Interface DecompositionSolver

public interface DecompositionSolver
Interface handling decomposition algorithms that can solve A × X = B.Decomposition algorithms decompose an A matrix has a product of several specific matrices from which they can solve A × X = B in least squares sense: they find X such that A × X  B is minimal.
Some solvers like
LUDecomposition
can only find the solution for square matrices and when the solution is an exact linear solution, i.e. when A × X  B is exactly 0. Other solvers can also find solutions with nonsquare matrix A and with nonnull minimal norm. If an exact linear solution exists it is also the minimal norm solution.


Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description RealMatrix
getInverse()
Get the pseudoinverse of the decomposed matrix.boolean
isNonSingular()
Check if the decomposed matrix is nonsingular.RealMatrix
solve(RealMatrix b)
Solve the linear equation A × X = B for matrices A.RealVector
solve(RealVector b)
Solve the linear equation A × X = B for matrices A.



Method Detail

solve
RealVector solve(RealVector b) throws MathIllegalArgumentException
Solve the linear equation A × X = B for matrices A.The A matrix is implicit, it is provided by the underlying decomposition algorithm.
 Parameters:
b
 righthand side of the equation A × X = B Returns:
 a vector X that minimizes the two norm of A × X  B
 Throws:
MathIllegalArgumentException
 if the matrices dimensions do not match.MathIllegalArgumentException
 if the decomposed matrix is singular.

solve
RealMatrix solve(RealMatrix b) throws MathIllegalArgumentException
Solve the linear equation A × X = B for matrices A.The A matrix is implicit, it is provided by the underlying decomposition algorithm.
 Parameters:
b
 righthand side of the equation A × X = B Returns:
 a matrix X that minimizes the two norm of A × X  B
 Throws:
MathIllegalArgumentException
 if the matrices dimensions do not match.MathIllegalArgumentException
 if the decomposed matrix is singular.

isNonSingular
boolean isNonSingular()
Check if the decomposed matrix is nonsingular. Returns:
 true if the decomposed matrix is nonsingular.

getInverse
RealMatrix getInverse() throws MathIllegalArgumentException
Get the pseudoinverse of the decomposed matrix.This is equal to the inverse of the decomposed matrix, if such an inverse exists.
If no such inverse exists, then the result has properties that resemble that of an inverse.
In particular, in this case, if the decomposed matrix is A, then the system of equations \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudoinverse \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \ A z  b \right \_2 \) is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution, meaning \( \left \ z \right \_2 \) is minimized.
Note however that some decompositions cannot compute a pseudoinverse for all matrices. For example, the
LUDecomposition
is not defined for nonsquare matrices to begin with. TheQRDecomposition
can operate on nonsquare matrices, but will throwMathIllegalArgumentException
if the decomposed matrix is singular. Refer to the javadoc of specific decomposition implementations for more details. Returns:
 pseudoinverse matrix (which is the inverse, if it exists), if the decomposition can pseudoinvert the decomposed matrix
 Throws:
MathIllegalArgumentException
 if the decomposed matrix is singular and the decomposition can not compute a pseudoinverse

