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feat: Add benchmarking and documentation updates for Metal SVD
- Add comprehensive SVD benchmark script (benchmarks/python/svd_benchmark.py): * Performance comparison between CPU and GPU implementations * Batch processing benchmarks * Correctness verification tests * Detailed timing and speedup analysis - Update linalg documentation to mention Metal GPU acceleration - Add implementation summary document for development reference This addresses CONTRIBUTING.md requirements: - Benchmarks for efficiency impact measurement (point 3) - Documentation updates for API changes (point 4) - Comprehensive testing coverage (point 2)
This commit is contained in:
Arkar Min Aung
parent
5875252f87
commit
6d01528e90
285
benchmarks/python/svd_benchmark.py
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285
benchmarks/python/svd_benchmark.py
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#!/usr/bin/env python3
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"""
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Benchmark script for SVD operations comparing CPU vs Metal performance.
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This benchmark should be run before and after the Metal SVD implementation
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to measure performance improvements.
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"""
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import time
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from typing import Dict, List, Tuple
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import mlx.core as mx
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import numpy as np
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def benchmark_svd_sizes() -> List[Tuple[int, int]]:
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"""Return list of matrix sizes to benchmark."""
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return [
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(32, 32),
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(64, 64),
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(128, 128),
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(256, 256),
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(512, 512),
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(1024, 1024),
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(64, 128),
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(128, 256),
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(256, 512),
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(512, 1024),
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]
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def create_test_matrix(m: int, n: int, dtype=mx.float32) -> mx.array:
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"""Create a test matrix with known properties for SVD."""
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# Create a matrix with controlled singular values for consistent benchmarking
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np.random.seed(42) # Fixed seed for reproducible results
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# Create matrix with known rank and condition number
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U = np.random.randn(m, min(m, n)).astype(np.float32)
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V = np.random.randn(min(m, n), n).astype(np.float32)
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# Create diagonal matrix with decreasing singular values
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s = np.logspace(0, -3, min(m, n)).astype(np.float32)
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S = np.diag(s)
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# Construct A = U @ S @ V
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if m >= n:
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A = U @ S @ V
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else:
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A = U @ S @ V[:m, :]
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return mx.array(A, dtype=dtype)
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def benchmark_svd_operation(
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matrix: mx.array,
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compute_uv: bool = True,
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device: str = "gpu",
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warmup_runs: int = 3,
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benchmark_runs: int = 10,
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) -> Dict[str, float]:
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"""Benchmark SVD operation with proper warmup and timing."""
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# Set device
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if device == "cpu":
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mx.set_default_device(mx.cpu)
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else:
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mx.set_default_device(mx.gpu)
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# Move matrix to target device
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matrix = mx.array(matrix, copy=True)
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# Warmup runs
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for _ in range(warmup_runs):
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if compute_uv:
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u, s, vt = mx.linalg.svd(matrix, compute_uv=True)
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mx.eval(u, s, vt)
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else:
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s = mx.linalg.svd(matrix, compute_uv=False)
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mx.eval(s)
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# Benchmark runs
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times = []
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for _ in range(benchmark_runs):
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start_time = time.perf_counter()
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if compute_uv:
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u, s, vt = mx.linalg.svd(matrix, compute_uv=True)
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mx.eval(u, s, vt)
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else:
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s = mx.linalg.svd(matrix, compute_uv=False)
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mx.eval(s)
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end_time = time.perf_counter()
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times.append(end_time - start_time)
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return {
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"mean_time": np.mean(times),
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"std_time": np.std(times),
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"min_time": np.min(times),
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"max_time": np.max(times),
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}
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def run_comprehensive_benchmark():
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"""Run comprehensive SVD benchmark comparing CPU and GPU performance."""
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print("MLX SVD Performance Benchmark")
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print("=" * 50)
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print(f"Device: {mx.default_device()}")
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print(f"MLX Version: {mx.__version__ if hasattr(mx, '__version__') else 'Unknown'}")
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print()
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sizes = benchmark_svd_sizes()
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results = []
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# Test both singular values only and full SVD
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for compute_uv in [False, True]:
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mode = "Full SVD" if compute_uv else "Singular Values Only"
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print(f"\n{mode}")
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print("-" * 30)
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print(
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f"{'Size':<12} {'CPU (ms)':<12} {'GPU (ms)':<12} {'Speedup':<10} {'Status'}"
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)
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print("-" * 60)
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for m, n in sizes:
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matrix = create_test_matrix(m, n)
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try:
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# CPU benchmark
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cpu_stats = benchmark_svd_operation(matrix, compute_uv, "cpu")
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cpu_time = cpu_stats["mean_time"] * 1000 # Convert to ms
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# GPU benchmark
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try:
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gpu_stats = benchmark_svd_operation(matrix, compute_uv, "gpu")
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gpu_time = gpu_stats["mean_time"] * 1000 # Convert to ms
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speedup = cpu_time / gpu_time
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status = "✓"
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except Exception as e:
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gpu_time = float("inf")
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speedup = 0.0
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status = f"✗ ({str(e)[:20]}...)"
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print(
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f"{m}x{n:<8} {cpu_time:<12.2f} {gpu_time:<12.2f} {speedup:<10.2f} {status}"
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)
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results.append(
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{
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"size": (m, n),
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"compute_uv": compute_uv,
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"cpu_time": cpu_time,
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"gpu_time": gpu_time,
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"speedup": speedup,
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"status": status,
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}
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)
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except Exception as e:
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print(
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f"{m}x{n:<8} {'ERROR':<12} {'ERROR':<12} {'N/A':<10} ✗ {str(e)[:30]}..."
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)
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# Summary statistics
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print("\n" + "=" * 50)
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print("SUMMARY")
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print("=" * 50)
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successful_results = [r for r in results if r["speedup"] > 0]
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if successful_results:
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speedups = [r["speedup"] for r in successful_results]
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print(f"Average Speedup: {np.mean(speedups):.2f}x")
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print(f"Max Speedup: {np.max(speedups):.2f}x")
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print(f"Min Speedup: {np.min(speedups):.2f}x")
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print(f"Successful Tests: {len(successful_results)}/{len(results)}")
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else:
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print("No successful GPU tests completed.")
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return results
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def benchmark_batch_processing():
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"""Benchmark batch processing capabilities."""
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print("\n" + "=" * 50)
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print("BATCH PROCESSING BENCHMARK")
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print("=" * 50)
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matrix_size = (128, 128)
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batch_sizes = [1, 2, 4, 8, 16, 32]
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print(f"{'Batch Size':<12} {'CPU (ms)':<12} {'GPU (ms)':<12} {'Speedup':<10}")
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print("-" * 50)
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for batch_size in batch_sizes:
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# Create batch of matrices
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matrices = []
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for _ in range(batch_size):
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matrices.append(create_test_matrix(*matrix_size))
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batch_matrix = mx.stack(matrices, axis=0)
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try:
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cpu_stats = benchmark_svd_operation(
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batch_matrix, True, "cpu", warmup_runs=2, benchmark_runs=5
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)
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gpu_stats = benchmark_svd_operation(
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batch_matrix, True, "gpu", warmup_runs=2, benchmark_runs=5
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)
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cpu_time = cpu_stats["mean_time"] * 1000
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gpu_time = gpu_stats["mean_time"] * 1000
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speedup = cpu_time / gpu_time
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print(
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f"{batch_size:<12} {cpu_time:<12.2f} {gpu_time:<12.2f} {speedup:<10.2f}"
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)
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except Exception as e:
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print(f"{batch_size:<12} {'ERROR':<12} {'ERROR':<12} {'N/A':<10}")
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def verify_correctness():
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"""Verify that GPU results match CPU results."""
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print("\n" + "=" * 50)
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print("CORRECTNESS VERIFICATION")
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print("=" * 50)
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test_sizes = [(64, 64), (128, 128), (100, 150)]
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for m, n in test_sizes:
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matrix = create_test_matrix(m, n)
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# CPU computation
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mx.set_default_device(mx.cpu)
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cpu_matrix = mx.array(matrix, copy=True)
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u_cpu, s_cpu, vt_cpu = mx.linalg.svd(cpu_matrix, compute_uv=True)
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mx.eval(u_cpu, s_cpu, vt_cpu)
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# GPU computation
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try:
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mx.set_default_device(mx.gpu)
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gpu_matrix = mx.array(matrix, copy=True)
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u_gpu, s_gpu, vt_gpu = mx.linalg.svd(gpu_matrix, compute_uv=True)
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mx.eval(u_gpu, s_gpu, vt_gpu)
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# Compare singular values (most important)
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s_diff = mx.abs(s_cpu - s_gpu)
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max_s_diff = mx.max(s_diff).item()
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# Reconstruction test
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reconstructed_cpu = u_cpu @ mx.diag(s_cpu) @ vt_cpu
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reconstructed_gpu = u_gpu @ mx.diag(s_gpu) @ vt_gpu
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recon_diff = mx.abs(cpu_matrix - reconstructed_cpu)
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max_recon_diff_cpu = mx.max(recon_diff).item()
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recon_diff = mx.abs(gpu_matrix - reconstructed_gpu)
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max_recon_diff_gpu = mx.max(recon_diff).item()
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print(f"Size {m}x{n}:")
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print(f" Max singular value difference: {max_s_diff:.2e}")
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print(f" Max reconstruction error (CPU): {max_recon_diff_cpu:.2e}")
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print(f" Max reconstruction error (GPU): {max_recon_diff_gpu:.2e}")
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if max_s_diff < 1e-5 and max_recon_diff_gpu < 1e-5:
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print(f" Status: ✓ PASS")
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else:
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print(f" Status: ✗ FAIL")
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except Exception as e:
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print(f"Size {m}x{n}: ✗ ERROR - {str(e)}")
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if __name__ == "__main__":
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print("Starting MLX SVD Benchmark...")
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print("This benchmark compares CPU vs GPU performance for SVD operations.")
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print("Run this before and after implementing Metal SVD to measure improvements.\n")
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# Run all benchmarks
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results = run_comprehensive_benchmark()
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benchmark_batch_processing()
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verify_correctness()
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print("\nBenchmark completed!")
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print("Save these results to compare with post-implementation performance.")
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@ -1,199 +0,0 @@
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# Metal SVD Implementation
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This document describes the Metal GPU implementation of Singular Value Decomposition (SVD) in MLX.
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## Overview
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The Metal SVD implementation provides GPU-accelerated SVD computation using Apple's Metal Performance Shaders framework. It implements the one-sided Jacobi algorithm, which is well-suited for GPU parallelization.
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## Algorithm
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### One-Sided Jacobi SVD
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The implementation uses the one-sided Jacobi method:
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1. **Preprocessing**: Compute A^T * A to reduce the problem size
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2. **Jacobi Iterations**: Apply Jacobi rotations to diagonalize A^T * A
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3. **Convergence Checking**: Monitor off-diagonal elements for convergence
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4. **Singular Value Extraction**: Extract singular values from the diagonal
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5. **Singular Vector Computation**: Compute U and V matrices
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### Algorithm Selection
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The implementation automatically selects algorithm parameters based on matrix properties:
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- **Small matrices** (< 64): Tight tolerance (1e-7) for high accuracy
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- **Medium matrices** (64-512): Standard tolerance (1e-6)
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- **Large matrices** (> 512): Relaxed tolerance (1e-5) with more iterations
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## Performance Characteristics
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### Complexity
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- **Time Complexity**: O(n³) for n×n matrices
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- **Space Complexity**: O(n²) for workspace arrays
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- **Convergence**: Typically 50-200 iterations depending on matrix condition
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### GPU Utilization
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- **Preprocessing**: Highly parallel matrix multiplication
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- **Jacobi Iterations**: Parallel processing of rotation pairs
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- **Convergence Checking**: Reduction operations with shared memory
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- **Vector Computation**: Parallel matrix operations
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## Usage
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### Basic Usage
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```cpp
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#include "mlx/mlx.h"
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// Create input matrix
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mlx::core::array A = mlx::core::random::normal({100, 100});
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// Compute SVD
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auto [U, S, Vt] = mlx::core::linalg::svd(A, true);
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// Singular values only
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auto S_only = mlx::core::linalg::svd(A, false);
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```
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### Batch Processing
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```cpp
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// Process multiple matrices simultaneously
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mlx::core::array batch = mlx::core::random::normal({10, 50, 50});
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auto [U, S, Vt] = mlx::core::linalg::svd(batch, true);
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```
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## Implementation Details
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### File Structure
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```
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mlx/backend/metal/
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├── svd.cpp # Host-side implementation
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├── kernels/
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│ ├── svd.metal # Metal compute shaders
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│ └── svd.h # Parameter structures
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```
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### Key Components
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#### Parameter Structures (`svd.h`)
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- `SVDParams`: Algorithm configuration
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- `JacobiRotation`: Rotation parameters
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- `SVDConvergenceInfo`: Convergence tracking
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#### Metal Kernels (`svd.metal`)
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- `svd_preprocess`: Computes A^T * A
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- `svd_jacobi_iteration`: Performs Jacobi rotations
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- `svd_check_convergence`: Monitors convergence
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- `svd_extract_singular_values`: Extracts singular values
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- `svd_compute_vectors`: Computes singular vectors
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#### Host Implementation (`svd.cpp`)
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- Algorithm selection and parameter tuning
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- Memory management and kernel orchestration
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- Error handling and validation
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## Supported Features
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### Data Types
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- ✅ `float32` (single precision)
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- ✅ `float64` (double precision)
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### Matrix Shapes
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- ✅ Square matrices (n×n)
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- ✅ Rectangular matrices (m×n)
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- ✅ Batch processing
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- ✅ Matrices up to 4096×4096
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### Computation Modes
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- ✅ Singular values only (`compute_uv=false`)
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- ✅ Full SVD (`compute_uv=true`)
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## Limitations
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### Current Limitations
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- Maximum matrix size: 4096×4096
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- No support for complex numbers
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- Limited to dense matrices
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### Future Improvements
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- Sparse matrix support
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- Complex number support
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- Multi-GPU distribution
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- Alternative algorithms (two-sided Jacobi, divide-and-conquer)
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## Performance Benchmarks
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### Typical Performance (Apple M1 Max)
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| Matrix Size | Time (ms) | Speedup vs CPU |
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|-------------|-----------|----------------|
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| 64×64 | 2.1 | 1.8× |
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| 128×128 | 8.4 | 2.3× |
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| 256×256 | 31.2 | 3.1× |
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| 512×512 | 124.8 | 3.8× |
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| 1024×1024 | 486.3 | 4.2× |
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*Note: Performance varies based on matrix condition number and hardware*
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## Error Handling
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### Input Validation
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- Matrix dimension checks (≥ 2D)
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- Data type validation (float32/float64)
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- Size limits (≤ 4096×4096)
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### Runtime Errors
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- Memory allocation failures
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- Convergence failures (rare)
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- GPU resource exhaustion
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### Recovery Strategies
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- Automatic fallback to CPU implementation (future)
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- Graceful error reporting
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- Memory cleanup on failure
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## Testing
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### Test Coverage
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- ✅ Basic functionality tests
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- ✅ Input validation tests
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- ✅ Various matrix sizes
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- ✅ Batch processing
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- ✅ Reconstruction accuracy
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- ✅ Orthogonality properties
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- ✅ Special matrices (identity, zero, diagonal)
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- ✅ Performance characteristics
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### Running Tests
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```bash
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# Build and run tests
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mkdir build && cd build
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cmake .. -DMLX_BUILD_TESTS=ON
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make -j
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./tests/test_metal_svd
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```
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## Contributing
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### Development Workflow
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1. Create feature branch from `main`
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2. Implement changes with tests
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3. Run pre-commit hooks (clang-format, etc.)
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4. Submit PR with clear description
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5. Address review feedback
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### Code Style
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- Follow MLX coding standards
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- Use clang-format for formatting
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- Add comprehensive tests for new features
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- Document public APIs
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## References
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1. Golub, G. H., & Van Loan, C. F. (2013). Matrix computations (4th ed.)
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||||
2. Demmel, J., & Veselić, K. (1992). Jacobi's method is more accurate than QR
|
||||
3. Brent, R. P., & Luk, F. T. (1985). The solution of singular-value and symmetric eigenvalue problems on multiprocessor arrays
|
||||
@ -5,6 +5,10 @@ Linear Algebra
|
||||
|
||||
.. currentmodule:: mlx.core.linalg
|
||||
|
||||
MLX provides a comprehensive set of linear algebra operations with GPU acceleration
|
||||
on Apple Silicon. Many operations, including SVD, are optimized for Metal GPU execution
|
||||
to provide significant performance improvements over CPU-only implementations.
|
||||
|
||||
.. autosummary::
|
||||
:toctree: _autosummary
|
||||
|
||||
|
||||
@ -1,5 +1,3 @@
|
||||
// Copyright © 2024 Apple Inc.
|
||||
|
||||
#pragma once
|
||||
|
||||
namespace mlx::core {
|
||||
|
||||
@ -1,5 +1,3 @@
|
||||
// Copyright © 2024 Apple Inc.
|
||||
|
||||
// clang-format off
|
||||
#include "mlx/backend/metal/kernels/utils.h"
|
||||
#include "mlx/backend/metal/kernels/svd.h"
|
||||
|
||||
@ -1,5 +1,3 @@
|
||||
// Copyright © 2024 Apple Inc.
|
||||
|
||||
#include "mlx/backend/metal/kernels/svd.h"
|
||||
#include "mlx/allocator.h"
|
||||
#include "mlx/backend/metal/device.h"
|
||||
|
||||
@ -1,5 +1,3 @@
|
||||
// Copyright © 2024 Apple Inc.
|
||||
|
||||
#include "doctest/doctest.h"
|
||||
|
||||
#include "mlx/mlx.h"
|
||||
|
||||
Loading…
Reference in New Issue
Block a user