⚡️ Speed up function manual_convolution_1d by 230%

[codeflash-ai]

📄 230% (2.30x) speedup for manual_convolution_1d in src/numpy_pandas/signal_processing.py

⏱️ Runtime : 11.0 milliseconds → 3.32 milliseconds (best of 309 runs)

📝 Explanation and details

The optimization replaces the nested Python loops with NumPy's vectorized np.dot operation. Instead of manually iterating through each kernel element and accumulating signal[i + j] * kernel[j], the code now uses np.dot(signal[i:i + kernel_len], kernel) to compute the dot product directly.

Key changes:

• Eliminated the inner for j in range(kernel_len) loop that was consuming 61.4% of execution time
• Replaced manual element-wise multiplication and accumulation with NumPy's optimized np.dot
• Array slicing signal[i:i + kernel_len] creates the appropriate signal window for each convolution step

Why this is faster:
NumPy's np.dot uses highly optimized C/BLAS implementations that can leverage SIMD instructions and avoid Python's interpretation overhead. The original nested loops required ~75,909 Python operations, while the optimized version performs the same computation with ~8,030 vectorized operations.

Performance characteristics:

• Small inputs (kernel size 1-3): Shows 20-50% slowdown due to NumPy function call overhead
• Medium inputs (kernel size 5-20): Neutral to modest gains
• Large inputs (kernel size 20+, signal 1000+): Massive speedups of 250-700% as vectorization benefits outweigh overhead

This optimization is most effective for larger convolution problems where the computational savings from vectorized operations significantly exceed the function call overhead.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 40 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 kernel [1] returns the original signal
    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 # 1.92μs -> 3.96μs (51.6% slower)

def test_basic_simple_sum():
    # Convolution with kernel [1, 1] computes sliding sum of pairs
    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_weighted_kernel():
    # Convolution with kernel [2, 0] doubles the first value in each window
    signal = np.array([1, 2, 3, 4])
    kernel = np.array([2, 0])
    expected = np.array([2, 4, 6])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.00μs -> 2.75μs (27.3% slower)

def test_basic_negative_kernel():
    # Convolution with kernel [-1, 1] computes discrete difference
    signal = np.array([5, 6, 9, 10])
    kernel = np.array([-1, 1])
    expected = np.array([1, 3, 1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.00μs -> 2.71μs (26.1% slower)

def test_basic_float_signal_and_kernel():
    # Test with floating point values
    signal = np.array([0.5, 1.5, 2.5])
    kernel = np.array([1.0, 0.5])
    expected = np.array([0.5*1.0 + 1.5*0.5, 1.5*1.0 + 2.5*0.5])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.50μs -> 1.88μs (20.0% slower)

def test_basic_kernel_longer_than_one():
    # Test with kernel of 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 # 2.54μs -> 2.79μs (8.96% slower)

# -------------------- Edge Test Cases --------------------

def test_edge_kernel_equals_signal_length():
    # Kernel same length as signal: result is a single value
    signal = np.array([1, 2, 3])
    kernel = np.array([4, 5, 6])
    expected = np.array([1*4 + 2*5 + 3*6])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.38μs -> 1.58μs (13.1% slower)

def test_edge_kernel_length_one():
    # Kernel of length 1 should return the original signal
    signal = np.array([7, 8, 9])
    kernel = np.array([2])
    expected = np.array([14, 16, 18])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.46μs -> 2.75μs (47.0% slower)

def test_edge_signal_length_one():
    # Signal of length 1, kernel of length 1
    signal = np.array([42])
    kernel = np.array([3])
    expected = np.array([126])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 958ns -> 1.58μs (39.5% slower)

def test_edge_empty_signal():
    # Empty signal should raise ValueError
    signal = np.array([])
    kernel = np.array([1, 2])
    with pytest.raises(ValueError):
        manual_convolution_1d(signal, kernel) # 667ns -> 625ns (6.72% faster)




def test_edge_multidimensional_input():
    # Multidimensional input should raise ValueError
    signal = np.array([[1, 2], [3, 4]])
    kernel = np.array([1, 2])
    with pytest.raises(ValueError):
        manual_convolution_1d(signal, kernel)
    signal = np.array([1, 2, 3])
    kernel = np.array([[1], [2]])
    with pytest.raises(ValueError):
        manual_convolution_1d(signal, kernel)

def test_edge_different_dtypes():
    # Test with integer signal and float kernel
    signal = np.array([1, 2, 3, 4], dtype=int)
    kernel = np.array([0.5, 1.5], dtype=float)
    expected = np.array([
        1*0.5 + 2*1.5,
        2*0.5 + 3*1.5,
        3*0.5 + 4*1.5
    ])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.50μs -> 3.12μs (20.0% slower)

def test_edge_negative_values():
    # Test with negative values in signal and kernel
    signal = np.array([-1, -2, -3])
    kernel = np.array([-1, 2])
    expected = np.array([-1*-1 + -2*2, -2*-1 + -3*2])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.67μs -> 2.38μs (29.8% slower)

def test_edge_zero_kernel():
    # Kernel of all zeros should return all zeros
    signal = np.array([1, 2, 3, 4])
    kernel = np.array([0, 0])
    expected = np.array([0, 0, 0])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.04μs -> 2.79μs (26.9% slower)

def test_edge_zero_signal():
    # Signal of all zeros should return all zeros
    signal = np.zeros(5)
    kernel = np.array([1, 2])
    expected = np.zeros(4)
    codeflash_output = manual_convolution_1d(signal, np.array([1])); result = codeflash_output # 1.92μs -> 4.21μs (54.5% slower)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.88μs -> 2.67μs (29.7% slower)

# -------------------- Large Scale Test Cases --------------------

def test_large_scale_random_signal_and_kernel():
    # Test with large random arrays
    rng = np.random.default_rng(42)
    signal = rng.random(1000)
    kernel = rng.random(10)
    # Use numpy's convolve for reference (valid mode)
    expected = np.convolve(signal, kernel, mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.53ms -> 378μs (304% faster)

def test_large_scale_all_ones():
    # Signal and kernel both all ones
    signal = np.ones(1000)
    kernel = np.ones(10)
    expected = np.full(1000 - 10 + 1, 10.0)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.53ms -> 378μs (305% faster)

def test_large_scale_increasing_signal():
    # Signal is increasing, kernel is decreasing
    signal = np.arange(1, 1001)
    kernel = np.arange(10, 0, -1)
    # Reference: numpy's convolve
    expected = np.convolve(signal, kernel, mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.76ms -> 492μs (258% faster)

def test_large_scale_kernel_length_one():
    # Large signal, kernel of length 1
    signal = np.random.random(1000)
    kernel = np.array([2.5])
    expected = signal * 2.5
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 182μs -> 381μs (52.1% slower)

def test_large_scale_kernel_equals_signal_length():
    # Both signal and kernel of length 1000
    signal = np.arange(1000)
    kernel = np.arange(1000)
    expected = np.array([np.dot(signal, kernel)])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 178μs -> 1.92μs (9214% faster)
# 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

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

def test_simple_identity_kernel():
    # Identity kernel should return the input 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 # 1.96μs -> 4.00μs (51.0% slower)

def test_simple_average_kernel():
    # Kernel [0.5, 0.5] computes the moving average of length 2
    signal = np.array([2, 4, 6, 8])
    kernel = np.array([0.5, 0.5])
    expected = np.array([3, 5, 7])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.38μs -> 3.00μs (20.8% slower)

def test_kernel_longer_than_one():
    # Kernel [1, 2] applied to [1, 2, 3]
    signal = np.array([1, 2, 3])
    kernel = np.array([1, 2])
    # [1*1 + 2*2, 2*1 + 3*2] = [1+4, 2+6] = [5, 8]
    expected = np.array([5, 8])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.62μs -> 2.25μs (27.8% slower)

def test_negative_values():
    # Test with negative values in signal and kernel
    signal = np.array([1, -2, 3])
    kernel = np.array([-1, 2])
    # [1*-1 + -2*2, -2*-1 + 3*2] = [-1-4, 2+6] = [-5, 8]
    expected = np.array([-5, 8])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.62μs -> 2.21μs (26.4% slower)

def test_float_and_int_mix():
    # Test with float signal and int kernel
    signal = np.array([1.5, 2.5, 3.5])
    kernel = np.array([2, 0])
    # [1.5*2 + 2.5*0, 2.5*2 + 3.5*0] = [3.0, 5.0]
    expected = np.array([3.0, 5.0])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.67μs -> 2.33μs (28.5% slower)

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

def test_kernel_length_equals_signal_length():
    # Should return a single value (dot product)
    signal = np.array([1, 2, 3])
    kernel = np.array([4, 5, 6])
    expected = np.array([1*4 + 2*5 + 3*6])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.42μs -> 1.58μs (10.6% slower)




def test_non_1d_signal_raises():
    # 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) # 3.46μs -> 2.17μs (59.6% faster)

def test_non_1d_kernel_raises():
    # 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) # 2.96μs -> 2.04μs (44.9% faster)


def test_signal_with_zeros():
    # Signal with zeros, kernel with ones
    signal = np.array([0, 0, 0, 0])
    kernel = np.array([1, 1])
    expected = np.array([0, 0, 0])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.12μs -> 3.04μs (30.1% slower)

def test_kernel_with_zeros():
    # Kernel with zeros, signal with ones
    signal = np.array([1, 1, 1, 1])
    kernel = np.array([0, 0])
    expected = np.array([0, 0, 0])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.04μs -> 2.88μs (29.0% slower)

def test_signal_and_kernel_all_zeros():
    # Both signal and kernel are zeros
    signal = np.zeros(5)
    kernel = np.zeros(3)
    expected = np.zeros(3)
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.33μs -> 2.42μs (3.44% slower)

def test_kernel_with_one_negative():
    # Kernel with one negative value
    signal = np.array([1, 2, 3, 4])
    kernel = np.array([1, -1])
    # [1*1 + 2*-1, 2*1 + 3*-1, 3*1 + 4*-1] = [1-2, 2-3, 3-4] = [-1, -1, -1]
    expected = np.array([-1, -1, -1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 2.04μs -> 2.83μs (28.0% slower)

def test_signal_and_kernel_with_large_values():
    # Large values to check for overflow/precision
    signal = np.array([1e10, -1e10, 1e10])
    kernel = np.array([1e10, 1])
    expected = np.array([1e10*1e10 + -1e10*1, -1e10*1e10 + 1e10*1])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.50μs -> 1.83μs (18.2% slower)

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

def test_large_signal_and_kernel():
    # Large signal and kernel, but under 1000 elements
    np.random.seed(42)
    signal = np.random.rand(1000)
    kernel = np.random.rand(20)
    # Compare with numpy's built-in convolution (valid mode)
    expected = np.convolve(signal, kernel, mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 3.01ms -> 376μs (701% faster)

def test_large_kernel_size_one():
    # Large signal, kernel of size 1 (should return signal)
    signal = np.random.rand(999)
    kernel = np.array([1.0])
    expected = signal.copy()
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 182μs -> 376μs (51.5% slower)

def test_large_kernel_size_equals_signal():
    # Both signal and kernel have the same large size
    signal = np.arange(500, dtype=np.float64)
    kernel = np.arange(500, dtype=np.float64)
    expected = np.array([np.dot(signal, kernel)])
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 76.8μs -> 1.33μs (5660% faster)

def test_large_kernel_all_ones():
    # Moving sum over large signal
    signal = np.ones(1000)
    kernel = np.ones(10)
    expected = np.convolve(signal, kernel, mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 1.53ms -> 372μs (311% faster)

def test_large_signal_with_pattern():
    # Signal with repeating pattern, kernel with alternating sign
    signal = np.tile([1, 2, 3, 4, 5], 200)  # length 1000
    kernel = np.array([1, -1, 1, -1, 1])
    expected = np.convolve(signal, kernel, mode='valid')
    codeflash_output = manual_convolution_1d(signal, kernel); result = codeflash_output # 908μs -> 487μs (86.4% 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-mfel6ojo and push.