Interface DecompositionSolver
Decomposition algorithms decompose an A matrix as 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
Modifier and TypeMethodDescriptionint
Returns the number of columns in the matrix.Get the pseudoinverse of the decomposed matrix.int
Returns the number of rows in the matrix.boolean
Check if the decomposed matrix is nonsingular.solve
(RealMatrix b) Solve the linear equation A × X = B for matrices A.solve
(RealVector b) Solve the linear equation A × X = B for matrices A.

Method Details

solve
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
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
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

getRowDimension
int getRowDimension()Returns the number of rows in the matrix. Returns:
 rowDimension
 Since:
 2.0

getColumnDimension
int getColumnDimension()Returns the number of columns in the matrix. Returns:
 columnDimension
 Since:
 2.0
