This work proposes a time warp invariant sparse coding and dictionary learning framework for time series clustering, where both input samples and atoms define time series of different lengths that involve variable delays. For that, first an l0 sparse coding problem is formalised and a time warp invariant orthogonal matching pursuit based on a new cosine maximisation time warp operator is proposed. A dictionary learning under time warp is then formalised and a gradient descent solution is developed. Lastly, a time series clustering based on the time warp sparse coding and dictionary learning is presented. The proposed approach is evaluated and compared to major alternative methods on several public datasets, with an application to deezer music data stream clustering.