LA: fix return type of Norms to double (instead of T)

src/Numerics/Distance.cs

@@ -47,7 +47,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
         /// </summary>
-        public static float SAD(Vector<float> a, Vector<float> b)
+        public static double SAD(Vector<float> a, Vector<float> b)
         {
             return (a - b).L1Norm();
         }
@@ -59,7 +59,7 @@ namespace MathNet.Numerics
         {
             if (a.Length != b.Length) throw new ArgumentException(Resources.ArgumentVectorsSameLength);
 
-            var sum = 0d;
+            double sum = 0d;
             for (var i = 0; i < a.Length; i++)
             {
                 sum += Math.Abs(a[i] - b[i]);
@@ -74,7 +74,7 @@ namespace MathNet.Numerics
         {
             if (a.Length != b.Length) throw new ArgumentException(Resources.ArgumentVectorsSameLength);
 
-            var sum = 0f;
+            float sum = 0f;
             for (var i = 0; i < a.Length; i++)
             {
                 sum += Math.Abs(a[i] - b[i]);
@@ -93,7 +93,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
         /// </summary>
-        public static float MAE(Vector<float> a, Vector<float> b)
+        public static double MAE(Vector<float> a, Vector<float> b)
         {
             return (a - b).L1Norm()/a.Count;
         }
@@ -126,7 +126,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
         /// </summary>
-        public static float SSD(Vector<float> a, Vector<float> b)
+        public static double SSD(Vector<float> a, Vector<float> b)
         {
             var norm = (a - b).L2Norm();
             return norm*norm;
@@ -164,7 +164,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
         /// </summary>
-        public static float MSE(Vector<float> a, Vector<float> b)
+        public static double MSE(Vector<float> a, Vector<float> b)
         {
             var norm = (a - b).L2Norm();
             return norm*norm/a.Count;
@@ -197,7 +197,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Euclidean Distance, i.e. the L2-norm of the difference.
         /// </summary>
-        public static float Euclidean(Vector<float> a, Vector<float> b)
+        public static double Euclidean(Vector<float> a, Vector<float> b)
         {
             return (a - b).L2Norm();
         }
@@ -229,7 +229,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Manhattan Distance, i.e. the L1-norm of the difference.
         /// </summary>
-        public static float Manhattan(Vector<float> a, Vector<float> b)
+        public static double Manhattan(Vector<float> a, Vector<float> b)
         {
             return (a - b).L1Norm();
         }
@@ -261,7 +261,7 @@ namespace MathNet.Numerics
         /// <summary>
         /// Chebyshev Distance, i.e. the Infinity-norm of the difference.
         /// </summary>
-        public static float Chebyshev(Vector<float> a, Vector<float> b)
+        public static double Chebyshev(Vector<float> a, Vector<float> b)
         {
             return (a - b).InfinityNorm();
         }
@@ -272,7 +272,7 @@ namespace MathNet.Numerics
         public static double Chebyshev(double[] a, double[] b)
         {
             if (a.Length != b.Length) throw new ArgumentOutOfRangeException("b");
-            var max = Math.Abs(a[0] - b[0]);
+            double max = Math.Abs(a[0] - b[0]);
             for (int i = 1; i < a.Length; i++)
             {
                 var next = Math.Abs(a[i] - b[i]);
@@ -290,7 +290,7 @@ namespace MathNet.Numerics
         public static float Chebyshev(float[] a, float[] b)
         {
             if (a.Length != b.Length) throw new ArgumentOutOfRangeException("b");
-            var max = Math.Abs(a[0] - b[0]);
+            float max = Math.Abs(a[0] - b[0]);
             for (int i = 1; i < a.Length; i++)
             {
                 var next = Math.Abs(a[i] - b[i]);

src/Numerics/LinearAlgebra/Complex/DenseVector.cs

@@ -552,9 +552,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override Complex L1Norm()
+        public override double L1Norm()
         {
-            var sum = Complex.Zero;
+            double sum = 0d;
             for (var i = 0; i < _length; i++)
             {
                 sum += _values[i].Magnitude;
@@ -566,7 +566,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Calculates the L2 norm of the vector, also known as Euclidean norm.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex L2Norm()
+        public override double L2Norm()
         {
             // TODO: native provider
             return _values.Aggregate(Complex.Zero, SpecialFunctions.Hypotenuse).Magnitude;
@@ -576,7 +576,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(_values, (i, v) => v.Magnitude, Math.Max, 0d);
         }
@@ -586,7 +586,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// </summary>
         /// <param name="p">The p value.</param>
         /// <returns>Scalar <c>ret = ( ∑|this[i]|^p )^(1/p)</c></returns>
-        public override Complex Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
@@ -594,7 +594,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var i = 0; i < _length; i++)
             {
                 sum += Math.Pow(_values[i].Magnitude, p);

src/Numerics/LinearAlgebra/Complex/Solvers/DivergenceStopCriterium.cs

@@ -220,7 +220,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers
 
             // Store the infinity norms of both the solution and residual vectors
             // These values will be used to calculate the relative drop in residuals later on.
-            _residualHistory[_residualHistory.Length - 1] = residualVector.InfinityNorm().Real;
+            _residualHistory[_residualHistory.Length - 1] = residualVector.InfinityNorm();
 
             // Check if we have NaN's. If so we've gone way beyond normal divergence.
             // Stop the iteration.

src/Numerics/LinearAlgebra/Complex/Solvers/FailureStopCriterium.cs

@@ -96,10 +96,10 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers
             }
 
             // Store the infinity norms of both the solution and residual vectors
-            var residualNorm = residualVector.InfinityNorm();
-            var solutionNorm = solutionVector.InfinityNorm();
+            double residualNorm = residualVector.InfinityNorm();
+            double solutionNorm = solutionVector.InfinityNorm();
 
-            _status = double.IsNaN(solutionNorm.Real) || double.IsNaN(residualNorm.Real) ? IterationStatus.Failure : IterationStatus.Continue;
+            _status = double.IsNaN(solutionNorm) || double.IsNaN(residualNorm) ? IterationStatus.Failure : IterationStatus.Continue;
 
             _lastIteration = iterationNumber;
             return _status;

src/Numerics/LinearAlgebra/Complex/Solvers/ILUTPPreconditioner.cs

@@ -435,7 +435,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers
                     // {
                     //     w(j) = 0
                     // }
-                    if (workVector[j].Magnitude <= _dropTolerance*vectorNorm.Real)
+                    if (workVector[j].Magnitude <= _dropTolerance*vectorNorm)
                     {
                         workVector[j] = 0.0;
                     }

src/Numerics/LinearAlgebra/Complex/Solvers/ResidualStopCriterium.cs

@@ -218,12 +218,12 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers
 
             // Check the residuals by calculating:
             // ||r_i|| <= stop_tol * ||b||
-            var stopCriterium = ComputeStopCriterium(sourceVector.InfinityNorm().Real);
+            var stopCriterium = ComputeStopCriterium(sourceVector.InfinityNorm());
 
             // First check that we have real numbers not NaN's.
             // NaN's can occur when the iterative process diverges so we
             // stop if that is the case.
-            if (double.IsNaN(stopCriterium) || double.IsNaN(residualNorm.Real))
+            if (double.IsNaN(stopCriterium) || double.IsNaN(residualNorm))
             {
                 _iterationCount = 0;
                 _status = IterationStatus.Diverged;
@@ -233,7 +233,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers
             // ||r_i|| <= stop_tol * ||b||
             // Stop the calculation if it's clearly smaller than the tolerance
             var decimalMagnitude = Math.Abs(stopCriterium.Magnitude()) + 1;
-            if (residualNorm.Real.IsSmallerWithDecimalPlaces(stopCriterium, decimalMagnitude))
+            if (residualNorm.IsSmallerWithDecimalPlaces(stopCriterium, decimalMagnitude))
             {
                 if (_lastIteration <= iterationNumber)
                 {

src/Numerics/LinearAlgebra/Complex/Solvers/TFQMR.cs

@@ -145,7 +145,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers
             double theta = 0;
 
             // Initialize
-            var tau = input.L2Norm().Real;
+            var tau = input.L2Norm();
             Complex rho = tau*tau;
 
             // Calculate the initial values for v
@@ -204,7 +204,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers
                 yinternal.Add(temp, d);
 
                 // theta = ||pseudoResiduals||_2 / tau
-                theta = pseudoResiduals.L2Norm().Real/tau;
+                theta = pseudoResiduals.L2Norm()/tau;
                 var c = 1/Math.Sqrt(1 + (theta*theta));
 
                 // tau = tau * theta * c

src/Numerics/LinearAlgebra/Complex/SparseVector.cs

@@ -711,9 +711,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override Complex L1Norm()
+        public override double L1Norm()
         {
-            double result = 0;
+            double result = 0d;
             for (var i = 0; i < _storage.ValueCount; i++)
             {
                 result += _storage.Values[i].Magnitude;
@@ -725,7 +725,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(0, _storage.ValueCount, i => _storage.Values[i].Magnitude, Math.Max, 0d);
         }
@@ -735,20 +735,20 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// </summary>
         /// <param name="p">The p value.</param>
         /// <returns>Scalar <c>ret = ( ∑|this[i]|^p )^(1/p)</c></returns>
-        public override Complex Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
             if (_storage.ValueCount == 0)
             {
-                return Complex.Zero;
+                return 0d;
             }
 
             if (p == 1d) return L1Norm();
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var index = 0; index < _storage.ValueCount; index++)
             {
                 sum += Math.Pow(_storage.Values[index].Magnitude, p);

src/Numerics/LinearAlgebra/Complex/Vector.cs

@@ -328,9 +328,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override Complex L1Norm()
+        public override double L1Norm()
         {
-            var sum = Complex.Zero;
+            double sum = 0d;
             for (var i = 0; i < Count; i++)
             {
                 sum += At(i).Magnitude;
@@ -342,16 +342,16 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// Calculates the L2 norm of the vector, also known as Euclidean norm.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex L2Norm()
+        public override double L2Norm()
         {
-            return DoConjugateDotProduct(this).SquareRoot();
+            return DoConjugateDotProduct(this).SquareRoot().Real;
         }
 
         /// <summary>
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(0, Count, i => At(i).Magnitude, Math.Max, 0d);
         }
@@ -365,7 +365,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// <returns>
         /// <c>Scalar ret = ( ∑|At(i)|^p )^(1/p)</c>
         /// </returns>
-        public override Complex Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
@@ -373,12 +373,12 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var index = 0; index < Count; index++)
             {
                 sum += Math.Pow(At(index).Magnitude, p);
             }
-            return Math.Pow(sum, 1.0 / p);
+            return Math.Pow(sum, 1.0/p);
         }
 
         /// <summary>
@@ -434,19 +434,19 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         /// </returns>
         public override Vector<Complex> Normalize(double p)
         {
-            if (p < 0.0)
+            if (p < 0d)
             {
                 throw new ArgumentOutOfRangeException("p");
             }
 
-            var norm = Norm(p);
+            double norm = Norm(p);
             var clone = Clone();
-            if (norm.Real == 0.0)
+            if (norm == 0d)
             {
                 return clone;
             }
 
-            clone.Multiply(1.0 / norm, clone);
+            clone.Multiply(1d / norm, clone);
 
             return clone;
         }

src/Numerics/LinearAlgebra/Complex32/DenseVector.cs

@@ -547,9 +547,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override Complex32 L1Norm()
+        public override double L1Norm()
         {
-            var sum = Complex32.Zero;
+            double sum = 0d;
             for (var i = 0; i < _length; i++)
             {
                 sum += _values[i].Magnitude;
@@ -561,7 +561,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Calculates the L2 norm of the vector, also known as Euclidean norm.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex32 L2Norm()
+        public override double L2Norm()
         {
             // TODO: native provider
             return _values.Aggregate(Complex32.Zero, SpecialFunctions.Hypotenuse).Magnitude;
@@ -571,7 +571,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex32 InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(_values, (i, v) => v.Magnitude, Math.Max, 0f);
         }
@@ -581,7 +581,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// </summary>
         /// <param name="p">The p value.</param>
         /// <returns>Scalar <c>ret = ( ∑|this[i]|^p )^(1/p)</c></returns>
-        public override Complex32 Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
@@ -589,12 +589,12 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var i = 0; i < _length; i++)
             {
                 sum += Math.Pow(_values[i].Magnitude, p);
             }
-            return (float)Math.Pow(sum, 1.0 / p);
+            return Math.Pow(sum, 1.0 / p);
         }
 
         /// <summary>

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

@@ -64,8 +64,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
 
             for (var k = 0; k < q.ColumnCount; k++)
             {
-                var norm = q.Column(k).L2Norm().Real;
-                if (norm == 0.0f)
+                var norm = (float) q.Column(k).L2Norm();
+                if (norm == 0f)
                 {
                     throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
                 }
@@ -73,7 +73,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
                 r.At(k, k, norm);
                 for (var i = 0; i < q.RowCount; i++)
                 {
-                    q.At(i, k, q.At(i, k) / norm);
+                    q.At(i, k, (q.At(i, k) / norm));
                 }
 
                 for (var j = k + 1; j < q.ColumnCount; j++)

src/Numerics/LinearAlgebra/Complex32/Solvers/DivergenceStopCriterium.cs

@@ -215,7 +215,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
 
             // Store the infinity norms of both the solution and residual vectors
             // These values will be used to calculate the relative drop in residuals later on.
-            _residualHistory[_residualHistory.Length - 1] = residualVector.InfinityNorm().Real;
+            _residualHistory[_residualHistory.Length - 1] = residualVector.InfinityNorm();
 
             // Check if we have NaN's. If so we've gone way beyond normal divergence.
             // Stop the iteration.

src/Numerics/LinearAlgebra/Complex32/Solvers/FailureStopCriterium.cs

@@ -91,10 +91,10 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
             }
 
             // Store the infinity norms of both the solution and residual vectors
-            var residualNorm = residualVector.InfinityNorm();
-            var solutionNorm = solutionVector.InfinityNorm();
+            double residualNorm = residualVector.InfinityNorm();
+            double solutionNorm = solutionVector.InfinityNorm();
 
-            _status = float.IsNaN(solutionNorm.Real) || float.IsNaN(residualNorm.Real) ? IterationStatus.Failure : IterationStatus.Continue;
+            _status = double.IsNaN(solutionNorm) || double.IsNaN(residualNorm) ? IterationStatus.Failure : IterationStatus.Continue;
 
             _lastIteration = iterationNumber;
             return _status;

src/Numerics/LinearAlgebra/Complex32/Solvers/ILUTPPreconditioner.cs

@@ -430,7 +430,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
                     // {
                     //     w(j) = 0
                     // }
-                    if (workVector[j].Magnitude <= _dropTolerance*vectorNorm.Real)
+                    if (workVector[j].Magnitude <= _dropTolerance*vectorNorm)
                     {
                         workVector[j] = 0.0f;
                     }

src/Numerics/LinearAlgebra/Complex32/Solvers/MlkBiCgStab.cs

@@ -193,7 +193,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
                 result.Add(orthogonalMatrix.Column(i));
 
                 // Normalize the result vector
-                result[i].Multiply(1 / result[i].L2Norm().Real, result[i]);
+                result[i].Multiply(1/(float) result[i].L2Norm(), result[i]);
             }
 
             return result;

src/Numerics/LinearAlgebra/Complex32/Solvers/ResidualStopCriterium.cs

@@ -209,16 +209,16 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
             // Store the infinity norms of both the solution and residual vectors
             // These values will be used to calculate the relative drop in residuals
             // later on.
-            var residualNorm = residualVector.InfinityNorm();
+            var residualNorm = (float) residualVector.InfinityNorm();
 
             // Check the residuals by calculating:
             // ||r_i|| <= stop_tol * ||b||
-            var stopCriterium = ComputeStopCriterium(sourceVector.InfinityNorm().Real);
+            var stopCriterium = ComputeStopCriterium((float) sourceVector.InfinityNorm());
 
             // First check that we have real numbers not NaN's.
             // NaN's can occur when the iterative process diverges so we
             // stop if that is the case.
-            if (float.IsNaN(stopCriterium) || float.IsNaN(residualNorm.Real))
+            if (float.IsNaN(stopCriterium) || float.IsNaN(residualNorm))
             {
                 _iterationCount = 0;
                 _status = IterationStatus.Diverged;
@@ -228,7 +228,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
             // ||r_i|| <= stop_tol * ||b||
             // Stop the calculation if it's clearly smaller than the tolerance
             var decimalMagnitude = Math.Abs(stopCriterium.Magnitude()) + 1;
-            if (residualNorm.Real.IsSmallerWithDecimalPlaces(stopCriterium, decimalMagnitude))
+            if (residualNorm.IsSmallerWithDecimalPlaces(stopCriterium, decimalMagnitude))
             {
                 if (_lastIteration <= iterationNumber)
                 {

src/Numerics/LinearAlgebra/Complex32/Solvers/TFQMR.cs

@@ -142,7 +142,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
             float theta = 0;
 
             // Initialize
-            var tau = input.L2Norm().Real;
+            var tau = (float) input.L2Norm();
             Numerics.Complex32 rho = tau*tau;
 
             // Calculate the initial values for v
@@ -201,7 +201,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Solvers
                 yinternal.Add(temp, d);
 
                 // theta = ||pseudoResiduals||_2 / tau
-                theta = pseudoResiduals.L2Norm().Real/tau;
+                theta = (float) pseudoResiduals.L2Norm()/tau;
                 var c = 1/(float) Math.Sqrt(1 + (theta*theta));
 
                 // tau = tau * theta * c

src/Numerics/LinearAlgebra/Complex32/SparseVector.cs

@@ -706,9 +706,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override Complex32 L1Norm()
+        public override double L1Norm()
         {
-            var result = 0f;
+            double result = 0d;
             for (var i = 0; i < _storage.ValueCount; i++)
             {
                 result += _storage.Values[i].Magnitude;
@@ -720,7 +720,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex32 InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(0, _storage.ValueCount, i => _storage.Values[i].Magnitude, Math.Max, 0f);
         }
@@ -730,25 +730,25 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// </summary>
         /// <param name="p">The p value.</param>
         /// <returns>Scalar <c>ret = ( ∑|this[i]|^p )^(1/p)</c></returns>
-        public override Complex32 Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
             if (_storage.ValueCount == 0)
             {
-                return Complex32.Zero;
+                return 0d;
             }
 
             if (p == 1d) return L1Norm();
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var index = 0; index < _storage.ValueCount; index++)
             {
                 sum += Math.Pow(_storage.Values[index].Magnitude, p);
             }
-            return (float)Math.Pow(sum, 1.0 / p);
+            return Math.Pow(sum, 1.0 / p);
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Complex32/Vector.cs

@@ -323,9 +323,9 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override Complex32 L1Norm()
+        public override double L1Norm()
         {
-            var sum = Complex32.Zero;
+            double sum = 0d;
             for (var i = 0; i < Count; i++)
             {
                 sum += At(i).Magnitude;
@@ -337,16 +337,16 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// Calculates the L2 norm of the vector, also known as Euclidean norm.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex32 L2Norm()
+        public override double L2Norm()
         {
-            return DoConjugateDotProduct(this).SquareRoot();
+            return DoConjugateDotProduct(this).SquareRoot().Real;
         }
 
         /// <summary>
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override Complex32 InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(0, Count, i => At(i).Magnitude, Math.Max, 0f);
         }
@@ -360,7 +360,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// <returns>
         /// <c>Scalar ret = ( ∑|At(i)|^p )^(1/p)</c>
         /// </returns>
-        public override Complex32 Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
@@ -368,12 +368,12 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var index = 0; index < Count; index++)
             {
                 sum += Math.Pow(At(index).Magnitude, p);
             }
-            return (float) Math.Pow(sum, 1.0/p);
+            return Math.Pow(sum, 1.0/p);
         }
 
         /// <summary>
@@ -429,19 +429,19 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
         /// </returns>
         public override Vector<Complex32> Normalize(double p)
         {
-            if (p < 0.0)
+            if (p < 0d)
             {
                 throw new ArgumentOutOfRangeException("p");
             }
 
-            var norm = Norm(p);
+            double norm = Norm(p);
             var clone = Clone();
-            if (norm.Real == 0.0f)
+            if (norm == 0d)
             {
                 return clone;
             }
 
-            clone.Multiply(1.0f / norm, clone);
+            clone.Multiply((float)(1d / norm), clone);
 
             return clone;
         }

src/Numerics/LinearAlgebra/Double/Solvers/FailureStopCriterium.cs

@@ -89,8 +89,8 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Solvers
             }
 
             // Store the infinity norms of both the solution and residual vectors
-            var residualNorm = residualVector.InfinityNorm();
-            var solutionNorm = solutionVector.InfinityNorm();
+            double residualNorm = residualVector.InfinityNorm();
+            double solutionNorm = solutionVector.InfinityNorm();
 
             _status = double.IsNaN(solutionNorm) || double.IsNaN(residualNorm) ? IterationStatus.Failure : IterationStatus.Continue;
 

src/Numerics/LinearAlgebra/Double/Vector.cs

@@ -457,19 +457,19 @@ namespace MathNet.Numerics.LinearAlgebra.Double
         /// </returns>
         public override Vector<double> Normalize(double p)
         {
-            if (p < 0.0)
+            if (p < 0d)
             {
                 throw new ArgumentOutOfRangeException("p");
             }
 
-            var norm = Norm(p);
+            double norm = Norm(p);
             var clone = Clone();
-            if (norm == 0.0)
+            if (norm == 0d)
             {
                 return clone;
             }
 
-            clone.Multiply(1.0 / norm, clone);
+            clone.Multiply(1d / norm, clone);
 
             return clone;
         }

src/Numerics/LinearAlgebra/Single/DenseVector.cs

@@ -608,9 +608,9 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override float L1Norm()
+        public override double L1Norm()
         {
-            var sum = 0f;
+            double sum = 0d;
             for (var i = 0; i < _length; i++)
             {
                 sum += Math.Abs(_values[i]);
@@ -622,7 +622,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Calculates the L2 norm of the vector, also known as Euclidean norm.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override float L2Norm()
+        public override double L2Norm()
         {
             // TODO: native provider
             return _values.Aggregate(0f, SpecialFunctions.Hypotenuse);
@@ -632,7 +632,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override float InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(_values, (i, v) => Math.Abs(v), Math.Max, 0f);
         }
@@ -642,7 +642,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// </summary>
         /// <param name="p">The p value.</param>
         /// <returns>Scalar <c>ret = ( ∑|this[i]|^p )^(1/p)</c></returns>
-        public override float Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
@@ -650,12 +650,12 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var index = 0; index < _length; index++)
             {
                 sum += Math.Pow(Math.Abs(_values[index]), p);
             }
-            return (float)Math.Pow(sum, 1.0 / p);
+            return Math.Pow(sum, 1.0 / p);
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Single/Factorization/UserGramSchmidt.cs

@@ -62,8 +62,8 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
 
             for (var k = 0; k < q.ColumnCount; k++)
             {
-                var norm = q.Column(k).L2Norm();
-                if (norm == 0.0)
+                var norm = (float) q.Column(k).L2Norm();
+                if (norm == 0f)
                 {
                     throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
                 }

src/Numerics/LinearAlgebra/Single/Solvers/FailureStopCriterium.cs

@@ -89,10 +89,10 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Solvers
             }
 
             // Store the infinity norms of both the solution and residual vectors
-            var residualNorm = residualVector.InfinityNorm();
-            var solutionNorm = solutionVector.InfinityNorm();
+            double residualNorm = residualVector.InfinityNorm();
+            double solutionNorm = solutionVector.InfinityNorm();
 
-            _status = float.IsNaN(solutionNorm) || float.IsNaN(residualNorm) ? IterationStatus.Failure : IterationStatus.Continue;
+            _status = double.IsNaN(solutionNorm) || double.IsNaN(residualNorm) ? IterationStatus.Failure : IterationStatus.Continue;
 
             _lastIteration = iterationNumber;
             return _status;

src/Numerics/LinearAlgebra/Single/Solvers/MlkBiCgStab.cs

@@ -196,7 +196,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Solvers
                 result.Add(orthogonalMatrix.Column(i));
 
                 // Normalize the result vector
-                result[i].Multiply(1 / result[i].L2Norm(), result[i]);
+                result[i].Multiply(1/(float) result[i].L2Norm(), result[i]);
             }
 
             return result;

src/Numerics/LinearAlgebra/Single/Solvers/ResidualStopCriterium.cs

@@ -207,11 +207,11 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Solvers
             // Store the infinity norms of both the solution and residual vectors
             // These values will be used to calculate the relative drop in residuals
             // later on.
-            var residualNorm = residualVector.InfinityNorm();
+            var residualNorm = (float) residualVector.InfinityNorm();
 
             // Check the residuals by calculating:
             // ||r_i|| <= stop_tol * ||b||
-            var stopCriterium = ComputeStopCriterium(sourceVector.InfinityNorm());
+            var stopCriterium = ComputeStopCriterium((float) sourceVector.InfinityNorm());
 
             // First check that we have real numbers not NaN's.
             // NaN's can occur when the iterative process diverges so we

src/Numerics/LinearAlgebra/Single/Solvers/TFQMR.cs

@@ -142,7 +142,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Solvers
             float theta = 0;
 
             // Initialize
-            var tau = input.L2Norm();
+            var tau = (float) input.L2Norm();
             var rho = tau*tau;
 
             // Calculate the initial values for v
@@ -201,7 +201,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Solvers
                 yinternal.Add(temp, d);
 
                 // theta = ||pseudoResiduals||_2 / tau
-                theta = pseudoResiduals.L2Norm()/tau;
+                theta = (float) pseudoResiduals.L2Norm()/tau;
                 var c = 1/(float) Math.Sqrt(1 + (theta*theta));
 
                 // tau = tau * theta * c

src/Numerics/LinearAlgebra/Single/SparseVector.cs

@@ -718,9 +718,9 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override float L1Norm()
+        public override double L1Norm()
         {
-            var result = 0f;
+            double result = 0d;
             for (var i = 0; i < _storage.ValueCount; i++)
             {
                 result += Math.Abs(_storage.Values[i]);
@@ -732,7 +732,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override float InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(0, _storage.ValueCount, i => Math.Abs(_storage.Values[i]), Math.Max, 0f);
         }
@@ -742,25 +742,25 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// </summary>
         /// <param name="p">The p value.</param>
         /// <returns>Scalar <c>ret = ( ∑|this[i]|^p )^(1/p)</c></returns>
-        public override float Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
             if (_storage.ValueCount == 0)
             {
-                return 0f;
+                return 0d;
             }
 
             if (p == 1d) return L1Norm();
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var index = 0; index < _storage.ValueCount; index++)
             {
                 sum += Math.Pow(Math.Abs(_storage.Values[index]), p);
             }
-            return (float)Math.Pow(sum, 1.0 / p);
+            return Math.Pow(sum, 1.0 / p);
         }
 
         /// <summary>

src/Numerics/LinearAlgebra/Single/Vector.cs

@@ -325,9 +325,9 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public override float L1Norm()
+        public override double L1Norm()
         {
-            var sum = 0.0f;
+            double sum = 0d;
             for (var i = 0; i < Count; i++)
             {
                 sum += Math.Abs(At(i));
@@ -339,16 +339,16 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// Calculates the L2 norm of the vector, also known as Euclidean norm.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override float L2Norm()
+        public override double L2Norm()
         {
-            return (float)Math.Sqrt(DoDotProduct(this));
+            return Math.Sqrt(DoDotProduct(this));
         }
 
         /// <summary>
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public override float InfinityNorm()
+        public override double InfinityNorm()
         {
             return CommonParallel.Aggregate(0, Count, i => Math.Abs(At(i)), Math.Max, 0f);
         }
@@ -362,7 +362,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// <returns>
         /// <c>Scalar ret = ( ∑|At(i)|^p )^(1/p)</c>
         /// </returns>
-        public override float Norm(double p)
+        public override double Norm(double p)
         {
             if (p < 0d) throw new ArgumentOutOfRangeException("p");
 
@@ -370,12 +370,12 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             if (p == 2d) return L2Norm();
             if (double.IsPositiveInfinity(p)) return InfinityNorm();
 
-            var sum = 0d;
+            double sum = 0d;
             for (var index = 0; index < Count; index++)
             {
                 sum += Math.Pow(Math.Abs(At(index)), p);
             }
-            return (float) Math.Pow(sum, 1.0/p);
+            return Math.Pow(sum, 1.0/p);
         }
 
         /// <summary>
@@ -457,19 +457,19 @@ namespace MathNet.Numerics.LinearAlgebra.Single
         /// </returns>
         public override Vector<float> Normalize(double p)
         {
-            if (p < 0.0)
+            if (p < 0d)
             {
                 throw new ArgumentOutOfRangeException("p");
             }
 
-            var norm = Norm(p);
+            double norm = Norm(p);
             var clone = Clone();
-            if (norm == 0.0)
+            if (norm == 0d)
             {
                 return clone;
             }
 
-            clone.Multiply(1.0f / norm, clone);
+            clone.Multiply((float)(1d / norm), clone);
 
             return clone;
         }

src/Numerics/LinearAlgebra/Vector.Arithmetic.cs

@@ -748,26 +748,26 @@ namespace MathNet.Numerics.LinearAlgebra
         /// Calculates the L1 norm of the vector, also known as Manhattan norm.
         /// </summary>
         /// <returns>The sum of the absolute values.</returns>
-        public abstract T L1Norm();
+        public abstract double L1Norm();
 
         /// <summary>
         /// Calculates the L2 norm of the vector, also known as Euclidean norm.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public abstract T L2Norm();
+        public abstract double L2Norm();
 
         /// <summary>
         /// Calculates the infinity norm of the vector.
         /// </summary>
         /// <returns>The square root of the sum of the squared values.</returns>
-        public abstract T InfinityNorm();
+        public abstract double InfinityNorm();
 
         /// <summary>
         /// Computes the p-Norm.
         /// </summary>
         /// <param name="p">The p value.</param>
         /// <returns><c>Scalar ret = (sum(abs(this[i])^p))^(1/p)</c></returns>
-        public abstract T Norm(double p);
+        public abstract double Norm(double p);
 
         /// <summary>
         /// Normalizes this vector to a unit vector with respect to the p-norm.
@@ -840,7 +840,7 @@ namespace MathNet.Numerics.LinearAlgebra
         /// Computes the sum of the absolute value of the vector's elements.
         /// </summary>
         /// <returns>The sum of the absolute value of the vector's elements.</returns>
-        public T SumMagnitudes()
+        public double SumMagnitudes()
         {
             return L1Norm();
         }

src/UnitTests/LinearAlgebraTests/Complex/VectorTests.cs

@@ -466,7 +466,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex
             var vector = CreateVector(testData);
             var actual = vector.SumMagnitudes();
             var expected = testData.Sum(complex => complex.Magnitude);
-            Assert.AreEqual(expected, actual.Real);
+            Assert.AreEqual(expected, actual);
         }
 
         /// <summary>

src/UnitTests/LinearAlgebraTests/Complex32/MatrixTests.Arithmetic.cs

@@ -839,7 +839,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32
             for (var j = 0; j < result.ColumnCount; j++)
             {
                 var col = result.Column(j);
-                AssertHelpers.AlmostEqual(Complex32.One, col.Norm(p), 6);
+                AssertHelpers.AlmostEqual(1d, col.Norm(p), 6);
             }
         }
 
@@ -864,7 +864,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32
             for (var i = 0; i < matrix.RowCount; i++)
             {
                 var row = matrix.Row(i);
-                AssertHelpers.AlmostEqual(Complex32.One, row.Norm(p), 6);
+                AssertHelpers.AlmostEqual(1d, row.Norm(p), 6);
             }
         }
 

src/UnitTests/LinearAlgebraTests/Complex32/VectorTests.Norm.cs

@@ -80,7 +80,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32
         public void CanComputeNormP(int p, float expected)
         {
             var vector = CreateVector(Data);
-            AssertHelpers.AlmostEqual(expected, vector.Norm(p).Real, 5);
+            AssertHelpers.AlmostEqual(expected, (float) vector.Norm(p), 5);
         }
 
         /// <summary>
@@ -90,8 +90,8 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32
         public void CanComputeNormInfinity()
         {
             var vector = CreateVector(Data);
-            AssertHelpers.AlmostEqual(5.0990195, vector.InfinityNorm().Real, 7);
-            AssertHelpers.AlmostEqual(5.0990195, vector.Norm(Single.PositiveInfinity).Real, 7);
+            AssertHelpers.AlmostEqual(5.0990195, vector.InfinityNorm(), 7);
+            AssertHelpers.AlmostEqual(5.0990195, vector.Norm(Single.PositiveInfinity), 7);
         }
 
         /// <summary>

src/UnitTests/LinearAlgebraTests/Complex32/VectorTests.cs

@@ -466,7 +466,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32
             var vector = CreateVector(testData);
             var actual = vector.SumMagnitudes();
             var expected = testData.Sum(complex => complex.Magnitude);
-            Assert.AreEqual(expected, actual.Real);
+            Assert.AreEqual(expected, (float) actual);
         }
 
         /// <summary>