def test_iadd(self):
row = np.array([0, 3, 1, 2, 3, 0])
col = np.array([0, 0, 1, 2, 3, 3])
data = np.array([2., 1, 3, 4, 5, 1])
m = coo_matrix((data, (row, col)), shape=(4, 4))
rank = comm.Get_rank()
# create mpi matrix
rank_ownership = [[0, -1], [-1, 1]]
bm = MPIBlockMatrix(2, 2, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m.copy())
if rank == 1:
bm.set_block(1, 1, m.copy())
serial_bm = BlockMatrix(2, 2)
serial_bm.set_block(0, 0, m.copy())
serial_bm.set_block(1, 1, m.copy())
bm += bm
serial_bm += serial_bm
rows, columns = np.nonzero(bm.ownership_mask)
for i, j in zip(rows, columns):
if bm.get_block(i, j) is not None:
self.assertTrue(
np.allclose(
bm.get_block(i, j).toarray(),
serial_bm.get_block(i, j).toarray()))
bm += serial_bm
serial_bm += serial_bm
self._compare_mpi_and_serial_block_matrices(bm, serial_bm)
def expansion_matrix_xu(self):
Pxu = BlockMatrix(self.nblocks + 1, self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
Pxu.set_block(sid, sid, nlp.expansion_matrix_xu())
Pxu[self.nblocks, self.nblocks] = coo_matrix((self.nz, 0))
return Pxu
def test_reset_bcol(self):
row = np.array([0, 3, 1, 2, 3, 0])
col = np.array([0, 0, 1, 2, 3, 3])
data = np.array([2., 1, 3, 4, 5, 1])
m = coo_matrix((data, (row, col)), shape=(4, 4))
rank = comm.Get_rank()
# create mpi matrix
rank_ownership = [[0, -1], [-1, 1]]
bm = MPIBlockMatrix(2, 2, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m)
if rank == 1:
bm.set_block(1, 1, m)
bm.broadcast_block_sizes()
serial_bm = BlockMatrix(2, 2)
serial_bm.set_block(0, 0, m)
serial_bm.set_block(1, 1, m)
self.assertTrue(
np.allclose(serial_bm.row_block_sizes(), bm.row_block_sizes()))
bm.reset_bcol(0)
serial_bm.reset_bcol(0)
self.assertTrue(
np.allclose(serial_bm.col_block_sizes(), bm.col_block_sizes()))
bm.reset_bcol(1)
serial_bm.reset_bcol(1)
self.assertTrue(
np.allclose(serial_bm.col_block_sizes(), bm.col_block_sizes()))
def test_abs(self):
row = np.array([0, 3, 1, 2, 3, 0])
col = np.array([0, 0, 1, 2, 3, 3])
data = np.array([2., 1, 3, 4, 5, 1])
m = coo_matrix((data, (row, col)), shape=(4, 4))
rank = comm.Get_rank()
# create mpi matrix
rank_ownership = [[0, -1], [-1, 1]]
bm = MPIBlockMatrix(2, 2, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m)
if rank == 1:
bm.set_block(1, 1, m)
bm.broadcast_block_sizes()
serial_bm = BlockMatrix(2, 2)
serial_bm.set_block(0, 0, m)
serial_bm.set_block(1, 1, m)
res = abs(bm)
serial_res = abs(serial_bm)
rows, columns = np.nonzero(bm.ownership_mask)
for i, j in zip(rows, columns):
if res.get_block(i, j) is not None:
self.assertTrue(
np.allclose(
res.get_block(i, j).toarray(),
serial_res.get_block(i, j).toarray()))
def test_isub(self):
row = np.array([0, 3, 1, 2, 3, 0])
col = np.array([0, 0, 1, 2, 3, 3])
data = np.array([2., 1, 3, 4, 5, 1])
m = coo_matrix((data, (row, col)), shape=(4, 4))
rank = comm.Get_rank()
# create mpi matrix
rank_ownership = [[0, -1], [-1, 1]]
bm = MPIBlockMatrix(2, 2, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m.copy())
if rank == 1:
bm.set_block(1, 1, m.copy())
bm.broadcast_block_sizes()
serial_bm = BlockMatrix(2, 2)
serial_bm.set_block(0, 0, m.copy())
serial_bm.set_block(1, 1, m.copy())
bm -= bm
serial_bm -= serial_bm
rows, columns = np.nonzero(bm.ownership_mask)
for i, j in zip(rows, columns):
if bm.get_block(i, j) is not None:
self.assertTrue(
np.allclose(
bm.get_block(i, j).toarray(),
serial_bm.get_block(i, j).toarray()))
with self.assertRaises(Exception) as context:
bm -= serial_bm
def test_setitem(self):
m = BlockMatrix(2, 2)
m.set_block(0, 1, self.block_m)
self.assertFalse(m.is_empty_block(0, 1))
self.assertEqual(m._brow_lengths[0], self.block_m.shape[0])
self.assertEqual(m._bcol_lengths[1], self.block_m.shape[1])
self.assertEqual(m.get_block(0, 1).shape, self.block_m.shape)
def test_getitem(self):
m = BlockMatrix(3, 3)
for i in range(3):
for j in range(3):
self.assertIsNone(m.get_block(i, j))
m.set_block(0, 1, self.block_m)
self.assertEqual(m.get_block(0, 1).shape, self.block_m.shape)
def jacobian_c(self, x, out=None, **kwargs):
"""Returns the Jacobian of the equalities evaluated at x
Parameters
----------
x : array_like
Array with values of primal variables.
out : BlockMatrix, optional
Output matrix with the structure of the jacobian already defined.
Returns
-------
BlockMatrix
"""
assert x.size == self.nx, 'Dimension mismatch'
if isinstance(x, BlockVector):
assert x.nblocks == self.nblocks + 1
x_ = x
elif isinstance(x, np.ndarray):
block_x = self.create_vector_x()
block_x.copyfrom(x)
x_ = block_x
else:
raise RuntimeError('Input vector format not recognized')
if out is None:
jac_c = BlockMatrix(2 * self.nblocks, self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
xi = x_.get_block(sid)
jac_c.set_block(sid, sid, nlp.jacobian_c(xi))
# coupling matrices Ai
jac_c[sid + self.nblocks,
sid] = self._AB_coo.get_block(sid, sid)
# coupling matrices Bi
jac_c[sid + self.nblocks, self.nblocks] = -identity(self.nz)
return jac_c
else:
assert isinstance(out, BlockMatrix), 'out must be a BlockMatrix'
assert out.bshape == (2 * self.nblocks,
self.nblocks + 1), "Block shape mismatch"
jac_c = out
for sid, nlp in enumerate(self._nlps):
xi = x_.get_block(sid)
nlp.jacobian_c(xi, out=jac_c.get_block(sid, sid))
Ai = jac_c[sid + self.nblocks, sid]
assert Ai.shape == self._AB_coo.get_block(sid, sid).shape, \
'Block {} mismatch shape'.format((sid + self.nblocks, sid))
assert Ai.nnz == self._AB_coo.get_block(sid, sid).nnz, \
'Block {} mismatch nnz'.format((sid + self.nblocks, sid))
Bi = jac_c[sid + self.nblocks, self.nblocks]
assert Bi.shape == (self.nz, self.nz), \
'Block {} mismatch shape'.format((sid + self.nblocks, self.nblocks))
assert Bi.nnz == self.nz, \
'Block {} mismatch nnz'.format((sid + self.nblocks, self.nblocks))
return jac_c
def coupling_matrix(self):
AB = BlockMatrix(self.nblocks + 1, self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
col = self._zid_to_vid[sid]
row = np.arange(self.nz, dtype=np.int)
data = np.ones(self.nz)
AB.set_block(
sid, sid,
csr_matrix((data, (row, col)), shape=(self.nz, nlp.nx)))
AB[self.nblocks, self.nblocks] = -identity(self.nz)
return AB
def create_blocks(self, m: np.ndarray, x: np.ndarray):
m = coo_matrix(m)
r = m * x
bm = BlockMatrix(2, 2)
bm.set_block(0, 0, m.copy())
bm.set_block(1, 1, m.copy())
br = BlockVector(2)
br.set_block(0, r.copy())
br.set_block(1, r.copy())
bx = BlockVector(2)
bx.set_block(0, x.copy())
bx.set_block(1, x.copy())
return bm, bx, br
def test_dimensions(self):
bm = BlockMatrix(2, 2)
self.assertTrue(bm.has_undefined_row_sizes())
self.assertTrue(bm.has_undefined_col_sizes())
with self.assertRaises(NotFullyDefinedBlockMatrixError):
shape = bm.shape
with self.assertRaises(NotFullyDefinedBlockMatrixError):
bm.set_block(0, 0, BlockMatrix(2, 2))
with self.assertRaises(NotFullyDefinedBlockMatrixError):
row_sizes = bm.row_block_sizes()
with self.assertRaises(NotFullyDefinedBlockMatrixError):
col_sizes = bm.col_block_sizes()
bm2 = BlockMatrix(2, 2)
bm2.set_block(0, 0, coo_matrix((2, 2)))
bm2.set_block(1, 1, coo_matrix((2, 2)))
bm3 = bm2.copy()
bm.set_block(0, 0, bm2)
bm.set_block(1, 1, bm3)
self.assertFalse(bm.has_undefined_row_sizes())
self.assertFalse(bm.has_undefined_col_sizes())
self.assertEqual(bm.shape, (8, 8))
bm.set_block(0, 0, None)
self.assertFalse(bm.has_undefined_row_sizes())
self.assertFalse(bm.has_undefined_col_sizes())
self.assertEqual(bm.shape, (8, 8))
self.assertTrue(np.all(bm.row_block_sizes() == np.ones(2) * 4))
self.assertTrue(np.all(bm.col_block_sizes() == np.ones(2) * 4))
self.assertTrue(
np.all(bm.row_block_sizes(copy=False) == np.ones(2) * 4))
self.assertTrue(
np.all(bm.col_block_sizes(copy=False) == np.ones(2) * 4))
def main():
m = create_model(4.5, 1.0)
opt = pyo.SolverFactory('ipopt')
results = opt.solve(m, tee=True)
nlp = PyomoNLP(m)
x = nlp.init_primals()
y = compute_init_lam(nlp, x=x)
nlp.set_primals(x)
nlp.set_duals(y)
J = nlp.extract_submatrix_jacobian(pyomo_variables=[m.x1, m.x2, m.x3],
pyomo_constraints=[m.const1, m.const2])
H = nlp.extract_submatrix_hessian_lag(
pyomo_variables_rows=[m.x1, m.x2, m.x3],
pyomo_variables_cols=[m.x1, m.x2, m.x3])
M = BlockMatrix(2, 2)
M.set_block(0, 0, H)
M.set_block(1, 0, J)
M.set_block(0, 1, J.transpose())
Np = BlockMatrix(2, 1)
Np.set_block(
0, 0,
nlp.extract_submatrix_hessian_lag(
pyomo_variables_rows=[m.x1, m.x2, m.x3],
pyomo_variables_cols=[m.eta1, m.eta2]))
Np.set_block(
1, 0,
nlp.extract_submatrix_jacobian(pyomo_variables=[m.eta1, m.eta2],
pyomo_constraints=[m.const1, m.const2]))
ds = spsolve(M.tocsc(), -Np.tocsc())
print("ds:\n", ds.todense())
#################################################################
p0 = np.array([pyo.value(m.nominal_eta1), pyo.value(m.nominal_eta2)])
p = np.array([4.45, 1.05])
dp = p - p0
dx = ds.dot(dp)[0:3]
x_indices = nlp.get_primal_indices([m.x1, m.x2, m.x3])
x_names = np.array(nlp.primals_names())
new_x_sens = x[x_indices] + dx
print("dp:", dp)
print("dx:", dx)
print("Variable names: \n", x_names[x_indices])
print("Sensitivity based x:\n", new_x_sens)
#################################################################
m = create_model(4.45, 1.05)
opt = pyo.SolverFactory('ipopt')
results = opt.solve(m, tee=False)
nlp = PyomoNLP(m)
new_x = nlp.init_primals()[nlp.get_primal_indices([m.x1, m.x2, m.x3])]
print("NLP based x:\n", new_x)
return new_x_sens, new_x
def _create_hessian_structure(self):
# Note: This method requires the complicated vars map to be
# created beforehand
hess_lag = BlockMatrix(self.nblocks + 1, self.nblocks + 1)
for sid, nlp in enumerate(self._nlps):
xi = nlp.x_init()
yi = nlp.y_init()
hess_lag.set_block(sid, sid, nlp.hessian_lag(xi, yi))
hess_lag[self.nblocks, self.nblocks] = coo_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 build_compression_matrix(compression_mask):
"""
Return a sparse matrix CM of ones such that
compressed_vector = CM*full_vector based on the
compression mask
Parameters
----------
compression_mask: np.ndarray or pyomo.contrib.pynumero.sparse.block_vector.BlockVector
Returns
-------
cm: coo_matrix or BlockMatrix
The compression matrix
"""
if isinstance(compression_mask, BlockVector):
n = compression_mask.nblocks
res = BlockMatrix(nbrows=n, nbcols=n)
for ndx, block in enumerate(compression_mask):
sub_matrix = build_compression_matrix(block)
res.set_block(ndx, ndx, sub_matrix)
return res
elif type(compression_mask) is np.ndarray:
cols = compression_mask.nonzero()[0]
nnz = len(cols)
rows = np.arange(nnz, dtype=np.int)
data = np.ones(nnz)
return coo_matrix((data, (rows, cols)),
shape=(nnz, len(compression_mask)))
elif isinstance(compression_mask, mpi_block_vector.MPIBlockVector):
from pyomo.contrib.pynumero.sparse.mpi_block_matrix import MPIBlockMatrix
n = compression_mask.nblocks
rank_ownership = np.ones((n, n), dtype=np.int64) * -1
for i in range(n):
rank_ownership[i, i] = compression_mask.rank_ownership[i]
res = MPIBlockMatrix(nbrows=n,
nbcols=n,
rank_ownership=rank_ownership,
mpi_comm=compression_mask.mpi_comm,
assert_correct_owners=False)
for ndx in compression_mask.owned_blocks:
block = compression_mask.get_block(ndx)
sub_matrix = build_compression_matrix(block)
res.set_block(ndx, ndx, sub_matrix)
return res
def test_abs(self):
row = np.array([0, 3, 1, 2, 3, 0])
col = np.array([0, 0, 1, 2, 3, 3])
data = -1.0 * np.array([2., 1, 3, 4, 5, 1])
m = coo_matrix((data, (row, col)), shape=(4, 4))
self.block_m = m
bm = BlockMatrix(2, 2)
bm.set_block(0, 0, m)
bm.set_block(1, 1, m)
bm.set_block(0, 1, m)
abs_flat = abs(bm.tocoo())
abs_mat = abs(bm)
self.assertIsInstance(abs_mat, BlockMatrix)
self.assertTrue(np.allclose(abs_flat.toarray(), abs_mat.toarray()))
def jacobian_d(self, x, out=None, **kwargs):
"""Returns the Jacobian of the inequalities evaluated at x
Parameters
----------
x : array_like
Array with values of primal variables.
out : coo_matrix, optional
Output matrix with the structure of the jacobian already defined.
Returns
-------
BlockMatrix
"""
assert x.size == self.nx, "Dimension mismatch"
if isinstance(x, BlockVector):
assert x.nblocks == self.nblocks + 1
x_ = x
elif isinstance(x, np.ndarray):
block_x = self.create_vector_x()
block_x.copyfrom(x)
x_ = block_x
else:
raise RuntimeError('Input vector format not recognized')
if out is None:
jac_d = BlockMatrix(self.nblocks, self.nblocks)
for sid, nlp in enumerate(self._nlps):
xi = x_.get_block(sid)
jac_d.set_block(sid, sid, nlp.jacobian_d(xi))
return jac_d
else:
assert isinstance(out, BlockMatrix), 'out must be a BlockMatrix'
assert out.bshape == (self.nblocks,
self.nblocks), 'Block shape mismatch'
jac_d = out
for sid, nlp in enumerate(self._nlps):
xi = x_.get_block(sid)
nlp.jacobian_d(xi, out=jac_d.get_block(sid, sid))
return jac_d
def test_dot(self):
A_dense = self.basic_m.toarray()
A_block = self.basic_m
x = np.ones(A_dense.shape[1])
block_x = BlockVector(2)
block_x.set_block(0, np.ones(self.block_m.shape[1]))
block_x.set_block(1, np.ones(self.block_m.shape[1]))
flat_res = A_block.dot(x).flatten()
block_res = A_block.dot(block_x)
self.assertTrue(np.allclose(A_dense.dot(x), flat_res))
self.assertTrue(np.allclose(A_dense.dot(x), block_res.flatten()))
self.assertEqual(block_res.bshape[0], 2)
m = BlockMatrix(2, 2)
sub_m = np.array([[1, 0], [0, 1]])
sub_m = coo_matrix(sub_m)
m.set_block(0, 1, sub_m.copy())
m.set_block(1, 0, sub_m.copy())
x = np.arange(4)
res = m * x
self.assertTrue(np.allclose(res.flatten(), np.array([2, 3, 0, 1])))
def compute_init_lam(nlp, x=None, lam_max=1e3):
if x is None:
x = nlp.init_primals()
else:
assert x.size == nlp.n_primals()
nlp.set_primals(x)
assert nlp.n_ineq_constraints(
) == 0, "only supported for equality constrained nlps for now"
nx = nlp.n_primals()
nc = nlp.n_constraints()
# create Jacobian
jac = nlp.evaluate_jacobian()
# create gradient of objective
df = nlp.evaluate_grad_objective()
# create KKT system
kkt = BlockMatrix(2, 2)
kkt.set_block(0, 0, identity(nx))
kkt.set_block(1, 0, jac)
kkt.set_block(0, 1, jac.transpose())
zeros = np.zeros(nc)
rhs = BlockVector(2)
rhs.set_block(0, -df)
rhs.set_block(1, zeros)
flat_kkt = kkt.tocoo().tocsc()
flat_rhs = rhs.flatten()
sol = spsolve(flat_kkt, flat_rhs)
return sol[nlp.n_primals():nlp.n_primals() + nlp.n_constraints()]
def setUp(self):
row = np.array([0, 3, 1, 2, 3, 0])
col = np.array([0, 0, 1, 2, 3, 3])
data = np.array([2., 1, 3, 4, 5, 1])
m = coo_matrix((data, (row, col)), shape=(4, 4))
self.block_m = m
bm = BlockMatrix(2, 2)
bm.name = 'basic_matrix'
bm.set_block(0, 0, m.copy())
bm.set_block(1, 1, m.copy())
bm.set_block(0, 1, m.copy())
self.basic_m = bm
self.dense = np.zeros((8, 8))
self.dense[0:4, 0:4] = m.toarray()
self.dense[0:4, 4:8] = m.toarray()
self.dense[4:8, 4:8] = m.toarray()
self.composed_m = BlockMatrix(2, 2)
self.composed_m.set_block(0, 0, self.block_m.copy())
self.composed_m.set_block(1, 1, self.basic_m.copy())
def test_get_block_row_index(self):
m = BlockMatrix(2, 4)
m.set_block(0, 0, coo_matrix((3, 2)))
m.set_block(0, 1, coo_matrix((3, 4)))
m.set_block(0, 2, coo_matrix((3, 3)))
m.set_block(0, 3, coo_matrix((3, 6)))
m.set_block(1, 3, coo_matrix((5, 6)))
brow = m.get_block_row_index(0)
self.assertEqual(brow, 0)
brow = m.get_block_row_index(6)
self.assertEqual(brow, 1)
def _setup_jacs(self):
self._jac_ineq.set_col_size(self._num_time_blocks,
self._total_num_coupling_vars)
for ndx, nlp in self._nlps.items():
self._jac_ineq.set_row_size(ndx, nlp.n_ineq_constraints())
self._jac_ineq.set_col_size(ndx, nlp.n_primals())
sub_block = BlockMatrix(nbrows=3, nbcols=1)
sub_block.set_row_size(0, nlp.n_eq_constraints())
sub_block.set_col_size(0, nlp.n_primals())
sub_block.set_block(1, 0, self._link_backward_matrices[ndx])
sub_block.set_block(2, 0, self._link_forward_matrices[ndx])
self._jac_eq.set_block(ndx, ndx, sub_block)
sub_block = BlockMatrix(nbrows=3, nbcols=1)
sub_block.set_row_size(0, nlp.n_eq_constraints())
sub_block.set_col_size(0, self._total_num_coupling_vars)
sub_block.set_block(1, 0,
-self._link_backward_coupling_matrices[ndx])
sub_block.set_block(2, 0,
-self._link_forward_coupling_matrices[ndx])
self._jac_eq.set_block(ndx, self._num_time_blocks, sub_block)
def test_get_block_column_index(self):
m = BlockMatrix(2, 4)
m.set_block(0, 0, coo_matrix((3, 2)))
m.set_block(0, 1, coo_matrix((3, 4)))
m.set_block(0, 2, coo_matrix((3, 3)))
m.set_block(0, 3, coo_matrix((3, 6)))
m.set_block(1, 3, coo_matrix((5, 6)))
bcol = m.get_block_column_index(8)
self.assertEqual(bcol, 2)
bcol = m.get_block_column_index(5)
self.assertEqual(bcol, 1)
bcol = m.get_block_column_index(14)
self.assertEqual(bcol, 3)
def main(show_plot=True):
if show_plot:
import matplotlib.pylab as plt
instance = create_problem(0.0, 10.0)
# Discretize model using Orthogonal Collocation
discretizer = pyo.TransformationFactory('dae.collocation')
discretizer.apply_to(instance, nfe=100, ncp=3, scheme='LAGRANGE-RADAU')
discretizer.reduce_collocation_points(instance,
var=instance.u,
ncp=1,
contset=instance.t)
# Interface pyomo model with nlp
nlp = PyomoNLP(instance)
x = nlp.create_new_vector('primals')
x.fill(1.0)
nlp.set_primals(x)
lam = nlp.create_new_vector('duals')
lam.fill(1.0)
nlp.set_duals(lam)
# Evaluate jacobian
jac = nlp.evaluate_jacobian()
if show_plot:
plt.spy(jac)
plt.title('Jacobian of the constraints\n')
plt.show()
# Evaluate hessian of the lagrangian
hess_lag = nlp.evaluate_hessian_lag()
if show_plot:
plt.spy(hess_lag)
plt.title('Hessian of the Lagrangian function\n')
plt.show()
# Build KKT matrix
kkt = BlockMatrix(2, 2)
kkt.set_block(0, 0, hess_lag)
kkt.set_block(1, 0, jac)
kkt.set_block(0, 1, jac.transpose())
if show_plot:
plt.spy(kkt.tocoo())
plt.title('KKT system\n')
plt.show()
def setUpClass(cls):
# test problem 1
row = np.array([0, 3, 1, 2, 3, 0])
col = np.array([0, 0, 1, 2, 3, 3])
data = np.array([2., 1, 3, 4, 5, 1])
m = coo_matrix((data, (row, col)), shape=(4, 4))
rank = comm.Get_rank()
# create mpi matrix
rank_ownership = [[0, -1], [-1, 1]]
bm = MPIBlockMatrix(2, 2, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m)
if rank == 1:
bm.set_block(1, 1, m)
# create serial matrix image
serial_bm = BlockMatrix(2, 2)
serial_bm.set_block(0, 0, m)
serial_bm.set_block(1, 1, m)
cls.square_serial_mat = serial_bm
bm.broadcast_block_sizes()
cls.square_mpi_mat = bm
# create mpi matrix
rank_ownership = [[0, -1], [-1, 1]]
bm = MPIBlockMatrix(2, 2, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m)
if rank == 1:
bm.set_block(1, 1, m)
cls.square_mpi_mat_no_broadcast = bm
# create matrix with shared blocks
rank_ownership = [[0, -1], [-1, 1]]
bm = MPIBlockMatrix(2, 2, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m)
if rank == 1:
bm.set_block(1, 1, m)
bm.set_block(0, 1, m)
bm.broadcast_block_sizes()
cls.square_mpi_mat2 = bm
# create serial matrix image
serial_bm = BlockMatrix(2, 2)
serial_bm.set_block(0, 0, m)
serial_bm.set_block(1, 1, m)
serial_bm.set_block(0, 1, m)
cls.square_serial_mat2 = serial_bm
row = np.array([0, 1, 2, 3])
col = np.array([0, 1, 0, 1])
data = np.array([1., 1., 1., 1.])
m2 = coo_matrix((data, (row, col)), shape=(4, 2))
rank_ownership = [[0, -1, 0], [-1, 1, -1]]
bm = MPIBlockMatrix(2, 3, rank_ownership, comm)
if rank == 0:
bm.set_block(0, 0, m)
bm.set_block(0, 2, m2)
if rank == 1:
bm.set_block(1, 1, m)
bm.broadcast_block_sizes()
cls.rectangular_mpi_mat = bm
bm = BlockMatrix(2, 3)
bm.set_block(0, 0, m)
bm.set_block(0, 2, m2)
bm.set_block(1, 1, m)
cls.rectangular_serial_mat = bm
def _setup_kkt_and_rhs_structure(self):
# First setup the diagonal blocks
for ndx, nlp in self._nlps.items():
sub_kkt = BlockMatrix(nbrows=2, nbcols=2)
n = nlp.n_primals() + nlp.n_eq_constraints(
) + 2 * nlp.n_ineq_constraints()
sub_kkt.set_row_size(0, n)
sub_kkt.set_col_size(0, n)
if ndx == 0:
sub_kkt.set_row_size(1, 0)
sub_kkt.set_col_size(1, 0)
else:
sub_kkt.set_row_size(1, self._num_states)
sub_kkt.set_col_size(1, self._num_states)
row_1 = BlockMatrix(nbrows=1, nbcols=4)
if ndx == 0:
row_1.set_row_size(0, 0)
else:
row_1.set_row_size(0, self._num_states)
row_1.set_col_size(0, nlp.n_primals())
row_1.set_col_size(1, nlp.n_ineq_constraints())
row_1.set_col_size(2, nlp.n_eq_constraints())
row_1.set_col_size(3, nlp.n_ineq_constraints())
row_1.set_block(0, 0, self._link_backward_matrices[ndx])
sub_kkt.set_block(1, 0, row_1)
sub_kkt.set_block(0, 1, row_1.transpose())
self._kkt.set_block(ndx, ndx, sub_kkt)
sub_rhs = BlockVector(2)
sub_rhs.set_block(0, np.zeros(n))
if ndx == 0:
sub_rhs.set_block(1, np.zeros(0))
else:
sub_rhs.set_block(1, np.zeros(self._num_states))
self._rhs.set_block(ndx, sub_rhs)
# Setup the border blocks
for ndx, nlp in self._nlps.items():
nlp = self._nlps[ndx]
block = BlockMatrix(nbrows=2, nbcols=2)
sub_block = BlockMatrix(nbrows=self._num_time_blocks, nbcols=4)
sub_block.set_col_size(0, nlp.n_primals())
sub_block.set_col_size(1, nlp.n_ineq_constraints())
sub_block.set_col_size(2, nlp.n_eq_constraints())
sub_block.set_col_size(3, nlp.n_ineq_constraints())
for sub_ndx in range(self._num_time_blocks):
if sub_ndx == self._num_time_blocks - 1:
sub_block.set_row_size(sub_ndx, 0)
else:
sub_block.set_row_size(sub_ndx, self._num_states)
sub_block.set_block(ndx, 0, self._link_forward_matrices[ndx])
block.set_block(0, 0, sub_block)
block.set_block(
1, 1, -self._link_backward_coupling_matrices[ndx].transpose())
self._kkt.set_block(self._num_time_blocks, ndx, block)
self._kkt.set_block(ndx, self._num_time_blocks, block.transpose())
# Setup the bottom right block
block = BlockMatrix(2, 2)
rhs_block = BlockVector(2)
sub_block = BlockMatrix(1, self._num_time_blocks)
sub_rhs_block = BlockVector(self._num_time_blocks)
for ndx in range(self._num_time_blocks):
sub_block.set_block(
0, ndx, -self._link_forward_coupling_matrices[ndx].transpose())
if ndx == self._num_time_blocks - 1:
sub_rhs_block.set_block(ndx, np.zeros(0))
else:
sub_rhs_block.set_block(ndx, np.zeros(self._num_states))
rhs_block.set_block(0, sub_rhs_block)
rhs_block.set_block(1, np.zeros(self._total_num_coupling_vars))
block.set_block(1, 0, sub_block)
block.set_block(0, 1, sub_block.transpose())
self._kkt.set_block(self._num_time_blocks, self._num_time_blocks,
block)
self._rhs.set_block(self._num_time_blocks, rhs_block)
# Interface pyomo model with nlp
nlp = PyomoNLP(instance)
x = nlp.create_new_vector('primals')
x.fill(1.0)
nlp.set_primals(x)
lam = nlp.create_new_vector('duals')
lam.fill(1.0)
nlp.set_duals(lam)
# Evaluate jacobian
jac = nlp.evaluate_jacobian()
plt.spy(jac)
plt.title('Jacobian of the constraints\n')
plt.show()
# Evaluate hessian of the lagrangian
hess_lag = nlp.evaluate_hessian_lag()
plt.spy(hess_lag)
plt.title('Hessian of the Lagrangian function\n')
plt.show()
# Build KKT matrix
kkt = BlockMatrix(2, 2)
kkt.set_block(0, 0, hess_lag)
kkt.set_block(1, 0, jac)
kkt.set_block(0, 1, jac.transpose())
plt.spy(kkt.tocoo())
plt.title('KKT system\n')
plt.show()
def evaluate_primal_dual_kkt_matrix(self, timer=None):
if timer is None:
timer = HierarchicalTimer()
timer.start('eval hess')
hessian = self._nlp.evaluate_hessian_lag()
timer.stop('eval hess')
timer.start('eval jac')
jac_eq = self._nlp.evaluate_jacobian_eq()
jac_ineq = self._nlp.evaluate_jacobian_ineq()
timer.stop('eval jac')
duals_primals_lb = self._duals_primals_lb
duals_primals_ub = self._duals_primals_ub
duals_slacks_lb = self._duals_slacks_lb
duals_slacks_ub = self._duals_slacks_ub
primals = self._nlp.get_primals()
timer.start('hess block')
data = (duals_primals_lb / (primals - self._nlp.primals_lb()) +
duals_primals_ub / (self._nlp.primals_ub() - primals))
n = self._nlp.n_primals()
indices = np.arange(n)
hess_block = scipy.sparse.coo_matrix((data, (indices, indices)),
shape=(n, n))
hess_block += hessian
timer.stop('hess block')
timer.start('slack block')
data = (duals_slacks_lb / (self._slacks - self._nlp.ineq_lb()) +
duals_slacks_ub / (self._nlp.ineq_ub() - self._slacks))
n = self._nlp.n_ineq_constraints()
indices = np.arange(n)
slack_block = scipy.sparse.coo_matrix((data, (indices, indices)),
shape=(n, n))
timer.stop('slack block')
timer.start('set block')
kkt = BlockMatrix(4, 4)
kkt.set_block(0, 0, hess_block)
kkt.set_block(1, 1, slack_block)
kkt.set_block(2, 0, jac_eq)
kkt.set_block(0, 2, jac_eq.transpose())
kkt.set_block(3, 0, jac_ineq)
kkt.set_block(0, 3, jac_ineq.transpose())
kkt.set_block(
3, 1, -scipy.sparse.identity(self._nlp.n_ineq_constraints(),
format='coo'))
kkt.set_block(
1, 3, -scipy.sparse.identity(self._nlp.n_ineq_constraints(),
format='coo'))
timer.stop('set block')
return kkt
results = opt.solve(m, tee=True)
#################################################################
nlp = PyomoNLP(m)
x = nlp.init_primals()
y = compute_init_lam(nlp, x=x)
nlp.set_primals(x)
nlp.set_duals(y)
J = nlp.extract_submatrix_jacobian(pyomo_variables=[m.x1, m.x2, m.x3],
pyomo_constraints=[m.const1, m.const2])
H = nlp.extract_submatrix_hessian_lag(pyomo_variables_rows=[m.x1, m.x2, m.x3],
pyomo_variables_cols=[m.x1, m.x2, m.x3])
M = BlockMatrix(2, 2)
M.set_block(0, 0, H)
M.set_block(1, 0, J)
M.set_block(0, 1, J.transpose())
Np = BlockMatrix(2, 1)
Np.set_block(
0, 0,
nlp.extract_submatrix_hessian_lag(pyomo_variables_rows=[m.x1, m.x2, m.x3],
pyomo_variables_cols=[m.eta1, m.eta2]))
Np.set_block(
1, 0,
nlp.extract_submatrix_jacobian(pyomo_variables=[m.eta1, m.eta2],
pyomo_constraints=[m.const1, m.const2]))
ds = spsolve(M.tocsc(), -Np.tocsc())
def test_mpi_schur_complement(self):
rank_by_index = list()
for ndx in range(3):
for _rank in range(size):
if (ndx - _rank) % size == 0:
rank_by_index.append(_rank)
rank_by_index.append(-1)
A = MPIBlockMatrix(nbrows=4,
nbcols=4,
rank_ownership=[
rank_by_index, rank_by_index, rank_by_index,
rank_by_index
],
mpi_comm=comm)
if rank_by_index[0] == rank:
A.set_block(
0, 0, coo_matrix(np.array([[1, 1], [0, 1]], dtype=np.double)))
if rank_by_index[1] == rank:
A.set_block(
1, 1, coo_matrix(np.array([[1, 0], [0, 1]], dtype=np.double)))
if rank_by_index[2] == rank:
A.set_block(
2, 2, coo_matrix(np.array([[1, 0], [1, 1]], dtype=np.double)))
A.set_block(3, 3,
coo_matrix(np.array([[0, 0], [0, 1]], dtype=np.double)))
if rank_by_index[0] == rank:
A.set_block(
3, 0, coo_matrix(np.array([[0, -1], [0, 0]], dtype=np.double)))
if rank_by_index[1] == rank:
A.set_block(
3, 1, coo_matrix(np.array([[-1, 0], [0, -1]],
dtype=np.double)))
if rank_by_index[2] == rank:
A.set_block(
3, 2, coo_matrix(np.array([[0, 0], [-1, 0]], dtype=np.double)))
A.broadcast_block_sizes()
local_A = BlockMatrix(4, 4)
local_A.set_block(
0, 0, coo_matrix(np.array([[1, 1], [0, 1]], dtype=np.double)))
local_A.set_block(
1, 1, coo_matrix(np.array([[1, 0], [0, 1]], dtype=np.double)))
local_A.set_block(
2, 2, coo_matrix(np.array([[1, 0], [1, 1]], dtype=np.double)))
local_A.set_block(
3, 3, coo_matrix(np.array([[0, 0], [0, 1]], dtype=np.double)))
local_A.set_block(
3, 0, coo_matrix(np.array([[0, -1], [0, 0]], dtype=np.double)))
local_A.set_block(
3, 1, coo_matrix(np.array([[-1, 0], [0, -1]], dtype=np.double)))
local_A.set_block(
3, 2, coo_matrix(np.array([[0, 0], [-1, 0]], dtype=np.double)))
local_A.set_block(0, 3, local_A.get_block(3, 0).transpose(copy=True))
local_A.set_block(1, 3, local_A.get_block(3, 1).transpose(copy=True))
local_A.set_block(2, 3, local_A.get_block(3, 2).transpose(copy=True))
rhs = MPIBlockVector(nblocks=4,
rank_owner=rank_by_index,
mpi_comm=comm)
if rank_by_index[0] == rank:
rhs.set_block(0, np.array([1, 0], dtype=np.double))
if rank_by_index[1] == rank:
rhs.set_block(1, np.array([0, 0], dtype=np.double))
if rank_by_index[2] == rank:
rhs.set_block(2, np.array([0, 1], dtype=np.double))
rhs.set_block(3, np.array([1, 1], dtype=np.double))
rhs.broadcast_block_sizes()
local_rhs = BlockVector(4)
local_rhs.set_block(0, np.array([1, 0], dtype=np.double))
local_rhs.set_block(1, np.array([0, 0], dtype=np.double))
local_rhs.set_block(2, np.array([0, 1], dtype=np.double))
local_rhs.set_block(3, np.array([1, 1], dtype=np.double))
x1 = np.linalg.solve(local_A.toarray(), local_rhs.flatten())
solver_class = parapint.linalg.MPISchurComplementLinearSolver
sc_solver = solver_class(
subproblem_solvers={
ndx: ScipyInterface(compute_inertia=True)
for ndx in range(3)
},
schur_complement_solver=ScipyInterface(compute_inertia=True))
sc_solver.do_symbolic_factorization(A)
sc_solver.do_numeric_factorization(A)
x2 = sc_solver.do_back_solve(rhs)
self.assertTrue(np.allclose(x1, x2.make_local_copy().flatten()))
inertia1 = sc_solver.get_inertia()
eig = np.linalg.eigvals(local_A.toarray())
pos = np.count_nonzero(eig > 0)
neg = np.count_nonzero(eig < 0)
zero = np.count_nonzero(eig == 0)
inertia2 = (pos, neg, zero)
self.assertEqual(inertia1, inertia2)
sc_solver.do_numeric_factorization(A)
x2 = sc_solver.do_back_solve(rhs)
self.assertTrue(np.allclose(x1, x2.make_local_copy().flatten()))
def test_matrix_multiply(self):
"""
Test
[A B C * [G J = [A*G + B*H + C*I A*J + B*K + C*L
D E F] H K D*G + E*H + F*I D*J + E*K + F*L]
I L]
"""
np.random.seed(0)
A = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
B = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
C = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
D = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
E = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
F = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
G = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
H = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
I = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
J = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
K = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
L = sp.csr_matrix(np.random.normal(0, 10, (2, 2)))
bm1 = BlockMatrix(2, 3)
bm2 = BlockMatrix(3, 2)
bm1.set_block(0, 0, A)
bm1.set_block(0, 1, B)
bm1.set_block(0, 2, C)
bm1.set_block(1, 0, D)
bm1.set_block(1, 1, E)
bm1.set_block(1, 2, F)
bm2.set_block(0, 0, G)
bm2.set_block(1, 0, H)
bm2.set_block(2, 0, I)
bm2.set_block(0, 1, J)
bm2.set_block(1, 1, K)
bm2.set_block(2, 1, L)
got = (bm1 * bm2).toarray()
exp00 = (A * G + B * H + C * I).toarray()
exp01 = (A * J + B * K + C * L).toarray()
exp10 = (D * G + E * H + F * I).toarray()
exp11 = (D * J + E * K + F * L).toarray()
exp = np.zeros((4, 4))
exp[0:2, 0:2] = exp00
exp[0:2, 2:4] = exp01
exp[2:4, 0:2] = exp10
exp[2:4, 2:4] = exp11
self.assertTrue(np.allclose(got, exp))
