Eigen: Split Array for OpenMP - c++

Question

I want to split an Eigen dynamic-size array by columns evenly over OpenMP threads.
thread 0 | thread 1 | thread 2
[[0, 1, 2], [[0], | [[1], | [[2],
[3, 4, 5], becomes: [3], | [4], | [5],
[6, 7, 8]] [6]] | [7]] | [8]]
I can use the block method to do that, but I am not sure if Eigen would recognize the subarray for each thread occupies contiguous memory.
When I read the documentation of block type, has an InnerPanel template parameter with the following description:
InnerPanel is true, if the block maps to a set of rows of a row major
matrix or to set of columns of a column major matrix (optional). The
parameter allows to determine at compile time whether aligned access
is possible on the block expression.
Does Eigen know that vectorization over the subarray for each OpenMP thread is possible because each subarray actually occupies contiguous memory?
If not, how to make Eigen know this?
Program:
#include <Eigen/Eigen>
#include <iostream>
int main() {
// The dimensions of the matrix is not necessary 8 x 8.
// The dimension is only known at run time.
Eigen::MatrixXi x(8,8);
x.fill(0);
int n_parts = 3;
#pragma omp parallel for
for (int i = 0; i < n_parts; ++i) {
int st = i * x.cols() / n_parts;
int en = (i + 1) * x.cols() / n_parts;
x.block(0, st, x.rows(), en - st).fill(i);
}
std::cout << x << "\n";
}
Result (g++ test.cpp -I<path to eigen includes> -fopenmp -lgomp):
0 0 1 1 1 2 2 2
0 0 1 1 1 2 2 2
0 0 1 1 1 2 2 2
0 0 1 1 1 2 2 2
0 0 1 1 1 2 2 2
0 0 1 1 1 2 2 2
0 0 1 1 1 2 2 2
0 0 1 1 1 2 2 2

Answer 1

To make sure that a block expression is indeed occupying contiguous memory, use middleCols (or leftCols or rightCols) instead:
#include <Eigen/Core>
template<typename XprType, int BlockRows, int BlockCols, bool InnerPanel>
void inspectBlock(const Eigen::Block<XprType, BlockRows, BlockCols, InnerPanel>& block)
{
std::cout << __PRETTY_FUNCTION__ << '\n';
}
int main() {
Eigen::MatrixXi x(8,8);
inspectBlock(x.block(0, 1, x.rows(), 2));
inspectBlock(x.middleCols(1, 2));
}
Result:
void inspectBlock(const Eigen::Block<ArgType, BlockRows, BlockCols, InnerPanel>&) [with XprType = Eigen::Matrix<int, -1, -1>; int BlockRows = -1; int BlockCols = -1; bool InnerPanel = false]
void inspectBlock(const Eigen::Block<ArgType, BlockRows, BlockCols, InnerPanel>&) [with XprType = Eigen::Matrix<int, -1, -1>; int BlockRows = -1; int BlockCols = -1; bool InnerPanel = true]
Note: -1 is the value of Eigen::Dynamic, i.e., not fixed at compile time.
And of course, if your matrix was row major, you could split int topRows, middleRows or bottomRows, instead.