sympy 计算表达式
from sympy import *
def test_matrix():
A = Matrix([[x, x*y], [sin(z)+4, x**z]])
sol = Matrix([[1, 2], [sin(3)+4, 1]])
f = lambdify((x,y,z), A, modules="sympy")
assert f(1,2,3) == sol
f = lambdify((x,y,z), (A, [A]), modules="sympy")
assert f(1,2,3) == (sol,[sol])
https://www.kutu66.com/Python-Module-Examples/article_66605
实例 1
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def test_threaded():
@threaded
def function(expr, *args):
return 2*expr + sum(args)
assert function(Matrix([[x, y], [1, x]]), 1, 2) ==
Matrix([[2*x + 3, 2*y + 3], [5, 2*x + 3]])
assert function(Eq(x, y), 1, 2) == Eq(2*x + 3, 2*y + 3)
assert function([x, y], 1, 2) == [2*x + 3, 2*y + 3]
assert function((x, y), 1, 2) == (2*x + 3, 2*y + 3)
assert function(set([x, y]), 1, 2) == set([2*x + 3, 2*y + 3])
@threaded
def function(expr, n):
return expr**n
assert function(x + y, 2) == x**2 + y**2
assert function(x, 2) == x**2
实例 2
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def test_prde_linear_constraints():
DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
G = [(Poly(2*x**3 + 3*x + 1, x), Poly(x**2 - 1, x)), (Poly(1, x), Poly(x - 1, x)),
(Poly(1, x), Poly(x + 1, x))]
assert prde_linear_constraints(Poly(1, x), Poly(0, x), G, DE) ==
((Poly(2*x, x), Poly(0, x), Poly(0, x)), Matrix([[1, 1, -1], [5, 1, 1]]))
G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert prde_linear_constraints(Poly(t + 1, t), Poly(t**2, t), G, DE) ==
((Poly(t, t), Poly(t**2, t), Poly(t**3, t)), Matrix())
G = [(Poly(2*x, t), Poly(t, t)), (Poly(-x, t), Poly(t, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
prde_linear_constraints(Poly(1, t), Poly(0, t), G, DE) ==
((Poly(0, t), Poly(0, t)), Matrix([[2*x, -x]]))
实例 3
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def z_sub(substr, n=5):
"""Generate a z vector with the subscript substr."""
states = ['x','th','M','V']
varnames = [item+substr for item in states]
mylist = []
for item in varnames:
mylist.append([item])
if n == 5:
mylist.append(['1'])
mat_str = str(mylist)
code = 'z_vect = sympy.Matrix(%s)' % mat_str
exec(code)
return z_vect
实例 4
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def z(x, F):
z_mat = sympy.Matrix([[x],[F],[1]])
return z_mat
实例 5
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def test_threaded():
x, y = symbols('xy')
@threaded()
def function(expr, *args):
return 2*expr + sum(args)
assert function(Matrix([[x, y], [1, x]]), 1, 2) ==
Matrix([[2*x+3, 2*y+3], [5, 2*x+3]])
assert function(Eq(x, y), 1, 2) == Eq(2*x+3, 2*y+3)
assert function([x, y], 1, 2) == [2*x+3, 2*y+3]
assert function((x, y), 1, 2) == (2*x+3, 2*y+3)
assert function(set([x, y]), 1, 2) == set([2*x+3, 2*y+3])
@threaded()
def function(expr, n):
return expr**n
assert function(x + y, 2) == x**2 + y**2
assert function(x, 2) == x**2
@threaded(use_add=False)
def function(expr, n):
return expr**n
assert function(x + y, 2) == (x + y)**2
实例 6
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def test_apart():
assert apart(1/(x+2)/(x+1), x) == 1/(1 + x) - 1/(2 + x)
assert apart(1/(x+1)/(x+5), x) == -1/(5 + x)/4 + 1/(1 + x)/4
f = apart(1/(x-y)/(x-z), x)
assert f.subs({y:1,z:2}) == apart(1/(x-1)/(x-2), x)
assert apart((E*x+2)/(x-pi)*(x-1), x) in [
2 - E + E*pi + E*x - 1/(x - pi)*( 2 - 2*pi + E*pi - E*pi**2),
2 - E + E*pi + E*x + 1/(x - pi)*(-2 + 2*pi - E*pi + E*pi**2),
]
M = Matrix(2, 2, lambda i, j: 1/(x-(i+1))/(x-(1-j)))
assert apart(M, x) in [
Matrix([
[(x-1)**(-2), -1/x-1/(1-x) ],
[1/(1-x)-1/(2-x), -S.Half/x-S.Half/(2-x)],
]),
Matrix([
[(-1+x)**(-2), -1/x+1/(-1+x) ],
[-1/(-1+x)+1/(-2+x), -S.Half/x+S.Half/(-2+x)],
]),
]
assert apart(Eq((x**2+1)/(x+1), sin(x)), x) ==
Eq(x - 1 + 2/(x+1), sin(x))
assert str(apart(1/(1+x**5), x, evaluate=False)) in [
"RootSum(Lambda(_a, -1/5/(x - _a)*_a), x**5 + 1, x)",
"RootSum(Lambda(_a, -_a/(5*(x - _a))), x**5 + 1, x)"]
实例 7
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def test_nsolve():
# onedimensional
from sympy import Symbol, sin, pi
x = Symbol('x')
assert nsolve(sin(x), 2) - pi.evalf() < 1e-16
assert nsolve(Eq(2*x, 2), x, -10) == nsolve(2*x - 2, -10)
# 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((f1, f2, f3), (x, y, z), x0)
assert mnorm(F(*root),1) <= 1.e-8
return root
assert map(round, getroot((1, 1, 1))) == [2.0, 1.0, 0.0]
a = Symbol('a')
assert nsolve(1/(0.001 + a)**3 - 6/(0.9 - a)**3, a, 0.3).ae(
mpf('0.31883011387318591'))
实例 8
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def test_matrix():
A = Matrix([[x, x*y], [sin(z)+4, x**z]])
sol = Matrix([[1, 2], [sin(3)+4, 1]])
f = lambdify((x,y,z), A, modules="sympy")
assert f(1,2,3) == sol
f = lambdify((x,y,z), (A, [A]), modules="sympy")
assert f(1,2,3) == (sol,[sol])
实例 9
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def main():
Format()
a = Matrix ( 2, 2, ( 1, 2, 3, 4 ) )
b = Matrix ( 2, 1, ( 5, 6 ) )
c = a * b
print a,b,'=',c
x, y = symbols ('x, y')
d = Matrix ( 1, 2, ( x ** 3, y ** 3 ))
e = Matrix ( 2, 2, ( x ** 2, 2 * x * y, 2 * x * y, y ** 2 ) )
f = d * e
print '%',d,e,'=',f
xpdf()
return
实例 10
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def main():
Format()
a = Matrix ( 2, 2, ( 1, 2, 3, 4 ) )
b = Matrix ( 2, 1, ( 5, 6 ) )
c = a * b
print a,b,'=',c
x, y = symbols ( 'x, y' )
d = Matrix ( 1, 2, ( x ** 3, y ** 3 ))
e = Matrix ( 2, 2, ( x ** 2, 2 * x * y, 2 * x * y, y ** 2 ) )
f = d * e
print '%',d,e,'=',f
xdvi()
return
实例 11
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def matrix(self):
if self.spinor:
self.lt_dict = {}
for base in self.Ga.basis:
self.lt_dict[base] = self(base).simplify()
self.spinor = False
mat = self.matrix()
self.spinor = True
return(mat)
else:
mat_rep = []
for base in self.Ga.basis:
if base in self.lt_dict:
row = []
image = (self.lt_dict[base])
if isinstance(image, mv.Mv):
image = image.obj
(coefs, bases) = metric.linear_expand(image)
for base in self.Ga.basis:
try:
i = bases.index(base)
row.append(coefs[i])
except:
row.append(0)
mat_rep.append(row)
else:
mat_rep.append(self.Ga.n * [0])
return(Matrix(mat_rep).transpose())
实例 12
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def _issue_7853_dep_check(namespaces, namespace, expr):
"""Used for checking things passed into modules kwarg for deprecation
issue #7853. This function and the call to it in lambdify should be
deleted once the cycle has ended."""
# If some module changed `ImmutableMatrix` to be something else
mat = namespace.get('ImmutableMatrix', False)
if not mat or 'numpy' not in namespaces or ('%s.%s' % (mat.__module__,
mat.__name__) == 'numpy.matrixlib.defmatrix.matrix'):
return
dicts = [m for m in namespaces if isinstance(m, dict)]
def test(expr):
return hasattr(expr, 'is_Matrix') and expr.is_Matrix
if test(expr) and not [d for d in dicts if 'ImmutableMatrix' in d]:
SymPyDeprecationWarning(
"Currently, `sympy.Matrix` is replaced with `numpy.matrix` if "
"the NumPy package is utilized in lambdify. In future versions "
"of SymPy (> 0.7.6), we will default to replacing "
"`sympy.Matrix` with `numpy.array`. To use the future "
"behavior now, supply the kwarg "
"`modules=[{'ImmutableMatrix': numpy.array}, 'numpy']`. "
"The old behavior can be retained in future versions by "
"supplying `modules=[{'ImmutableMatrix': numpy.matrix}, "
"'numpy']`.", issue=7853).warn()
实例 13
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def test_threaded():
@threaded
def function(expr, *args):
return 2*expr + sum(args)
assert function(Matrix([[x, y], [1, x]]), 1, 2) ==
Matrix([[2*x + 3, 2*y + 3], [5, 2*x + 3]])
assert function(Eq(x, y), 1, 2) == Eq(2*x + 3, 2*y + 3)
assert function([x, y], 1, 2) == [2*x + 3, 2*y + 3]
assert function((x, y), 1, 2) == (2*x + 3, 2*y + 3)
assert function({x, y}, 1, 2) == {2*x + 3, 2*y + 3}
@threaded
def function(expr, n):
return expr**n
assert function(x + y, 2) == x**2 + y**2
assert function(x, 2) == x**2
实例 14
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def test_constant_system():
A = Matrix([[-(x + 3)/(x - 1), (x + 1)/(x - 1), 1],
[-x - 3, x + 1, x - 1],
[2*(x + 3)/(x - 1), 0, 0]])
u = Matrix([(x + 1)/(x - 1), x + 1, 0])
DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
assert constant_system(A, u, DE) ==
(Matrix([[1, 0, 0],
[0, 1, 0],
[0, 0, 0],
[0, 0, 1]]), Matrix([0, 1, 0, 0]))
实例 15
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def _eval_term( self, sol, term, args, sops ):
"""Works for scalar, single unknown terms only!"""
expr = term.symbolic['expression']
arg_map = term.symbolic['map']
env = {'x' : sops.Symbol( 'x' ),
'y' : sops.Symbol( 'y' ),
'z' : sops.Symbol( 'z' ),
'dim' : dim}
for key, val in arg_map.iteritems():
if val == 'state':
env[key] = sol
else:
env[key] = term.get_args( [val], **args )[0]
if val[:8] == 'material':
aux = nm.array( env[key] )
if nm.prod( aux.shape ) == 1:
env[key] = aux.squeeze()
else:
import sympy
env[key] = sympy.Matrix( aux )
# print env
self.report( ' <= ', sol )
sops.set_dim( dim )
val = str( eval( expr, sops.__dict__, env ) )
self.report( ' =>', val )
return val
##
# c: 07.05.2007, r: 30.06.2008