/**
* <p>
* Performs a matrix inversion operation on the specified matrix and stores the results
* in the same matrix.<br>
* <br>
* a = 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>
*
* @param A The matrix that is to be inverted. Results are stored here. Modified.
* @return true if it could invert the matrix false if it could not.
*/
public static bool invert(ZMatrixRMaj A)
{
LinearSolverDense <ZMatrixRMaj> solver = LinearSolverFactory_ZDRM.lu(A.numRows);
if (solver.setA(A))
{
solver.invert(A);
}
else
{
return(false);
}
return(true);
}
/**
* <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_ZDRM} instead.
* </p>
*
* @param input The matrix that is to be inverted. Not modified.
* @param 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(ZMatrixRMaj input, ZMatrixRMaj output)
{
LinearSolverDense <ZMatrixRMaj> solver = LinearSolverFactory_ZDRM.lu(input.numRows);
if (solver.modifiesA())
{
input = input.copy();
}
if (!solver.setA(input))
{
return(false);
}
solver.invert(output);
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_ZDRM}
* instead.
* </p>
*
* <p>
* It is ok for 'b' and 'x' to be the same matrix.
* </p>
*
* @param a A matrix that is m by n. Not modified.
* @param b A matrix that is n by k. Not modified.
* @param x 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(ZMatrixRMaj a, ZMatrixRMaj b, ZMatrixRMaj x)
{
LinearSolverDense <ZMatrixRMaj> solver;
if (a.numCols == a.numRows)
{
solver = LinearSolverFactory_ZDRM.lu(a.numRows);
}
else
{
solver = LinearSolverFactory_ZDRM.qr(a.numRows, a.numCols);
}
// make sure the inputs 'a' and 'b' are not modified
solver = new LinearSolverSafe <ZMatrixRMaj>(solver);
if (!solver.setA(a))
{
return(false);
}
solver.solve(b, x);
return(true);
}