Update documentations

Author: Radonirinaunimi

docs/cli-tutorials.md

@@ -64,7 +64,7 @@ neopdf read num_subgrids --pdf-name NNPDF40_nnlo_as_01180
 To get the knot values for a given subgrid:
 
 ```bash
-neopdf read subgrid_info --pdf-name NNPDF40_nnlo_as_01180 --member 0 --subgrid-index 1
+neopdf read subgrid-info --pdf-name NNPDF40_nnlo_as_01180 --member 0 --subgrid-index 1
 ```
 
 - `--pdf-name`: Name of the PDF set.
@@ -74,13 +74,18 @@ neopdf read subgrid_info --pdf-name NNPDF40_nnlo_as_01180 --member 0 --subgrid-i
 The above command will print out the following output:
 
 ```yaml
-Nucleon Numbers A: [1.0], shape=[1], strides=[1], layout=CFcf (0xf), const ndim=1
-Alphas values: [0.118], shape=[1], strides=[1], layout=CFcf (0xf), const ndim=1
+Nucleon Numbers A: [0.0], shape=[1], strides=[1], layout=CFcf (0xf), const ndim=1
+Alphas values: [0.0], shape=[1], strides=[1], layout=CFcf (0xf), const ndim=1
 kT values: [0.0], shape=[1], strides=[1], layout=CFcf (0xf), const ndim=1
 x values: [1e-9, 1.2970848e-9, ...], shape=[196], strides=[1], layout=CFcf (0xf), const ndim=1
 Q2 values: [2.7224999999999997, ...], shape=[12], strides=[1], layout=CFcf (0xf), const ndim=1
 ```
 
+!!! note
+
+    Note that the values of `A` and `alphas` are set to zero by default as there is no
+    proper way to extract their values from LHAPDF.
+
 ### Updating Grid Metadata
 
 The metadata of a given `NeoPDF` grid can be updated by running the following command:
@@ -242,3 +247,39 @@ neopdf compute xfx_q2 --pdf-name NNPDF40_nnlo.neopdf.lz4 --member 0 --pid 21 0.1
     ```
 
     This approach is not fullproof and some PDF sets might not be supported at all.
+
+---
+
+## Inspecting subgrid contents
+
+The contents of the subgrids can be printed into human-readable format. Given that a set might contain
+multiple subgrids (as we have seen before using the `subgrid-info` command), it is instructive to check
+first how many subgrids a given set member contains.
+
+```bash
+> neopdf read num_subgrids --pdf-name NNPDF40_nnlo_as_01180.neopdf.lz4
+
+2
+```
+
+We can look at the contents of the first subgrid for the **gluon** PDF:
+
+```bash
+> neopdf read subgrid --pdf-name NNPDF40_nnlo_as_01180.neopdf.lz4 --member 0 --subgrid-index 0 --pid 21
+
+  [x | Q2]   2.72250e0   3.19494e0   3.77488e0   4.49175e0   5.38430e0   6.50400e0   7.91974e0
+1.00000e-9  1.48441e-1  -1.47266e0  -3.42816e0  -5.57841e0  -7.73893e0  -9.65268e0  -1.10375e1
+1.29708e-9  1.53954e-1  -1.36579e0  -3.16487e0  -5.10066e0  -6.98714e0  -8.57386e0  -9.57904e0
+1.68243e-9  1.59670e-1  -1.26122e0  -2.90961e0  -4.64076e0  -6.26809e0  -7.54804e0  -8.20073e0
+2.18225e-9  1.65601e-1  -1.15891e0  -2.66220e0  -4.19823e0  -5.58080e0  -6.57342e0  -6.89951e0
+2.83057e-9  1.71754e-1  -1.05882e0  -2.42248e0  -3.77263e0  -4.92430e0  -5.64825e0  -5.67242e0
+3.67149e-9  1.78142e-1 -9.60911e-1  -2.19028e0  -3.36352e0  -4.29764e0  -4.77083e0  -4.51658e0
+...
+  [x | Q2]   9.72449e0   1.20449e1   1.50550e1   1.89961e1   2.42064e1
+1.00000e-9  -1.15252e1  -1.06011e1  -7.88260e0  -2.66303e0   5.44604e0
+1.29708e-9  -9.64489e0  -8.29955e0  -5.12278e0  5.21491e-1   8.89615e0
+1.68243e-9  -7.87939e0  -6.15103e0  -2.56742e0   3.44402e0   1.20386e1
+2.18225e-9  -6.22381e0  -4.14868e0 -2.06304e-1   6.11881e0   1.48905e1
+2.83057e-9  -4.67345e0  -2.28589e0   1.97036e0   8.55949e0   1.74680e1
+...
+```

docs/custom.css

@@ -99,3 +99,10 @@ div.highlight pre,
 pre {
     font-size: 1.06em !important;
 }
+
+.center-medium {
+    display: block;
+    margin: 0 auto;
+    width: 75%;
+    height: auto;
+}

docs/design-and-features.md

@@ -32,8 +32,8 @@ and future plans.
   </tr>
   <tr>
     <td style="border: 1px solid #888;">Fortran API</td>
-    <td style="border: 1px solid #888;">❌</td>
-    <td style="border: 1px solid #888;">Not yet implemented</td>
+    <td style="border: 1px solid #888;">✅</td>
+    <td style="border: 1px solid #888;">Fully supported</td>
   </tr>
   <tr>
     <td rowspan="7" style="text-align: center; vertical-align: middle; border: 1px solid #888;">Features</td>
@@ -242,22 +242,6 @@ into diverse computational workflows:
 This compatibility is crucial for the physics community, as it allows for immediate adoption
 without requiring extensive code rewrites or validation efforts.
 
-### Thread and Memory Safety
-
-`NeoPDF` leverages Rust's safety guarantees for robust multi-threaded applications:
-
-- **Memory Safety**:
-  Rust's ownership system prevents common memory errors (use-after-free, double-free, data races)
-  that could lead to incorrect physics results or program crashes.
-
-- **Thread Safety**:
-  Built-in support for safe concurrent access to PDF objects, essential for parallel event
-  generation and Monte Carlo simulations.
-
-- **FFI Safety**:
-  Careful design of the foreign function interface ensures that safety guarantees extend to Python,
-  C, and C++ code, preventing crashes and undefined behavior.
-
 ### Extensible Interpolation
 
 `NeoPDF`'s modular architecture enables easy extension and customization:
@@ -294,6 +278,22 @@ without requiring extensive code rewrites or validation efforts.
   Comprehensive benchmarking against LHAPDF ensures that performance improvements don't come at the
   cost of accuracy, maintaining the precision required for physics calculations.
 
+### Thread and Memory Safety
+
+`NeoPDF` leverages Rust's safety guarantees for robust multi-threaded applications:
+
+- **Memory Safety**:
+  Rust's ownership system prevents common memory errors (use-after-free, double-free, data races)
+  that could lead to incorrect physics results or program crashes.
+
+- **Thread Safety**:
+  Built-in support for safe concurrent access to PDF objects, essential for parallel event
+  generation and Monte Carlo simulations.
+
+- **FFI Safety**:
+  Careful design of the foreign function interface ensures that safety guarantees extend to Python,
+  C, and C++ code, preventing crashes and undefined behavior.
+
 ## Architecture Overview
 
 ```mermaid
@@ -321,4 +321,5 @@ Lower-dimensional (bilinear, (log)-tricubic) are also available for performance
     The difference between NeoPDF and LHAPDF, using the default interpolation, is **below machine
     precision** for floating-point numbers.
 
-    ![diff_NNPDF40_nnlo_as_01180_flav21](https://github.com/user-attachments/assets/d47bfa13-9930-4247-89fb-f2c2eab68bd7)
+    ![as_x](https://github.com/user-attachments/assets/90faf0ad-bbaf-4917-81e1-fb4edd351766)
+    ![as_q](https://github.com/user-attachments/assets/3cbeecfe-9e12-4900-99ad-dd92d8bcf299)

docs/design.md

@@ -18,7 +18,7 @@ respectively.
   built for each subgrid and flavor, supporting log-space and linear strategies for high accuracy.
 
 Therefore, using the notations from [[2112.09703](https://arxiv.org/pdf/2112.09703)], the full
-`GridArray`, which is a conjunction of $k$ subgrids, can be represented as:
+`GridArray` (for 1D grid), which is a conjunction of $k$ subgrids, can be represented as:
 
 $$ \left[ z_0, z_1, \cdots, z_{\mathrm{max}} \right]_{\left( n_1, n_2, \cdots, n_k \right)} \qquad \text{with} \qquad z=A, \alpha_s, k_T, x, Q^2 $$
 
@@ -28,9 +28,10 @@ points is $n_{\mathrm{pts}} = \sum_i n_i - (k - i)$.
 
 The diagram below schematically summarizes the `NeoPDF` data structure:
 
-![data-structure](https://github.com/user-attachments/assets/dff9a9cd-ce24-485e-a08c-106f2845b437)
+![grid](https://github.com/user-attachments/assets/0637f61f-348f-4507-a6f5-08fac127368f){ .center-medium }
 
-where the `GridArray` object represents an instance of a set member.
+where the `GridArray` object represents an instance of a set member. The subgrid $S_k$ is a
+**hyperrectangle** given by the **Cartesian** product of the dependent variables.
 
 This design enables:
 
@@ -64,7 +65,7 @@ by half the size of a given LHAPDF PDF set:
 | NNPDF4.0 NNLO      | 100         | 158 MB        | 85 MB  |
 | NNPDF4.0 NNLO      | 1000        | 1.55 GB       | 830 MB |
 | Combined nNNPDF3.0 | 200         | -             | 1.43 GB|
-| MAP22 FF @N3LL     | 250         | 2.50 GB       | 1.65 GB|
+| MAP22 FF @N3LL     | 250         | 2.50 GB       | 950 MB |
 
 !!! info "Note"