def linear_trans2d(arr:list[list[float]],x:list[float]) -> list[float]:
    '''
    @param arr:
        [
            [a,b],
            [c,d]
        ]
        
    @param x:
        [x1,x2]
    
    @return
        arr times x
    '''
    return [x[0]*arr[0][0]+x[1]*arr[0][1], x[0]*arr[1][0]+x[1]*arr[1][1]]

def linear_trans(arr:list[list[float]],x:list[float]) -> list[float]:
    if len(arr) != len(x):
        raise ValueError("Shape must be same.")
    return [sum(map(lambda x: x[0]*x[1],zip(line,x))) for line in arr]

import numpy as np

def linear_trans_np(arr:np.ndarray,x:np.ndarray) -> np.ndarray:
    if not arr.shape[0] == arr.shape[1] == x.shape[0]:
        raise ValueError("Shape must be (k,k) and (k,)")
    return np.array([np.sum(line * x) for line in arr])

if __name__ == "__main__":
    # check code with np
    import numpy as np
    np.random.seed()
    
    for i in range(100):
        arr = np.random.random_sample((4,4))
        x = np.random.random_sample((4,))

        ans = np.dot(arr,x)
        out = linear_trans_np(arr,x)
        # print(out)
        # out = np.array(out)
        assert np.all(np.abs(ans-out)<0.0001)