#<GRADED> def findknn(xTr,xTe,k): """ function [indices,dists]=findknn(xTr,xTe,k); Finds the k nearest neighbors of xTe in xTr. Input: xTr = nxd input matrix with n row-vectors of dimensionality d xTe = mxd input matrix with m row-vectors of dimensionality d k = number of nearest neighbors to be found Output: indices = kxm matrix, where indices(i,j) is the i^th nearest neighbor of xTe(j,:) dists = Euclidean distances to the respective nearest neighbors """ # Enter your code here raise NotImplementedError('Your code goes here!') return indices, dists # until here #</GRADED> without using the for loop in python

To implement the findknn function without using a for loop, we can use numpy's broadcasting and vectorized operations. Here's how you can do it:

import numpy as np

def findknn(xTr, xTe, k):
    # Compute all pairwise distances between xTr and xTe
    dists = np.sqrt(np.sum((xTr[:, np.newaxis] - xTe)**2, axis=2))

    # Get the indices of the k smallest distances for each test point
    indices = np.argpartition(dists, k, axis=0)[:k]

    # Sort the indices and distances along the first axis
    sorted_indices = np.argsort(dists[indices, np.arange(dists.shape[1])], axis=0)
    indices = indices[sorted_indices, np.arange(dists.shape[1])]
    dists = dists[indices, np.arange(dists.shape[1])]

    return indices, dists

In this code, we first compute all pairwise distances between the training and test points. Then, we use np.argpartition to get the indices of the k smallest distances for each test point. Finally, we sort the indices and distances along the first axis to get the k nearest neighbors and their distances for each test point.