field.py

# 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) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.

from __future__ import division
from builtins import range
import numpy as np
from . import utilities
from .domain_tuple import DomainTuple
from functools import reduce
from . import dobj

__all__ = ["Field", "sqrt", "exp", "log", "conjugate"]


class Field(object):
    """ The discrete representation of a continuous field over multiple spaces.

    In NIFTy, Fields are used to store data arrays and carry all the needed
    metainformation (i.e. the domain) for operators to be able to work on them.

    Parameters
    ----------
    domain : None, DomainTuple, tuple(Domain), or Domain

    val : None, Field, data_object, or scalar
        The values the array should contain after init. A scalar input will
        fill the whole array with this scalar. If a data_object is provided,
        its dimensions must match the domain's.

    dtype : type
        A numpy.type. Most common are float and complex.

    copy: boolean
    """

    def __init__(self, domain=None, val=None, dtype=None, copy=False):
        self._domain = self._infer_domain(domain=domain, val=val)

        dtype = self._infer_dtype(dtype=dtype, val=val)
        if isinstance(val, Field):
            if self._domain != val._domain:
                raise ValueError("Domain mismatch")
            self._val = dobj.from_object(val.val, dtype=dtype, copy=copy)
        elif (np.isscalar(val)):
            self._val = dobj.full(self._domain.shape, dtype=dtype,
                                  fill_value=val)
        elif isinstance(val, dobj.data_object):
            if self._domain.shape == val.shape:
                self._val = dobj.from_object(val, dtype=dtype, copy=copy)
            else:
                raise ValueError("Shape mismatch")
        elif val is None:
            self._val = dobj.empty(self._domain.shape, dtype=dtype)
        else:
            raise TypeError("unknown source type")

    @staticmethod
    def full(domain, val, dtype=None):
        if not np.isscalar(val):
            raise TypeError("val must be a scalar")
        return Field(DomainTuple.make(domain), val, dtype)

    @staticmethod
    def ones(domain, dtype=None):
        return Field(DomainTuple.make(domain), 1., dtype)

    @staticmethod
    def zeros(domain, dtype=None):
        return Field(DomainTuple.make(domain), 0., dtype)

    @staticmethod
    def empty(domain, dtype=None):
        return Field(DomainTuple.make(domain), None, dtype)

    @staticmethod
    def full_like(field, val, dtype=None):
        if not isinstance(field, Field):
            raise TypeError("field must be of Field type")
        return Field.full(field._domain, val, dtype)

    @staticmethod
    def zeros_like(field, dtype=None):
        if not isinstance(field, Field):
            raise TypeError("field must be of Field type")
        if dtype is None:
            dtype = field.dtype
        return Field.zeros(field._domain, dtype)

    @staticmethod
    def ones_like(field, dtype=None):
        if not isinstance(field, Field):
            raise TypeError("field must be of Field type")
        if dtype is None:
            dtype = field.dtype
        return Field.ones(field._domain, dtype)

    @staticmethod
    def empty_like(field, dtype=None):
        if not isinstance(field, Field):
            raise TypeError("field must be of Field type")
        if dtype is None:
            dtype = field.dtype
        return Field.empty(field._domain, dtype)

    @staticmethod
    def _infer_domain(domain, val=None):
        if domain is None:
            if isinstance(val, Field):
                return val._domain
            if np.isscalar(val):
                return DomainTuple.make(())  # empty domain tuple
            raise TypeError("could not infer domain from value")
        return DomainTuple.make(domain)

    @staticmethod
    def _infer_dtype(dtype, val):
        if dtype is not None:
            return dtype
        if val is None:
            raise ValueError("could not infer dtype")
        if isinstance(val, Field):
            return val.dtype
        return np.result_type(val)

    @staticmethod
    def from_random(random_type, domain, dtype=np.float64, **kwargs):
        """ Draws a random field with the given parameters.

        Parameters
        ----------
        random_type : String
            'pm1', 'normal', 'uniform' are the supported arguments for this
            method.

        domain : DomainTuple
            The domain of the output random field

        dtype : type
            The datatype of the output random field

        Returns
        -------
        out : Field
            The output object.
        """
        domain = DomainTuple.make(domain)
        return Field(domain=domain,
                     val=dobj.from_random(random_type, dtype=dtype,
                                          shape=domain.shape, **kwargs))

    def fill(self, fill_value):
        self._val.fill(fill_value)

    @property
    def val(self):
        """ Returns the data object associated with this Field.
        No copy is made.
        """
        return self._val

    @property
    def dtype(self):
        return self._val.dtype

    @property
    def domain(self):
        return self._domain

    @property
    def shape(self):
        """ Returns the total shape of the Field's data array.

        Returns
        -------
        Integer tuple containing the dimensions of the spaces in domain.
        """
        return self._domain.shape

    @property
    def size(self):
        """ Returns the total number of pixel-dimensions the field has.

        Effectively, all values from shape are multiplied.

        Returns
        -------
        out : int
            The dimension of the Field.
        """
        return self._domain.size

    @property
    def real(self):
        """ The real part of the field (data is not copied)."""
        if not np.issubdtype(self.dtype, np.complexfloating):
            return self
        return Field(self._domain, self.val.real)

    @property
    def imag(self):
        """ The imaginary part of the field (data is not copied)."""
        if not np.issubdtype(self.dtype, np.complexfloating):
            raise ValueError(".imag called on a non-complex Field")
        return Field(self._domain, self.val.imag)

    def copy(self):
        """ Returns a full copy of the Field.

        The returned object will be an identical copy of the original Field.

        Returns
        -------
        out : Field
            The output object. An identical copy of 'self'.
        """
        return Field(val=self, copy=True)

    def scalar_weight(self, spaces=None):
        if np.isscalar(spaces):
            return self._domain[spaces].scalar_dvol()

        if spaces is None:
            spaces = range(len(self._domain))
        res = 1.
        for i in spaces:
            tmp = self._domain[i].scalar_dvol()
            if tmp is None:
                return None
            res *= tmp
        return res

    def total_volume(self, spaces=None):
        if np.isscalar(spaces):
            return self._domain[spaces].total_volume()

        if spaces is None:
            spaces = range(len(self._domain))
        res = 1.
        for i in spaces:
            res *= self._domain[i].total_volume()
        return res

    def weight(self, power=1, spaces=None, out=None):
        """ Weights the pixels of `self` with their invidual pixel-volume.

        Parameters
        ----------
        power : number
            The pixels get weighted with the volume-factor**power.

        spaces : tuple of ints
            Determines on which subspace the operation takes place.

        out : Field or None
            if not None, the result is returned in a new Field
            otherwise the contents of "out" are overwritten with the result.
            "out" may be identical to "self"!

        Returns
        -------
        out : Field
            The weighted field.
        """
        if out is None:
            out = self.copy()
        else:
            if out is not self:
                out.copy_content_from(self)

        spaces = utilities.parse_spaces(spaces, len(self._domain))

        fct = 1.
        for ind in spaces:
            wgt = self._domain[ind].dvol()
            if np.isscalar(wgt):
                fct *= wgt
            else:
                new_shape = np.ones(len(self.shape), dtype=np.int)
                new_shape[self._domain.axes[ind][0]:
                          self._domain.axes[ind][-1]+1] = wgt.shape
                wgt = wgt.reshape(new_shape)
                if dobj.distaxis(self._val) >= 0 and ind == 0:
                    # we need to distribute the weights along axis 0
                    wgt = dobj.local_data(dobj.from_global_data(wgt))
                lout = dobj.local_data(out.val)
                lout *= wgt**power
        fct = fct**power
        if fct != 1.:
            out *= fct

        return out

    def vdot(self, x=None, spaces=None):
        """ Computes the volume-factor-aware dot product of 'self' with x.

        Parameters
        ----------
        x : Field
            x must live on the same domain as `self`.

        spaces : None, int or tuple of ints (default: None)
            The dot product is only carried out over the sub-domains in this
            tuple. If None, it is carried out over all sub-domains.

        Returns
        -------
        out : float, complex, either scalar (for full dot products)
                              or Field (for partial dot products)
        """
        if not isinstance(x, Field):
            raise ValueError("The dot-partner must be an instance of " +
                             "the NIFTy field class")

        if x._domain != self._domain:
            raise ValueError("Domain mismatch")

        ndom = len(self._domain)
        spaces = utilities.parse_spaces(spaces, ndom)

        if len(spaces) == ndom:
            return dobj.vdot(self.val, x.val)
        # If we arrive here, we have to do a partial dot product.
        # For the moment, do this the explicit, non-optimized way
        return (self.conjugate()*x).sum(spaces=spaces)

    def norm(self):
        """ Computes the L2-norm of the field values.

        Returns
        -------
        norm : float
            The L2-norm of the field values.
        """
        return np.sqrt(np.abs(self.vdot(x=self)))

    def conjugate(self):
        """ Returns the complex conjugate of the field.

        Returns
        -------
        The complex conjugated field.
        """
        return Field(self._domain, self.val.conjugate())

    # ---General unary/contraction methods---

    def __pos__(self):
        return self.copy()

    def __neg__(self):
        return Field(self._domain, -self.val)

    def __abs__(self):
        return Field(self._domain, dobj.abs(self.val))

    def _contraction_helper(self, op, spaces):
        if spaces is None:
            return getattr(self.val, op)()

        spaces = utilities.parse_spaces(spaces, len(self._domain))

        axes_list = tuple(self._domain.axes[sp_index] for sp_index in spaces)

        if len(axes_list) > 0:
            axes_list = reduce(lambda x, y: x+y, axes_list)

        # perform the contraction on the data
        data = getattr(self.val, op)(axis=axes_list)

        # check if the result is scalar or if a result_field must be constr.
        if np.isscalar(data):
            return data
        else:
            return_domain = tuple(dom
                                  for i, dom in enumerate(self._domain)
                                  if i not in spaces)

            return Field(domain=return_domain, val=data, copy=False)

    def sum(self, spaces=None):
        return self._contraction_helper('sum', spaces)

    def integrate(self, spaces=None):
        swgt = self.scalar_weight(spaces)
        if swgt is not None:
            res = self.sum(spaces)
            res *= swgt
            return res
        tmp = self.weight(1, spaces=spaces)
        return tmp.sum(spaces)

    def prod(self, spaces=None):
        return self._contraction_helper('prod', spaces)

    def all(self, spaces=None):
        return self._contraction_helper('all', spaces)

    def any(self, spaces=None):
        return self._contraction_helper('any', spaces)

    def min(self, spaces=None):
        return self._contraction_helper('min', spaces)

    def max(self, spaces=None):
        return self._contraction_helper('max', spaces)

    def mean(self, spaces=None):
        if self.scalar_weight(spaces) is not None:
            return self._contraction_helper('mean', spaces)
        # MR FIXME: not very efficient
        tmp = self.weight(1)
        return tmp.sum(spaces)*(1./tmp.total_volume(spaces))

    def var(self, spaces=None):
        if self.scalar_weight(spaces) is not None:
            return self._contraction_helper('var', spaces)
        # MR FIXME: not very efficient or accurate
        m1 = self.mean(spaces)
        if np.issubdtype(self.dtype, np.complexfloating):
            sq = abs(self)**2
            m1 = abs(m1)**2
        else:
            sq = self**2
            m1 **= 2
        return sq.mean(spaces) - m1

    def std(self, spaces=None):
        if self.scalar_weight(spaces) is not None:
            return self._contraction_helper('std', spaces)
        return sqrt(self.var(spaces))

    def copy_content_from(self, other):
        if not isinstance(other, Field):
            raise TypeError("argument must be a Field")
        if other._domain != self._domain:
            raise ValueError("domains are incompatible.")
        dobj.local_data(self.val)[()] = dobj.local_data(other.val)[()]

    def _binary_helper(self, other, op):
        # if other is a field, make sure that the domains match
        if isinstance(other, Field):
            if other._domain != self._domain:
                raise ValueError("domains are incompatible.")
            tval = getattr(self.val, op)(other.val)
            return self if tval is self.val else Field(self._domain, tval)

        if np.isscalar(other) or isinstance(other, dobj.data_object):
            tval = getattr(self.val, op)(other)
            return self if tval is self.val else Field(self._domain, tval)

        return NotImplemented

    def __add__(self, other):
        return self._binary_helper(other, op='__add__')

    def __radd__(self, other):
        return self._binary_helper(other, op='__radd__')

    def __iadd__(self, other):
        return self._binary_helper(other, op='__iadd__')

    def __sub__(self, other):
        return self._binary_helper(other, op='__sub__')

    def __rsub__(self, other):
        return self._binary_helper(other, op='__rsub__')

    def __isub__(self, other):
        return self._binary_helper(other, op='__isub__')

    def __mul__(self, other):
        return self._binary_helper(other, op='__mul__')

    def __rmul__(self, other):
        return self._binary_helper(other, op='__rmul__')

    def __imul__(self, other):
        return self._binary_helper(other, op='__imul__')

    def __div__(self, other):
        return self._binary_helper(other, op='__div__')

    def __truediv__(self, other):
        return self._binary_helper(other, op='__truediv__')

    def __rdiv__(self, other):
        return self._binary_helper(other, op='__rdiv__')

    def __rtruediv__(self, other):
        return self._binary_helper(other, op='__rtruediv__')

    def __idiv__(self, other):
        return self._binary_helper(other, op='__idiv__')

    def __pow__(self, other):
        return self._binary_helper(other, op='__pow__')

    def __rpow__(self, other):
        return self._binary_helper(other, op='__rpow__')

    def __ipow__(self, other):
        return self._binary_helper(other, op='__ipow__')

    def __repr__(self):
        return "<nifty4.Field>"

    def __str__(self):
        return "nifty4.Field instance\n- domain      = " + \
               self._domain.__str__() + \
               "\n- val         = " + repr(self.val)


# Arithmetic functions working on Fields

def _math_helper(x, function, out):
    if not isinstance(x, Field):
        raise TypeError("This function only accepts Field objects.")
    if out is not None:
        if not isinstance(out, Field) or x._domain != out._domain:
            raise ValueError("Bad 'out' argument")
        function(x.val, out=out.val)
        return out
    else:
        return Field(domain=x._domain, val=function(x.val))


def sqrt(x, out=None):
    return _math_helper(x, dobj.sqrt, out)


def exp(x, out=None):
    return _math_helper(x, dobj.exp, out)


def log(x, out=None):
    return _math_helper(x, dobj.log, out)


def tanh(x, out=None):
    return _math_helper(x, dobj.tanh, out)


def conjugate(x, out=None):
    return _math_helper(x, dobj.conjugate, out)