Matlab Files

Duals:

BioBack deletes the requested vector j from a given basis taken from a dictionary
BioDictDel deletes a vector from a basis selected from a given dictionary and appropriately modifies biorthogonal functions, orthonormal functions spanning the same space as the basis, and unselected dictionary atoms subtracted by their components in the selected basis.
BioDictIns enlarges a basis selected from a given dictionary by one vector
BioFor enlargers the dual/biorthogonal basis enlarger by one vector
BioInsert adds an atom to a basis. It also appropriately modifies the corresponding biorthogonal basis and orthonormal basis (obtained by modified Gram-Schmidt)
DRE Dictionary Redundancy Elimination
DREOr uses DRE method to produce and orthogonal basis from a dictionary and gives dictionary's indices of the atoms spannig the space
DREOrp uses Dre method to produce and orthogonal basis from a dictionary
FrDelete deletes the requested vector from a given frame
FrInsert adds a vector to a frame. It also appropriately modifies the corresponding dual frame
FrInsertBlock adds vectors to a basis and gives the duals spanning the same space
NBioDictIns enlarges a basis selected from a given dictionary by one vector. It modifies the biorthogonal basis for the same space and gives the projection of the remainding atoms onto the orthogonal complementary space
NBioInsert adds an atom to a basis and modifies the biorthogonal basis for the same space

To download all the routines click here.
All the presented routines are described in detail in our manual (ps,pdf).