From f0b1b1df9bb893b5fb7d6673b33dad794105c811 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 16 Feb 2015 19:09:22 +0100
Subject: [PATCH] Fix SparseLU::signDeterminant() method, and add a
 SparseLU::determinant() method.

---
 Eigen/src/SparseLU/SparseLU.h | 55 ++++++++++++++++++++++++++++++++---
 test/sparselu.cpp             |  3 ++
 2 files changed, 54 insertions(+), 4 deletions(-)

diff --git a/Eigen/src/SparseLU/SparseLU.h b/Eigen/src/SparseLU/SparseLU.h
index 1e448f2ab..1a21c2a08 100644
--- a/Eigen/src/SparseLU/SparseLU.h
+++ b/Eigen/src/SparseLU/SparseLU.h
@@ -302,7 +302,50 @@ class SparseLU : public SparseSolverBase<SparseLU<_MatrixType,_OrderingType> >,
     Scalar signDeterminant()
     {
       eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
-      return Scalar(m_detPermR);
+      // Initialize with the determinant of the row matrix
+      Index det = 1;
+      // Note that the diagonal blocks of U are stored in supernodes,
+      // which are available in the  L part :)
+      for (Index j = 0; j < this->cols(); ++j)
+      {
+        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+        {
+          if(it.index() == j)
+          {
+            if(it.value()<0)
+              det = -det;
+            else if(it.value()==0)
+              return 0;
+            break;
+          }
+        }
+      }
+      return det * m_detPermR * m_detPermC;
+    }
+    
+    /** \returns The determinant of the matrix.
+      *
+      * \sa absDeterminant(), logAbsDeterminant()
+      */
+    Scalar determinant()
+    {
+      eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
+      // Initialize with the determinant of the row matrix
+      Scalar det = Scalar(1.);
+      // Note that the diagonal blocks of U are stored in supernodes,
+      // which are available in the  L part :)
+      for (Index j = 0; j < this->cols(); ++j)
+      {
+        for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it)
+        {
+          if(it.index() == j)
+          {
+            det *= it.value();
+            break;
+          }
+        }
+      }
+      return det * (m_detPermR * m_detPermC);
     }
 
   protected:
@@ -337,7 +380,7 @@ class SparseLU : public SparseSolverBase<SparseLU<_MatrixType,_OrderingType> >,
     internal::perfvalues m_perfv;
     RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot
     Index m_nnzL, m_nnzU; // Nonzeros in L and U factors
-    Index m_detPermR; // Determinant of the coefficient matrix
+    Index m_detPermR, m_detPermC; // Determinants of the permutation matrices
   private:
     // Disable copy constructor 
     SparseLU (const SparseLU& );
@@ -617,7 +660,8 @@ void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
       }
       
       // Update the determinant of the row permutation matrix
-      if (pivrow != jj) m_detPermR *= -1;
+      // FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not directly the row pivot.
+      if (pivrow != jj) m_detPermR = -m_detPermR;
 
       // Prune columns (0:jj-1) using column jj
       Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu); 
@@ -632,10 +676,13 @@ void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix)
     jcol += panel_size;  // Move to the next panel
   } // end for -- end elimination 
   
+  m_detPermR = m_perm_r.determinant();
+  m_detPermC = m_perm_c.determinant();
+  
   // Count the number of nonzeros in factors 
   Base::countnz(n, m_nnzL, m_nnzU, m_glu); 
   // Apply permutation  to the L subscripts 
-  Base::fixupL(n, m_perm_r.indices(), m_glu); 
+  Base::fixupL(n, m_perm_r.indices(), m_glu);
   
   // Create supernode matrix L 
   m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup); 
diff --git a/test/sparselu.cpp b/test/sparselu.cpp
index 52371cb12..37eb069a9 100644
--- a/test/sparselu.cpp
+++ b/test/sparselu.cpp
@@ -47,6 +47,9 @@ template<typename T> void test_sparselu_T()
   
   check_sparse_square_abs_determinant(sparselu_colamd);
   check_sparse_square_abs_determinant(sparselu_amd);
+  
+  check_sparse_square_determinant(sparselu_colamd);
+  check_sparse_square_determinant(sparselu_amd);
 }
 
 void test_sparselu()