def expansion_matrix_xu(self):
Pxu = BlockMatrix(self.nblocks + 1, self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
Pxu[sid, sid] = nlp.expansion_matrix_xu()
Pxu[self.nblocks, self.nblocks] = empty_matrix(self.nz, 0)
return Pxu
def expansion_matrix_xu(self):
Pxu = BlockMatrix(self.nblocks + 1, self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
Pxu[sid, sid] = nlp.expansion_matrix_xu()
Pxu[self.nblocks, self.nblocks] = empty_matrix(self.nz, 0)
return Pxu
def jacobian_c(self, x, out=None, **kwargs):
"""Return the jacobian of equality constraints evaluated at x
Parameters
----------
x : 1d-array
array with values of primal variables. Size nx
out : 1d-array
coo_matrix with the structure of the jacobian already defined. Optional
Returns
-------
The jacobian of the equality contraints in a coo_matrix format
"""
return empty_matrix(0, self.nx)
def jacobian_c(self, x, out=None, **kwargs):
"""Return the jacobian of equality constraints evaluated at x
Parameters
----------
x : 1d-array
array with values of primal variables. Size nx
out : 1d-array
coo_matrix with the structure of the jacobian already defined. Optional
Returns
-------
The jacobian of the equality contraints in a coo_matrix format
"""
return empty_matrix(0, self.nx)
def _create_hessian_structure(self):
# Note: This method requires the complicated vars map to be
# created beforehand
hess_lag = BlockSymMatrix(self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
xi = nlp.x_init()
yi = nlp.y_init()
hess_lag[sid, sid] = nlp.hessian_lag(xi, yi)
hess_lag[self.nblocks, self.nblocks] = empty_matrix(self.nz, self.nz)
flat_hess = hess_lag.tocoo()
self._irows_hess = flat_hess.row
self._jcols_hess = flat_hess.col
self._nnz_hess_lag = flat_hess.nnz
def _create_hessian_structure(self):
# Note: This method requires the complicated vars map to be
# created beforehand
hess_lag = BlockSymMatrix(self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
xi = nlp.x_init()
yi = nlp.y_init()
hess_lag[sid, sid] = nlp.hessian_lag(xi, yi)
hess_lag[self.nblocks, self.nblocks] = empty_matrix(self.nz, self.nz)
flat_hess = hess_lag.tocoo()
self._irows_hess = flat_hess.row
self._jcols_hess = flat_hess.col
self._nnz_hess_lag = flat_hess.nnz
def hessian_lag(self, x, y, out=None, **kwargs):
"""Return the Hessian of the Lagrangian function evaluated at x and y
Parameters
----------
x : array_like
Array with values of primal variables.
y : array_like
Array with values of dual variables.
out : BlockMatrix
Output matrix with the structure of the hessian already defined. Optional
Returns
-------
BlockMatrix
"""
assert x.size == self.nx, 'Dimension mismatch'
assert y.size == self.ng, 'Dimension mismatch'
eval_f_c = kwargs.pop('eval_f_c', True)
if isinstance(x, BlockVector) and isinstance(y, BlockVector):
assert x.nblocks == self.nblocks + 1
assert y.nblocks == 2 * self.nblocks
x_ = x
y_ = y
elif isinstance(x, np.ndarray) and isinstance(y, BlockVector):
assert y.nblocks == 2 * self.nblocks
block_x = self.create_vector_x()
block_x.copyfrom(x)
x_ = block_x
y_ = y
elif isinstance(x, BlockVector) and isinstance(y, np.ndarray):
assert x.nblocks == self.nblocks + 1
x_ = x
block_y = self.create_vector_y()
block_y.copyfrom(y)
y_ = block_y
elif isinstance(x, np.ndarray) and isinstance(y, np.ndarray):
block_x = self.create_vector_x()
block_x.copyfrom(x)
x_ = block_x
block_y = self.create_vector_y()
block_y.copyfrom(y)
y_ = block_y
else:
raise NotImplementedError('Input vector format not recognized')
if out is None:
hess_lag = BlockSymMatrix(self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
xi = x_[sid]
yi = y_[sid]
hess_lag[sid, sid] = nlp.hessian_lag(xi, yi, eval_f_c=eval_f_c)
hess_lag[self.nblocks,
self.nblocks] = empty_matrix(self.nz, self.nz)
return hess_lag
else:
assert isinstance(out, BlockSymMatrix), \
'out must be a BlockSymMatrix'
assert out.bshape == (self.nblocks + 1, self.nblocks + 1), \
'Block shape mismatch'
hess_lag = out
for sid, nlp in enumerate(self._nlps):
xi = x_[sid]
yi = y_[sid]
nlp.hessian_lag(xi,
yi,
out=hess_lag[sid, sid],
eval_f_c=eval_f_c)
Hz = hess_lag[self.nblocks, self.nblocks]
nb = self.nblocks
assert Hz.shape == (self.nz, self.nz), \
'out must have an {}x{} empty matrix in block {}'.format(nb,
nb,
(nb, nb))
assert Hz.nnz == 0, \
'out must have an empty matrix in block {}'.format((nb, nb))
return hess_lag
def hessian_lag(self, x, y, out=None, **kwargs):
"""Return the Hessian of the Lagrangian function evaluated at x and y
Parameters
----------
x : array_like
Array with values of primal variables.
y : array_like
Array with values of dual variables.
out : BlockMatrix
Output matrix with the structure of the hessian already defined. Optional
Returns
-------
BlockMatrix
"""
assert x.size == self.nx, 'Dimension mismatch'
assert y.size == self.ng, 'Dimension mismatch'
eval_f_c = kwargs.pop('eval_f_c', True)
if isinstance(x, BlockVector) and isinstance(y, BlockVector):
assert x.nblocks == self.nblocks + 1
assert y.nblocks == 2 * self.nblocks
x_ = x
y_ = y
elif isinstance(x, np.ndarray) and isinstance(y, BlockVector):
assert y.nblocks == 2 * self.nblocks
block_x = self.create_vector_x()
block_x.copyfrom(x)
x_ = block_x
y_ = y
elif isinstance(x, BlockVector) and isinstance(y, np.ndarray):
assert x.nblocks == self.nblocks + 1
x_ = x
block_y = self.create_vector_y()
block_y.copyfrom(y)
y_ = block_y
elif isinstance(x, np.ndarray) and isinstance(y, np.ndarray):
block_x = self.create_vector_x()
block_x.copyfrom(x)
x_ = block_x
block_y = self.create_vector_y()
block_y.copyfrom(y)
y_ = block_y
else:
raise NotImplementedError('Input vector format not recognized')
if out is None:
hess_lag = BlockSymMatrix(self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
xi = x_[sid]
yi = y_[sid]
hess_lag[sid, sid] = nlp.hessian_lag(xi, yi, eval_f_c=eval_f_c)
hess_lag[self.nblocks, self.nblocks] = empty_matrix(self.nz, self.nz)
return hess_lag
else:
assert isinstance(out, BlockSymMatrix), \
'out must be a BlockSymMatrix'
assert out.bshape == (self.nblocks + 1, self.nblocks + 1), \
'Block shape mismatch'
hess_lag = out
for sid, nlp in enumerate(self._nlps):
xi = x_[sid]
yi = y_[sid]
nlp.hessian_lag(xi,
yi,
out=hess_lag[sid, sid],
eval_f_c=eval_f_c)
Hz = hess_lag[self.nblocks, self.nblocks]
nb = self.nblocks
assert Hz.shape == (self.nz, self.nz), \
'out must have an {}x{} empty matrix in block {}'.format(nb,
nb,
(nb, nb))
assert Hz.nnz == 0, \
'out must have an empty matrix in block {}'.format((nb, nb))
return hess_lag