⚡️ Speed up function manual_convolution_1d by 710%

[codeflash-ai]

📄 710% (7.10x) speedup for manual_convolution_1d in src/numpy_pandas/signal_processing.py

⏱️ Runtime : 23.3 milliseconds → 2.88 milliseconds (best of 317 runs)

📝 Explanation and details

The optimized code achieves a 709% speedup by replacing nested Python loops with vectorized NumPy operations, specifically using np.dot() for the inner convolution computation.

Key Optimizations Applied:

1. Vectorized dot product: Replaced the inner for j in range(kernel_len) loop with np.dot(signal[i:i + kernel_len], kernel). This eliminates 143,486 individual array element multiplications and additions that were happening in Python.

2. Memory allocation change: Switched from np.zeros() to np.empty() for result array initialization, avoiding unnecessary zero-filling since all values will be overwritten.

Why This Leads to Speedup:

• Reduced Python overhead: The original code had ~149K hits on the inner loop executing Python bytecode for each multiplication and addition. The optimized version moves this computation into NumPy's C implementation via np.dot().
• Vectorized operations: np.dot() leverages optimized BLAS libraries that can perform element-wise operations much faster than Python loops, using CPU vector instructions and better memory access patterns.
• Cache efficiency: Vectorized operations have better memory locality since they process contiguous array slices in single operations rather than individual element accesses.

Performance Analysis by Test Case:

• Small inputs (basic tests): Paradoxically slower by 15-50% due to NumPy function call overhead dominating for tiny arrays where the original simple loops are more efficient.
• Medium inputs (50-500 elements): Shows dramatic improvements of 300-5000% speedup as vectorization benefits outweigh overhead.
• Large inputs (1000+ elements): Consistent 300-1800% improvements where vectorized operations truly shine, especially for longer kernels where the inner loop elimination has maximum impact.

The optimization is most effective for larger-scale convolutions where kernel lengths are substantial, making it ideal for signal processing applications with meaningful filter sizes.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 39 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	🔘 None Found
📊 Tests Coverage	100.0%

🌀 Generated Regression Tests and Runtime

import numpy as np
# imports
import pytest  # used for our unit tests
from src.numpy_pandas.signal_processing import manual_convolution_1d

# unit tests

# ---------------- BASIC TEST CASES ----------------

def test_basic_identity_kernel():
    # Convolution with [1] should return the original signal
    signal = np.array([2, 4, 6, 8], dtype=float)
    kernel = np.array([1], dtype=float)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.62μs -> 2.75μs (40.9% slower)

def test_basic_simple_kernel():
    # Convolution with [1, 0] should return the first (n-1) elements
    signal = np.array([1, 2, 3, 4])
    kernel = np.array([1, 0])
    expected = np.array([1, 2, 3])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.08μs -> 2.96μs (29.6% slower)

def test_basic_sum_kernel():
    # Convolution with [1, 1] computes moving sum of length 2
    signal = np.array([1, 2, 3, 4])
    kernel = np.array([1, 1])
    expected = np.array([3, 5, 7])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.00μs -> 2.79μs (28.4% slower)

def test_basic_negative_kernel():
    # Convolution with [-1, 1] computes discrete difference
    signal = np.array([10, 20, 30, 40])
    kernel = np.array([-1, 1])
    expected = np.array([10, 10, 10])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.00μs -> 2.71μs (26.1% slower)

def test_basic_float_kernel():
    # Convolution with float kernel
    signal = np.array([1.0, 2.0, 3.0, 4.0])
    kernel = np.array([0.5, 0.5])
    expected = np.array([1.5, 2.5, 3.5])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.83μs -> 2.25μs (18.5% slower)

def test_basic_kernel_longer_than_one():
    # Convolution with kernel length 3
    signal = np.array([1, 2, 3, 4, 5])
    kernel = np.array([1, 0, -1])
    expected = np.array([1*1+2*0+3*-1, 2*1+3*0+4*-1, 3*1+4*0+5*-1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.50μs -> 2.75μs (9.09% slower)

# ---------------- EDGE TEST CASES ----------------

def test_edge_kernel_length_one():
    # Kernel of length 1 should return original signal
    signal = np.array([5, 6, 7])
    kernel = np.array([1])
    expected = np.array([5, 6, 7])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.38μs -> 2.75μs (50.0% slower)

def test_edge_signal_equals_kernel_length():
    # Signal and kernel of equal length: result is a single value (dot product)
    signal = np.array([2, 3, 4])
    kernel = np.array([1, 0, -1])
    expected = np.array([2*1 + 3*0 + 4*-1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.38μs -> 1.62μs (15.4% slower)





def test_edge_negative_values():
    # Handles negative values in signal and kernel
    signal = np.array([-1, -2, -3, -4])
    kernel = np.array([1, -1])
    expected = np.array([-1*1 + -2*-1, -2*1 + -3*-1, -3*1 + -4*-1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.12μs -> 3.08μs (31.1% slower)

def test_edge_non_integer_types():
    # Handles float32 and int32 arrays
    signal = np.array([1, 2, 3], dtype=np.float32)
    kernel = np.array([0.5, 0.5], dtype=np.float32)
    expected = np.array([1*0.5+2*0.5, 2*0.5+3*0.5], dtype=np.float32)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.75μs -> 2.12μs (17.6% slower)

def test_edge_result_type_promotion():
    # Result dtype should be promoted if signal and kernel have different types
    signal = np.array([1, 2, 3], dtype=np.int32)
    kernel = np.array([0.5, 0.5], dtype=np.float64)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.92μs -> 2.38μs (19.3% slower)

# ---------------- LARGE SCALE TEST CASES ----------------

def test_large_scale_signal_and_kernel():
    # Large signal and kernel, but <1000 elements
    np.random.seed(42)
    signal = np.random.randn(1000)
    kernel = np.random.randn(50)
    # Compare with numpy's result (using 'valid' mode and flipping kernel for convolution)
    expected = np.convolve(signal, kernel[::-1], mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 7.17ms -> 369μs (1838% faster)

def test_large_scale_kernel_length_one():
    # Large signal, kernel length 1
    signal = np.arange(1000)
    kernel = np.array([1])
    expected = signal
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 204μs -> 492μs (58.4% slower)

def test_large_scale_kernel_equals_signal():
    # Both signal and kernel length 500
    signal = np.arange(500)
    kernel = np.arange(500)
    expected = np.array([np.dot(signal, kernel)])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 88.0μs -> 1.75μs (4926% faster)

def test_large_scale_all_ones():
    # Signal and kernel of all ones
    signal = np.ones(1000)
    kernel = np.ones(10)
    # Each result should be 10
    expected = np.full(991, 10.0)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.52ms -> 381μs (298% faster)

def test_large_scale_random_integers():
    # Random integer signal and kernel
    np.random.seed(123)
    signal = np.random.randint(-100, 100, 500)
    kernel = np.random.randint(-10, 10, 20)
    expected = np.convolve(signal, kernel[::-1], mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.66ms -> 242μs (585% faster)

# ------------- ADDITIONAL EDGE/ROBUSTNESS TESTS -------------

def test_edge_single_element_signal_and_kernel():
    # Both signal and kernel are length 1
    signal = np.array([42])
    kernel = np.array([2])
    expected = np.array([84])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 958ns -> 1.71μs (43.9% slower)

def test_edge_kernel_with_zeros():
    # Kernel has zeros
    signal = np.array([1, 2, 3, 4, 5])
    kernel = np.array([0, 1, 0])
    expected = np.array([2, 3, 4])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.54μs -> 2.88μs (11.6% slower)

def test_edge_signal_with_zeros():
    # Signal has zeros
    signal = np.array([0, 1, 0, 2, 0, 3])
    kernel = np.array([1, 2])
    expected = np.array([0*1+1*2, 1*1+0*2, 0*1+2*2, 2*1+0*2, 0*1+3*2])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.75μs -> 3.83μs (28.3% slower)

def test_edge_large_kernel_length_minus_one():
    # Kernel length is signal length minus one
    signal = np.arange(100)
    kernel = np.arange(99)
    expected = np.array([np.dot(signal[:99], kernel), np.dot(signal[1:], kernel)])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 33.9μs -> 1.92μs (1670% faster)

def test_edge_kernel_all_negative():
    # Kernel is all negative
    signal = np.array([1, 2, 3, 4, 5])
    kernel = np.array([-1, -2])
    expected = np.array([1*-1+2*-2, 2*-1+3*-2, 3*-1+4*-2, 4*-1+5*-2])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.33μs -> 3.25μs (28.2% slower)
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

import numpy as np
# imports
import pytest  # used for our unit tests
from src.numpy_pandas.signal_processing import manual_convolution_1d

# unit tests

# 1. Basic Test Cases
def test_basic_identity_kernel():
    # Identity kernel should return the original signal (for kernel=[1])
    signal = np.array([1, 2, 3, 4, 5])
    kernel = np.array([1])
    expected = np.array([1, 2, 3, 4, 5])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.83μs -> 3.79μs (51.7% slower)

def test_basic_simple_kernel():
    # Simple kernel of length 2
    signal = np.array([1, 2, 3, 4])
    kernel = np.array([1, 1])
    expected = np.array([1+2, 2+3, 3+4])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.96μs -> 2.71μs (27.7% slower)

def test_basic_weighted_kernel():
    # Weighted kernel
    signal = np.array([1, 2, 3, 4])
    kernel = np.array([2, 0])
    expected = np.array([1*2 + 2*0, 2*2 + 3*0, 3*2 + 4*0])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.96μs -> 2.71μs (27.7% slower)

def test_basic_negative_values():
    # Signal and kernel with negative values
    signal = np.array([-1, -2, 3, 4])
    kernel = np.array([1, -1])
    expected = np.array([-1*1 + -2*-1, -2*1 + 3*-1, 3*1 + 4*-1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.96μs -> 2.71μs (27.7% slower)

def test_basic_float_values():
    # Signal and kernel with float values
    signal = np.array([1.5, 2.5, 3.5])
    kernel = np.array([0.5, 1.5])
    expected = np.array([1.5*0.5 + 2.5*1.5, 2.5*0.5 + 3.5*1.5])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.46μs -> 1.88μs (22.2% slower)

# 2. Edge Test Cases




def test_edge_signal_and_kernel_length_equal():
    # Signal and kernel same length: result is single value
    signal = np.array([2, 3, 4])
    kernel = np.array([1, 0, -1])
    expected = np.array([2*1 + 3*0 + 4*-1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.54μs -> 1.92μs (19.6% slower)

def test_edge_kernel_length_one():
    # Kernel length 1: output should be same as input
    signal = np.array([5, 6, 7])
    kernel = np.array([2])
    expected = np.array([5*2, 6*2, 7*2])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.50μs -> 2.92μs (48.6% slower)

def test_edge_signal_length_one():
    # Signal length 1, kernel length 1: output is product
    signal = np.array([4])
    kernel = np.array([3])
    expected = np.array([12])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 958ns -> 1.62μs (41.0% slower)

def test_edge_non_1d_signal():
    # Non-1D signal should raise ValueError
    signal = np.array([[1, 2], [3, 4]])
    kernel = np.array([1, 2])
    with pytest.raises(ValueError):
        manual_convolution_1d(signal, kernel) # 3.71μs -> 2.21μs (67.9% faster)

def test_edge_non_1d_kernel():
    # Non-1D kernel should raise ValueError
    signal = np.array([1, 2, 3])
    kernel = np.array([[1, 2]])
    with pytest.raises(ValueError):
        manual_convolution_1d(signal, kernel) # 3.12μs -> 1.96μs (59.6% faster)


def test_edge_signal_with_zeros():
    # Signal with all zeros
    signal = np.zeros(5)
    kernel = np.array([1, -1])
    expected = np.zeros(4)
    codeflash_output = manual_convolution_1d(signal, np.array([0])); result = codeflash_output # 1.96μs -> 4.38μs (55.2% slower)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.88μs -> 2.71μs (30.8% slower)

def test_edge_kernel_with_zeros():
    # Kernel with all zeros
    signal = np.array([1, 2, 3, 4])
    kernel = np.zeros(2)
    expected = np.zeros(3)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.33μs -> 2.88μs (18.9% slower)

def test_edge_signal_and_kernel_with_large_and_small_values():
    # Signal and kernel with large and small values
    signal = np.array([1e10, 1e-10, -1e10, -1e-10])
    kernel = np.array([1, -1])
    expected = np.array([1e10*1 + 1e-10*-1, 1e-10*1 + -1e10*-1, -1e10*1 + -1e-10*-1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.00μs -> 2.79μs (28.4% slower)

# 3. Large Scale Test Cases

def test_large_scale_long_signal_short_kernel():
    # Long signal, short kernel
    signal = np.arange(1000)
    kernel = np.array([1, -1])
    # The result should be signal[i] - signal[i+1]
    expected = signal[:-1] - signal[1:]
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 383μs -> 489μs (21.7% slower)

def test_large_scale_long_signal_long_kernel():
    # Long signal and long kernel
    signal = np.arange(500)
    kernel = np.arange(100)
    # Compute expected using numpy's built-in convolve for 'valid' mode
    expected = np.convolve(signal, kernel, mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 6.81ms -> 209μs (3152% faster)

def test_large_scale_large_values():
    # Large values in signal and kernel
    signal = np.full(1000, 1e6)
    kernel = np.full(10, 1e6)
    # Each result should be sum of 10 elements, each 1e6*1e6 = 1e12, so sum = 10e12
    expected = np.full(991, 10 * 1e12)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.52ms -> 382μs (298% faster)

def test_large_scale_random_values():
    # Random values, check against numpy's convolve
    rng = np.random.default_rng(42)
    signal = rng.integers(-100, 100, size=500)
    kernel = rng.integers(-10, 10, size=50)
    expected = np.convolve(signal, kernel, mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 3.87ms -> 231μs (1571% faster)
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

from src.numpy_pandas.signal_processing import manual_convolution_1d

To edit these changes git checkout codeflash/optimize-manual_convolution_1d-mdpha1ji and push.