Add documentation

VERSION

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-0.0.10
+0.0.11

docs/data.md

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+# Data Generation
+
+In order to create process curves with a realistic behaviour of process drifts, `driftbench`
+synthesizes curves by solving nonlinear optimization problems. By defining a function $f(w(t), t)$ 
+and support points $x$ and $y$, we can solve for the internal parameters $w(t)$ such that 
+all the conditions given by the support points are satisfied. The schema is explained in
+the following section.
+
+![Example curve](./figures/example_curve.png)
+
+## Synthetization 
+In the first step, we need to define latent information which encodes the shape of the curves
+to synthesize. This is done by formulating such a spec in a `yaml`-file.
+For example, the following spec defines a polynomial of 7-th degree:
+```yaml
+example:
+  N: 10000
+  dimensions: 100
+  x_scale: 0.2 
+  y_scale: 0.2
+  func: w[7]* x**7 + w[6]* x**6 + w[5]* x**5 +w[4]* x**4 + w[3] * x**3 + w[2] * x**2 + w[1] * x + w[0]
+  w_init: np.zeros(8)
+  latent_information:
+    !LatentInformation
+    x0: [0, 1, 3, 2, 4]
+    y0: [0, 4, 7, 5, 0]
+    x1: [1, 3]
+    y1: [0, 0]
+    x2: [1]
+    y2: [0]
+  drifts:
+    !DriftSequence
+      - !LinearDrift
+        start: 1000
+        end: 1100
+        feature: y0     
+        dimension: 2    
+        m: 0.002
+```
+The root key defines the name of the dataset, in this case `example`.
+The other keys of this `yaml` structure are:
+
+- `N`: The number of curves to synthesize.
+- `dimensions`: The number of timesteps one curve consists of.
+- `x_scale`: The scale of a random gaussian noise which is applied to the `x`-latent information.
+If set to 0, no scale noise is applied.
+- `y_scale`: The scale of a random gaussian noise which is applied to the `y`-latent information.
+If set to 0, no scale noise is applied.
+- `func`: The function which defines the shape of a curve. The internal parameters are denoted as
+`w`, while the timesteps which are used to evaluate the curve are denoted as `x`.
+- `w_init`: The initial guess for the internal parameters. Must match the number of internal
+parameters defined in `func`.
+- `latent_information`: Contains a `LatentInformation` structure, which holds the latent information
+which defines the support points of the curves. The `x_i`denote the `x`-information for the `i`-th
+derivative of `func`, while the `y_i`denote the `y`-information respectively.
+- `drifts`: Contains a [`DriftSequence`][driftbench.data_generation.drifts.DriftSequence] structure, which in turn holds a list of drifts, for example
+`LinearDrift`-structures. These drifts are applied in the specified manner on the latent 
+information for each timestep defined as `start` as `end` within the `N` curves. The drift structure 
+defines the `feature` and the `dimension` as well as internal parameters, like in this case 
+the slope `m`.
+
+After setting up such an input, you can call the `sample_curves`-function, and retrieve the
+coefficients, respective latent information and curve for each timestep.
+```python
+coefficients, latent_information, curves = sample_curves(dataset["example"], measurement_scale=0.1)
+```
+By specifying a value for `measurment_scale` some gaussian noise witht the specified scale is applied
+on each value for every curve. By default, $5\%$ of the mean of the curves is used. If you want to
+omit the scale, set it to `0.0` explictly.

mkdocs.yml

@@ -39,6 +39,10 @@ markdown_extensions:
           class: mermaid
           format: !!python/name:pymdownx.superfences.fence_code_format
 
+extra_javascript:
+  - javascripts/mathjax.js
+  - https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js
+
 nav:
   - About: index.md
   - Data generation: data.md