def contact_forces(self):
"""Returns contact forces on each wheel."""
self.conForceNoncontri = self._kane.auxiliary_eqs.applyfunc(
lambda w: factor_terms(signsimp(w))).subs(self._kdd)
return self.conForceNoncontri
def test_DiracDelta():
assert DiracDelta(1) == 0
assert DiracDelta(5.1) == 0
assert DiracDelta(-pi) == 0
assert DiracDelta(5, 7) == 0
assert DiracDelta(i) == 0
assert DiracDelta(j) == 0
assert DiracDelta(k) == 0
assert DiracDelta(nan) == nan
assert DiracDelta(0).func is DiracDelta
assert DiracDelta(x).func is DiracDelta
# FIXME: this is generally undefined @ x=0
# But then limit(Delta(c)*Heaviside(x),x,-oo)
# need's to be implemented.
#assert 0*DiracDelta(x) == 0
assert adjoint(DiracDelta(x)) == DiracDelta(x)
assert adjoint(DiracDelta(x - y)) == DiracDelta(x - y)
assert conjugate(DiracDelta(x)) == DiracDelta(x)
assert conjugate(DiracDelta(x - y)) == DiracDelta(x - y)
assert transpose(DiracDelta(x)) == DiracDelta(x)
assert transpose(DiracDelta(x - y)) == DiracDelta(x - y)
assert DiracDelta(x).diff(x) == DiracDelta(x, 1)
assert DiracDelta(x, 1).diff(x) == DiracDelta(x, 2)
assert DiracDelta(x).is_simple(x) is True
assert DiracDelta(3*x).is_simple(x) is True
assert DiracDelta(x**2).is_simple(x) is False
assert DiracDelta(sqrt(x)).is_simple(x) is False
assert DiracDelta(x).is_simple(y) is False
assert DiracDelta(x*y).expand(diracdelta=True, wrt=x) == DiracDelta(x)/abs(y)
assert DiracDelta(x*y).expand(diracdelta=True, wrt=y) == DiracDelta(y)/abs(x)
assert DiracDelta(x**2*y).expand(diracdelta=True, wrt=x) == DiracDelta(x**2*y)
assert DiracDelta(y).expand(diracdelta=True, wrt=x) == DiracDelta(y)
assert DiracDelta((x - 1)*(x - 2)*(x - 3)).expand(diracdelta=True, wrt=x) == (
DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
assert DiracDelta(2*x) != DiracDelta(x) # scaling property
assert DiracDelta(x) == DiracDelta(-x) # even function
assert DiracDelta(-x, 2) == DiracDelta(x, 2)
assert DiracDelta(-x, 1) == -DiracDelta(x, 1) # odd deriv is odd
assert DiracDelta(-oo*x) == DiracDelta(oo*x)
assert DiracDelta(x - y) != DiracDelta(y - x)
assert signsimp(DiracDelta(x - y) - DiracDelta(y - x)) == 0
with raises(SymPyDeprecationWarning):
assert DiracDelta(x*y).simplify(x) == DiracDelta(x)/abs(y)
assert DiracDelta(x*y).simplify(y) == DiracDelta(y)/abs(x)
assert DiracDelta(x**2*y).simplify(x) == DiracDelta(x**2*y)
assert DiracDelta(y).simplify(x) == DiracDelta(y)
assert DiracDelta((x - 1)*(x - 2)*(x - 3)).simplify(x) == (
DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
raises(ArgumentIndexError, lambda: DiracDelta(x).fdiff(2))
raises(ValueError, lambda: DiracDelta(x, -1))
raises(ValueError, lambda: DiracDelta(I))
raises(ValueError, lambda: DiracDelta(2 + 3*I))
def test_DiracDelta():
assert DiracDelta(1) == 0
assert DiracDelta(5.1) == 0
assert DiracDelta(-pi) == 0
assert DiracDelta(5, 7) == 0
assert DiracDelta(i) == 0
assert DiracDelta(j) == 0
assert DiracDelta(k) == 0
assert DiracDelta(nan) == nan
assert DiracDelta(0).func is DiracDelta
assert DiracDelta(x).func is DiracDelta
# FIXME: this is generally undefined @ x=0
# But then limit(Delta(c)*Heaviside(x),x,-oo)
# need's to be implemented.
#assert 0*DiracDelta(x) == 0
assert adjoint(DiracDelta(x)) == DiracDelta(x)
assert adjoint(DiracDelta(x - y)) == DiracDelta(x - y)
assert conjugate(DiracDelta(x)) == DiracDelta(x)
assert conjugate(DiracDelta(x - y)) == DiracDelta(x - y)
assert transpose(DiracDelta(x)) == DiracDelta(x)
assert transpose(DiracDelta(x - y)) == DiracDelta(x - y)
assert DiracDelta(x).diff(x) == DiracDelta(x, 1)
assert DiracDelta(x, 1).diff(x) == DiracDelta(x, 2)
assert DiracDelta(x).is_simple(x) is True
assert DiracDelta(3*x).is_simple(x) is True
assert DiracDelta(x**2).is_simple(x) is False
assert DiracDelta(sqrt(x)).is_simple(x) is False
assert DiracDelta(x).is_simple(y) is False
assert DiracDelta(x*y).expand(diracdelta=True, wrt=x) == DiracDelta(x)/abs(y)
assert DiracDelta(x*y).expand(diracdelta=True, wrt=y) == DiracDelta(y)/abs(x)
assert DiracDelta(x**2*y).expand(diracdelta=True, wrt=x) == DiracDelta(x**2*y)
assert DiracDelta(y).expand(diracdelta=True, wrt=x) == DiracDelta(y)
assert DiracDelta((x - 1)*(x - 2)*(x - 3)).expand(diracdelta=True, wrt=x) == (
DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
assert DiracDelta(2*x) != DiracDelta(x) # scaling property
assert DiracDelta(x) == DiracDelta(-x) # even function
assert DiracDelta(-x, 2) == DiracDelta(x, 2)
assert DiracDelta(-x, 1) == -DiracDelta(x, 1) # odd deriv is odd
assert DiracDelta(-oo*x) == DiracDelta(oo*x)
assert DiracDelta(x - y) != DiracDelta(y - x)
assert signsimp(DiracDelta(x - y) - DiracDelta(y - x)) == 0
with raises(SymPyDeprecationWarning):
assert DiracDelta(x*y).simplify(x) == DiracDelta(x)/abs(y)
assert DiracDelta(x*y).simplify(y) == DiracDelta(y)/abs(x)
assert DiracDelta(x**2*y).simplify(x) == DiracDelta(x**2*y)
assert DiracDelta(y).simplify(x) == DiracDelta(y)
assert DiracDelta((x - 1)*(x - 2)*(x - 3)).simplify(x) == (
DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
raises(ArgumentIndexError, lambda: DiracDelta(x).fdiff(2))
raises(ValueError, lambda: DiracDelta(x, -1))
raises(ValueError, lambda: DiracDelta(I))
raises(ValueError, lambda: DiracDelta(2 + 3*I))
def test_issue_10285():
assert FiniteSet(-x - 1).intersect(Interval.Ropen(1, 2)) == FiniteSet(x).intersect(Interval.Lopen(-3, -2))
eq = -x - 2 * (-x - y)
s = signsimp(eq)
ivl = Interval.open(0, 1)
assert FiniteSet(eq).intersect(ivl) == FiniteSet(s).intersect(ivl)
assert FiniteSet(-eq).intersect(ivl) == FiniteSet(s).intersect(Interval.open(-1, 0))
eq -= 1
ivl = Interval.Lopen(1, oo)
assert FiniteSet(eq).intersect(ivl) == FiniteSet(s).intersect(Interval.Lopen(2, oo))
def test_issue_10285():
assert FiniteSet(-x - 1).intersect(Interval.Ropen(1, 2)) == \
FiniteSet(x).intersect(Interval.Lopen(-3, -2))
eq = -x - 2 * (-x - y)
s = signsimp(eq)
ivl = Interval.open(0, 1)
assert FiniteSet(eq).intersect(ivl) == FiniteSet(s).intersect(ivl)
assert FiniteSet(-eq).intersect(ivl) == \
FiniteSet(s).intersect(Interval.open(-1, 0))
eq -= 1
ivl = Interval.Lopen(1, oo)
assert FiniteSet(eq).intersect(ivl) == \
FiniteSet(s).intersect(Interval.Lopen(2, oo))
def test_signsimp():
e = x*(-x + 1) + x*(x - 1)
assert signsimp(Eq(e, 0)) is S.true
assert Abs(x - 1) == Abs(1 - x)
assert signsimp(y - x) == y - x
assert signsimp(y - x, evaluate=False) == Mul(-1, x - y, evaluate=False)
def test_issue_17524():
a = symbols("a", real=True)
e = (-1 - a**2) * sqrt(1 + a**2)
assert signsimp(powsimp(e)) == signsimp(e) == -(a**2 + 1)**(S(3) / 2)
def __call__(self, equations, variables=None, method_options=None):
method_options = extract_method_options(method_options,
{'simplify': True})
if equations.is_stochastic:
raise UnsupportedEquationsException('Cannot solve stochastic '
'equations with this state '
'updater.')
if variables is None:
variables = {}
# Get a representation of the ODE system in the form of
# dX/dt = M*X + B
varnames, matrix, constants = get_linear_system(equations, variables)
# No differential equations, nothing to do (this occurs sometimes in the
# test suite where the whole model is nothing more than something like
# 'v : 1')
if matrix.shape == (0, 0):
return ''
# Make sure that the matrix M is constant, i.e. it only contains
# external variables or constant variables
t = Symbol('t', real=True, positive=True)
# Check for time dependence
dt_value = variables['dt'].get_value()[0] if 'dt' in variables else None
# This will raise an error if we meet the symbol "t" anywhere
# except as an argument of a locally constant function
for entry in itertools.chain(matrix, constants):
if not is_constant_over_dt(entry, variables, dt_value):
raise UnsupportedEquationsException(
('Expression "{}" is not guaranteed to be constant over a '
'time step').format(sympy_to_str(entry)))
symbols = [Symbol(variable, real=True) for variable in varnames]
solution = sp.solve_linear_system(matrix.row_join(constants), *symbols)
if solution is None or set(symbols) != set(solution.keys()):
raise UnsupportedEquationsException('Cannot solve the given '
'equations with this '
'stateupdater.')
b = sp.ImmutableMatrix([solution[symbol] for symbol in symbols])
# Solve the system
dt = Symbol('dt', real=True, positive=True)
try:
A = (matrix * dt).exp()
except NotImplementedError:
raise UnsupportedEquationsException('Cannot solve the given '
'equations with this '
'stateupdater.')
if method_options['simplify']:
A = A.applyfunc(lambda x:
sp.factor_terms(sp.cancel(sp.signsimp(x))))
C = sp.ImmutableMatrix(A * b) - b
_S = sp.MatrixSymbol('_S', len(varnames), 1)
updates = A * _S + C
updates = updates.as_explicit()
# The solution contains _S[0, 0], _S[1, 0] etc. for the state variables,
# replace them with the state variable names
abstract_code = []
for idx, (variable, update) in enumerate(zip(varnames, updates)):
rhs = update
if rhs.has(I, re, im):
raise UnsupportedEquationsException('The solution to the linear system '
'contains complex values '
'which is currently not implemented.')
for row_idx, varname in enumerate(varnames):
rhs = rhs.subs(_S[row_idx, 0], varname)
# Do not overwrite the real state variables yet, the update step
# of other state variables might still need the original values
abstract_code.append('_' + variable + ' = ' + sympy_to_str(rhs))
# Update the state variables
for variable in varnames:
abstract_code.append('{variable} = _{variable}'.format(variable=variable))
return '\n'.join(abstract_code)
def __call__(self, equations, variables=None, method_options=None):
method_options = extract_method_options(method_options,
{'simplify': True})
if equations.is_stochastic:
raise UnsupportedEquationsException("Cannot solve stochastic "
"equations with this state "
"updater.")
if variables is None:
variables = {}
# Get a representation of the ODE system in the form of
# dX/dt = M*X + B
varnames, matrix, constants = get_linear_system(equations, variables)
# No differential equations, nothing to do (this occurs sometimes in the
# test suite where the whole model is nothing more than something like
# 'v : 1')
if matrix.shape == (0, 0):
return ''
# Make sure that the matrix M is constant, i.e. it only contains
# external variables or constant variables
# Check for time dependence
dt_value = variables['dt'].get_value(
)[0] if 'dt' in variables else None
# This will raise an error if we meet the symbol "t" anywhere
# except as an argument of a locally constant function
for entry in itertools.chain(matrix, constants):
if not is_constant_over_dt(entry, variables, dt_value):
raise UnsupportedEquationsException(
f"Expression '{sympy_to_str(entry)}' is not guaranteed to be "
f"constant over a time step.")
symbols = [Symbol(variable, real=True) for variable in varnames]
solution = sp.solve_linear_system(matrix.row_join(constants), *symbols)
if solution is None or set(symbols) != set(solution.keys()):
raise UnsupportedEquationsException("Cannot solve the given "
"equations with this "
"stateupdater.")
b = sp.ImmutableMatrix([solution[symbol] for symbol in symbols])
# Solve the system
dt = Symbol('dt', real=True, positive=True)
try:
A = (matrix * dt).exp()
except NotImplementedError:
raise UnsupportedEquationsException("Cannot solve the given "
"equations with this "
"stateupdater.")
if method_options['simplify']:
A = A.applyfunc(
lambda x: sp.factor_terms(sp.cancel(sp.signsimp(x))))
C = sp.ImmutableMatrix(A * b) - b
_S = sp.MatrixSymbol('_S', len(varnames), 1)
updates = A * _S + C
updates = updates.as_explicit()
# The solution contains _S[0, 0], _S[1, 0] etc. for the state variables,
# replace them with the state variable names
abstract_code = []
for idx, (variable, update) in enumerate(zip(varnames, updates)):
rhs = update
if rhs.has(I, re, im):
raise UnsupportedEquationsException(
"The solution to the linear system "
"contains complex values "
"which is currently not implemented.")
for row_idx, varname in enumerate(varnames):
rhs = rhs.subs(_S[row_idx, 0], varname)
# Do not overwrite the real state variables yet, the update step
# of other state variables might still need the original values
abstract_code.append(f"_{variable} = {sympy_to_str(rhs)}")
# Update the state variables
for variable in varnames:
abstract_code.append(f"{variable} = _{variable}")
return '\n'.join(abstract_code)
def test_signsimp():
e = x*(-x + 1) + x*(x - 1)
assert signsimp(Eq(e, 0)) is S.true
assert Abs(x - 1) == Abs(1 - x)
def test_issue_18991():
A = MatrixSymbol('A', 2, 2)
assert signsimp(-A * A - A) == -A * A - A
def __call__(self, equations, variables=None, simplify=True):
if equations.is_stochastic:
raise UnsupportedEquationsException('Cannot solve stochastic '
'equations with this state '
'updater.')
if variables is None:
variables = {}
# Get a representation of the ODE system in the form of
# dX/dt = M*X + B
varnames, matrix, constants = get_linear_system(equations, variables)
# No differential equations, nothing to do (this occurs sometimes in the
# test suite where the whole model is nothing more than something like
# 'v : 1')
if matrix.shape == (0, 0):
return ''
# Make sure that the matrix M is constant, i.e. it only contains
# external variables or constant variables
t = Symbol('t', real=True, positive=True)
# Check for time dependence
if 'dt' in variables:
dt_value = variables['dt'].get_value()[0]
# This will raise an error if we meet the symbol "t" anywhere
# except as an argument of a locally constant function
t = Symbol('t', real=True, positive=True)
for entry in itertools.chain(matrix, constants):
_check_for_locally_constant(entry, variables, dt_value, t)
symbols = [Symbol(variable, real=True) for variable in varnames]
solution = sp.solve_linear_system(matrix.row_join(constants), *symbols)
if solution is None or set(symbols) != set(solution.keys()):
raise UnsupportedEquationsException('Cannot solve the given '
'equations with this '
'stateupdater.')
b = sp.ImmutableMatrix([solution[symbol]
for symbol in symbols]).transpose()
# Solve the system
dt = Symbol('dt', real=True, positive=True)
try:
A = (matrix * dt).exp()
except NotImplementedError:
raise UnsupportedEquationsException('Cannot solve the given '
'equations with this '
'stateupdater.')
if simplify:
A = A.applyfunc(
lambda x: sp.factor_terms(sp.cancel(sp.signsimp(x))))
C = sp.ImmutableMatrix([A.dot(b)]) - b
_S = sp.MatrixSymbol('_S', len(varnames), 1)
updates = A * _S + C.transpose()
updates = updates.as_explicit()
# The solution contains _S[0, 0], _S[1, 0] etc. for the state variables,
# replace them with the state variable names
abstract_code = []
for idx, (variable, update) in enumerate(zip(varnames, updates)):
rhs = update
for row_idx, varname in enumerate(varnames):
rhs = rhs.subs(_S[row_idx, 0], varname)
# Do not overwrite the real state variables yet, the update step
# of other state variables might still need the original values
abstract_code.append('_' + variable + ' = ' + sympy_to_str(rhs))
# Update the state variables
for variable in varnames:
abstract_code.append(
'{variable} = _{variable}'.format(variable=variable))
return '\n'.join(abstract_code)
#u5--rear wheel ang. vel., u6--front wheel ang. vel.
(fr, frstar)= kane.kanes_equations(forceList, bodyList)
kdd = kane.kindiffdict()
#path
path1 = '/home/stefenyin'
path2 = '/home/stefenstudy'
if os.path.exists(path1):
path = path1
else:
path = path2
con_forces_noncontri = kane.auxiliary_eqs.applyfunc(
lambda w: factor_terms(signsimp(w))).subs(kdd)
CF = con_forces_noncontri
"""
#==============================================================================
print('building a file and writing the equations into it')
#-----------------
print('building')
path = path + '/bicycle/bi_equations_writing/con_force_nonslip_non_para_input.txt'
try:
f = open(path,'w')
f.write('')
f.close()
del f
def test_signsimp():
e = x*(-x + 1) + x*(x - 1)
assert signsimp(Eq(e, 0)) == True
def test_signsimp():
e = x * (-x + 1) + x * (x - 1)
assert signsimp(Eq(e, 0)) is S.true
assert Abs(x - 1) == Abs(1 - x)
assert signsimp(y - x) == y - x
assert signsimp(y - x, evaluate=False) == Mul(-1, x - y, evaluate=False)
def test_signsimp():
e = x*(-x + 1) + x*(x - 1)
assert signsimp(Eq(e, 0)) == True
def test_signsimp():
e = x * (-x + 1) + x * (x - 1)
assert signsimp(Eq(e, 0)) is S.true
assert Abs(x - 1) == Abs(1 - x)
def simp(exp):
"""Sign and trig simplify an expression. This can take a *long*
time, especially when trying to render the expression in a notebook!
"""
return sym.signsimp(sym.trigsimp(exp))