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#!/usr/bin/env python3
# encoding: utf-8
"""
_FourierTransform.py
Created by Graham Dennis on 2008-07-30.
Copyright (c) 2008-2012, Graham Dennis
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 2 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/>.
"""
from xpdeint.Features.Transforms._Transform import _Transform
from xpdeint.Geometry.DimensionRepresentation import DimensionRepresentation
from xpdeint.Geometry.UniformDimensionRepresentation import UniformDimensionRepresentation
from xpdeint.Geometry.SplitUniformDimensionRepresentation import SplitUniformDimensionRepresentation
from xpdeint.Utilities import lazy_property
import math, operator
from itertools import groupby
from functools import reduce
class _FourierTransformFFTW3 (_Transform):
transformName = 'FourierTransform'
fftwSuffix = ''
coordinateSpaceTag = DimensionRepresentation.registerTag('FFTW coordinate space', parent = 'coordinate')
fourierSpaceTag = DimensionRepresentation.registerTag('FFTW Fourier space', parent = 'spectral')
def __init__(self, *args, **KWs):
_Transform.__init__(self, *args, **KWs)
self.transformNameMap = {}
@lazy_property
def fftwPrefix(self):
precision = self.getVar('precision')
return {'double': 'fftw', 'single': 'fftwf'}[precision]
@lazy_property
def fftwLibVersionName(self):
return {'fftw': 'fftw3', 'fftwf': 'fftw3f'}[self.fftwPrefix]
@lazy_property
def wisdomExtension(self):
result = '.' + self.fftwLibVersionName
if self.fftwSuffix:
result += '_' + self.fftwSuffix
return result
@lazy_property
def uselib(self):
result = [self.fftwLibVersionName]
if self.fftwSuffix:
result.append(self.fftwLibVersionName + '_' + self.fftwSuffix)
return result
def newDimension(self, name, lattice, minimum, maximum,
parent, transformName, aliases = set(),
spectralLattice = None,
type = 'real', volumePrefactor = None,
xmlElement = None):
assert type == 'real'
assert transformName in ['dft', 'dct', 'dst']
dim = super(_FourierTransformFFTW3, self).newDimension(name, lattice, minimum, maximum,
parent, transformName, aliases,
type, volumePrefactor, xmlElement)
self.transformNameMap[dim.name] = transformName
if transformName == 'dft':
# x-space representation
xspace = UniformDimensionRepresentation(name = name, type = type, runtimeLattice = lattice,
_minimum = minimum, _maximum = maximum, parent = dim,
tag = self.coordinateSpaceTag,
**self.argumentsToTemplateConstructors)
# kspace representation
kspace = SplitUniformDimensionRepresentation(
name = 'k' + name, type = type, runtimeLattice = lattice,
_range = '%s - %s' % (xspace.maximum, xspace.minimum),
parent = dim, tag = self.fourierSpaceTag,
reductionMethod = SplitUniformDimensionRepresentation.ReductionMethod.fixedStep,
**self.argumentsToTemplateConstructors
)
else:
# x-space representation
stepSize = '((real)%(maximum)s - %(minimum)s)/(%(lattice)s)' % locals()
xspace = UniformDimensionRepresentation(
name = name, type = type, runtimeLattice = lattice,
_stepSize = stepSize, tag = self.coordinateSpaceTag,
parent = dim, **self.argumentsToTemplateConstructors
)
# Modify the minimum and maximum values to deal with the 0.5*stepSize offset
xspace._minimum = '%s + 0.5*%s' % (minimum, xspace.stepSize)
xspace._maximum = '%s + 0.5*%s' % (maximum, xspace.stepSize)
if transformName == 'dct':
# kspace representation
kspace = UniformDimensionRepresentation(
name = 'k' + name, type = type, runtimeLattice = lattice,
_minimum = '0.0', _stepSize = '(M_PI/(%(maximum)s - %(minimum)s))' % locals(),
tag = self.fourierSpaceTag,
reductionMethod = UniformDimensionRepresentation.ReductionMethod.fixedStep,
parent = dim, **self.argumentsToTemplateConstructors
)
kspace._maximum = '%s * %s' % (kspace.stepSize, kspace.globalLattice)
else:
kspace = UniformDimensionRepresentation(
name = 'k' + name, type = type, runtimeLattice = lattice,
_stepSize = '(M_PI/(%(maximum)s - %(minimum)s))' % locals(),
tag = self.fourierSpaceTag,
reductionMethod = UniformDimensionRepresentation.ReductionMethod.fixedStep,
parent = dim, **self.argumentsToTemplateConstructors
)
kspace._minimum = '%s' % kspace.stepSize
kspace._maximum = '%s * (%s + 1)' % (kspace.stepSize, kspace.globalLattice)
dim.addRepresentation(xspace)
dim.addRepresentation(kspace)
return dim
def r2rKindForDimensionAndDirection(self, dim, direction):
dimName = dim.name if not isinstance(dim, basestring) else dim
transformName = self.transformNameMap[dimName]
return {'dct': {'forward': 'FFTW_REDFT10', 'backward': 'FFTW_REDFT01'},
'dst': {'forward': 'FFTW_RODFT10', 'backward': 'FFTW_RODFT01'}}[transformName][direction]
def fftCost(self, dimNames):
geometry = self.getVar('geometry')
untransformedDimReps = dict([(dimName, geometry.dimensionWithName(dimName).representations[0]) for dimName in dimNames])
cost = sum([int(math.ceil(math.log(untransformedDimReps[dimName].latticeEstimate))) for dimName in dimNames], 0)
cost *= reduce(operator.mul, [untransformedDimReps[dimName].latticeEstimate for dimName in dimNames], 1)
return cost
@staticmethod
def scaleFactorForDimReps(dimReps):
return ' * '.join(['_inverse_sqrt_2pi * _d' + dimRepName for dimRepName in dimReps])
def availableTransformations(self):
results = []
geometry = self.getVar('geometry')
sortedDimNames = [(geometry.indexOfDimensionName(dimName), dimName) for dimName in self.transformNameMap]
sortedDimNames.sort()
sortedDimNames = [o[1] for o in sortedDimNames]
transformFunctions = dict(
geometryDependent = True,
transformFunction = self.transformFunction,
)
for dimName in sortedDimNames:
dimReps = [rep for rep in geometry.dimensionWithName(dimName).representations if not rep.hasLocalOffset]
results.append(dict(
transformations = [tuple(rep.name for rep in dimReps)],
cost = self.fftCost([dimName]),
forwardScale = self.scaleFactorForDimReps([dimReps[0].name]),
backwardScale = self.scaleFactorForDimReps([dimReps[1].name]),
requiresScaling = True,
transformType = 'complex' if self.transformNameMap[dimName] == 'dft' else 'real',
**transformFunctions
))
if self.hasattr('mpiDimensions'):
for dim in [dim for dim in self.mpiDimensions if dim.name in sortedDimNames]:
sortedDimNames.remove(dim.name)
c2cDimNames = [dimName for dimName in sortedDimNames if self.transformNameMap[dimName] == 'dft']
r2rDimNames = [dimName for dimName in sortedDimNames if self.transformNameMap[dimName] in ['dct', 'dst']]
untransformedDimReps = dict([(dimName, geometry.dimensionWithName(dimName).representations[0]) for dimName in sortedDimNames])
transformedDimReps = dict([(dimName, geometry.dimensionWithName(dimName).representations[1]) for dimName in sortedDimNames])
# Create optimised forward/backward transforms
keyFunc = lambda x: {'dft': 'complex', 'dct': 'real', 'dst': 'real'}[self.transformNameMap[x]]
for transformType, dimNames in groupby(sortedDimNames, keyFunc):
dimNames = list(dimNames)
if len(dimNames) <= 1: continue
cost = self.fftCost(dimNames)
untransformedBasis = tuple(untransformedDimReps[dimName].name for dimName in dimNames)
transformedBasis = tuple(transformedDimReps[dimName].name for dimName in dimNames)
bases = tuple([untransformedBasis, transformedBasis])
results.append(dict(
transformations = [bases],
cost = cost,
forwardScale = self.scaleFactorForDimReps(untransformedBasis),
backwardScale = self.scaleFactorForDimReps(transformedBasis),
requiresScaling = True,
transformType = transformType,
**transformFunctions
))
final_transforms = []
for transform in results:
final_transforms.append(transform.copy())
transform['outOfPlace'] = True
final_transforms.append(transform)
return final_transforms
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