/// <summary>
/// Creates a new <see cref="SparseMatrix"/> and inserts the given row at the given index.
/// </summary>
/// <param name="rowIndex">The index of where to insert the row.</param>
/// <param name="row">The row to insert.</param>
/// <returns>A new <see cref="SparseMatrix"/> with the inserted column.</returns>
/// <exception cref="ArgumentNullException">If <paramref name="row"/> is <see langword="null" />. </exception>
/// <exception cref="ArgumentOutOfRangeException">If <paramref name="rowIndex"/> is < zero or > the number of rows.</exception>
/// <exception cref="ArgumentException">If the size of <paramref name="row"/> != the number of columns.</exception>
public override Matrix <double> InsertRow(int rowIndex, Vector <double> row)
{
if (row == null)
{
throw new ArgumentNullException("row");
}
if (rowIndex < 0 || rowIndex > RowCount)
{
throw new ArgumentOutOfRangeException("rowIndex");
}
if (row.Count != ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension, "row");
}
var result = new SparseMatrix(RowCount + 1, ColumnCount);
for (var i = 0; i < rowIndex; i++)
{
result.At(i, i, At(i, i));
}
result.SetRow(rowIndex, row);
for (var i = rowIndex + 1; i < result.RowCount; i++)
{
result.At(i, i - 1, At(i - 1, i - 1));
}
return(result);
}
/// <summary>
/// Get the 1D Laplacian matrix (with Dirichlet boundary conditions).
/// </summary>
/// <param name="nx">Grid size.</param>
/// <param name="eigenvalues">Vector to store eigenvalues (optional).</param>
/// <returns>Laplacian sparse matrix.</returns>
public static SparseMatrix Laplacian(int nx, DenseVector eigenvalues = null)
{
if (nx == 1)
{
// Handle special case n = 1.
var A = new SparseMatrix(nx, nx);
A.At(0, 0, 2.0);
return(A);
}
var C = new CoordinateStorage <double>(nx, nx);
for (int i = 0; i < nx; i++)
{
C.At(i, i, 2.0);
if (i == 0)
{
C.At(i, i + 1, -1.0);
}
else if (i == (nx - 1))
{
C.At(i, i - 1, -1.0);
}
else
{
C.At(i, i - 1, -1.0);
C.At(i, i + 1, -1.0);
}
}
if (eigenvalues != null)
{
// Compute eigenvalues.
int count = Math.Min(nx, eigenvalues.Count);
var eigs = new double[nx];
for (int i = 0; i < count; i++)
{
eigs[i] = 4 * Math.Pow(Math.Sin((i + 1) * Math.PI / (2 * (nx + 1))), 2);
}
Array.Sort(eigs);
for (int i = 0; i < count; ++i)
{
eigenvalues.At(i, eigs[i]);
}
}
return((SparseMatrix)C.ToSparseMatrix());
}
/// <summary>
/// Outer product of two vectors
/// </summary>
/// <param name="u">First vector</param>
/// <param name="v">Second vector</param>
/// <returns>Matrix M[i,j] = u[i]*v[j] </returns>
/// <exception cref="ArgumentNullException">If the u vector is <see langword="null" />.</exception>
/// <exception cref="ArgumentNullException">If the v vector is <see langword="null" />.</exception>
public static Matrix <double> OuterProduct(SparseVector u, SparseVector v)
{
if (u == null)
{
throw new ArgumentNullException("u");
}
if (v == null)
{
throw new ArgumentNullException("v");
}
var matrix = new SparseMatrix(u.Count, v.Count);
for (var i = 0; i < u._storage.ValueCount; i++)
{
for (var j = 0; j < v._storage.ValueCount; j++)
{
matrix.At(i, j, u._storage.Values[i] * v._storage.Values[j]);
}
}
return(matrix);
}
/// <summary>
/// Creates a new <see cref="SparseMatrix"/> and inserts the given row at the given index.
/// </summary>
/// <param name="rowIndex">The index of where to insert the row.</param>
/// <param name="row">The row to insert.</param>
/// <returns>A new <see cref="SparseMatrix"/> with the inserted column.</returns>
/// <exception cref="ArgumentNullException">If <paramref name="row"/> is <see langword="null" />. </exception>
/// <exception cref="ArgumentOutOfRangeException">If <paramref name="rowIndex"/> is < zero or > the number of rows.</exception>
/// <exception cref="ArgumentException">If the size of <paramref name="row"/> != the number of columns.</exception>
public override Matrix<double> InsertRow(int rowIndex, Vector<double> row)
{
if (row == null)
{
throw new ArgumentNullException("row");
}
if (rowIndex < 0 || rowIndex > RowCount)
{
throw new ArgumentOutOfRangeException("rowIndex");
}
if (row.Count != ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension, "row");
}
var result = new SparseMatrix(RowCount + 1, ColumnCount);
for (var i = 0; i < rowIndex; i++)
{
result.At(i, i, At(i, i));
}
result.SetRow(rowIndex, row);
for (var i = rowIndex + 1; i < result.RowCount; i++)
{
result.At(i, i - 1, At(i - 1, i - 1));
}
return result;
}
/// <summary>
/// Outer product of two vectors
/// </summary>
/// <param name="u">First vector</param>
/// <param name="v">Second vector</param>
/// <returns>Matrix M[i,j] = u[i]*v[j] </returns>
/// <exception cref="ArgumentNullException">If the u vector is <see langword="null" />.</exception>
/// <exception cref="ArgumentNullException">If the v vector is <see langword="null" />.</exception>
public static Matrix<double> OuterProduct(SparseVector u, SparseVector v)
{
if (u == null)
{
throw new ArgumentNullException("u");
}
if (v == null)
{
throw new ArgumentNullException("v");
}
var matrix = new SparseMatrix(u.Count, v.Count);
for (var i = 0; i < u._storage.ValueCount; i++)
{
for (var j = 0; j < v._storage.ValueCount; j++)
{
matrix.At(i, j, u._storage.Values[i] * v._storage.Values[j]);
}
}
return matrix;
}
/// <summary>
/// Create a matrix based on this vector in row form (one single row).
/// </summary>
/// <returns>This vector as a row matrix.</returns>
public override Matrix<double> ToRowMatrix()
{
var matrix = new SparseMatrix(1, Count);
for (var i = 0; i < NonZerosCount; i++)
{
matrix.At(0, _nonZeroIndices[i], _nonZeroValues[i]);
}
return matrix;
}
/// <summary>
/// Create a matrix based on this vector in column form (one single column).
/// </summary>
/// <returns>This vector as a column matrix.</returns>
public override Matrix<double> ToColumnMatrix()
{
var matrix = new SparseMatrix(Count, 1);
for (var i = 0; i < NonZerosCount; i++)
{
matrix.At(_nonZeroIndices[i], 0, _nonZeroValues[i]);
}
return matrix;
}
/// <summary>
/// Outer product of two vectors
/// </summary>
/// <param name="u">First vector</param>
/// <param name="v">Second vector</param>
/// <returns>Matrix M[i,j] = u[i]*v[j] </returns>
/// <exception cref="ArgumentNullException">If the u vector is <see langword="null" />.</exception>
/// <exception cref="ArgumentNullException">If the v vector is <see langword="null" />.</exception>
/*SparseMatrix*/
public static Matrix OuterProduct(SparseVector u, SparseVector v)
{
if (u == null)
{
throw new ArgumentNullException("u");
}
if (v == null)
{
throw new ArgumentNullException("v");
}
var matrix = new SparseMatrix(u.Count, v.Count);
for (var i = 0; i < u.NonZerosCount; i++)
{
for (var j = 0; j < v.NonZerosCount; j++)
{
if (u._nonZeroIndices[i] == v._nonZeroIndices[j])
{
matrix.At(i, j, u._nonZeroValues[i] * v._nonZeroValues[j]);
}
}
}
return matrix;
}
/// <summary>
/// Create a matrix based on this vector in row form (one single row).
/// </summary>
/// <returns>This vector as a row matrix.</returns>
public override Matrix<double> ToRowMatrix()
{
var indices = _storage.Indices;
var values = _storage.Values;
var matrix = new SparseMatrix(1, Count);
for (var i = 0; i < _storage.ValueCount; i++)
{
matrix.At(0, indices[i], values[i]);
}
return matrix;
}
/// <summary>
/// Create a matrix based on this vector in column form (one single column).
/// </summary>
/// <returns>This vector as a column matrix.</returns>
public override Matrix<double> ToColumnMatrix()
{
var indices = _storage.Indices;
var values = _storage.Values;
var matrix = new SparseMatrix(Count, 1);
for (var i = 0; i < _storage.ValueCount; i++)
{
matrix.At(indices[i], 0, values[i]);
}
return matrix;
}