本文整理汇总了Python中sympy.matrices.Matrix.cross方法的典型用法代码示例。如果您正苦于以下问题：Python Matrix.cross方法的具体用法？Python Matrix.cross怎么用？Python Matrix.cross使用的例子？那么恭喜您, 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.matrices.Matrix的用法示例。
在下文中一共展示了Matrix.cross方法的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: perpendicular_plane
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
def perpendicular_plane(self, pt):
"""
Plane perpendicular to the given plane and passing through the point pt.
Parameters
==========
pt: Point3D
Returns
=======
Plane
Examples
========
>>> from sympy import Plane, Point3D
>>> a = Plane(Point3D(1,4,6), normal_vector=[2, 4, 6])
>>> a.perpendicular_plane(Point3D(2, 3, 5))
Plane(Point3D(2, 3, 5), [2, 8, -6])
"""
a = Matrix(self.normal_vector)
b, c = pt, self.p1
d = Matrix(b.direction_ratio(c))
e = list(d.cross(a))
return Plane(pt, normal_vector=e)示例2: is_perpendicular
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
def is_perpendicular(self, l):
"""is the given geometric entity perpendicualar to the given plane?
Parameters
==========
LinearEntity3D or Plane
Returns
=======
Boolean
Examples
========
>>> from sympy import Plane, Point3D
>>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6))
>>> b = Plane(Point3D(2, 2, 2), normal_vector=(-1, 2, -1))
>>> a.is_perpendicular(b)
True
"""
from sympy.geometry.line3d import LinearEntity3D
if isinstance(l, LinearEntity3D):
a = Matrix(l.direction_ratio)
b = Matrix(self.normal_vector)
if a.cross(b).is_zero:
return True
else:
return False
elif isinstance(l, Plane):
a = Matrix(l.normal_vector)
b = Matrix(self.normal_vector)
if a.dot(b) == 0:
return True
else:
return False
else:
return False示例3: is_parallel
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
def is_parallel(self, l):
"""Is the given geometric entity parallel to the plane?
Parameters
==========
LinearEntity3D or Plane
Returns
=======
Boolean
Examples
========
>>> from sympy import Plane, Point3D
>>> a = Plane(Point3D(1,4,6), normal_vector=(2, 4, 6))
>>> b = Plane(Point3D(3,1,3), normal_vector=(4, 8, 12))
>>> a.is_parallel(b)
True
"""
from sympy.geometry.line3d import LinearEntity3D
if isinstance(l, LinearEntity3D):
a = l.direction_ratio
b = self.normal_vector
c = sum([i * j for i, j in zip(a, b)])
if c == 0:
return True
else:
return False
elif isinstance(l, Plane):
a = Matrix(l.normal_vector)
b = Matrix(self.normal_vector)
if a.cross(b).is_zero:
return True
else:
return False示例4: are_coplanar
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
def are_coplanar(*lines):
""" Returns True if the given lines are coplanar otherwise False
Parameters
==========
lines: list
Returns
=======
Boolean
Examples
========
>>> from sympy import Plane, Point3D, Line3D
>>> a = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1))
>>> b = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1))
>>> c = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9))
>>> Plane.are_coplanar(a, b, c)
False
"""
if all(isinstance(i, Line3D) for i in lines):
if len(lines) < 2:
return False
a = Matrix(lines[0].direction_ratio)
b = Matrix(lines[1].direction_ratio)
c = list(a.cross(b))
d = Plane(lines[0].p1, normal_vector=c)
for i in lines[2:]:
if i not in d:
return False
return True
else:
ValueError('Enter Lines only')示例5: intersection
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
def intersection(self, o):
""" The intersection with other geometrical entity.
Parameters
==========
Point, Point3D, LinearEntity, LinearEntity3D, Plane
Returns
=======
List
Examples
========
>>> from sympy import Point, Point3D, Line, Line3D, Plane
>>> a = Plane(Point3D(1, 2, 3), normal_vector=[1, 1, 1])
>>> b = Point3D(1, 2, 3)
>>> a.intersection(b)
Point3D(1, 2, 3)
>>> c = Line3D(Point3D(1, 4, 7), Point3D(2, 2, 2))
>>> a.intersection(c)
Point3D(2, 2, 2)
>>> d = Plane(Point3D(6, 0, 0), normal_vector=[2, -5, 3])
>>> e = Plane(Point3D(2, 0, 0), normal_vector=[3, 4, -3])
>>> d.intersection(e)
[Line3D(Point3D(78/23, -24/23, 0), Point3D(147/23, 321/23, 23))]
"""
from sympy.geometry.line3d import LinearEntity3D
from sympy.geometry.line import LinearEntity
if isinstance(o, Point) or isinstance(o, Point3D):
if o in self:
return o
else:
return []
if isinstance(o, LinearEntity3D):
t = symbols('t')
x, y, z = symbols("x y z")
if o in self:
return [o]
else:
a = o.arbitrary_point(t)
b = self.equation(x, y, z)
c = solve(b.subs([(x, a.x), (y, a.y), (z, a.z)]))
if c == []:
return []
else:
a = a.subs(t, c[0])
if a in o:
return a
else:
return []
if isinstance(o, LinearEntity):
t = symbols('t')
x, y, z = symbols("x y z")
if o in self:
return [o]
else:
a = self.equation(x, y, z).subs(z,0)
b = o.equation(x, y)
c = solve((a,b),[x, y])
if c is {}:
return []
else:
return [Point(c[x], c[y])]
if isinstance(o, Plane):
if o == self:
return self
if self.is_parallel(o):
return []
else:
x, y, z = symbols("x y z")
a, b= Matrix([self.normal_vector]), Matrix([o.normal_vector])
c = list(a.cross(b))
d = self.equation(x, y, z)
e = o.equation(x, y, z)
f = solve((d.subs(z,0), e.subs(z,0)),[x, y])
g = solve((d.subs(y,0), e.subs(y,0)),[x, z])
h = solve((d.subs(x,0), e.subs(x,0)),[y, z])
if len(f) == 2:
return [Line3D(Point3D(f[x], f[y], 0), direction_ratio=c)]
if len(g) == 2:
return [Line3D(Point3D(g[x], 0, g[z]), direction_ratio=c)]
if len(h) == 2:
return [Line3D(Point3D(0, h[y], h[z]), direction_ratio=c)]示例6: test_sparse_matrix
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
#.........这里部分代码省略.........
A = SparseMatrix([[0, -1, 2],
[5, 10, 7],
[8, 3, 4]])
x = SparseMatrix(3, 1, [-1, 2, 5])
b = A*x
soln = A.LUsolve(b)
assert soln == x
# test_inverse
A = sparse_eye(4)
assert A.inv() == sparse_eye(4)
assert A.inv(method="CH") == sparse_eye(4)
assert A.inv(method="LDL") == sparse_eye(4)
A = SparseMatrix([[2, 3, 5],
[3, 6, 2],
[7, 2, 6]])
Ainv = SparseMatrix(Matrix(A).inv())
assert A*Ainv == sparse_eye(3)
assert A.inv(method="CH") == Ainv
assert A.inv(method="LDL") == Ainv
A = SparseMatrix([[2, 3, 5],
[3, 6, 2],
[5, 2, 6]])
Ainv = SparseMatrix(Matrix(A).inv())
assert A*Ainv == sparse_eye(3)
assert A.inv(method="CH") == Ainv
assert A.inv(method="LDL") == Ainv
# test_cross
v1 = Matrix(1, 3, [1, 2, 3])
v2 = Matrix(1, 3, [3, 4, 5])
assert v1.cross(v2) == Matrix(1, 3, [-2, 4, -2])
assert v1.norm(2)**2 == 14
# conjugate
a = SparseMatrix(((1, 2 + I), (3, 4)))
assert a.C == SparseMatrix([
[1, 2 - I],
[3, 4]
])
# mul
assert a*Matrix(2, 2, [1, 0, 0, 1]) == a
assert a + Matrix(2, 2, [1, 1, 1, 1]) == SparseMatrix([
[2, 3 + I],
[4, 5]
])
# col join
assert a.col_join(sparse_eye(2)) == SparseMatrix([
[1, 2 + I],
[3, 4],
[1, 0],
[0, 1]
])
# symmetric
assert not a.is_symmetric(simplify=False)
# test_cofactor
assert sparse_eye(3) == sparse_eye(3).cofactor_matrix()
test = SparseMatrix([[1, 3, 2], [2, 6, 3], [2, 3, 6]])
assert test.cofactor_matrix() == \
SparseMatrix([[27, -6, -6], [-12, 2, 3], [-3, 1, 0]])示例7: intersection
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
def intersection(self, o):
""" The intersection with other geometrical entity.
Parameters
==========
Point, Point3D, LinearEntity, LinearEntity3D, Plane
Returns
=======
List
Examples
========
>>> from sympy import Point, Point3D, Line, Line3D, Plane
>>> a = Plane(Point3D(1, 2, 3), normal_vector=(1, 1, 1))
>>> b = Point3D(1, 2, 3)
>>> a.intersection(b)
[Point3D(1, 2, 3)]
>>> c = Line3D(Point3D(1, 4, 7), Point3D(2, 2, 2))
>>> a.intersection(c)
[Point3D(2, 2, 2)]
>>> d = Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3))
>>> e = Plane(Point3D(2, 0, 0), normal_vector=(3, 4, -3))
>>> d.intersection(e)
[Line3D(Point3D(78/23, -24/23, 0), Point3D(147/23, 321/23, 23))]
"""
from sympy.geometry.line import LinearEntity, LinearEntity3D
if not isinstance(o, GeometryEntity):
o = Point(o, dim=3)
if isinstance(o, Point):
if o in self:
return [o]
else:
return []
if isinstance(o, (LinearEntity, LinearEntity3D)):
if o in self:
p1, p2 = o.p1, o.p2
if isinstance(o, Segment):
o = Segment3D(p1, p2)
elif isinstance(o, Ray):
o = Ray3D(p1, p2)
elif isinstance(o, Line):
o = Line3D(p1, p2)
else:
raise ValueError('unhandled linear entity: %s' % o.func)
return [o]
else:
x, y, z = map(Dummy, 'xyz')
t = Dummy() # unnamed else it may clash with a symbol in o
a = Point3D(o.arbitrary_point(t))
b = self.equation(x, y, z)
# TODO: Replace solve with solveset, when this line is tested
c = solve(b.subs(list(zip((x, y, z), a.args))), t)
if not c:
return []
else:
p = a.subs(t, c[0])
if p not in self:
return [] # e.g. a segment might not intersect a plane
return [p]
if isinstance(o, Plane):
if self.equals(o):
return [self]
if self.is_parallel(o):
return []
else:
x, y, z = map(Dummy, 'xyz')
a, b = Matrix([self.normal_vector]), Matrix([o.normal_vector])
c = list(a.cross(b))
d = self.equation(x, y, z)
e = o.equation(x, y, z)
result = list(linsolve([d, e], x, y, z))[0]
for i in (x, y, z): result = result.subs(i, 0)
return [Line3D(Point3D(result), direction_ratio=c)]示例8: intersection
# 需要导入模块: from sympy.matrices import Matrix [as 别名]
# 或者: from sympy.matrices.Matrix import cross [as 别名]
def intersection(self, o):
""" The intersection with other geometrical entity.
Parameters
==========
Point, Point3D, LinearEntity, LinearEntity3D, Plane
Returns
=======
List
Examples
========
>>> from sympy import Point, Point3D, Line, Line3D, Plane
>>> a = Plane(Point3D(1, 2, 3), normal_vector=(1, 1, 1))
>>> b = Point3D(1, 2, 3)
>>> a.intersection(b)
[Point3D(1, 2, 3)]
>>> c = Line3D(Point3D(1, 4, 7), Point3D(2, 2, 2))
>>> a.intersection(c)
[Point3D(2, 2, 2)]
>>> d = Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3))
>>> e = Plane(Point3D(2, 0, 0), normal_vector=(3, 4, -3))
>>> d.intersection(e)
[Line3D(Point3D(78/23, -24/23, 0), Point3D(147/23, 321/23, 23))]
"""
from sympy.geometry.line3d import LinearEntity3D
from sympy.geometry.line import LinearEntity
if isinstance(o, (Point, Point3D)):
if o in self:
return [Point3D(o)]
else:
return []
if isinstance(o, (LinearEntity, LinearEntity3D)):
if o in self:
p1, p2 = o.p1, o.p2
if isinstance(o, Segment):
o = Segment3D(p1, p2)
elif isinstance(o, Ray):
o = Ray3D(p1, p2)
elif isinstance(o, Line):
o = Line3D(p1, p2)
else:
raise ValueError('unhandled linear entity: %s' % o.func)
return [o]
else:
x, y, z = map(Dummy, 'xyz')
t = Dummy() # unnamed else it may clash with a symbol in o
a = Point3D(o.arbitrary_point(t))
b = self.equation(x, y, z)
c = solve(b.subs(list(zip((x, y, z), a.args))), t)
if not c:
return []
else:
p = a.subs(t, c[0])
if p not in self:
return [] # e.g. a segment might not intersect a plane
return [p]
if isinstance(o, Plane):
if o == self:
return [self]
if self.is_parallel(o):
return []
else:
x, y, z = map(Dummy, 'xyz')
a, b = Matrix([self.normal_vector]), Matrix([o.normal_vector])
c = list(a.cross(b))
d = self.equation(x, y, z)
e = o.equation(x, y, z)
f = solve((d.subs(z, 0), e.subs(z, 0)), [x, y])
if len(f) == 2:
return [Line3D(Point3D(f[x], f[y], 0), direction_ratio=c)]
g = solve((d.subs(y, 0), e.subs(y, 0)),[x, z])
if len(g) == 2:
return [Line3D(Point3D(g[x], 0, g[z]), direction_ratio=c)]
h = solve((d.subs(x, 0), e.subs(x, 0)),[y, z])
if len(h) == 2:
return [Line3D(Point3D(0, h[y], h[z]), direction_ratio=c)]