Fix infinite loop in complex non-symmetric eigenvalue decomposition

src/Numerics.Tests/LinearAlgebraTests/Complex/Factorization/EvdTests.cs

@@ -259,5 +259,26 @@ public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Valu
             AssertHelpers.AlmostEqual(ACopy, A, 14);
             AssertHelpers.AlmostEqual(BCopy, B, 14);
         }
+
+        /// <summary>
+        /// Factorizing a defective matrix with a repeated eigenvalue throws
+        /// NonConvergenceException instead of looping forever (see issue #11).
+        /// This exercises the managed provider path used by DenseMatrix.Evd().
+        /// </summary>
+        [Test]
+        public void DefectiveMatrixThrowsNonConvergenceException()
+        {
+            // Lower-triangular with a single eigenvalue (0.9275488) of algebraic
+            // multiplicity 3 - a defective (non-diagonalizable) matrix that the
+            // non-symmetric complex QR iteration cannot converge on.
+            var matrix = Matrix<Complex>.Build.DenseOfArray(new[,]
+            {
+                { new Complex(0.9275488, 0), Complex.Zero, Complex.Zero },
+                { new Complex(-0.9275488, 0), new Complex(0.9275488, 0), Complex.Zero },
+                { Complex.Zero, new Complex(-0.9275488, 0), new Complex(0.9275488, 0) }
+            });
+
+            Assert.Throws<NonConvergenceException>(() => matrix.Evd());
+        }
     }
 }

src/Numerics.Tests/LinearAlgebraTests/Complex/Factorization/UserEvdTests.cs

@@ -314,5 +314,25 @@ public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Valu
             AssertHelpers.AlmostEqual(ACopy, A, 14);
             AssertHelpers.AlmostEqual(BCopy, B, 14);
         }
+
+        /// <summary>
+        /// Factorizing a defective matrix with a repeated eigenvalue throws
+        /// NonConvergenceException instead of looping forever (see issue #11).
+        /// </summary>
+        [Test]
+        public void DefectiveMatrixThrowsNonConvergenceException()
+        {
+            // Lower-triangular with a single eigenvalue (0.9275488) of algebraic
+            // multiplicity 3 - a defective (non-diagonalizable) matrix that the
+            // non-symmetric complex QR iteration cannot converge on.
+            var matrixA = new UserDefinedMatrix(new[,]
+            {
+                { new Complex(0.9275488, 0), Complex.Zero, Complex.Zero },
+                { new Complex(-0.9275488, 0), new Complex(0.9275488, 0), Complex.Zero },
+                { Complex.Zero, new Complex(-0.9275488, 0), new Complex(0.9275488, 0) }
+            });
+
+            Assert.Throws<NonConvergenceException>(() => matrixA.Evd());
+        }
     }
 }

src/Numerics.Tests/LinearAlgebraTests/Complex32/Factorization/EvdTests.cs

@@ -257,5 +257,26 @@ public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Valu
             AssertHelpers.AlmostEqual(ACopy, A, 14);
             AssertHelpers.AlmostEqual(BCopy, B, 14);
         }
+
+        /// <summary>
+        /// Factorizing a defective matrix with a repeated eigenvalue throws
+        /// NonConvergenceException instead of looping forever (see issue #11).
+        /// This exercises the managed provider path used by DenseMatrix.Evd().
+        /// </summary>
+        [Test]
+        public void DefectiveMatrixThrowsNonConvergenceException()
+        {
+            // Lower-triangular with a single eigenvalue (0.9275488) of algebraic
+            // multiplicity 3 - a defective (non-diagonalizable) matrix that the
+            // non-symmetric complex QR iteration cannot converge on.
+            var matrix = Matrix<Complex32>.Build.DenseOfArray(new[,]
+            {
+                { new Complex32(0.9275488f, 0f), Complex32.Zero, Complex32.Zero },
+                { new Complex32(-0.9275488f, 0f), new Complex32(0.9275488f, 0f), Complex32.Zero },
+                { Complex32.Zero, new Complex32(-0.9275488f, 0f), new Complex32(0.9275488f, 0f) }
+            });
+
+            Assert.Throws<NonConvergenceException>(() => matrix.Evd());
+        }
     }
 }

src/Numerics.Tests/LinearAlgebraTests/Complex32/Factorization/UserEvdTests.cs

@@ -312,5 +312,25 @@ public void CanSolveForRandomMatrixAndSymmetricMatrixWhenResultMatrixGiven([Valu
             AssertHelpers.AlmostEqual(ACopy, A, 14);
             AssertHelpers.AlmostEqual(BCopy, B, 14);
         }
+
+        /// <summary>
+        /// Factorizing a defective matrix with a repeated eigenvalue throws
+        /// NonConvergenceException instead of looping forever (see issue #11).
+        /// </summary>
+        [Test]
+        public void DefectiveMatrixThrowsNonConvergenceException()
+        {
+            // Lower-triangular with a single eigenvalue (0.9275488) of algebraic
+            // multiplicity 3 - a defective (non-diagonalizable) matrix that the
+            // non-symmetric complex QR iteration cannot converge on.
+            var matrixA = new UserDefinedMatrix(new[,]
+            {
+                { new Complex32(0.9275488f, 0f), Complex32.Zero, Complex32.Zero },
+                { new Complex32(-0.9275488f, 0f), new Complex32(0.9275488f, 0f), Complex32.Zero },
+                { Complex32.Zero, new Complex32(-0.9275488f, 0f), new Complex32(0.9275488f, 0f) }
+            });
+
+            Assert.Throws<NonConvergenceException>(() => matrixA.Evd());
+        }
     }
 }

src/Numerics/LinearAlgebra/Complex/Factorization/UserEvd.cs

@@ -662,6 +662,10 @@ static void NonsymmetricReduceHessenberToRealSchur(Matrix<Complex> eigenVectors,
 
                     exshift += s;
                     iter++;
+                    if (iter >= 30*order)
+                    {
+                        throw new NonConvergenceException();
+                    }
 
                     // Reduce to triangle (rows)
                     for (var i = l + 1; i <= n; i++)

src/Numerics/LinearAlgebra/Complex32/Factorization/UserEvd.cs

@@ -666,6 +666,10 @@ static void NonsymmetricReduceHessenberToRealSchur(Matrix<Complex32> eigenVector
 
                     exshift += s;
                     iter++;
+                    if (iter >= 30*order)
+                    {
+                        throw new NonConvergenceException();
+                    }
 
                     // Reduce to triangle (rows)
                     for (var i = l + 1; i <= n; i++)

src/Numerics/Providers/LinearAlgebra/ManagedLinearAlgebraProvider.Complex.cs

@@ -3055,6 +3055,10 @@ internal static void NonsymmetricReduceHessenberToRealSchur(Complex[] vectorV, C
 
                     exshift += s;
                     iter++;
+                    if (iter >= 30*order)
+                    {
+                        throw new NonConvergenceException();
+                    }
 
                     // Reduce to triangle (rows)
                     for (var i = l + 1; i <= n; i++)

src/Numerics/Providers/LinearAlgebra/ManagedLinearAlgebraProvider.Complex32.cs

@@ -3057,6 +3057,10 @@ internal static void NonsymmetricReduceHessenberToRealSchur(Complex32[] vectorV,
 
                     exshift += s;
                     iter++;
+                    if (iter >= 30*order)
+                    {
+                        throw new NonConvergenceException();
+                    }
 
                     // Reduce to triangle (rows)
                     for (var i = l + 1; i <= n; i++)