本文整理汇总了Python中sympy.cos方法的典型用法代码示例。如果您正苦于以下问题:Python sympy.cos方法的具体用法?Python sympy.cos怎么用?Python sympy.cos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.cos方法的15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: get_equations
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def get_equations(self):
"""
:return: Functions to calculate A, B and f given state x and input u
"""
f = sp.zeros(3, 1)
x = sp.Matrix(sp.symbols('x y theta', real=True))
u = sp.Matrix(sp.symbols('v w', real=True))
f[0, 0] = u[0, 0] * sp.cos(x[2, 0])
f[1, 0] = u[0, 0] * sp.sin(x[2, 0])
f[2, 0] = u[1, 0]
f = sp.simplify(f)
A = sp.simplify(f.jacobian(x))
B = sp.simplify(f.jacobian(u))
f_func = sp.lambdify((x, u), f, 'numpy')
A_func = sp.lambdify((x, u), A, 'numpy')
B_func = sp.lambdify((x, u), B, 'numpy')
return f_func, A_func, B_func
示例2: get_equations
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def get_equations(self):
"""
:return: Functions to calculate A, B and f given state x and input u
"""
f = sp.zeros(6, 1)
x = sp.Matrix(sp.symbols('rx ry vx vy t w', real=True))
u = sp.Matrix(sp.symbols('gimbal T', real=True))
f[0, 0] = x[2, 0]
f[1, 0] = x[3, 0]
f[2, 0] = 1 / self.m * sp.sin(x[4, 0] + u[0, 0]) * u[1, 0]
f[3, 0] = 1 / self.m * (sp.cos(x[4, 0] + u[0, 0]) * u[1, 0] - self.m * self.g)
f[4, 0] = x[5, 0]
f[5, 0] = 1 / self.I * (-sp.sin(u[0, 0]) * u[1, 0] * self.r_T)
f = sp.simplify(f)
A = sp.simplify(f.jacobian(x))
B = sp.simplify(f.jacobian(u))
f_func = sp.lambdify((x, u), f, 'numpy')
A_func = sp.lambdify((x, u), A, 'numpy')
B_func = sp.lambdify((x, u), B, 'numpy')
return f_func, A_func, B_func
示例3: derivatives_in_spherical_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_spherical_coordinates():
Print_Function()
X = (r,th,phi) = symbols('r theta phi')
curv = [[r*cos(phi)*sin(th),r*sin(phi)*sin(th),r*cos(th)],[1,r,r*sin(th)]]
(er,eth,ephi,grad) = MV.setup('e_r e_theta e_phi',metric='[1,1,1]',coords=X,curv=curv)
f = MV('f','scalar',fct=True)
A = MV('A','vector',fct=True)
B = MV('B','grade2',fct=True)
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
print('-I*(grad^A) =',-MV.I*(grad^A))
print('grad^B =',grad^B)
return
示例4: derivatives_in_spherical_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_spherical_coordinates():
X = (r,th,phi) = symbols('r theta phi')
curv = [[r*cos(phi)*sin(th),r*sin(phi)*sin(th),r*cos(th)],[1,r,r*sin(th)]]
(er,eth,ephi,grad) = MV.setup('e_r e_theta e_phi',metric='[1,1,1]',coords=X,curv=curv)
f = MV('f','scalar',fct=True)
A = MV('A','vector',fct=True)
B = MV('B','grade2',fct=True)
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
print('-I*(grad^A) =',-MV.I*(grad^A))
print('grad^B =',grad^B)
return
示例5: derivatives_in_spherical_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_spherical_coordinates():
Print_Function()
X = (r,th,phi) = symbols('r theta phi')
curv = [[r*cos(phi)*sin(th),r*sin(phi)*sin(th),r*cos(th)],[1,r,r*sin(th)]]
(er,eth,ephi,grad) = MV.setup('e_r e_theta e_phi',metric='[1,1,1]',coords=X,curv=curv)
f = MV('f','scalar',fct=True)
A = MV('A','vector',fct=True)
B = MV('B','grade2',fct=True)
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
print('-I*(grad^A) =',(-MV.I*(grad^A)).simplify())
print('grad^B =',grad^B)
示例6: derivatives_in_paraboloidal_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_paraboloidal_coordinates():
#Print_Function()
coords = (u,v,phi) = symbols('u v phi', real=True)
(par3d,er,eth,ephi) = Ga.build('e_u e_v e_phi',X=[u*v*cos(phi),u*v*sin(phi),(u**2-v**2)/2],coords=coords,norm=True)
grad = par3d.grad
f = par3d.mv('f','scalar',f=True)
A = par3d.mv('A','vector',f=True)
B = par3d.mv('B','bivector',f=True)
print('#Derivatives in Paraboloidal Coordinates')
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
(-par3d.i*(grad^A)).Fmt(3,'grad\\times A = -I*(grad^A)')
print('grad^B =',grad^B)
return
示例7: derivatives_in_elliptic_cylindrical_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_elliptic_cylindrical_coordinates():
#Print_Function()
a = symbols('a', real=True)
coords = (u,v,z) = symbols('u v z', real=True)
(elip3d,er,eth,ephi) = Ga.build('e_u e_v e_z',X=[a*cosh(u)*cos(v),a*sinh(u)*sin(v),z],coords=coords,norm=True)
grad = elip3d.grad
f = elip3d.mv('f','scalar',f=True)
A = elip3d.mv('A','vector',f=True)
B = elip3d.mv('B','bivector',f=True)
print('#Derivatives in Elliptic Cylindrical Coordinates')
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
print('-I*(grad^A) =',-elip3d.i*(grad^A))
print('grad^B =',grad^B)
return
示例8: derivatives_in_prolate_spheroidal_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_prolate_spheroidal_coordinates():
#Print_Function()
a = symbols('a', real=True)
coords = (xi,eta,phi) = symbols('xi eta phi', real=True)
(ps3d,er,eth,ephi) = Ga.build('e_xi e_eta e_phi',X=[a*sinh(xi)*sin(eta)*cos(phi),a*sinh(xi)*sin(eta)*sin(phi),
a*cosh(xi)*cos(eta)],coords=coords,norm=True)
grad = ps3d.grad
f = ps3d.mv('f','scalar',f=True)
A = ps3d.mv('A','vector',f=True)
B = ps3d.mv('B','bivector',f=True)
print('#Derivatives in Prolate Spheroidal Coordinates')
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
(-ps3d.i*(grad^A)).Fmt(3,'-I*(grad^A)')
(grad^B).Fmt(3,'grad^B')
return
示例9: derivatives_in_oblate_spheroidal_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_oblate_spheroidal_coordinates():
Print_Function()
a = symbols('a', real=True)
coords = (xi,eta,phi) = symbols('xi eta phi', real=True)
(os3d,er,eth,ephi) = Ga.build('e_xi e_eta e_phi',X=[a*cosh(xi)*cos(eta)*cos(phi),a*cosh(xi)*cos(eta)*sin(phi),
a*sinh(xi)*sin(eta)],coords=coords,norm=True)
grad = os3d.grad
f = os3d.mv('f','scalar',f=True)
A = os3d.mv('A','vector',f=True)
B = os3d.mv('B','bivector',f=True)
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
print('-I*(grad^A) =',-os3d.i*(grad^A))
print('grad^B =',grad^B)
return
示例10: derivatives_in_toroidal_coordinates
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def derivatives_in_toroidal_coordinates():
Print_Function()
a = symbols('a', real=True)
coords = (u,v,phi) = symbols('u v phi', real=True)
(t3d,eu,ev,ephi) = Ga.build('e_u e_v e_phi',X=[a*sinh(v)*cos(phi)/(cosh(v)-cos(u)),
a*sinh(v)*sin(phi)/(cosh(v)-cos(u)),
a*sin(u)/(cosh(v)-cos(u))],coords=coords,norm=True)
grad = t3d.grad
f = t3d.mv('f','scalar',f=True)
A = t3d.mv('A','vector',f=True)
B = t3d.mv('B','bivector',f=True)
print('f =',f)
print('A =',A)
print('B =',B)
print('grad*f =',grad*f)
print('grad|A =',grad|A)
print('-I*(grad^A) =',-t3d.i*(grad^A))
print('grad^B =',grad^B)
return
示例11: test_conv7b
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def test_conv7b():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
assert sympify(sympy.sin(x/3)) == sin(Symbol("x") / 3)
assert sympify(sympy.sin(x/3)) != cos(Symbol("x") / 3)
assert sympify(sympy.cos(x/3)) == cos(Symbol("x") / 3)
assert sympify(sympy.tan(x/3)) == tan(Symbol("x") / 3)
assert sympify(sympy.cot(x/3)) == cot(Symbol("x") / 3)
assert sympify(sympy.csc(x/3)) == csc(Symbol("x") / 3)
assert sympify(sympy.sec(x/3)) == sec(Symbol("x") / 3)
assert sympify(sympy.asin(x/3)) == asin(Symbol("x") / 3)
assert sympify(sympy.acos(x/3)) == acos(Symbol("x") / 3)
assert sympify(sympy.atan(x/3)) == atan(Symbol("x") / 3)
assert sympify(sympy.acot(x/3)) == acot(Symbol("x") / 3)
assert sympify(sympy.acsc(x/3)) == acsc(Symbol("x") / 3)
assert sympify(sympy.asec(x/3)) == asec(Symbol("x") / 3)
示例12: xiu
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def xiu(n):
points = []
for k in range(n + 1):
pt = []
# Slight adaptation:
# The article has points for the weight 1/sqrt(2*pi) exp(−x**2/2)
# so divide by sqrt(2) to adapt for 1/sqrt(pi) exp(−x ** 2)
for r in range(1, n // 2 + 1):
alpha = (2 * r * k * pi) / (n + 1)
pt += [cos(alpha), sin(alpha)]
if n % 2 == 1:
pt += [(-1) ** k / sqrt(2)]
points.append(pt)
points = numpy.array(points)
weights = numpy.full(n + 1, frac(1, n + 1))
return Enr2Scheme("Xiu", n, weights, points, 2, source)
示例13: stroud_s2_9_3
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def stroud_s2_9_3():
# spherical product gauss 9
sqrt = numpy.vectorize(sympy.sqrt)
pm_ = numpy.array([+1, -1])
cos = numpy.vectorize(sympy.cos)
sin = numpy.vectorize(sympy.sin)
frac = sympy.Rational
pi = sympy.pi
r1, r2 = sqrt((6 - pm_ * sqrt(6)) / 10)
a = (numpy.arange(10) + 1) * pi / 5
x = numpy.array([cos(a), sin(a)]).T
B0 = frac(1, 9)
B1, B2 = (16 + pm_ * sqrt(6)) / 360
data = [(B0, z(2)), (B1, r1 * x), (B2, r2 * x)]
points, weights = untangle(data)
return S2Scheme("Stroud S2 9-3", weights, points, 9, _source)
示例14: albrecht_4
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def albrecht_4():
sqrt111 = sqrt(111)
rho1, rho2 = sqrt((96 - pm_ * 4 * sqrt(111)) / 155)
alpha = 2 * numpy.arange(6) * pi / 6
s = numpy.array([cos(alpha), sin(alpha)]).T
alpha = (2 * numpy.arange(6) + 1) * pi / 6
t = numpy.array([cos(alpha), sin(alpha)]).T
B0 = frac(251, 2304)
B1, B2 = (110297 + pm_ * 5713 * sqrt111) / 2045952
C = frac(125, 3072)
data = [(B0, z(2)), (B1, rho1 * s), (B2, rho2 * s), (C, sqrt(frac(4, 5)) * t)]
points, weights = untangle(data)
return S2Scheme("Albrecht 4", weights, points, 9, _source)
示例15: hammer_stroud_18
# 需要导入模块: import sympy [as 别名]
# 或者: from sympy import cos [as 别名]
def hammer_stroud_18():
# ENH The article only gives floats, but really this is the spherical-product gauss
# formula as described in Strouds book, S2 7-2.
#
# data = [
# (frac(1, 16), fs([0.4247082002778669, 0.1759198966061612])),
# (frac(1, 16), fs([0.8204732385702833, 0.3398511429799874])),
# ]
r1, r2 = sqrt((3 - pm_ * sqrt(3)) / 6)
a = (2 * numpy.arange(8) + 1) * pi / 8
x = numpy.array([cos(a), sin(a)]).T
data = [(frac(1, 16), r1 * x), (frac(1, 16), r2 * x)]
points, weights = untangle(data)
return S2Scheme("Hammer-Stroud 18", weights, points, 7, _source)