def factorize(self):
u"""Factorize matrix A as limited-memory LDLᵀ.
:returns:
:L: L as a llmat matrix
:d: as a Numpy array
"""
super(CySparseLLDLSolver, self).factorize()
nnz = len(self.lvals)
row = np.empty(nnz, dtype=np.int64)
col = np.empty(nnz, dtype=np.int64)
val = np.empty(nnz, dtype=np.float64)
elem = 0
for j in xrange(len(self.colptr) - 1):
for k in xrange(self.colptr[j], self.colptr[j + 1]):
row[elem] = self.rowind[k]
col[elem] = j
val[elem] = self.lvals[k]
elem += 1
L = LLSparseMatrix(size=self.n,
itype=INT64_T,
dtype=FLOAT64_T)
L.put_triplet(row, col, val)
return (L, self.d)
def jac(self, *args, **kwargs):
"""Evaluate constraints Jacobian at x."""
vals, rows, cols = super(CySparseNLPModel, self).jac(*args, **kwargs)
J = LLSparseMatrix(nrow=self.ncon,
ncol=self.nvar,
size_hint=vals.size,
store_symmetric=False,
itype=types.INT64_T,
dtype=types.FLOAT64_T)
J.put_triplet(rows, cols, vals)
return J
def hess(self, *args, **kwargs):
"""Evaluate Lagrangian Hessian at (x, z).
Note that `rows`, `cols` and `vals` must represent a LOWER triangular
sparse matrix in the coordinate format (COO).
"""
vals, rows, cols = super(CySparseNLPModel, self).hess(*args, **kwargs)
H = LLSparseMatrix(size=self.nvar,
size_hint=vals.size,
store_symmetric=True,
itype=types.INT64_T,
dtype=types.FLOAT64_T)
H.put_triplet(rows, cols, vals)
return H
class LLMatPutTripletBenchmark(benchmark.Benchmark):
label = "Simple put_triplet with 100 elements, size = 1,000 and put_size = 1,000"
each = 100
def setUp(self):
self.nbr_elements = 100
self.size = 1000
self.put_size = 1000
assert self.put_size <= self.size
self.A_c = LLSparseMatrix(size=self.size,
size_hint=self.nbr_elements,
itype=INT32_T,
dtype=FLOAT64_T)
construct_sparse_matrix(self.A_c, self.size, self.nbr_elements)
self.A_p = spmatrix.ll_mat(self.size, self.size, self.nbr_elements)
construct_sparse_matrix(self.A_p, self.size, self.nbr_elements)
self.A_sppy = None
self.id1 = np.arange(0, self.put_size, dtype=np.int32)
self.id2 = np.full(self.put_size, 37, dtype=np.int32)
self.b = np.arange(0, self.put_size, dtype=np.float64)
def eachSetUp(self):
self.A_sppy = csarray((self.size, self.size),
dtype=np.float64,
storagetype='row')
#def tearDown(self):
# for i in xrange(self.size):
# for j in xrange(self.size):
# assert self.A_c[i, j] == self.A_p[i, j]
def test_pysparse(self):
self.A_p.put(self.b, self.id1, self.id2)
return
def test_cysparse(self):
self.A_c.put_triplet(self.id1, self.id2, self.b)
return
def test_sppy(self):
self.A_sppy.put(self.b, self.id1, self.id2, init=True)
def A(self, *args, **kwargs):
"""
Evaluate sparse Jacobian of the linear part of the
constraints. Useful to obtain constraint matrix
when problem is a linear programming problem.
"""
vals, rows, cols = super(CySparseAmplModel,
self).A(*args, **kwargs)
A = LLSparseMatrix(nrow=self.ncon,
ncol=self.nvar,
size_hint=vals.size,
store_symmetric=False,
type=types.INT64_T,
dtype=types.FLOAT64_T)
A.put_triplet(rows, cols, vals)
return A
class LLMatPutTripletBenchmark(benchmark.Benchmark):
label = "Simple put_triplet with 100 elements, size = 1,000 and put_size = 1,000"
each = 100
def setUp(self):
self.nbr_elements = 100
self.size = 1000
self.put_size = 1000
assert self.put_size <= self.size
self.A_c = LLSparseMatrix(size=self.size, size_hint=self.nbr_elements, itype=INT32_T, dtype=FLOAT64_T)
construct_sparse_matrix(self.A_c, self.size, self.nbr_elements)
self.A_p = spmatrix.ll_mat(self.size, self.size, self.nbr_elements)
construct_sparse_matrix(self.A_p, self.size, self.nbr_elements)
self.A_sppy = None
self.id1 = np.arange(0, self.put_size, dtype=np.int32)
self.id2 = np.full(self.put_size, 37, dtype=np.int32)
self.b = np.arange(0, self.put_size,dtype=np.float64)
def eachSetUp(self):
self.A_sppy = csarray((self.size, self.size), dtype=np.float64, storagetype='row')
#def tearDown(self):
# for i in xrange(self.size):
# for j in xrange(self.size):
# assert self.A_c[i, j] == self.A_p[i, j]
def test_pysparse(self):
self.A_p.put(self.b, self.id1, self.id2)
return
def test_cysparse(self):
self.A_c.put_triplet(self.id1, self.id2, self.b)
return
def test_sppy(self):
self.A_sppy.put(self.b, self.id1, self.id2, init=True)
def _jac(self, x, lp=False):
"""Helper method to assemble the Jacobian matrix.
See the documentation of :meth:`jac` for more information.
The positional argument `lp` should be set to `True` only if the
problem is known to be a linear program. In this case, the evaluation
of the constraint matrix is cheaper and the argument `x` is ignored.
"""
m = self.m
model = self.model
on = self.original_n
lowerC = np.array(model.lowerC, dtype=np.int64)
nlowerC = model.nlowerC
upperC = np.array(model.upperC, dtype=np.int64)
nupperC = model.nupperC
rangeC = np.array(model.rangeC, dtype=np.int64)
nrangeC = model.nrangeC
# Initialize sparse Jacobian
nnzJ = self.model.nnzj + m
J = LLSparseMatrix(nrow=self.ncon,
ncol=self.nvar,
size_hint=nnzJ,
store_symmetric=False,
itype=types.INT64_T,
dtype=types.FLOAT64_T)
# Insert contribution of general constraints
if lp:
J[:on, :on] = self.model.A()
else:
J[:on, :on] = self.model.jac(x[:on])
# Create a few index lists
rlowerC = np.array(range(nlowerC), dtype=np.int64)
rupperC = np.array(range(nupperC), dtype=np.int64)
rrangeC = np.array(range(nrangeC), dtype=np.int64)
# Insert contribution of slacks on general constraints
J.put_triplet(lowerC, on + rlowerC,
-1.0 * np.ones(nlowerC, dtype=np.float64))
J.put_triplet(upperC, on + nlowerC + rupperC,
-1.0 * np.ones(nupperC, dtype=np.float64))
J.put_triplet(rangeC, on + nlowerC + nupperC + rrangeC,
-1.0 * np.ones(nrangeC, dtype=np.float64))
return J