public void PolynomialSet2zeroTest()
{
Polynomial P1 = new Polynomial(3, new double[] { 1, 1, 2, 1 });
Assert.IsFalse(P1.isZero());
Assert.IsFalse(P1.isZero(1));
Assert.IsTrue(P1.isZero(2));
P1.set2Zero();
Assert.IsTrue(P1.isZero());
P1 = new Polynomial(3, new double[] { 1, 1, 2, 1 });
P1.set2Zero(2);
Assert.IsTrue(P1.isZero(1));
}
/// <summary>
/// Solves the equation<para/>
/// <para/>
/// X U = B<para/>
/// <para/>
/// by back-substitution, where:<para/>
/// <para/>
/// U : m-by-m upper triangular matrix, non-singular<para/>
/// X : m-by-n matrix<para/>
/// B : m-by-n matrix, overwritten with the solution on output.<para/>
/// <para/>
/// The X_ik are calculated making few modifications to the function 'utsolve' for UX=B.<para/>
/// </summary>
/// <param name="B">an object of type Matrix that is the independent term on input</param>
public void utxsolve(Matrix B)
{
Polynomial sum = new Polynomial(_dimT);
for( int k = 0; k < B._rows; k++ )
{
B._data[k, 0] /= _data[0, 0];
for( int i = 1; i < B._cols; i++ )
{
sum.set2Zero();
for( int j = 0; j < i; j++ )
{
sum += _data[j, i] * B._data[k, j];
}
B._data[k, i] = (B._data[k, i] - sum) / _data[i, i];
}
}
}
/// <summary>
/// Solves the equation<para/>
/// <para/>
/// U X = B<para/>
/// <para/>
/// by back-substitution, where:<para/>
/// <para/>
/// U : m-by-m upper triangular matrix, non-singular<para/>
/// X : m-by-n matrix<para/>
/// B : m-by-n matrix, overwritten with the solution on output.<para/>
///<para/>
/// The X_ik are calculated making few modifications to the algorithm 3.1.2, p.89 from <para/>
/// Golub & Van Loan's book:<para/>
/// <para/>
/// x_ik = ( b_ik - sum_{j=i+1}^{m} u_ij * x_jk ) / u_ii for k=1,...,n<para/>
/// <para/>
/// </summary>
/// <param name="B">an object of type Matrix that is the independent</param>
/// <param name="X">an object of type Matrix that is the independent</param>
/// <param name="piv"></param>
public void utsolve(Matrix B, Matrix X, int[] piv)
{
Polynomial sum = new Polynomial(_dimT);
for( int k = 0; k < B._cols; k++ )
{
X[_rows - 1, k] = B[piv[_rows - 1], k] / _data[piv[_rows - 1], _rows - 1];
for( int i = _rows - 2; i > -1; i--)
{
sum.set2Zero();
for( int j = i + 1; j < _rows; j++ )
{
sum += _data[piv[i], j] * X[j, k];
}
X[i, k] = (B[piv[i], k] - sum) / _data[piv[i], i];
}
}
}
/// <summary>
/// Solves the equation<para/>
/// <para/>
/// U x = b<para/>
/// <para/>
/// by back-substitution, where:<para/>
/// <para/>
/// U : n-by-n upper triangular matrix, non-singular<para/>
/// x : n vector<para/>
/// B : n vector, overwritten with the solution on output.<para/>
/// <para/>
/// The x_i are calculated following the algorithm 3.1.2, p.89 from Golub & Van Loan's book:<para/>
/// <para/>
/// x_i = ( b_i - sum_{j=i+1}^{n} u_ij * x_j ) / u_ii<para/>
/// </summary>
/// <param name="b">an object of type Matrix that is the independent term on input</param>
public void utsolve(Polynomial[] b)
{
Polynomial sum = new Polynomial(_dimT);
b[_rows - 1] /= _data[_rows - 1,_rows - 1];
for( int i = _rows - 2; i > -1; i-- )
{
sum.set2Zero();
for( int j = i + 1; j < _rows; j++ )
{
sum += _data[i,j] * b[j];
}
b[i] = (b[i] - sum) / _data[i,i];
}
}
/// <summary>
/// Solves the equation<para/>
/// <para/>
/// U X = B<para/>
/// <para/>
/// by back-substitution, where:<para/>
/// <para/>
/// U : m-by-m upper triangular matrix, non-singular<para/>
/// X : m-by-n matrix<para/>
/// B : m-by-n matrix, overwritten with the solution on output.<para/>
/// <para/>
/// The X_ik are calculated making few modifications to the algorithm 3.1.2, p.89 from <para/>
/// Golub & Van Loan's book:<para/>
/// <para/>
/// x_ik = ( b_ik - sum_{j=i+1}^{m} u_ij * x_jk ) / u_ii for k=1,...,n<para/>
/// <para/>
/// </summary>
/// <param name="B">an object of type Matrix that is the independent </param>
public void utsolve(Matrix B)
{
if (!isSquare())
{
throw new MathException("U (=this) must be u squra matrix.");
}
if (B._rows != _rows)
{
throw new MathException(String.Format("The numebr rows in B ({0:d}) must match the number of rows in U (=this) ({1:d}).", B._rows, _rows));
}
Polynomial sum = new Polynomial(_dimT);
Polynomial temp;
for( int k = 0; k < B._cols; k++ )
{
temp = B[_rows - 1, k];
B[_rows - 1, k] /= _data[_rows - 1,_rows - 1];
temp = B[_rows - 1, k];
for( int i = _rows - 2; i > -1; i-- )
{
sum.set2Zero();
for( int j = i + 1; j < _rows; j++ )
{
sum += _data[i,j] * B._data[j,k];
}
B._data[i,k] = (B._data[i,k] - sum) / _data[i,i];
}
}
}
