The r2_score function in the hana_ml.algorithms.pal.metrics module computes the coefficient of determination for regression results, taking a DataFrame of true and predicted values, and the names of the columns containing these values, and returning a float that indicates the accuracy of the regression, with 1.0 being an exact match.
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Here is a Python code template based on the provided help documentation:

```python
# Import necessary libraries
from hana_ml.algorithms.pal.metrics import r2_score
from hana_ml import DataFrame

# Assuming that connection_context is already defined
# Create DataFrame for actual and predicted values
df = DataFrame(connection_context, 'SELECT * FROM <your_table>')

# Compute R2 score
r2 = r2_score(data=df, label_true='ACTUAL', label_pred='PREDICTED')
print("R2 Score: ", r2)

# Create DataFrame for perfect predictions
df_perfect = DataFrame(connection_context, 'SELECT * FROM <your_perfect_table>')

# Compute R2 score for perfect predictions
r2_perfect = r2_score(data=df_perfect, label_true='ACTUAL', label_pred='PREDICTED')
print("R2 Score for Perfect Predictions: ", r2_perfect)

# Create DataFrame for mean predictions
df_mean = DataFrame(connection_context, 'SELECT * FROM <your_mean_table>')

# Compute R2 score for mean predictions
r2_mean = r2_score(data=df_mean, label_true='ACTUAL', label_pred='PREDICTED')
print("R2 Score for Mean Predictions: ", r2_mean)

# Create DataFrame for awful predictions
df_awful = DataFrame(connection_context, 'SELECT * FROM <your_awful_table>')

# Compute R2 score for awful predictions
r2_awful = r2_score(data=df_awful, label_true='ACTUAL', label_pred='PREDICTED')
print("R2 Score for Awful Predictions: ", r2_awful)
```

Please replace `<your_table>`, `<your_perfect_table>`, `<your_mean_table>`, and `<your_awful_table>` with your actual table names. Also, ensure that `connection_context` is defined and connected to your HANA database.