本文整理汇总了Python中sympy.Abs方法的典型用法代码示例。如果您正苦于以下问题:Python sympy.Abs方法的具体用法?Python sympy.Abs怎么用?Python sympy.Abs使用的例子?那么, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类sympy
的用法示例。
在下文中一共展示了sympy.Abs方法的7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: eliminate
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import Abs [as 别名]
def eliminate(rxns, wrt):
""" Linear combination coefficients for elimination of a substance
Parameters
----------
rxns : iterable of Equilibrium instances
wrt : str (substance key)
Examples
--------
>>> e1 = Equilibrium({'Cd+2': 4, 'H2O': 4}, {'Cd4(OH)4+4': 1, 'H+': 4}, 10**-32.5)
>>> e2 = Equilibrium({'Cd(OH)2(s)': 1}, {'Cd+2': 1, 'OH-': 2}, 10**-14.4)
>>> Equilibrium.eliminate([e1, e2], 'Cd+2')
[1, 4]
>>> print(1*e1 + 4*e2)
4 Cd(OH)2(s) + 4 H2O = Cd4(OH)4+4 + 4 H+ + 8 OH-; 7.94e-91
"""
import sympy
viol = [r.net_stoich([wrt])[0] for r in rxns]
factors = defaultdict(int)
for v in viol:
for f in sympy.primefactors(v):
factors[f] = max(factors[f], sympy.Abs(v//f))
rcd = reduce(mul, (k**v for k, v in factors.items()))
viol[0] *= -1
return [rcd//v for v in viol]
示例2: test_events
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import Abs [as 别名]
def test_events():
# use bouncing ball to test events work
# simulate in block diagram
int_opts = block_diagram.DEFAULT_INTEGRATOR_OPTIONS.copy()
int_opts['rtol'] = 1E-12
int_opts['atol'] = 1E-15
int_opts['nsteps'] = 1000
int_opts['max_step'] = 2**-3
x = x1, x2 = Array(dynamicsymbols('x_1:3'))
mu, g = sp.symbols('mu g')
constants = {mu: 0.8, g: 9.81}
ic = np.r_[10, 15]
sys = SwitchedSystem(
x1, Array([0]),
state_equations=r_[x2, -g],
state_update_equation=r_[sp.Abs(x1), -mu*x2],
state=x,
constants_values=constants,
initial_condition=ic
)
bd = BlockDiagram(sys)
res = bd.simulate(5, integrator_options=int_opts)
# compute actual impact time
tvar = dynamicsymbols._t
impact_eq = (x2*tvar - g*tvar**2/2 + x1).subs(
{x1: ic[0], x2: ic[1], g: 9.81}
)
t_impact = sp.solve(impact_eq, tvar)[-1]
# make sure simulation actually changes velocity sign around impact
abs_diff_impact = np.abs(res.t - t_impact)
impact_idx = np.where(abs_diff_impact == np.min(abs_diff_impact))[0]
assert np.sign(res.x[impact_idx-1, 1]) != np.sign(res.x[impact_idx+1, 1])
示例3: monkey_patch_function
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import Abs [as 别名]
def monkey_patch_function(expr):
"""
Name says it all
Monkey patch any functions with bad func names (abs -> Abs)
If anything else needs to be fixed, goes here
"""
return expr.replace(sympify("abs(x)").func, Abs)
示例4: initialize_damp
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import Abs [as 别名]
def initialize_damp(damp, nbl, spacing, abc_type="damp", fs=False):
"""
Initialize damping field with an absorbing boundary layer.
Parameters
----------
damp : Function
The damping field for absorbing boundary condition.
nbl : int
Number of points in the damping layer.
spacing :
Grid spacing coefficient.
mask : bool, optional
whether the dampening is a mask or layer.
mask => 1 inside the domain and decreases in the layer
not mask => 0 inside the domain and increase in the layer
"""
dampcoeff = 1.5 * np.log(1.0 / 0.001) / (nbl)
eqs = [Eq(damp, 1.0)] if abc_type == "mask" else []
for d in damp.dimensions:
if not fs or d is not damp.dimensions[-1]:
# left
dim_l = SubDimension.left(name='abc_%s_l' % d.name, parent=d,
thickness=nbl)
pos = Abs((nbl - (dim_l - d.symbolic_min) + 1) / float(nbl))
val = dampcoeff * (pos - sin(2*np.pi*pos)/(2*np.pi))
val = -val if abc_type == "mask" else val
eqs += [Inc(damp.subs({d: dim_l}), val/d.spacing)]
# right
dim_r = SubDimension.right(name='abc_%s_r' % d.name, parent=d,
thickness=nbl)
pos = Abs((nbl - (d.symbolic_max - dim_r) + 1) / float(nbl))
val = dampcoeff * (pos - sin(2*np.pi*pos)/(2*np.pi))
val = -val if abc_type == "mask" else val
eqs += [Inc(damp.subs({d: dim_r}), val/d.spacing)]
Operator(eqs, name='initdamp')()
示例5: norm
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import Abs [as 别名]
def norm(f, order=2):
"""
Compute the norm of a Function.
Parameters
----------
f : Function
Input Function.
order : int, optional
The order of the norm. Defaults to 2.
"""
kwargs = {}
if f.is_TimeFunction and f._time_buffering:
kwargs[f.time_dim.max_name] = f._time_size - 1
# Protect SparseFunctions from accessing duplicated (out-of-domain) data,
# otherwise we would eventually be summing more than expected
p, eqns = f.guard() if f.is_SparseFunction else (f, [])
s = dv.types.Scalar(name='sum', dtype=f.dtype)
with MPIReduction(f) as mr:
op = dv.Operator([dv.Eq(s, 0.0)] +
eqns +
[dv.Inc(s, Abs(Pow(p, order))), dv.Eq(mr.n[0], s)],
name='norm%d' % order)
op.apply(**kwargs)
v = Pow(mr.v, 1/order)
return f.dtype(v)
示例6: convert_comp
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import Abs [as 别名]
def convert_comp(comp):
if comp.group():
return convert_expr(comp.group().expr())
elif comp.abs_group():
return sympy.Abs(convert_expr(comp.abs_group().expr()), evaluate=False)
elif comp.atom():
return convert_atom(comp.atom())
elif comp.frac():
return convert_frac(comp.frac())
elif comp.func():
return convert_func(comp.func())
示例7: setup_w_over_q
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import Abs [as 别名]
def setup_w_over_q(wOverQ, w, qmin, qmax, npad, sigma=0):
"""
Initialise spatially variable w/Q field used to implement attenuation and
absorb outgoing waves at the edges of the model. Uses Devito Operator.
Parameters
----------
wOverQ : Function, required
The omega over Q field used to implement attenuation in the model,
and the absorbing boundary condition for outgoing waves.
w : float32, required
center angular frequency, e.g. peak frequency of Ricker source wavelet
used for modeling.
qmin : float32, required
Q value at the edge of the model. Typically set to 0.1 to strongly
attenuate outgoing waves.
qmax : float32, required
Q value in the interior of the model. Typically set to 100 as a
reasonable and physically meaningful Q value.
npad : int, required
Number of points in the absorbing boundary region. Note that we expect
this to be the same on all sides of the model.
sigma : float32, optional, defaults to None
sigma value for call to scipy gaussian smoother, default 5.
"""
# sanity checks
assert w > 0, "supplied w value [%f] must be positive" % (w)
assert qmin > 0, "supplied qmin value [%f] must be positive" % (qmin)
assert qmax > 0, "supplied qmax value [%f] must be positive" % (qmax)
assert npad > 0, "supplied npad value [%f] must be positive" % (npad)
for n in wOverQ.grid.shape:
if n - 2*npad < 1:
raise ValueError("2 * npad must not exceed dimension size!")
lqmin = np.log(qmin)
lqmax = np.log(qmax)
# 1. Get distance to closest boundary in all dimensions
# 2. Logarithmic variation between qmin, qmax across the absorbing boundary
eqs = [Eq(wOverQ, 1)]
for d in wOverQ.dimensions:
# left
dim_l = SubDimension.left(name='abc_%s_l' % d.name, parent=d,
thickness=npad)
pos = Abs(dim_l - d.symbolic_min) / float(npad)
eqs.append(Eq(wOverQ.subs({d: dim_l}), Min(wOverQ.subs({d: dim_l}), pos)))
# right
dim_r = SubDimension.right(name='abc_%s_r' % d.name, parent=d,
thickness=npad)
pos = Abs(d.symbolic_max - dim_r) / float(npad)
eqs.append(Eq(wOverQ.subs({d: dim_r}), Min(wOverQ.subs({d: dim_r}), pos)))
eqs.append(Eq(wOverQ, w / exp(lqmin + wOverQ * (lqmax - lqmin))))
# 2020.05.04 currently does not support spatial smoothing of the Q field
# due to MPI weirdness in reassignment of the numpy array
Operator(eqs, name='WOverQ_Operator')()