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https://github.com/flatironinstitute/sparse_dot

Python wrapper for Intel Math Kernel Library (MKL) matrix multiplication
https://github.com/flatironinstitute/sparse_dot

matrix-multiplication mkl numpy python scipy sparse sparse-matrix

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Python wrapper for Intel Math Kernel Library (MKL) matrix multiplication

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# sparse_dot_mkl

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This is a wrapper for the sparse matrix multiplication in the intel MKL library.

It is implemented entirely in native python using `ctypes`.

The main advantage to MKL (which motivated this) is multithreaded sparse matrix multiplication. 

The scipy sparse implementation is single-threaded at the time of writing (2020-01-03).

A secondary advantage is the direct multiplication of a sparse and a dense matrix without requiring any

intermediate conversion (also multithreaded). 



Three python functions are explicitly available (`dot_product_mkl`, `gram_matrix_mkl`, and `sparse_qr_solve_mkl`),

and several wrapped MKL functions (e.g. `mkl_get_version_string`, `pardiso`) are accessible:



#### dot_product_mkl



`dot_product_mkl(matrix_a, matrix_b, cast=False, copy=True, reorder_output=False, dense=False, debug=False, out=None, out_scalar=None)`



`matrix_a` and `matrix_b` are either numpy arrays (1d or 2d) or scipy sparse matrices (CSR, CSC, or BSR).

BSR matrices are supported for matrix-matrix multiplication only if one matrix is a dense array or both sparse matrices are BSR.

Sparse COO matrices are not supported. 

Numpy arrays must be contiguous. 

Non-contiguous arrays should be copied to a contiguous array prior to calling this 

function.



This package only works with float or complex float data.

`cast=True` will convert data to double-precision floats or complex floats by making an internal copy if necessary.

If A and B are both single-precision floats or complex floats they will be used as is.

`cast=False` will raise a ValueError if the input arrays are not both double-precision or both single-precision.

This defaults to `False` on the principle that potentially unsafe dtype conversions should not occur without explicit

instruction.



The output will be a dense array, unless both inputs are sparse, in which case the output will be a sparse matrix.

The sparse matrix output format will be the same as the left (A) input sparse matrix.

`dense=True` will directly produce a dense array during sparse matrix multiplication. 

`dense` has no effect if a dense array would be produced anyway. 

Dense array outputs may be row-ordered or column-ordered, depending on input ordering.



`copy` is deprecated and has no effect.



`reorder_output=True` will order sparse matrix indices in the output matrix. 

It has no effect if the output is a dense array.

Input sparse matrices may be reordered without warning in place. 

This will not change data, only the way it is stored.

Scipy matrix multiplication does not produce ordered outputs, so this defaults to `False`.



`out` is an optional reference to a dense output array to which the product of the matrix multiplication will be added. 

This must be identical in attributes to the array that would be returned if it was not used.

Specifically it must have the correct shape, dtype, and column- or row-major order and it must be contiguous. 

A ValueError will be raised if any attribute of this array is incorrect.

This function will return a reference to the same array object when `out` is set.



`out_scalar` is an optional element-wise scaling of `out`, if `out` is provided.

It will multiply `out` prior to adding the matrix multiplication such that 

`out := matrix_a * matrix_b + out_scalar * out`



#### sparse_qr_solve_mkl



`sparse_qr_solve_mkl(matrix_a, matrix_b, cast=False, debug=False)`



This is a QR solver for systems of linear equations (AX = B) where `matrix_a` is a sparse CSR matrix 

and `matrix_b` is a dense matrix.

It will return a dense array X.



`cast=True` will convert data to compatible floats by making an internal copy if necessary.

It will also convert a CSC matrix to a CSR matrix if necessary.



#### gram_matrix_mkl



`gram_matrix_mkl(matrix, transpose=False, cast=False, dense=False, debug=False, reorder_output=False)`



This will calculate the gram matrix ATA for matrix A, where matrix A is dense or a sparse CSR matrix.

It will return the upper triangular portion of the resulting symmetric matrix.

If A is sparse, it will return a sparse matrix unless `dense=True` is set.



`transpose=True` will instead return AAT 



`reorder_output=True` will order sparse matrix indices in the output matrix. 



`cast=True` will convert data to compatible floats by making an internal copy if necessary.

It will also convert a CSC matrix to a CSR matrix if necessary.



#### PARDISO



`pardisoinit(mtype, pt=None, iparm=None, single_precision=None, zero_indexing=True)`



`pardiso(A, B, pt, mtype, iparm, phase=13, maxfct=1, mnum=1, perm=None, msglvl=0, X=None, quiet=False)`



Wrapper for MKL pardiso solver and the pardisoinit function which initializes `pt` and `iparm`.

This is a direct solver for real or complex systems of linear equations (AX = B) where `A`

is a sparse CSR matrix and `B` is a dense matrix with one or more right-hand sides.

It will return a dense array X.



Refer to the pardiso documentation for detailed description of options.

Consider this wrapper to be experimental.



#### Service Functions



Several service functions are available and can be imported from the base `sparse_dot_mkl` package.



`mkl_get_max_threads()` returns the maximum number of threads used by MKL as an integer



`mkl_set_num_threads(n_threads)` will set a maximum number of threads hint for MKL 



`mkl_set_num_threads_local(n_threads)` will set a maximum thread hint for the current MKL thread only



`mkl_get_version()` returns a tuple of MKL version information

(MajorVersion, MinorVersion, UpdateVersion, ProductStatus, Build, Processor, Platform)



`mkl_get_version_string()` returns a descriptive string of the current MKL version



`mkl_interface_integer_dtype()` returns the numpy dtype for sparse matrix index arrays



#### Requirements



This package requires the MKL runtime linking library `libmkl_rt.so` 

(or `libmkl_rt.dylib` for OSX, or `mkl_rt.dll` for WIN).

If the MKL library cannot be loaded an `ImportError` will be raised when the package is first imported. 

MKL is distributed with the full version of conda,

and can be installed into Miniconda with `conda install -c intel mkl`.

Alternatively, you may add need to add the path to MKL shared objects to `LD_LIBRARY_PATH`

(e.g. `export LD_LIBRARY_PATH=/opt/intel/mkl/lib/intel64:$LD_LIBRARY_PATH`).