[Mlir-commits] [mlir] [MLIR][Presburger][WIP] Implement vertex enumeration and chamber decomposition for polytope generating function computation. (PR #78987)

[Arjun P]

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@@ -147,6 +148,324 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
                             std::vector({denominator}));
 }
 
+/// We use Gaussian elimination to find the solution to a set of d equations
+/// of the form
+/// a_1 x_1 + ... + a_d x_d + b_1 m_1 + ... + b_p m_p + c = 0
+/// where x_i are variables,
+/// m_i are parameters and
+/// a_i, b_i, c are rational coefficients.
+/// The solution expresses each x_i as an affine function of the m_i, and is
+/// therefore represented as a matrix of size d x (p+1).
+/// If there is no solution, we return null.
+std::optional<ParamPoint>
+mlir::presburger::detail::solveParametricEquations(FracMatrix equations) {
+  // equations is a d x (d + p + 1) matrix.
+  // Each row represents an equation.
+  unsigned d = equations.getNumRows();
+  unsigned numCols = equations.getNumColumns();
+
+  // If the determinant is zero, there is no unique solution.
+  // Thus we return null.
+  if (FracMatrix(equations.getSubMatrix(/*fromRow=*/0, /*toRow=*/d - 1,
+                                        /*fromColumn=*/0,
+                                        /*toColumn=*/d - 1))
+          .determinant() == 0)
+    return std::nullopt;
+
+  for (unsigned i = 0; i < d; ++i) {
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Superty wrote:

Write a comment like "Perform row operations to make the ith column all zeros except for the diagonal element, which is made to be one"

https://github.com/llvm/llvm-project/pull/78987