def __call__(self, *args, backend='auto', device_id=-1, ranges=None):
r"""
To apply the routine on arbitrary torch Tensors.
Warning:
Even for variables of size 1 (e.g. :math:`a_i\in\mathbb{R}`
for :math:`i\in[0,M)`), KeOps expects inputs to be formatted
as 2d Tensors of size ``(M,dim)``. In practice,
``a.view(-1,1)`` should be used to turn a vector of weights
into a *list of scalar values*.
Args:
*args (2d Tensors (variables ``Vi(..)``, ``Vj(..)``) and 1d Tensors (parameters ``Pm(..)``)): The input numerical arrays,
which should all have the same ``dtype``, be **contiguous** and be stored on
the **same device**. KeOps expects one array per alias,
with the following compatibility rules:
- All ``Vi(Dim_k)`` variables are encoded as **2d-tensors** with ``Dim_k`` columns and the same number of lines :math:`M`.
- All ``Vj(Dim_k)`` variables are encoded as **2d-tensors** with ``Dim_k`` columns and the same number of lines :math:`N`.
- All ``Pm(Dim_k)`` variables are encoded as **1d-tensors** (vectors) of size ``Dim_k``.
Keyword Args:
backend (string): Specifies the map-reduce scheme.
The supported values are:
- ``"auto"`` (default): let KeOps decide which backend is best suited to your data, based on the tensors' shapes. ``"GPU_1D"`` will be chosen in most cases.
- ``"CPU"``: use a simple C++ ``for`` loop on a single CPU core.
- ``"GPU_1D"``: use a `simple multithreading scheme <https://github.com/getkeops/keops/blob/master/keops/core/GpuConv1D.cu>`_ on the GPU - basically, one thread per value of the output index.
- ``"GPU_2D"``: use a more sophisticated `2D parallelization scheme <https://github.com/getkeops/keops/blob/master/keops/core/GpuConv2D.cu>`_ on the GPU.
- ``"GPU"``: let KeOps decide which one of the ``"GPU_1D"`` or the ``"GPU_2D"`` scheme will run faster on the given input.
device_id (int, default=-1): Specifies the GPU that should be used
to perform the computation; a negative value lets your system
choose the default GPU. This parameter is only useful if your
system has access to several GPUs.
ranges (6-uple of IntTensors, None by default):
Ranges of integers that specify a
:doc:`block-sparse reduction scheme <../../sparsity>`
with *Mc clusters along axis 0* and *Nc clusters along axis 1*.
If None (default), we simply loop over all indices
:math:`i\in[0,M)` and :math:`j\in[0,N)`.
**The first three ranges** will be used if **axis** = 1
(reduction along the axis of ":math:`j` variables"),
and to compute gradients with respect to ``Vi(..)`` variables:
- ``ranges_i``, (Mc,2) IntTensor - slice indices
:math:`[\operatorname{start}^I_k,\operatorname{end}^I_k)` in :math:`[0,M]`
that specify our Mc blocks along the axis 0
of ":math:`i` variables".
- ``slices_i``, (Mc,) IntTensor - consecutive slice indices
:math:`[\operatorname{end}^S_1, ..., \operatorname{end}^S_{M_c}]`
that specify Mc ranges :math:`[\operatorname{start}^S_k,\operatorname{end}^S_k)` in ``redranges_j``,
with :math:`\operatorname{start}^S_k = \operatorname{end}^S_{k-1}`.
**The first 0 is implicit**, meaning that :math:`\operatorname{start}^S_0 = 0`, and we typically expect that
``slices_i[-1] == len(redrange_j)``.
- ``redranges_j``, (Mcc,2) IntTensor - slice indices
:math:`[\operatorname{start}^J_\ell,\operatorname{end}^J_\ell)` in :math:`[0,N]`
that specify reduction ranges along the axis 1
of ":math:`j` variables".
If **axis** = 1,
these integer arrays allow us to say
that ``for k in range(Mc)``, the output values for
indices ``i in range( ranges_i[k,0], ranges_i[k,1] )``
should be computed using a Map-Reduce scheme over
indices ``j in Union( range( redranges_j[l, 0], redranges_j[l, 1] ))``
for ``l in range( slices_i[k-1], slices_i[k] )``.
**Likewise, the last three ranges** will be used if **axis** = 0
(reduction along the axis of ":math:`i` variables"),
and to compute gradients with respect to ``Vj(..)`` variables:
- ``ranges_j``, (Nc,2) IntTensor - slice indices
:math:`[\operatorname{start}^J_k,\operatorname{end}^J_k)` in :math:`[0,N]`
that specify our Nc blocks along the axis 1
of ":math:`j` variables".
- ``slices_j``, (Nc,) IntTensor - consecutive slice indices
:math:`[\operatorname{end}^S_1, ..., \operatorname{end}^S_{N_c}]`
that specify Nc ranges :math:`[\operatorname{start}^S_k,\operatorname{end}^S_k)` in ``redranges_i``,
with :math:`\operatorname{start}^S_k = \operatorname{end}^S_{k-1}`.
**The first 0 is implicit**, meaning that :math:`\operatorname{start}^S_0 = 0`, and we typically expect that
``slices_j[-1] == len(redrange_i)``.
- ``redranges_i``, (Ncc,2) IntTensor - slice indices
:math:`[\operatorname{start}^I_\ell,\operatorname{end}^I_\ell)` in :math:`[0,M]`
that specify reduction ranges along the axis 0
of ":math:`i` variables".
If **axis** = 0,
these integer arrays allow us to say
that ``for k in range(Nc)``, the output values for
indices ``j in range( ranges_j[k,0], ranges_j[k,1] )``
should be computed using a Map-Reduce scheme over
indices ``i in Union( range( redranges_i[l, 0], redranges_i[l, 1] ))``
for ``l in range( slices_j[k-1], slices_j[k] )``.
Returns:
(M,D) or (N,D) Tensor:
The output of the reduction, stored on the same device
as the input Tensors. The output of a Genred call is always a
**2d-tensor** with :math:`M` or :math:`N` lines (if **axis** = 1
or **axis** = 0, respectively) and a number of columns
that is inferred from the **formula**.
"""
nx, ny = get_sizes(self.aliases, *args)
nout, nred = (nx, ny) if self.axis == 1 else (ny, nx)
if "Arg" in self.reduction_op:
# when using Arg type reductions,
# if nred is greater than 16 millions and dtype=float32, the result is not reliable
# because we encode indices as floats, so we raise an exception ;
# same with float16 type and nred>2048
if nred > 1.6e7 and self.dtype in ("float32", "float"):
raise ValueError(
'size of input array is too large for Arg type reduction with single precision. Use double precision.'
)
elif nred > 2048 and self.dtype in ("float16", "half"):
raise ValueError(
'size of input array is too large for Arg type reduction with float16 dtype..'
)
if self.dtype in ('float16', 'half'):
args, ranges, tag_dummy, N = preprocess_half2(
args, self.aliases, self.axis, ranges, nx, ny)
out = GenredAutograd.apply(self.formula, self.aliases, backend,
self.dtype, device_id, ranges,
self.accuracy_flags, *args)
if self.dtype in ('float16', 'half'):
out = postprocess_half2(out, tag_dummy, self.reduction_op, N)
return postprocess(out, "torch", self.reduction_op, nout, self.opt_arg,
self.dtype)
def __call__(self, *args, backend='auto', device_id=-1, ranges=None):
r"""
Apply the routine on arbitrary NumPy arrays.
Warning:
Even for variables of size 1 (e.g. :math:`a_i\in\mathbb{R}`
for :math:`i\in[0,M)`), KeOps expects inputs to be formatted
as 2d Tensors of size ``(M,dim)``. In practice,
``a.view(-1,1)`` should be used to turn a vector of weights
into a *list of scalar values*.
Args:
*args (2d arrays (variables ``Vi(..)``, ``Vj(..)``) and 1d arrays (parameters ``Pm(..)``)): The input numerical arrays,
which should all have the same ``dtype``, be **contiguous** and be stored on
the **same device**. KeOps expects one array per alias,
with the following compatibility rules:
- All ``Vi(Dim_k)`` variables are encoded as **2d-arrays** with ``Dim_k`` columns and the same number of lines :math:`M`.
- All ``Vj(Dim_k)`` variables are encoded as **2d-arrays** with ``Dim_k`` columns and the same number of lines :math:`N`.
- All ``Pm(Dim_k)`` variables are encoded as **1d-arrays** (vectors) of size ``Dim_k``.
Keyword Args:
backend (string): Specifies the map-reduce scheme.
The supported values are:
- ``"auto"`` (default): let KeOps decide which backend is best suited to your data, based on the tensors' shapes. ``"GPU_1D"`` will be chosen in most cases.
- ``"CPU"``: use a simple C++ ``for`` loop on a single CPU core.
- ``"GPU_1D"``: use a `simple multithreading scheme <https://github.com/getkeops/keops/blob/master/keops/core/GpuConv1D.cu>`_ on the GPU - basically, one thread per value of the output index.
- ``"GPU_2D"``: use a more sophisticated `2D parallelization scheme <https://github.com/getkeops/keops/blob/master/keops/core/GpuConv2D.cu>`_ on the GPU.
- ``"GPU"``: let KeOps decide which one of the ``"GPU_1D"`` or the ``"GPU_2D"`` scheme will run faster on the given input.
device_id (int, default=-1): Specifies the GPU that should be used
to perform the computation; a negative value lets your system
choose the default GPU. This parameter is only useful if your
system has access to several GPUs.
ranges (6-uple of integer arrays, None by default):
Ranges of integers that specify a
:doc:`block-sparse reduction scheme <../../sparsity>`
with *Mc clusters along axis 0* and *Nc clusters along axis 1*.
If None (default), we simply loop over all indices
:math:`i\in[0,M)` and :math:`j\in[0,N)`.
**The first three ranges** will be used if **axis** = 1
(reduction along the axis of ":math:`j` variables"),
and to compute gradients with respect to ``Vi(..)`` variables:
- ``ranges_i``, (Mc,2) integer array - slice indices
:math:`[\operatorname{start}^I_k,\operatorname{end}^I_k)` in :math:`[0,M]`
that specify our Mc blocks along the axis 0
of ":math:`i` variables".
- ``slices_i``, (Mc,) integer array - consecutive slice indices
:math:`[\operatorname{end}^S_1, ..., \operatorname{end}^S_{M_c}]`
that specify Mc ranges :math:`[\operatorname{start}^S_k,\operatorname{end}^S_k)` in ``redranges_j``,
with :math:`\operatorname{start}^S_k = \operatorname{end}^S_{k-1}`.
**The first 0 is implicit**, meaning that :math:`\operatorname{start}^S_0 = 0`, and we typically expect that
``slices_i[-1] == len(redrange_j)``.
- ``redranges_j``, (Mcc,2) integer array - slice indices
:math:`[\operatorname{start}^J_l,\operatorname{end}^J_l)` in :math:`[0,N]`
that specify reduction ranges along the axis 1
of ":math:`j` variables".
If **axis** = 1,
these integer arrays allow us to say
that ``for k in range(Mc)``, the output values for
indices ``i in range( ranges_i[k,0], ranges_i[k,1] )``
should be computed using a Map-Reduce scheme over
indices ``j in Union( range( redranges_j[l, 0], redranges_j[l, 1] ))``
for ``l in range( slices_i[k-1], slices_i[k] )``.
**Likewise, the last three ranges** will be used if **axis** = 0
(reduction along the axis of ":math:`i` variables"),
and to compute gradients with respect to ``Vj(..)`` variables:
- ``ranges_j``, (Nc,2) integer array - slice indices
:math:`[\operatorname{start}^J_k,\operatorname{end}^J_k)` in :math:`[0,N]`
that specify our Nc blocks along the axis 1
of ":math:`j` variables".
- ``slices_j``, (Nc,) integer array - consecutive slice indices
:math:`[\operatorname{end}^S_1, ..., \operatorname{end}^S_{N_c}]`
that specify Nc ranges :math:`[\operatorname{start}^S_k,\operatorname{end}^S_k)` in ``redranges_i``,
with :math:`\operatorname{start}^S_k = \operatorname{end}^S_{k-1}`.
**The first 0 is implicit**, meaning that :math:`\operatorname{start}^S_0 = 0`, and we typically expect that
``slices_j[-1] == len(redrange_i)``.
- ``redranges_i``, (Ncc,2) integer array - slice indices
:math:`[\operatorname{start}^I_l,\operatorname{end}^I_l)` in :math:`[0,M]`
that specify reduction ranges along the axis 0
of ":math:`i` variables".
If **axis** = 0,
these integer arrays allow us to say
that ``for k in range(Nc)``, the output values for
indices ``j in range( ranges_j[k,0], ranges_j[k,1] )``
should be computed using a Map-Reduce scheme over
indices ``i in Union( range( redranges_i[l, 0], redranges_i[l, 1] ))``
for ``l in range( slices_j[k-1], slices_j[k] )``.
Returns:
(M,D) or (N,D) array:
The output of the reduction,
a **2d-tensor** with :math:`M` or :math:`N` lines (if **axis** = 1
or **axis** = 0, respectively) and a number of columns
that is inferred from the **formula**.
"""
# Get tags
tagCpuGpu, tag1D2D, _ = get_tag_backend(backend, args)
if ranges is None:
ranges = () # To keep the same type
out = self.myconv.genred_numpy(tagCpuGpu, tag1D2D, 0, device_id,
ranges, *args)
nx, ny = get_sizes(self.aliases, *args)
nout = nx if self.axis == 1 else ny
return postprocess(out, "numpy", self.reduction_op, nout, self.opt_arg,
self.dtype)