The function takes an input string and shifts all alphabetical characters two positions forward in the alphabet. Numbers and special characters remain unchanged.

[CODE]: 
```python
def encode_string(input_str):
    output_str = ""
    for char in input_str:
        if 'a' <= char <= 'z':
            output_str += chr(((ord(char) - ord('a') + 2) % 26) + ord('a'))
        elif 'A' <= char <= 'Z':
            output_str += chr(((ord(char) - ord('A') + 2) % 26) + ord('A'))
        else:
            output_str += char
    return output_str
```

This code defines a function `encode_string` that approximates the behavior observed in the given `function.py` script.