How to test the GET method that takes parser inputs in flask/flask-restx?

Considering unit-testing tag, I'll present what I came up with on how you could test it in total isolation. Basically, get method makes two function calls on dependencies, so in unit sense, you have to check if these calls have indeed been made, as well as assert the arguments, right?

Project structure for purpose of the example:

+---Project
|   |   
|   |   __init__.py
|   |   config.py
|   |   dimension_calculator.py
|   |   parser_impl.py
|   |   user_output.py
|   |   user_output_test.py

So, everything is flat for simplicity.

Most importantly, you have to decouple your UserOutput module from dependencies. You shouldn't be hard-coding dependencies like that:

from .services.calculator import DimensionCalculator

Hypothetically, DimensionCalculator could contain complex business logic which shouldn't be in scope of the test. So, here's how the UserOutput module could look like:

from flask_restx import Resource, Api
from flask import Flask
from .config import Config

app = Flask(__name__)
api = Api(app)
ns = api.namespace('todos', description='TODO operations')

@ns.route("/output")
class UserOutput(Resource):
    @ns.expect(Config.get_parser_impl(), validation=True)
    def get(self):
        args = Config.get_parser_impl().parse_args()
        return Config.get_dimension_calculator_impl().inputs(**args)


if __name__ == '__main__':
    app.run(debug=True)

As you can see, "external" dependencies can now be easily stubbed (this is part of a common pattern called dependency injection). Config module looks as follows:

from .parser_impl import parser
from .dimension_calculator import DimensionCalculator


class Config(object):
    parser_impl = parser
    calculator = DimensionCalculator

    @staticmethod
    def configure_dimension_calculator_impl(impl):
        Config.calculator = impl

    @staticmethod
    def configure_parser_impl(impl):
        Config.parser_impl = impl

    @staticmethod
    def get_dimension_calculator_impl():
        return Config.calculator

    @staticmethod
    def get_parser_impl():
        return Config.parser_impl

Last, but not least, is the place where we'll be stubbing the dependencies and injecting them:

from .user_output import UserOutput
from flask import Flask
from .config import Config

class ParserStub(object):
    parse_args_call_count = 0
    @staticmethod
    def parse_args():
        ParserStub.parse_args_call_count = ParserStub.parse_args_call_count + 1
        return {'parser_stub': 2}

class DimensionCalculatorStub(object):
    inputs_call_count = 0
    @staticmethod
    def inputs(**args):
        DimensionCalculatorStub.inputs_call_count = DimensionCalculatorStub.inputs_call_count + 1
        return {'stub': 1}

app = Flask(__name__)

def test_user_request_get():
    with app.test_request_context():
        # given
        Config.configure_dimension_calculator_impl(DimensionCalculatorStub)
        Config.configure_parser_impl(ParserStub)
        uo = UserOutput()
        
        # when
        uo.get()
        
        # then
        assert DimensionCalculatorStub.inputs_call_count == 1
        assert ParserStub.parse_args_call_count == 1
        # assert arguments as well!

Test passes in my case. One thing missing is validation of arguments.

For completeness, I'll also include DimensionCalculator and the parser itself, though they are exactly the same as in your example. I've only modularized them:

from flask_restx import reqparse

parser = reqparse.RequestParser()
parser.add_argument("dimensions", type=float,
                    required=True,
                    action='split',
                    help="Dimensions of the rectangle (in meters)")
parser.add_argument("angle_inclination", type=float,
                    required=True,
                    action='append',
                    help="Angle of inclination of the Dachfläche (Neigung)")

and the dimension_calculator.py:

class DimensionCalculator:
    @staticmethod
    def inputs(**user_input):
        installation_place = user_input['installation_place']
        num_rectangles = user_input['num_rectangles']
        dimensions = user_input['dimensions']
        angle_inclination = user_input['angle_inclination']
        alignment = user_input['alignment']
        direction = user_input['direction']
        vendor = user_input['vendor']
        output = {
                    "installation_place": installation_place,
                    "num_rectangles": num_rectangles,
                    "area_shape": "EMPTY",
                    "vendor": vendor
                }
        return output

Important definitely there are dedicated frameworks for such stubs/mocks preparation and configuration (for example: https://pypi.org/project/pytest-mock/). I just wanted to present the concept and easiest approach possible.