public override /**/ double quality()
{
return(SpecializedOps_DDRM.qualityTriangular(QR));
}
/**
* Solves for X using the QR decomposition.
*
* @param B A matrix that is n by m. Not modified.
* @param X An n by m matrix where the solution is writen to. Modified.
*/
public override void solve(DMatrixRMaj B, DMatrixRMaj X)
{
if (X.numRows != numCols)
{
throw new ArgumentException("Unexpected dimensions for X");
}
else if (B.numRows != numRows || B.numCols != X.numCols)
{
throw new ArgumentException("Unexpected dimensions for B");
}
int BnumCols = B.numCols;
// solve each column one by one
for (int colB = 0; colB < BnumCols; colB++)
{
// make a copy of this column in the vector
for (int i = 0; i < numRows; i++)
{
a[i] = B.data[i * BnumCols + colB];
}
// Solve Qa=b
// a = Q'b
// a = Q_{n-1}...Q_2*Q_1*b
//
// Q_n*b = (I-gamma*u*u^T)*b = b - u*(gamma*U^T*b)
for (int n = 0; n < numCols; n++)
{
u[n] = 1;
double ub = a[n];
// U^T*b
for (int i = n + 1; i < numRows; i++)
{
ub += (u[i] = QR.unsafe_get(i, n)) * a[i];
}
// gamma*U^T*b
ub *= gammas[n];
for (int i = n; i < numRows; i++)
{
a[i] -= u[i] * ub;
}
}
// solve for Rx = b using the standard upper triangular solver
TriangularSolver_DDRM.solveU(QR.data, a, numCols);
// save the results
for (int i = 0; i < numCols; i++)
{
X.data[i * X.numCols + colB] = a[i];
}
}
}
/**
* <p>
* Checks to see if a matrix is lower triangular or Hessenberg. A Hessenberg matrix of degree N
* has the following property:<br>
* <br>
* a<sub>ij</sub> ≤ 0 for all i < j+N<br>
* <br>
* A triangular matrix is a Hessenberg matrix of degree 0.
* </p>
*
* @param A Matrix being tested. Not modified.
* @param hessenberg The degree of being hessenberg.
* @param tol How close to zero the lower left elements need to be.
* @return If it is an upper triangular/hessenberg matrix or not.
*/
public static bool isLowerTriangle(DMatrixRMaj A, int hessenberg, double tol)
{
for (int i = 0; i < A.numRows - hessenberg - 1; i++)
{
for (int j = i + hessenberg + 1; j < A.numCols; j++)
{
if (!(Math.Abs(A.unsafe_get(i, j)) <= tol))
{
return(false);
}
}
}
return(true);
}
/**
* <p>
* Checks to see if a matrix is upper triangular or Hessenberg. A Hessenberg matrix of degree N
* has the following property:<br>
* <br>
* a<sub>ij</sub> ≤ 0 for all i < j+N<br>
* <br>
* A triangular matrix is a Hessenberg matrix of degree 0.
* </p>
*
* @param A Matrix being tested. Not modified.
* @param hessenberg The degree of being hessenberg.
* @param tol How close to zero the lower left elements need to be.
* @return If it is an upper triangular/hessenberg matrix or not.
*/
public static bool isUpperTriangle(DMatrixRMaj A, int hessenberg, double tol)
{
for (int i = hessenberg + 1; i < A.numRows; i++)
{
int maxCol = Math.Min(i - hessenberg, A.numCols);
for (int j = 0; j < maxCol; j++)
{
if (!(Math.Abs(A.unsafe_get(i, j)) <= tol))
{
return(false);
}
}
}
return(true);
}
/**
* Returns the R matrix.
*/
public DMatrixRMaj getR()
{
DMatrixRMaj R = new DMatrixRMaj(QR.numRows, QR.numCols);
int N = Math.Min(QR.numCols, QR.numRows);
for (int i = 0; i < N; i++)
{
for (int j = i; j < QR.numCols; j++)
{
R.unsafe_set(i, j, QR.unsafe_get(i, j));
}
}
return(R);
}