def test_conjugate():
M = OperationsOnlyMatrix([[0, I, 5],
[1, 2, 0]])
assert M.T == Matrix([[0, 1],
[I, 2],
[5, 0]])
assert M.C == Matrix([[0, -I, 5],
[1, 2, 0]])
assert M.C == M.conjugate()
assert M.H == M.T.C
assert M.H == Matrix([[ 0, 1],
[-I, 2],
[ 5, 0]])
python类Matrix()的实例源码
def test_valued_tensor_get_matrix():
numpy = import_module("numpy")
if numpy is None:
skip("numpy not installed.")
(A, B, AB, BA, C, Lorentz, E, px, py, pz, LorentzD, mu0, mu1, mu2, ndm, n0, n1,
n2, NA, NB, NC, minkowski, ba_matrix, ndm_matrix, i0, i1, i2, i3, i4) = _get_valued_base_test_variables()
matab = AB(i0, i1).get_matrix()
assert matab == Matrix([
[1, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, -1, 0],
[0, 0, 0, -1],
])
# when alternating contravariant/covariant with [1, -1, -1, -1] metric
# it becomes the identity matrix:
assert AB(i0, -i1).get_matrix() == eye(4)
# covariant and contravariant forms:
assert A(i0).get_matrix() == Matrix([E, px, py, pz])
assert A(-i0).get_matrix() == Matrix([E, -px, -py, -pz])
def as_matrix(self):
"""Returns the data of the table in Matrix form.
Examples
========
>>> from sympy import TableForm
>>> t = TableForm([[5, 7], [4, 2], [10, 3]], headings='automatic')
>>> t
| 1 2
--------
1 | 5 7
2 | 4 2
3 | 10 3
>>> t.as_matrix()
Matrix([
[ 5, 7],
[ 4, 2],
[10, 3]])
"""
from sympy import Matrix
return Matrix(self._lines)
def test_Matrix_mul():
M = Matrix([[1, 2, 3], [x, y, x]])
m = matrix([[2, 4], [x, 6], [x, z**2]])
assert M*m == Matrix([
[ 2 + 5*x, 16 + 3*z**2],
[2*x + x*y + x**2, 4*x + 6*y + x*z**2],
])
assert m*M == Matrix([
[ 2 + 4*x, 4 + 4*y, 6 + 4*x],
[ 7*x, 2*x + 6*y, 9*x],
[x + x*z**2, 2*x + y*z**2, 3*x + x*z**2],
])
a = array([2])
assert a[0] * M == 2 * M
assert M * a[0] == 2 * M
def fcts(self):
j = sympy.Matrix([
r**2 * z,
r * z**2
])
# Create an isotropic sigma vector
Sig = sympy.Matrix([
[420/(sympy.pi)*(r*z)**2, 0],
[0, 420/(sympy.pi)*(r*z)**2],
])
return j, Sig
def fcts(self):
j = sympy.Matrix([
r**2 * z,
r * z**2
])
# Create an isotropic sigma vector
Sig = sympy.Matrix([
[120/(sympy.pi)*(r*z)**2, 0],
[0, 420/(sympy.pi)*(r*z)**2],
])
return j, Sig
def fcts(self):
h = sympy.Matrix([r**2 * z])
# Create an isotropic sigma vector
Sig = sympy.Matrix([200/(sympy.pi)*(r*z)**2])
return h, Sig
def __init__(self, settings):
settings.update(output_dim=4)
super().__init__(settings)
params = sp.symbols('x1, x2, x3, x4, tau')
x1, x2, x3, x4, tau = params
x = [x1, x2, x3, x4]
h = sp.Matrix([[x1]])
f = sp.Matrix([[x2],
[st.B * x1 * x4 ** 2 - st.B * st.G * sin(x3)],
[x4],
[(tau - 2 * st.M * x1 * x2 * x4
- st.M * st.G * x1 * cos(x3)) / (
st.M * x1 ** 2 + st.J + st.Jb)]])
q = sp.Matrix(pm.lie_derivatives(h, f, x, len(x) - 1))
dq = q.jacobian(x)
if dq.rank() != len(x):
raise Exception("System might not be observable")
# gets p = [p0, p1, ... pn-1]
p = pm.char_coefficients(self._settings["poles"])
k = p[::-1]
l = dq.inv() @ k
mat2array = [{'ImmutableMatrix': np.array}, 'numpy']
self.h_func = sp.lambdify((x1, x2, x3, x4, tau), h, modules=mat2array)
self.l_func = sp.lambdify((x1, x2, x3, x4, tau), l, modules=mat2array)
self.f_func = sp.lambdify((x1, x2, x3, x4, tau), f, modules=mat2array)
self.output = np.array(self._settings["initial state"], dtype=float)
def setUp(self):
self._x1, self._x2 = sp.symbols("x y")
self.x = sp.Matrix([self._x1, self._x2])
self.f = sp.Matrix([-self._x2**2, sp.sin(self._x1)])
self.h = sp.Matrix([self._x1**2 - sp.sin(self._x2)])
def __repr__(self):
return sp.Matrix(self.matrix.tolist()).__repr__()
def _build_feature_matrix(prop, features, desired_data):
transformed_features = sympy.Matrix([feature_transforms[prop](i) for i in features])
all_samples = get_samples(desired_data)
feature_matrix = np.empty((len(all_samples), len(transformed_features)), dtype=np.float)
feature_matrix[:, :] = [transformed_features.subs({v.T: temp, 'YS': compf[0],
'Z': compf[1]}).evalf()
for temp, compf in all_samples]
return feature_matrix
def _compute_basis(self, closed_form):
"""
Compute a set of functions B=(f1, ..., fn), a nxn matrix M
and a 1xn matrix C such that:
closed_form = C B
z d/dz B = M B.
"""
from sympy.matrices import Matrix, eye, zeros
afactors = [_x + a for a in self.func.ap]
bfactors = [_x + b - 1 for b in self.func.bq]
expr = _x*Mul(*bfactors) - self.z*Mul(*afactors)
poly = Poly(expr, _x)
n = poly.degree() - 1
b = [closed_form]
for _ in xrange(n):
b.append(self.z*b[-1].diff(self.z))
self.B = Matrix(b)
self.C = Matrix([[1] + [0]*n])
m = eye(n)
m = m.col_insert(0, zeros(n, 1))
l = poly.all_coeffs()[1:]
l.reverse()
self.M = m.row_insert(n, -Matrix([l])/poly.all_coeffs()[0])
def test_iterable_is_sequence():
ordered = [list(), tuple(), Tuple(), Matrix([[]])]
unordered = [set()]
not_sympy_iterable = [{}, '', u('')]
assert all(is_sequence(i) for i in ordered)
assert all(not is_sequence(i) for i in unordered)
assert all(iterable(i) for i in ordered + unordered)
assert all(not iterable(i) for i in not_sympy_iterable)
assert all(iterable(i, exclude=None) for i in not_sympy_iterable)
def test_nsolve():
# onedimensional
x = Symbol('x')
assert nsolve(sin(x), 2) - pi.evalf() < 1e-15
assert nsolve(Eq(2*x, 2), x, -10) == nsolve(2*x - 2, -10)
# Testing checks on number of inputs
raises(TypeError, lambda: nsolve(Eq(2*x, 2)))
raises(TypeError, lambda: nsolve(Eq(2*x, 2), x, 1, 2))
# issue 4829
assert nsolve(x**2/(1 - x)/(1 - 2*x)**2 - 100, x, 0) # doesn't fail
# multidimensional
x1 = Symbol('x1')
x2 = Symbol('x2')
f1 = 3 * x1**2 - 2 * x2**2 - 1
f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8
f = Matrix((f1, f2)).T
F = lambdify((x1, x2), f.T, modules='mpmath')
for x0 in [(-1, 1), (1, -2), (4, 4), (-4, -4)]:
x = nsolve(f, (x1, x2), x0, tol=1.e-8)
assert mnorm(F(*x), 1) <= 1.e-10
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago (z was added to make it 3-dimensional)
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
f1 = -x + 2*y
f2 = (x**2 + x*(y**2 - 2) - 4*y) / (x + 4)
f3 = sqrt(x**2 + y**2)*z
f = Matrix((f1, f2, f3)).T
F = lambdify((x, y, z), f.T, modules='mpmath')
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
assert list(map(round, getroot((1, 1, 1)))) == [2.0, 1.0, 0.0]
assert nsolve([Eq(
f1), Eq(f2), Eq(f3)], [x, y, z], (1, 1, 1)) # just see that it works
a = Symbol('a')
assert nsolve(1/(0.001 + a)**3 - 6/(0.9 - a)**3, a, 0.3).ae(
mpf('0.31883011387318591'))
def is_normal_transformation_ok(eq):
A = transformation_to_normal(eq)
X, Y, Z = A*Matrix([x, y, z])
simplified = _mexpand(Subs(eq, (x, y, z), (X, Y, Z)).doit())
coeff = dict([reversed(t.as_independent(*[X, Y, Z])) for t in simplified.args])
for term in [X*Y, Y*Z, X*Z]:
if term in coeff.keys():
return False
return True
def get_target_matrix(self, format='sympy'):
if format == 'sympy':
return Matrix([[1, 0], [0, exp(Integer(2)*pi*I/(Integer(2)**self.k))]])
raise NotImplementedError(
'Invalid format for the R_k gate: %r' % format)
def _represent_ZGate(self, basis, **options):
"""
Represents the (I)QFT In the Z Basis
"""
nqubits = options.get('nqubits', 0)
if nqubits == 0:
raise QuantumError(
'The number of qubits must be given as nqubits.')
if nqubits < self.min_qubits:
raise QuantumError(
'The number of qubits %r is too small for the gate.' % nqubits
)
size = self.size
omega = self.omega
#Make a matrix that has the basic Fourier Transform Matrix
arrayFT = [[omega**(
i*j % size)/sqrt(size) for i in range(size)] for j in range(size)]
matrixFT = Matrix(arrayFT)
#Embed the FT Matrix in a higher space, if necessary
if self.label[0] != 0:
matrixFT = matrix_tensor_product(eye(2**self.label[0]), matrixFT)
if self.min_qubits < nqubits:
matrixFT = matrix_tensor_product(
matrixFT, eye(2**(nqubits - self.min_qubits)))
return matrixFT
def sympy_to_numpy(m, **options):
"""Convert a sympy Matrix/complex number to a numpy matrix or scalar."""
if not np:
raise ImportError
dtype = options.get('dtype', 'complex')
if isinstance(m, Matrix):
return np.matrix(m.tolist(), dtype=dtype)
elif isinstance(m, Expr):
if m.is_Number or m.is_NumberSymbol or m == I:
return complex(m)
raise TypeError('Expected Matrix or complex scalar, got: %r' % m)
def sympy_to_scipy_sparse(m, **options):
"""Convert a sympy Matrix/complex number to a numpy matrix or scalar."""
if not np or not sparse:
raise ImportError
dtype = options.get('dtype', 'complex')
if isinstance(m, Matrix):
return sparse.csr_matrix(np.matrix(m.tolist(), dtype=dtype))
elif isinstance(m, Expr):
if m.is_Number or m.is_NumberSymbol or m == I:
return complex(m)
raise TypeError('Expected Matrix or complex scalar, got: %r' % m)
def scipy_sparse_to_sympy(m, **options):
"""Convert a scipy.sparse matrix to a sympy matrix."""
return Matrix(m.todense())
