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static void | backSubst (InputArray w, InputArray u, InputArray vt, InputArray rhs, OutputArray dst) |
| performs back substitution More...
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template<typename _Tp , int m, int n, int nm, int nb> |
static void | backSubst (const Matx< _Tp, nm, 1 > &w, const Matx< _Tp, m, nm > &u, const Matx< _Tp, n, nm > &vt, const Matx< _Tp, m, nb > &rhs, Matx< _Tp, n, nb > &dst) |
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static void | compute (InputArray src, OutputArray w, OutputArray u, OutputArray vt, int flags=0) |
| decomposes matrix and stores the results to user-provided matrices More...
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static void | compute (InputArray src, OutputArray w, int flags=0) |
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template<typename _Tp , int m, int n, int nm> |
static void | compute (const Matx< _Tp, m, n > &a, Matx< _Tp, nm, 1 > &w, Matx< _Tp, m, nm > &u, Matx< _Tp, n, nm > &vt) |
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template<typename _Tp , int m, int n, int nm> |
static void | compute (const Matx< _Tp, m, n > &a, Matx< _Tp, nm, 1 > &w) |
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static void | solveZ (InputArray src, OutputArray dst) |
| solves an under-determined singular linear system More...
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Singular Value Decomposition.
Class for computing Singular Value Decomposition of a floating-point matrix. The Singular Value Decomposition is used to solve least-square problems, under-determined linear systems, invert matrices, compute condition numbers, and so on.
If you want to compute a condition number of a matrix or an absolute value of its determinant, you do not need u
and vt
. You can pass flags=SVD::NO_UV|... . Another flag SVD::FULL_UV indicates that full-size u and vt must be computed, which is not necessary most of the time.
- See also
- invert, solve, eigen, determinant
performs a singular value back substitution.
The method calculates a back substitution for the specified right-hand side:
\[\texttt{x} = \texttt{vt} ^T \cdot diag( \texttt{w} )^{-1} \cdot \texttt{u} ^T \cdot \texttt{rhs} \sim \texttt{A} ^{-1} \cdot \texttt{rhs}\]
Using this technique you can either get a very accurate solution of the convenient linear system, or the best (in the least-squares terms) pseudo-solution of an overdetermined linear system.
- Parameters
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rhs | right-hand side of a linear system (u*w*v')*dst = rhs to be solved, where A has been previously decomposed. |
dst | found solution of the system. |
- Note
- Explicit SVD with the further back substitution only makes sense if you need to solve many linear systems with the same left-hand side (for example, src ). If all you need is to solve a single system (possibly with multiple rhs immediately available), simply call solve add pass DECOMP_SVD there. It does absolutely the same thing.
the operator that performs SVD. The previously allocated u, w and vt are released.
The operator performs the singular value decomposition of the supplied matrix. The u,vt
, and the vector of singular values w are stored in the structure. The same SVD structure can be reused many times with different matrices. Each time, if needed, the previous u,vt
, and w are reclaimed and the new matrices are created, which is all handled by Mat::create.
- Parameters
-
src | decomposed matrix. The depth has to be CV_32F or CV_64F. |
flags | operation flags (SVD::Flags) |
solves an under-determined singular linear system
The method finds a unit-length solution x of a singular linear system A*x = 0. Depending on the rank of A, there can be no solutions, a single solution or an infinite number of solutions. In general, the algorithm solves the following problem:
\[dst = \arg \min _{x: \| x \| =1} \| src \cdot x \|\]
- Parameters
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src | left-hand-side matrix. |
dst | found solution. |