import unittest
import numpy as np
import user_code  # ÐºÐ¾Ð´ ÑÑÑÐ´ÐµÐ½ÑÐ°

def _dynamic(tc, ok, ok_msg, fail_msg):
    tc._testMethodName = ok_msg if ok else fail_msg
    (tc.assertTrue if ok else tc.fail)(tc._testMethodName)

RTOL = 1e-7
ATOL = 1e-7

class TestCombinedTransformations(unittest.TestCase):

    def test_base_objects(self):
        reasons = []

        v = getattr(user_code, "v", None)
        S = getattr(user_code, "S", None)
        R = getattr(user_code, "R", None)

        # ÐÐµÑÐµÐ²ÑÑÐºÐ° Ð½Ð°ÑÐ²Ð½Ð¾ÑÑÑ ÑÐ° ÑÐ¾ÑÐ¼
        if not (isinstance(v, np.ndarray) and v.shape == (2,1)):
            reasons.append(f"v must be a (2,1) array; got {None if v is None else v.shape}")
        if not (isinstance(S, np.ndarray) and S.shape == (2,2)):
            reasons.append(f"S must be a (2,2) array; got {None if S is None else S.shape}")
        if not (isinstance(R, np.ndarray) and R.shape == (2,2)):
            reasons.append(f"R must be a (2,2) array; got {None if R is None else R.shape}")

        # ÐÑÑÐºÑÐ²Ð°Ð½Ñ Ð·Ð½Ð°ÑÐµÐ½Ð½Ñ Ð·Ð° ÑÐ¼Ð¾Ð²Ð¾Ñ
        v_exp = np.array([[2.0],[3.0]])
        S_exp = np.array([[2.0, 0.0],
                          [0.0, 0.5]])
        # ÐÐ»Ñ R Ð¾ÑÑÐºÑÑÐ¼Ð¾ 90Â° CCW: [[0,-1],[1,0]] Ð· Ð¼Ð¾Ð¶Ð»Ð¸Ð²Ð¾Ñ Ð¿Ð¾ÑÐ¸Ð±ÐºÐ¾Ñ
        R_exp = np.array([[0.0, -1.0],
                          [1.0,  0.0]])

        if isinstance(v, np.ndarray) and v.shape == (2,1) and not np.allclose(v, v_exp, rtol=RTOL, atol=ATOL):
            reasons.append(f"v values incorrect; expected {v_exp.ravel().tolist()}, got {v.ravel().tolist()}")
        if isinstance(S, np.ndarray) and S.shape == (2,2) and not np.allclose(S, S_exp, rtol=RTOL, atol=ATOL):
            reasons.append(f"S values incorrect; expected {S_exp.tolist()}, got {S.tolist()}")
        if isinstance(R, np.ndarray) and R.shape == (2,2) and not np.allclose(R, R_exp, rtol=1e-6, atol=1e-6):
            reasons.append(f"R should be 90Â° CCW rotation; expected approx {R_exp.tolist()}, got {R.tolist()}")

        _dynamic(self,
                 len(reasons) == 0,
                 "PASS: base objects (v, S, R) are correct",
                 "FAIL: " + " | ".join(reasons) if reasons else "FAIL")

    def test_scaled_vector(self):
        reasons = []

        v = getattr(user_code, "v", None)
        S = getattr(user_code, "S", None)
        scaled_v = getattr(user_code, "scaled_v", None)

        if not (isinstance(scaled_v, np.ndarray) and scaled_v.shape == (2,1)):
            reasons.append(f"scaled_v must be a (2,1) array; got {None if scaled_v is None else scaled_v.shape}")
        else:
            exp_scaled = S @ v
            if not np.allclose(scaled_v, exp_scaled, rtol=RTOL, atol=ATOL):
                reasons.append(f"scaled_v != S @ v; expected {exp_scaled.ravel().tolist()}, got {scaled_v.ravel().tolist()}")

        _dynamic(self,
                 len(reasons) == 0,
                 "PASS: scaled_v equals S @ v",
                 "FAIL: " + " | ".join(reasons) if reasons else "FAIL")

    def test_rotated_vector(self):
        reasons = []

        R = getattr(user_code, "R", None)
        scaled_v = getattr(user_code, "scaled_v", None)
        rotated_v = getattr(user_code, "rotated_v", None)

        if not (isinstance(rotated_v, np.ndarray) and rotated_v.shape == (2,1)):
            reasons.append(f"rotated_v must be a (2,1) array; got {None if rotated_v is None else rotated_v.shape}")
        else:
            exp_rot = R @ scaled_v
            if not np.allclose(rotated_v, exp_rot, rtol=1e-6, atol=1e-6):
                reasons.append(f"rotated_v != R @ scaled_v; expected {exp_rot.ravel().tolist()}, got {rotated_v.ravel().tolist()}")

            # ÐÐ¾Ð´Ð°ÑÐºÐ¾Ð²Ð¸Ð¹ ÑÐ¸ÑÐ»Ð¾Ð²Ð¸Ð¹ ÑÐµÐº Ð¾ÑÑÐºÑÐ²Ð°Ð½Ð¸Ñ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°Ñ (-1.5, 4)
            exp_num = np.array([[-1.5],[4.0]])
            if not np.allclose(rotated_v, exp_num, rtol=1e-6, atol=1e-6):
                reasons.append(f"rotated_v should be approximately [-1.5, 4]; got {rotated_v.ravel().tolist()}")

        _dynamic(self,
                 len(reasons) == 0,
                 "PASS: rotated_v equals R @ scaled_v and matches expected coords",
                 "FAIL: " + " | ".join(reasons) if reasons else "FAIL")


test_code.py

Master the mathematical foundations essential for data science. Explore core concepts in functions, calculus, linear algebra, probability, and dimensionality reduction. Build both theoretical understanding and practical coding experience to strengthen your ability to analyze data, model complex systems, and apply advanced techniques in machine learning.

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Build strong knowledge of vectors, matrices, and transformations. Learn decomposition methods and eigenvalue analysis, while reinforcing concepts with Python coding challenges and practical data science applications.

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Challenge: Combined Transformations of a Vector

Your task:

Solution

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Challenge: Combined Transformations of a Vector

Your task:

Solution