/// <summary>
/// Get a copy of the Toeplitz matrix.
/// </summary>
public ComplexDoubleMatrix GetMatrix()
{
int i, j;
// allocate memory for the matrix
ComplexDoubleMatrix tm = new ComplexDoubleMatrix(m_Order);
#if MANAGED
// fill top row
Complex[] top = tm.data[0];
Array.Copy(m_LeftColumn.data, 0, top, 0, m_Order);
if (m_Order > 1)
{
// fill bottom row (reverse order)
Complex[] bottom = tm.data[m_Order - 1];
for (i = 0, j = m_Order - 1; i < m_Order; i++, j--)
{
bottom[i] = m_LeftColumn[j];
}
// fill rows in-between
for (i = 1, j = m_Order - 1 ; j > 1; i++)
{
Array.Copy(top, 0, tm.data[i], i, j--);
Array.Copy(bottom, j, tm.data[i], 0, i);
}
}
#else
if (m_Order > 1)
{
Complex[] top = new Complex[m_Order];
Array.Copy(m_LeftColumn.data, 0, top, 0, m_Order);
tm.SetRow(0, top);
// fill bottom row (reverse order)
Complex[] bottom = new Complex[m_Order];
for (i = 0, j = m_Order - 1; i < m_Order; i++, j--)
{
bottom[i] = m_LeftColumn[j];
}
// fill rows in-between
for (i = 1, j = m_Order - 1 ; j > 0; i++)
{
Complex[] temp = new Complex[m_Order];
Array.Copy(top, 0, temp, i, j--);
Array.Copy(bottom, j, temp, 0, i);
tm.SetRow(i, temp);
}
}
else
{
Array.Copy(m_LeftColumn.data, 0, tm.data, 0, m_Order);
}
#endif
return tm;
}
/// <summary>
/// Solve a square Toeplitz system with a right-side matrix.
/// </summary>
/// <param name="col">The left-most column of the Toeplitz matrix.</param>
/// <param name="row">The top-most row of the Toeplitz matrix.</param>
/// <param name="Y">The right-side matrix of the system.</param>
/// <returns>The solution matrix.</returns>
/// <exception cref="ArgumentNullException">
/// <EM>col</EM> is a null reference,
/// <para>or</para>
/// <para><EM>row</EM> is a null reference,</para>
/// <para>or</para>
/// <para><EM>Y</EM> is a null reference.</para>
/// </exception>
/// <exception cref="RankException">
/// The length of <EM>col</EM> is 0,
/// <para>or</para>
/// <para>the lengths of <EM>col</EM> and <EM>row</EM> are not equal,</para>
/// <para>or</para>
/// <para>the number of rows in <EM>Y</EM> does not the length of <EM>col</EM> and <EM>row</EM>.</para>
/// </exception>
/// <exception cref="SingularMatrixException">
/// The Toeplitz matrix or one of the the leading sub-matrices is singular.
/// </exception>
/// <exception cref="ArithmeticException">
/// The values of the first element of <EM>col</EM> and <EM>row</EM> are not equal.
/// </exception>
/// <remarks>
/// This method solves the linear system <B>AX</B> = <B>Y</B>. Where
/// <B>T</B> is a square Toeplitz matrix, <B>X</B> is an unknown
/// matrix and <B>Y</B> is a known matrix.
/// <para>
/// The classic Levinson algorithm is used to solve the system. The algorithm
/// assumes that all the leading sub-matrices of the Toeplitz matrix are
/// non-singular. When a sub-matrix is near singular, accuracy will
/// be degraded. This member requires approximately <B>N</B> squared
/// FLOPS to calculate a solution, where <B>N</B> is the matrix order.
/// </para>
/// <para>
/// This static method has minimal storage requirements as it combines
/// the <b>UDL</b> decomposition with the calculation of the solution vector
/// in a single algorithm.
/// </para>
/// </remarks>
public static ComplexDoubleMatrix Solve(IROComplexDoubleVector col, IROComplexDoubleVector row, IROComplexDoubleMatrix Y)
{
// check parameters
if (col == null)
{
throw new System.ArgumentNullException("col");
}
else if (col.Length == 0)
{
throw new RankException("The length of col is zero.");
}
else if (row == null)
{
throw new System.ArgumentNullException("row");
}
else if (col.Length != row.Length)
{
throw new RankException("The lengths of col and row are not equal.");
}
else if (col[0] != row[0])
{
throw new ArithmeticException("The values of the first element of col and row are not equal.");
}
else if (Y == null)
{
throw new System.ArgumentNullException("Y");
}
else if (col.Length != Y.Columns)
{
throw new RankException("The numer of rows in Y does not match the length of col and row.");
}
// check if leading diagonal is zero
if (col[0] == Complex.Zero)
{
throw new SingularMatrixException("One of the leading sub-matrices is singular.");
}
// decompose matrix
int order = col.Length;
Complex[] A = new Complex[order];
Complex[] B = new Complex[order];
Complex[] Z = new Complex[order];
ComplexDoubleMatrix X = new ComplexDoubleMatrix(order);
Complex Q, S, Ke, Kr, e;
Complex Inner;
int i, j, l;
// setup the zero order solution
A[0] = Complex.One;
B[0] = Complex.One;
e = Complex.One / col[0];
X.SetRow(0, e * ComplexDoubleVector.GetRow(Y, 0));
for (i = 1; i < order; i++)
{
// calculate inner products
Q = Complex.Zero;
for (j = 0, l = 1; j < i; j++, l++)
{
Q += col[l] * A[j];
}
S = Complex.Zero;
for (j = 0, l = 1; j < i; j++, l++)
{
S += row[l] * B[j];
}
// reflection coefficients
Kr = -S * e;
Ke = -Q * e;
// update lower triangle (in temporary storage)
Z[0] = Complex.Zero;
Array.Copy(A, 0, Z, 1, i);
for (j = 0, l = i - 1; j < i; j++, l--)
{
Z[j] += Ke * B[l];
}
// update upper triangle
for (j = i; j > 0; j--)
{
B[j] = B[j - 1];
}
B[0] = Complex.Zero;
for (j = 0, l = i - 1; j < i; j++, l--)
{
B[j] += Kr * A[l];
}
// copy from temporary storage to lower triangle
Array.Copy(Z, 0, A, 0, i + 1);
// check for singular sub-matrix)
if (Ke * Kr == Complex.One)
{
throw new SingularMatrixException("One of the leading sub-matrices is singular.");
}
// update diagonal
e = e / (Complex.One - Ke * Kr);
for (l = 0; l < Y.Rows; l++)
{
ComplexDoubleVector W = X.GetColumn(l);
ComplexDoubleVector M = ComplexDoubleVector.GetColumn(Y, l);
Inner = M[i];
for (j = 0; j < i; j++)
{
Inner += A[j] * M[j];
}
Inner *= e;
W[i] = Inner;
for (j = 0; j < i; j++)
{
W[j] += Inner * B[j];
}
X.SetColumn(l, W);
}
}
return(X);
}
/// <summary>
/// Solve a square Toeplitz system with a right-side matrix.
/// </summary>
/// <param name="col">The left-most column of the Toeplitz matrix.</param>
/// <param name="row">The top-most row of the Toeplitz matrix.</param>
/// <param name="Y">The right-side matrix of the system.</param>
/// <returns>The solution matrix.</returns>
/// <exception cref="ArgumentNullException">
/// <EM>col</EM> is a null reference,
/// <para>or</para>
/// <para><EM>row</EM> is a null reference,</para>
/// <para>or</para>
/// <para><EM>Y</EM> is a null reference.</para>
/// </exception>
/// <exception cref="RankException">
/// The length of <EM>col</EM> is 0,
/// <para>or</para>
/// <para>the lengths of <EM>col</EM> and <EM>row</EM> are not equal,</para>
/// <para>or</para>
/// <para>the number of rows in <EM>Y</EM> does not the length of <EM>col</EM> and <EM>row</EM>.</para>
/// </exception>
/// <exception cref="SingularMatrixException">
/// The Toeplitz matrix or one of the the leading sub-matrices is singular.
/// </exception>
/// <exception cref="ArithmeticException">
/// The values of the first element of <EM>col</EM> and <EM>row</EM> are not equal.
/// </exception>
/// <remarks>
/// This method solves the linear system <B>AX</B> = <B>Y</B>. Where
/// <B>T</B> is a square Toeplitz matrix, <B>X</B> is an unknown
/// matrix and <B>Y</B> is a known matrix.
/// <para>
/// The classic Levinson algorithm is used to solve the system. The algorithm
/// assumes that all the leading sub-matrices of the Toeplitz matrix are
/// non-singular. When a sub-matrix is near singular, accuracy will
/// be degraded. This member requires approximately <B>N</B> squared
/// FLOPS to calculate a solution, where <B>N</B> is the matrix order.
/// </para>
/// <para>
/// This static method has minimal storage requirements as it combines
/// the <b>UDL</b> decomposition with the calculation of the solution vector
/// in a single algorithm.
/// </para>
/// </remarks>
public static ComplexDoubleMatrix Solve(IROComplexDoubleVector col, IROComplexDoubleVector row, IROComplexDoubleMatrix Y)
{
// check parameters
if (col == null)
{
throw new System.ArgumentNullException("col");
}
else if (col.Length == 0)
{
throw new RankException("The length of col is zero.");
}
else if (row == null)
{
throw new System.ArgumentNullException("row");
}
else if (col.Length != row.Length)
{
throw new RankException("The lengths of col and row are not equal.");
}
else if (col[0] != row[0])
{
throw new ArithmeticException("The values of the first element of col and row are not equal.");
}
else if (Y == null)
{
throw new System.ArgumentNullException("Y");
}
else if (col.Length != Y.Columns)
{
throw new RankException("The numer of rows in Y does not match the length of col and row.");
}
// check if leading diagonal is zero
if (col[0] == Complex.Zero)
{
throw new SingularMatrixException("One of the leading sub-matrices is singular.");
}
// decompose matrix
int order = col.Length;
Complex[] A = new Complex[order];
Complex[] B = new Complex[order];
Complex[] Z = new Complex[order];
ComplexDoubleMatrix X = new ComplexDoubleMatrix(order);
Complex Q, S, Ke, Kr, e;
Complex Inner;
int i, j, l;
// setup the zero order solution
A[0] = Complex.One;
B[0] = Complex.One;
e = Complex.One / col[0];
X.SetRow(0, e * ComplexDoubleVector.GetRow(Y, 0));
for (i = 1; i < order; i++)
{
// calculate inner products
Q = Complex.Zero;
for (j = 0, l = 1; j < i; j++, l++)
{
Q += col[l] * A[j];
}
S = Complex.Zero;
for (j = 0, l = 1; j < i; j++, l++)
{
S += row[l] * B[j];
}
// reflection coefficients
Kr = -S * e;
Ke = -Q * e;
// update lower triangle (in temporary storage)
Z[0] = Complex.Zero;
Array.Copy(A, 0, Z, 1, i);
for (j = 0, l = i - 1; j < i; j++, l--)
{
Z[j] += Ke * B[l];
}
// update upper triangle
for (j = i; j > 0; j--)
{
B[j] = B[j - 1];
}
B[0] = Complex.Zero;
for (j = 0, l = i - 1; j < i; j++, l--)
{
B[j] += Kr * A[l];
}
// copy from temporary storage to lower triangle
Array.Copy(Z, 0, A, 0, i + 1);
// check for singular sub-matrix)
if (Ke * Kr == Complex.One)
{
throw new SingularMatrixException("One of the leading sub-matrices is singular.");
}
// update diagonal
e = e / (Complex.One - Ke * Kr);
for (l = 0; l < Y.Rows; l++)
{
ComplexDoubleVector W = X.GetColumn(l);
ComplexDoubleVector M = ComplexDoubleVector.GetColumn(Y, l);
Inner = M[i];
for (j = 0; j < i; j++)
{
Inner += A[j] * M[j];
}
Inner *= e;
W[i] = Inner;
for (j = 0; j < i; j++)
{
W[j] += Inner * B[j];
}
X.SetColumn(l, W);
}
}
return X;
}
public void SetRowArrayWrongRank()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(2, 2);
Complex[] b = new Complex[3];
a.SetRow(1, b);
}
/// <summary>
/// Get a copy of the Toeplitz matrix.
/// </summary>
public ComplexDoubleMatrix GetMatrix()
{
int i, j;
// allocate memory for the matrix
ComplexDoubleMatrix tm = new ComplexDoubleMatrix(m_Order);
#if MANAGED
// fill top row
Complex[] top = tm.data[0];
Array.Copy(m_LeftColumn.data, 0, top, 0, m_Order);
if (m_Order > 1)
{
// fill bottom row (reverse order)
Complex[] bottom = tm.data[m_Order - 1];
for (i = 0, j = m_Order - 1; i < m_Order; i++, j--)
{
bottom[i] = m_LeftColumn[j];
}
// fill rows in-between
for (i = 1, j = m_Order - 1; j > 1; i++)
{
Array.Copy(top, 0, tm.data[i], i, j--);
Array.Copy(bottom, j, tm.data[i], 0, i);
}
}
#else
if (m_Order > 1)
{
Complex[] top = new Complex[m_Order];
Array.Copy(m_LeftColumn.data, 0, top, 0, m_Order);
tm.SetRow(0, top);
// fill bottom row (reverse order)
Complex[] bottom = new Complex[m_Order];
for (i = 0, j = m_Order - 1; i < m_Order; i++, j--)
{
bottom[i] = m_LeftColumn[j];
}
// fill rows in-between
for (i = 1, j = m_Order - 1; j > 0; i++)
{
Complex[] temp = new Complex[m_Order];
Array.Copy(top, 0, temp, i, j--);
Array.Copy(bottom, j, temp, 0, i);
tm.SetRow(i, temp);
}
}
else
{
Array.Copy(m_LeftColumn.data, 0, tm.data, 0, m_Order);
}
#endif
return(tm);
}
public void SetRowArrayOutOfRange()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(2, 2);
Complex[] b = new Complex[2];
a.SetRow(2, b);
}
public void SetRowArray()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(2, 2);
Complex[] b = new Complex[2];
b[0] = new Complex(1, 1);
b[1] = new Complex(2, 2);
a.SetRow(0, b);
Assert.AreEqual(b[0], a[0, 0]);
Assert.AreEqual(b[1], a[0, 1]);
}
public void SetRowWrongRank()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(2, 2);
ComplexDoubleVector b = new ComplexDoubleVector(3);
a.SetRow(1, b);
}
public void SetRowOutOfRange()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(2, 2);
ComplexDoubleVector b = new ComplexDoubleVector(2);
a.SetRow(2, b);
}
public void SetRow()
{
ComplexDoubleMatrix a = new ComplexDoubleMatrix(2, 2);
ComplexDoubleVector b = new ComplexDoubleVector(2);
b[0] = new Complex(1, 1);
b[1] = new Complex(2, 2);
a.SetRow(0, b);
Assert.AreEqual(b[0], a[0, 0]);
Assert.AreEqual(b[1], a[0, 1]);
}