Low-Rank Reconstruction

Reconstruct a matrix from only its first $kk$ singular components (a truncated singular value decomposition).

Implement solve(A, k).

Returns. Return a NumPy array of the same shape as A. The rank k is clipped into the valid range, and k = 0 gives an all-zero matrix.

Examples

Example 1

Input:

solve([[3.0, 0.0], [0.0, 1.0]], 1)

Output:

[[3.0, 0.0], [0.0, 0.0]]

Example 2

Input:

solve([[1.0, 2.0], [3.0, 4.0]], 2)

Output:

[[1.0, 2.0], [3.0, 4.0]]