/// <summary>
/// Multiplies a tri-diagonal matrix by a real constant.
/// </summary>
/// <param name="f">The constant.</param>
/// <param name="T">The matrix.</param>
/// <returns>The product matrix.</returns>
public static TridiagonalMatrix operator *(double f, TridiagonalMatrix T)
{
if (T == null)
{
throw new ArgumentNullException(nameof(T));
}
int n = T.Dimension;
TridiagonalMatrix fT = new TridiagonalMatrix(n);
fT.SetDiagonalElement(0, f * T.GetDiagonalElement(0));
int i0 = 0;
int i1 = 1;
while (i1 < n)
{
fT.SetDiagonalElement(i1, f * T.GetDiagonalElement(i1));
fT.SetSubdiagonalElement(i0, f * T.GetSubdiagonalElement(i0));
fT.SetSuperdiagonalElement(i0, f * T.GetSuperdiagonalElement(i0));
i0 = i1;
i1++;
}
return(fT);
}
public TridiagonalMatrix CreateRandomTridiagonalMatrix(int n, Random rng)
{
TridiagonalMatrix T = new TridiagonalMatrix(n);
for (int i = 0; i < (n-1); i++) {
T[i, i] = 2.0 * rng.NextDouble() - 1.0;
T[i + 1, i] = 2.0 * rng.NextDouble() - 1.0;
T[i, i + 1] = 2.0 * rng.NextDouble() - 1.0;
}
T[n - 1, n - 1] = 2.0 * rng.NextDouble() - 1.0;
return (T);
}
/// <summary>
/// Creates a transpose of the matrix.
/// </summary>
/// <returns>The matrix transpose M<sup>T</sup>.</returns>
public TridiagonalMatrix Transpose()
{
TridiagonalMatrix T = new TridiagonalMatrix(dimension);
for (int i = 0; i < (dimension - 1); i++)
{
T.SetDiagonalElement(i, GetDiagonalElement(i));
T.SetSubdiagonalElement(i, GetSuperdiagonalElement(i));
T.SetSuperdiagonalElement(i, GetSubdiagonalElement(i));
}
T.SetDiagonalElement(dimension - 1, GetDiagonalElement(dimension - 1));
return(T);
}
/// <summary>
/// Copies the matrix.
/// </summary>
/// <returns>An independent copy of the matrix.</returns>
public TridiagonalMatrix Copy()
{
TridiagonalMatrix C = new TridiagonalMatrix(dimension);
for (int i = 0; i < (dimension - 1); i++)
{
C.SetDiagonalElement(i, GetDiagonalElement(i));
C.SetSubdiagonalElement(i, GetSubdiagonalElement(i));
C.SetSuperdiagonalElement(i, GetSuperdiagonalElement(i));
}
C.SetDiagonalElement(dimension - 1, GetDiagonalElement(dimension - 1));
return(C);
}
/// <summary>
/// Subtracts two tri-diagonal matrices.
/// </summary>
/// <param name="A">The first matrix.</param>
/// <param name="B">The second matrix.</param>
/// <returns>The difference matrix A - B.</returns>
public static TridiagonalMatrix operator -(TridiagonalMatrix A, TridiagonalMatrix B)
{
if (A == null)
{
throw new ArgumentNullException(nameof(A));
}
if (B == null)
{
throw new ArgumentNullException(nameof(B));
}
int n = A.Dimension;
if (B.Dimension != n)
{
throw new DimensionMismatchException();
}
TridiagonalMatrix T = new TridiagonalMatrix(n);
// add the elements
// this is a glorified for-next loop structured so as to minimize the
// integer arithmetic required to keep track of two numbers one unit apart
// and avoid if-tests inside the loop
T.SetDiagonalElement(0, A.GetDiagonalElement(0) - B.GetDiagonalElement(0));
int i0 = 0;
int i1 = 1;
while (i1 < n)
{
T.SetDiagonalElement(i1, A.GetDiagonalElement(i1) - B.GetDiagonalElement(i1));
T.SetSubdiagonalElement(i0, A.GetSubdiagonalElement(i0) - B.GetSubdiagonalElement(i0));
T.SetSuperdiagonalElement(i0, A.GetSuperdiagonalElement(i0) - B.GetSuperdiagonalElement(i0));
i0 = i1;
i1++;
}
return(T);
}
public void TridiagonalMatrixInvalidSetTest()
{
TridiagonalMatrix T = new TridiagonalMatrix(4);
T[0, 3] = 1.0;
}
/// <summary>
/// Creates a transpose of the matrix.
/// </summary>
/// <returns>The matrix transpose M<sup>T</sup>.</returns>
public TridiagonalMatrix Transpose()
{
TridiagonalMatrix T = new TridiagonalMatrix(dimension);
for (int i = 0; i < (dimension - 1); i++) {
T.SetDiagonalElement(i, GetDiagonalElement(i));
T.SetSubdiagonalElement(i, GetSuperdiagonalElement(i));
T.SetSuperdiagonalElement(i, GetSubdiagonalElement(i));
}
T.SetDiagonalElement(dimension - 1, GetDiagonalElement(dimension - 1));
return (T);
}
/// <summary>
/// Copies the matrix.
/// </summary>
/// <returns>An independent copy of the matrix.</returns>
public TridiagonalMatrix Copy()
{
TridiagonalMatrix C = new TridiagonalMatrix(dimension);
for (int i = 0; i < (dimension-1); i++) {
C.SetDiagonalElement(i, GetDiagonalElement(i));
C.SetSubdiagonalElement(i, GetSubdiagonalElement(i));
C.SetSuperdiagonalElement(i, GetSuperdiagonalElement(i));
}
C.SetDiagonalElement(dimension - 1, GetDiagonalElement(dimension - 1));
return (C);
}
/// <summary>
/// Subtracts two tridiagonal matrices.
/// </summary>
/// <param name="T1">The first matrix M<sub>1</sub>.</param>
/// <param name="T2">The first matrix M<sub>2</sub>.</param>
/// <returns>The difference M<sub>1</sub> - M<sub>2</sub>.</returns>
public static TridiagonalMatrix operator -(TridiagonalMatrix T1, TridiagonalMatrix T2)
{
if (T1 == null) throw new ArgumentNullException("T1");
if (T2 == null) throw new ArgumentNullException("T1");
int n = T1.Dimension;
if (T2.Dimension != n) throw new DimensionMismatchException();
TridiagonalMatrix T = new TridiagonalMatrix(n);
// add the elements
// this is a glorified for-next loop structured so as to minimize the
// integer arithmetic required to keep track of two numbers one unit apart
// and avoid if-tests inside the loop
T.SetDiagonalElement(0, T1.GetDiagonalElement(0) - T2.GetDiagonalElement(0));
int i0 = 0;
int i1 = 1;
while (i1 < n) {
T.SetDiagonalElement(i1, T1.GetDiagonalElement(i1) - T2.GetDiagonalElement(i1));
T.SetSubdiagonalElement(i0, T1.GetSubdiagonalElement(i0) - T2.GetSubdiagonalElement(i0));
T.SetSuperdiagonalElement(i0, T1.GetSuperdiagonalElement(i0) - T2.GetSuperdiagonalElement(i0));
i0 = i1;
i1++;
}
return (T);
}
/// <summary>
/// Multiplies a tridiagonal matrix by a real constant.
/// </summary>
/// <param name="f">The constant.</param>
/// <param name="T">The matrix.</param>
/// <returns>The product matrix.</returns>
public static TridiagonalMatrix operator *(double f, TridiagonalMatrix T)
{
if (T == null) throw new ArgumentNullException("T");
int n = T.Dimension;
TridiagonalMatrix fT = new TridiagonalMatrix(n);
fT.SetDiagonalElement(0, f * T.GetDiagonalElement(0));
int i0 = 0;
int i1 = 1;
while (i1 < n) {
fT.SetDiagonalElement(i1, f * T.GetDiagonalElement(i1));
fT.SetSubdiagonalElement(i0, f * T.GetSubdiagonalElement(i0));
fT.SetSuperdiagonalElement(i0, f * T.GetSuperdiagonalElement(i0));
i0 = i1;
i1++;
}
return (fT);
}