/// <summary>
/// MATLAB 'backslash' solver for the system
/// <paramref name="M"/>*<paramref name="X"/> = <paramref name="RHS"/>.
/// </summary>
/// <param name="M">
/// Matrix of the linear system.
/// </param>
/// <param name="RHS">
/// Input, the right hand side of the linear system.
/// </param>
/// <param name="X">
/// Output, the solution.
/// </param>
/// <param name="__WorkingPath"></param>
public static void SolveMATLAB <T1, T2>(this IMutableMatrixEx M, T1 X, T2 RHS, string __WorkingPath = null)
where T1 : IList <double>
where T2 : IList <double> //
{
if (M.RowPartitioning.LocalLength != RHS.Count)
{
throw new ArgumentException("Mismatch between number of rows and length of right-hand-side.");
}
if (M.ColPartition.LocalLength != X.Count)
{
throw new ArgumentException("Mismatch between number of columns and length of unknown vector.");
}
MultidimensionalArray Xwrapper = MultidimensionalArray.Create(X.Count, 1);
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(1, 1);
connector.PutSparseMatrix(M, "Matrix");
connector.PutVector(RHS, "RHS");
connector.Cmd("X = Matrix \\ RHS ;");
connector.GetMatrix(Xwrapper, "X");
connector.Execute(false);
Xwrapper.GetColumn(0, X);
}
}
/// <summary>
/// MATLAB function 'eigs' (eigenvalues and eigenvectors);
/// </summary>
/// <param name="M">
/// A sparse Matrix.
/// </param>
/// <param name="__WorkingPath"></param>
public static (double[] EigenVals, MultidimensionalArray EigenVect) eigsV(this IMatrix M, string __WorkingPath = null)
{
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
if (M == null)
{
throw new ArgumentNullException();
}
if (M.NoOfCols != M.NoOfRows)
{
throw new ArgumentException("Not supported for non-symmetrical matrices.");
}
int N = M.NoOfCols;
MultidimensionalArray eVect = MultidimensionalArray.Create(N, N);
MultidimensionalArray eVal = MultidimensionalArray.Create(N, 1);
connector.PutMatrix(M, "Matrix");
connector.Cmd(string.Format("[V,D] = eigs(Matrix,{0});", M.NoOfCols));
connector.Cmd(string.Format("ev = diag(D);"));
connector.GetMatrix(eVect, "V");
connector.GetMatrix(eVal, "ev");
connector.Execute(false);
return(eVal.GetColumn(0), eVect);
}
}
/// <summary>
/// MATLAB function 'condest' (condition number estimation for sparse
/// matrices)
/// </summary>
public static double condest(this IMutableMatrixEx M, string __WorkingPath = null)
{
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(1, 1);
connector.PutSparseMatrix(M, "Matrix");
connector.Cmd("cond = condest(Matrix)");
connector.GetMatrix(output, "cond");
connector.Execute(false);
return(output[0, 0]);
}
}
/// <summary>
/// MATLAB function 'eigs' (eigenvalues of a matrix);
/// </summary>
/// <param name="C">
/// options, ('lm': largest magnitude, etc.) see MATLAB documentation.
/// </param>
/// <param name="K">
/// Number of eigenvalues.
/// </param>
/// <param name="M">
/// Matrix.
/// </param>
/// <param name="__WorkingPath"></param>
public static double[] eigs(this IMutableMatrixEx M, int K, string C, string __WorkingPath = null)
{
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(1, 1);
connector.PutSparseMatrix(M, "Matrix");
connector.Cmd(string.Format("EV = eigs(Matrix,{0},'{1}')", K, C));
connector.GetMatrix(output, "EV");
connector.Execute(false);
return(output.GetColumn(0));
}
}
/// <summary>
/// Tests, via a Cholesky factorization, if a symmetric matrix is negative definite.
/// </summary>
public static bool IsNegDef(this IMutableMatrixEx M, string __WorkingPath = null)
{
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(1, 1);
connector.PutSparseMatrix(M, "Matrix");
connector.Cmd("[V,r]=chol(-0.5*(Matrix+Matrix'));");
connector.GetMatrix(output, "r");
connector.Execute(false);
return(output[0, 0] == 0);
}
}
/// <summary>
/// Evaluation of the condition number of a full matrix
/// <paramref name="M"/>.
/// </summary>
/// <param name="M">A full square matrix</param>
/// <param name="workingPath"></param>
/// <returns>
/// The condition number of <paramref name="M"/>
/// </returns>
public static double cond(this IMatrix M, string workingPath = null)
{
if (M == null)
{
throw new ArgumentNullException();
}
using (var connector = new BatchmodeConnector(WorkingPath: workingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(1, 1);
connector.PutMatrix(M, "Matrix");
connector.Cmd("cond = cond(Matrix)");
connector.GetMatrix(output, "cond");
connector.Execute(false);
return(output[0, 0]);
}
}
/// <summary>
/// MATLAB function 'rank' (rank of a matrix);
/// </summary>
public static double rank(this IMutableMatrixEx M, string __WorkingPath = null)
{
if (M == null)
{
throw new ArgumentNullException();
}
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(1, 1);
connector.PutSparseMatrix(M, "Matrix");
connector.Cmd("rank = rank(full(Matrix))");
connector.GetMatrix(output, "rank");
connector.Execute(false);
return(output[0, 0]);
}
}
/// <summary>
/// Evaluation of the eigenvalues of a full matrix
/// <paramref name="M"/>.
/// </summary>
/// <param name="M">A full square matrix</param>
/// <param name="workingPath"></param>
/// <returns>
/// The eigenvalues of <paramref name="M"/> in ascending order
/// </returns>
public static double[] eig(this IMatrix M, string workingPath = null)
{
if (M.NoOfCols != M.NoOfRows)
{
throw new ArgumentException("Matrix must be square");
}
using (var connector = new BatchmodeConnector(WorkingPath: workingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(M.NoOfCols, 1);
connector.PutMatrix(M, "Matrix");
connector.Cmd("eig = eig(Matrix)");
connector.GetMatrix(output, "eig");
connector.Execute(false);
return(output.Storage);
}
}
/// <summary>
/// Tests, via a Cholesky factorization, if a symmetric matrix is positive or negative definite.
/// </summary>
public static bool IsDefinite(this IMutableMatrixEx M, string __WorkingPath = null)
{
if (M == null)
{
throw new ArgumentNullException();
}
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
MultidimensionalArray output = MultidimensionalArray.Create(1, 2);
connector.PutSparseMatrix(M, "Matrix");
connector.Cmd("[V,pr]=chol( 0.5*(Matrix+Matrix'));");
connector.Cmd("[V,nr]=chol(-0.5*(Matrix+Matrix'));");
connector.Cmd("ret=[pr,nr]");
connector.GetMatrix(output, "ret");
connector.Execute(false);
return(output[0, 0] == 0 || output[0, 1] == 0);
}
}
/// <summary>
/// MATLAB function 'eigs' (eigenvalues of a sparse matrix);
/// </summary>
/// <param name="C">
/// options, ('lm': largest magnitude, etc.) see MATLAB documentation.
/// </param>
/// <param name="K">
/// Number of eigenvalues.
/// </param>
/// <param name="M">
/// A sparse Matrix.
/// </param>
/// <param name="__WorkingPath"></param>
public static double[] eigs(this IMutableMatrixEx M, int K, string C, string __WorkingPath = null)
{
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
if (M == null)
{
throw new ArgumentNullException();
}
if (K < 1)
{
throw new ArgumentOutOfRangeException();
}
MultidimensionalArray output = MultidimensionalArray.Create(K, 1);
connector.PutSparseMatrix(M, "Matrix");
connector.Cmd(string.Format("EV = eigs(Matrix,{0},'{1}');", K, C));
connector.GetMatrix(output, "EV");
connector.Execute(false);
return(output.GetColumn(0));
}
}
/// <summary>
/// MATLAB function 'eigs' (eigenvalues of a dense matrix);
/// </summary>
/// <param name="M">
/// A sparse Matrix.
/// </param>
/// <param name="__WorkingPath"></param>
public static double[] eigs(this IMatrix M, string __WorkingPath = null)
{
using (var connector = new BatchmodeConnector(WorkingPath: __WorkingPath)) {
if (M == null)
{
throw new ArgumentNullException();
}
if (M.NoOfCols != M.NoOfRows)
{
throw new ArgumentException("Not supported for non-symmetrical matrices.");
}
int N = M.NoOfCols;
MultidimensionalArray output = MultidimensionalArray.Create(N, 1);
connector.PutMatrix(M, "Matrix");
connector.Cmd(string.Format("EV = eigs(Matrix,{0});", M.NoOfCols));
connector.GetMatrix(output, "EV");
connector.Execute(false);
return(output.GetColumn(0));
}
}