def forward(ctx, formula, aliases, varinvpos, alpha, backend, dtype,
device_id, eps, ranges, accuracy_flags, *args):
optional_flags = ['-DPYTORCH_INCLUDE_DIR=' + ';'.join(include_dirs)
] + accuracy_flags
myconv = LoadKeOps(formula, aliases, dtype, 'torch',
optional_flags).import_module()
# Context variables: save everything to compute the gradient:
ctx.formula = formula
ctx.aliases = aliases
ctx.varinvpos = varinvpos
ctx.alpha = alpha
ctx.backend = backend
ctx.dtype = dtype
ctx.device_id = device_id
ctx.eps = eps
ctx.myconv = myconv
ctx.ranges = ranges
ctx.accuracy_flags = accuracy_flags
if ranges is None: ranges = () # To keep the same type
varinv = args[varinvpos]
ctx.varinvpos = varinvpos
tagCPUGPU, tag1D2D, tagHostDevice = get_tag_backend(backend, args)
if tagCPUGPU == 1 & tagHostDevice == 1:
device_id = args[0].device.index
for i in range(1, len(args)):
if args[i].device.index != device_id:
raise ValueError(
"[KeOps] Input arrays must be all located on the same device."
)
(categories, dimensions) = parse_aliases(aliases)
def linop(var):
newargs = args[:varinvpos] + (var, ) + args[varinvpos + 1:]
res = myconv.genred_pytorch(tagCPUGPU, tag1D2D, tagHostDevice,
device_id, ranges, categories,
dimensions, *newargs)
if alpha:
res += alpha * var
return res
global copy
result = ConjugateGradientSolver('torch', linop, varinv.data, eps)
# relying on the 'ctx.saved_variables' attribute is necessary if you want to be able to differentiate the output
# of the backward once again. It helps pytorch to keep track of 'who is who'.
ctx.save_for_backward(*args, result)
return result
def forward(ctx, formula, aliases, varinvpos, alpha, backend, dtype,
device_id, eps, ranges, optional_flags, rec_multVar_highdim,
*args):
optional_flags += include_dirs
# N.B. when rec_multVar_highdim option is set, it means that formula is of the form "sum(F*b)", where b is a variable
# with large dimension. In this case we set compiler option MULT_VAR_HIGHDIM to allow for the use of the special "final chunk" computation
# mode. However, this may not be also true for the gradients of the same formula. In fact only the gradient
# with respect to variable b will have the same form. Hence, we save optional_flags current status into ctx,
# before adding the MULT_VAR_HIGHDIM compiler option.
ctx.optional_flags = optional_flags.copy()
if rec_multVar_highdim is not None:
optional_flags += ["-DMULT_VAR_HIGHDIM=1"]
myconv = LoadKeOps(formula, aliases, dtype, "torch",
optional_flags).import_module()
# Context variables: save everything to compute the gradient:
ctx.formula = formula
ctx.aliases = aliases
ctx.varinvpos = varinvpos
ctx.alpha = alpha
ctx.backend = backend
ctx.dtype = dtype
ctx.device_id = device_id
ctx.eps = eps
ctx.myconv = myconv
ctx.ranges = ranges
ctx.rec_multVar_highdim = rec_multVar_highdim
ctx.optional_flags = optional_flags
if ranges is None:
ranges = () # To keep the same type
varinv = args[varinvpos]
ctx.varinvpos = varinvpos
tagCPUGPU, tag1D2D, tagHostDevice = get_tag_backend(backend, args)
if tagCPUGPU == 1 & tagHostDevice == 1:
device_id = args[0].device.index
for i in range(1, len(args)):
if args[i].device.index != device_id:
raise ValueError(
"[KeOps] Input arrays must be all located on the same device."
)
def linop(var):
newargs = args[:varinvpos] + (var, ) + args[varinvpos + 1:]
res = myconv.genred_pytorch(tagCPUGPU, tag1D2D, tagHostDevice,
device_id, ranges, *newargs)
if alpha:
res += alpha * var
return res
global copy
result = ConjugateGradientSolver("torch", linop, varinv.data, eps)
# relying on the 'ctx.saved_variables' attribute is necessary if you want to be able to differentiate the output
# of the backward once again. It helps pytorch to keep track of 'who is who'.
ctx.save_for_backward(*args, result)
return result
def __call__(self,
*args,
backend='auto',
device_id=-1,
alpha=1e-10,
eps=1e-6,
ranges=None):
r"""
To 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 arrays 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:
alpha (float, default = 1e-10): Non-negative
**ridge regularization** parameter, added to the diagonal
of the Kernel matrix :math:`K_{xx}`.
backend (string): Specifies the map-reduce scheme,
as detailed in the documentation
of the :class:`numpy.Genred <pykeops.numpy.Genred>` module.
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*,
as detailed in the documentation
of the :class:`numpy.Genred <pykeops.numpy.Genred>` module.
If **None** (default), we simply use a **dense Kernel matrix**
as we loop over all indices
:math:`i\in[0,M)` and :math:`j\in[0,N)`.
Returns:
(M,D) or (N,D) array:
The solution of the optimization problem, which is always a
**2d-array** 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)
varinv = args[self.varinvpos]
if ranges is None: ranges = () # ranges should be encoded as a tuple
def linop(var):
newargs = args[:self.varinvpos] + (var, ) + args[self.varinvpos +
1:]
res = self.myconv.genred_numpy(tagCpuGpu, tag1D2D, 0, device_id,
ranges, *newargs)
if alpha:
res += alpha * var
return res
return ConjugateGradientSolver('numpy', linop, varinv, eps=eps)