NAThompson / MGARD

MGARD: MultiGrid Adaptive Reduction of Data

MGARD

MGARD (MultiGrid Adaptive Reduction of Data) is a technique for multilevel lossy compression of scientific data based on the theory of multigrid methods. This is an experimental C++ API for integration with existing software, use at your own risk!

The double precision API consists of a header file: mgard_api.h, for single precision the header file is mgard_api_float.h.

Users need only include this header file, and link against the static library libmgard.a.

This header file provides prototypes for the following overloaded functions:

unsigned char *mgard_compress(int itype_flag, double/float *data, int& out_size,
                              int n1, int n2, int n3, double/float tol, [qoi, s = infinity])

It returns a pointer to an unsigned char array of compressed data. The arguments are:

 itype_flag: Data type, 0 for float, 1 for double
 data : Pointer to the input buffer (interpreted as 2D matrix) to compress with MGARD,
        this buffer will be destroyed!
 out_size: size of input data, returns compressed size on exit
 n1: Size of first dimension
 n2: Size of second dimension
 n3: Size of third dimension
 tol: Upper bound for desired tolerance. Note that this tolerance is relative not absolute: ||u - C[u]||_s \le tol*||u||_s
 qoi: Function pointer to the quantity of interest
 s: The norm in which the error will be preserved, L-\infty assumed if not present in the function call.

These APIs are outdated and will be updated.

The next overload is

void *mgard_decompress(int itype_flag, unsigned char *data,
int data_len, int n1, int n2, int n3,[s = infinity])

This returns a void pointer to an array of decompressed data, which must be cast to float or double. The arguments are:

 itype_flag: Data type, 0 for float, 1 for double
 data : Pointer to the input buffer (interpreted as 2D matrix) to decompress with MGARD,
        this buffer will be destroyed!
 data_len: size of input data in bytes
 n1: Size of first dimension
 n2: Size of second dimension
 n3: Size of third dimension
 s: The norm in which the error will be preserved, L-\infty assumed if not present in the function call.

The qoi function pointer must compute the quantity of interest, Q(v). Its only use is to estimate the Besov s-norm of the operator Q; if this can be derived independently, then there is no need to provide it.

Paper [1] should be the first reference to glimpse into the theory behind MGARD. For more information consult [2] and [3]:

Caveats

If you use a certain value of s to compress your data, you must use the same value of s to decompress it. You cannot agnostically decompress the compressed representation, and the value of s is not stored in the compressed stream. In addition, there is currently no way to detect if an inconsistent value of s has been passed, so the code returns corrupted data silently.

If you forget the value of s that you used to compress your data, then your data is gone.

1. Multilevel Techniques for Compression and Reduction of Scientific Data—The Univariate case M Ainsworth, O Tugluk, B Whitney, K Scott. Computing and Visualization in Science, 8, 2018

2. Multilevel Techniques for Compression and Reduction of Scientific Data---The Multivariate Case M Ainsworth, O Tugluk, B Whitney, S Klasky. SIAM Journal on Scientific Computing 41 (2), A1278-A1303, 2019

3. Multilevel Techniques for Compression and Reduction of Scientific Data-Quantitative Control of Accuracy in Derived Quantities. M Ainsworth, O Tugluk, B Whitney, S Klasky. SIAM Journal on Scientific Computing 41 (4), A2146-A2171, 2019