Add condition estimation to Cholesky (LLT) factorization.

Eigen/src/Cholesky/LLT.h

@@ -10,7 +10,7 @@
 #ifndef EIGEN_LLT_H
 #define EIGEN_LLT_H
 
-namespace Eigen { 
+namespace Eigen {
 
 namespace internal{
 template<typename MatrixType, int UpLo> struct LLT_Traits;
@@ -40,7 +40,7 @@ template<typename MatrixType, int UpLo> struct LLT_Traits;
   *
   * Example: \include LLT_example.cpp
   * Output: \verbinclude LLT_example.out
-  *    
+  *
   * \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
   */
  /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH)
@@ -135,6 +135,16 @@ template<typename _MatrixType, int _UpLo> class LLT
     template<typename InputType>
     LLT& compute(const EigenBase<InputType>& matrix);
 
+    /** \returns an estimate of the reciprocal condition number of the matrix of
+     *  which *this is the Cholesky decomposition.
+     */
+    RealScalar rcond() const
+    {
+      eigen_assert(m_isInitialized && "LLT is not initialized.");
+      eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
+      return ConditionEstimator<LLT<MatrixType, UpLo>, true >::rcond(m_l1_norm, *this);
+    }
+
     /** \returns the LLT decomposition matrix
       *
       * TODO: document the storage layout
@@ -164,7 +174,7 @@ template<typename _MatrixType, int _UpLo> class LLT
 
     template<typename VectorType>
     LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
-    
+
     #ifndef EIGEN_PARSED_BY_DOXYGEN
     template<typename RhsType, typename DstType>
     EIGEN_DEVICE_FUNC
@@ -172,17 +182,18 @@ template<typename _MatrixType, int _UpLo> class LLT
     #endif
 
   protected:
-    
+
     static void check_template_parameters()
     {
       EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
     }
-    
+
     /** \internal
       * Used to compute and store L
       * The strict upper part is not used and even not initialized.
       */
     MatrixType m_matrix;
+    RealScalar m_l1_norm;
     bool m_isInitialized;
     ComputationInfo m_info;
 };
@@ -268,7 +279,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower>
   static Index unblocked(MatrixType& mat)
   {
     using std::sqrt;
-    
+
     eigen_assert(mat.rows()==mat.cols());
     const Index size = mat.rows();
     for(Index k = 0; k < size; ++k)
@@ -328,7 +339,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower>
     return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
   }
 };
-  
+
 template<typename Scalar> struct llt_inplace<Scalar, Upper>
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
@@ -387,12 +398,32 @@ template<typename InputType>
 LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
 {
   check_template_parameters();
-  
+
   eigen_assert(a.rows()==a.cols());
   const Index size = a.rows();
   m_matrix.resize(size, size);
   m_matrix = a.derived();
 
+  // Compute matrix L1 norm = max abs column sum.
+  m_l1_norm = RealScalar(0);
+  if (_UpLo == Lower) {
+    for (int col = 0; col < size; ++col) {
+      const RealScalar abs_col_sum = m_matrix.col(col).tail(size - col).cwiseAbs().sum() +
+          m_matrix.row(col).tail(col).cwiseAbs().sum();
+      if (abs_col_sum > m_l1_norm) {
+        m_l1_norm = abs_col_sum;
+      }
+    }
+  } else {
+    for (int col = 0; col < a.cols(); ++col) {
+      const RealScalar abs_col_sum = m_matrix.col(col).tail(col).cwiseAbs().sum() +
+          m_matrix.row(col).tail(size - col).cwiseAbs().sum();
+      if (abs_col_sum > m_l1_norm) {
+        m_l1_norm = abs_col_sum;
+      }
+    }
+  }
+
   m_isInitialized = true;
   bool ok = Traits::inplace_decomposition(m_matrix);
   m_info = ok ? Success : NumericalIssue;
@@ -419,7 +450,7 @@ LLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, c
 
   return *this;
 }
- 
+
 #ifndef EIGEN_PARSED_BY_DOXYGEN
 template<typename _MatrixType,int _UpLo>
 template<typename RhsType, typename DstType>
@@ -431,7 +462,7 @@ void LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
 #endif
 
 /** \internal use x = llt_object.solve(x);
-  * 
+  *
   * This is the \em in-place version of solve().
   *
   * \param bAndX represents both the right-hand side matrix b and result x.
@@ -483,7 +514,7 @@ SelfAdjointView<MatrixType, UpLo>::llt() const
   return LLT<PlainObject,UpLo>(m_matrix);
 }
 #endif // __CUDACC__
-  
+
 } // end namespace Eigen
 
 #endif // EIGEN_LLT_H

Eigen/src/Core/ConditionEstimator.h

@@ -13,11 +13,11 @@
 namespace Eigen {
 
 namespace internal {
-template <typename Decomposition, bool IsComplex>
+template <typename Decomposition, bool IsSelfAdjoint, bool IsComplex>
 struct EstimateInverseMatrixL1NormImpl {};
 }  // namespace internal
 
-template <typename Decomposition>
+template <typename Decomposition, bool IsSelfAdjoint = false>
 class ConditionEstimator {
  public:
   typedef typename Decomposition::MatrixType MatrixType;
@@ -101,7 +101,8 @@ class ConditionEstimator {
       return 0;
     }
     return internal::EstimateInverseMatrixL1NormImpl<
-        Decomposition, NumTraits<Scalar>::IsComplex>::compute(dec);
+        Decomposition, IsSelfAdjoint,
+        NumTraits<Scalar>::IsComplex != 0>::compute(dec);
   }
 
   /**
@@ -116,9 +117,27 @@ class ConditionEstimator {
 
 namespace internal {
 
+template <typename Decomposition, typename Vector, bool IsSelfAdjoint = false>
+struct solve_helper {
+  static inline Vector solve_adjoint(const Decomposition& dec,
+                                     const Vector& v) {
+    return dec.adjoint().solve(v);
+  }
+};
+
+// Partial specialization for self_adjoint matrices.
+template <typename Decomposition, typename Vector>
+struct solve_helper<Decomposition, Vector, true> {
+  static inline Vector solve_adjoint(const Decomposition& dec,
+                                     const Vector& v) {
+    return dec.solve(v);
+  }
+};
+
+
 // Partial specialization for real matrices.
-template <typename Decomposition>
-struct EstimateInverseMatrixL1NormImpl<Decomposition, 0> {
+template <typename Decomposition, bool IsSelfAdjoint>
+struct EstimateInverseMatrixL1NormImpl<Decomposition, IsSelfAdjoint, false> {
   typedef typename Decomposition::MatrixType MatrixType;
   typedef typename internal::traits<MatrixType>::Scalar Scalar;
   typedef typename internal::plain_col_type<MatrixType>::type Vector;
@@ -152,7 +171,7 @@ struct EstimateInverseMatrixL1NormImpl<Decomposition, 0> {
     int old_v_max_abs_index = v_max_abs_index;
     for (int k = 0; k < 4; ++k) {
       // argmax |inv(matrix)^T * sign_vector|
-      v = dec.adjoint().solve(sign_vector);
+      v = solve_helper<Decomposition, Vector, IsSelfAdjoint>::solve_adjoint(dec, sign_vector);
       v.cwiseAbs().maxCoeff(&v_max_abs_index);
       if (v_max_abs_index == old_v_max_abs_index) {
         // Break if the solution stagnated.
@@ -200,8 +219,8 @@ struct EstimateInverseMatrixL1NormImpl<Decomposition, 0> {
 };
 
 // Partial specialization for complex matrices.
-template <typename Decomposition>
-struct EstimateInverseMatrixL1NormImpl<Decomposition, 1> {
+template <typename Decomposition, bool IsSelfAdjoint>
+struct EstimateInverseMatrixL1NormImpl<Decomposition, IsSelfAdjoint, true> {
   typedef typename Decomposition::MatrixType MatrixType;
   typedef typename internal::traits<MatrixType>::Scalar Scalar;
   typedef typename NumTraits<Scalar>::Real RealScalar;
@@ -238,7 +257,7 @@ struct EstimateInverseMatrixL1NormImpl<Decomposition, 1> {
       RealVector abs_v = v.cwiseAbs();
       const Vector psi =
           (abs_v.array() == 0).select(v.cwiseQuotient(abs_v), ones);
-      v = dec.adjoint().solve(psi);
+      v = solve_helper<Decomposition, Vector, IsSelfAdjoint>::solve_adjoint(dec, psi);
       const RealVector z = v.real();
       z.cwiseAbs().maxCoeff(&v_max_abs_index);
       if (v_max_abs_index == old_v_max_abs_index) {