[1.3. How to launch the demos with matfaust?](#mat_three)
[1.4. How can I launch the integrated unit tests of matfaust?](#mat_four)
[1.5. How to run the PALM4MSA algorithm in a step-by-step fashion?](#mat_five)
[2.6. Why this no_normalization parameter for PALM4MSA and hierarchical factorization?](#mat_six)
**2. About pyfaust:**
[2.1. How can I launch the integrated unit tests of pyfaust?](#py_one)
[2.2. How to launch the demos with pyfaust?](#py_two)
[2.3. How to run the PALM4MSA algorithm in a step-by-step fashion?](#py_three)
[2.4. Why do I get the error 'Library not loaded: @rpath/libomp.dylib' when I use pyfaust on Mac OS X and How to fix it?](#py_four)
[2.5. Why this no_normalization parameter for PALM4MSA and hierarchical factorization?](#py_five)
**3. About CUDA (for GPU FAµST API support)**
[3.1 Where can I find the CUDA 9 / 11 installer for my system?](#cuda_one)
[3.2 How do I need to configure the CUDA 9 / 11 installer on Windows 10?](#cuda_two)
# 1. About matfaust
\anchor mat_one
...
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@@ -170,13 +173,19 @@ And for the last and simplest demo, the [quickstart script](https://faustgrp.git
\anchor mat_four
## 1.4. How can I launch the integrated unit tests of matfaust?
TODO (in the meanwhile you can see the pyfaust entry)
TODO (in the meanwhile you can read the [pyfaust entry](#py_two))
\anchor mat_five
## 1.5. How to run the PALM4MSA algorithm in a step-by-step fashion?
TODO (in the meanwhile you can see the pyfaust entry)
TODO (in the meanwhile you can read the [pyfaust entry](#py_three))
\anchor mat_six
## 1.5 Why this no_normalization parameter for PALM4MSA and hierarchical factorization?
TODO (in the meanwhile you can read the [pyfaust entry](#py_five))
# 2. About pyfaust
\anchor py_one
...
...
@@ -267,6 +276,70 @@ Once Macports is installed, launch a terminal and type this command:
Note that starting from pyfaust 3.11.1 the libomp library is embedded in the pyfaust package, so you shouldn't meet this issue again for this version and the next.
\anchor py_five
## 2.5 Why this no_normalization parameter for PALM4MSA and hierarchical factorization?
Well, you must know that in PALM4MSA updating a factor consists to first applying the gradient on it and then passing the resulting matrix through a proximity operator to enforce the structure/sparsity. After this two stages, the prox output matrix is often normalized.
Experiments have shown that it is totally possible to fail the normalization stage when the norm of the matrix is too high to be a number (or at least to be encoded in a floating point data type), it is in fact infinite. So you might end up with a zero matrix after normalization. In other close cases it can give NaN as matrix elements.
Hence disabling the normalization can help to avoid those overflows. That's why this option has been added to the parameters in both [pyfaust](https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/classpyfaust_1_1factparams_1_1ParamsHierarchical.html#a663cfce79af6baa7006ee0af7006e18e) and [matfaust](https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/classmatfaust_1_1factparams_1_1ParamsHierarchical.html#a0e596bab0beffb2d5892fadbe3e185aa).
For example, running the hierarchical factorization algorithm on a Hadamard matrix of numpy dtype float32 and size 512x512 is a case where this kind of error occur.
Below I reproduce the code firstly with the normalization enabled and the error it produces, secondly without normalization to show that if fixes the issue.
Note that this new parameter is limited to the 2020 implementations of PALM4MSA and the hierarchical algorithm.
Error case:
from pyfaust import wht
from pyfaust.fact import hierarchical
from time import time
import numpy as np
dim = 512
H = wht(dim, dtype='float')
M = H.toarray()
F = hierarchical(M, 'hadamard', on_gpu=False, backend=2020)
print("error:", (F-H).norm()/H.norm())
Output:
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
terminate called after throwing an instance of 'std::runtime_error'
what(): Error in update_lambda: S (the Faust) contains nan elements in at least one of its matrices, can't compute lambda.
Aborted
Fixed case:
from pyfaust import wht
from pyfaust.fact import hierarchical
from pyfaust.factparams import ParamsHierarchicalSquareMat
from time import time
import numpy as np
dim = 512
H = wht(dim, dtype='float')
M = H.toarray()
p = ParamsHierarchicalSquareMat.createParams(M, 'hadamard')
p.no_normalization = True
F = hierarchical(M, p, on_gpu=False, backend=2020)
