gauss jordan

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/math/simplex/sparse_matrix_ops.h

@@ -0,0 +1,68 @@
+/*++
+Copyright (c) 2014 Microsoft Corporation
+
+Module Name:
+
+    sparse_matrix_ops.h
+
+Abstract:
+
+    
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2014-01-15
+
+Notes:
+
+--*/
+
+#pragma once
+
+#include "math/simplex/sparse_matrix.h"
+#include "util/rational.h"
+
+namespace simplex {
+
+    class sparse_matrix_ops {
+    public:
+        static void gauss_jordan(sparse_matrix<mpq_ext>& M) {
+            mpq_ext::numeral coeff;
+            vector<unsigned> c, d;
+            unsigned m = M.num_vars();
+            for (unsigned v = 0; v < m; ++v)
+                c.push_back(0);
+            
+            for (auto const& row : M.get_rows()) {
+                // scan for non-zero variable in row
+                bool found = false;
+                for (auto const& [coeff1, v] : M.get_row(row)) {
+                    if (mpq_manager<false>::is_zero(coeff1))
+                        continue;
+                    found = true;
+                    d.push_back(v);
+                    c[v] = row.id() + 1;
+                    // eliminate v from other rows.
+                    for (auto const& [row2, row_entry2] : M.get_rows(v)) {
+                        if (row.id() == row2.id())
+                            continue;
+                        if (row_entry2->m_coeff == 0)
+                            continue;
+                        M.get_manager().set(coeff, (- row_entry2->m_coeff / coeff1).to_mpq());
+                        M.add(row2, coeff, row);
+                    }
+                    break;
+                }
+                if (!found)
+                    d.push_back(0);
+                
+            }
+
+            M.get_manager().del(coeff);
+
+            // TODO: do something with c and d
+        }
+    };
+
+
+}
+