Add an info() method to the SVDBase class to make it possible to tell the user that the computation failed, possibly due to invalid input.

Make Jacobi and divide-and-conquer fail fast and return info() == InvalidInput if the matrix contains NaN or +/-Inf.

Eigen/src/SVD/BDCSVD.h

@@ -208,6 +208,7 @@ protected:
   using Base::m_computeThinV;
   using Base::m_matrixU;
   using Base::m_matrixV;
+  using Base::m_info;
   using Base::m_isInitialized;
   using Base::m_nonzeroSingularValues;
 
@@ -256,16 +257,25 @@ BDCSVD<MatrixType>& BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsign
   {
     // FIXME this line involves temporaries
     JacobiSVD<MatrixType> jsvd(matrix,computationOptions);
+    m_isInitialized = true;
+    m_info = jsvd.info();
+    if (m_info == Success || m_info == NoConvergence) {
       if(computeU()) m_matrixU = jsvd.matrixU();
       if(computeV()) m_matrixV = jsvd.matrixV();
       m_singularValues = jsvd.singularValues();
       m_nonzeroSingularValues = jsvd.nonzeroSingularValues();
-    m_isInitialized = true;
+    }
     return *this;
   }
   
   //**** step 0 - Copy the input matrix and apply scaling to reduce over/under-flows
-  RealScalar scale = matrix.cwiseAbs().maxCoeff();
+  RealScalar scale = matrix.cwiseAbs().template maxCoeff<PropagateNaN>();
+  if (!(numext::isfinite)(scale)) {
+    m_isInitialized = true;
+    m_info = InvalidInput;
+    return *this;
+  }
+
   if(scale==Literal(0)) scale = Literal(1);
   MatrixX copy;
   if (m_isTranspose) copy = matrix.adjoint()/scale;
@@ -282,6 +292,10 @@ BDCSVD<MatrixType>& BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsign
   m_computed.topRows(m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();
   m_computed.template bottomRows<1>().setZero();
   divide(0, m_diagSize - 1, 0, 0, 0);
+  if (m_info != Success && m_info != NoConvergence) {
+    m_isInitialized = true;
+    return *this;
+  }
     
   //**** step 3 - Copy singular values and vectors
   for (int i=0; i<m_diagSize; i++)
@@ -394,7 +408,7 @@ void BDCSVD<MatrixType>::structured_update(Block<MatrixXr,Dynamic,Dynamic> A, co
 //@param shift : Each time one takes the left submatrix, one must add 1 to the shift. Why? Because! We actually want the last column of the U submatrix 
 // to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper.
 template<typename MatrixType>
-void BDCSVD<MatrixType>::divide (Eigen::Index firstCol, Eigen::Index lastCol, Eigen::Index firstRowW, Eigen::Index firstColW, Eigen::Index shift)
+void BDCSVD<MatrixType>::divide(Eigen::Index firstCol, Eigen::Index lastCol, Eigen::Index firstRowW, Eigen::Index firstColW, Eigen::Index shift)
 {
   // requires rows = cols + 1;
   using std::pow;
@@ -414,6 +428,8 @@ void BDCSVD<MatrixType>::divide (Eigen::Index firstCol, Eigen::Index lastCol, Ei
   {
     // FIXME this line involves temporaries
     JacobiSVD<MatrixXr> b(m_computed.block(firstCol, firstCol, n + 1, n), ComputeFullU | (m_compV ? ComputeFullV : 0));
+    m_info = b.info();
+    if (m_info != Success && m_info != NoConvergence) return;
     if (m_compU)
       m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() = b.matrixU();
     else 
@@ -433,7 +449,9 @@ void BDCSVD<MatrixType>::divide (Eigen::Index firstCol, Eigen::Index lastCol, Ei
   // and the divide of the right submatrice reads one column of the left submatrice. That's why we need to treat the 
   // right submatrix before the left one. 
   divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);
+  if (m_info != Success && m_info != NoConvergence) return;
   divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);
+  if (m_info != Success && m_info != NoConvergence) return;
 
   if (m_compU)
   {

Eigen/src/SVD/JacobiSVD.h

@@ -585,6 +585,7 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
     using Base::m_matrixU;
     using Base::m_matrixV;
     using Base::m_singularValues;
+    using Base::m_info;
     using Base::m_isInitialized;
     using Base::m_isAllocated;
     using Base::m_usePrescribedThreshold;
@@ -625,6 +626,7 @@ void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Eigen::Index rows, Eigen:
 
   m_rows = rows;
   m_cols = cols;
+  m_info = Success;
   m_isInitialized = false;
   m_isAllocated = true;
   m_computationOptions = computationOptions;
@@ -674,7 +676,12 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
   const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
 
   // Scaling factor to reduce over/under-flows
-  RealScalar scale = matrix.cwiseAbs().maxCoeff();
+  RealScalar scale = matrix.cwiseAbs().template maxCoeff<PropagateNaN>();
+  if (!(numext::isfinite)(scale)) {
+    m_isInitialized = true;
+    m_info = InvalidInput;
+    return *this;
+  }
   if(scale==RealScalar(0)) scale = RealScalar(1);
   
   /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */

Eigen/src/SVD/SVDBase.h

@@ -52,7 +52,7 @@ template<typename Derived> struct traits<SVDBase<Derived> >
  * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
  * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
  *  
- * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
+ * If the input matrix has inf or nan coefficients, the result of the computation is undefined, and \a info() will return \a InvalidInput, but the computation is guaranteed to
  * terminate in finite (and reasonable) time.
  * \sa class BDCSVD, class JacobiSVD
  */
@@ -97,7 +97,7 @@ public:
    */
   const MatrixUType& matrixU() const
   {
-    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    _check_compute_assertions();
     eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
     return m_matrixU;
   }
@@ -113,7 +113,7 @@ public:
    */
   const MatrixVType& matrixV() const
   {
-    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    _check_compute_assertions();
     eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
     return m_matrixV;
   }
@@ -125,14 +125,14 @@ public:
    */
   const SingularValuesType& singularValues() const
   {
-    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    _check_compute_assertions();
     return m_singularValues;
   }
 
   /** \returns the number of singular values that are not exactly 0 */
   Index nonzeroSingularValues() const
   {
-    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    _check_compute_assertions();
     return m_nonzeroSingularValues;
   }
   
@@ -145,7 +145,7 @@ public:
   inline Index rank() const
   {
     using std::abs;
-    eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+    _check_compute_assertions();
     if(m_singularValues.size()==0) return 0;
     RealScalar premultiplied_threshold = numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)());
     Index i = m_nonzeroSingularValues-1;
@@ -224,6 +224,18 @@ public:
   solve(const MatrixBase<Rhs>& b) const;
   #endif
 
+
+  /** \brief Reports whether previous computation was successful.
+   *
+   * \returns \c Success if computation was successful.
+   */
+  EIGEN_DEVICE_FUNC
+  ComputationInfo info() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    return m_info;
+  }
+
   #ifndef EIGEN_PARSED_BY_DOXYGEN
   template<typename RhsType, typename DstType>
   void _solve_impl(const RhsType &rhs, DstType &dst) const;
@@ -239,10 +251,16 @@ protected:
     EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
   }
 
+  void _check_compute_assertions() const {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    eigen_assert(m_info != InvalidInput && "SVD failed due to invalid input.");
+    eigen_assert(m_info != NumericalIssue && "SVD failed due to invalid input.");
+  }
+
   template<bool Transpose_, typename Rhs>
   void _check_solve_assertion(const Rhs& b) const {
       EIGEN_ONLY_USED_FOR_DEBUG(b);
-      eigen_assert(m_isInitialized && "SVD is not initialized.");
+      _check_compute_assertions();
       eigen_assert(computeU() && computeV() && "SVDBase::solve(): Both unitaries U and V are required to be computed (thin unitaries suffice).");
       eigen_assert((Transpose_?cols():rows())==b.rows() && "SVDBase::solve(): invalid number of rows of the right hand side matrix b");
   }
@@ -253,6 +271,7 @@ protected:
   MatrixUType m_matrixU;
   MatrixVType m_matrixV;
   SingularValuesType m_singularValues;
+  ComputationInfo m_info;
   bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
   bool m_computeFullU, m_computeThinU;
   bool m_computeFullV, m_computeThinV;
@@ -265,7 +284,8 @@ protected:
    * Default constructor of SVDBase
    */
   SVDBase()
-    : m_isInitialized(false),
+    : m_info(Success),
+      m_isInitialized(false),
       m_isAllocated(false),
       m_usePrescribedThreshold(false),
       m_computeFullU(false),
@@ -327,6 +347,7 @@ bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computat
 
   m_rows = rows;
   m_cols = cols;
+  m_info = Success;
   m_isInitialized = false;
   m_isAllocated = true;
   m_computationOptions = computationOptions;

test/svd_common.h

@@ -298,7 +298,8 @@ EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
 // workaround aggressive optimization in ICC
 template<typename T> EIGEN_DONT_INLINE  T sub(T a, T b) { return a - b; }
 
-// all this function does is verify we don't iterate infinitely on nan/inf values
+// This function verifies we don't iterate infinitely on nan/inf values,
+// and that info() returns InvalidInput.
 template<typename SvdType, typename MatrixType>
 void svd_inf_nan()
 {
@@ -307,18 +308,22 @@ void svd_inf_nan()
   Scalar some_inf = Scalar(1) / zero<Scalar>();
   VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
   svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
+  VERIFY(svd.info() == InvalidInput);
 
   Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
   VERIFY(nan != nan);
   svd.compute(MatrixType::Constant(10,10,nan), ComputeFullU | ComputeFullV);
+  VERIFY(svd.info() == InvalidInput);  
 
   MatrixType m = MatrixType::Zero(10,10);
   m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
   svd.compute(m, ComputeFullU | ComputeFullV);
+  VERIFY(svd.info() == InvalidInput);
 
   m = MatrixType::Zero(10,10);
   m(internal::random<int>(0,9), internal::random<int>(0,9)) = nan;
   svd.compute(m, ComputeFullU | ComputeFullV);
+  VERIFY(svd.info() == InvalidInput);
   
   // regression test for bug 791
   m.resize(3,3);
@@ -326,6 +331,7 @@ void svd_inf_nan()
        0,   -0.5,                             0,
        nan,  0,                               0;
   svd.compute(m, ComputeFullU | ComputeFullV);
+  VERIFY(svd.info() == InvalidInput);
   
   m.resize(4,4);
   m <<  1, 0, 0, 0,
@@ -333,6 +339,7 @@ void svd_inf_nan()
         1, 0, 1, nan,
         0, nan, nan, 0;
   svd.compute(m, ComputeFullU | ComputeFullV);
+  VERIFY(svd.info() == InvalidInput);
 }
 
 // Regression test for bug 286: JacobiSVD loops indefinitely with some