where ' ≤' denotes the element-wise operation if used between vectors.
In our case, normalizing the weights is an example of an element-wise operation.
Given a function f and a vector v, the element-wise operation f↦v applies the function f on every element of the vector such that fmapstomathbf{v} = left[f v_{1}), f v_{2}), ldots, f v_{N} right].
To deal with element-wise operation, ICON-GPU uses a 2D distribution of threads with a fixed block size of 32 × 32 and a fixed grid size of 4β, β is a parameter to be determined according to the matrix size N. ICON-GPU assigns the operation of one element to one thread according to the index of element.
The additions, multiplication, and inversion in Figure 1 are element-wise operations.
Open image in new window Fig. 5 Pseudo codes for calling a kernel function and the operations inside a kernel function for element-wise operations.
The parallel strategy of type 1 is the same as the strategy described in Section "Parallelizing element-wise operations of matrices".
We classified the operations of these two steps into three types: (1) the summation of a matrix; (2) element-wise operations of matrices; (3) the NUFFT and the adjoint NUFFT.
The operations in 2D NUFFT and 2D adjoint NUFFT can be classified into three types: (1) element-wise operations of matrices; (2) 2D FFT; (3) calculation of window functions φ(x) and (hat{varphi }left( k right)).
The procedure can be described using element-wise operations (see Section 4.1), sum (see Section 4.3), cumulative sum (see Section 4.4), rotations (see Section 4.2) and sort (see Section 4.7).
After this initial sort, the procedure can be described using element-wise operations (see Section 4.1), sum (see Section 4.3), cumulative sum (see Section 4.4) and rotations (see Section 4.2).
