Implement 2D convolution using NumPy slicing
Company: NVIDIA
Role: Software Engineer
Category: Data Manipulation (SQL/Python)
Difficulty: medium
Interview Round: Technical Screen
Implement 2D convolution on a 4×4 input and a 3×3 filter with stride 1 using NumPy. Avoid explicit Python loops by relying on array slicing, broadcasting, or vectorization. Return the resulting 2×2 output array.
Overview: This question evaluates a candidate's proficiency with array manipulation and vectorized numerical computation using NumPy, focusing on 2D convolution concepts such as slicing, broadcasting, and filter application.
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You are given a 4x4 input matrix and a 3x3 convolution kernel, each stored as separate tables in row/column form. Implement a valid 2D convolution with stride 1 in SQL.
Definitions:
- The input matrix is 4x4, with rows and columns indexed from 1 to 4.
- The kernel (filter) is 3x3, with rows and columns indexed from 1 to 3.
- Use **valid** convolution with stride 1 (no padding), so the top-left of the kernel can start at positions (1,1), (1,2), (2,1), and (2,2) on the input.
- For an output position (out_row, out_col), the convolution value is:
SUM over kernel_row = 1..3 and kernel_col = 1..3 of
input_value(out_row + kernel_row - 1, out_col + kernel_col - 1) * kernel_weight(kernel_row, kernel_col)
Write a SQL query that returns the 2x2 output of this convolution as 4 rows with columns:
- out_row (INT)
- out_col (INT)
- conv_value (INT)
Use the provided tables and sample data below.
Tables
input_matrix(row_idx INT, col_idx INT, value INT)
kernel(kernel_row INT, kernel_col INT, weight INT)
Hints
- Generate the 4 valid output positions (out_row, out_col) using a VALUES clause or a small derived table.
- Join the kernel to the input_matrix by shifting input indices with (out_row + kernel_row - 1, out_col + kernel_col - 1), then aggregate the product of value and weight.