/**
* <p>
* Performs a matrix inversion operation that does not modify the original
* and stores the results in another matrix. The two matrices must have the
* same dimension.<br>
* <br>
* B = A<sup>-1</sup>
* </p>
*
* <p>
* If the algorithm could not invert the matrix then false is returned. If it returns true
* that just means the algorithm finished. The results could still be bad
* because the matrix is singular or nearly singular.
* </p>
*
* <p>
* For medium to large matrices there might be a slight performance boost to using
* {@link LinearSolverFactory_DSCC} instead.
* </p>
*
* @param A (Input) The matrix that is to be inverted. Not modified.
* @param inverse (Output) Where the inverse matrix is stored. Modified.
* @return true if it could invert the matrix false if it could not.
*/
public static bool invert(DMatrixSparseCSC A, DMatrixRMaj inverse)
{
if (A.numRows != A.numCols)
{
throw new ArgumentException("A must be a square matrix");
}
if (A.numRows != inverse.numRows || A.numCols != inverse.numCols)
{
throw new ArgumentException("A and inverse must have the same shape.");
}
LinearSolverSparse <DMatrixSparseCSC, DMatrixRMaj> solver;
solver = LinearSolverFactory_DSCC.lu(FillReducing.NONE);
// Ensure that the input isn't modified
if (solver.modifiesA())
{
A = (DMatrixSparseCSC)A.copy();
}
DMatrixRMaj I = CommonOps_DDRM.identity(A.numRows);
// decompose then solve the matrix
if (!solver.setA(A))
{
return(false);
}
solver.solve(I, inverse);
return(true);
}
/**
* <p>
* Solves for x in the following equation:<br>
* <br>
* A*x = b
* </p>
*
* <p>
* If the system could not be solved then false is returned. If it returns true
* that just means the algorithm finished operating, but the results could still be bad
* because 'A' is singular or nearly singular.
* </p>
*
* <p>
* If repeat calls to solve are being made then one should consider using {@link LinearSolverFactory_DSCC}
* instead.
* </p>
*
* <p>
* It is ok for 'b' and 'x' to be the same matrix.
* </p>
*
* @param a (Input) A matrix that is m by n. Not modified.
* @param b (Input) A matrix that is n by k. Not modified.
* @param x (Output) A matrix that is m by k. Modified.
*
* @return true if it could invert the matrix false if it could not.
*/
public static bool solve(DMatrixSparseCSC a,
DMatrixRMaj b,
DMatrixRMaj x)
{
LinearSolverSparse <DMatrixSparseCSC, DMatrixRMaj> solver;
if (a.numRows > a.numCols)
{
solver = LinearSolverFactory_DSCC.qr(FillReducing.NONE); // todo specify a filling that makes sense
}
else
{
solver = LinearSolverFactory_DSCC.lu(FillReducing.NONE);
}
// Ensure that the input isn't modified
if (solver.modifiesA())
{
a = (DMatrixSparseCSC)a.copy();
}
if (solver.modifiesB())
{
b = (DMatrixRMaj)b.copy();
}
// decompose then solve the matrix
if (!solver.setA(a))
{
return(false);
}
solver.solve(b, x);
return(true);
}