Roofline Model Analysis for GPU Operations

Implement a function that performs Roofline Model analysis for a set of GPU operations given hardware specifications. The Roofline Model is a visual performance model used to determine whether a computational kernel is compute bound or memory bound on a given hardware platform. It provides an upper bound on attainable performance based on the interplay between peak computational throughput and peak memory bandwidth. Your function should accept: peak gflops: Peak computational throughput of the GPU in GFLOPS (giga floating point operations per second) peak bandwidth gbs: Peak memory bandwidth in GB/s (gigabytes per second) operations: A list of dictionaries, each with keys 'name' (string), 'flops' (total floating point operations as float), and 'bytes' (total bytes transferred as float) Your function should return a dictionary containing: 'ridge point': The operational intensity (FLOP/byte) at which the hardware transitions from memory bound to compute bound behavior 'operations': A list of dictionaries, one per input operation, each containing: 'name': The operation name 'operational intensity': The ratio of FLOPs to bytes for this operation (FLOP/byte) 'attainable gflops': The maximum achievable performance in GFLOPS for this operation on the given hardware 'bottleneck': Either 'compute bound' or 'memory bound', indicating which resource limits the operation. An operation whose operational intensity is at or above the ridge point is considered compute bound. 'efficiency': The percentage of peak compute that this operation can achieve (0 to 100) Use only Python standard library and/or NumPy.