diff --git a/gen_doc/Faust_factorization.html b/gen_doc/Faust_factorization.html
index d4126b2ea2157bbd36e74fedfb70350aa4ee0e4e..6e5679213371065be0b7a5ed97fb82f04eb41b2e 100644
--- a/gen_doc/Faust_factorization.html
+++ b/gen_doc/Faust_factorization.html
@@ -12111,7 +12111,7 @@ Actually, this is quite clear now I think, but this function implements the hiea
<strong>2.</strong> (the <em>global optimization</em>) At the end of each iteration $i$, PALM4MSA is called again to ideally compute the $argmin_{\{S_1, ..., S_i\}, R_i}$ $\|M - (\prod_{j=1}^i S_j) R_i\|$ </li>
<li>So ideally at the end of the iteration (J-1) you'll get something like $M \approx \prod_{i=1}^J S_i$ taking $S_J = R_{J-1} $.</li>
</ul>
-<h3 id="1.2.1-Defining-the-Constraints">1.2.1 Defining the Constraints<a class="anchor-link" href="#1.2.1-Defining-the-Constraints">¶</a></h3><p>The explanation above is eluding something primary: the sparsity constraints. Indeed, he purpose of the algorithm is not only to decompose a matrix but also to enhance its sparsity, as hinted by the FAµST acronym: Flexible Approximate Multi-layer Sparse Transform.</p>
+<h3 id="1.2.1-Defining-the-Constraints">1.2.1 Defining the Constraints<a class="anchor-link" href="#1.2.1-Defining-the-Constraints">¶</a></h3><p>The explanation above is eluding something primary: the sparsity constraints. Indeed, the purpose of the algorithm is not only to decompose a matrix but also to enhance its sparsity, as hinted by the FAµST acronym: Flexible Approximate Multi-layer Sparse Transform.</p>
<p>So you'll need to feed the algorithm with sparsity constraints. In fact, you'll define one pair of constraints per iteration, the first is for the factor $S_{i}$ and the second for $R_i$ (the <em>residuum</em>).</p>
<p>The pyfaust API is here to help you define the constraints in one shot but you can if you want define constraints one by one as we'll see later.</p>
<p>Let's unveil the factorization constraints to decompose the Hadamard matrix $H \in \mathbb R^{n \times n}$. Generally in pyfaust, the constraints are defined in terms of norms, in our case of Hadamard factorization we'll use 0-norms:</p>
@@ -12152,7 +12152,7 @@ Actually, this is quite clear now I think, but this function implements the hiea
<div class="text_cell_render border-box-sizing rendered_html">
<p>The <code>'splincol'</code> constraint used here is for defining the maximum number of nonzeros elements to respect for any row or column of the considered matrix (here $S_i$ or $R_i$).
Looking at <code>S_constraints</code> initialization, we see in the first line <code>'splincol', 2, n, n</code>; the value 2 means we impose 2 nonzeros per-column and per-row, the next arguments define the size of the matrix to constrain (its number of rows and columns).</p>
-<p>So in the example of <code>S_constraints</code> all the matrix will have a 0-norm equal to 2n, that is exactly what (C1) defined.<br/>
+<p>So in the example of <code>S_constraints</code> all the matrices will have a 0-norm equal to 2n, that is exactly what (C1) defined.<br/>
I let you decrypt why <code>R_constraints</code> correspond likewise to (C2).</p>
<p>But wait a minute, what would happen if we have a set of one hundred constraints? Don't worry! The pyfaust API allows to alternatively set the constraints one by one:</p>
@@ -12181,7 +12181,7 @@ I let you decrypt why <code>R_constraints</code> correspond likewise to (C2).</p
<p><code>S_constraints</code> and <code>R_constraints</code> are still the exact same set of constraints as before.</p>
<p><a href="https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/classpyfaust_1_1factparams_1_1ConstraintInt.html">ConstraintInt</a> is a family of integer constraints. More globally, there is a hierarchy of classes whose parent class is <a href="https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/classpyfaust_1_1factparams_1_1ConstraintGeneric.html">ConstraintGeneric</a> where you'll find other kind of constraints ; <a href="https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/classpyfaust_1_1factparams_1_1ConstraintMat.html">ConstraintMat</a>, <a href="https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/classpyfaust_1_1factparams_1_1ConstraintReal.html">ConstraintReal</a>.</p>
<p>The table <a href="https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/constraint.png">here</a> can give you an idea of each constraint definition. A constraint is always associated to a proximal operator which projects the matrix into the set of matrices defined by the constraint or at least it tries to (because it's not necessarily possible).</p>
-<p>In the last versions of FAµST it's possible to <code>project</code> matrices from the wrappers themselves, let's try one ConstraintInt:</p>
+<p>In the latest version of FAµST it's possible to <code>project</code> matrices from the wrappers themselves, let's try one ConstraintInt:</p>
</div>
</div>
diff --git a/gen_doc/Faust_factorization.ipynb b/gen_doc/Faust_factorization.ipynb
index a8e6bffef88f6cd79e81b736a70be52fba879324..66938d936a261c6107b7f9b6692d3668c586fb35 100644
--- a/gen_doc/Faust_factorization.ipynb
+++ b/gen_doc/Faust_factorization.ipynb
@@ -179,7 +179,7 @@
"\n",
"### 1.2.1 Defining the Constraints\n",
"\n",
- "The explanation above is eluding something primary: the sparsity constraints. Indeed, he purpose of the algorithm is not only to decompose a matrix but also to enhance its sparsity, as hinted by the FAµST acronym: Flexible Approximate Multi-layer Sparse Transform.\n",
+ "The explanation above is eluding something primary: the sparsity constraints. Indeed, the purpose of the algorithm is not only to decompose a matrix but also to enhance its sparsity, as hinted by the FAµST acronym: Flexible Approximate Multi-layer Sparse Transform.\n",
"\n",
"So you'll need to feed the algorithm with sparsity constraints. In fact, you'll define one pair of constraints per iteration, the first is for the factor $S_{i}$ and the second for $R_i$ (the _residuum_).\n",
"\n",
@@ -218,7 +218,7 @@
"The ```'splincol'``` constraint used here is for defining the maximum number of nonzeros elements to respect for any row or column of the considered matrix (here $S_i$ or $R_i$). \n",
"Looking at ```S_constraints``` initialization, we see in the first line ```'splincol', 2, n, n```; the value 2 means we impose 2 nonzeros per-column and per-row, the next arguments define the size of the matrix to constrain (its number of rows and columns). \n",
"\n",
- "So in the example of ```S_constraints``` all the matrix will have a 0-norm equal to 2n, that is exactly what (C1) defined.<br/>\n",
+ "So in the example of ```S_constraints``` all the matrices will have a 0-norm equal to 2n, that is exactly what (C1) defined.<br/>\n",
"I let you decrypt why ```R_constraints``` correspond likewise to (C2).\n",
"\n",
"But wait a minute, what would happen if we have a set of one hundred constraints? Don't worry! The pyfaust API allows to alternatively set the constraints one by one:\n"
@@ -245,7 +245,7 @@
"\n",
"The table [here](https://faustgrp.gitlabpages.inria.fr/faust/last-doc/html/constraint.png) can give you an idea of each constraint definition. A constraint is always associated to a proximal operator which projects the matrix into the set of matrices defined by the constraint or at least it tries to (because it's not necessarily possible).\n",
"\n",
- "In the last versions of FAµST it's possible to ```project``` matrices from the wrappers themselves, let's try one ConstraintInt:"
+ "In the latest version of FAµST it's possible to ```project``` matrices from the wrappers themselves, let's try one ConstraintInt:"
]
},
{
diff --git a/gen_doc/Faust_manipulation.html b/gen_doc/Faust_manipulation.html
index 2539a095f0f2c8bf2df309e6f3e26c524cd7e8fd..8ef37574a567e4260672e7e1c53f5ac4fb3cada5 100644
--- a/gen_doc/Faust_manipulation.html
+++ b/gen_doc/Faust_manipulation.html
@@ -13857,7 +13857,7 @@ ASAAAECQIQAEAAAIMv8fomx0rLQsLooAAAAASUVORK5CYII=
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<p>The FAµST API support equally the Faust to array addition and subtraction.</p>
+<p>The FAµST API supports equally the Faust to array addition and subtraction.</p>
</div>
</div>
@@ -14192,7 +14192,7 @@ FG is a Faust too!</p>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>Let's launch a timer to compare the execution times of Faust-vector multiplication and Faust's dense matrix-vector multiplication</p>
-<p>Note that appliying a Faust on a <code>numpy.ndarray</code> or a <code>numpy.matrix</code> can be done with the function dot(), the operator @ (python3 only) or * exactly as <code>numpy.matrix</code> allows. Indeed, a Faust is to be seen as a <code>numpy.matrix</code> not a <code>numpy.ndarray</code> (for the latter the two operators are not the same, * performs an elementwise multiplication while @ or dot() is the matrix product).</p>
+<p>Note that appliying a Faust on a <code>numpy.ndarray</code> or a <code>numpy.matrix</code> can be done with the function dot(), the operator @ (python3 only) or * exactly as <code>numpy.matrix</code> allows. Indeed, a Faust is to be seen as a <code>numpy.matrix</code> not a <code>numpy.ndarray</code> (for the latter the two operators are not the same, * performs an elementwise multiplication while @ and dot() are the matrix product).</p>
</div>
</div>
@@ -15298,7 +15298,7 @@ This function is really close to <code>numpy.linalg.norm</code> function.</p>
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
-<p>As you I'm sure you guessed that likewise you can concatenate Faust objects.</p>
+<p>I'm sure you guessed that likewise you can concatenate Faust objects. That's right!</p>
</div>
</div>
diff --git a/gen_doc/Faust_manipulation.ipynb b/gen_doc/Faust_manipulation.ipynb
index 8657097cffd48cc414e2ed828d504dbee832fdec..18f2ba38edd11a61e6f70c5edd2a8443316f6900 100644
--- a/gen_doc/Faust_manipulation.ipynb
+++ b/gen_doc/Faust_manipulation.ipynb
@@ -971,7 +971,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "The FAµST API support equally the Faust to array addition and subtraction."
+ "The FAµST API supports equally the Faust to array addition and subtraction."
]
},
{
@@ -1094,7 +1094,7 @@
"source": [
"Let's launch a timer to compare the execution times of Faust-vector multiplication and Faust's dense matrix-vector multiplication\n",
"\n",
- "Note that appliying a Faust on a ```numpy.ndarray``` or a ```numpy.matrix``` can be done with the function dot(), the operator @ (python3 only) or \\* exactly as ```numpy.matrix``` allows. Indeed, a Faust is to be seen as a ```numpy.matrix``` not a ```numpy.ndarray``` (for the latter the two operators are not the same, \\* performs an elementwise multiplication while @ or dot() is the matrix product)."
+ "Note that appliying a Faust on a ```numpy.ndarray``` or a ```numpy.matrix``` can be done with the function dot(), the operator @ (python3 only) or \\* exactly as ```numpy.matrix``` allows. Indeed, a Faust is to be seen as a ```numpy.matrix``` not a ```numpy.ndarray``` (for the latter the two operators are not the same, \\* performs an elementwise multiplication while @ and dot() are the matrix product)."
]
},
{
@@ -1505,7 +1505,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "As you I'm sure you guessed that likewise you can concatenate Faust objects."
+ "I'm sure you guessed that likewise you can concatenate Faust objects. That's right!"
]
},
{