本文整理汇总了Python中sympy.N属性的典型用法代码示例。如果您正苦于以下问题:Python sympy.N属性的具体用法?Python sympy.N怎么用?Python sympy.N使用的例子?那么, 这里精选的属性代码示例或许可以为您提供帮助。您也可以进一步了解该属性所在类sympy
的用法示例。
在下文中一共展示了sympy.N属性的8个代码示例,这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞,您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: _scheme_from_rc_mpmath
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def _scheme_from_rc_mpmath(alpha, beta):
# Create vector cut of the first value of beta
n = len(alpha)
b = mp.zeros(n, 1)
for i in range(n - 1):
b[i] = mp.sqrt(beta[i + 1])
z = mp.zeros(1, n)
z[0, 0] = 1
d = mp.matrix(alpha)
tridiag_eigen(mp, d, b, z)
# nx1 matrix -> list of mpf
x = numpy.array([mp.mpf(sympy.N(xx, mp.dps)) for xx in d])
w = numpy.array([mp.mpf(sympy.N(beta[0], mp.dps)) * mp.power(ww, 2) for ww in z])
return x, w
示例2: event_bounds_expressions
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def event_bounds_expressions(self, event_bounds_exp):
if hasattr(self, 'output_equations'):
assert len(event_bounds_exp)+1 == self.output_equations.shape[0]
if hasattr(self, 'output_equations_functions'):
assert len(event_bounds_exp)+1 == \
self.output_equations_functions.size
if getattr(self, 'state_equations', None) is not None:
assert len(event_bounds_exp)+1 == self.state_equations.shape[0]
if getattr(self, 'state_equations_functions', None) is not None:
assert len(event_bounds_exp)+1 == \
self.state_equations_functions.size
self._event_bounds_expressions = event_bounds_exp
self.event_bounds = np.array(
[sp.N(bound, subs=self.constants_values)
for bound in event_bounds_exp],
dtype=np.float_
)
示例3: Nga
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def Nga(x, prec=5):
"""
Like :func:`sympy.N`, but also works on multivectors
For multivectors with coefficients that contain floating point numbers, this
rounds all these numbers to a precision of ``prec`` and returns the rounded
multivector.
"""
if isinstance(x, Mv):
return Mv(Nsympy(x.obj, prec), ga=x.Ga)
else:
return Nsympy(x, prec)
示例4: test_Wigner3j_values
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def test_Wigner3j_values():
from sympy import N
from sympy.physics.wigner import wigner_3j
from spherical_functions import Wigner3j
j_max = 8
for j1 in range(j_max+1):
for j2 in range(j1, j_max+1):
for j3 in range(j2, j_max+1):
for m1 in range(-j1, j1 + 1):
for m2 in range(-j2, j2 + 1):
m3 = -m1-m2
if j3 >= abs(m3):
sf_3j = Wigner3j(j1, j2, j3, m1, m2, m3)
sy_3j = N(wigner_3j(j1, j2, j3, m1, m2, m3))
assert abs(sf_3j - sy_3j) < precision_Wigner3j
示例5: wigner_d_naive
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def wigner_d_naive(l, m, n, beta):
"""
Numerically naive implementation of the Wigner-d function.
This is useful for checking the correctness of other implementations.
:param l: the degree of the Wigner-d function. l >= 0
:param m: the order of the Wigner-d function. -l <= m <= l
:param n: the order of the Wigner-d function. -l <= n <= l
:param beta: the argument. 0 <= beta <= pi
:return: d^l_mn(beta) in the TODO: what basis? complex, quantum(?), centered, cs(?)
"""
from scipy.special import eval_jacobi
try:
from scipy.misc import factorial
except:
from scipy.special import factorial
from sympy.functions.special.polynomials import jacobi, jacobi_normalized
from sympy.abc import j, a, b, x
from sympy import N
#jfun = jacobi_normalized(j, a, b, x)
jfun = jacobi(j, a, b, x)
# eval_jacobi = lambda q, r, p, o: float(jfun.eval(int(q), int(r), int(p), float(o)))
# eval_jacobi = lambda q, r, p, o: float(N(jfun, int(q), int(r), int(p), float(o)))
eval_jacobi = lambda q, r, p, o: float(jfun.subs({j:int(q), a:int(r), b:int(p), x:float(o)}))
mu = np.abs(m - n)
nu = np.abs(m + n)
s = l - (mu + nu) / 2
xi = 1 if n >= m else (-1) ** (n - m)
# print(s, mu, nu, np.cos(beta), type(s), type(mu), type(nu), type(np.cos(beta)))
jac = eval_jacobi(s, mu, nu, np.cos(beta))
z = np.sqrt((factorial(s) * factorial(s + mu + nu)) / (factorial(s + mu) * factorial(s + nu)))
# print(l, m, n, beta, np.isfinite(mu), np.isfinite(nu), np.isfinite(s), np.isfinite(xi), np.isfinite(jac), np.isfinite(z))
assert np.isfinite(mu) and np.isfinite(nu) and np.isfinite(s) and np.isfinite(xi) and np.isfinite(jac) and np.isfinite(z)
assert np.isfinite(xi * z * np.sin(beta / 2) ** mu * np.cos(beta / 2) ** nu * jac)
return xi * z * np.sin(beta / 2) ** mu * np.cos(beta / 2) ** nu * jac
示例6: test_xk
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def test_xk(k):
n = 10
moments = quadpy.tools.integrate(
lambda x: [x ** (i + k) for i in range(2 * n)], -1, +1
)
alpha, beta = quadpy.tools.chebyshev(moments)
assert (alpha == 0).all()
assert beta[0] == moments[0]
assert beta[1] == sympy.S(k + 1) / (k + 3)
assert beta[2] == sympy.S(4) / ((k + 5) * (k + 3))
quadpy.tools.scheme_from_rc(
numpy.array([sympy.N(a) for a in alpha], dtype=float),
numpy.array([sympy.N(b) for b in beta], dtype=float),
mode="numpy",
)
def leg_polys(x):
return orthopy.line_segment.tree_legendre(x, 19, "monic", symbolic=True)
moments = quadpy.tools.integrate(
lambda x: [x ** k * leg_poly for leg_poly in leg_polys(x)], -1, +1
)
_, _, a, b = orthopy.line_segment.recurrence_coefficients.legendre(
2 * n, "monic", symbolic=True
)
alpha, beta = quadpy.tools.chebyshev_modified(moments, a, b)
assert (alpha == 0).all()
assert beta[0] == moments[0]
assert beta[1] == sympy.S(k + 1) / (k + 3)
assert beta[2] == sympy.S(4) / ((k + 5) * (k + 3))
points, weights = quadpy.tools.scheme_from_rc(
numpy.array([sympy.N(a) for a in alpha], dtype=float),
numpy.array([sympy.N(b) for b in beta], dtype=float),
mode="numpy",
)
示例7: get_generating_function
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def get_generating_function(f, T=None):
"""
Get the generating function
:param f: function addr
:param T: edges matrix of the function f
:return: the generating function
"""
if not T:
edges = [(a[0].addr, a[1].addr) for a in f.graph.edges()]
N = sorted([x for x in f.block_addrs])
T = []
for b1 in N:
T.append([])
for b2 in N:
if b1 == b2 or (b1, b2) in edges:
T[-1].append(1)
else:
T[-1].append(0)
else:
N = T[0]
T = sympy.Matrix(T)
z = sympy.var('z')
I = sympy.eye(len(N))
tmp = I - z * T
tmp.row_del(len(N) - 1)
tmp.col_del(0)
det_num = tmp.det()
det_den = (I - z * T).det()
quot = det_num / det_den
g_z = ((-1) ** (len(N) + 1)) * quot
return g_z
示例8: get_path_n
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import N [as 别名]
def get_path_n(f, T=None):
# TODO cire paper here
"""
Get the formula to estimate the number of path of a function, given its longest path.
:param f: function addr
:param T: edges matrix of the function f
:return: formula to estimate the number of paths
"""
g_z = get_generating_function(f, T)
expr = g_z.as_numer_denom()[1]
rs = sympy.roots(expr)
D = len(set(rs.keys())) # number of distinct roots
d = sum(rs.values()) # number of roots
# get taylor coefficients
f = sympy.utilities.lambdify(list(g_z.free_symbols), g_z)
taylor_coeffs = mpmath.taylor(f, 0, d - 1) # get the first d terms of taylor expansion
#
# calculate path_n
#
n = sympy.var('n')
e_path_n = 0
e_upper_n = 0
coeff = []
for i in xrange(1, D + 1):
ri, mi = rs.items()[i - 1]
for j in xrange(mi):
c_ij = sympy.var('c_' + str(i) + str(j))
coeff.append(c_ij)
e_path_n += c_ij * (n ** j) * ((1 / ri) ** n)
if ri.is_complex:
ri = sympy.functions.Abs(ri)
e_upper_n += c_ij * (n ** j) * ((1 / ri) ** n)
equations = []
for i, c in enumerate(taylor_coeffs):
equations.append(sympy.Eq(e_path_n.subs(n, i), c))
coeff_sol = sympy.linsolve(equations, coeff)
# assert unique solution
assert type(coeff_sol) == sympy.sets.FiniteSet, "Zero or more solutions returned for path_n coefficients"
coeff_sol = list(coeff_sol)[0]
coeff_sol = [sympy.N(c, ROUND) for c in coeff_sol]
for val, var in zip(coeff_sol, coeff):
name = var.name
e_path_n = e_path_n.subs(name, val)
e_upper_n = e_upper_n.subs(name, val)
return sympy.utilities.lambdify(list(e_path_n.free_symbols), e_path_n), sympy.utilities.lambdify(
list(e_upper_n.free_symbols), e_upper_n)