format_var_aliases: Format formula argument list in triplet (type, dimension,...

In rkeops: Kernel Operations on GPU or CPU, with Autodiff, without Memory Overflows

Description

The function format_var_aliases formats KeOps formula arguments to be understood by the C++ code.

Usage

format_var_aliases(args)

Arguments

args	vector of text string, formula input arguments (see Details).

Details

Mathematical formula: sum_i e^(lambda*||x_i - y_j||^2) where x_i, y_j are 3d vectors, and lambda is a scaler parameter.

Corresponding KeOps formula and input parameters:

formula = "Sum_Reduction(Exp(lambda * SqNorm2(x-y)), 0)"
args = c("x=Vi(3)", "y=Vj(3)", "lambda=Pm(1)")

Input arguments can be of different types:

|———|————————-|———–| | keyword | meaning | type | |———|————————-|———–| | Vi | variable indexed by i | 0 | | Vj | variable indexed by j | 1 | | Pm | parameter | 2 | |———|————————-|———–|

An input parameters should be defined as follows "x=YY(dim)" or "x=YY(pos, dim)" where YY can be Vi, Vj or Pm:

• dim is the dimension of the variable or parameter. For Vi and Vj, the range of i or j is not known at compile time, only at runtime.

• pos is the position of the variable as it will be supplied to the operator, starting from 0. This position should be specify for all variable or none, if not specify the natural order in the vector args is used.

For the formula "Sum_Reduction(Exp(lambda * SqNorm2(x-y)), 0)", both args = c("x=Vi(3)", "y=Vj(3)", "lambda=Pm(1)") and args <- c("x=Vi(0,3)", "y=Vj(1,3)", "beta=Vj(2,3)", "lambda=Pm(3,1)") are equivalent. When specifying the pos parameter, the natural order in the vector args may not correspond to the order of the formula input arguments.

Note: we recommand to use the Vi(dim) notation and let the position be determined by the argument order.

Value

a list with different information about formula input arguments:

args	vector of text string, input parameter args
var_name	vector of text string, corresponding name of formula arguments
var_type	vector of text string, corresponding type of formula arguments (among Vi, Vj, Pm).
var_pos	vector of integer, corresponding arguments positions.
var_aliases	text string, declaration of formula input arguments for the C++ KeOps API.

Author(s)

Ghislain Durif

rkeops documentation built on Feb. 17, 2021, 5:08 p.m.