merged master

nifty5/__init__.py

@@ -43,8 +43,9 @@ from .operators.slope_operator import SlopeOperator
 from .operators.smoothness_operator import SmoothnessOperator
 from .operators.symmetrizing_operator import SymmetrizingOperator
 from .operators.block_diagonal_operator import BlockDiagonalOperator
+from .operators.outer_product_operator import OuterProduct
 from .operators.simple_linear_operators import (
-    VdotOperator, SumReductionOperator, ConjugationOperator, Realizer,
+    VdotOperator, ConjugationOperator, Realizer,
     FieldAdapter, GeometryRemover, NullOperator)
 from .operators.energy_operators import (
     EnergyOperator, GaussianEnergy, PoissonianEnergy, InverseGammaLikelihood,

nifty5/fft.py

+from __future__ import absolute_import, division, print_function
+
+from .utilities import iscomplextype
+import numpy as np
+
+
+_use_fftw = True
+
+
+if _use_fftw:
+    import pyfftw
+    from pyfftw.interfaces.numpy_fft import fftn, rfftn, ifftn
+    pyfftw.interfaces.cache.enable()
+    pyfftw.interfaces.cache.set_keepalive_time(1000.)
+    # Optional extra arguments for the FFT calls
+    # if exact reproducibility is needed,
+    # set "planner_effort" to "FFTW_ESTIMATE"
+    import os
+    nthreads = int(os.getenv("OMP_NUM_THREADS", "1"))
+    _fft_extra_args = dict(planner_effort='FFTW_ESTIMATE', threads=nthreads)
+else:
+    from numpy.fft import fftn, rfftn, ifftn
+    _fft_extra_args={}
+
+
+def hartley(a, axes=None):
+    # Check if the axes provided are valid given the shape
+    if axes is not None and \
+            not all(axis < len(a.shape) for axis in axes):
+        raise ValueError("Provided axes do not match array shape")
+    if iscomplextype(a.dtype):
+        raise TypeError("Hartley transform requires real-valued arrays.")
+
+    tmp = rfftn(a, axes=axes, **_fft_extra_args)
+
+    def _fill_array(tmp, res, axes):
+        if axes is None:
+            axes = tuple(range(tmp.ndim))
+        lastaxis = axes[-1]
+        ntmplast = tmp.shape[lastaxis]
+        slice1 = (slice(None),)*lastaxis + (slice(0, ntmplast),)
+        np.add(tmp.real, tmp.imag, out=res[slice1])
+
+        def _fill_upper_half(tmp, res, axes):
+            lastaxis = axes[-1]
+            nlast = res.shape[lastaxis]
+            ntmplast = tmp.shape[lastaxis]
+            nrem = nlast - ntmplast
+            slice1 = [slice(None)]*lastaxis + [slice(ntmplast, None)]
+            slice2 = [slice(None)]*lastaxis + [slice(nrem, 0, -1)]
+            for i in axes[:-1]:
+                slice1[i] = slice(1, None)
+                slice2[i] = slice(None, 0, -1)
+            slice1 = tuple(slice1)
+            slice2 = tuple(slice2)
+            np.subtract(tmp[slice2].real, tmp[slice2].imag, out=res[slice1])
+            for i, ax in enumerate(axes[:-1]):
+                dim1 = (slice(None),)*ax + (slice(0, 1),)
+                axes2 = axes[:i] + axes[i+1:]
+                _fill_upper_half(tmp[dim1], res[dim1], axes2)
+
+        _fill_upper_half(tmp, res, axes)
+        return res
+
+    return _fill_array(tmp, np.empty_like(a), axes)
+
+
+# Do a real-to-complex forward FFT and return the _full_ output array
+def my_fftn_r2c(a, axes=None):
+    # Check if the axes provided are valid given the shape
+    if axes is not None and \
+            not all(axis < len(a.shape) for axis in axes):
+        raise ValueError("Provided axes do not match array shape")
+    if iscomplextype(a.dtype):
+        raise TypeError("Transform requires real-valued input arrays.")
+
+    tmp = rfftn(a, axes=axes, **_fft_extra_args)
+
+    def _fill_complex_array(tmp, res, axes):
+        if axes is None:
+            axes = tuple(range(tmp.ndim))
+        lastaxis = axes[-1]
+        ntmplast = tmp.shape[lastaxis]
+        slice1 = [slice(None)]*lastaxis + [slice(0, ntmplast)]
+        res[tuple(slice1)] = tmp
+
+        def _fill_upper_half_complex(tmp, res, axes):
+            lastaxis = axes[-1]
+            nlast = res.shape[lastaxis]
+            ntmplast = tmp.shape[lastaxis]
+            nrem = nlast - ntmplast
+            slice1 = [slice(None)]*lastaxis + [slice(ntmplast, None)]
+            slice2 = [slice(None)]*lastaxis + [slice(nrem, 0, -1)]
+            for i in axes[:-1]:
+                slice1[i] = slice(1, None)
+                slice2[i] = slice(None, 0, -1)
+            # np.conjugate(tmp[slice2], out=res[slice1])
+            res[tuple(slice1)] = np.conjugate(tmp[tuple(slice2)])
+            for i, ax in enumerate(axes[:-1]):
+                dim1 = tuple([slice(None)]*ax + [slice(0, 1)])
+                axes2 = axes[:i] + axes[i+1:]
+                _fill_upper_half_complex(tmp[dim1], res[dim1], axes2)
+
+        _fill_upper_half_complex(tmp, res, axes)
+        return res
+
+    return _fill_complex_array(tmp, np.empty_like(a, dtype=tmp.dtype), axes)
+
+
+def my_fftn(a, axes=None):
+    return fftn(a, axes=axes, **_fft_extra_args)

nifty5/field.py

@@ -327,6 +327,23 @@ class Field(object):
 
         return Field.from_local_data(self._domain, aout)
 
+    def outer(self, x):
+        """ Computes the outer product of 'self' with x.
+
+        Parameters
+        ----------
+        x : Field
+
+        Returns
+        ----------
+        Field, lives on the product space of self.domain and x.domain
+        """
+        if not isinstance(x, Field):
+            raise TypeError("The multiplier must be an instance of " +
+                            "the NIFTy field class")
+        from .operators.outer_product_operator import OuterProduct
+        return OuterProduct(self, x.domain)(x)
+
     def vdot(self, x=None, spaces=None):
         """ Computes the dot product of 'self' with x.
 

nifty5/library/correlated_fields.py

@@ -28,15 +28,18 @@ from ..operators.simple_linear_operators import FieldAdapter
 from ..operators.scaling_operator import ScalingOperator
 
 
-def CorrelatedField(s_space, amplitude_model):
+def CorrelatedField(s_space, amplitude_model, name='xi'):
     '''
     Function for construction of correlated fields
 
     Parameters
     ----------
-    s_space : Field domain
-
-    amplitude_model : model for correlation structure
+    s_space : Domain
+        Field domain
+    amplitude_model: Operator
+        model for correlation structure
+    name : string
+        MultiField component name
     '''
     h_space = s_space.get_default_codomain()
     ht = HarmonicTransformOperator(h_space, s_space)
@@ -45,11 +48,11 @@ def CorrelatedField(s_space, amplitude_model):
     A = power_distributor(amplitude_model)
     vol = h_space.scalar_dvol
     vol = ScalingOperator(vol ** (-0.5),h_space)
-    return ht(vol(A)*FieldAdapter(MultiDomain.make({"xi": h_space}), "xi"))
+    return ht(vol(A)*FieldAdapter(MultiDomain.make({name: h_space}), name))
 
 
 def MfCorrelatedField(s_space_spatial, s_space_energy, amplitude_model_spatial,
-                      amplitude_model_energy):
+                      amplitude_model_energy, name="xi"):
     '''
     Method for construction of correlated multi-frequency fields
     '''
@@ -67,11 +70,11 @@ def MfCorrelatedField(s_space_spatial, s_space_energy, amplitude_model_spatial,
     pd_energy = PowerDistributor(pd_spatial.domain, p_space_energy, 1)
     pd = pd_spatial(pd_energy)
 
-    dom_distr_spatial = ContractionOperator(pd.domain, 0).adjoint
-    dom_distr_energy = ContractionOperator(pd.domain, 1).adjoint
+    dom_distr_spatial = ContractionOperator(pd.domain, 1).adjoint
+    dom_distr_energy = ContractionOperator(pd.domain, 0).adjoint
 
     a_spatial = dom_distr_spatial(amplitude_model_spatial)
     a_energy = dom_distr_energy(amplitude_model_energy)
     a = a_spatial*a_energy
     A = pd(a)
-    return ht(A*FieldAdapter(MultiDomain.make({"xi": h_space}), "xi"))
+    return ht(A*FieldAdapter(MultiDomain.make({name: h_space}), name))

nifty5/linearization.py

@@ -126,6 +126,19 @@ class Linearization(object):
     def __rmul__(self, other):
         return self.__mul__(other)
 
+    def outer(self, other):
+        from .operators.outer_product_operator import OuterProduct
+        if isinstance(other, Linearization):
+            return self.new(
+                OuterProduct(self._val, other.target)(other._val),
+                OuterProduct(self._jac(self._val), other.target)._myadd(
+                    OuterProduct(self._val, other.target)(other._jac), False))
+        if np.isscalar(other):
+            return self.__mul__(other)
+        if isinstance(other, (Field, MultiField)):
+            return self.new(OuterProduct(self._val, other.domain)(other),
+                            OuterProduct(self._jac(self._val), other.domain))
+
     def vdot(self, other):
         from .operators.simple_linear_operators import VdotOperator
         if isinstance(other, (Field, MultiField)):
@@ -137,11 +150,27 @@ class Linearization(object):
             VdotOperator(self._val)(other._jac) +
             VdotOperator(other._val)(self._jac))
 
-    def sum(self):
-        from .operators.simple_linear_operators import SumReductionOperator
-        return self.new(
-            Field.scalar(self._val.sum()),
-            SumReductionOperator(self._jac.target)(self._jac))
+    def sum(self, spaces=None):
+        from .operators.contraction_operator import ContractionOperator
+        if spaces is None:
+            return self.new(
+                Field.scalar(self._val.sum()),
+                ContractionOperator(self._jac.target, None)(self._jac))
+        else:
+            return self.new(
+                self._val.sum(spaces),
+                ContractionOperator(self._jac.target, spaces)(self._jac))
+
+    def integrate(self, spaces=None):
+        from .operators.contraction_operator import ContractionOperator
+        if spaces is None:
+            return self.new(
+                Field.scalar(self._val.integrate()),
+                ContractionOperator(self._jac.target, None, 1)(self._jac))
+        else:
+            return self.new(
+                self._val.integrate(spaces),
+                ContractionOperator(self._jac.target, spaces, 1)(self._jac))
 
     def exp(self):
         tmp = self._val.exp()
@@ -178,6 +207,14 @@ class Linearization(object):
         return Linearization(field, NullOperator(field.domain, field.domain),
                              want_metric=want_metric)
 
+    @staticmethod
+    def make_const_empty_input(field, want_metric=False):
+        from .operators.simple_linear_operators import NullOperator
+        from .multi_domain import MultiDomain
+        return Linearization(
+            field, NullOperator(MultiDomain.make({}), field.domain),
+            want_metric=want_metric)
+
     @staticmethod
     def make_partial_var(field, constants, want_metric=False):
         from .operators.scaling_operator import ScalingOperator

nifty5/operators/contraction_operator.py

@@ -37,28 +37,37 @@ class ContractionOperator(LinearOperator):
     ----------
     domain : Domain, tuple of Domain or DomainTuple
     spaces : int or tuple of int
-        The elements of "domain" which are taken as target.
+        The elements of "domain" which are contracted.
+    weight : int, default=0
+        if nonzero, the fields living on self.domain are weighted with the
+        specified power.
     """
 
-    def __init__(self, domain, spaces):
+    def __init__(self, domain, spaces, weight=0):
         self._domain = DomainTuple.make(domain)
         self._spaces = utilities.parse_spaces(spaces, len(self._domain))
         self._target = [
-            dom for i, dom in enumerate(self._domain) if i in self._spaces
+            dom for i, dom in enumerate(self._domain) if i not in self._spaces
         ]
         self._target = DomainTuple.make(self._target)
+        self._weight = weight
         self._capability = self.TIMES | self.ADJOINT_TIMES
 
     def apply(self, x, mode):
         self._check_input(x, mode)
         if mode == self.ADJOINT_TIMES:
-            ldat = x.local_data if 0 in self._spaces else x.to_global_data()
+            ldat = x.to_global_data() if 0 in self._spaces else x.local_data
             shp = []
             for i, dom in enumerate(self._domain):
                 tmp = dom.shape if i > 0 else dom.local_shape
-                shp += tmp if i in self._spaces else (1,)*len(dom.shape)
+                shp += tmp if i not in self._spaces else (1,)*len(dom.shape)
             ldat = np.broadcast_to(ldat.reshape(shp), self._domain.local_shape)
-            return Field.from_local_data(self._domain, ldat)
+            res = Field.from_local_data(self._domain, ldat)
+            if self._weight != 0:
+                res = res.weight(self._weight, spaces=self._spaces)
+            return res
         else:
-            return x.sum(
-                [s for s in range(len(x.domain)) if s not in self._spaces])
+            if self._weight != 0:
+                x = x.weight(self._weight, spaces=self._spaces)
+            res = x.sum(self._spaces)
+            return res if isinstance(res, Field) else Field.scalar(res)

nifty5/operators/harmonic_operators.py

@@ -20,7 +20,7 @@ from __future__ import absolute_import, division, print_function
 
 import numpy as np
 
-from .. import dobj, utilities
+from .. import dobj, utilities, fft
 from ..compat import *
 from ..domain_tuple import DomainTuple
 from ..domains.gl_space import GLSpace
@@ -74,8 +74,6 @@ class FFTOperator(LinearOperator):
         adom.check_codomain(target)
         target.check_codomain(adom)
 
-        utilities.fft_prep()
-
     def apply(self, x, mode):
         from pyfftw.interfaces.numpy_fft import fftn, ifftn
         self._check_input(x, mode)
@@ -174,8 +172,6 @@ class HartleyOperator(LinearOperator):
         adom.check_codomain(target)
         target.check_codomain(adom)
 
-        utilities.fft_prep()
-
     def apply(self, x, mode):
         self._check_input(x, mode)
         if utilities.iscomplextype(x.dtype):
@@ -190,14 +186,14 @@ class HartleyOperator(LinearOperator):
         oldax = dobj.distaxis(x.val)
         if oldax not in axes:  # straightforward, no redistribution needed
             ldat = x.local_data
-            ldat = utilities.hartley(ldat, axes=axes)
+            ldat = fft.hartley(ldat, axes=axes)
             tmp = dobj.from_local_data(x.val.shape, ldat, distaxis=oldax)
         elif len(axes) < len(x.shape) or len(axes) == 1:
             # we can use one Hartley pass in between the redistributions
             tmp = dobj.redistribute(x.val, nodist=axes)
             newax = dobj.distaxis(tmp)
             ldat = dobj.local_data(tmp)
-            ldat = utilities.hartley(ldat, axes=axes)
+            ldat = fft.hartley(ldat, axes=axes)
             tmp = dobj.from_local_data(tmp.shape, ldat, distaxis=newax)
             tmp = dobj.redistribute(tmp, dist=oldax)
         else:  # two separate, full FFTs needed
@@ -211,7 +207,7 @@ class HartleyOperator(LinearOperator):
             rem_axes = tuple(i for i in axes if i != oldax)
             tmp = x.val
             ldat = dobj.local_data(tmp)
-            ldat = utilities.my_fftn_r2c(ldat, axes=rem_axes)
+            ldat = fft.my_fftn_r2c(ldat, axes=rem_axes)
             if oldax != 0:
                 raise ValueError("bad distribution")
             ldat2 = ldat.reshape((ldat.shape[0],
@@ -220,7 +216,7 @@ class HartleyOperator(LinearOperator):
             tmp = dobj.from_local_data(shp2d, ldat2, distaxis=0)
             tmp = dobj.transpose(tmp)
             ldat2 = dobj.local_data(tmp)
-            ldat2 = utilities.my_fftn(ldat2, axes=(1,))
+            ldat2 = fft.my_fftn(ldat2, axes=(1,))
             ldat2 = ldat2.real+ldat2.imag
             tmp = dobj.from_local_data(tmp.shape, ldat2, distaxis=0)
             tmp = dobj.transpose(tmp)
@@ -289,6 +285,10 @@ class SHTOperator(LinearOperator):
         else:
             self.sjob.set_Healpix_geometry(target.nside)
 
+    def __reduce__(self):
+        return (_unpickleSHTOperator,
+                (self._domain, self._target[self._space], self._space))
+
     def apply(self, x, mode):
         self._check_input(x, mode)
         if utilities.iscomplextype(x.dtype):
@@ -337,6 +337,10 @@ class SHTOperator(LinearOperator):
         return Field(tdom, dobj.ensure_default_distributed(odat))
 
 
+def _unpickleSHTOperator(*args):
+    return SHTOperator(*args)
+
+
 class HarmonicTransformOperator(LinearOperator):
     """Transforms between a harmonic domain and a position domain counterpart.
 

nifty5/operators/operator_adapter.py

@@ -69,6 +69,6 @@ class OperatorAdapter(LinearOperator):
 
     def __repr__(self):
         from ..utilities import indent
-        mode = ["adjoint", "inverse", "adjoint inverse"][self._trafo]
+        mode = ["adjoint", "inverse", "adjoint inverse"][self._trafo-1]
         res = "OperatorAdapter: {}\n".format(mode)
         return res + indent(self._op.__repr__())

nifty5/operators/outer_product_operator.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 absolute_import, division, print_function
+
+import itertools
+
+import numpy as np
+
+from .. import dobj, utilities
+from ..compat import *
+from ..domain_tuple import DomainTuple
+from ..domains.rg_space import RGSpace
+from ..multi_field import MultiField, MultiDomain
+from ..field import Field
+from .linear_operator import LinearOperator
+import operator
+
+
+class OuterProduct(LinearOperator):
+    """Performs the pointwise outer product of two fields.
+
+    Parameters
+    ---------
+    field: Field,
+    domain: DomainTuple, the domain of the input field
+    ---------
+    """
+
+    def __init__(self, field, domain):
+
+        self._domain = domain
+        self._field = field
+        self._target = DomainTuple.make(
+            tuple(sub_d for sub_d in field.domain._dom + domain._dom))
+
+        self._capability = self.TIMES | self.ADJOINT_TIMES
+
+    def apply(self, x, mode):
+        self._check_input(x, mode)
+        if mode == self.TIMES:
+            return Field.from_global_data(
+                self._target, np.multiply.outer(
+                    self._field.to_global_data(), x.to_global_data()))
+        axes = len(self._field.shape)
+        return Field.from_global_data(
+            self._domain, np.tensordot(
+                self._field.to_global_data(), x.to_global_data(),  axes))
+

nifty5/operators/qht_operator.py

@@ -20,9 +20,10 @@ from __future__ import absolute_import, division, print_function
 
 from .. import dobj
 from ..compat import *
+from .. import fft
 from ..domain_tuple import DomainTuple
 from ..field import Field
-from ..utilities import hartley, infer_space
+from ..utilities import infer_space
 from .linear_operator import LinearOperator
 
 
@@ -69,5 +70,5 @@ class QHTOperator(LinearOperator):
         for i in rng:
             sl = (slice(None),)*i + (slice(1, None),)
             v, tmp = dobj.ensure_not_distributed(v, (i,))
-            tmp[sl] = hartley(tmp[sl], axes=(i,))
+            tmp[sl] = fft.hartley(tmp[sl], axes=(i,))
         return Field(self._tgt(mode), dobj.ensure_default_distributed(v))

nifty5/operators/simple_linear_operators.py

@@ -43,19 +43,6 @@ class VdotOperator(LinearOperator):
         return self._field*x.local_data[()]
 
 
-class SumReductionOperator(LinearOperator):
-    def __init__(self, domain):
-        self._domain = DomainTuple.make(domain)
-        self._target = DomainTuple.scalar_domain()
-        self._capability = self.TIMES | self.ADJOINT_TIMES
-
-    def apply(self, x, mode):
-        self._check_input(x, mode)
-        if mode == self.TIMES:
-            return Field.scalar(x.sum())
-        return full(self._domain, x.local_data[()])
-
-
 class ConjugationOperator(EndomorphicOperator):
     def __init__(self, domain):
         self._domain = DomainTuple.make(domain)

nifty5/operators/symmetrizing_operator.py

@@ -42,4 +42,5 @@ class SymmetrizingOperator(EndomorphicOperator):
             lead = (slice(None),)*i
             v, loc = dobj.ensure_not_distributed(v, (i,))
             loc[lead+(slice(1, None),)] -= loc[lead+(slice(None, 0, -1),)]
+            loc /= 2
         return Field(self.target, dobj.ensure_default_distributed(v))

nifty5/plot.py

@@ -75,7 +75,7 @@ def _makeplot(name):
         plt.close()
         return
     extension = os.path.splitext(name)[1]
-    if extension in (".pdf", ".png"):
+    if extension in (".pdf", ".png", ".svg"):
         plt.savefig(name)
         plt.close()
     else:

nifty5/utilities.py

@@ -22,15 +22,13 @@ import collections
 from itertools import product
 
 import numpy as np
-import pyfftw
 from future.utils import with_metaclass
-from pyfftw.interfaces.numpy_fft import fftn, rfftn
 
 from .compat import *
 
 __all__ = ["get_slice_list", "safe_cast", "parse_spaces", "infer_space",
-           "memo", "NiftyMetaBase", "fft_prep", "hartley", "my_fftn_r2c",
-           "my_fftn", "my_sum", "my_lincomb_simple", "my_lincomb", "indent",
+           "memo", "NiftyMetaBase", "my_sum", "my_lincomb_simple",
+           "my_lincomb", "indent",
            "my_product", "frozendict", "special_add_at", "iscomplextype"]
 
 
@@ -187,117 +185,6 @@ def NiftyMetaBase():
     return with_metaclass(NiftyMeta, type('NewBase', (object,), {}))
 
 
-def nthreads():
-    if nthreads._val is None:
-        import os
-        nthreads._val = int(os.getenv("OMP_NUM_THREADS", "1"))
-    return nthreads._val
-
-
-nthreads._val = None
-
-# Optional extra arguments for the FFT calls
-# _fft_extra_args = {}
-# if exact reproducibility is needed, use this:
-_fft_extra_args = dict(planner_effort='FFTW_ESTIMATE')
-
-
-def fft_prep():
-    if not fft_prep._initialized:
-        pyfftw.interfaces.cache.enable()
-        pyfftw.interfaces.cache.set_keepalive_time(1000.)
-        fft_prep._initialized = True
-fft_prep._initialized = False
-
-
-def hartley(a, axes=None):
-    # Check if the axes provided are valid given the shape
-    if axes is not None and \
-            not all(axis < len(a.shape) for axis in axes):
-        raise ValueError("Provided axes do not match array shape")
-    if iscomplextype(a.dtype):
-        raise TypeError("Hartley transform requires real-valued arrays.")
-
-    tmp = rfftn(a, axes=axes, threads=nthreads(), **_fft_extra_args)
-
-    def _fill_array(tmp, res, axes):
-        if axes is None:
-            axes = tuple(range(tmp.ndim))
-        lastaxis = axes[-1]
-        ntmplast = tmp.shape[lastaxis]
-        slice1 = (slice(None),)*lastaxis + (slice(0, ntmplast),)
-        np.add(tmp.real, tmp.imag, out=res[slice1])
-
-        def _fill_upper_half(tmp, res, axes):
-            lastaxis = axes[-1]
-            nlast = res.shape[lastaxis]
-            ntmplast = tmp.shape[lastaxis]
-            nrem = nlast - ntmplast
-            slice1 = [slice(None)]*lastaxis + [slice(ntmplast, None)]
-            slice2 = [slice(None)]*lastaxis + [slice(nrem, 0, -1)]
-            for