Sections in this tutorial:

- Creating a GPU Faust object
- Generating a GPU Faust
- Manipulating GPU Fausts and CPU interoperability
- Benchmarking your GPU with matfaust!
- Running some FAµST algorithms on GPU
- Manually loading the matfaust GPU module

In this tutorial we’ll see quickly how to leverage the GPU computing power with matfaust. Since matfaust 3.0.0 the API has been modified to make the GPU available directly from the Matlab wrapper. Indeed, an independent GPU module (aka gpu_mod) has been developed for this purpose.

The first question you might ask is: does it work on my computer? Here is the answer: the loading of this module is quite transparent, if an NVIDIA GPU is available and CUDA (11 or 12) is properly installed on your system, you have normally nothing to do except installing matfaust to get the GPU implementations at your fingertips. We’ll see at the end of this tutorial how to load manually the module and how to get further information in case of an error.

It is worthy to note that Mac OS X is not supported because NVIDIA has stopped to support this OS.

Also please notice that the GPU module support is still considered in beta status as the code is relatively young and still evolving. However the API shouldn’t evolve that much in a near future.

Let’s start with some basic Faust creations on the GPU. Almost all the ways of creating a Faust object in CPU memory are also available to create a GPU Faust. First of all, creating a Faust using the constructor works seamlessly on GPU, the only need is to specify the dev keyword argument, as follows:

import matfaust.Faust

M = rand(10, 10);

N = rand(10, 15);

gpuF = Faust({M, N}, 'dev', 'gpu')

gpuF =

Faust size 10x15, density 1.66667, nnz_sum 250, 2 factor(s):
- FACTOR 0 (double) [GPU] DENSE, size 10x10, density 1, nnz 100, addr: 0x7f7c00c94060
- FACTOR 1 (double) [GPU] DENSE, size 10x15, density 1, nnz 150, addr: 0x7f7b8d9795d0

It’s clearly indicated in the output that the Faust object is instantiated in GPU memory (the N and M numpy arrays are copied from the CPU to the GPU memory). However it’s also possible to check this programmatically:

device(gpuF)

ans = 'gpu'

While for a CPU Faust you’ll get:

device(Faust({M, N}, 'dev', 'cpu'))

ans = 'cpu'

In gpuF the factors are dense matrices but it’s totally possible to instantiate sparse matrices on the GPU as you can do on CPU side.

S = sprand(10, 15, .25);

T = sprand(15, 10, .05);

sparse_gpuF = Faust({S, T}, 'dev', 'gpu')

sparse_gpuF =

Faust size 10x10, density 0.42, nnz_sum 42, 2 factor(s):
- FACTOR 0 (double) [GPU] SPARSE, size 10x15, density 0.226667, nnz 34, addr: 0x7f7b8ebe2cc0
- FACTOR 1 (double) [GPU] SPARSE, size 15x10, density 0.0533333, nnz 8, addr: 0x7f7b8ebe7000

You can also create a GPU Faust by explicitly copying a CPU Faust to the GPU memory. Actually, at anytime you can copy a CPU Faust to GPU and conversely. The clone() member function is here precisely for this purpose. Below we copy gpuF to CPU and back again to GPU in the new Faust gpuF2.

cpuF = clone(gpuF, 'cpu')

cpuF =

Faust size 10x15, density 1.66667, nnz_sum 250, 2 factor(s):
- FACTOR 0 (double) DENSE, size 10x10, density 1, nnz 100
- FACTOR 1 (double) DENSE, size 10x15, density 1, nnz 150

gpuF2 = clone(cpuF, 'gpu')

gpuF2 =

Faust size 10x15, density 1.66667, nnz_sum 250, 2 factor(s):
- FACTOR 0 (double) [GPU] DENSE, size 10x10, density 1, nnz 100, addr: 0x7f7b70361e20
- FACTOR 1 (double) [GPU] DENSE, size 10x15, density 1, nnz 150, addr: 0x7f7b70396600

Many of the functions for generating a Faust object on CPU are available on GPU too. It is always the same, you precise the dev argument by assigning the 'gpu' value and you’ll get a GPU Faust instead of a CPU Faust.

For example, the code below will successively create a random GPU Faust, a Hadamard transform GPU Faust, an identity GPU Faust and finally a DFT GPU Faust.

import matfaust.wht

import matfaust.dft

% Random GPU Faust

matfaust.rand(10, 10, 'num_factors', 11, 'dev', 'gpu')

ans =

Faust size 10x10, density 5.5, nnz_sum 550, 11 factor(s):
- FACTOR 0 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b703d09e0
- FACTOR 1 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b704ad520
- FACTOR 2 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b703cbf90
- FACTOR 3 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b70496990
- FACTOR 4 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b703cb5c0
- FACTOR 5 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b704ab2f0
- FACTOR 6 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b704a2bc0
- FACTOR 7 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b704a2d30
- FACTOR 8 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b70497000
- FACTOR 9 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b7049f150
- FACTOR 10 (double) [GPU] SPARSE, size 10x10, density 0.5, nnz 50, addr: 0x7f7b7049b770

% Hadamard GPU Faust

wht(32, 'dev', 'gpu')

ans =

Faust size 32x32, density 0.3125, nnz_sum 320, 5 factor(s):
- FACTOR 0 (double) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b703c1c60
- FACTOR 1 (double) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b703c74c0
- FACTOR 2 (double) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b703ba0b0
- FACTOR 3 (double) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b703c2530
- FACTOR 4 (double) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b703bacb0

% Identity GPU Faust

matfaust.eye(16, 'dev', 'gpu')

ans =

Faust size 16x16, density 0.0625, nnz_sum 16, 1 factor(s):
- FACTOR 0 (double) [GPU] SPARSE, size 16x16, density 0.0625, nnz 16, addr: 0x7f7b703ce290

% DFT GPU Faust

dft(32, 'dev', 'gpu')

ans =

Faust size 32x32, density 0.34375, nnz_sum 352, 6 factor(s):
- FACTOR 0 (complex) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b704be470
- FACTOR 1 (complex) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b704be0e0
- FACTOR 2 (complex) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b704ba770
- FACTOR 3 (complex) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b704aaaa0
- FACTOR 4 (complex) [GPU] SPARSE, size 32x32, density 0.0625, nnz 64, addr: 0x7f7b704ba2a0
- FACTOR 5 (complex) [GPU] SPARSE, size 32x32, density 0.03125, nnz 32, addr: 0x7f7b704c4ca0

Once you’ve created GPU Faust objects, you can perform operations on them staying in GPU world (that is, with no array transfer to CPU memory). That’s of course not always possible.

For example, let’s consider Faust-scalar multiplication and Faust-matrix product. In the first case the scalar is copied to the GPU memory and likewise in the second case the matrix is copied from CPU to GPU in order to proceed to the computation. However in both cases the Faust factors stay into GPU memory and don’t move during the computation.

% Faust-scalar multiplication

2*gpuF

ans =

Faust size 10x15, density 1.66667, nnz_sum 250, 2 factor(s):
- FACTOR 0 (double) [GPU] DENSE, size 10x10, density 1, nnz 100, addr: 0x7f7b704ca4c0
- FACTOR 1 (double) [GPU] DENSE, size 10x15, density 1, nnz 150, addr: 0x7f7b8d9795d0

When you make a scalar multiplication only one factor is multiplied, the others don’t change, they are shared between the Faust being multiplied and the resulting Faust. This is an optimization and to go further in this direction the factor chosen to be multiplied is the smallest in memory (not necessarily the first one).

% Faust-matrix product (the matrix is copied to GPU

% then the multiplication is performed on GPU)

gpuF*rand(size(gpuF,2), 15)

ans = 10×15

19.5188 15.8627 16.3494 20.0092 17.8775 15.2394 18.8780 20.4982 17.9227 17.8550 16.4497 16.1623 21.2342 17.3840 20.0797
16.6294 12.7984 13.2690 17.6679 14.7213 13.4675 15.8209 17.1853 15.6553 14.1920 14.0095 13.5296 18.9866 15.4844 17.4967
22.9040 18.5855 19.1411 24.2191 20.6279 18.5282 22.2976 24.3699 21.7080 20.3446 19.8407 19.2123 26.6791 21.4684 23.7823
20.2891 16.7623 16.5466 21.7549 18.7845 16.6076 20.2857 21.9744 19.6952 18.8697 17.7469 17.4555 23.7157 18.9584 22.0221
23.9356 18.7735 19.4222 24.7610 20.8382 18.4186 22.8625 24.9051 22.1823 21.1143 19.9065 19.2679 26.9927 22.2751 24.9935
16.9493 14.1255 14.4688 17.4038 15.6445 13.6824 16.4207 18.1339 15.7387 15.3461 14.4891 14.3344 19.0035 15.2028 17.4503
20.6190 16.5093 17.3293 21.5318 18.8465 16.6641 19.7383 21.8821 19.2809 17.9509 17.5920 17.3533 23.4642 19.0278 21.3797
17.4974 13.7856 14.2992 19.0386 15.9878 14.2171 17.1030 18.6477 16.9732 15.4865 15.3269 14.9055 20.3935 16.6752 18.6180
21.7549 17.4454 18.2602 23.2019 20.3546 17.4574 21.1492 23.0594 20.5578 19.5494 18.9371 18.6304 24.2629 19.8503 22.5232
17.6941 13.9832 14.2790 19.2290 16.1250 14.3518 17.3875 18.6344 17.0925 15.8015 15.3906 14.8908 20.5301 16.6689 18.8594

On the contrary, and that matters for optimization, there is no CPU-GPU transfer at all when you create another GPU Faust named for example gpuF2 on the GPU and decide to multiply the two of them like this:

gpuF2 = matfaust.rand(size(gpuF, 2), 18, 'dev', 'gpu')

gpuF2 =

Faust size 15x18, density 1.51852, nnz_sum 410, 5 factor(s):
- FACTOR 0 (double) [GPU] SPARSE, size 15x18, density 0.277778, nnz 75, addr: 0x7f7b72b727c0
- FACTOR 1 (double) [GPU] SPARSE, size 18x16, density 0.3125, nnz 90, addr: 0x7f7b72b51710
- FACTOR 2 (double) [GPU] SPARSE, size 16x16, density 0.3125, nnz 80, addr: 0x7f7b72b57410
- FACTOR 3 (double) [GPU] SPARSE, size 16x17, density 0.294118, nnz 80, addr: 0x7f7b72b57430
- FACTOR 4 (double) [GPU] SPARSE, size 17x18, density 0.277778, nnz 85, addr: 0x7f7b72b6f2b0

gpuF3 = gpuF * gpuF2

gpuF3 =

Faust size 10x18, density 3.66667, nnz_sum 660, 7 factor(s):
- FACTOR 0 (double) [GPU] DENSE, size 10x10, density 1, nnz 100, addr: 0x7f7c00c94060
- FACTOR 1 (double) [GPU] DENSE, size 10x15, density 1, nnz 150, addr: 0x7f7b8d9795d0
- FACTOR 2 (double) [GPU] SPARSE, size 15x18, density 0.277778, nnz 75, addr: 0x7f7b72b727c0
- FACTOR 3 (double) [GPU] SPARSE, size 18x16, density 0.3125, nnz 90, addr: 0x7f7b72b51710
- FACTOR 4 (double) [GPU] SPARSE, size 16x16, density 0.3125, nnz 80, addr: 0x7f7b72b57410
- FACTOR 5 (double) [GPU] SPARSE, size 16x17, density 0.294118, nnz 80, addr: 0x7f7b72b57430
- FACTOR 6 (double) [GPU] SPARSE, size 17x18, density 0.277778, nnz 85, addr: 0x7f7b72b6f2b0

Besides, it’s important to note that gpuF3 factors are not duplicated in memory because they already exist for gpuF and gpuF2, that’s an extra optimization: gpuF3 is just a memory view of the factors of gpuF and gpuF2 (the same GPU arrays are shared between Faust objects). That works pretty well the same for CPU Faust objects.

Finally, please notice that CPU Faust objects are not directly interoperable with GPU Fausts objects. You can try, it’ll end up with an error.

cpuF = matfaust.rand(5, 5, 'num_factors', 5, 'dev', 'cpu');

gpuF = matfaust.rand(5, 5, 'num_factors', 6, 'dev', 'gpu');

% A first try to multiply a CPU Faust with a GPU one...

cpuF * gpuF

Error using mexFaustReal

Handle not valid.

Handle not valid.

Error in matfaust.Faust/call_mex (line 5560)

[varargout{1:nargout}] = mexFaustReal(func_name, F.matrix.objectHandle, varargin{:});

Error in * (line 1323)

C = matfaust.Faust(F, call_mex(F, 'mul_faust', A.matrix.objectHandle));

It doesn't work, you must either convert cpuF to a GPU Faust or gpuF to a CPU Faust before multiplying. Below is a second try using conversion as needed...

clone(cpuF, 'gpu') * gpuF

ans =

Faust size 5x5, density 11, nnz_sum 275, 11 factor(s):
- FACTOR 0 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b6914e590
- FACTOR 1 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b69150700
- FACTOR 2 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b690ca660
- FACTOR 3 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b6914e9c0
- FACTOR 4 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b69138340
- FACTOR 5 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b72b82480
- FACTOR 6 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b72b82570
- FACTOR 7 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b7035c540
- FACTOR 8 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b7035c620
- FACTOR 9 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b72b80870
- FACTOR 10 (double) [GPU] SPARSE, size 5x5, density 1, nnz 25, addr: 0x7f7b72b88750

Now it works!

Of course when we run some code on GPU rather than on CPU, it is clearly to enhance the performance. So let’s try your GPU and find out if it is worth it or not compared to your CPU. First, measure how much time it takes on CPU to compute a Faust norm and the dense array corresponding to the product of its factors:

cpuF = matfaust.rand(1024, 1024, 'num_factors', 10, 'fac_type', 'dense');

timeit(@() norm(cpuF, 2))

ans = 0.1806

timeit(@() full(cpuF))

ans = 0.9955

Now let’s make some GPU heat with norms and matrix products!

gpuF = clone(cpuF, 'dev', 'gpu');

timeit(@() norm(gpuF, 2))

ans = 0.0312

timeit(@() full(gpuF))

ans = 0.1873

Of course not all GPUs are equal. For example, on a Tesla V100 I've got respectively 7.6e-3 and 1.03e-2 seconds for the 2-norm and the full array.

Likewise let’s compare the performance obtained for a sparse Faust:

cpuF2 = matfaust.rand(1024, 1024, 'num_factors', 10, 'fac_type', 'sparse');

gpuF2 = clone(cpuF2, 'dev', 'gpu');

timeit(@() norm(gpuF2, 2))

ans = 0.0050

timeit(@() full(gpuF2))

ans = 0.0196

Some of the FAµST algorithms implemented in the C++ core are now also available in pure GPU mode.

For example, let’s compare the factorization times taken by the hierarchical factorization when launched on CPU and GPU.

When running on GPU, the matrix to factorize is copied in GPU memory and almost all operations executed during the algorithm don’t imply the CPU in any manner (the only exception at this stage of development is the proximal operators that only run on CPU).

First please copy the following function in the appropriate filename factorize_MEG.m into in the current working directory of Matlab (or by adding the destination directory to your path by calling addpath).

function [MEG16, total_time, err] = factorize_MEG(dev)

import matfaust.fact.hierarchical

import matfaust.factparams.ParamsHierarchicalRectMat

load('matrix_MEG.mat')

MEG = matrix.';

num_facts = 9;

k = 10;

s = 8;

tic

p = ParamsHierarchicalRectMat.createParams(MEG, {'rectmat', num_facts, k, s});

MEG16 = hierarchical(MEG, p, 'backend', 2020, 'gpu', strcmp(dev, 'gpu'));

total_time = toc;

err = norm(MEG16-MEG, 'fro')/norm(MEG, 'fro');

end

Now we can run the hierarchical algorithm on CPU and then GPU. For more information about this algorithm please consult the API doc.

Warning: THE COMPUTATION CAN LAST TEN TO THIRTY MINUTES OR SO ON CPU

[MEG16, total_time, err] = factorize_MEG('cpu')

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Faust::hierarchical: 6/8
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Faust::hierarchical: 7/8
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MEG16 =

Faust size 204x8193, density 0.0631655, nnz_sum 105573, 9 factor(s):
- FACTOR 0 (double) DENSE, size 204x204, density 0.293613, nnz 12219
- FACTOR 1 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 2 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 3 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 4 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 5 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 6 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 7 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 8 (double) DENSE, size 204x8193, density 0.0490196, nnz 81930

total_time = 715.0017

err = 0.1291

[MEG16, total_time, err] = factorize_MEG('gpu')

Faust::hierarchical: 1/8
Faust::hierarchical: 2/8
Faust::hierarchical: 3/8
Faust::hierarchical: 4/8
Faust::hierarchical: 5/8
Faust::hierarchical: 6/8
Faust::hierarchical: 7/8
Faust::hierarchical: 8/8

MEG16 =

Faust size 204x8193, density 0.0631655, nnz_sum 105573, 9 factor(s):
- FACTOR 0 (double) DENSE, size 204x204, density 0.293613, nnz 12219
- FACTOR 1 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 2 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 3 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 4 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 5 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 6 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 7 (double) DENSE, size 204x204, density 0.0392157, nnz 1632
- FACTOR 8 (double) DENSE, size 204x8193, density 0.0490196, nnz 81930

total_time = 168.5770

err = 0.1291

For the comparison here are the results I got on a Tesla V100 GPU:

[~, total_time, err] = factorize_MEG('gpu')

total_time =

49.49

err =

0.1296

As you see it’s far faster than with the CPU!

If something goes wrong when trying to use the GPU matfaust extension, here is how to manually load the module and obtain more information.

This function allows to give another try to gpu_mod loading with the verbose mode enabled.

Below I copy output that show what it should look like when it doesn’t work:

matfaust.enable_gpu_mod('silent', false)

Output:

WARNING: you must call enable_gpu_mod() before using GPUModHandler singleton.

loading libgm

libgm.so: cannot open shared object file: No such file or directory

NOTE: this tutorial was made upon the following FAµST version

matfaust.version()

ans = '3.38.9'