本文整理汇总了Python中sympy.Matrix.row_join方法的典型用法代码示例。如果您正苦于以下问题:Python Matrix.row_join方法的具体用法?Python Matrix.row_join怎么用?Python Matrix.row_join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.row_join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: _form_permutation_matrices
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import row_join [as 别名]
def _form_permutation_matrices(self):
"""Form the permutation matrices Pq and Pu."""
# Extract dimension variables
l, m, n, o, s, k = self._dims
# Compute permutation matrices
if n != 0:
self._Pq = permutation_matrix(self.q, Matrix([self.q_i, self.q_d]))
if l > 0:
self._Pqi = self._Pq[:, :-l]
self._Pqd = self._Pq[:, -l:]
else:
self._Pqi = self._Pq
self._Pqd = Matrix()
if o != 0:
self._Pu = permutation_matrix(self.u, Matrix([self.u_i, self.u_d]))
if m > 0:
self._Pui = self._Pu[:, :-m]
self._Pud = self._Pu[:, -m:]
else:
self._Pui = self._Pu
self._Pud = Matrix()
# Compute combination permutation matrix for computing A and B
P_col1 = Matrix([self._Pqi, zeros(o + k, n - l)])
P_col2 = Matrix([zeros(n, o - m), self._Pui, zeros(k, o - m)])
if P_col1:
if P_col2:
self.perm_mat = P_col1.row_join(P_col2)
else:
self.perm_mat = P_col1
else:
self.perm_mat = P_col2
示例2: compute_lambda
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import row_join [as 别名]
def compute_lambda(robo, symo, j, antRj, antPj, lam):
"""Internal function. Computes the inertia parameters
transformation matrix
Notes
=====
lam is the output paramete
"""
lamJJ_list = []
lamJMS_list = []
for e1 in xrange(3):
for e2 in xrange(e1, 3):
u = vec_mut_J(antRj[j][:, e1], antRj[j][:, e2])
if e1 != e2:
u += vec_mut_J(antRj[j][:, e2], antRj[j][:, e1])
lamJJ_list.append(u.T)
for e1 in xrange(3):
v = vec_mut_MS(antRj[j][:, e1], antPj[j])
lamJMS_list.append(v.T)
lamJJ = Matrix(lamJJ_list).T # , 'LamJ', j)
lamJMS = symo.mat_replace(Matrix(lamJMS_list).T, 'LamMS', j)
lamJM = symo.mat_replace(vec_mut_M(antPj[j]), 'LamM', j)
lamJ = lamJJ.row_join(lamJMS).row_join(lamJM)
lamMS = sympy.zeros(3, 6).row_join(antRj[j]).row_join(antPj[j])
lamM = sympy.zeros(1, 10)
lamM[9] = 1
lam[j] = Matrix([lamJ, lamMS, lamM])
示例3: LagrangesMethod
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import row_join [as 别名]
#.........这里部分代码省略.........
flist = zip(*_f_list_parser(self.forcelist, N))
for i, qd in enumerate(qds):
for obj, force in self.forcelist:
self._term4[i] = sum(v.diff(qd, N) & f for (v, f) in flist)
else:
self._term4 = zeros(n, 1)
# Form the dynamic mass and forcing matrices
without_lam = self._term1 - self._term2 - self._term4
self._m_d = without_lam.jacobian(self._qdoubledots)
self._f_d = -without_lam.subs(qdd_zero)
# Form the EOM
self.eom = without_lam - self._term3
return self.eom
@property
def mass_matrix(self):
"""Returns the mass matrix, which is augmented by the Lagrange
multipliers, if necessary.
If the system is described by 'n' generalized coordinates and there are
no constraint equations then an n X n matrix is returned.
If there are 'n' generalized coordinates and 'm' constraint equations
have been supplied during initialization then an n X (n+m) matrix is
returned. The (n + m - 1)th and (n + m)th columns contain the
coefficients of the Lagrange multipliers.
"""
if self.eom is None:
raise ValueError('Need to compute the equations of motion first')
if self.coneqs:
return (self._m_d).row_join(self.lam_coeffs.T)
else:
return self._m_d
@property
def mass_matrix_full(self):
"""Augments the coefficients of qdots to the mass_matrix."""
if self.eom is None:
raise ValueError('Need to compute the equations of motion first')
n = len(self.q)
m = len(self.coneqs)
row1 = eye(n).row_join(zeros(n, n + m))
row2 = zeros(n, n).row_join(self.mass_matrix)
if self.coneqs:
row3 = zeros(m, n).row_join(self._m_cd).row_join(zeros(m, m))
return row1.col_join(row2).col_join(row3)
else:
return row1.col_join(row2)
@property
def forcing(self):
"""Returns the forcing vector from 'lagranges_equations' method."""
if self.eom is None:
raise ValueError('Need to compute the equations of motion first')
return self._f_d
@property
def forcing_full(self):
"""Augments qdots to the forcing vector above."""
if self.eom is None:
示例4: linearize
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import row_join [as 别名]
def linearize(self, op_point=None, A_and_B=False, simplify=False):
"""Linearize the system about the operating point. Note that
q_op, u_op, qd_op, ud_op must satisfy the equations of motion.
These may be either symbolic or numeric.
Parameters
----------
op_point : dict or iterable of dicts, optional
Dictionary or iterable of dictionaries containing the operating
point conditions. These will be substituted in to the linearized
system before the linearization is complete. Leave blank if you
want a completely symbolic form. Note that any reduction in
symbols (whether substituted for numbers or expressions with a
common parameter) will result in faster runtime.
A_and_B : bool, optional
If A_and_B=False (default), (M, A, B) is returned for forming
[M]*[q, u]^T = [A]*[q_ind, u_ind]^T + [B]r. If A_and_B=True,
(A, B) is returned for forming dx = [A]x + [B]r, where
x = [q_ind, u_ind]^T.
simplify : bool, optional
Determines if returned values are simplified before return.
For large expressions this may be time consuming. Default is False.
Note that the process of solving with A_and_B=True is computationally
intensive if there are many symbolic parameters. For this reason,
it may be more desirable to use the default A_and_B=False,
returning M, A, and B. More values may then be substituted in to these
matrices later on. The state space form can then be found as
A = P.T*M.LUsolve(A), B = P.T*M.LUsolve(B), where
P = Linearizer.perm_mat.
"""
# Compose dict of operating conditions
if isinstance(op_point, dict):
op_point_dict = op_point
elif isinstance(op_point, collections.Iterable):
op_point_dict = {}
for op in op_point:
op_point_dict.update(op)
else:
op_point_dict = {}
# Extract dimension variables
l, m, n, o, s, k = self._dims
# Rename terms to shorten expressions
M_qq = self._M_qq
M_uqc = self._M_uqc
M_uqd = self._M_uqd
M_uuc = self._M_uuc
M_uud = self._M_uud
M_uld = self._M_uld
A_qq = self._A_qq
A_uqc = self._A_uqc
A_uqd = self._A_uqd
A_qu = self._A_qu
A_uuc = self._A_uuc
A_uud = self._A_uud
B_u = self._B_u
C_0 = self._C_0
C_1 = self._C_1
C_2 = self._C_2
# Build up Mass Matrix
# |M_qq 0_nxo 0_nxk|
# M = |M_uqc M_uuc 0_mxk|
# |M_uqd M_uud M_uld|
if o != 0:
col2 = Matrix([zeros(n, o), M_uuc, M_uud])
if k != 0:
col3 = Matrix([zeros(n + m, k), M_uld])
if n != 0:
col1 = Matrix([M_qq, M_uqc, M_uqd])
if o != 0 and k != 0:
M = col1.row_join(col2).row_join(col3)
elif o != 0:
M = col1.row_join(col2)
else:
M = col1
elif k != 0:
M = col2.row_join(col3)
else:
M = col2
M_eq = _subs_keep_derivs(M, op_point_dict)
# Build up state coefficient matrix A
# |(A_qq + A_qu*C_1)*C_0 A_qu*C_2|
# A = |(A_uqc + A_uuc*C_1)*C_0 A_uuc*C_2|
# |(A_uqd + A_uud*C_1)*C_0 A_uud*C_2|
# Col 1 is only defined if n != 0
if n != 0:
r1c1 = A_qq
if o != 0:
r1c1 += (A_qu * C_1)
r1c1 = r1c1 * C_0
if m != 0:
r2c1 = A_uqc
if o != 0:
#.........这里部分代码省略.........
示例5: len
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import row_join [as 别名]
(A*B).transpose(),\
(A**2*B).transpose(),\
(A**3*B).transpose()])
Qs = QsT.transpose()
print 'Qs: ',Qs
print 'A: ',A
print 'B: ',B
print 'C: ',C
'''
Nachweis der Steuerbarkeit des erweiterten Zustandsraummodells
'''
Aquer = A.col_join(C).row_join(sp.zeros(5,1))
Bquer = B.col_join(sp.zeros(1,1))
Cquer = C.row_join(sp.zeros(1,1))
'''
Übertragungsfunktion des Linearisierten Systems
'''
G = C*(sp.eye(4)*s - A)**-1*B
# Steuerbarkeitsmatrix berechnen
n = 5
Qsquer = sp.Matrix()
for i in range(5):
q = (Aquer**i)*Bquer
if len(Qsquer) == 0:
Qsquer = Bquer
else:
示例6: JacoV
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import row_join [as 别名]
U1=A[1]*A[2]*A[3]*A[4]*A[5]
J1=Matrix([[U1[0,3]*U1[1,0]-U1[1,3]*U1[0,0]],[U1[0,3]*U1[1,1]-U0[1,3]*U1[0,1]],[U1[0,3]*U1[1,2]-U1[1,3]*U1[0,2]],[U1[2,0]],[U1[2,1]],[U1[2,2]]])
U2=A[2]*A[3]*A[4]*A[5]
J2=Matrix([[U2[0,3]*U2[1,0]-U2[1,3]*U2[0,0]],[U2[0,3]*U2[1,1]-U2[1,3]*U2[0,1]],[U2[0,3]*U2[1,2]-U2[1,3]*U2[0,2]],[U2[2,0]],[U2[2,1]],[U2[2,2]]])
U3=A[3]*A[4]*A[5]
J3=Matrix([[U3[0,3]*U3[1,0]-U3[1,3]*U3[0,0]],[U3[0,3]*U3[1,1]-U3[1,3]*U3[0,1]],[U3[0,3]*U3[1,2]-U3[1,3]*U3[0,2]],[U3[2,0]],[U3[2,1]],[U3[2,2]]])
U4=A[4]*A[5]
J4=Matrix([[U4[0,3]*U4[1,0]-U4[1,3]*U4[0,0]],[U4[0,3]*U4[1,1]-U4[1,3]*U4[0,1]],[U4[0,3]*U4[1,2]-U4[1,3]*U4[0,2]],[U4[2,0]],[U4[2,1]],[U4[2,2]]])
U5=A[5]
J5=Matrix([[U5[0,3]*U5[1,0]-U5[1,3]*U5[0,0]],[U5[0,3]*U5[1,1]-U5[1,3]*U5[0,1]],[U5[0,3]*U5[1,2]-U5[1,3]*U5[0,2]],[U5[2,0]],[U5[2,1]],[U5[2,2]]])
Jd=J0.row_join(J1).row_join(J2).row_join(J3).row_join(J4).row_join(J5)
# The vector cross product sub-routine
def JacoV(QJ):
return np.array(Jv.subs(q[0],QJ[0]).subs(q[1],QJ[1]).subs(q[2],QJ[2]).subs(q[3],QJ[3]).subs(q[4],QJ[4]).subs(q[5],QJ[5]))
# Defining Camera Transformation
Tstart=np.array([[ 0.9983323 , 0.03651881, 0.04471023, -0.12004546],[-0.02196539, -0.47593777, 0.87920462, -4.18794775],[ 0.0533868 , -0.87872044, -0.47434189, 2.22462606],[ 0. , 0. , 0. , 1. ]])
Tcirc=np.array([[ 0.20604119, 0.33831506, -0.9181993 , 3.84545088],[ 0.97824604, -0.09434114, 0.18475504, -0.79177779],[-0.02411856, -0.93629198, -0.35039353, 1.40385485],[ 0. , 0. , 0. , 1. ]])
Tline=np.array([[ 0.02187936, 0.99890052, 0.04146134, 0.02088733],[ 0.98965908, -0.01575924, -0.14257124, 0.30318534],[-0.14176108, 0.04415196, -0.98891577, 2.93201566],[ 0. , 0. , 0. , 1. ]])
p=raw_input('Enter Path for XML File\n') # Change the path here
env=Environment();
示例7: solve
# 需要导入模块: from sympy import Matrix [as 别名]
# 或者: from sympy.Matrix import row_join [as 别名]
def solve(A, b):
"""
Finds small solutions to systems of diophantine equations, A x = b, where A
is a M x N matrix of coefficents, b is a M x 1 vector and x is the
N x 1 solution vector, e.g.
>>> from sympy import Matrix
>>> from diophantine import solve
>>> A = Matrix([[1, 0, 0, 2], [0, 2, 3, 5], [2, 0, 3, 1], [-6, -1, 0, 2],
[0, 1, 1, 1], [-1, 2, 0,1], [-1, -2, 1, 0]]).T
>>> b = Matrix([1, 1, 1, 1])
>>> solve(A, b)
[Matrix([
[-1],
[ 1],
[ 0],
[ 0],
[-1],
[-1],
[-1]])]
The returned solution vector will tend to be one with the smallest norms.
If multiple solutions with the same norm are found they will all be
returned. If there are no solutions the empty list will be returned.
"""
A = Matrix(A)
b = Matrix(b)
if b.shape != (A.shape[0], 1):
raise Exception("Length of b vector ({}) does not match number of rows"
" in A matrix ({})".format(b.shape[0], A.shape[0]))
if verbose_solve:
Ab = A.row_join(b)
print 'Ab: "' + ' '.join(str(v) for v in Ab.T.vec()) + '"'
G = zeros(A.shape[1] + 1, A.shape[0] + 1)
G[:-1, :-1] = A.T
G[-1, :-1] = b.reshape(1, b.shape[0])
G[-1, -1] = 1
# A is m x n, b is m x 1, solving AX=b, X is n x 1+
# Ab is the (n+1) x m transposed augmented matrix. G=[A^t|0] [b^t]1]
if verbose_solve:
print "G:"
printnp(G)
hnf, P, rank = lllhermite(G)
if verbose_solve:
print "HNF(G):"
printnp(hnf)
print "P:"
printnp(P)
print "Rank: {}".format(rank)
r = rank - 1 # For convenience
if not any(chain(hnf[:r, -1], hnf[r, :-1])) and hnf[r, -1] == 1:
nullity = hnf.shape[0] - rank
if nullity:
basis = P[rank:, :-1].col_join(-P[r, :-1])
if verbose_solve:
print "Basis:\n"
printnp(basis)
solutions = get_solutions(basis)
else:
raise NotImplementedError("Ax=B has unique solution in integers")
else:
solutions = []
return solutions