## Contents

- 1 Introduction
- 2 Installation
- 3 Dictionary Learning and Matrix Factorization Toolbox
  - 3.1 Function mexTrainDL
  - 3.2 Function mexTrainDL_Memory
  - 3.3 Function mexStructTrainDL
  - 3.4 Function nmf
  - 3.5 Function nnsc
- 4 Sparse Decomposition Toolbox
  - 4.1 Function mexOMP
  - 4.2 Function mexOMPMask
  - 4.3 Function mexRidgeRegression
  - 4.4 Function mexLasso
  - 4.5 Function mexLassoWeighted
  - 4.6 Function mexLassoMask
  - 4.7 Function mexCD
  - 4.8 Function mexSOMP
  - 4.9 Function mexL1L2BCD
  - 4.10 Function mexSparseProject
- 5 Proximal Toolbox
  - 5.1 Regularization Functions
  - 5.2 Function mexProximalFlat
  - 5.3 Function mexProximalTree
  - 5.4 Function mexProximalGraph
  - 5.5 Function mexProximalPathCoding
  - 5.6 Function mexEvalPathCoding
  - 5.7 Problems Addressed
    - 5.7.1 Regression Problems with the Square Loss
    - 5.7.2 Classification Problems with the Logistic Loss
    - 5.7.3 Multi-class Classification Problems with the Softmax Loss
    - 5.7.4 Multi-task Regression Problems with the Square Loss
    - 5.7.5 Multi-task Classification Problems with the Logistic Loss
    - 5.7.6 Multi-task and Multi-class Classification Problems with the Softmax Loss
  - 5.8 Function mexFistaFlat
  - 5.9 Function mexFistaTree
  - 5.10 Function mexFistaGraph
  - 5.11 Function mexFistaPathCoding
  - 5.12 Function mexIncrementalProx
  - 5.13 Function mexStochasticProx
- 6 Miscellaneous Functions
  - 6.1 Function mexConjGrad
  - 6.2 Function mexBayer
  - 6.3 Function mexCalcAAt
  - 6.4 Function mexCalcXAt
  - 6.5 Function mexCalcXY
  - 6.6 Function mexCalcXYt
  - 6.7 Function mexCalcXtY
  - 6.8 Function mexInvSym
  - 6.9 Function mexNormalize
  - 6.10 Function mexSort
  - 6.11 Function mexDisplayPatches
  - 6.12 Function mexCountPathsDAG
  - 6.13 Function mexRemoveCyclesGraph
  - 6.14 Function mexCountConnexComponents
  - 6.15 Function mexGraphOfGroupStruct
  - 6.16 Function mexGroupStructOfString
  - 6.17 Function mexReadGroupStruct
  - 6.18 Function mexTreeOfGroupStruct
  - 6.19 Function mexSimpleGroupTree
- A Duality Gaps with Fenchel Duality
  - A.0.1 Duality Gaps without Intercepts
  - A.0.2 Duality Gaps with Intercepts