Eigen
3.3.4

Base class of SVD algorithms.
Derived  the type of the actual SVD decomposition 
SVD decomposition consists in decomposing any nbyp matrix A as a product
where U is a nbyn unitary, V is a pbyp unitary, and S is a nbyp real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively.
Singular values are always sorted in decreasing order.
You can ask for only thin U or V to be computed, meaning the following. In case of a rectangular nbyp matrix, letting m be the smaller value among n and p, there are only m singular vectors; the remaining columns of U and V do not correspond to actual singular vectors. Asking for thin U or V means asking for only their m first columns to be formed. So U is then a nbym matrix, and V is then a pbym matrix. Notice that thin U and V are all you need for (least squares) solving.
If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to terminate in finite (and reasonable) time.
Public Types  
typedef Eigen::Index  Index 
Public Member Functions  
bool  computeU () const 
bool  computeV () const 
const MatrixUType &  matrixU () const 
const MatrixVType &  matrixV () const 
Index  nonzeroSingularValues () const 
Index  rank () const 
Derived &  setThreshold (const RealScalar &threshold) 
Derived &  setThreshold (Default_t) 
const SingularValuesType &  singularValues () const 
template<typename Rhs >  
const Solve< Derived, Rhs >  solve (const MatrixBase< Rhs > &b) const 
RealScalar  threshold () const 
Protected Member Functions  
SVDBase ()  
Default Constructor. More...  
typedef Eigen::Index Eigen::SVDBase< Derived >::Index 

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Default Constructor.
Default constructor of SVDBase

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For the SVD decomposition of a nbyp matrix, letting m be the minimum of n and p, the U matrix is nbyn if you asked for ComputeFullU , and is nbym if you asked for ComputeThinU .
The m first columns of U are the left singular vectors of the matrix being decomposed.
This method asserts that you asked for U to be computed.

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For the SVD decomposition of a nbyp matrix, letting m be the minimum of n and p, the V matrix is pbyp if you asked for ComputeFullV , and is pbym if you asked for ComputeThinV .
The m first columns of V are the right singular vectors of the matrix being decomposed.
This method asserts that you asked for V to be computed.

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*this
is the SVD.

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Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(), which need to determine when singular values are to be considered nonzero. This is not used for the SVD decomposition itself.
When it needs to get the threshold value, Eigen calls threshold(). The default is NumTraits<Scalar>::epsilon()
threshold  The new value to use as the threshold. 
A singular value will be considered nonzero if its value is strictly greater than .
If you want to come back to the default behavior, call setThreshold(Default_t)

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Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.
You should pass the special object Eigen::Default as parameter here.
See the documentation of setThreshold(const RealScalar&).

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For the SVD decomposition of a nbyp matrix, letting m be the minimum of n and p, the returned vector has size m. Singular values are always sorted in decreasing order.

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b  the righthandside of the equation to solve. 

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Returns the threshold that will be used by certain methods such as rank().
See the documentation of setThreshold(const RealScalar&).