801, 2.9171210468920399]
A = A4.copy()
b = b4
A, p = LU_decomp(A)
y = L_solve(A, b, p)
x = U_solve(A, y)
assert p == [0, 3, 4, 3]
assert [round(i, 14) for i in x] == [2.6383625899619201, 2.6643834462368399,
0.79208015947958998, -2.5088376454101899, -1.0567657691375001]
A = randmatrix(3)
bak = A.copy()
LU_decomp(A, overwrite=1)
assert A != bak
def test_exp_pade():
for i in range(3):
dps = 15
extra = 5
mp.dps = dps + extra
dm = 0
while not dm:
m = randmatrix(3)
dm = det(m)
m = m / dm
a = diag([1, 2, 3])
a1 = m**-1 * a * m
mp.dps = dps
e1 = exp_pade(a1)
mp.dps = dps + extra
e2 = m * a1 * m**-1
d = e2 - a
#print d
mp.dps = dps
assert norm(d, inf).ae(0)
mp.dps = 15
def test_LU_cache():
A = randmatrix(3)
LU = LU_decomp(A)
assert A._LU == LU_decomp(A)
A[0, 0] = -1000
assert A._LU is None
def test_LU_cache():
A = randmatrix(3)
LU = LU_decomp(A)
assert A._LU == LU_decomp(A)
A[0,0] = -1000
assert A._LU is None
def test_precision():
A = randmatrix(10, 10)
assert mnorm_1(inverse(inverse(A)) - A) < 1.e-45
def test_factorization():
A = randmatrix(5)
P, L, U = lu(A)
assert mnorm_1(P*A - L*U) < 1.e-15
def test_improve_solution():
A = randmatrix(5, min=1e-20, max=1e20)
b = randmatrix(5, 1, min=-1000, max=1000)
x1 = lu_solve(A, b) + randmatrix(5, 1, min=-1e-5, max=1.e-5)
x2 = improve_solution(A, x1, b)
assert norm_p(residual(A, x2, b), 2) < norm_p(residual(A, x1, b), 2)
def test_factorization():
A = randmatrix(5)
P, L, U = lu(A)
assert mnorm(P * A - L * U, 1) < 1.e-15
def test_improve_solution():
A = randmatrix(5, min=1e-20, max=1e20)
b = randmatrix(5, 1, min=-1000, max=1000)
x1 = lu_solve(A, b) + randmatrix(5, 1, min=-1e-5, max=1.e-5)
x2 = improve_solution(A, x1, b)
assert norm(residual(A, x2, b), 2) < norm(residual(A, x1, b), 2)
def test_precision():
A = randmatrix(10, 10)
assert mnorm(inverse(inverse(A)) - A, 1) < 1.e-45