def split_solve(self):
'''
Mehtod to solve the splitting problem
function takes the weight_available_matrix of the split instance
and find the optimum number of weights types in the candidated holes_available
that minimize the error.
Args:
split model instance
Returns:
S: numpy array of the same shape as weight_available_matrix of a model
'''
# define mixed integer matrix in cvxpy
_S = cp.Variable(self.weight_available_matrix.shape, integer=True)
# define objective function
_Real = cp.sum(
cp.multiply(np.real(self.weight_available_matrix),
_S)) - np.real(self.weight)
_Imag = cp.sum(
cp.multiply(np.imag(self.weight_available_matrix),
_S)) - np.imag(self.weight)
_Residuals = cp.norm(cp.hstack([_Real, _Imag]))
_obj_split = cp.Minimize(_Residuals)
# constraints
_const_splitting = [_S >= 0]
if self.max_number_weights_per_hole:
if isinstance(self.max_number_weights_per_hole, int):
_const_splitting += [
cp.sum(_S, axis=0) <= self.max_number_weights_per_hole
]
else:
raise tools.CustomError(
'`max_number_weights_per_hole` should be integer number'
)
if self.max_weight_per_plane:
if isinstance(self.max_weight_per_plane, (float, int)):
_const_splitting += [
cp.sum(_S.T @ self.weights_available, axis=0) <=
self.max_weight_per_plane
]
else:
raise tools.CustomError(
'`max_weight_per_plane` should be float number')
# solve
_prob_S = cp.Problem(_obj_split, _const_splitting)
_prob_S.solve(solver=cp.XPRESS
) # TODO make solver options PYTHON_MIP(), ECOS_BB
_S = np.array(np.round(_S.value))
self._S = _S
self._prob_S = _prob_S.value
_W_equ_split = np.sum(self.weight_available_matrix * self._S)
self._W_equ_split = _W_equ_split
return _S
def solve(self, solver='OLE'):
'''
Method to solve the model
Args:
solver:'OLE' Ordinary Least Squares method
'Huber': Uses Huber smoother to down estimate the outliers.
'''
W = cp.Variable((self.N, 1), complex=True)
if solver.upper() == 'OLE': # Ordinary least squares
_objective = cp.Minimize(cp.sum_squares(self.ALPHA @ W + self.A))
elif solver.upper(
) == 'HUBER': # TODO test Huber solver for robust optimization
_real = cp.real(self.ALPHA @ W + self.A)
_imag = cp.imag(self.ALPHA @ W + self.A)
_objective = cp.Minimize(
cp.sum_squares(cp.huber(cp.hstack([_real, _imag]), M=0)))
elif solver.upper() == 'WLS': # TODO test weighted least squares
_objective = cp.Minimize(
cp.sum_squares(cp.diag(self.C) @ (self.ALPHA @ W + self.A)))
else:
raise tools.CustomError('Unrecognized Solver name')
prob = cp.Problem(_objective)
prob.solve()
self.W = W.value
return W.value
def error(self, options='error'):
'''
Method to determine different ways of error in the splitting.
Args:
Instance of split model
options: kwarg to define the type of error.
'error': default value returns the relative value of error.
'problem_error': returns the accuracy of the solution.
'equ': returns the equivilant weight of splitting solution
in math form.
'''
# Error equivilant weight after splitting
_error = abs(self._W_equ_split - self.weight)
# Estimate the error generated by using minmax instead of norm2 in the objective function
_problem_error = (self._prob_S - _error) / abs(self.weight)
if options == 'error':
return _error
elif options == 'problem_error':
return _problem_error
elif options == 'equ':
return tools.convert_cart_math(self._W_equ_split)
else:
raise tools.CustomError(
'Invalid options. Choose options="error" for solution error'
'caused by splitting, options="problem_error" for solution'
' accuracy and options="equ" for equivilant weight.')
def solve(self, solver=None):
'''
Method to solve the Minmax model
'''
W = cp.Variable((self.N, 1), complex=True)
_objective = cp.Minimize(cp.norm((self.ALPHA @ W + self.A), "inf"))
# Define weight constraints
_constrains = []
if self.weight_const != {}:
try:
for key, value in self.weight_const.items():
_constrains += [cp.norm(W[key]) <= value]
except NameError:
raise tools.CustomError('Invalid weight constraint format')
else:
pass
prob = cp.Problem(_objective, _constrains)
prob.solve()
self.W = W.value
return W.value
def solve(self, solver=None):
'''
solving the LMI model
returns solution matrix W
'''
# Weight constraints
N = self.N
M = self.M
_wc = np.zeros(N)
if self.weight_const != {}:
try:
for key, value in self.weight_const.items():
_wc[key] = value
except NameError:
raise tools.CustomError('Invalid weight constraint format')
else:
pass
# Identify critical planes
if self.V_max:
_Vm = self.V_max
else:
raise tools.CustomError('V_max is not specified')
if self.critical_planes and len(self.critical_planes) > 0:
_list_cr = self.critical_planes
else:
raise tools.CustomError('Critical Planes are not set.')
_ALPHA = self.ALPHA.copy()
A = self.A.copy()
_ALPHAcr = _ALPHA[_list_cr]
Acr = A[_list_cr]
_ALPHAncr = np.delete(_ALPHA, _list_cr, axis=0)
_Ancr = np.delete(A, _list_cr, axis=0)
# assign cvxpy variables
_WR = cp.Variable((N, 1))
_WI = cp.Variable((N, 1))
_Vc = cp.Variable()
_RRfcr = cp.diag(
np.real(Acr) + np.real(_ALPHAcr) @ _WR - np.imag(_ALPHAcr) @ _WI)
_IRfcr = cp.diag(
np.imag(Acr) + np.imag(_ALPHAcr) @ _WR + np.real(_ALPHAcr) @ _WI)
_RRfNcr = cp.diag(
np.real(_Ancr) + np.real(_ALPHAncr) @ _WR -
np.imag(_ALPHAncr) @ _WI)
_IRfNcr = cp.diag(
np.imag(_Ancr) + np.imag(_ALPHAncr) @ _WR +
np.real(_ALPHAncr) @ _WI)
_zcr = np.zeros((_RRfcr.shape[0], _RRfcr.shape[1]))
_Icr = np.eye(_RRfcr.shape[0])
_zncr = np.zeros((_RRfNcr.shape[0], _RRfNcr.shape[1]))
_Incr = np.eye(_RRfNcr.shape[0])
_objective = cp.Minimize(_Vc)
_LMI_real = cp.bmat([[_Vc * _Icr, _RRfcr, _zcr, -_IRfcr],
[_RRfcr, _Icr, _IRfcr, _zcr],
[_zcr, _IRfcr, _Vc * _Icr, _RRfcr],
[-_IRfcr, _zcr, _RRfcr, _Icr]])
_LMI_imag = cp.bmat([[_Vm**2 * _Incr, _RRfNcr, _zncr, -_IRfNcr],
[_RRfNcr, _Incr, _IRfNcr, _zncr],
[_zncr, _IRfNcr, _Vm**2 * _Incr, _RRfNcr],
[-_IRfNcr, _zncr, _RRfNcr, _Incr]])
# Model weight constraints
_const_LMI_w = []
for i in range(N):
_LMI_weight = cp.bmat([[_wc[i]**2, _WR[i], 0, -_WI[i]],
[_WR[i], 1, _WI[i], 0],
[0, _WI[i], _wc[i]**2, _WR[i]],
[-_WI[i], 0, _WR[i], 1]])
_const_LMI_w.append(_LMI_weight >> 0)
_const_LMI_w.append(_LMI_real >> 0)
_const_LMI_w.append(_LMI_imag >> 0)
# Stating the problem
prob = cp.Problem(_objective, _const_LMI_w)
prob.solve(cp.CVXOPT, kktsolver=cp.ROBUST_KKTSOLVER)
W = _WR + _WI * 1j
self.W = W.value
return self.W
def __init__(self,
A: 'initial_vibration' = None,
alpha: 'instance of Alpha class' = None,
conditions: 'list of condition instances' = None,
name: 'string' = ''):
""" Instantiate the model
Args:
A: Initial vibration vector -> np.ndarray
ALPHA: Influence coefficient matrix -> class Alpha
conditions: List of conditions instance that express the model various
setpoints for balancing -> list of `class Condition`
name: optional name of the model -> string
"""
self.name = name
self.alpha = alpha
self.W = None
self.split_instance = [
] # List of all related splits that has modified the solution
self.conditions = conditions
if self.conditions is None:
if A is None or alpha is None:
raise TypeError(
'Either (A and Alpha) or `conditions` should be assigned.')
try:
if A.shape[1] == 1:
self.A = A
except AttributeError:
raise tools.CustomError('Either direct_matrix or (A,B,U) '
'should be passed "numpy arrays"')
except IndexError:
raise tools.CustomError(
'`A` should be a column vector (Mx1) dimension')
# Test if Alpha is an instance of Alpha class
if not isinstance(alpha, Alpha):
raise tools.CustomError(
'Please create an `Alpha instance` first --> ex. alpha = Alpha()'
)
else:
self.alpha = alpha
self.ALPHA = alpha.value
elif isinstance(self.conditions, list) == False:
raise TypeError('Conditions should be a list')
else:
if all(
isinstance(condition, Condition)
for condition in self.conditions):
self.ALPHA = np.vstack(
[condition.alpha.value for condition in self.conditions])
self.A = np.vstack(
[condition.A for condition in self.conditions])
else:
raise TypeError(
'''`conditions` should be a list of `Condition class` try condition
= Condition()''')
try:
_ = self.ALPHA.shape # Test that alpha.value returns np.array
self.N = self.ALPHA.shape[1] # Get N number of balancing_planes
self.M = self.ALPHA.shape[0] # Get M number of measuring points
except AttributeError:
raise tools.CustomError('Missing valid ALPHA value')
def split_setup(self,
balancing_plane_index,
holes_available,
weights_available,
max_number_weights_per_hole=None,
max_weight_per_plane=None):
"""
Split method to determine the optimized splitted weight
over available holes and with some availabe weight types
the optimization is mixed integer quadratic type that
minimize the residule of the caluclated model weight from
a combination of availabe weights on the availble holes
Args:
balancing_plane_index: the index of weight to be split
from the model. (model.W[index]) -> complex class
holes_available: list of holes available, this can be
entered as numpy array (ex. np.arange(0, 100, 10) represents
the holes from 0 deg to 100 deg spaced 10 degress each)-> list
weights_available: list of type of weights available
ex. [185, 90] represents that factory weights available
are 185 and 90 grams for instance. -> list
max_number_weights_per_hole: maximum number of weights premissible
to be added in each hole. (ex. 1 -> only one weight is allowable
per hole) -> int
max_weight_per_plane: max weight allowable per plane.
(ex 2000 -> maximum weight allowable per plane is 2 kg) -> float
Returns: weight_available_matrix which represents all possible weights at
all possible holes.
"""
self.balancing_plane_index = balancing_plane_index
self.holes_available = holes_available
self.weights_available = weights_available
self.max_number_weights_per_hole = max_number_weights_per_hole
self.max_weight_per_plane = max_weight_per_plane
self.weight = self.model.W[balancing_plane_index]
# Vectorizing cmath `rect` function to be applied on holes
vrect = np.vectorize(cmath.rect)
# list to np.array
if isinstance(holes_available, list):
if holes_available:
holes_available = np.array(holes_available)
else:
raise tools.CustomError(
'holes_available should contian at least one element')
else:
raise tools.CustomError('holes_available should be a list')
if isinstance(weights_available, list):
if weights_available:
weights_available = np.array(weights_available)
else:
raise tools.CustomError(
'weights_available should contain at least one element'
)
else:
raise tools.CustomError('weights_available should be a list')
# Transfer weights from row to column
weights_available = weights_available[:, np.newaxis]
# Make weight matrix in complex form
weight_available_matrix = weights_available * vrect(
1, holes_available * cmath.pi / 180) # from deg to rad
self.weight_available_matrix = weight_available_matrix
pass
def add(
self,
direct_matrix: 'np.array' = None,
A: 'initial_vibration numpy.array' = None,
B: 'trial matrix numpy.array' = None,
U: 'trial weight row vector numpy.array' = None,
keep_trial:
'optional keep the previous trial weight in every succeeding trial' = False,
name: 'string' = ''):
'''
Method to add new values for Alpha instance
either the direct_matrix is needed or ALL of (A, B, U)
Args:
direct_matrix: numpy array M rows -> measuring points,
N columns -> balancing planes
A: Initial vibration column array -> numpy array
B: Trial matrix MxN array -> numpy array
'''
self.A = A
self.B = B
self.U = U
self.keep_trial = keep_trial
try: # test if direct input
_ = direct_matrix.shape
if direct_matrix.ndim < 2:
raise IndexError(
'Influence coefficient matrix should be of more than 1 dimensions.'
)
if direct_matrix.shape[0] >= direct_matrix.shape[1]:
self.value = direct_matrix
else:
raise tools.CustomError(
'Number of rows(measuring points) should be '
'equal or more than the number of columns '
'(balancing planes)!')
if self.A is not None or self.B is not None or self.U is not None:
raise ValueError(
'Either (direct Matrix) or (A, B, U) should be input, but not both.'
)
except AttributeError:
# if direct matrix is not input calculate it from A, B, U
# test the exstiance of A, A0, B, U to calculate ALPHA
try:
all([A.shape, B.shape, U.shape])
# Test dimensions
if A.shape[1] > 1:
raise tools.CustomError('`A` should be column vector')
elif U.ndim > 1:
raise tools.CustomError('`U` should be row vector')
elif B.shape[0] != A.shape[0] or B.shape[1] != U.shape[0]:
raise tools.CustomError(
'`B` dimensions should match `A`and `U`')
else:
self.A = A
self.B = B
self.U = U
if not keep_trial:
self.value = (self.B - self.A) / self.U
else:
_A_keep_trial = np.delete(
(np.insert(self.B, [0], self.A, axis=1)),
-1,
axis=1)
self.value = (self.B - _A_keep_trial) / self.U
except AttributeError:
raise tools.CustomError('Either direct_matrix or (A,B,U) '
'should be passed "numpy arrays"')
if self.value is not None:
self.M = self.value.shape[0]
self.N = self.value.shape[1]