feat(poly): refactoring PolytropeOperator to work on the reduced system so as to avoid rank deficiencies

src/poly/utils/private/utilities.cpp

@@ -1,5 +1,96 @@
-//
-// Created by Emily Boudreaux on 6/4/25.
-//
-
 #include "utilities.h"
+#include "mfem.hpp"
+
+namespace serif::utilities {
+    mfem::SparseMatrix buildReducedMatrix(
+        const mfem::SparseMatrix& matrix,
+        const mfem::Array<int>& trialEssentialDofs,
+        const mfem::Array<int>& testEssentialDofs
+    ) {
+        int M_orig = matrix.Height();
+        int N_orig = matrix.Width();
+
+        // 1. Create boolean lookup tables for eliminated rows/columns
+        // These tables help quickly check if an original row/column index is eliminated.
+        mfem::Array<bool> row_is_eliminated(M_orig);
+        row_is_eliminated = false; // Initialize all to false (no rows eliminated yet)
+        for (int i = 0; i < testEssentialDofs.Size(); ++i) {
+            int r_idx = testEssentialDofs[i];
+            if (r_idx >= 0 && r_idx < M_orig) { // Check for valid index
+                row_is_eliminated[r_idx] = true;
+            }
+        }
+
+        mfem::Array<bool> col_is_eliminated(N_orig);
+        col_is_eliminated = false; // Initialize all to false (no columns eliminated yet)
+        for (int i = 0; i < trialEssentialDofs.Size(); ++i) {
+            int c_idx = trialEssentialDofs[i];
+            if (c_idx >= 0 && c_idx < N_orig) { // Check for valid index
+                col_is_eliminated[c_idx] = true;
+            }
+        }
+
+        // 2. Create mappings from old (original) indices to new indices
+        // Also, count the number of rows and columns in the new, reduced matrix.
+        mfem::Array<int> old_row_to_new_row(M_orig);
+        int num_new_rows = 0;
+        for (int i = 0; i < M_orig; ++i) {
+            if (row_is_eliminated[i]) {
+                old_row_to_new_row[i] = -1; // Mark as eliminated (no corresponding new row)
+            } else {
+                old_row_to_new_row[i] = num_new_rows++; // Assign the next available new row index
+            }
+        }
+
+        mfem::Array<int> old_col_to_new_col(N_orig);
+        int num_new_cols = 0;
+        for (int i = 0; i < N_orig; ++i) {
+            if (col_is_eliminated[i]) {
+                old_col_to_new_col[i] = -1; // Mark as eliminated (no corresponding new column)
+            } else {
+                old_col_to_new_col[i] = num_new_cols++; // Assign the next available new column index
+            }
+        }
+
+        // 3. Create the new sparse matrix with the calculated reduced dimensions.
+        // It's initially empty (no non-zero entries).
+        mfem::SparseMatrix A_new(num_new_rows, num_new_cols);
+
+        // 4. Iterate through the non-zero entries of the original matrix (A_orig).
+        // A_orig is typically stored in Compressed Sparse Row (CSR) format.
+        // GetI() returns row pointers, GetJ() returns column indices, GetData() returns values.
+        const int* I_orig = matrix.GetI();
+        const int* J_orig = matrix.GetJ();
+        const double* V_orig = matrix.GetData(); // Assuming double, can be templated if needed
+
+        for (int r_orig = 0; r_orig < M_orig; ++r_orig) {
+            // If the original row is marked for elimination, skip all its entries.
+            if (row_is_eliminated[r_orig]) {
+                continue;
+            }
+
+            // Get the new row index for the current original row.
+            int r_new = old_row_to_new_row[r_orig];
+
+            // Iterate through non-zero entries in the current original row r_orig.
+            // I_orig[r_orig] is the start index in J_orig and V_orig for row r_orig.
+            // I_orig[r_orig+1]-1 is the end index.
+            for (int k = I_orig[r_orig]; k < I_orig[r_orig + 1]; ++k) {
+                int c_orig = J_orig[k]; // Original column index of the non-zero entry
+                double val = V_orig[k]; // Value of the non-zero entry
+
+                if (col_is_eliminated[c_orig]) {
+                    continue;
+                }
+
+                int c_new = old_col_to_new_col[c_orig];
+
+                A_new.Add(r_new, c_new, val);
+            }
+        }
+
+        A_new.Finalize();
+
+        return A_new;
+    }
+}