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 non-square matrix A and with non-null 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 pseudo-inverse of the decomposed matrix.int
Returns the number of rows in the matrix.boolean
Check if the decomposed matrix is non-singular.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
- right-hand 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
- right-hand 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 non-singular.- Returns:
- true if the decomposed matrix is non-singular.
-
getInverse
Get the pseudo-inverse 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 pseudo-inverse \( A^+ \) 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 pseudo-inverse for all matrices. For example, the
LUDecomposition
is not defined for non-square matrices to begin with. TheQRDecomposition
can operate on non-square matrices, but will throwMathIllegalArgumentException
if the decomposed matrix is singular. Refer to the javadoc of specific decomposition implementations for more details.- Returns:
- pseudo-inverse matrix (which is the inverse, if it exists), if the decomposition can pseudo-invert the decomposed matrix
- Throws:
MathIllegalArgumentException
- if the decomposed matrix is singular and the decomposition can not compute a pseudo-inverse
-
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
-