# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2022 Max-Planck-Society, Philipp Arras
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from functools import reduce
from operator import add
import numpy as np
from .. import utilities
from ..domain_tuple import DomainTuple
from ..field import Field
from ..linearization import Linearization
from ..multi_domain import MultiDomain
from ..multi_field import MultiField
from ..sugar import makeDomain, makeOp
from ..utilities import iscomplextype, myassert
from .adder import Adder
from .linear_operator import LinearOperator
from .operator import Operator, _OpChain, _OpSum
from .sampling_enabler import SamplingEnabler
from .sandwich_operator import SandwichOperator
from .scaling_operator import ScalingOperator
from .simple_linear_operators import FieldAdapter, VdotOperator
def _check_sampling_dtype(domain, dtypes):
if dtypes is None:
return
if isinstance(domain, DomainTuple):
np.dtype(dtypes)
return
elif isinstance(domain, MultiDomain):
if isinstance(dtypes, dict):
for dt in dtypes.values():
np.dtype(dt)
if set(domain.keys()) == set(dtypes.keys()):
return
else:
np.dtype(dtypes)
return
raise TypeError
def _field_to_dtype(field):
if isinstance(field, Field):
dt = field.dtype
elif isinstance(field, MultiField):
dt = {kk: ff.dtype for kk, ff in field.items()}
else:
raise TypeError
_check_sampling_dtype(field.domain, dt)
return dt
[docs]
class EnergyOperator(Operator):
"""Operator which has a scalar domain as target domain.
It is intended as an objective function for field inference. It can
implement a positive definite, symmetric form (called `metric`) that is
used as curvature for second-order minimizations.
Examples
--------
- Information Hamiltonian, i.e. negative-log-probabilities.
- Gibbs free energy, i.e. an averaged Hamiltonian, aka Kullback-Leibler
divergence.
"""
_target = DomainTuple.scalar_domain()
[docs]
class LikelihoodEnergyOperator(EnergyOperator):
"""Represent a negative log-likelihood.
The input to the Operator are the parameters of the negative log-likelihood.
Unlike a general `EnergyOperator`, the metric of a
`LikelihoodEnergyOperator` is the Fisher information metric of the
likelihood.
"""
[docs]
def __init__(self, data_residual, sqrt_data_metric_at):
from ..extra import is_operator
if data_residual is not None and not is_operator(data_residual):
raise TypeError(f"{data_residual} is not an operator")
self._res = data_residual
self._sqrt_data_metric_at = sqrt_data_metric_at
self._name = None
[docs]
def normalized_residual(self, x):
return (self._sqrt_data_metric_at(x) @ self._res).force(x)
@property
def data_domain(self):
if self._res is None:
return None
return self._res.target
def __matmul__(self, other):
return _LikelihoodChain(self, other)
def __rmatmul__(self, other):
return _LikelihoodChain(other, self)
def __add__(self, other):
return _LikelihoodSum.make([self, other])
def __radd__(self, other):
return _LikelihoodSum.make([other, self])
[docs]
def get_metric_at(self, x):
"""Compute the Fisher information metric for a `LikelihoodEnergyOperator`
at `x` using the Jacobian of the coordinate transformation given by
:func:`~nifty8.operators.operator.Operator.get_transformation`. """
dtp, f = self.get_transformation()
bun = f(Linearization.make_var(x)).jac
return SandwichOperator.make(bun, sampling_dtype=dtp)
@property
def name(self):
return self._name
@name.setter
def name(self, x):
if isinstance(self, _LikelihoodSum):
raise RuntimeError("The name of a LikelihoodSum cannot be set. "
"Set the name of each individual LikelihoodEnergy separately.")
self._name = x
class _LikelihoodChain(LikelihoodEnergyOperator):
def __init__(self, op1, op2):
from .simple_linear_operators import PartialExtractor
self._op = _OpChain.make((op1, op2))
self._domain = self._op.domain
if isinstance(op1, ScalingOperator):
res = op2._res
sqrt_data_metric_at = op2._sqrt_data_metric_at
elif op1._res is None:
res = None
sqrt_data_metric_at = None
else:
if isinstance(op2.target, MultiDomain):
extract = PartialExtractor(op2.target, op1._res.domain)
else:
extract = Operator.identity_operator(op2.target)
res = op1._res @ extract @ op2
sqrt_data_metric_at = lambda x: op1._sqrt_data_metric_at(op2.force(x))
super(_LikelihoodChain, self).__init__(res, sqrt_data_metric_at)
self.name = (op2 if isinstance(op1, ScalingOperator) else op1).name
def get_transformation(self):
scaled_lh = isinstance(self._op._ops[0], ScalingOperator)
ii = 1 if scaled_lh else 0
tr = self._op._ops[ii].get_transformation()
if tr is None:
return tr
dtype, trafo = tr
if scaled_lh:
trafo = trafo.scale(np.sqrt(self._op._ops[0]._factor))
return dtype, _OpChain.make((trafo,)+self._op._ops[ii+1:])
def apply(self, x):
self._check_input(x)
return self._op(x)
def _simplify_for_constant_input_nontrivial(self, c_inp):
return self._op._simplify_for_constant_input_nontrivial(c_inp)
def __repr__(self):
return self._op.__repr__()
class _LikelihoodSum(LikelihoodEnergyOperator):
def __init__(self, ops, _callingfrommake=False):
from .simple_linear_operators import PrependKey
if not _callingfrommake:
raise NotImplementedError
if len(set([isinstance(oo.domain, DomainTuple) for oo in ops])) > 1:
raise RuntimeError("Some operators have DomainTuple and others have "
"MultiDomain as domain. This should not happen.")
self._ops = ops
res, prep, data_ops = [], [], []
for ii, oo in enumerate(ops):
rr = oo._res
if rr is None:
continue
tgt = oo.data_domain
lprep = Operator.identity_operator(tgt)
key = self._get_name(ii)
if isinstance(lprep.target, DomainTuple):
lprep = lprep.ducktape_left("")
else:
key = key + ": "
lprep = PrependKey(lprep.target, key) @ lprep
prep.append(lprep)
res.append(lprep @ rr)
data_ops.append(oo)
def sqrt_data_metric_at(x):
return reduce(add, (pp @ oo._sqrt_data_metric_at(x) @ pp.adjoint
for pp, oo in zip(prep, data_ops)))
lst = self._all_names()
if len(lst) != len(set(lst)):
raise ValueError(f"Name collision in likelihoods detected: {lst}")
data_residuals = reduce(add, res)
super(_LikelihoodSum, self).__init__(data_residuals, sqrt_data_metric_at)
self._domain = data_residuals.domain
@classmethod
def unpack(cls, ops, res):
for op in ops:
if isinstance(op, cls):
res = cls.unpack(op._ops, res)
else:
res = res + [op]
return res
@classmethod
def make(cls, ops):
res = cls.unpack(ops, [])
if len(res) == 1:
return res[0]
return cls(res, _callingfrommake=True)
def apply(self, x):
from ..linearization import Linearization
self._check_input(x)
return _OpSum._apply_operator_sum(x, self._ops)
def get_transformation(self):
from .simple_linear_operators import PrependKey
if any(oo.get_transformation() is None for oo in self._ops):
return None
dtype, trafo = {}, []
for ii, lh in enumerate(self._ops):
dtp, tr = lh.get_transformation()
key = self._get_name(ii)
if isinstance(tr.target, MultiDomain):
key = key + ": "
dtype.update({key+d: dtp[d] for d in dtp.keys()})
tr = PrependKey(tr.target, key) @ tr
else:
dtype[key] = dtp
tr = tr.ducktape_left(key)
trafo.append(tr)
return dtype, reduce(add, trafo)
def _all_names(self):
return [self._get_name(ii) for ii in range(len(self._ops))]
def _get_name(self, i):
res = self._ops[i].name
if res is None:
return f"Likelihood {i}"
return res
def __repr__(self):
subs = []
for ii, oo in enumerate(self._ops):
subs.append(f"*{self._get_name(ii)}*")
subs.append(oo.__repr__())
return "_LikelihoodSum:\n" + utilities.indent("\n".join(subs))
[docs]
class Squared2NormOperator(EnergyOperator):
"""Computes the square of the L2-norm of the output of an operator.
Parameters
----------
domain : Domain, DomainTuple or tuple of Domain
Domain of the operator in which the L2-norm shall be computed.
"""
[docs]
def __init__(self, domain):
self._domain = domain
[docs]
def apply(self, x):
self._check_input(x)
if x.jac is None:
return x.vdot(x)
res = x.val.vdot(x.val)
return x.new(res, VdotOperator(2*x.val))
[docs]
class VariableCovarianceGaussianEnergy(LikelihoodEnergyOperator):
"""Computes the negative log pdf of a Gaussian with unknown covariance.
The covariance is assumed to be diagonal.
.. math ::
E(s,D) = - \\log G(s, C) = 0.5 (s)^\\dagger C (s) - 0.5 tr log(C),
an information energy for a Gaussian distribution with residual s and
inverse diagonal covariance C.
The domain of this energy will be a MultiDomain with two keys,
the target will be the scalar domain.
Parameters
----------
domain : Domain, DomainTuple, tuple of Domain
domain of the residual and domain of the covariance diagonal.
residual_key : key
Residual key of the Gaussian.
inverse_covariance_key : key
Inverse covariance diagonal key of the Gaussian.
sampling_dtype : np.dtype
Data type of the samples. Usually either 'np.float*' or 'np.complex*'
use_full_fisher: boolean
Determines if the proper Fisher information metric should be used as
`metric`. If False, the same approximation as in `get_transformation`
is used. Default is True.
"""
[docs]
def __init__(self, domain, residual_key, inverse_covariance_key,
sampling_dtype, use_full_fisher=True):
self._kr = str(residual_key)
self._ki = str(inverse_covariance_key)
dom = DomainTuple.make(domain)
self._domain = MultiDomain.make({self._kr: dom, self._ki: dom})
self._dt = {self._kr: sampling_dtype, self._ki: np.float64}
_check_sampling_dtype(self._domain, self._dt)
self._cplx = iscomplextype(sampling_dtype)
self._use_full_fisher = use_full_fisher
super(VariableCovarianceGaussianEnergy, self).__init__(
Operator.identity_operator(dom).ducktape(self._kr),
lambda x: makeOp(x[self._ki].sqrt()))
[docs]
def apply(self, x):
self._check_input(x)
r, i = x[self._kr], x[self._ki]
if self._cplx:
res = 0.5*r.vdot(r*i.real).real - i.log().sum()
else:
res = 0.5*(r.vdot(r*i) - i.log().sum())
if not x.want_metric:
return res
if not self._use_full_fisher:
return res.add_metric(self.get_metric_at(x.val))
fct = 1. if self._cplx else 0.5
met = {self._kr: i.val, self._ki: fct*i.val**(-2)}
met = MultiField.from_dict(met, domain=self._domain)
met = makeOp(met, sampling_dtype=self._dt)
return res.add_metric(met)
def _simplify_for_constant_input_nontrivial(self, c_inp):
from .simplify_for_const import ConstantLikelihoodEnergyOperator
myassert(len(c_inp.keys()) == 1)
key = c_inp.keys()[0]
myassert(key in self._domain.keys())
cst = c_inp[key]
if key == self._kr:
res = _SpecialGammaEnergy(cst).ducktape(self._ki)
else:
icov = makeOp(cst, sampling_dtype=self._dt[self._kr])
res = GaussianEnergy(data=None, inverse_covariance=icov).ducktape(self._kr)
trlog = cst.log().sum().val_rw()
if not self._cplx:
trlog /= 2
res = res + ConstantLikelihoodEnergyOperator(-trlog)
res = res + ConstantLikelihoodEnergyOperator(0.)
myassert(res.target is self.target)
return None, res
class _SpecialGammaEnergy(LikelihoodEnergyOperator):
def __init__(self, residual):
from .simplify_for_const import ConstantOperator
self._domain = DomainTuple.make(residual.domain)
self._resi = residual
self._cplx = iscomplextype(self._resi.dtype)
self._dt = self._resi.dtype
super(_SpecialGammaEnergy, self).__init__(
ConstantOperator(self._resi, domain=self._domain),
lambda x: self.get_metric_at(x).get_sqrt())
def apply(self, x):
self._check_input(x)
r = self._resi
if self._cplx:
res = 0.5*(r*x.real).vdot(r).real - x.log().sum()
else:
res = 0.5*((r*x).vdot(r) - x.log().sum())
if not x.want_metric:
return res
return res.add_metric(self.get_metric_at(x.val))
def get_transformation(self):
sc = 1. if self._cplx else np.sqrt(0.5)
return self._dt, Operator.identity_operator(self._domain).log().scale(sc)
[docs]
class GaussianEnergy(LikelihoodEnergyOperator):
"""Computes a negative-log Gaussian.
Represents up to constants in :math:`d`:
.. math ::
E(f) = - \\log G(f-d, D) = 0.5 (f-d)^\\dagger D^{-1} (f-d),
an information energy for a Gaussian distribution with data d and
covariance D.
Parameters
----------
data : :class:`nifty8.field.Field` or None
Observed data of the Gaussian likelihood. If `inverse_covariance` is
`None`, the `dtype` of `data` is used for sampling. Default is
0.
inverse_covariance : LinearOperator
Inverse covariance of the Gaussian. Default is the identity operator.
domain : Domain, DomainTuple, tuple of Domain or MultiDomain
Operator domain. By default it is inferred from `data` or
`covariance` if specified
sampling_dtype : dtype or dict of dtype
Type used for sampling from the inverse covariance if
`inverse_covariance` and `data` is `None`. Otherwise, this parameter
does not have an effect. Default: None.
Note
----
At least one of the arguments has to be provided.
"""
[docs]
def __init__(self, data=None, inverse_covariance=None, domain=None, sampling_dtype=None):
from ..sugar import full
if inverse_covariance is not None and not isinstance(inverse_covariance, LinearOperator):
raise TypeError
self._domain = self._parseDomain(data, inverse_covariance, domain)
if not isinstance(data, (Field, MultiField)) and data is not None:
raise TypeError
self._icov = inverse_covariance
if inverse_covariance is None:
self._op = Squared2NormOperator(self._domain).scale(0.5)
dt = sampling_dtype if data is None else data.dtype
self._icov = ScalingOperator(self._domain, 1., dt)
else:
self._op = QuadraticFormOperator(inverse_covariance)
self._icov = inverse_covariance
self._data = data
if data is None:
res = Operator.identity_operator(self._domain)
else:
res = Adder(data, neg=True)
super(GaussianEnergy, self).__init__(res, lambda x: self.get_metric_at(x).get_sqrt())
icovdtype = self._icov.sampling_dtype
if icovdtype is not None and data is not None and icovdtype != data.dtype:
for i0, i1 in [(icovdtype, data.dtype), (data.dtype, icovdtype)]:
if isinstance(i0, dict) and not isinstance(i1, dict):
fst = list(i0.values())[0]
if all(elem == fst for elem in i0.values()) and i1 == fst:
return
s = "Sampling dtype of inverse covariance does not match dtype of data.\n"
s += f"icov.sampling_dtype: {icovdtype}\n"
s += f"data.dtype: {data.dtype}"
raise RuntimeError(s)
@staticmethod
def _checkEquivalence(olddom, newdom):
newdom = makeDomain(newdom)
if olddom is None:
return newdom
utilities.check_object_identity(olddom, newdom)
return newdom
def _parseDomain(self, data, inverse_covariance, domain):
dom = None
if inverse_covariance is not None:
dom = self._checkEquivalence(dom, inverse_covariance.domain)
if data is not None:
dom = self._checkEquivalence(dom, data.domain)
if domain is not None:
dom = self._checkEquivalence(dom, domain)
if dom is None:
raise ValueError("no domain given")
return dom
[docs]
def apply(self, x):
self._check_input(x)
residual = x if self._data is None else x - self._data
res = self._op(residual).real
if x.want_metric:
return res.add_metric(self.get_metric_at(x.val))
return res
[docs]
def __repr__(self):
dom = '()' if isinstance(self.domain, DomainTuple) else self.domain.keys()
return f'GaussianEnergy {dom}'
[docs]
class PoissonianEnergy(LikelihoodEnergyOperator):
"""Computes likelihood Hamiltonians of expected count field constrained by
Poissonian count data.
Represents up to an f-independent term :math:`log(d!)`:
.. math ::
E(f) = -\\log \\text{Poisson}(d|f) = \\sum f - d^\\dagger \\log(f),
where f is a :class:`Field` in data space with the expectation values for
the counts.
Parameters
----------
d : :class:`nifty8.field.Field`
Data field with counts. Needs to have integer dtype and all field
values need to be non-negative.
"""
[docs]
def __init__(self, d):
if not isinstance(d, Field) or not np.issubdtype(d.dtype, np.integer):
te = "data is of invalid data-type; counts need to be integers"
raise TypeError(te)
if np.any(d.val < 0):
ve = "count data is negative and thus can not be Poissonian"
raise ValueError(ve)
self._d = d
self._domain = DomainTuple.make(d.domain)
super(PoissonianEnergy, self).__init__(Adder(d, neg=True),
lambda x: self.get_metric_at(x).get_sqrt())
[docs]
def apply(self, x):
self._check_input(x)
res = x.sum() - x.log().vdot(self._d)
if not x.want_metric:
return res
return res.add_metric(self.get_metric_at(x.val))
[docs]
class InverseGammaEnergy(LikelihoodEnergyOperator):
"""Computes the negative log-likelihood of the inverse gamma distribution.
It negative log-pdf(x) is given by
.. math ::
\\sum_i (\\alpha_i+1)*\\ln(x_i) + \\beta_i/x_i
This is the likelihood for the variance :math:`x=S_k` given data
:math:`\\beta = 0.5 |s_k|^2` where the :class:`nifty8.field.Field`
:math:`s` is known to have the covariance :math:`S_k`.
Parameters
----------
beta : :class:`nifty8.field.Field`
beta parameter of the inverse gamma distribution
alpha : Scalar, :class:`nifty8.field.Field`, optional
alpha parameter of the inverse gamma distribution
"""
[docs]
def __init__(self, beta, alpha=-0.5):
from .simplify_for_const import ConstantOperator
if not isinstance(beta, Field):
raise TypeError
self._domain = DomainTuple.make(beta.domain)
self._beta = beta
if np.isscalar(alpha):
alpha = Field(beta.domain, np.full(beta.shape, alpha))
elif not isinstance(alpha, Field):
raise TypeError
self._alphap1 = alpha+1
if not self._beta.dtype == np.float64:
# FIXME Add proper complex support for this energy
raise TypeError
self._sampling_dtype = _field_to_dtype(self._beta)
super(InverseGammaEnergy, self).__init__(
2*ConstantOperator(self._beta, domain=self._domain),
lambda x: makeOp(x.reciprocal().sqrt()))
[docs]
def apply(self, x):
self._check_input(x)
res = x.log().vdot(self._alphap1) + x.reciprocal().vdot(self._beta)
if not x.want_metric:
return res
return res.add_metric(self.get_metric_at(x.val))
[docs]
class StudentTEnergy(LikelihoodEnergyOperator):
"""Computes likelihood energy corresponding to Student's t-distribution.
.. math ::
E_\\theta(f) = -\\log \\text{StudentT}_\\theta(f)
= \\frac{\\theta + 1}{2} \\log(1 + \\frac{f^2}{\\theta}),
where f is a field defined on `domain`. Assumes that the data is `float64`
for sampling.
Parameters
----------
domain : `Domain` or `DomainTuple`
Domain of the operator
theta : Scalar or :class:`nifty8.field.Field`
Degree of freedom parameter for the student t distribution
"""
[docs]
def __init__(self, domain, theta):
self._domain = DomainTuple.make(domain)
self._theta = theta
inp = Operator.identity_operator(self._domain)
super(StudentTEnergy, self).__init__(inp, lambda x: self.get_metric_at(x).get_sqrt())
[docs]
def apply(self, x):
self._check_input(x)
res = (((self._theta+1)/2)*(x**2/self._theta).log1p()).sum()
if not x.want_metric:
return res
return res.add_metric(self.get_metric_at(x.val))
[docs]
class BernoulliEnergy(LikelihoodEnergyOperator):
"""Computes likelihood energy of expected event frequency constrained by
event data.
.. math ::
E(f) = -\\log \\text{Bernoulli}(d|f)
= -d^\\dagger \\log f - (1-d)^\\dagger \\log(1-f),
where f is a field defined on `d.domain` with the expected
frequencies of events.
Parameters
----------
d : :class:`nifty8.field.Field`
Data field with events (1) or non-events (0).
"""
[docs]
def __init__(self, d):
if not isinstance(d, Field) or not np.issubdtype(d.dtype, np.integer):
raise TypeError
if np.any(np.logical_and(d.val != 0, d.val != 1)):
raise ValueError
self._d = d
self._domain = DomainTuple.make(d.domain)
super(BernoulliEnergy, self).__init__(Adder(d, neg=True),
lambda x: self.get_metric_at(x).get_sqrt())
[docs]
def apply(self, x):
self._check_input(x)
res = -x.log().vdot(self._d) + (1.-x).log().vdot(self._d-1.)
if not x.want_metric:
return res
return res.add_metric(self.get_metric_at(x.val))
[docs]
class StandardHamiltonian(EnergyOperator):
"""Computes an information Hamiltonian in its standard form, i.e. with the
prior being a real-valued Gaussian with unit covariance.
Let the likelihood energy be :math:`E_{lh}`. Then this operator computes:
.. math ::
H(f) = 0.5 f^\\dagger f + E_{lh}(f):
Other field priors can be represented via transformations of a white
Gaussian field into a field with the desired prior probability structure.
By implementing prior information this way, the field prior is represented
by a generative model, from which NIFTy can draw samples and infer a field
using the Maximum a Posteriori (MAP) or the Variational Bayes (VB) method.
The metric of this operator can be used as covariance for drawing Gaussian
samples.
Parameters
----------
lh : EnergyOperator
The likelihood energy.
ic_samp : IterationController
Tells an internal :class:`SamplingEnabler` which convergence criterion
to use to draw Gaussian samples.
See also
--------
`Encoding prior knowledge in the structure of the likelihood`,
Jakob Knollmüller, Torsten A. Ensslin,
`<https://arxiv.org/abs/1812.04403>`_
"""
[docs]
def __init__(self, lh, ic_samp=None):
self._lh = lh
self._prior = GaussianEnergy(data=None, domain=lh.domain, sampling_dtype=float)
self._ic_samp = ic_samp
self._domain = lh.domain
[docs]
def apply(self, x):
self._check_input(x)
lhx, prx = self._lh(x), self._prior(x)
if not x.want_metric or self._ic_samp is None:
return lhx + prx
met = SamplingEnabler(lhx.metric, prx.metric, self._ic_samp)
return (lhx+prx).add_metric(met)
@property
def prior_energy(self):
return self._prior
@property
def likelihood_energy(self):
return self._lh
@property
def iteration_controller(self):
return self._ic_samp
[docs]
def __repr__(self):
subs = 'Likelihood energy:\n{}'.format(utilities.indent(self._lh.__repr__()))
subs += '\nPrior energy:\n{}'.format(self._prior)
return 'StandardHamiltonian:\n' + utilities.indent(subs)
def _simplify_for_constant_input_nontrivial(self, c_inp):
out, lh1 = self._lh.simplify_for_constant_input(c_inp)
return out, StandardHamiltonian(lh1, self._ic_samp)
[docs]
class AveragedEnergy(EnergyOperator):
"""Averages an energy over samples.
Parameters
----------
h: Hamiltonian
The energy to be averaged.
res_samples : iterable of :class:`nifty8.field.Field`
Set of residual sample points to be added to mean field for
approximate estimation of the KL.
Notes
-----
- Having symmetrized residual samples, with both :math:`v_i` and
:math:`-v_i` being present, ensures that the distribution mean is
exactly represented.
- :class:`AveragedEnergy(h)` approximates
:math:`\\left< H(f) \\right>_{G(f-m,D)}` if the residuals :math:`f-m`
are drawn from a Gaussian distribution with covariance :math:`D`.
"""
[docs]
def __init__(self, h, res_samples):
self._h = h
self._domain = h.domain
self._res_samples = tuple(res_samples)
[docs]
def apply(self, x):
self._check_input(x)
mymap = map(lambda v: self._h(x+v), self._res_samples)
return utilities.my_sum(mymap)/len(self._res_samples)