Using the syntax in C++/Cuda code

The expressions and variables presented in the common documentation all correspond to specific C++ types of variables defined by the KeOps library. The C++ keyword auto allows us to define them without having to worry about explicit type naming:

auto p = Pm(0,1);
auto a = Vj(1,1);
auto x = Vi(2,3);
auto y = Vj(3,3);
auto f = Square(p-y)*Exp(x+y);

Here, the f variable represents a symbolic computation; as a C++ object, it is completely useless.

The list of available operations to build a formula is given in the following table: Math operators.

Next we define the type of reduction that we want to perform, as follows:

auto Sum_f = Sum_Reduction(f,0);

This means that we want to perform a sum reduction over the “j” indices, resulting in an “i”-indexed output. We would use Sum_Reduction(f,1) for a reduction over the “i” indices.

The list of available reductions is given in the following table: Reductions. The code name of the reduction must be followed by _Reduction in C++ code.

The convolution operation is then performed using one of these three calls:

EvalRed<CpuConv>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
EvalRed<GpuConv1D_FromHost>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
EvalRed<GpuConv2D_FromHost>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);

where pc, pp, pa, px, and py are pointers to their respective arrays in (Cpu) memory, pc denoting the output. These three functions correspond to computations performed respectively on the Cpu, on the Gpu with a “1D” tiling algorithm, and with a “2D” tiling algorithm.

For a minimal working example code, see the files `./keops/examples/test_simple.cpp`_ and `./keops/examples/`_

If data arrays are already located in the GPU memory, these functions should be favored:

EvalRed<GpuConv1D_FromDevice>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
EvalRed<GpuConv2D_FromDevice>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);