/// <summary>
/// Create an n x n Toeplitz matrix based on the specified first row and column.
/// </summary>
/// <param name="firstRow"></param>
/// <param name="firstColumn"></param>
/// <returns></returns>
public static Matrix Toeplitz(Vector firstRow, Vector firstColumn)
{
if (firstRow.Size != firstColumn.Size) {
throw new IncompatibleMatrixDimensionsException(firstRow, firstColumn);
}
if (firstRow[0] != firstColumn[0]) {
throw new MatrixException("The first indices of the specified vectors don't match!");
}
Matrix newMat = new Matrix(firstRow.Size);
for (int i = 0; i < firstRow.Size; i++) {
newMat[firstRow.Size - i - 1, Vector.Arrange(firstRow.Size - i - 1, firstRow.Size)] = firstRow.SubMatrix(0, i + 1, 0, 1).ToColumnVector();
}
for (int i = 1; i < firstColumn.Size; i++) {
newMat[i, Vector.Arrange(i)] = firstColumn.SubMatrix(1, i + 1, 0, 1).ToColumnVector();
}
return newMat;
}