class LowRankHessian:
"""
Operator that represents the action of the low rank approximation
of the Hessian and of its inverse.
"""
def __init__(self, prior, d, U):
self.prior = prior
self.LowRankH = LowRankOperator(d, U)
dsolve = d / (np.ones(d.shape, dtype=d.dtype) + d)
self.LowRankHinv = LowRankOperator(dsolve, U)
self.help = Vector(U[0].mpi_comm())
self.init_vector(self.help, 0)
self.help1 = Vector(U[0].mpi_comm())
self.init_vector(self.help1, 0)
def init_vector(self, x, dim):
self.prior.init_vector(x, dim)
def inner(self, x, y):
Hx = Vector(self.help.mpi_comm())
self.init_vector(Hx, 0)
self.mult(x, Hx)
return Hx.inner(y)
def mult(self, x, y):
self.prior.R.mult(x, y)
self.LowRankH.mult(y, self.help)
self.prior.R.mult(self.help, self.help1)
y.axpy(1, self.help1)
def solve(self, sol, rhs):
self.prior.Rsolver.solve(sol, rhs)
self.LowRankHinv.mult(rhs, self.help)
sol.axpy(-1, self.help)
class LowRankHessian:
"""
Operator that represents the action of the low rank approximation
of the Hessian and of its inverse.
"""
def __init__(self, prior, d, U):
self.prior = prior
self.LowRankH = LowRankOperator(d, U)
dsolve = d / (np.ones(d.shape, dtype=d.dtype) + d)
self.LowRankHinv = LowRankOperator(dsolve, U)
self.help = Vector(U[0].mpi_comm())
self.init_vector(self.help, 0)
self.help1 = Vector(U[0].mpi_comm())
self.init_vector(self.help1, 0)
def init_vector(self,x, dim):
self.prior.init_vector(x,dim)
def inner(self,x,y):
Hx = Vector(self.help.mpi_comm())
self.init_vector(Hx, 0)
self.mult(x, Hx)
return Hx.inner(y)
def mult(self, x, y):
self.prior.R.mult(x,y)
self.LowRankH.mult(y, self.help)
self.prior.R.mult(self.help,self.help1)
y.axpy(1, self.help1)
def solve(self, sol, rhs):
self.prior.Rsolver.solve(sol, rhs)
self.LowRankHinv.mult(rhs, self.help)
sol.axpy(-1, self.help)
def trace(A):
"""
Compute the trace of a sparse matrix A.
"""
v = Vector()
A.init_vector(v)
mpi_comm = v.mpi_comm()
nprocs = MPI.size(mpi_comm)
if nprocs > 1:
raise Exception("trace is only serial")
n = A.size(0)
tr = 0.
for i in range(0, n):
[j, val] = A.getrow(i)
tr += val[j == i]
return tr
def to_dense(A):
"""
Convert a sparse matrix A to dense.
For debugging only.
"""
v = Vector()
A.init_vector(v)
mpi_comm = v.mpi_comm()
nprocs = MPI.size(mpi_comm)
if nprocs > 1:
raise Exception("to_dense is only serial")
if hasattr(A, "getrow"):
n = A.size(0)
m = A.size(1)
B = np.zeros((n, m), dtype=np.float64)
for i in range(0, n):
[j, val] = A.getrow(i)
B[i, j] = val
return B
else:
x = Vector()
Ax = Vector()
A.init_vector(x, 1)
A.init_vector(Ax, 0)
n = Ax.array().shape[0]
m = x.array().shape[0]
B = np.zeros((n, m), dtype=np.float64)
for i in range(0, m):
i_ind = np.array([i], dtype=np.intc)
x.set_local(np.ones(i_ind.shape), i_ind)
x.apply("sum_values")
A.mult(x, Ax)
B[:, i] = Ax.array()
x.set_local(np.zeros(i_ind.shape), i_ind)
x.apply("sum_values")
return B