本文整理汇总了Python中sympy.integrals.deltafunctions.deltaintegrate函数的典型用法代码示例。如果您正苦于以下问题：Python deltaintegrate函数的具体用法？Python deltaintegrate怎么用？Python deltaintegrate使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了deltaintegrate函数的5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，您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: _eval_integral
#.........这里部分代码省略.........
parts.append(coeff*x)
continue
# g(x) = expr + O(x**n)
order_term = g.getO()
if order_term is not None:
h = self._eval_integral(g.removeO(), x)
if h is not None:
h_order_expr = self._eval_integral(order_term.expr, x)
if h_order_expr is not None:
h_order_term = order_term.func(h_order_expr, *order_term.variables)
parts.append(coeff*(h + h_order_term))
continue
# NOTE: if there is O(x**n) and we fail to integrate then there is
# no point in trying other methods because they will fail anyway.
return None
# c
# g(x) = (a*x+b)
if g.is_Pow and not g.exp.has(x) and not meijerg:
a = Wild('a', exclude=[x])
b = Wild('b', exclude=[x])
M = g.base.match(a*x + b)
if M is not None:
if g.exp == -1:
h = C.log(g.base)
else:
h = g.base**(g.exp + 1) / (g.exp + 1)
parts.append(coeff * h / M[a])
continue
# poly(x)
# g(x) = -------
# poly(x)
if g.is_rational_function(x) and not meijerg:
parts.append(coeff * ratint(g, x))
continue
if not meijerg:
# g(x) = Mul(trig)
h = trigintegrate(g, x)
if h is not None:
parts.append(coeff * h)
continue
# g(x) has at least a DiracDelta term
h = deltaintegrate(g, x)
if h is not None:
parts.append(coeff * h)
continue
if not meijerg:
# fall back to the more general algorithm
try:
h = heurisch(g, x, hints=[])
except PolynomialError:
# XXX: this exception means there is a bug in the
# implementation of heuristic Risch integration
# algorithm.
h = None
else:
h = None
if meijerg is not False and h is None:
# rewrite using G functions
h = meijerint_indefinite(g, x)
if h is not None:
parts.append(coeff * h)
continue
# if we failed maybe it was because we had
# a product that could have been expanded,
# so let's try an expansion of the whole
# thing before giving up; we don't try this
# out the outset because there are things
# that cannot be solved unless they are
# NOT expanded e.g., x**x*(1+log(x)). There
# should probably be a checker somewhere in this
# routine to look for such cases and try to do
# collection on the expressions if they are already
# in an expanded form
if not h and len(args) == 1:
f = f.expand(mul=True, deep=False)
if f.is_Add:
return self._eval_integral(f, x, meijerg)
if h is not None:
parts.append(coeff * h)
else:
return None
return Add(*parts)
开发者ID:manoj2378，项目名称:sympy，代码行数:101，代码来源:integrals.py
示例2: _eval_integral
#.........这里部分代码省略.........
a = Wild('a', exclude=[x])
b = Wild('b', exclude=[x])
M = g.base.match(a*x + b)
if M is not None:
if g.exp == -1:
h = C.log(g.base)
elif conds != 'piecewise':
h = g.base**(g.exp + 1) / (g.exp + 1)
else:
h1 = C.log(g.base)
h2 = g.base**(g.exp + 1) / (g.exp + 1)
h = Piecewise((h1, Eq(g.exp, -1)), (h2, True))
parts.append(coeff * h / M[a])
continue
# poly(x)
# g(x) = -------
# poly(x)
if g.is_rational_function(x) and not meijerg:
parts.append(coeff * ratint(g, x))
continue
if not meijerg:
# g(x) = Mul(trig)
h = trigintegrate(g, x, conds=conds)
if h is not None:
parts.append(coeff * h)
continue
# g(x) has at least a DiracDelta term
h = deltaintegrate(g, x)
if h is not None:
parts.append(coeff * h)
continue
# Try risch again.
if risch is not False:
try:
h, i = risch_integrate(g, x, separate_integral=True, conds=conds)
except NotImplementedError:
h = None
else:
if i:
h = h + i.doit(risch=False)
parts.append(coeff*h)
continue
# fall back to heurisch
try:
if conds == 'piecewise':
h = heurisch_wrapper(g, x, hints=[])
else:
h = heurisch(g, x, hints=[])
except PolynomialError:
# XXX: this exception means there is a bug in the
# implementation of heuristic Risch integration
# algorithm.
h = None
else:
h = None
if meijerg is not False and h is None:
开发者ID:hrashk，项目名称:sympy，代码行数:67，代码来源:integrals.py
示例3: _eval_integral
#.........这里部分代码省略.........
(b) using Trager's algorithm - possibly faster than (a) but needs
implementation :)
(3) Whichever implementation of pmInt (Mateusz, Kirill's or a
combination of both).
- this way we can handle efficiently huge class of elementary and
special functions
(4) Recursive Risch algorithm as described in Bronstein's integration
tutorial.
- this way we can handle those integrable functions for which (3)
fails
(5) Powerful heuristics based mostly on user defined rules.
- handle complicated, rarely used cases
"""
# if it is a poly(x) then let the polynomial integrate itself (fast)
#
# It is important to make this check first, otherwise the other code
# will return a sympy expression instead of a Polynomial.
#
# see Polynomial for details.
if isinstance(f, Poly):
return f.integrate(x)
# Piecewise antiderivatives need to call special integrate.
if f.func is Piecewise:
return f._eval_integral(x)
# let's cut it short if `f` does not depend on `x`
if not f.has(x):
return f*x
# try to convert to poly(x) and then integrate if successful (fast)
poly = f.as_poly(x)
if poly is not None:
return poly.integrate(x).as_basic()
# since Integral(f=g1+g2+...) == Integral(g1) + Integral(g2) + ...
# we are going to handle Add terms separately,
# if `f` is not Add -- we only have one term
parts = []
for g in make_list(f, Add):
coeff, g = g.as_independent(x)
# g(x) = const
if g is S.One:
parts.append(coeff * x)
continue
# c
# g(x) = (a*x+b)
if g.is_Pow and not g.exp.has(x):
a = Wild('a', exclude=[x])
b = Wild('b', exclude=[x])
M = g.base.match(a*x + b)
if M is not None:
if g.exp == -1:
h = C.log(g.base)
else:
h = g.base**(g.exp+1) / (g.exp+1)
parts.append(coeff * h / M[a])
continue
# poly(x)
# g(x) = -------
# poly(x)
if g.is_rational_function(x):
parts.append(coeff * ratint(g, x))
continue
# g(x) = Mul(trig)
h = trigintegrate(g, x)
if h is not None:
parts.append(coeff * h)
continue
# g(x) has at least a DiracDelta term
h = deltaintegrate(g,x)
if h is not None:
parts.append(coeff * h)
continue
# fall back to the more general algorithm
h = heurisch(g, x, hints=[])
if h is not None:
parts.append(coeff * h)
else:
return None
return C.Add(*parts)
开发者ID:smichr，项目名称:sympy-live，代码行数:101，代码来源:integrals.py
示例4: test_J17
def test_J17():
assert deltaintegrate(f((x + 2)/5)*DiracDelta((x - 2)/3) - g(x)*diff(DiracDelta(x - 1), x), (x, 0, 3))
开发者ID:batya239，项目名称:sympy，代码行数:2，代码来源:test_wester.py
示例5: test_deltaintegrate
def test_deltaintegrate():
assert deltaintegrate(x, x) is None
assert deltaintegrate(x + DiracDelta(x), x) is None
assert deltaintegrate(DiracDelta(x, 0), x) == Heaviside(x)
for n in range(10):
assert deltaintegrate(DiracDelta(x, n + 1), x) == DiracDelta(x, n)
assert deltaintegrate(DiracDelta(x), x) == Heaviside(x)
assert deltaintegrate(DiracDelta(-x), x) == Heaviside(x)
assert deltaintegrate(DiracDelta(x - y), x) == Heaviside(x - y)
assert deltaintegrate(DiracDelta(y - x), x) == Heaviside(x - y)
assert deltaintegrate(x*DiracDelta(x), x) == 0
assert deltaintegrate((x - y)*DiracDelta(x - y), x) == 0
assert deltaintegrate(DiracDelta(x)**2, x) == DiracDelta(0)*Heaviside(x)
assert deltaintegrate(y*DiracDelta(x)**2, x) == \
y*DiracDelta(0)*Heaviside(x)
assert deltaintegrate(DiracDelta(x, 1), x) == DiracDelta(x, 0)
assert deltaintegrate(y*DiracDelta(x, 1), x) == y*DiracDelta(x, 0)
assert deltaintegrate(DiracDelta(x, 1)**2, x) == -DiracDelta(0, 2)*Heaviside(x)
assert deltaintegrate(y*DiracDelta(x, 1)**2, x) == -y*DiracDelta(0, 2)*Heaviside(x)
assert deltaintegrate(DiracDelta(x) * f(x), x) == f(0) * Heaviside(x)
assert deltaintegrate(DiracDelta(-x) * f(x), x) == f(0) * Heaviside(x)
assert deltaintegrate(DiracDelta(x - 1) * f(x), x) == f(1) * Heaviside(x - 1)
assert deltaintegrate(DiracDelta(1 - x) * f(x), x) == f(1) * Heaviside(x - 1)
assert deltaintegrate(DiracDelta(x**2 + x - 2), x) == \
Heaviside(x - 1)/3 + Heaviside(x + 2)/3
p = cos(x)*(DiracDelta(x) + DiracDelta(x**2 - 1))*sin(x)*(x - pi)
assert deltaintegrate(p, x) - (-pi*(cos(1)*Heaviside(-1 + x)*sin(1)/2 - \
cos(1)*Heaviside(1 + x)*sin(1)/2) + \
cos(1)*Heaviside(1 + x)*sin(1)/2 + \
cos(1)*Heaviside(-1 + x)*sin(1)/2) == 0
p = x_2*DiracDelta(x - x_2)*DiracDelta(x_2 - x_1)
assert deltaintegrate(p, x_2) == x*DiracDelta(x - x_1)*Heaviside(x_2 - x)
p = x*y**2*z*DiracDelta(y - x)*DiracDelta(y - z)*DiracDelta(x - z)
assert deltaintegrate(p, y) == x**3*z*DiracDelta(x - z)**2*Heaviside(y - x)
assert deltaintegrate((x + 1)*DiracDelta(2*x), x) == S(1)/2 * Heaviside(x)
assert deltaintegrate((x + 1)*DiracDelta(2*x/3 + 4/S(9)), x) == \
S(1)/2 * Heaviside(x + S(2)/3)
a, b, c = symbols('a b c', commutative=False)
assert deltaintegrate(DiracDelta(x - y)*f(x - b)*f(x - a), x) == \
f(y - b)*f(y - a)*Heaviside(x - y)
p = f(x - a)*DiracDelta(x - y)*f(x - c)*f(x - b)
assert deltaintegrate(p, x) == f(y - a)*f(y - c)*f(y - b)*Heaviside(x - y)
p = DiracDelta(x - z)*f(x - b)*f(x - a)*DiracDelta(x - y)
assert deltaintegrate(p, x) == DiracDelta(y - z)*f(y - b)*f(y - a) * \
Heaviside(x - y)
开发者ID:AlexanderKulka，项目名称:sympy，代码行数:55，代码来源:test_deltafunctions.py
注：本文中的sympy.integrals.deltafunctions.deltaintegrate函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。 |
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