SVD Class Reference
[Operations on arrays]

Enumerator:

MODIFY_A	allow the algorithm to modify the decomposed matrix; it can save space and speed up processing. currently ignored.
NO_UV	indicates that only a vector of singular values `w` is to be processed, while u and vt will be set to empty matrices
FULL_UV	when the matrix is not square, by default the algorithm produces u and vt matrices of sufficiently large size for the further A reconstruction; if, however, FULL_UV flag is specified, u and vt will be full-size square orthogonal matrices.

Definition at line 2507 of file core.hpp.

the default constructor

initializes an empty SVD structure

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. initializes an empty SVD structure and then calls SVD::operator()

Parameters:

src	decomposed matrix.
flags	operation flags (SVD::Flags)

performs back substitution

performs a singular value back substitution.

The method calculates a back substitution for the specified right-hand side:

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:

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.

decomposes matrix and stores the results to user-provided matrices

The methods/functions perform SVD of matrix. Unlike SVD::SVD constructor and SVD::operator(), they store the results to the user-provided matrices:

 {.cpp}
    Mat A, w, u, vt;
    SVD::compute(A, w, u, vt);

Parameters:

src	decomposed matrix
w	calculated singular values
u	calculated left singular vectors
vt	transposed matrix of right singular values
flags	operation flags - see SVD::SVD.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. computes singular values of a matrix.

Parameters:

src	decomposed matrix
w	calculated singular values
flags	operation flags - see SVD::Flags.

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.
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:

Parameters:

src	left-hand-side matrix.
dst	found solution.