def pow(dtype, power_dtype=None):
"""
Returns a :py:class:`~reikna.cluda.Module` with a function of two arguments
that raises the first argument of type ``dtype`` (must be a real or complex data type)
to the power of the second argument (a corresponding real data type or an integer).
"""
if dtypes.is_complex(power_dtype):
raise NotImplementedError("pow() with a complex power is not supported")
if power_dtype is None:
if dtypes.is_integer(dtype):
raise ValueError("Power dtype must be specified for an integer argument")
elif dtypes.is_real(dtype):
power_dtype = dtype
else:
power_dtype = dtypes.real_for(dtype)
if dtypes.is_complex(dtype):
r_dtype = dtypes.real_for(dtype)
elif dtypes.is_real(dtype):
r_dtype = dtype
elif dtypes.is_real(power_dtype):
r_dtype = power_dtype
else:
r_dtype = numpy.float32
if dtypes.is_integer(dtype) and dtypes.is_real(power_dtype):
dtype = power_dtype
return Module(
TEMPLATE.get_def('pow'),
render_kwds=dict(
dtype=dtype, power_dtype=power_dtype,
mul_=mul(dtype, dtype), div_=div(dtype, dtype),
polar_=polar(r_dtype)))
def norm_const(arr_t, order):
"""
Returns a transformation that calculates the ``order``-norm
(1 output, 1 input): ``output = abs(input) ** order``.
"""
if dtypes.is_complex(arr_t.dtype):
out_dtype = dtypes.real_for(arr_t.dtype)
else:
out_dtype = arr_t.dtype
return Transformation(
[
Parameter('output', Annotation(Type(out_dtype, arr_t.shape), 'o')),
Parameter('input', Annotation(arr_t, 'i'))],
"""
${input.ctype} val = ${input.load_same};
${output.ctype} norm = ${norm}(val);
%if order != 2:
norm = pow(norm, ${dtypes.c_constant(order / 2, output.dtype)});
%endif
${output.store_same}(norm);
""",
render_kwds=dict(
norm=functions.norm(arr_t.dtype),
order=order))
def hanning_window(arr, NFFT):
"""
Applies the von Hann window to the rows of a 2D array.
To account for zero padding (which we do not want to window), NFFT is provided separately.
"""
if dtypes.is_complex(arr.dtype):
coeff_dtype = dtypes.real_for(arr.dtype)
else:
coeff_dtype = arr.dtype
return Transformation([
Parameter('output', Annotation(arr, 'o')),
Parameter('input', Annotation(arr, 'i')),
],
"""
${dtypes.ctype(coeff_dtype)} coeff;
%if NFFT != output.shape[0]:
if (${idxs[1]} >= ${NFFT})
{
coeff = 1;
}
else
%endif
{
coeff = 0.5 * (1 - cos(2 * ${numpy.pi} * ${idxs[-1]} / (${NFFT} - 1)));
}
${output.store_same}(${mul}(${input.load_same}, coeff));
""",
render_kwds=dict(coeff_dtype=coeff_dtype,
NFFT=NFFT,
mul=functions.mul(
arr.dtype, coeff_dtype)))
def norm_const(arr_t, order):
"""
Returns a transformation that calculates the ``order``-norm
(1 output, 1 input): ``output = abs(input) ** order``.
"""
if dtypes.is_complex(arr_t.dtype):
out_dtype = dtypes.real_for(arr_t.dtype)
else:
out_dtype = arr_t.dtype
return Transformation(
[
Parameter('output', Annotation(Type(out_dtype, arr_t.shape), 'o')),
Parameter('input', Annotation(arr_t, 'i'))],
"""
${input.ctype} val = ${input.load_same};
${output.ctype} norm = ${norm}(val);
%if order != 2:
norm = pow(norm, ${dtypes.c_constant(order / 2, output.dtype)});
%endif
${output.store_same}(norm);
""",
render_kwds=dict(
norm=functions.norm(arr_t.dtype),
order=order))
def hanning_window(arr, NFFT):
"""
Applies the von Hann window to the rows of a 2D array.
To account for zero padding (which we do not want to window), NFFT is provided separately.
"""
if dtypes.is_complex(arr.dtype):
coeff_dtype = dtypes.real_for(arr.dtype)
else:
coeff_dtype = arr.dtype
return Transformation(
[
Parameter('output', Annotation(arr, 'o')),
Parameter('input', Annotation(arr, 'i')),
],
"""
${dtypes.ctype(coeff_dtype)} coeff;
%if NFFT != output.shape[0]:
if (${idxs[1]} >= ${NFFT})
{
coeff = 1;
}
else
%endif
{
coeff = 0.5 * (1 - cos(2 * ${numpy.pi} * ${idxs[-1]} / (${NFFT} - 1)));
}
${output.store_same}(${mul}(${input.load_same}, coeff));
""",
render_kwds=dict(
coeff_dtype=coeff_dtype, NFFT=NFFT,
mul=functions.mul(arr.dtype, coeff_dtype)))
def get_test_array(shape, dtype, strides=None, no_zeros=False, high=None):
shape = wrap_in_tuple(shape)
dtype = dtypes.normalize_type(dtype)
if dtype.names is not None:
result = numpy.empty(shape, dtype)
for name in dtype.names:
result[name] = get_test_array(shape, dtype[name], no_zeros=no_zeros, high=high)
else:
if dtypes.is_integer(dtype):
low = 1 if no_zeros else 0
if high is None:
high = 100 # will work even with signed chars
get_arr = lambda: numpy.random.randint(low, high, shape).astype(dtype)
else:
low = 0.01 if no_zeros else 0
if high is None:
high = 1.0
get_arr = lambda: numpy.random.uniform(low, high, shape).astype(dtype)
if dtypes.is_complex(dtype):
result = get_arr() + 1j * get_arr()
else:
result = get_arr()
if strides is not None:
result = as_strided(result, result.shape, strides)
return result
def get_test_array(shape, dtype, strides=None, no_zeros=False, high=None):
shape = wrap_in_tuple(shape)
dtype = dtypes.normalize_type(dtype)
if dtype.names is not None:
result = numpy.empty(shape, dtype)
for name in dtype.names:
result[name] = get_test_array(shape,
dtype[name],
no_zeros=no_zeros,
high=high)
else:
if dtypes.is_integer(dtype):
low = 1 if no_zeros else 0
if high is None:
high = 100 # will work even with signed chars
get_arr = lambda: numpy.random.randint(low, high, shape).astype(
dtype)
else:
low = 0.01 if no_zeros else 0
if high is None:
high = 1.0
get_arr = lambda: numpy.random.uniform(low, high, shape).astype(
dtype)
if dtypes.is_complex(dtype):
result = get_arr() + 1j * get_arr()
else:
result = get_arr()
if strides is not None:
result = as_strided(result, result.shape, strides)
return result
def generate_modes(mshape, dtype, batch=None, random=True):
"""
Generates list of sparse modes for the problem of given shape.
"""
max_modes_per_batch = 20
modelist = []
if product(mshape) <= max_modes_per_batch:
# If there are not many modes, fill all of them
modenums = itertools.product(*[range(modes) for modes in mshape])
if batch is not None:
for b in range(batch):
modelist += [((b, ) + modenum) for modenum in modenums]
else:
modelist += list(modenums)
else:
# If there are many modes, fill some random ones
rand_coord = lambda: tuple(
numpy.random.randint(0, mshape[i]) for i in range(len(mshape)))
if batch is not None:
for b in range(batch):
for i in range(max_modes_per_batch):
modelist.append((b, ) + rand_coord())
else:
for i in range(max_modes_per_batch):
modelist.append(rand_coord())
# add corner modes, to make sure extreme cases are still processed correctly
corner_modes = itertools.product(*[(0, mshape[i] - 1)
for i in range(len(mshape))])
for modenum in corner_modes:
if batch is not None:
for b in range(batch):
modelist.append((b, ) + modenum)
else:
modelist.append(modenum)
modelist = set(modelist) # remove duplicates
# Assign coefficients
modes = []
for coord in modelist:
get_coeff = lambda: numpy.random.normal() if random else 1
if dtypes.is_complex(dtype):
coeff = get_coeff() + 1j * get_coeff()
else:
coeff = get_coeff()
coeff = dtype(coeff)
# scaling coefficients for higher modes because of the lower precision in this case
modenums = coord if batch is None else coord[1:]
coeff /= sum(modenums) + 1
modes.append((coeff, coord))
return modes
def generate_modes(mshape, dtype, batch=None, random=True):
"""
Generates list of sparse modes for the problem of given shape.
"""
max_modes_per_batch = 20
modelist = []
if product(mshape) <= max_modes_per_batch:
# If there are not many modes, fill all of them
modenums = itertools.product(*[range(modes) for modes in mshape])
if batch is not None:
for b in range(batch):
modelist += [((b,) + modenum) for modenum in modenums]
else:
modelist += list(modenums)
else:
# If there are many modes, fill some random ones
rand_coord = lambda: tuple(
numpy.random.randint(0, mshape[i]) for i in range(len(mshape)))
if batch is not None:
for b in range(batch):
for i in range(max_modes_per_batch):
modelist.append((b,) + rand_coord())
else:
for i in range(max_modes_per_batch):
modelist.append(rand_coord())
# add corner modes, to make sure extreme cases are still processed correctly
corner_modes = itertools.product(*[(0, mshape[i]-1) for i in range(len(mshape))])
for modenum in corner_modes:
if batch is not None:
for b in range(batch):
modelist.append((b,) + modenum)
else:
modelist.append(modenum)
modelist = set(modelist) # remove duplicates
# Assign coefficients
modes = []
for coord in modelist:
get_coeff = lambda: numpy.random.normal() if random else 1
if dtypes.is_complex(dtype):
coeff = get_coeff() + 1j * get_coeff()
else:
coeff = get_coeff()
coeff = dtype(coeff)
# scaling coefficients for higher modes because of the lower precision in this case
modenums = coord if batch is None else coord[1:]
coeff /= sum(modenums) + 1
modes.append((coeff, coord))
return modes
def normal_bm(bijection, dtype, mean=0, std=1):
"""
Generates normally distributed random numbers with the mean ``mean`` and
the standard deviation ``std`` using Box-Muller transform.
Supported dtypes: ``float(32/64)``, ``complex(64/128)``.
Produces two random numbers per call for real types and one number for complex types.
Returns a :py:class:`~reikna.cbrng.samplers.Sampler` object.
.. note::
In case of a complex ``dtype``, ``std`` refers to the standard deviation of the
complex numbers (same as ``numpy.std()`` returns), not real and imaginary components
(which will be normally distributed with the standard deviation ``std / sqrt(2)``).
Consequently, while ``mean`` is of type ``dtype``, ``std`` must be real.
"""
if dtypes.is_complex(dtype):
r_dtype = dtypes.real_for(dtype)
c_dtype = dtype
else:
r_dtype = dtype
c_dtype = dtypes.complex_for(dtype)
uf = uniform_float(bijection, r_dtype, low=0, high=1)
module = Module(TEMPLATE.get_def("normal_bm"),
render_kwds=dict(complex_res=dtypes.is_complex(dtype),
r_dtype=r_dtype,
r_ctype=dtypes.ctype(r_dtype),
c_dtype=c_dtype,
c_ctype=dtypes.ctype(c_dtype),
polar_unit=functions.polar_unit(r_dtype),
bijection=bijection,
mean=mean,
std=std,
uf=uf))
return Sampler(bijection,
module,
dtype,
deterministic=uf.deterministic,
randoms_per_call=1 if dtypes.is_complex(dtype) else 2)
def conj(dtype):
"""
Returns a :py:class:`~reikna.cluda.Module` with a function of one argument
that conjugates the value of type ``dtype`` (must be a complex data type).
"""
if not dtypes.is_complex(dtype):
raise NotImplementedError("conj() of " + str(dtype) + " is not supported")
return Module(
TEMPLATE.get_def('conj'),
render_kwds=dict(dtype=dtype))
def pow(dtype, exponent_dtype=None, output_dtype=None):
"""
Returns a :py:class:`~reikna.cluda.Module` with a function of two arguments
that raises the first argument of type ``dtype``
to the power of the second argument of type ``exponent_dtype``
(an integer or real data type).
If ``exponent_dtype`` or ``output_dtype`` are not given, they default to ``dtype``.
If ``dtype`` is not the same as ``output_dtype``,
the input is cast to ``output_dtype`` *before* exponentiation.
If ``exponent_dtype`` is real, but both ``dtype`` and ``output_dtype`` are integer,
a ``ValueError`` is raised.
"""
if exponent_dtype is None:
exponent_dtype = dtype
if output_dtype is None:
output_dtype = dtype
if dtypes.is_complex(exponent_dtype):
raise NotImplementedError("pow() with a complex exponent is not supported")
if dtypes.is_real(exponent_dtype):
if dtypes.is_complex(output_dtype):
exponent_dtype = dtypes.real_for(output_dtype)
elif dtypes.is_real(output_dtype):
exponent_dtype = output_dtype
else:
raise ValueError("pow(integer, float): integer is not supported")
kwds = dict(
dtype=dtype, exponent_dtype=exponent_dtype, output_dtype=output_dtype,
div_=None, mul_=None, cast_=None, polar_=None)
if output_dtype != dtype:
kwds['cast_'] = cast(output_dtype, dtype)
if dtypes.is_integer(exponent_dtype) and not dtypes.is_real(output_dtype):
kwds['mul_'] = mul(output_dtype, output_dtype)
kwds['div_'] = div(output_dtype, output_dtype)
if dtypes.is_complex(output_dtype):
kwds['polar_'] = polar(dtypes.real_for(output_dtype))
return Module(TEMPLATE.get_def('pow'), render_kwds=kwds)
def normal_bm(bijection, dtype, mean=0, std=1):
"""
Generates normally distributed random numbers with the mean ``mean`` and
the standard deviation ``std`` using Box-Muller transform.
Supported dtypes: ``float(32/64)``, ``complex(64/128)``.
Produces two random numbers per call for real types and one number for complex types.
Returns a :py:class:`~reikna.cbrng.samplers.Sampler` object.
.. note::
In case of a complex ``dtype``, ``std`` refers to the standard deviation of the
complex numbers (same as ``numpy.std()`` returns), not real and imaginary components
(which will be normally distributed with the standard deviation ``std / sqrt(2)``).
Consequently, while ``mean`` is of type ``dtype``, ``std`` must be real.
"""
if dtypes.is_complex(dtype):
r_dtype = dtypes.real_for(dtype)
c_dtype = dtype
else:
r_dtype = dtype
c_dtype = dtypes.complex_for(dtype)
uf = uniform_float(bijection, r_dtype, low=0, high=1)
module = Module(
TEMPLATE.get_def("normal_bm"),
render_kwds=dict(
complex_res=dtypes.is_complex(dtype),
r_dtype=r_dtype, r_ctype=dtypes.ctype(r_dtype),
c_dtype=c_dtype, c_ctype=dtypes.ctype(c_dtype),
polar_unit=functions.polar_unit(r_dtype),
bijection=bijection,
mean=mean,
std=std,
uf=uf))
return Sampler(
bijection, module, dtype,
deterministic=uf.deterministic, randoms_per_call=1 if dtypes.is_complex(dtype) else 2)
def generate_dtypes(out_code, in_codes):
test_dtype = lambda idx: dict(i=numpy.int32, f=numpy.float32, c=numpy.complex64)[idx]
in_dtypes = list(map(test_dtype, in_codes))
out_dtype = dtypes.result_type(*in_dtypes) if out_code == 'auto' else test_dtype(out_code)
if not any(map(dtypes.is_double, in_dtypes)):
# numpy thinks that int32 * float32 == float64,
# but we still need to run this test on older videocards
if dtypes.is_complex(out_dtype):
out_dtype = numpy.complex64
elif dtypes.is_real(out_dtype):
out_dtype = numpy.float32
return out_dtype, in_dtypes
def __init__(self, arr_t, axes=None):
if not dtypes.is_complex(arr_t.dtype):
raise ValueError("FFT computation requires array of a complex dtype")
Computation.__init__(self, [
Parameter('output', Annotation(arr_t, 'o')),
Parameter('input', Annotation(arr_t, 'i')),
Parameter('inverse', Annotation(numpy.int32), default=0)])
if axes is None:
axes = tuple(range(len(arr_t.shape)))
else:
axes = tuple(axes)
self._axes = axes
def __init__(self, arr_t, axes=None):
if not dtypes.is_complex(arr_t.dtype):
raise ValueError("FFT computation requires array of a complex dtype")
Computation.__init__(self, [
Parameter('output', Annotation(arr_t, 'o')),
Parameter('input', Annotation(arr_t, 'i')),
Parameter('inverse', Annotation(numpy.int32), default=0)])
if axes is None:
axes = tuple(range(len(arr_t.shape)))
else:
axes = tuple(axes)
self._axes = axes
def generate_dtypes(out_code, in_codes):
test_dtype = lambda idx: dict(
i=numpy.int32, f=numpy.float32, c=numpy.complex64)[idx]
in_dtypes = list(map(test_dtype, in_codes))
out_dtype = dtypes.result_type(
*in_dtypes) if out_code == 'auto' else test_dtype(out_code)
if not any(map(dtypes.is_double, in_dtypes)):
# numpy thinks that int32 * float32 == float64,
# but we still need to run this test on older videocards
if dtypes.is_complex(out_dtype):
out_dtype = numpy.complex64
elif dtypes.is_real(out_dtype):
out_dtype = numpy.float32
return out_dtype, in_dtypes
def Multiply(type):
return PureParallel([
Parameter('output', Annotation(type, 'o')),
Parameter('in1', Annotation(type, 'i')),
Parameter('in2', Annotation(type, 'i'))
],
"""
${ctype} f1 = ${in1.load_same}, f2 = ${in2.load_same};
#if ${complex}
${output.store_same}((${ctype})(f1.x*f2.x - f1.y*f2.y, f1.x*f2.y + f1.y*f2.x));
#else
${output.store_same}(f1*f2);
#endif
""",
render_kwds=dict(ctype=type.ctype,
complex=int(dtypes.is_complex(type))))
def __init__(self, arr_t, padding=False, axes=None, **kwargs):
'''
Wrapper around `reikna.fft.FFT` with automatic real-to-complex casting
and optional padding for higher performance.
Input
-----
padding: bool, default=True
If True, the input array is padded to the next power of two on the
transformed axes.
axes: tuple
Axes over which to perform the transform. Defaults to all axes.
Note
----
Because reikna does not allow nodes of the transformation tree with the
identical names, the input array is called `input_`.
'''
if axes is None:
axes = range(len(arr_t.shape)) # if axes is None else tuple(axes)
else:
axes = tuple(v + len(arr_t.shape) if v < 0 else v for v in axes)
for v in axes:
if v not in range(0, len(arr_t.shape)):
raise IndexError('axis is out of range')
dtype = (arr_t.dtype if dtypes.is_complex(arr_t.dtype) else
dtypes.complex_for(arr_t.dtype))
if padding:
shape = tuple(1 << int(np.ceil(np.log2(v))) if ax in axes else v
for ax, v in enumerate(arr_t.shape))
else:
shape = arr_t.shape
super(FFT, self).__init__(Type(dtype, shape), axes=axes, **kwargs)
input = self.parameter.input
if dtype != arr_t.dtype:
complex_tr = Complex(Type(arr_t.dtype, input.shape))
input.connect(complex_tr,
complex_tr.output,
in_real=complex_tr.input)
input = self.parameter.in_real
if shape != arr_t.shape:
pad_tr = Padded(input, arr_t, default='0.')
input.connect(pad_tr, pad_tr.output, in_padded=pad_tr.input)
input = self.parameter.in_padded
copy_tr = copy(input)
input.connect(copy_tr, copy_tr.output, input_=copy_tr.input)
def __init__(self, shape, drift, trajectories=1, diffusion=None, iterations=3, noise_type=None):
if dtypes.is_complex(drift.dtype):
real_dtype = dtypes.real_for(drift.dtype)
else:
real_dtype = drift.dtype
state_type = Type(drift.dtype, (trajectories, drift.components) + shape)
self._noise = diffusion is not None
Computation.__init__(self,
[Parameter('output', Annotation(state_type, 'o')),
Parameter('input', Annotation(state_type, 'i'))]
+ ([Parameter('dW', Annotation(noise_type, 'i'))] if self._noise else []) +
[Parameter('t', Annotation(real_dtype)),
Parameter('dt', Annotation(real_dtype))])
self._prop_iter = get_prop_iter(
state_type, drift, iterations,
diffusion=diffusion, noise_type=noise_type)
def _build_plan(self, plan_factory, _device_params, output_arr, input_arr):
plan = plan_factory()
dtype = input_arr.dtype
p_dtype = dtypes.real_for(dtype) if dtypes.is_complex(dtype) else dtype
mode_shape = input_arr.shape if self._inverse else output_arr.shape
current_mem = input_arr
seq_axes = list(range(len(input_arr.shape)))
current_axes = list(range(len(input_arr.shape)))
for i, axis in enumerate(self._axes):
current_mem, current_axes = self._add_transpose(plan, current_mem, current_axes, axis)
tr_matrix = plan.persistent_array(
self._get_transformation_matrix(p_dtype, mode_shape[axis], self._add_points[axis]))
dot = MatrixMul(current_mem, tr_matrix)
if i == len(self._axes) - 1 and current_axes == seq_axes:
dot_output = output_arr
else:
# Cannot write to output if it is not the last transform,
# or if we need to return to the initial axes order
dot_output = plan.temp_array_like(dot.parameter.output)
plan.computation_call(dot, dot_output, current_mem, tr_matrix)
current_mem = dot_output
# If we ended up with the wrong order of axes,
# return to the original order.
if current_axes != seq_axes:
tr_axes = [current_axes.index(i) for i in range(len(current_axes))]
transpose = Transpose(current_mem, output_arr_t=output_arr, axes=tr_axes)
plan.add_computation(transpose, output_arr, current_mem)
return plan
def __init__(self, in1_type, in2_type, axis=-1):
'''
Fast convolution with FFT
Uses transforms of length N1+N2 padded to a power of two, because
overlap-add is not significantly faster for the indended shape ranges.
Input
-----
in1_type, in2_type: `reikna.core.Type`
Shape and dtype of the arrays to be convolved.
axis: `int`
Array axis over which the convolution is evaluated.
Notes
-----
* The output is always an array of complex numbers.
* The arrays are matched using numpy's broadcasting rules.
'''
self._thread = None
# normalize axis
ndim = max(len(in1_type.shape), len(in2_type.shape))
if axis < 0:
axis += ndim
if axis not in range(ndim):
raise ValueError('axis is out of range.')
# check if in1 and in2 are broadcastable
for ax, s1, s2 in zip(range(ndim - 1, 0, -1), in1_type.shape[::-1],
in2_type.shape[::-1]):
if (ax != axis) and (s1 != s2) and (s1 != 1) and (s2 != 1):
raise ValueError('in1 and in2 have incompatible shapes')
# calculate shapes
in1_shape = (1, ) * (ndim - len(in1_type.shape)) + in1_type.shape
in2_shape = (1, ) * (ndim - len(in2_type.shape)) + in2_type.shape
in1_padded = in1_shape[:axis] + (in1_shape[axis] + in2_shape[axis] -
1, ) + in1_shape[axis + 1:]
in2_padded = in2_shape[:axis] + (in1_shape[axis] + in2_shape[axis] -
1, ) + in2_shape[axis + 1:]
out_shape = tuple(
max(s1, s2) for s1, s2 in zip(in1_padded, in2_padded))
out_dtype = (in1_type.dtype if dtypes.is_complex(in1_type.dtype) else
dtypes.complex_for(in1_type.dtype))
fft1 = FFT(Type(in1_type.dtype, in1_padded), axes=(axis, ))
pad_in1 = Padded(fft1.parameter.input_,
Type(in1_type.dtype, in1_shape),
default='0.')
fft1.parameter.input_.connect(pad_in1,
pad_in1.output,
input_p=pad_in1.input)
fft2 = FFT(Type(in2_type.dtype, in2_padded), axes=(axis, ))
pad_in2 = Padded(fft2.parameter.input_,
Type(in2_type.dtype, in2_shape),
default='0.')
fft2.parameter.input_.connect(pad_in2,
pad_in2.output,
input_p=pad_in2.input)
mul = Multiply(Type(out_dtype, out_shape))
bcast_in1 = Broadcast(out_shape, fft1.parameter.output)
mul.parameter.in1.connect(bcast_in1,
bcast_in1.output,
in1_p=bcast_in1.input)
bcast_in2 = Broadcast(out_shape, fft2.parameter.output)
mul.parameter.in2.connect(bcast_in2,
bcast_in2.output,
in2_p=bcast_in2.input)
ifft = FFT(Type(out_dtype, out_shape), axes=(axis, ))
self._comps = [fft1, fft2, mul, ifft]
# emulate reikna parameter attribute
parameters = namedtuple('DummyParameters', ['output', 'in1', 'in2'])
self.parameter = parameters(ifft.parameter.output, in1_type, in2_type)
def reference_mul(*args):
res = product(args)
if not dtypes.is_complex(out_dtype) and dtypes.is_complex(res.dtype):
res = res.real
return res.astype(out_dtype)
def get_prop_iter(state_type, drift, iterations, diffusion=None, noise_type=None):
if dtypes.is_complex(state_type.dtype):
real_dtype = dtypes.real_for(state_type.dtype)
else:
real_dtype = state_type.dtype
if diffusion is not None:
noise_dtype = noise_type.dtype
else:
noise_dtype = real_dtype
return PureParallel(
[
Parameter('output', Annotation(state_type, 'o')),
Parameter('input', Annotation(state_type, 'i'))]
+ ([Parameter('dW', Annotation(noise_type, 'i'))] if diffusion is not None else []) +
[Parameter('t', Annotation(real_dtype)),
Parameter('dt', Annotation(real_dtype))],
"""
<%
coords = ", ".join(idxs[1:])
trajectory = idxs[0]
components = drift.components
if diffusion is not None:
noise_sources = diffusion.noise_sources
psi_args = ", ".join("psi_" + str(c) + "_tmp" for c in range(components))
if diffusion is None:
dW = None
%>
%for comp in range(components):
${output.ctype} psi_${comp} = ${input.load_idx}(${trajectory}, ${comp}, ${coords});
${output.ctype} psi_${comp}_tmp = psi_${comp};
${output.ctype} dpsi_${comp};
%endfor
%if diffusion is not None:
%for ncomp in range(noise_sources):
${dW.ctype} dW_${ncomp} = ${dW.load_idx}(${trajectory}, ${ncomp}, ${coords});
%endfor
%endif
%for i in range(iterations):
%for comp in range(components):
dpsi_${comp} =
${mul_cr}(
${mul_cr}(${drift.module}${comp}(
${coords}, ${psi_args}, ${t} + ${dt} / 2), ${dt})
%if diffusion is not None:
%for ncomp in range(noise_sources):
+ ${mul_cn}(${diffusion.module}${comp}_${ncomp}(
${coords}, ${psi_args}, ${t} + ${dt} / 2), dW_${ncomp})
%endfor
%endif
, 0.5);
%endfor
%for comp in range(components):
psi_${comp}_tmp = psi_${comp} + dpsi_${comp};
%endfor
%endfor
%for comp in range(components):
${output.store_idx}(${trajectory}, ${comp}, ${coords}, psi_${comp}_tmp + dpsi_${comp});
%endfor
""",
guiding_array=(state_type.shape[0],) + state_type.shape[2:],
render_kwds=dict(
drift=drift,
diffusion=diffusion,
iterations=iterations,
mul_cr=functions.mul(state_type.dtype, real_dtype),
mul_cn=functions.mul(state_type.dtype, noise_dtype)))
def reference_add(*args):
res = sum(args)
if not dtypes.is_complex(out_dtype) and dtypes.is_complex(res.dtype):
res = res.real
return res.astype(out_dtype)
def check_information_loss(out_dtype, expected_dtype):
if dtypes.is_complex(expected_dtype) and not dtypes.is_complex(out_dtype):
warn("Imaginary part ignored during the downcast from " +
str(expected_dtype) + " to " + str(out_dtype),
numpy.ComplexWarning)
def reference_mul(*args):
res = product(args)
if not dtypes.is_complex(out_dtype) and dtypes.is_complex(res.dtype):
res = res.real
return res.astype(out_dtype)
def reference_add(*args):
res = sum(args)
if not dtypes.is_complex(out_dtype) and dtypes.is_complex(res.dtype):
res = res.real
return res.astype(out_dtype)