def norm(f, order=2):
"""
Compute the norm of a Function.
Parameters
----------
f : Function
Input Function.
order : int, optional
The order of the norm. Defaults to 2.
"""
kwargs = {}
if f.is_TimeFunction and f._time_buffering:
kwargs[f.time_dim.max_name] = f._time_size - 1
# Protect SparseFunctions from accessing duplicated (out-of-domain) data,
# otherwise we would eventually be summing more than expected
p, eqns = f.guard() if f.is_SparseFunction else (f, [])
with MPIReduction(f) as mr:
op = dv.Operator(eqns + [dv.Inc(mr.n[0], Abs(Pow(p, order)))],
name='norm%d' % order)
op.apply(**kwargs)
v = Pow(mr.v, 1 / order)
return np.float(v)
def sumall(f):
"""
Compute the sum of all Function data.
Parameters
----------
f : Function
Input Function.
"""
kwargs = {}
if f.is_TimeFunction and f._time_buffering:
kwargs[f.time_dim.max_name] = f._time_size - 1
# Protect SparseFunctions from accessing duplicated (out-of-domain) data,
# otherwise we would eventually be summing more than expected
p, eqns = f.guard() if f.is_SparseFunction else (f, [])
s = dv.types.Scalar(name='sum', dtype=f.dtype)
with MPIReduction(f) as mr:
op = dv.Operator([dv.Eq(s, 0.0)] + eqns +
[dv.Inc(s, p), dv.Eq(mr.n[0], s)],
name='sum')
op.apply(**kwargs)
return f.dtype(mr.v)
def inner(f, g):
"""
Inner product of two Functions.
Parameters
----------
f : Function
First input operand
g : Function
Second input operand
Raises
------
ValueError
If the two input Functions are defined over different grids, or have
different dimensionality, or their dimension-wise sizes don't match.
If in input are two SparseFunctions and their coordinates don't match,
the exception is raised.
Notes
-----
The inner product is the sum of all dimension-wise products. For 1D Functions,
the inner product corresponds to the dot product.
"""
# Input check
if f.is_TimeFunction and f._time_buffering != g._time_buffering:
raise ValueError(
"Cannot compute `inner` between save/nosave TimeFunctions")
if f.shape != g.shape:
raise ValueError("`f` and `g` must have same shape")
if f._data is None or g._data is None:
raise ValueError("Uninitialized input")
if f.is_SparseFunction and not np.all(
f.coordinates_data == g.coordinates_data):
raise ValueError("Non-matching coordinates")
kwargs = {}
if f.is_TimeFunction and f._time_buffering:
kwargs[f.time_dim.max_name] = f._time_size - 1
# Protect SparseFunctions from accessing duplicated (out-of-domain) data,
# otherwise we would eventually be summing more than expected
rhs, eqns = f.guard(f * g) if f.is_SparseFunction else (f * g, [])
s = dv.types.Scalar(name='sum', dtype=f.dtype)
with MPIReduction(f, g) as mr:
op = dv.Operator([dv.Eq(s, 0.0)] + eqns +
[dv.Inc(s, rhs), dv.Eq(mr.n[0], s)],
name='inner')
op.apply(**kwargs)
return f.dtype(mr.v)
def sumall(f):
"""
Compute the sum of the values in a :class:`Function`.
Parameters
----------
f : Function
Input Function.
"""
kwargs = {}
if f.is_TimeFunction and f._time_buffering:
kwargs[f.time_dim.max_name] = f._time_size - 1
# Protect SparseFunctions from accessing duplicated (out-of-domain) data,
# otherwise we would eventually be summing more than expected
p, eqns = f.guard() if f.is_SparseFunction else (f, [])
with MPIReduction(f) as mr:
op = dv.Operator(eqns + [dv.Inc(mr.n[0], p)], name='sum')
op.apply(**kwargs)
return np.float(mr.v)
