PCA Reconstruction

Reconstruct data from its PCA coordinates: map the k retained coordinates back to the original feature space and add the mean back, $\widehat{X}=ZV[:,:k{]}^{\mathrm{\top }}+\mu \backslash hat\; X=Z\backslash ,V[:,\; :k]^\backslash top+\backslash mu$.

Implement solve(Z, components, k, mean).

Returns. Return an $n\times dn\backslash times\; d$ NumPy array.

Examples

Example 1

Input:

solve([[1.0], [3.0]], [[1.0, 0.0], [0.0, 1.0]], 1, [10.0, 20.0])

Output:

[[11.0, 20.0], [13.0, 20.0]]

Example 2

Input:

solve([[2.0, -1.0]], [[0.0, 1.0], [1.0, 0.0]], 2, [0.0, 0.0])

Output:

[[-1.0, 2.0]]