本文整理汇总了Python中sympy.Matrix.nullspace方法的典型用法代码示例。如果您正苦于以下问题：Python Matrix.nullspace方法的具体用法？Python Matrix.nullspace怎么用？Python Matrix.nullspace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.Matrix的用法示例。
在下文中一共展示了Matrix.nullspace方法的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，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: test_nullspace
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import nullspace [as 别名]
def test_nullspace():
# first test reduced row-ech form
R = Rational
M = Matrix([[5,7,2,1],
[1,6,2,-1]])
out, tmp = M.rref()
assert out == Matrix([[1,0,-R(2)/23,R(13)/23],
[0,1,R(8)/23, R(-6)/23]])
M = Matrix([[-5,-1, 4,-3,-1],
[ 1,-1,-1, 1, 0],
[-1, 0, 0, 0, 0],
[ 4, 1,-4, 3, 1],
[-2, 0, 2,-2,-1]])
assert M*M.nullspace()[0] == Matrix(5,1,[0]*5)
M = Matrix([[1,3,0,2,6,3,1],
[-2,-6,0,-2,-8,3,1],
[3,9,0,0,6,6,2],
[-1,-3,0,1,0,9,3]])
out, tmp = M.rref()
assert out == Matrix([[1,3,0,0,2,0,0],
[0,0,0,1,2,0,0],
[0,0,0,0,0,1,R(1)/3],
[0,0,0,0,0,0,0]])
# now check the vectors
basis = M.nullspace()
assert basis[0] == Matrix([-3,1,0,0,0,0,0])
assert basis[1] == Matrix([0,0,1,0,0,0,0])
assert basis[2] == Matrix([-2,0,0,-2,1,0,0])
assert basis[3] == Matrix([0,0,0,0,0,R(-1)/3, 1])示例2: getInvariants
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import nullspace [as 别名]
def getInvariants(qds, verbosity=1, print_stream=sys.stdout):
n_inter = len(qds.interactions)
n_types = qds.ntypes
int_matrix = np.zeros([n_inter, n_types], dtype=int)
for (idx, (i, j, k, l)) in enumerate(qds.interactions):
int_matrix[idx, i] += 1
int_matrix[idx, j] += 1
int_matrix[idx, k] -= 1
int_matrix[idx, l] -= 1
IM = Matrix(int_matrix)
invs = np.array(IM.nullspace(), dtype=float)
if verbosity > 0:
print("The invariants for the system are the following: \n\n",
file=print_stream)
for i in range(invs.shape[0]):
inv_str = ""
for j in range(invs.shape[1]):
if invs[i, j] != 0:
if inv_str != "":
inv_str += " + %.3f x p_%d" % (invs[i, j], j)
else:
inv_str += "%.3f x p_%d" % (invs[i, j], j)
print(inv_str + "\n", file=print_stream)
return invs示例3: find_symbolic_dependent_columns
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import nullspace [as 别名]
def find_symbolic_dependent_columns(x):
"""
Find linearly dependent columns using symbolic calculations.
:param x: The input numpy array
:return: The linear combination matrix (Null Space of MAtrix).
"""
x = Matrix(x)
return(x.nullspace())示例4: compute_steadystate
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import nullspace [as 别名]
def compute_steadystate(self, nnc=2): #nnc is the position of the constant in the state vector
""" Find non-stochastic steady-state of the economy """
zx = Matrix(np.eye(self.A0.shape[0])-self.A0)
self.zz = zx.nullspace()
self.zz = array(self.zz)
self.zz = self.zz.T
self.zz = zz = self.zz/self.zz[nnc]
self.css = self.Sc.dot(self.zz).astype(float)
self.sss = self.Ss.dot(self.zz).astype(float)
self.iss = self.Si.dot(self.zz).astype(float)
self.dss = self.Sd.dot(self.zz).astype(float)
self.bss = self.Sb.dot(self.zz).astype(float)
self.kss = self.Sk.dot(self.zz).astype(float)
self.hss = self.Sh.dot(self.zz).astype(float)示例5: test_sparse_matrix
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import nullspace [as 别名]
#.........这里部分代码省略.........
# test_inverse
A = eye(4)
assert A.inv() == eye(4)
assert A.inv("LU") == eye(4)
assert A.inv("ADJ") == eye(4)
A = SMatrix([[2,3,5],
[3,6,2],
[8,3,6]])
Ainv = A.inv()
assert A*Ainv == eye(3)
assert A.inv("LU") == Ainv
assert A.inv("ADJ") == 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(v1) == 14
# test_cofactor
assert eye(3) == eye(3).cofactorMatrix()
test = SMatrix([[1,3,2],[2,6,3],[2,3,6]])
assert test.cofactorMatrix() == SMatrix([[27,-6,-6],[-12,2,3],[-3,1,0]])
test = SMatrix([[1,2,3],[4,5,6],[7,8,9]])
assert test.cofactorMatrix() == SMatrix([[-3,6,-3],[6,-12,6],[-3,6,-3]])
# test_jacobian
x = Symbol('x')
y = Symbol('y')
L = SMatrix(1,2,[x**2*y, 2*y**2 + x*y])
syms = [x,y]
assert L.jacobian(syms) == Matrix([[2*x*y, x**2],[y, 4*y+x]])
L = SMatrix(1,2,[x, x**2*y**3])
assert L.jacobian(syms) == SMatrix([[1, 0], [2*x*y**3, x**2*3*y**2]])
# test_QR
A = Matrix([[1,2],[2,3]])
Q, S = A.QRdecomposition()
R = Rational
assert Q == Matrix([[5**R(-1,2), (R(2)/5)*(R(1)/5)**R(-1,2)], [2*5**R(-1,2), (-R(1)/5)*(R(1)/5)**R(-1,2)]])
assert S == Matrix([[5**R(1,2), 8*5**R(-1,2)], [0, (R(1)/5)**R(1,2)]])
assert Q*S == A
assert Q.T * Q == eye(2)
# test nullspace
# first test reduced row-ech form
R = Rational
M = Matrix([[5,7,2,1],
[1,6,2,-1]])
out, tmp = M.rref()
assert out == Matrix([[1,0,-R(2)/23,R(13)/23],
[0,1,R(8)/23, R(-6)/23]])
M = Matrix([[1,3,0,2,6,3,1],
[-2,-6,0,-2,-8,3,1],
[3,9,0,0,6,6,2],
[-1,-3,0,1,0,9,3]])
out, tmp = M.rref()
assert out == Matrix([[1,3,0,0,2,0,0],
[0,0,0,1,2,0,0],
[0,0,0,0,0,1,R(1)/3],
[0,0,0,0,0,0,0]])
# now check the vectors
basis = M.nullspace()
assert basis[0] == Matrix([[-3,1,0,0,0,0,0]])
assert basis[1] == Matrix([[0,0,1,0,0,0,0]])
assert basis[2] == Matrix([[-2,0,0,-2,1,0,0]])
assert basis[3] == Matrix([[0,0,0,0,0,R(-1)/3, 1]])
# test eigen
x = Symbol('x')
y = Symbol('y')
eye3 = eye(3)
assert eye3.charpoly(x) == (1-x)**3
assert eye3.charpoly(y) == (1-y)**3
# test values
M = Matrix([(0,1,-1),
(1,1,0),
(-1,0,1) ])
vals = M.eigenvals()
vals.sort()
assert vals == [-1, 1, 2]
R = Rational
M = Matrix([ [1,0,0],
[0,1,0],
[0,0,1]])
assert M.eigenvects() == [[1, 3, [Matrix(1,3,[1,0,0]), Matrix(1,3,[0,1,0]), Matrix(1,3,[0,0,1])]]]
M = Matrix([ [5,0,2],
[3,2,0],
[0,0,1]])
assert M.eigenvects() == [[1, 1, [Matrix(1,3,[R(-1)/2,R(3)/2,1])]],
[2, 1, [Matrix(1,3,[0,1,0])]],
[5, 1, [Matrix(1,3,[1,1,0])]]]
assert M.zeros((3, 5)) == SMatrix(3, 5, {})