• SynLab:

    Available at https://github.com/HaizhaoYang/SynLab

    1D synchrosqueezed wave packet transforms (SSWPT):
       

    Analyzing instantaneous properties (instantaneous frequencies, phases and amplitudes) of non-linear oscillatory signals in a superposition.

    A tool for mode decomposition and general mode decomposition with general wave shapes.

    2D synchrosqueezed curvelet transform (SSCT):
       

    Anlayzing local properties of non-linear oscillatory textures in a superposition.

    3D synchrosqueezed wave packet transform.
       
    Applications:

    Geophysics:  seismic wave field separation and ground-roll removal.
    Materials science:  atomic crystal image analysis, grain boundary and local defects identification, elastic deformation estimation.
    Art:  Canvas painting analysis for art forensics.

    For a comparison of the statistical properties of the synchrosqueezed wavelet transform, the synchrosqeezed short-time Fourier transform, the synchrosqeezed wave packet transform, and the multitaper time-frequency reassignment, please visit http://github.com/HaizhaoYang/SST_compare.



    SynCrystal:

    Available at https://github.com/SynCrystal/SynCrystal

    SynCrystal is a MATLAB toolbox to analyze atomic crystal images. For a given atomic crystal image, it contains several tools to identify grain boundary, crystal orientation, elastic deformation. A few examples of synthetic and real atomic crystal images are provided to illustrate how to use these tools.

    The first method in SynCrystal applies 2D synchrosqueezed transform to efficiently analyze atomic crystal images.

    The second method in SynCrystal applies a variational optimization to optimize the results provided by the first method.



    ButterflyLab:

    Fast algorithms for complementary low-rank matrices, e.g. Fourier integral operators (FIOs) for wave equations and a class of imaging methods, a class of transforms for harmonic analysis and special functions. Available at Codes.

    Multiscale butterfly algorithm:
       

    Fast evaluation of FIOs for wave equations and a class of imaging methods.

    2D and 3D codes and numerical examples available.

    Butterfly factorization:
       

    1D Butterfly Factorizatio:

    Butterfly factorization for all 1D problems.

    2D Butterfly Factorization:

    General Butterfly Factorization (GBF): Butterfly factorization for 2D problems without singularity at origin.

    Polar Butterfly Factorization (PBF): Butterfly factorization for 2D problems with singularity at origin.

    Multiscale Butterfly Factorization (MBF): Butterfly factorization for 2D problems with singularity at origin.

    2D and 3D codes and numerical examples available.

    Interpolative butterfly factorization:
       

    Fast algorithms to construct and apply the butterfly factorization of FIOs with nearly optimal time complexity.

    1D, 2D and 3D codes and numerical examples available.



    PSP:

    Available at https://wordpress.elsi-interchange.org/

    Distributed and parallel basic linear algebra subroutines for sparse matrices
       

    1D and 2D block cyclic distribution

    Similar interface to Scalapack.

    Distributed and parallel eigensolvers for sparse matrices:
       

    Under development.



    ZoloEig:

    Available at ZoloEig

    Interior eigenvalue solver based on fast direct solver and the best high order rational function approximation to step functions.
       

    Can be implemented in spectrum slicing libraries for full diagonalization.

    Can also be used to compute leading eigenpairs.

    Distributed and parallel version:
       

    Under development.