Class BaseLinearSolverQrp_DDRM
 All Implemented Interfaces:
LinearSolver<DMatrixRMaj,
,DMatrixRMaj> LinearSolverDense<DMatrixRMaj>
 Direct Known Subclasses:
LinearSolverQrpHouseCol_DDRM
,SolvePseudoInverseQrp_DDRM
Base class for QR pivot based pseudo inverse classes. It will return either the basic of minimal 2norm solution. See [1] for details. The minimal 2norm solution refers to the solution 'x' whose 2norm is the smallest making it unique, not some other error function.
R = [ R12 R12 ] r P^T*x = [ y ] r Q^T*b = [ c ] r [ 0 0 ] mr [ z ] n r [ d ] mr r nr where r is the rank of the matrix and (m,n) is the dimension of the linear system.
The solution 'x' is found by solving the system below. The basic solution is found by setting z=0 [ R_11^1*(c  R12*z) ] x = [ z ]
NOTE: The matrix rank is determined using the provided QR decomposition. [1] mentions that this will not always work and could cause some problems.
[1] See page 258259 in Gene H. Golub and Charles F. Van Loan "Matrix Computations" 3rd Ed, 1996

Field Summary
Modifier and TypeFieldDescriptionprotected DMatrixRMaj
protected LinearSolverDense<DMatrixRMaj>
protected boolean
protected DMatrixRMaj
protected DMatrixRMaj
protected int
protected DMatrixRMaj
Fields inherited from class org.ejml.dense.row.linsol.LinearSolverAbstract_DDRM
A, numCols, numRows

Constructor Summary
ModifierConstructorDescriptionprotected
BaseLinearSolverQrp_DDRM
(QRPDecomposition_F64<DMatrixRMaj> decomposition, boolean norm2Solution) Configures internal parameters. 
Method Summary
Modifier and TypeMethodDescriptionIf a decomposition class was used internally then this will return that class.void
invert
(DMatrixRMaj A_inv) Computes the inverse of of the 'A' matrix passed intoLinearSolver.setA(Matrix)
and writes the results to the provided matrix.double
quality()
Returns a very quick to compute measure of how singular the system is.boolean
setA
(DMatrixRMaj A) Specifies the A matrix in the linear equation.protected void
Upgrades the basic solution to the optimal 2norm solution.Methods inherited from class org.ejml.dense.row.linsol.LinearSolverAbstract_DDRM
_setA, getA
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface org.ejml.interfaces.linsol.LinearSolver
modifiesA, modifiesB, solve

Field Details

norm2Solution
protected boolean norm2Solution 
Y

R

R11

I

rank
protected int rank 
internalSolver


Constructor Details

BaseLinearSolverQrp_DDRM
protected BaseLinearSolverQrp_DDRM(QRPDecomposition_F64<DMatrixRMaj> decomposition, boolean norm2Solution) Configures internal parameters. Parameters:
decomposition
 Used to solve the linear system.norm2Solution
 If true then the optimal 2norm solution will be computed for degenerate systems.


Method Details

setA
Description copied from interface:LinearSolver
Specifies the A matrix in the linear equation. A reference might be saved and it might also be modified depending on the implementation. If it is modified then
LinearSolver.modifiesA()
will return true.If this value returns true that does not guarantee a valid solution was generated. This is because some decompositions don't detect singular matrices.
 Parameters:
A
 The 'A' matrix in the linear equation. Might be modified or save the reference. Returns:
 true if it can be processed.

quality
public double quality()Description copied from interface:LinearSolver
Returns a very quick to compute measure of how singular the system is. This measure will be invariant to the scale of the matrix and always be positive, with larger values indicating it is less singular. If not supported by the solver then the runtime exception IllegalArgumentException is thrown. This is NOT the matrix's condition.
How this function is implemented is not specified. One possible implementation is the following: In many decompositions a triangular matrix is extracted. The determinant of a triangular matrix is easily computed and once normalized to be scale invariant and its absolute value taken it will provide functionality described above.
 Returns:
 The quality of the linear system.

upgradeSolution
Upgrades the basic solution to the optimal 2norm solution.
First solves for 'z'  x_b  P*[ R_11^1 * R_12 ] * z 2 min z  [  I_{nr} ] 
 Parameters:
X
 basic solution, also output solution

invert
Description copied from interface:LinearSolverDense
Computes the inverse of of the 'A' matrix passed intoLinearSolver.setA(Matrix)
and writes the results to the provided matrix. If 'A_inv' needs to be different from 'A' is implementation dependent. Specified by:
invert
in interfaceLinearSolverDense<DMatrixRMaj>
 Overrides:
invert
in classLinearSolverAbstract_DDRM
 Parameters:
A_inv
 Where the inverted matrix saved. Modified.

getDecomposition
Description copied from interface:LinearSolver
If a decomposition class was used internally then this will return that class. Most linear solvers decompose the input matrix into a more simplistic form. However some solutions do not require decomposition, e.g. inverse by minor. Returns:
 Internal decomposition class. If there is none then null.
