public void NullParameterTestforSolveMatrix()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
ComplexDoubleMatrix X = cdsl.Solve(null as ComplexDoubleMatrix);
}
public void MismatchRowsTestforSolveMatrix()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T4);
ComplexDoubleMatrix X = cdsl.Solve(I5);
}
public void MismatchRowsTestforSolveVector()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T4);
ComplexDoubleVector X = cdsl.Solve(X5);
}
public void SolveVector5()
{
int i;
double e, me;
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
ComplexDoubleVector X = cdsl.Solve(Y5);
// determine the maximum error
me = 0.0;
for (i = 0; i < cdsl.Order; i++)
{
e = ComplexMath.Absolute((X5[i] - X[i]) / X5[i]);
if (e > me)
{
me = e;
}
}
Assert.IsTrue(me < Tolerance5, "Maximum Error = " + me.ToString());
}
public void GetDeterminantMethodTest5()
{
// calculate determinant from diagonal
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
// check results match
double e = ComplexMath.Absolute((cdsl.GetDeterminant() - Det5) / Det5);
Assert.IsTrue(e < Tolerance5);
}
public void NullParameterTestforSolveVector()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
ComplexDoubleVector X = cdsl.Solve(null as ComplexDoubleVector);
}
public void SingularityPropertyTest5()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
Assert.IsFalse(cdsl.IsSingular);
}
public void NullParameterTestforConstructor()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(null as ComplexDoubleVector);
}
public void OrderPropertyTest()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
Assert.IsTrue(cdsl.Order == 5);
}
public void DecompositionTest5()
{
int i, j;
double e, me;
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
ComplexDoubleMatrix U = cdsl.U;
ComplexDoubleMatrix D = cdsl.D;
ComplexDoubleMatrix L = cdsl.L;
// check U is the transpose of L
Assert.IsTrue(U.Equals(L.GetTranspose()));
// check the lower triangle
me = 0.0;
for (i = 0; i < cdsl.Order; i++)
{
for (j = 0; j <= i; j++)
{
e = ComplexMath.Absolute((L5[i, j] - L[i, j]) / L5[i, j]);
if (e > me)
{
me = e;
}
}
}
Assert.IsTrue(me < Tolerance5, "Maximum Error = " + me.ToString());
// check the diagonal
me = 0.0;
for (i = 0; i < cdsl.Order; i++)
{
e = ComplexMath.Absolute((D5[i] - D[i, i]) / D5[i]);
if (e > me)
{
me = e;
}
}
Assert.IsTrue(me < Tolerance5, "Maximum Error = " + me.ToString());
}
public void GetMatrixMemberTest()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
ComplexDoubleMatrix cdsldm = cdsl.GetMatrix();
for (int row = 0; row < T5.Length; row++)
{
for (int column = 0; column < T5.Length; column++)
{
if (column < row)
{
Assert.IsTrue(cdsldm[row, column] == T5[row - column]);
}
else
{
Assert.IsTrue(cdsldm[row, column] == T5[column - row]);
}
}
}
}
public void GetVectorMemberTest()
{
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
ComplexDoubleVector TT = cdsl.GetVector();
Assert.IsTrue(T5.Equals(TT));
}
public void ZeroLengthVectorTestsforConstructor1()
{
ComplexDoubleVector cdv = new ComplexDoubleVector(1, 0.0);
cdv.RemoveAt(0);
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(cdv);
}
public void SolveMatrix1()
{
int i, j;
double e, me;
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T1);
// check inverse
ComplexDoubleMatrix I = cdsl.Solve(ComplexDoubleMatrix.CreateIdentity(1));
me = 0.0;
for (i = 0; i < cdsl.Order; i++)
{
for (j = 0; j < cdsl.Order; j++)
{
e = ComplexMath.Absolute((I1[i, j] - I[i, j]) / I1[i, j]);
if (e > me)
{
me = e;
}
}
}
Assert.IsTrue(me < Tolerance1, "Maximum Error = " + me.ToString());
}
public void SingularityPropertyTest()
{
ComplexDoubleVector T = new ComplexDoubleVector(10);
for (int i = 1; i < 10; i++)
{
T[i] = new Complex((double)(i + 1), (double)(i + 1));
}
T[0] = new Complex(2.0, 2.0);
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T);
Assert.IsTrue(cdsl.IsSingular);
}
/// <summary>
/// Invert a symmetric square Toeplitz matrix.
/// </summary>
/// <param name="T">The left-most column of the symmetric Toeplitz matrix.</param>
/// <returns>The inverse matrix.</returns>
/// <exception cref="ArgumentNullException">
/// <B>T</B> is a null reference.
/// </exception>
/// <exception cref="RankException">
/// The length of <B>T</B> must be greater than zero.
/// </exception>
/// <exception cref="SingularMatrixException">
/// The Toeplitz matrix or one of the the leading sub-matrices is singular.
/// </exception>
/// <remarks>
/// This static member combines the <b>UDL</b> decomposition and Trench's algorithm into a
/// single algorithm. When compared to the non-static member it requires minimal data storage
/// and suffers from no speed penalty.
/// <para>
/// Trench's algorithm requires <b>N</b> squared FLOPS, compared to <b>N</b> cubed FLOPS
/// if we simply solved a linear Toeplitz system with a right-side identity matrix (<b>N</b> is the matrix order).
/// </para>
/// </remarks>
public static ComplexDoubleMatrix Inverse(IROComplexDoubleVector T)
{
ComplexDoubleMatrix X;
// check parameters
if (T == null)
{
throw new System.ArgumentNullException("T");
}
else if (T.Length < 1)
{
throw new System.RankException("The length of T must be greater than zero.");
}
else if (T.Length == 1)
{
X = new ComplexDoubleMatrix(1);
X[0, 0] = Complex.One / T[0];
}
else
{
int N = T.Length;
Complex f, g;
int i, j, l, k, m, n;
X = new ComplexDoubleMatrix(N);
// calculate the predictor coefficients
ComplexDoubleVector Y = ComplexDoubleSymmetricLevinson.YuleWalker(T);
// calculate gamma
f = T[0];
for (i = 1, j = 0; i < N; i++, j++)
{
f += T[i] * Y[j];
}
g = Complex.One / f;
// calculate first row of inverse
X[0, 0] = g;
for (i = 1, j = 0; i < N; i++, j++)
{
X[0, i] = g * Y[j];
}
// calculate successive rows of upper wedge
for (i = 0, j = 1, k = N - 2; i < N / 2; i++, j++, k--)
{
for (l = j, m = i, n = N - 1 - j; l < N - j; l++, m++, n--)
{
X[j, l] = X[i, m] + g * (Y[i] * Y[m] - Y[k] * Y[n]);
}
}
// this is symmetric matrix ...
for (i = 0; i <= N / 2; i++)
{
for (j = i + 1; j < N - i; j++)
{
X[j, i] = X[i, j];
}
}
// and a persymmetric matrix.
for (i = 0, j = N - 1; i < N; i++, j--)
{
for (k = 0, l = N - 1; k < j; k++, l--)
{
X[l, j] = X[i, k];
}
}
}
return(X);
}
public void GetInverse5()
{
int i, j;
double e, me;
ComplexDoubleSymmetricLevinson cdsl = new ComplexDoubleSymmetricLevinson(T5);
// check inverse
ComplexDoubleMatrix I = cdsl.GetInverse();
me = 0.0;
for (i = 0; i < cdsl.Order; i++)
{
for (j = 0; j < cdsl.Order; j++)
{
e = ComplexMath.Absolute((I5[i, j] - I[i, j]) / I5[i, j]);
if (e > me)
{
me = e;
}
}
}
Assert.IsTrue(me < Tolerance5, "Maximum Error = " + me.ToString());
}