// <copyright file="ManagedLinearAlgebraProvider.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
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// http://mathnetnumerics.codeplex.com
//
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//
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namespace MathNet.Numerics.Algorithms.LinearAlgebra
{
    using System;
    using System.Numerics;
    using Properties;
    using Threading;

    /// <summary>
    /// The managed linear algebra provider.
    /// </summary>
    public class ManagedLinearAlgebraProvider : ILinearAlgebraProvider
    {
        #region ILinearAlgebraProvider<double> Members

        /// <summary>
        /// Adds a scaled vector to another: <c>y += alpha*x</c>.
        /// </summary>
        /// <param name="y">The vector to update.</param>
        /// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
        /// <param name="x">The vector to add to <paramref name="y"/>.</param>
        /// <remarks>This equivalent to the AXPY BLAS routine.</remarks>
        public void AddVectorToScaledVector(double[] y, double alpha, double[] x)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            if (alpha == 0.0)
            {
                return;
            }

            if (alpha == 1.0)
            {
                CommonParallel.For(0, y.Length, 
                                   index => { y[index] += x[index]; });
            }
            else
            {
                CommonParallel.For(0, y.Length, 
                                   index => { y[index] += alpha * x[index]; });
            }
        }

        /// <summary>
        /// Scales an array. Can be used to scale a vector and a matrix.
        /// </summary>
        /// <param name="alpha">The scalar.</param>
        /// <param name="x">The values to scale.</param>
        /// <remarks>This is equivalent to the SCAL BLAS routine.</remarks>
        public void ScaleArray(double alpha, double[] x)
        {
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (alpha == 1.0)
            {
                return;
            }

            CommonParallel.For(0, x.Length, 
                               index => { x[index] = alpha * x[index]; });
        }

        /// <summary>
        /// Computes the dot product of x and y.
        /// </summary>
        /// <param name="x">The vector x.</param>
        /// <param name="y">The vector y.</param>
        /// <returns>The dot product of x and y.</returns>
        /// <remarks>This is equivalent to the DOT BLAS routine.</remarks>
        public double DotProduct(double[] x, double[] y)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            return CommonParallel.Aggregate(0, y.Length, index => y[index] * x[index]);
        }

        /// <summary>
        /// Does a point wise add of two arrays <c>z = x + y</c>. This can be used 
        /// to add vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the addition.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void AddArrays(double[] x, double[] y, double[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, index => { result[index] = x[index] + y[index]; });
        }

        /// <summary>
        /// Does a point wise subtraction of two arrays <c>z = x - y</c>. This can be used 
        /// to subtract vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the subtraction.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void SubtractArrays(double[] x, double[] y, double[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, 
                               index => { result[index] = x[index] - y[index]; });
        }

        /// <summary>
        /// Does a point wise multiplication of two arrays <c>z = x * y</c>. This can be used
        /// to multiple elements of vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the point wise multiplication.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void PointWiseMultiplyArrays(double[] x, double[] y, double[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, 
                               index => { result[index] = x[index] * y[index]; });
        }

        public double MatrixNorm(Norm norm, double[] matrix)
        {
            throw new NotImplementedException();
        }

        public double MatrixNorm(Norm norm, double[] matrix, double[] work)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Multiples two matrices. <c>result = x * y</c>
        /// </summary>
        /// <param name="x">The x matrix.</param>
        /// <param name="xRows">The number of rows in the x matrix.</param>
        /// <param name="xColumns">The number of columns in the x matrix.</param>
        /// <param name="y">The y matrix.</param>
        /// <param name="yRows">The number of rows in the y matrix.</param>
        /// <param name="yColumns">The number of columns in the y matrix.</param>
        /// <param name="result">Where to store the result of the multiplication.</param>
        /// <remarks>This is a simplified version of the BLAS GEMM routine with alpha
        /// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks>
        public void MatrixMultiply(double[] x, int xRows, int xColumns, double[] y, int yRows, int yColumns, double[] result)
        {
            // First check some basic requirement on the parameters of the matrix multiplication.
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (xRows * xColumns != x.Length)
            {
                throw new ArgumentException("x.Length != xRows * xColumns");
            }

            if (yRows * yColumns != y.Length)
            {
                throw new ArgumentException("y.Length != yRows * yColumns");
            }

            if (xColumns != yRows)
            {
                throw new ArgumentException("xColumns != yRows");
            }

            if (xRows * yColumns != result.Length)
            {
                throw new ArgumentException("xRows * yColumns != result.Length");
            }

            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            double[] xdata;
            if (ReferenceEquals(x, result))
            {
                xdata = (double[])x.Clone();
            }
            else
            {
                xdata = x;
            }

            double[] ydata;
            if (ReferenceEquals(y, result))
            {
                ydata = (double[])y.Clone();
            }
            else
            {
                ydata = y;
            }

            // Start the actual matrix multiplication.
            // TODO - For small matrices we should get rid of the parallelism because of startup costs.
            // Perhaps the following implementations would be a good one
            // http://blog.feradz.com/2009/01/cache-efficient-matrix-multiplication/
            this.MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, 1.0, xdata, xRows, xColumns, ydata, yRows, yColumns, 0.0, result);
        }

        /// <summary>
        /// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
        /// </summary>
        /// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
        /// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
        /// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
        /// <param name="a">The a matrix.</param>
        /// <param name="aRows">The number of rows in the <paramref name="a"/> matrix.</param>
        /// <param name="aColumns">The number of columns in the <paramref name="a"/> matrix.</param>
        /// <param name="b">The b matrix</param>
        /// <param name="bRows">The number of rows in the <paramref name="b"/> matrix.</param>
        /// <param name="bColumns">The number of columns in the <paramref name="b"/> matrix.</param>
        /// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
        /// <param name="c">The c matrix.</param>
        public void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, double alpha, double[] a, 
                                             int aRows, int aColumns, double[] b, int bRows, int bColumns, double beta, double[] c)
        {
            // Choose nonsensical values for the number of rows in c; fill them in depending
            // on the operations on a and b.
            var cRows = -1;

            // First check some basic requirement on the parameters of the matrix multiplication.
            if (a == null)
            {
                throw new ArgumentNullException("a");
            }

            if (b == null)
            {
                throw new ArgumentNullException("b");
            }

            if ((int)transposeA > 111 && (int)transposeB > 111)
            {
                if (aRows != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
            }
            else if ((int)transposeA > 111)
            {
                if (aRows != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
            }
            else if ((int)transposeB > 111)
            {
                if (aColumns != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
            }
            else
            {
                if (aColumns != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
            }

            if (alpha == 0.0 && beta == 0.0)
            {
                Array.Clear(c, 0, c.Length);
                return;
            }

            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            double[] adata;
            if (ReferenceEquals(a, c))
            {
                adata = (double[])a.Clone();
            }
            else
            {
                adata = a;
            }

            double[] bdata;
            if (ReferenceEquals(b, c))
            {
                bdata = (double[])b.Clone();
            }
            else
            {
                bdata = b;
            }

            if (alpha == 1.0)
            {
                if (beta == 0.0)
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, 
                                           j =>
                                           {
                                               var jIndex = j * cRows;
                                               for (var i = 0; i != bRows; i++)
                                               {
                                                   var iIndex = i * aRows;
                                                   double s = 0;
                                                   for (var l = 0; l != bColumns; l++)
                                                   {
                                                       s += adata[iIndex + l] * bdata[l * bRows + j];
                                                   }

                                                   c[jIndex + i] = s;
                                               }
                                           });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, 
                                           j =>
                                           {
                                               var jcIndex = j * cRows;
                                               var jbIndex = j * bRows;
                                               for (var i = 0; i != aColumns; i++)
                                               {
                                                   var iIndex = i * aRows;
                                                   double s = 0;
                                                   for (var l = 0; l != aRows; l++)
                                                   {
                                                       s += adata[iIndex + l] * bdata[jbIndex + l];
                                                   }

                                                   c[jcIndex + i] = s;
                                               }
                                           });
                    }
                    else if ((int)transposeB > 111)
                    {
                        CommonParallel.For(0, bRows, 
                                           j =>
                                           {
                                               var jIndex = j * cRows;
                                               for (var i = 0; i != aRows; i++)
                                               {
                                                   double s = 0;
                                                   for (var l = 0; l != aColumns; l++)
                                                   {
                                                       s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                   }

                                                   c[jIndex + i] = s;
                                               }
                                           });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, 
                                           j =>
                                           {
                                               var jcIndex = j * cRows;
                                               var jbIndex = j * bRows;
                                               for (var i = 0; i != aRows; i++)
                                               {
                                                   double s = 0;
                                                   for (var l = 0; l != aColumns; l++)
                                                   {
                                                       s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                   }

                                                   c[jcIndex + i] = s;
                                               }
                                           });
                    }
                }
                else
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, 
                                           j =>
                                           {
                                               var jIndex = j * cRows;
                                               for (var i = 0; i != bRows; i++)
                                               {
                                                   var iIndex = i * aRows;
                                                   double s = 0;
                                                   for (var l = 0; l != bColumns; l++)
                                                   {
                                                       s += adata[iIndex + l] * bdata[l * bRows + j];
                                                   }

                                                   c[jIndex + i] = c[jIndex + i] * beta + s;
                                               }
                                           });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, 
                                           j =>
                                           {
                                               var jcIndex = j * cRows;
                                               var jbIndex = j * bRows;
                                               for (var i = 0; i != aColumns; i++)
                                               {
                                                   var iIndex = i * aRows;
                                                   double s = 0;
                                                   for (var l = 0; l != aRows; l++)
                                                   {
                                                       s += adata[iIndex + l] * bdata[jbIndex + l];
                                                   }

                                                   c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                               }
                                           });
                    }
                    else if ((int)transposeB > 111)
                    {
                        CommonParallel.For(0, bRows, 
                                           j =>
                                           {
                                               var jIndex = j * cRows;
                                               for (var i = 0; i != aRows; i++)
                                               {
                                                   double s = 0;
                                                   for (var l = 0; l != aColumns; l++)
                                                   {
                                                       s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                   }

                                                   c[jIndex + i] = s + c[jIndex + i] * beta;
                                               }
                                           });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, 
                                           j =>
                                           {
                                               var jcIndex = j * cRows;
                                               var jbIndex = j * bRows;
                                               for (var i = 0; i != aRows; i++)
                                               {
                                                   double s = 0;
                                                   for (var l = 0; l != aColumns; l++)
                                                   {
                                                       s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                   }

                                                   c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                               }
                                           });
                    }
                }
            }
            else
            {
                if ((int)transposeA > 111 && (int)transposeB > 111)
                {
                    CommonParallel.For(0, aColumns, 
                                       j =>
                                       {
                                           var jIndex = j * cRows;
                                           for (var i = 0; i != bRows; i++)
                                           {
                                               var iIndex = i * aRows;
                                               double s = 0;
                                               for (var l = 0; l != bColumns; l++)
                                               {
                                                   s += adata[iIndex + l] * bdata[l * bRows + j];
                                               }

                                               c[jIndex + i] = c[jIndex + i] * beta + alpha * s;
                                           }
                                       });
                }
                else if ((int)transposeA > 111)
                {
                    CommonParallel.For(0, bColumns, 
                                       j =>
                                       {
                                           var jcIndex = j * cRows;
                                           var jbIndex = j * bRows;
                                           for (var i = 0; i != aColumns; i++)
                                           {
                                               var iIndex = i * aRows;
                                               double s = 0;
                                               for (var l = 0; l != aRows; l++)
                                               {
                                                   s += adata[iIndex + l] * bdata[jbIndex + l];
                                               }

                                               c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                           }
                                       });
                }
                else if ((int)transposeB > 111)
                {
                    CommonParallel.For(0, bRows, 
                                       j =>
                                       {
                                           var jIndex = j * cRows;
                                           for (var i = 0; i != aRows; i++)
                                           {
                                               double s = 0;
                                               for (var l = 0; l != aColumns; l++)
                                               {
                                                   s += adata[l * aRows + i] * bdata[l * bRows + j];
                                               }

                                               c[jIndex + i] = alpha * s + c[jIndex + i] * beta;
                                           }
                                       });
                }
                else
                {
                    CommonParallel.For(0, bColumns, 
                                       j =>
                                       {
                                           var jcIndex = j * cRows;
                                           var jbIndex = j * bRows;
                                           for (var i = 0; i != aRows; i++)
                                           {
                                               double s = 0;
                                               for (var l = 0; l != aColumns; l++)
                                               {
                                                   s += adata[l * aRows + i] * bdata[jbIndex + l];
                                               }

                                               c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                           }
                                       });
                }
            }
        }

        /// <summary>
        /// Computes the LUP factorization of A. P*A = L*U.
        /// </summary>
        /// <param name="data">An <paramref name="order"/> by <paramref name="order"/> matrix. The matrix is overwritten with the
        /// the LU factorization on exit. The lower triangular factor L is stored in under the diagonal of <paramref name="data"/> (the diagonal is always 1.0
        /// for the L factor). The upper triangular factor U is stored on and above the diagonal of <paramref name="data"/>.</param>
        /// <param name="order">The order of the square matrix <paramref name="data"/>.</param>
        /// <param name="ipiv">On exit, it contains the pivot indices. The size of the array must be <paramref name="order"/>.</param>
        /// <remarks>This is equivalent to the GETRF LAPACK routine.</remarks>
        public void LUFactor(double[] data, int order, int[] ipiv)
        {
            // Initialize the pivot matrix to the identity permutation.
            for (int i = 0; i < order; i++)
            {
                ipiv[i] = i;
            }

            double[] LUcolj = new double[order];

            // Outer loop.
            for (int j = 0; j < order; j++)
            {
                int indexj = j * order;
                int indexjj = indexj + j;
                // Make a copy of the j-th column to localize references.
                for (int i = 0; i < order; i++)
                {
                    LUcolj[i] = data[indexj + i];
                }

                // Apply previous transformations.
                for (int i = 0; i < order; i++)
                {
                    // Most of the time is spent in the following dot product.
                    int kmax = System.Math.Min(i, j);
                    double s = 0.0;
                    for (int k = 0; k < kmax; k++)
                    {
                        s += data[k * order + i] * LUcolj[k];
                    }

                    data[indexj + i] = LUcolj[i] -= s;
                }

                // Find pivot and exchange if necessary.
                int p = j;
                for (int i = j + 1; i < order; i++)
                {
                    if (System.Math.Abs(LUcolj[i]) > System.Math.Abs(LUcolj[p]))
                    {
                        p = i;
                    }
                }
                if (p != j)
                {
                    for (int k = 0; k < order; k++)
                    {
                        int indexk = k * order;
                        int indexkp = indexk + p;
                        int indexkj = indexk + j;
                        double temp = data[indexkp];
                        data[indexkp] = data[indexkj];
                        data[indexkj] = temp;
                    }
                    ipiv[j] = p;
                }

                // Compute multipliers.
                if (j < order & data[indexjj] != 0.0)
                {
                    for (int i = j + 1; i < order; i++)
                    {
                        data[indexj + i] /= data[indexjj];
                    }
                }
            }
        }

        public void LUInverse(double[] a)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(double[] a, int[] ipiv)
        {
            throw new NotImplementedException();
        }

        public void LUInverse(double[] a, double[] work)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(double[] a, int[] ipiv, double[] work)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(int columnsOfB, double[] a, double[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(int columnsOfB, double[] a, int ipiv, double[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(Transpose transposeA, int columnsOfB, double[] a, double[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(Transpose transposeA, int columnsOfB, double[] a, int ipiv, double[] b)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Computes the Cholesky factorization of A.
        /// </summary>
        /// <param name="a">On entry, a square, positive definite matrix. On exit, the matrix is overwritten with the
        /// the Cholesky factorization.</param>
        /// <param name="order">The number of rows or columns in the matrix.</param>
        /// <remarks>This is equivalent to the POTRF LAPACK routine.</remarks>
        public void CholeskyFactor(double[] a, int order)
        {
            if (a == null)
            {
                throw new ArgumentNullException("a");
            }

            for (var j = 0; j < order; j++)
            {
                var d = 0.0;
                int index;
                for (var k = 0; k < j; k++)
                {
                    var s = 0.0;
                    int i;
                    for (i = 0; i < k; i++)
                    {
                        s += a[i * order + k] * a[i * order + j];
                    }

                    var tmp = k * order;
                    index = tmp + j;
                    a[index] = s = (a[index] - s) / a[tmp + k];
                    d += s * s;
                }

                index = j * order + j;
                d = a[index] - d;
                if (d <= 0.0)
                {
                    throw new ArgumentException(Resources.ArgumentMatrixPositiveDefinite);
                }

                a[index] = Math.Sqrt(d);
                for (var k = j + 1; k < order; k++)
                {
                    a[k * order + j] = 0.0;
                }
            }
        }

        /// <summary>
        /// Solves A*X=B for X using Cholesky factorization.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRF add POTRS LAPACK routines.</remarks>
        public void CholeskySolve(double[] a, int aOrder, double[] b, int bRows, int bColumns)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Solves A*X=B for X using a previously factored A matrix.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A. Has to be different than <paramref name="B"/>.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix. Has to be different than <paramref name="A"/>.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRS LAPACK routine.</remarks>
        public void CholeskySolveFactored(double[] a, int aOrder, double[] b, int bRows, int bColumns)
        {
            if (a == null)
            {
                throw new ArgumentNullException("a");
            }

            if (b == null)
            {
                throw new ArgumentNullException("b");
            }

            if (aOrder != bRows)
            {
                throw new ArgumentException(Resources.ArgumentMatrixDimensions);
            }

            if (Object.ReferenceEquals(a, b))
            {
                throw new ArgumentException(Resources.ArgumentReferenceDifferent);
            }

            CommonParallel.For(0, bColumns, c =>
            {
                int cindex = c * aOrder;

                // Solve L*Y = B;
                double sum;
                for (int i = 0; i < aOrder; i++)
                {
                    sum = b[cindex + i];
                    for (int k = i - 1; k >= 0; k--)
                    {
                        sum -= a[k * aOrder + i] * b[cindex + k];
                    }
                    b[cindex + i] = sum / a[i * aOrder + i];
                }

                // Solve L'*X = Y;
                for (int i = aOrder - 1; i >= 0; i--)
                {
                    sum = b[cindex + i];
                    int iindex = i * aOrder;
                    for (int k = i + 1; k < aOrder; k++)
                    {
                        sum -= a[iindex + k] * b[cindex + k];
                    }
                    b[cindex + i] = sum / a[iindex + i];
                }
            });
        }

        public void QRFactor(double[] r, double[] q)
        {
            throw new NotImplementedException();
        }

        public void QRFactor(double[] r, double[] q, double[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, double[] r, double[] q, double[] b, double[] x)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, double[] r, double[] q, double[] b, double[] x, double[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolveFactored(int columnsOfB, double[] q, double[] r, double[] b, double[] x)
        {
            throw new NotImplementedException();
        }

        public void SinguarValueDecomposition(bool computeVectors, double[] a, double[] s, double[] u, double[] vt)
        {
            throw new NotImplementedException();
        }

        public void SingularValueDecomposition(bool computeVectors, double[] a, double[] s, double[] u, double[] vt, double[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(double[] a, double[] s, double[] u, double[] vt, double[] b, double[] x)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(double[] a, double[] s, double[] u, double[] vt, double[] b, double[] x, double[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolveFactored(int columnsOfB, double[] s, double[] u, double[] vt, double[] b, double[] x)
        {
            throw new NotImplementedException();
        }

        #endregion

        #region ILinearAlgebraProvider<float> Members

        /// <summary>
        /// Adds a scaled vector to another: <c>y += alpha*x</c>.
        /// </summary>
        /// <param name="y">The vector to update.</param>
        /// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
        /// <param name="x">The vector to add to <paramref name="y"/>.</param>
        /// <remarks>This equivalent to the AXPY BLAS routine.</remarks>
        public void AddVectorToScaledVector(float[] y, float alpha, float[] x)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            if (alpha == 0.0)
            {
                return;
            }

            if (alpha == 1.0)
            {
                CommonParallel.For(0, y.Length, i => y[i] += x[i]);
            }
            else
            {
                CommonParallel.For(0, y.Length, i => y[i] += alpha * x[i]);
            }
        }

        /// <summary>
        /// Scales an array. Can be used to scale a vector and a matrix.
        /// </summary>
        /// <param name="alpha">The scalar.</param>
        /// <param name="x">The values to scale.</param>
        /// <remarks>This is equivalent to the SCAL BLAS routine.</remarks>
        public void ScaleArray(float alpha, float[] x)
        {
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (alpha == 1.0)
            {
                return;
            }

            CommonParallel.For(0, x.Length, i => x[i] = alpha * x[i]);
        }

        /// <summary>
        /// Computes the dot product of x and y.
        /// </summary>
        /// <param name="x">The vector x.</param>
        /// <param name="y">The vector y.</param>
        /// <returns>The dot product of x and y.</returns>
        /// <remarks>This is equivalent to the DOT BLAS routine.</remarks>
        public float DotProduct(float[] x, float[] y)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            var d = 0.0F;

            for (var i = 0; i < y.Length; i++)
            {
                d += y[i] * x[i];
            }

            return d;
        }

        /// <summary>
        /// Does a point wise add of two arrays <c>z = x + y</c>. This can be used 
        /// to add vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the addition.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void AddArrays(float[] x, float[] y, float[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] + y[i]);
        }

        /// <summary>
        /// Does a point wise subtraction of two arrays <c>z = x - y</c>. This can be used 
        /// to subtract vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the subtraction.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void SubtractArrays(float[] x, float[] y, float[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] - y[i]);
        }

        /// <summary>
        /// Does a point wise multiplication of two arrays <c>z = x * y</c>. This can be used
        /// to multiple elements of vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the point wise multiplication.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void PointWiseMultiplyArrays(float[] x, float[] y, float[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] * y[i]);
        }

        public float MatrixNorm(Norm norm, float[] matrix)
        {
            throw new NotImplementedException();
        }

        public float MatrixNorm(Norm norm, float[] matrix, float[] work)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Multiples two matrices. <c>result = x * y</c>
        /// </summary>
        /// <param name="x">The x matrix.</param>
        /// <param name="xRows">The number of rows in the x matrix.</param>
        /// <param name="xColumns">The number of columns in the x matrix.</param>
        /// <param name="y">The y matrix.</param>
        /// <param name="yRows">The number of rows in the y matrix.</param>
        /// <param name="yColumns">The number of columns in the y matrix.</param>
        /// <param name="result">Where to store the result of the multiplication.</param>
        /// <remarks>This is a simplified version of the BLAS GEMM routine with alpha
        /// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks>
        public void MatrixMultiply(float[] x, int xRows, int xColumns, float[] y, int yRows, int yColumns, float[] result)
        {
            // First check some basic requirement on the parameters of the matrix multiplication.
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (xRows * xColumns != x.Length)
            {
                throw new ArgumentException("x.Length != xRows * xColumns");
            }

            if (yRows * yColumns != y.Length)
            {
                throw new ArgumentException("y.Length != yRows * yColumns");
            }

            if (xColumns != yRows)
            {
                throw new ArgumentException("xColumns != yRows");
            }

            if (xRows * yColumns != result.Length)
            {
                throw new ArgumentException("xRows * yColumns != result.Length");
            }

            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            float[] xdata;
            if (ReferenceEquals(x, result))
            {
                xdata = (float[])x.Clone();
            }
            else
            {
                xdata = x;
            }

            float[] ydata;
            if (ReferenceEquals(y, result))
            {
                ydata = (float[])y.Clone();
            }
            else
            {
                ydata = y;
            }

            // Start the actual matrix multiplication.
            // TODO - For small matrices we should get rid of the parallelism because of startup costs.
            // Perhaps the following implementations would be a good one
            // http://blog.feradz.com/2009/01/cache-efficient-matrix-multiplication/
            this.MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, 1.0f, x, xRows, xColumns, y, yRows, yColumns, 0.0f, result);
        }

        /// <summary>
        /// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
        /// </summary>
        /// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
        /// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
        /// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
        /// <param name="a">The a matrix.</param>
        /// <param name="aRows">The number of rows in the <paramref name="a"/> matrix.</param>
        /// <param name="aColumns">The number of columns in the <paramref name="a"/> matrix.</param>
        /// <param name="b">The b matrix</param>
        /// <param name="bRows">The number of rows in the <paramref name="b"/> matrix.</param>
        /// <param name="bColumns">The number of columns in the <paramref name="b"/> matrix.</param>
        /// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
        /// <param name="c">The c matrix.</param>
        public void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, float alpha, float[] a, 
                                             int aRows, int aColumns, float[] b, int bRows, int bColumns, float beta, float[] c)
        {
            // Choose nonsensical values for the number of rows and columns in c; fill them in depending
            // on the operations on a and b.
            var cRows = -1;
            var cColumns = -1;

            // First check some basic requirement on the parameters of the matrix multiplication.
            if (a == null)
            {
                throw new ArgumentNullException("a");
            }

            if (b == null)
            {
                throw new ArgumentNullException("b");
            }

            if ((int)transposeA > 111 && (int)transposeB > 111)
            {
                if (aRows != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
                cColumns = bRows;
            }
            else if ((int)transposeA > 111)
            {
                if (aRows != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
                cColumns = bColumns;
            }
            else if ((int)transposeB > 111)
            {
                if (aColumns != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
                cColumns = bRows;
            }
            else
            {
                if (aColumns != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
                cColumns = bColumns;
            }

            if (alpha == 0.0 && beta == 0.0)
            {
                Array.Clear(c, 0, c.Length);
                return;
            }


            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            float[] adata;
            if (ReferenceEquals(a, c))
            {
                adata = (float[])a.Clone();
            }
            else
            {
                adata = a;
            }

            float[] bdata;
            if (ReferenceEquals(b, c))
            {
                bdata = (float[])b.Clone();
            }
            else
            {
                bdata = b;
            }

            if (alpha == 1.0)
            {
                if (beta == 0.0)
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, j =>
                                                  {
                                                      var jIndex = j * cRows;
                                                      for (var i = 0; i != bRows; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          float s = 0;
                                                          for (var l = 0; l != bColumns; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[l * bRows + j];
                                                          }

                                                          c[jIndex + i] = s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aColumns; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          float s = 0;
                                                          for (var l = 0; l != aRows; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeB > 111)
                    {
                        CommonParallel.For(0, bRows, j =>
                                               {
                                                   var jIndex = j * cRows;
                                                   for (var i = 0; i != aRows; i++)
                                                   {
                                                       float s = 0;
                                                       for (var l = 0; l != aColumns; l++)
                                                       {
                                                           s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                       }

                                                       c[jIndex + i] = s;
                                                   }
                                               });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aRows; i++)
                                                      {
                                                          float s = 0;
                                                          for (var l = 0; l != aColumns; l++)
                                                          {
                                                              s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s;
                                                      }
                                                  });
                    }
                }
                else
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, j =>
                                                  {
                                                      var jIndex = j * cRows;
                                                      for (var i = 0; i != bRows; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          float s = 0;
                                                          for (var l = 0; l != bColumns; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[l * bRows + j];
                                                          }

                                                          c[jIndex + i] = c[jIndex + i] * beta + s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aColumns; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          float s = 0;
                                                          for (var l = 0; l != aRows; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                                      }
                                                  });
                    }
                    else if ((int)transposeB > 111)
                    {
                       CommonParallel.For(0, bRows, j =>
                                               {
                                                   var jIndex = j * cRows;
                                                   for (var i = 0; i != aRows; i++)
                                                   {
                                                       float s = 0;
                                                       for (var l = 0; l != aColumns; l++)
                                                       {
                                                           s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                       }

                                                       c[jIndex + i] = s + c[jIndex + i] * beta;
                                                   }
                                               });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aRows; i++)
                                                      {
                                                          float s = 0;
                                                          for (var l = 0; l != aColumns; l++)
                                                          {
                                                              s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                                      }
                                                  });
                    }
                }
            }
            else
            {
                if ((int)transposeA > 111 && (int)transposeB > 111)
                {
                    CommonParallel.For(0, aColumns, j =>
                                              {
                                                  var jIndex = j * cRows;
                                                  for (var i = 0; i != bRows; i++)
                                                  {
                                                      var iIndex = i * aRows;
                                                      float s = 0;
                                                      for (var l = 0; l != bColumns; l++)
                                                      {
                                                          s += adata[iIndex + l] * bdata[l * bRows + j];
                                                      }

                                                      c[jIndex + i] = c[jIndex + i] * beta + alpha * s;
                                                  }
                                              });
                }
                else if ((int)transposeA > 111)
                {
                    CommonParallel.For(0, bColumns, j =>
                                              {
                                                  var jcIndex = j * cRows;
                                                  var jbIndex = j * bRows;
                                                  for (var i = 0; i != aColumns; i++)
                                                  {
                                                      var iIndex = i * aRows;
                                                      float s = 0;
                                                      for (var l = 0; l != aRows; l++)
                                                      {
                                                          s += adata[iIndex + l] * bdata[jbIndex + l];
                                                      }

                                                      c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                                  }
                                              });
                }
                else if ((int)transposeB > 111)
                {
                    CommonParallel.For(0, bRows, j =>
                                           {
                                               var jIndex = j * cRows;
                                               for (var i = 0; i != aRows; i++)
                                               {
                                                   float s = 0;
                                                   for (var l = 0; l != aColumns; l++)
                                                   {
                                                       s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                   }

                                                   c[jIndex + i] = alpha * s + c[jIndex + i] * beta;
                                               }
                                           });
                }
                else
                {
                    CommonParallel.For(0, bColumns, j =>
                                              {
                                                  var jcIndex = j * cRows;
                                                  var jbIndex = j * bRows;
                                                  for (var i = 0; i != aRows; i++)
                                                  {
                                                      float s = 0;
                                                      for (var l = 0; l != aColumns; l++)
                                                      {
                                                          s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                      }

                                                      c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                                  }
                                              });
                }
            }
        }

        /// <summary>
        /// Computes the LUP factorization of A. P*A = L*U.
        /// </summary>
        /// <param name="data">An <paramref name="order"/> by <paramref name="order"/> matrix. The matrix is overwritten with the
        /// the LU factorization on exit. The lower triangular factor L is stored in under the diagonal of <paramref name="data"/> (the diagonal is always 1.0
        /// for the L factor). The upper triangular factor U is stored on and above the diagonal of <paramref name="data"/>.</param>
        /// <param name="order">The order of the square matrix <paramref name="data"/>.</param>
        /// <param name="ipiv">On exit, it contains the pivot indices. The size of the array must be <paramref name="order"/>.</param>
        /// <remarks>This is equivalent to the GETRF LAPACK routine.</remarks>
        public void LUFactor(float[] data, int order, int[] ipiv)
        {
            throw new NotImplementedException();
        }

        public void LUInverse(float[] a)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(float[] a, int[] ipiv)
        {
            throw new NotImplementedException();
        }

        public void LUInverse(float[] a, float[] work)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(float[] a, int[] ipiv, float[] work)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(int columnsOfB, float[] a, float[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(int columnsOfB, float[] a, int ipiv, float[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(Transpose transposeA, int columnsOfB, float[] a, float[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(Transpose transposeA, int columnsOfB, float[] a, int ipiv, float[] b)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Computes the Cholesky factorization of A.
        /// </summary>
        /// <param name="a">On entry, a square, positive definite matrix. On exit, the matrix is overwritten with the
        /// the Cholesky factorization.</param>
        /// <param name="order">The number of rows or columns in the matrix.</param>
        /// <remarks>This is equivalent to the POTRF LAPACK routine.</remarks>
        public void CholeskyFactor(float[] a, int order)
        {
            var factor = new float[a.Length];

            for (var j = 0; j < order; j++)
            {
                var d = 0.0F;
                int index;
                for (var k = 0; k < j; k++)
                {
                    var s = 0.0F;
                    int i;
                    for (i = 0; i < k; i++)
                    {
                        s += factor[i * order + k] * factor[i * order + j];
                    }

                    var tmp = k * order;
                    index = tmp + j;
                    factor[index] = s = (a[index] - s) / factor[tmp + k];
                    d += s * s;
                }

                index = j * order + j;
                d = a[index] - d;
                if (d <= 0.0F)
                {
                    throw new ArgumentException(Resources.ArgumentMatrixPositiveDefinite);
                }

                factor[index] = (float)Math.Sqrt(d);
                for (var k = j + 1; k < order; k++)
                {
                    factor[k * order + j] = 0.0F;
                }
            }

            Buffer.BlockCopy(factor, 0, a, 0, factor.Length * Constants.SizeOfFloat);
        }

        /// <summary>
        /// Solves A*X=B for X using Cholesky factorization.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRF add POTRS LAPACK routines.</remarks>
        public void CholeskySolve(float[] a, int aOrder, float[] b, int bRows, int bColumns)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Solves A*X=B for X using a previously factored A matrix.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRS LAPACK routine.</remarks>
        public void CholeskySolveFactored(float[] a, int aOrder, float[] b, int bRows, int bColumns)
        {
            throw new NotImplementedException();
        }

        public void QRFactor(float[] r, float[] q)
        {
            throw new NotImplementedException();
        }

        public void QRFactor(float[] r, float[] q, float[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, float[] r, float[] q, float[] b, float[] x)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, float[] r, float[] q, float[] b, float[] x, float[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolveFactored(int columnsOfB, float[] q, float[] r, float[] b, float[] x)
        {
            throw new NotImplementedException();
        }

        public void SinguarValueDecomposition(bool computeVectors, float[] a, float[] s, float[] u, float[] vt)
        {
            throw new NotImplementedException();
        }

        public void SingularValueDecomposition(bool computeVectors, float[] a, float[] s, float[] u, float[] vt, float[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(float[] a, float[] s, float[] u, float[] vt, float[] b, float[] x)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(float[] a, float[] s, float[] u, float[] vt, float[] b, float[] x, float[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolveFactored(int columnsOfB, float[] s, float[] u, float[] vt, float[] b, float[] x)
        {
            throw new NotImplementedException();
        }

        #endregion

        #region ILinearAlgebraProvider<Complex> Members

        /// <summary>
        /// Adds a scaled vector to another: <c>y += alpha*x</c>.
        /// </summary>
        /// <param name="y">The vector to update.</param>
        /// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
        /// <param name="x">The vector to add to <paramref name="y"/>.</param>
        /// <remarks>This equivalent to the AXPY BLAS routine.</remarks>
        public void AddVectorToScaledVector(Complex[] y, Complex alpha, Complex[] x)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            if (alpha == 0.0)
            {
                return;
            }

            if (alpha == 1.0)
            {
                CommonParallel.For(0, y.Length, i => y[i] += x[i]);
            }
            else
            {
                CommonParallel.For(0, y.Length, i => y[i] += alpha * x[i]);
            }
        }

        /// <summary>
        /// Scales an array. Can be used to scale a vector and a matrix.
        /// </summary>
        /// <param name="alpha">The scalar.</param>
        /// <param name="x">The values to scale.</param>
        /// <remarks>This is equivalent to the SCAL BLAS routine.</remarks>
        public void ScaleArray(Complex alpha, Complex[] x)
        {
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (alpha == 1.0)
            {
                return;
            }

            CommonParallel.For(0, x.Length, i => x[i] = alpha * x[i]);
        }

        /// <summary>
        /// Computes the dot product of x and y.
        /// </summary>
        /// <param name="x">The vector x.</param>
        /// <param name="y">The vector y.</param>
        /// <returns>The dot product of x and y.</returns>
        /// <remarks>This is equivalent to the DOT BLAS routine.</remarks>
        public Complex DotProduct(Complex[] x, Complex[] y)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            var d = new Complex(0.0, 0.0);

            for (var i = 0; i < y.Length; i++)
            {
                d += y[i] * x[i];
            }

            return d;
        }

        /// <summary>
        /// Does a point wise add of two arrays <c>z = x + y</c>. This can be used 
        /// to add vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the addition.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void AddArrays(Complex[] x, Complex[] y, Complex[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] + y[i]);
        }

        /// <summary>
        /// Does a point wise subtraction of two arrays <c>z = x - y</c>. This can be used 
        /// to subtract vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the subtraction.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void SubtractArrays(Complex[] x, Complex[] y, Complex[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] - y[i]);
        }

        /// <summary>
        /// Does a point wise multiplication of two arrays <c>z = x * y</c>. This can be used
        /// to multiple elements of vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the point wise multiplication.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void PointWiseMultiplyArrays(Complex[] x, Complex[] y, Complex[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] * y[i]);
        }

        public Complex MatrixNorm(Norm norm, Complex[] matrix)
        {
            throw new NotImplementedException();
        }

        public Complex MatrixNorm(Norm norm, Complex[] matrix, Complex[] work)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Multiples two matrices. <c>result = x * y</c>
        /// </summary>
        /// <param name="x">The x matrix.</param>
        /// <param name="xRows">The number of rows in the x matrix.</param>
        /// <param name="xColumns">The number of columns in the x matrix.</param>
        /// <param name="y">The y matrix.</param>
        /// <param name="yRows">The number of rows in the y matrix.</param>
        /// <param name="yColumns">The number of columns in the y matrix.</param>
        /// <param name="result">Where to store the result of the multiplication.</param>
        /// <remarks>This is a simplified version of the BLAS GEMM routine with alpha
        /// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks>
        public void MatrixMultiply(Complex[] x, int xRows, int xColumns, Complex[] y, int yRows, int yColumns, Complex[] result)
        {
            // First check some basic requirement on the parameters of the matrix multiplication.
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (xRows * xColumns != x.Length)
            {
                throw new ArgumentException("x.Length != xRows * xColumns");
            }

            if (yRows * yColumns != y.Length)
            {
                throw new ArgumentException("y.Length != yRows * yColumns");
            }

            if (xColumns != yRows)
            {
                throw new ArgumentException("xColumns != yRows");
            }

            if (xRows * yColumns != result.Length)
            {
                throw new ArgumentException("xRows * yColumns != result.Length");
            }

            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            Complex[] xdata;
            if (ReferenceEquals(x, result))
            {
                xdata = (Complex[])x.Clone();
            }
            else
            {
                xdata = x;
            }

            Complex[] ydata;
            if (ReferenceEquals(y, result))
            {
                ydata = (Complex[])y.Clone();
            }
            else
            {
                ydata = y;
            }

            // Start the actual matrix multiplication.
            // TODO - For small matrices we should get rid of the parallelism because of startup costs.
            // Perhaps the following implementations would be a good one
            // http://blog.feradz.com/2009/01/cache-efficient-matrix-multiplication/
            this.MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, Complex.One, x, xRows, xColumns, y, yRows, yColumns, Complex.Zero, result);
        }

        /// <summary>
        /// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
        /// </summary>
        /// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
        /// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
        /// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
        /// <param name="a">The a matrix.</param>
        /// <param name="aRows">The number of rows in the <paramref name="a"/> matrix.</param>
        /// <param name="aColumns">The number of columns in the <paramref name="a"/> matrix.</param>
        /// <param name="b">The b matrix</param>
        /// <param name="bRows">The number of rows in the <paramref name="b"/> matrix.</param>
        /// <param name="bColumns">The number of columns in the <paramref name="b"/> matrix.</param>
        /// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
        /// <param name="c">The c matrix.</param>
        public void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex alpha, Complex[] a, 
                                             int aRows, int aColumns, Complex[] b, int bRows, int bColumns, Complex beta, Complex[] c)
        {
            // Choose nonsensical values for the number of rows and columns in c; fill them in depending
            // on the operations on a and b.
            var cRows = -1;
            var cColumns = -1;

            // First check some basic requirement on the parameters of the matrix multiplication.
            if (a == null)
            {
                throw new ArgumentNullException("a");
            }

            if (b == null)
            {
                throw new ArgumentNullException("b");
            }

            if ((int)transposeA > 111 && (int)transposeB > 111)
            {
                if (aRows != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
                cColumns = bRows;
            }
            else if ((int)transposeA > 111)
            {
                if (aRows != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
                cColumns = bColumns;
            }
            else if ((int)transposeB > 111)
            {
                if (aColumns != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
                cColumns = bRows;
            }
            else
            {
                if (aColumns != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
                cColumns = bColumns;
            }

            if (alpha == 0.0 && beta == 0.0)
            {
                Array.Clear(c, 0, c.Length);
                return;
            }


            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            Complex[] adata;
            if (ReferenceEquals(a, c))
            {
                adata = (Complex[])a.Clone();
            }
            else
            {
                adata = a;
            }

            Complex[] bdata;
            if (ReferenceEquals(b, c))
            {
                bdata = (Complex[])b.Clone();
            }
            else
            {
                bdata = b;
            }

            if (alpha == 1.0)
            {
                if (beta == 0.0)
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, j =>
                                                  {
                                                      var jIndex = j * cRows;
                                                      for (var i = 0; i != bRows; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex s = 0;
                                                          for (var l = 0; l != bColumns; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[l * bRows + j];
                                                          }

                                                          c[jIndex + i] = s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aColumns; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex s = 0;
                                                          for (var l = 0; l != aRows; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeB > 111)
                    {
                        CommonParallel.For(0, bRows, j =>
                                               {
                                                   var jIndex = j * cRows;
                                                   for (var i = 0; i != aRows; i++)
                                                   {
                                                       Complex s = 0;
                                                       for (var l = 0; l != aColumns; l++)
                                                       {
                                                           s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                       }

                                                       c[jIndex + i] = s;
                                                   }
                                               });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aRows; i++)
                                                      {
                                                          Complex s = 0;
                                                          for (var l = 0; l != aColumns; l++)
                                                          {
                                                              s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s;
                                                      }
                                                  });
                    }
                }
                else
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, j =>
                                                  {
                                                      var jIndex = j * cRows;
                                                      for (var i = 0; i != bRows; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex s = 0;
                                                          for (var l = 0; l != bColumns; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[l * bRows + j];
                                                          }

                                                          c[jIndex + i] = c[jIndex + i] * beta + s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aColumns; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex s = 0;
                                                          for (var l = 0; l != aRows; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                                      }
                                                  });
                    }
                    else if ((int)transposeB > 111)
                    {
                        CommonParallel.For(0, bRows, j =>
                                               {
                                                   var jIndex = j * cRows;
                                                   for (var i = 0; i != aRows; i++)
                                                   {
                                                       Complex s = 0;
                                                       for (var l = 0; l != aColumns; l++)
                                                       {
                                                           s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                       }

                                                       c[jIndex + i] = s + c[jIndex + i] * beta;
                                                   }
                                               });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aRows; i++)
                                                      {
                                                          Complex s = 0;
                                                          for (var l = 0; l != aColumns; l++)
                                                          {
                                                              s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                                      }
                                                  });
                    }
                }
            }
            else
            {
                if ((int)transposeA > 111 && (int)transposeB > 111)
                {
                    CommonParallel.For(0, aColumns, j =>
                                              {
                                                  var jIndex = j * cRows;
                                                  for (var i = 0; i != bRows; i++)
                                                  {
                                                      var iIndex = i * aRows;
                                                      Complex s = 0;
                                                      for (var l = 0; l != bColumns; l++)
                                                      {
                                                          s += adata[iIndex + l] * bdata[l * bRows + j];
                                                      }

                                                      c[jIndex + i] = c[jIndex + i] * beta + alpha * s;
                                                  }
                                              });
                }
                else if ((int)transposeA > 111)
                {
                    CommonParallel.For(0, bColumns, j =>
                                              {
                                                  var jcIndex = j * cRows;
                                                  var jbIndex = j * bRows;
                                                  for (var i = 0; i != aColumns; i++)
                                                  {
                                                      var iIndex = i * aRows;
                                                      Complex s = 0;
                                                      for (var l = 0; l != aRows; l++)
                                                      {
                                                          s += adata[iIndex + l] * bdata[jbIndex + l];
                                                      }

                                                      c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                                  }
                                              });
                }
                else if ((int)transposeB > 111)
                {
                   CommonParallel.For(0, bRows, j =>
                                           {
                                               var jIndex = j * cRows;
                                               for (var i = 0; i != aRows; i++)
                                               {
                                                   Complex s = 0;
                                                   for (var l = 0; l != aColumns; l++)
                                                   {
                                                       s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                   }

                                                   c[jIndex + i] = alpha * s + c[jIndex + i] * beta;
                                               }
                                           });
                }
                else
                {
                    CommonParallel.For(0, bColumns, j =>
                                              {
                                                  var jcIndex = j * cRows;
                                                  var jbIndex = j * bRows;
                                                  for (var i = 0; i != aRows; i++)
                                                  {
                                                      Complex s = 0;
                                                      for (var l = 0; l != aColumns; l++)
                                                      {
                                                          s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                      }

                                                      c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                                  }
                                              });
                }
            }
        }

        /// <summary>
        /// Computes the LUP factorization of A. P*A = L*U.
        /// </summary>
        /// <param name="data">An <paramref name="order"/> by <paramref name="order"/> matrix. The matrix is overwritten with the
        /// the LU factorization on exit. The lower triangular factor L is stored in under the diagonal of <paramref name="data"/> (the diagonal is always 1.0
        /// for the L factor). The upper triangular factor U is stored on and above the diagonal of <paramref name="data"/>.</param>
        /// <param name="order">The order of the square matrix <paramref name="data"/>.</param>
        /// <param name="ipiv">On exit, it contains the pivot indices. The size of the array must be <paramref name="order"/>.</param>
        /// <remarks>This is equivalent to the GETRF LAPACK routine.</remarks>
        public void LUFactor(Complex[] data, int order, int[] ipiv)
        {
            throw new NotImplementedException();
        }

        public void LUInverse(Complex[] a)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(Complex[] a, int[] ipiv)
        {
            throw new NotImplementedException();
        }

        public void LUInverse(Complex[] a, Complex[] work)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(Complex[] a, int[] ipiv, Complex[] work)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(int columnsOfB, Complex[] a, Complex[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(int columnsOfB, Complex[] a, int ipiv, Complex[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(Transpose transposeA, int columnsOfB, Complex[] a, Complex[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(Transpose transposeA, int columnsOfB, Complex[] a, int ipiv, Complex[] b)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Computes the Cholesky factorization of A.
        /// </summary>
        /// <param name="a">On entry, a square, positive definite matrix. On exit, the matrix is overwritten with the
        /// the Cholesky factorization.</param>
        /// <param name="order">The number of rows or columns in the matrix.</param>
        /// <remarks>This is equivalent to the POTRF LAPACK routine.</remarks>
        public void CholeskyFactor(Complex[] a, int order)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Solves A*X=B for X using Cholesky factorization.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRF add POTRS LAPACK routines.</remarks>
        public void CholeskySolve(Complex[] a, int aOrder, Complex[] b, int bRows, int bColumns)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Solves A*X=B for X using a previously factored A matrix.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRS LAPACK routine.</remarks>
        public void CholeskySolveFactored(Complex[] a, int aOrder, Complex[] b, int bRows, int bColumns)
        {
            throw new NotImplementedException();
        }

        public void QRFactor(Complex[] r, Complex[] q)
        {
            throw new NotImplementedException();
        }

        public void QRFactor(Complex[] r, Complex[] q, Complex[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, Complex[] r, Complex[] q, Complex[] b, Complex[] x)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, Complex[] r, Complex[] q, Complex[] b, Complex[] x, Complex[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolveFactored(int columnsOfB, Complex[] q, Complex[] r, Complex[] b, Complex[] x)
        {
            throw new NotImplementedException();
        }

        public void SinguarValueDecomposition(bool computeVectors, Complex[] a, Complex[] s, Complex[] u, Complex[] vt)
        {
            throw new NotImplementedException();
        }

        public void SingularValueDecomposition(bool computeVectors, Complex[] a, Complex[] s, Complex[] u, Complex[] vt, Complex[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(Complex[] a, Complex[] s, Complex[] u, Complex[] vt, Complex[] b, Complex[] x)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(Complex[] a, Complex[] s, Complex[] u, Complex[] vt, Complex[] b, Complex[] x, Complex[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolveFactored(int columnsOfB, Complex[] s, Complex[] u, Complex[] vt, Complex[] b, Complex[] x)
        {
            throw new NotImplementedException();
        }

        #endregion

        #region ILinearAlgebraProvider<Complex32> Members

        /// <summary>
        /// Adds a scaled vector to another: <c>y += alpha*x</c>.
        /// </summary>
        /// <param name="y">The vector to update.</param>
        /// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
        /// <param name="x">The vector to add to <paramref name="y"/>.</param>
        /// <remarks>This equivalent to the AXPY BLAS routine.</remarks>
        public void AddVectorToScaledVector(Complex32[] y, Complex32 alpha, Complex32[] x)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            if (alpha == 0.0F)
            {
                return;
            }

            if (alpha == 1.0F)
            {
                CommonParallel.For(0, y.Length, i => y[i] += x[i]);
            }
            else
            {
                CommonParallel.For(0, y.Length, i => y[i] += alpha * x[i]);
            }
        }

        /// <summary>
        /// Scales an array. Can be used to scale a vector and a matrix.
        /// </summary>
        /// <param name="alpha">The scalar.</param>
        /// <param name="x">The values to scale.</param>
        /// <remarks>This is equivalent to the SCAL BLAS routine.</remarks>
        public void ScaleArray(Complex32 alpha, Complex32[] x)
        {
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (alpha.IsOne())
            {
                return;
            }

            CommonParallel.For(0, x.Length, i => x[i] = alpha * x[i]);
        }

        /// <summary>
        /// Computes the dot product of x and y.
        /// </summary>
        /// <param name="x">The vector x.</param>
        /// <param name="y">The vector y.</param>
        /// <returns>The dot product of x and y.</returns>
        /// <remarks>This is equivalent to the DOT BLAS routine.</remarks>
        public Complex32 DotProduct(Complex32[] x, Complex32[] y)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y.Length != x.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            var d = new Complex32(0.0F, 0.0F);

            for (var i = 0; i < y.Length; i++)
            {
                d += y[i] * x[i];
            }

            return d;
        }

        /// <summary>
        /// Does a point wise add of two arrays <c>z = x + y</c>. This can be used 
        /// to add vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the addition.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void AddArrays(Complex32[] x, Complex32[] y, Complex32[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] + y[i]);
        }

        /// <summary>
        /// Does a point wise subtraction of two arrays <c>z = x - y</c>. This can be used 
        /// to subtract vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the subtraction.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void SubtractArrays(Complex32[] x, Complex32[] y, Complex32[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] - y[i]);
        }

        /// <summary>
        /// Does a point wise multiplication of two arrays <c>z = x * y</c>. This can be used
        /// to multiple elements of vectors or matrices.
        /// </summary>
        /// <param name="x">The array x.</param>
        /// <param name="y">The array y.</param>
        /// <param name="result">The result of the point wise multiplication.</param>
        /// <remarks>There is no equivalent BLAS routine, but many libraries
        /// provide optimized (parallel and/or vectorized) versions of this
        /// routine.</remarks>
        public void PointWiseMultiplyArrays(Complex32[] x, Complex32[] y, Complex32[] result)
        {
            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (y.Length != x.Length || y.Length != result.Length)
            {
                throw new ArgumentException(Resources.ArgumentVectorsSameLength);
            }

            CommonParallel.For(0, y.Length, i => result[i] = x[i] * y[i]);
        }

        public Complex32 MatrixNorm(Norm norm, Complex32[] matrix)
        {
            throw new NotImplementedException();
        }

        public Complex32 MatrixNorm(Norm norm, Complex32[] matrix, Complex32[] work)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Multiples two matrices. <c>result = x * y</c>
        /// </summary>
        /// <param name="x">The x matrix.</param>
        /// <param name="xRows">The number of rows in the x matrix.</param>
        /// <param name="xColumns">The number of columns in the x matrix.</param>
        /// <param name="y">The y matrix.</param>
        /// <param name="yRows">The number of rows in the y matrix.</param>
        /// <param name="yColumns">The number of columns in the y matrix.</param>
        /// <param name="result">Where to store the result of the multiplication.</param>
        /// <remarks>This is a simplified version of the BLAS GEMM routine with alpha
        /// set to 1.0 and beta set to 0.0, and x and y are not transposed.</remarks>
        public void MatrixMultiply(Complex32[] x, int xRows, int xColumns, Complex32[] y, int yRows, int yColumns, Complex32[] result)
        {
            // First check some basic requirement on the parameters of the matrix multiplication.
            if (x == null)
            {
                throw new ArgumentNullException("x");
            }

            if (y == null)
            {
                throw new ArgumentNullException("y");
            }

            if (result == null)
            {
                throw new ArgumentNullException("result");
            }

            if (xRows * xColumns != x.Length)
            {
                throw new ArgumentException("x.Length != xRows * xColumns");
            }

            if (yRows * yColumns != y.Length)
            {
                throw new ArgumentException("y.Length != yRows * yColumns");
            }

            if (xColumns != yRows)
            {
                throw new ArgumentException("xColumns != yRows");
            }

            if (xRows * yColumns != result.Length)
            {
                throw new ArgumentException("xRows * yColumns != result.Length");
            }

            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            Complex32[] xdata;
            if (ReferenceEquals(x, result))
            {
                xdata = (Complex32[])x.Clone();
            }
            else
            {
                xdata = x;
            }

            Complex32[] ydata;
            if (ReferenceEquals(y, result))
            {
                ydata = (Complex32[])y.Clone();
            }
            else
            {
                ydata = y;
            }

            // Start the actual matrix multiplication.
            // TODO - For small matrices we should get rid of the parallelism because of startup costs.
            // Perhaps the following implementations would be a good one
            // http://blog.feradz.com/2009/01/cache-efficient-matrix-multiplication/
            this.MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, Complex32.One, x, xRows, xColumns, y, yRows, yColumns, Complex32.Zero, result);
        }

        /// <summary>
        /// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
        /// </summary>
        /// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
        /// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
        /// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
        /// <param name="a">The a matrix.</param>
        /// <param name="aRows">The number of rows in the <paramref name="a"/> matrix.</param>
        /// <param name="aColumns">The number of columns in the <paramref name="a"/> matrix.</param>
        /// <param name="b">The b matrix</param>
        /// <param name="bRows">The number of rows in the <paramref name="b"/> matrix.</param>
        /// <param name="bColumns">The number of columns in the <paramref name="b"/> matrix.</param>
        /// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
        /// <param name="c">The c matrix.</param>
        public void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex32 alpha, Complex32[] a, 
                                             int aRows, int aColumns, Complex32[] b, int bRows, int bColumns, Complex32 beta, Complex32[] c)
        {
            // Choose nonsensical values for the number of rows and columns in c; fill them in depending
            // on the operations on a and b.
            var cRows = -1;
            var cColumns = -1;

            // First check some basic requirement on the parameters of the matrix multiplication.
            if (a == null)
            {
                throw new ArgumentNullException("a");
            }

            if (b == null)
            {
                throw new ArgumentNullException("b");
            }

            if ((int)transposeA > 111 && (int)transposeB > 111)
            {
                if (aRows != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
                cColumns = bRows;
            }
            else if ((int)transposeA > 111)
            {
                if (aRows != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aColumns * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aColumns;
                cColumns = bColumns;
            }
            else if ((int)transposeB > 111)
            {
                if (aColumns != bColumns)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bRows != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
                cColumns = bRows;
            }
            else
            {
                if (aColumns != bRows)
                {
                    throw new ArgumentOutOfRangeException();
                }

                if (aRows * bColumns != c.Length)
                {
                    throw new ArgumentOutOfRangeException();
                }

                cRows = aRows;
                cColumns = bColumns;
            }

            if (alpha.IsZero() && beta.IsZero())
            {
                Array.Clear(c, 0, c.Length);
                return;
            }


            // Check whether we will be overwriting any of our inputs and make copies if necessary.
            // TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
            // as result, we can do it on a row wise basis. We should investigate this.
            Complex32[] adata;
            if (ReferenceEquals(a, c))
            {
                adata = (Complex32[])a.Clone();
            }
            else
            {
                adata = a;
            }

            Complex32[] bdata;
            if (ReferenceEquals(b, c))
            {
                bdata = (Complex32[])b.Clone();
            }
            else
            {
                bdata = b;
            }

            if (alpha.IsOne())
            {
                if (beta.IsZero())
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, j =>
                                                  {
                                                      var jIndex = j * cRows;
                                                      for (var i = 0; i != bRows; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex32 s = 0;
                                                          for (var l = 0; l != bColumns; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[l * bRows + j];
                                                          }

                                                          c[jIndex + i] = s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aColumns; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex32 s = 0;
                                                          for (var l = 0; l != aRows; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeB > 111)
                    {
                        CommonParallel.For(0, bRows, j =>
                                               {
                                                   var jIndex = j * cRows;
                                                   for (var i = 0; i != aRows; i++)
                                                   {
                                                       Complex32 s = 0;
                                                       for (var l = 0; l != aColumns; l++)
                                                       {
                                                           s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                       }

                                                       c[jIndex + i] = s;
                                                   }
                                               });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aRows; i++)
                                                      {
                                                          Complex32 s = 0;
                                                          for (var l = 0; l != aColumns; l++)
                                                          {
                                                              s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s;
                                                      }
                                                  });
                    }
                }
                else
                {
                    if ((int)transposeA > 111 && (int)transposeB > 111)
                    {
                        CommonParallel.For(0, aColumns, j =>
                                                  {
                                                      var jIndex = j * cRows;
                                                      for (var i = 0; i != bRows; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex32 s = 0;
                                                          for (var l = 0; l != bColumns; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[l * bRows + j];
                                                          }

                                                          c[jIndex + i] = c[jIndex + i] * beta + s;
                                                      }
                                                  });
                    }
                    else if ((int)transposeA > 111)
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aColumns; i++)
                                                      {
                                                          var iIndex = i * aRows;
                                                          Complex32 s = 0;
                                                          for (var l = 0; l != aRows; l++)
                                                          {
                                                              s += adata[iIndex + l] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                                      }
                                                  });
                    }
                    else if ((int)transposeB > 111)
                    {
                        CommonParallel.For(0, bRows, j =>
                                               {
                                                   var jIndex = j * cRows;
                                                   for (var i = 0; i != aRows; i++)
                                                   {
                                                       Complex32 s = 0;
                                                       for (var l = 0; l != aColumns; l++)
                                                       {
                                                           s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                       }

                                                       c[jIndex + i] = s + c[jIndex + i] * beta;
                                                   }
                                               });
                    }
                    else
                    {
                        CommonParallel.For(0, bColumns, j =>
                                                  {
                                                      var jcIndex = j * cRows;
                                                      var jbIndex = j * bRows;
                                                      for (var i = 0; i != aRows; i++)
                                                      {
                                                          Complex32 s = 0;
                                                          for (var l = 0; l != aColumns; l++)
                                                          {
                                                              s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                          }

                                                          c[jcIndex + i] = s + c[jcIndex + i] * beta;
                                                      }
                                                  });
                    }
                }
            }
            else
            {
                if ((int)transposeA > 111 && (int)transposeB > 111)
                {
                    CommonParallel.For(0, aColumns, j =>
                                              {
                                                  var jIndex = j * cRows;
                                                  for (var i = 0; i != bRows; i++)
                                                  {
                                                      var iIndex = i * aRows;
                                                      Complex32 s = 0;
                                                      for (var l = 0; l != bColumns; l++)
                                                      {
                                                          s += adata[iIndex + l] * bdata[l * bRows + j];
                                                      }

                                                      c[jIndex + i] = c[jIndex + i] * beta + alpha * s;
                                                  }
                                              });
                }
                else if ((int)transposeA > 111)
                {
                    CommonParallel.For(0, bColumns, j =>
                                              {
                                                  var jcIndex = j * cRows;
                                                  var jbIndex = j * bRows;
                                                  for (var i = 0; i != aColumns; i++)
                                                  {
                                                      var iIndex = i * aRows;
                                                      Complex32 s = 0;
                                                      for (var l = 0; l != aRows; l++)
                                                      {
                                                          s += adata[iIndex + l] * bdata[jbIndex + l];
                                                      }

                                                      c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                                  }
                                              });
                }
                else if ((int)transposeB > 111)
                {
                    CommonParallel.For(0, bRows, j =>
                                           {
                                               var jIndex = j * cRows;
                                               for (var i = 0; i != aRows; i++)
                                               {
                                                   Complex32 s = 0;
                                                   for (var l = 0; l != aColumns; l++)
                                                   {
                                                       s += adata[l * aRows + i] * bdata[l * bRows + j];
                                                   }

                                                   c[jIndex + i] = alpha * s + c[jIndex + i] * beta;
                                               }
                                           });
                }
                else
                {
                    CommonParallel.For(0, bColumns, j =>
                                              {
                                                  var jcIndex = j * cRows;
                                                  var jbIndex = j * bRows;
                                                  for (var i = 0; i != aRows; i++)
                                                  {
                                                      Complex32 s = 0;
                                                      for (var l = 0; l != aColumns; l++)
                                                      {
                                                          s += adata[l * aRows + i] * bdata[jbIndex + l];
                                                      }

                                                      c[jcIndex + i] = alpha * s + c[jcIndex + i] * beta;
                                                  }
                                              });
                }
            }
        }

        /// <summary>
        /// Computes the LUP factorization of A. P*A = L*U.
        /// </summary>
        /// <param name="data">An <paramref name="order"/> by <paramref name="order"/> matrix. The matrix is overwritten with the
        /// the LU factorization on exit. The lower triangular factor L is stored in under the diagonal of <paramref name="data"/> (the diagonal is always 1.0
        /// for the L factor). The upper triangular factor U is stored on and above the diagonal of <paramref name="data"/>.</param>
        /// <param name="order">The order of the square matrix <paramref name="data"/>.</param>
        /// <param name="ipiv">On exit, it contains the pivot indices. The size of the array must be <paramref name="order"/>.</param>
        /// <remarks>This is equivalent to the GETRF LAPACK routine.</remarks>
        public void LUFactor(Complex32[] data, int order, int[] ipiv)
        {
            throw new NotImplementedException();
        }

        public void LUInverse(Complex32[] a)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(Complex32[] a, int[] ipiv)
        {
            throw new NotImplementedException();
        }

        public void LUInverse(Complex32[] a, Complex32[] work)
        {
            throw new NotImplementedException();
        }

        public void LUInverseFactored(Complex32[] a, int[] ipiv, Complex32[] work)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(int columnsOfB, Complex32[] a, Complex32[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(int columnsOfB, Complex32[] a, int ipiv, Complex32[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolve(Transpose transposeA, int columnsOfB, Complex32[] a, Complex32[] b)
        {
            throw new NotImplementedException();
        }

        public void LUSolveFactored(Transpose transposeA, int columnsOfB, Complex32[] a, int ipiv, Complex32[] b)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Computes the Cholesky factorization of A.
        /// </summary>
        /// <param name="a">On entry, a square, positive definite matrix. On exit, the matrix is overwritten with the
        /// the Cholesky factorization.</param>
        /// <param name="order">The number of rows or columns in the matrix.</param>
        /// <remarks>This is equivalent to the POTRF LAPACK routine.</remarks>
        public void CholeskyFactor(Complex32[] a, int order)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Solves A*X=B for X using Cholesky factorization.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRF add POTRS LAPACK routines.</remarks>
        public void CholeskySolve(Complex32[] a, int aOrder, Complex32[] b, int bRows, int bColumns)
        {
            throw new NotImplementedException();
        }

        /// <summary>
        /// Solves A*X=B for X using a previously factored A matrix.
        /// </summary>
        /// <param name="a">The square, positive definite matrix A.</param>
        /// <param name="aOrder">The number of rows and columns in A.</param>
        /// <param name="b">The B matrix.</param>
        /// <param name="bRows">The number of rows in the B matrix.</param>
        /// <param name="bColumns">The number of columns in the B matrix.</param>
        /// <remarks>This is equivalent to the POTRS LAPACK routine.</remarks>
        public void CholeskySolveFactored(Complex32[] a, int aOrder, Complex32[] b, int bRows, int bColumns)
        {
            throw new NotImplementedException();
        }

        public void QRFactor(Complex32[] r, Complex32[] q)
        {
            throw new NotImplementedException();
        }

        public void QRFactor(Complex32[] r, Complex32[] q, Complex32[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, Complex32[] r, Complex32[] q, Complex32[] b, Complex32[] x)
        {
            throw new NotImplementedException();
        }

        public void QRSolve(int columnsOfB, Complex32[] r, Complex32[] q, Complex32[] b, Complex32[] x, Complex32[] work)
        {
            throw new NotImplementedException();
        }

        public void QRSolveFactored(int columnsOfB, Complex32[] q, Complex32[] r, Complex32[] b, Complex32[] x)
        {
            throw new NotImplementedException();
        }

        public void SinguarValueDecomposition(bool computeVectors, Complex32[] a, Complex32[] s, Complex32[] u, Complex32[] vt)
        {
            throw new NotImplementedException();
        }

        public void SingularValueDecomposition(bool computeVectors, Complex32[] a, Complex32[] s, Complex32[] u, Complex32[] vt, Complex32[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(Complex32[] a, Complex32[] s, Complex32[] u, Complex32[] vt, Complex32[] b, Complex32[] x)
        {
            throw new NotImplementedException();
        }

        public void SvdSolve(Complex32[] a, Complex32[] s, Complex32[] u, Complex32[] vt, Complex32[] b, Complex32[] x, Complex32[] work)
        {
            throw new NotImplementedException();
        }

        public void SvdSolveFactored(int columnsOfB, Complex32[] s, Complex32[] u, Complex32[] vt, Complex32[] b, Complex32[] x)
        {
            throw new NotImplementedException();
        }

        #endregion
    }
}