docs: Add example in Livebook format

README.md

@@ -60,6 +60,10 @@ components = Soothsayer.predict_components(fitted_model, Series.from_list(Enum.t
 #> %{comboned: ..., trend: ..., yearly_seasonality: ..., weekly_seasonality: ...}
 ```
 
+### Livebook Example
+
+You can check the `livebook` dir with some examples on how to use Soothsayer.
+
 ### Customizing the Model
 
 You can customize various aspects of the model:

livebook/soothsayer_demo_1_1_1.livemd

@@ -0,0 +1,222 @@
+# Soothsayer Demo
+
+```elixir
+# Livebook Setup
+
+Mix.install([
+  {:soothsayer, path: "~/code/soothsayer"},
+  {:explorer, "~> 0.9.1"},
+  {:vega_lite, ">= 0.0.0"},
+  {:kino_vega_lite, ">= 0.0.0"},
+  {:kino_explorer, "~> 0.1.20"},
+  {:req, "~> 0.5.6"}
+])
+
+alias Explorer.DataFrame
+alias Explorer.Series
+alias VegaLite, as: Vl
+
+Nx.global_default_backend(EXLA.Backend)
+```
+
+## Section
+
+```elixir
+# Generate synthetic data
+
+start_date = ~D[2020-01-01]
+end_date = ~D[2023-12-31]
+dates = Date.range(start_date, end_date)
+
+y =
+  Enum.map(dates, fn date ->
+    days_since_start = Date.diff(date, start_date)
+    trend = 1000 + 0.5 * days_since_start
+    yearly_seasonality = 50 * :math.sin(2 * :math.pi() * days_since_start / 365.25)
+    weekly_seasonality = 20 * :math.cos(2 * :math.pi() * Date.day_of_week(date) / 7)
+    noise = :rand.normal(0, 200)
+    trend + yearly_seasonality + weekly_seasonality + noise
+  end)
+
+df = DataFrame.new(%{"ds" => dates, "y" => y})
+```
+
+<!-- livebook:{"attrs":"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","chunks":null,"kind":"Elixir.KinoVegaLite.ChartCell","livebook_object":"smart_cell"} -->
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(df, only: ["ds", "y"])
+|> Vl.mark(:line)
+|> Vl.encode_field(:x, "ds", type: :temporal)
+|> Vl.encode_field(:y, "y", type: :quantitative)
+```
+
+```elixir
+# Create and fit Soothsayer model
+
+model =
+  Soothsayer.new(%{
+    trend_config: %{enabled: true},
+    seasonality_config: %{
+      yearly: %{enabled: true},
+      weekly: %{enabled: true}
+    },
+    epochs: 10
+  })
+
+fitted_model = Soothsayer.fit(model, df)
+```
+
+```elixir
+# Make predictions and extract components
+predictions = Soothsayer.predict(fitted_model, df["ds"])
+
+df_with_predictions =
+  df
+  |> DataFrame.put("yhat", predictions)
+
+df_with_predictions
+```
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(df_with_predictions, only: ["ds", "y", "yhat"])
+|> Vl.layers([
+  Vl.new()
+  |> Vl.mark(:line)
+  |> Vl.encode_field(:x, "ds", type: :temporal)
+  |> Vl.encode_field(:y, "y", type: :quantitative),
+  Vl.new()
+  |> Vl.mark(:line, color: "tomato")
+  |> Vl.encode_field(:x, "ds", type: :temporal)
+  |> Vl.encode_field(:y, "yhat", type: :quantitative)
+])
+```
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(df_with_predictions, only: ["ds", "y", "yhat"])
+|> Vl.layers([
+  Vl.new()
+  |> Vl.mark(:line)
+  |> Vl.encode_field(:x, "ds",
+    type: :temporal,
+    scale: [domain: ["2023-05-01", "2023-06-30"]]
+  )
+  |> Vl.encode_field(:y, "y", type: :quantitative),
+  Vl.new()
+  |> Vl.mark(:line, color: "tomato")
+  |> Vl.encode_field(:x, "ds",
+    type: :temporal,
+    scale: [domain: ["2023-05-01", "2023-06-30"]]
+  )
+  |> Vl.encode_field(:y, "yhat", type: :quantitative)
+])
+```
+
+```elixir
+input = %{
+  "trend" => Nx.template({1, 1}, :f32),
+  "yearly" => Nx.template({1, 12}, :f32),  # Assuming 6 Fourier terms for yearly seasonality
+  "weekly" => Nx.template({1, 6}, :f32)    # Assuming 3 Fourier terms for weekly seasonality
+}
+
+# Display the graph
+Axon.Display.as_graph(model.network, input)
+```
+
+```elixir
+components = Soothsayer.predict_components(fitted_model, df["ds"])
+
+df_with_components =
+  df
+  |> DataFrame.put("yhat", predictions)
+  |> DataFrame.put("trend", components.trend)
+  |> DataFrame.put("yearly_seasonality", components.yearly_seasonality)
+  |> DataFrame.put("weekly_seasonality", components.weekly_seasonality)
+```
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(df_with_components)
+|> Vl.layers([
+  Vl.new()
+  |> Vl.mark(:line)
+  |> Vl.encode_field(:x, "ds", type: :temporal)
+  |> Vl.encode_field(:y, "trend", type: :quantitative),
+])
+```
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(df_with_components)
+|> Vl.layers([
+  Vl.new()
+  |> Vl.mark(:line)
+  |> Vl.encode_field(:x, "ds", type: :temporal)
+  |> Vl.encode_field(:y, "yearly_seasonality", type: :quantitative),
+])
+```
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(df_with_components)
+|> Vl.layers([
+  Vl.new()
+  |> Vl.mark(:line)
+  |> Vl.encode_field(:x, "ds", type: :temporal, scale: [domain: ["2023-01-01", "2023-06-30"]])
+  |> Vl.encode_field(:y, "weekly_seasonality", type: :quantitative, scale: [domain: [1000, 1400]])
+])
+```
+
+## Real data
+
+Daily energy price data over the 4 years from Spain.
+
+```elixir
+real_df = DataFrame.from_csv!("https://raw.githubusercontent.com/ourownstory/neuralprophet-data/main/kaggle-energy/datasets/tutorial01.csv")
+
+real_df =
+  real_df
+  |> DataFrame.put("ds", real_df["ds"] |> Explorer.Series.cast(:date))
+```
+
+<!-- livebook:{"attrs":"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","chunks":null,"kind":"Elixir.KinoVegaLite.ChartCell","livebook_object":"smart_cell"} -->
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(real_df, only: ["ds", "y"])
+|> Vl.mark(:point)
+|> Vl.encode_field(:x, "ds", type: :temporal)
+|> Vl.encode_field(:y, "y", type: :quantitative)
+```
+
+```elixir
+model = Soothsayer.new(%{epochs: 100})
+fitted_model = Soothsayer.fit(model, real_df)
+```
+
+```elixir
+predictions = Soothsayer.predict(fitted_model, real_df["ds"])
+
+real_df_with_predictions =
+  real_df
+  |> DataFrame.put("yhat", predictions)
+
+real_df_with_predictions
+```
+
+```elixir
+Vl.new(width: 800, height: 600)
+|> Vl.data_from_values(real_df_with_predictions, only: ["ds", "y", "yhat"])
+|> Vl.layers([
+  Vl.new()
+  |> Vl.mark(:line)
+  |> Vl.encode_field(:x, "ds", type: :temporal)
+  |> Vl.encode_field(:y, "y", type: :quantitative),
+  Vl.new()
+  |> Vl.mark(:line, color: "tomato")
+  |> Vl.encode_field(:x, "ds", type: :temporal)
+  |> Vl.encode_field(:y, "yhat", type: :quantitative)
+])
+```