Several improvements in sparse module:

* add a LDL^T factorization with solver using code from T. Davis's LDL
  library (LPGL2.1+)
* various bug fixes in trianfular solver, matrix product, etc.
* improve cmake files for the supported libraries
* split the sparse unit test
* etc.

1 files changed, 180 insertions, 0 deletions

diff --git a/test/sparse_solvers.cpp b/test/sparse_solvers.cpp
new file mode 100644
index 000000000..b73494879
--- /dev/null
+++ b/test/sparse_solvers.cpp
@@ -0,0 +1,180 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "sparse.h"
+
+template<typename Scalar> void sparse_solvers(int rows, int cols)
+{
+  double density = std::max(8./(rows*cols), 0.01);
+  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+  typedef Matrix<Scalar,Dynamic,1> DenseVector;
+  Scalar eps = 1e-6;
+
+  DenseVector vec1 = DenseVector::Random(rows);
+
+  std::vector<Vector2i> zeroCoords;
+  std::vector<Vector2i> nonzeroCoords;
+
+  // test triangular solver
+  {
+    DenseVector vec2 = vec1, vec3 = vec1;
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+
+    // lower
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<Lower>().solveTriangular(vec2),
+                     m2.template marked<Lower>().solveTriangular(vec3));
+
+    // upper
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<Upper>().solveTriangular(vec2),
+                     m2.template marked<Upper>().solveTriangular(vec3));
+
+    // TODO test row major
+  }
+
+  // test LLT
+  if (!NumTraits<Scalar>::IsComplex)
+  {
+    // TODO fix the issue with complex (see SparseLLT::solveInPlace)
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2(rows, cols);
+
+    DenseVector b = DenseVector::Random(cols);
+    DenseVector refX(cols), x(cols);
+
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+    refMat2 += refMat2.adjoint();
+    refMat2.diagonal() *= 0.5;
+
+    refMat2.llt().solve(b, &refX);
+    typedef SparseMatrix<Scalar,Lower|SelfAdjoint> SparseSelfAdjointMatrix;
+    x = b;
+    SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x);
+    //VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
+    #ifdef EIGEN_CHOLMOD_SUPPORT
+    x = b;
+    SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x);
+    VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
+    #endif
+    #ifdef EIGEN_TAUCS_SUPPORT
+    x = b;
+    SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x);
+    VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)");
+    x = b;
+    SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x);
+    VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)");
+    x = b;
+    SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x);
+    VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)");
+    #endif
+  }
+
+  // test LDLT
+  if (!NumTraits<Scalar>::IsComplex)
+  {
+    // TODO fix the issue with complex (see SparseLDT::solveInPlace)
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2(rows, cols);
+
+    DenseVector b = DenseVector::Random(cols);
+    DenseVector refX(cols), x(cols);
+
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+    refMat2 += refMat2.adjoint();
+    refMat2.diagonal() *= 0.5;
+
+    refMat2.ldlt().solve(b, &refX);
+    typedef SparseMatrix<Scalar,Lower|SelfAdjoint> SparseSelfAdjointMatrix;
+    x = b;
+    SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
+    if (ldlt.succeeded())
+      ldlt.solveInPlace(x);
+    VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
+  }
+
+  // test LU
+  {
+    static int count = 0;
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2(rows, cols);
+
+    DenseVector b = DenseVector::Random(cols);
+    DenseVector refX(cols), x(cols);
+
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords);
+
+    LU<DenseMatrix> refLu(refMat2);
+    refLu.solve(b, &refX);
+    Scalar refDet = refLu.determinant();
+    x.setZero();
+    // // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x);
+    // // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default");
+    #ifdef EIGEN_SUPERLU_SUPPORT
+    {
+      x.setZero();
+      SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2);
+      if (slu.succeeded())
+      {
+        if (slu.solve(b,&x)) {
+          VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
+        }
+        // std::cerr << refDet << " == " << slu.determinant() << "\n";
+        if (count==0) {
+          VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
+        }
+      }
+    }
+    #endif
+    #ifdef EIGEN_UMFPACK_SUPPORT
+    {
+      // check solve
+      x.setZero();
+      SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2);
+      if (slu.succeeded()) {
+        if (slu.solve(b,&x)) {
+          if (count==0) {
+            VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack");  // FIXME solve is not very stable for complex
+          }
+        }
+        VERIFY_IS_APPROX(refDet,slu.determinant());
+        // TODO check the extracted data
+        //std::cerr << slu.matrixL() << "\n";
+      }
+    }
+    #endif
+    count++;
+  }
+
+}
+
+void test_sparse_solvers()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( sparse_solvers<double>(8, 8) );
+    CALL_SUBTEST( sparse_solvers<std::complex<double> >(16, 16) );
+    CALL_SUBTEST( sparse_solvers<double>(33, 33) );
+  }
+}