Polynomial Features

Expand features into powers $1,\dots ,d1,\backslash dots,d$. A length-$nn$ vector x becomes an $n\times dn\backslash times\; d$ matrix whose column $jj$ is $x^{j}x^\{j\}$. A 2-D input is expanded block by block: all columns to the power 1, then all columns to the power 2, and so on.

Implement solve(x,degree).

Returns. Return a float NumPy array. For a vector of length $nn$ the shape is $n\times \text{degree}n\backslash times\backslash text\{degree\}$.

Examples

Example 1

Input:

solve([1.0, 2.0, 3.0], 3)

Output:

[[1.0, 1.0, 1.0], [2.0, 4.0, 8.0], [3.0, 9.0, 27.0]]

Example 2

Input:

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

Output:

[[1.0, 2.0, 1.0, 4.0], [3.0, 4.0, 9.0, 16.0]]