Compares implementations of ReduceMax

This example compares the numpy for the operator ReduceMax to onnxruntime implementation. If available, tensorflow and pytorch are included as well.

Available optimisation

The code shows which parallelisation optimisation could be used, AVX or SSE and the number of available processors.

import numpy
import pandas
import matplotlib.pyplot as plt
from onnxruntime import InferenceSession
from skl2onnx.common.data_types import FloatTensorType
from skl2onnx.algebra.onnx_ops import OnnxReduceMax
from cpyquickhelper.numbers import measure_time
from tqdm import tqdm
from mlprodict.testing.experimental_c_impl.experimental_c import code_optimisation
print(code_optimisation())

Out:

AVX-omp=8

ReduceMax implementations

try:
    from tensorflow.math import reduce_max as tf_reduce_max
    from tensorflow import convert_to_tensor
except ImportError:
    tf_reduce_max = None
try:
    from torch import max as torch_max, from_numpy
except ImportError:
    torch_max = None


def build_ort_reducemax(axes, op_version=14):  # opset=13, 14, ...
    node = OnnxReduceMax('x', axes=axes, op_version=op_version,
                         output_names=['z'])
    onx = node.to_onnx(inputs=[('x', FloatTensorType())],
                       target_opset=op_version)
    sess = InferenceSession(onx.SerializeToString())
    return lambda x, y: sess.run(None, {'x': x})


def loop_fct(fct, xs, ys):
    for x, y in zip(xs, ys):
        fct(x, y)


def benchmark_op(axes, repeat=2, number=5, name="ReduceMax", shape_fct=None):
    if shape_fct is None:
        def shape_fct(dim):
            return (3, dim, 1, 128, 64)
    ort_fct = build_ort_reducemax(axes)
    res = []
    for dim in tqdm([8, 16, 32, 64, 100, 128, 200,
                     256, 400, 512, 1024]):
        shape = shape_fct(dim)
        n_arrays = 10 if dim < 512 else 4
        xs = [numpy.random.rand(*shape).astype(numpy.float32)
              for _ in range(n_arrays)]
        ys = [numpy.array(axes, dtype=numpy.int64)
              for _ in range(n_arrays)]
        info = dict(axes=axes, shape=shape)

        # numpy
        ctx = dict(
            xs=xs, ys=ys,
            fct=lambda x, y: numpy.amax(x, tuple(y)),
            loop_fct=loop_fct)
        obs = measure_time(
            "loop_fct(fct, xs, ys)",
            div_by_number=True, context=ctx, repeat=repeat, number=number)
        obs['dim'] = dim
        obs['fct'] = 'numpy'
        obs.update(info)
        res.append(obs)

        # onnxruntime
        ctx['fct'] = ort_fct
        obs = measure_time(
            "loop_fct(fct, xs, ys)",
            div_by_number=True, context=ctx, repeat=repeat, number=number)
        obs['dim'] = dim
        obs['fct'] = 'ort'
        obs.update(info)
        res.append(obs)

        if tf_reduce_max is not None:
            # tensorflow
            ctx['fct'] = tf_reduce_max
            ctx['xs'] = [convert_to_tensor(x) for x in xs]
            ctx['ys'] = ys
            obs = measure_time(
                "loop_fct(fct, xs, ys)",
                div_by_number=True, context=ctx, repeat=repeat, number=number)
            obs['dim'] = dim
            obs['fct'] = 'tf'
            obs.update(info)
            res.append(obs)

        if torch_max is not None:
            def torch_max1(x, y):
                return torch_max(x, y[0])

            def torch_max2(x, y):
                return torch_max(torch_max(x, y[1])[0], y[0])[0]

            # torch
            ctx['fct'] = torch_max1 if len(axes) == 1 else torch_max2
            ctx['xs'] = [from_numpy(x) for x in xs]
            ctx['ys'] = ys  # [from_numpy(y) for y in ys]
            obs = measure_time(
                "loop_fct(fct, xs, ys)",
                div_by_number=True, context=ctx, repeat=repeat, number=number)
            obs['dim'] = dim
            obs['fct'] = 'torch'
            obs.update(info)
            res.append(obs)

    # Dataframes
    shape_name = str(shape).replace(str(dim), "N")
    df = pandas.DataFrame(res)
    df.columns = [_.replace('dim', 'N') for _ in df.columns]
    piv = df.pivot('N', 'fct', 'average')

    rs = piv.copy()
    for c in ['ort', 'torch', 'tf', 'tf_copy']:
        if c in rs.columns:
            rs[c] = rs['numpy'] / rs[c]
    rs['numpy'] = 1.

    # Graphs.
    fig, ax = plt.subplots(1, 2, figsize=(12, 4))
    piv.plot(logx=True, logy=True, ax=ax[0],
             title="%s benchmark\n%r - %r"
                   " lower better" % (name, shape_name, axes))
    ax[0].legend(prop={"size": 9})
    rs.plot(logx=True, logy=True, ax=ax[1],
            title="%s Speedup, baseline=numpy\n%r - %r"
                  " higher better" % (name, shape_name, axes))
    ax[1].plot([min(rs.index), max(rs.index)], [0.5, 0.5], 'g--')
    ax[1].plot([min(rs.index), max(rs.index)], [2., 2.], 'g--')
    ax[1].legend(prop={"size": 9})
    return df, rs, ax


dfs = []

Reduction on a particular case KR

Consecutive axis not reduced and consecutive reduced axis are merged. KR means kept axis - reduced axis

(8, 24, 48, N), axis=(3, )

axes = (3, )
df, piv, ax = benchmark_op(axes, shape_fct=lambda dim: (8, 24, 48, dim))
dfs.append(df)
df.pivot("fct", "N", "average")

Out:

  0%|          | 0/11 [00:00<?, ?it/s]
  9%|9         | 1/11 [00:01<00:10,  1.09s/it]
 18%|#8        | 2/11 [00:01<00:08,  1.11it/s]
 27%|##7       | 3/11 [00:03<00:08,  1.08s/it]
 36%|###6      | 4/11 [00:04<00:08,  1.23s/it]
 45%|####5     | 5/11 [00:06<00:08,  1.37s/it]
 55%|#####4    | 6/11 [00:08<00:07,  1.51s/it]
 64%|######3   | 7/11 [00:09<00:06,  1.61s/it]
 73%|#######2  | 8/11 [00:12<00:05,  1.83s/it]
 82%|########1 | 9/11 [00:15<00:04,  2.18s/it]
 91%|######### | 10/11 [00:16<00:01,  1.94s/it]
100%|##########| 11/11 [00:18<00:00,  2.05s/it]
100%|##########| 11/11 [00:18<00:00,  1.71s/it]

N	8	16	32	64	100	128	200	256	400	512	1024
fct
numpy	0.018162	0.024256	0.026089	0.027449	0.028488	0.031048	0.035552	0.038757	0.047936	0.022352	0.038103
ort	0.003302	0.001599	0.002524	0.004254	0.004987	0.005713	0.007586	0.010507	0.013066	0.007601	0.013998
torch	0.082772	0.046211	0.090157	0.093903	0.098461	0.102381	0.076816	0.102986	0.114965	0.046541	0.053641

Reduction on a particular case RK

Consecutive axis not reduced and consecutive reduced axis are merged. RK means reduced axis - kept axis,

(8, 24, 48, N), axis=(0, )

axes = (0, )
df, piv, ax = benchmark_op(axes, shape_fct=lambda dim: (8, 24, 48, dim))
dfs.append(df)
df.pivot("fct", "N", "average")

Out:

  0%|          | 0/11 [00:00<?, ?it/s]
  9%|9         | 1/11 [00:00<00:09,  1.01it/s]
 18%|#8        | 2/11 [00:02<00:09,  1.05s/it]
 27%|##7       | 3/11 [00:03<00:09,  1.18s/it]
 36%|###6      | 4/11 [00:05<00:09,  1.40s/it]
 45%|####5     | 5/11 [00:07<00:10,  1.67s/it]
 55%|#####4    | 6/11 [00:09<00:09,  1.89s/it]
 64%|######3   | 7/11 [00:12<00:09,  2.35s/it]
 73%|#######2  | 8/11 [00:16<00:08,  2.84s/it]
 82%|########1 | 9/11 [00:22<00:07,  3.71s/it]
 91%|######### | 10/11 [00:25<00:03,  3.42s/it]
100%|##########| 11/11 [00:30<00:00,  3.95s/it]
100%|##########| 11/11 [00:30<00:00,  2.76s/it]

N	8	16	32	64	100	128	200	256	400	512	1024
fct
numpy	0.005682	0.010565	0.020549	0.039940	0.062587	0.080118	0.123943	0.157168	0.244119	0.124867	0.248741
ort	0.001659	0.002620	0.004749	0.010224	0.012667	0.017180	0.025427	0.030803	0.046660	0.024044	0.046242
torch	0.089271	0.090861	0.098514	0.103386	0.108183	0.096529	0.118908	0.123994	0.151078	0.067124	0.096205

Reduction on a particular case KRK

Consecutive axis not reduced and consecutive reduced axis are merged. KRK means kept axis - reduced axis - kept axis,

(8, 24, 48, N), axis=(1, 2)

axes = (1, 2)
df, piv, ax = benchmark_op(axes, shape_fct=lambda dim: (8, 24, 48, dim))
dfs.append(df)
df.pivot("fct", "N", "average")

Out:

  0%|          | 0/11 [00:00<?, ?it/s]
  9%|9         | 1/11 [00:01<00:10,  1.04s/it]
 18%|#8        | 2/11 [00:02<00:10,  1.19s/it]
 27%|##7       | 3/11 [00:03<00:08,  1.11s/it]
 36%|###6      | 4/11 [00:04<00:09,  1.29s/it]
 45%|####5     | 5/11 [00:05<00:07,  1.18s/it]
 55%|#####4    | 6/11 [00:07<00:06,  1.26s/it]
 64%|######3   | 7/11 [00:10<00:07,  1.88s/it]
 73%|#######2  | 8/11 [00:12<00:06,  2.03s/it]
 82%|########1 | 9/11 [00:16<00:05,  2.61s/it]
 91%|######### | 10/11 [00:19<00:02,  2.52s/it]
100%|##########| 11/11 [00:23<00:00,  3.15s/it]
100%|##########| 11/11 [00:23<00:00,  2.15s/it]

N	8	16	32	64	100	128	200	256	400	512	1024
fct
numpy	0.011017	0.013082	0.018692	0.028396	0.039680	0.048182	0.070414	0.087690	0.132109	0.066579	0.129754
ort	0.000975	0.001610	0.003347	0.005648	0.006301	0.008852	0.010433	0.035026	0.019736	0.033839	0.075520
torch	0.088854	0.109464	0.069957	0.101884	0.021326	0.046015	0.174519	0.033094	0.115419	0.071050	0.129555

(8, 24 * 48, N), axis=1

axes = (1, )
df, piv, ax = benchmark_op(axes, shape_fct=lambda dim: (8, 24 * 48, dim))
dfs.append(df)
df.pivot("fct", "N", "average")

Out:

  0%|          | 0/11 [00:00<?, ?it/s]
  9%|9         | 1/11 [00:01<00:10,  1.05s/it]
 18%|#8        | 2/11 [00:01<00:06,  1.38it/s]
 27%|##7       | 3/11 [00:02<00:06,  1.25it/s]
 36%|###6      | 4/11 [00:03<00:07,  1.04s/it]
 45%|####5     | 5/11 [00:04<00:05,  1.01it/s]
 55%|#####4    | 6/11 [00:06<00:06,  1.35s/it]
 64%|######3   | 7/11 [00:09<00:06,  1.74s/it]
 73%|#######2  | 8/11 [00:13<00:07,  2.53s/it]
 82%|########1 | 9/11 [00:17<00:05,  2.93s/it]
 91%|######### | 10/11 [00:20<00:03,  3.05s/it]
100%|##########| 11/11 [00:27<00:00,  4.09s/it]
100%|##########| 11/11 [00:27<00:00,  2.47s/it]

N	8	16	32	64	100	128	200	256	400	512	1024
fct
numpy	0.010905	0.013113	0.018562	0.028505	0.039592	0.048290	0.070319	0.087665	0.131991	0.066587	0.129752
ort	0.000969	0.002156	0.002802	0.004310	0.006204	0.009063	0.010331	0.035272	0.021653	0.033794	0.076582
torch	0.089673	0.029356	0.057212	0.087373	0.014500	0.108763	0.113134	0.221537	0.107943	0.169199	0.315968

(2, 8, 12, 24, 2, N), axis=(2, 3)

axes = (2, 3)
df, piv, ax = benchmark_op(axes, shape_fct=lambda dim: (2, 8, 12, 24, 2, dim))
dfs.append(df)
df.pivot("fct", "N", "average")

Out:

  0%|          | 0/11 [00:00<?, ?it/s]
  9%|9         | 1/11 [00:01<00:18,  1.87s/it]
 18%|#8        | 2/11 [00:03<00:17,  1.93s/it]
 27%|##7       | 3/11 [00:05<00:15,  1.99s/it]
 36%|###6      | 4/11 [00:07<00:13,  2.00s/it]
 45%|####5     | 5/11 [00:10<00:13,  2.24s/it]
 55%|#####4    | 6/11 [00:13<00:12,  2.48s/it]
 64%|######3   | 7/11 [00:16<00:11,  2.80s/it]
 73%|#######2  | 8/11 [00:20<00:09,  3.07s/it]
 82%|########1 | 9/11 [00:25<00:07,  3.70s/it]
 91%|######### | 10/11 [00:28<00:03,  3.31s/it]
100%|##########| 11/11 [00:32<00:00,  3.67s/it]
100%|##########| 11/11 [00:32<00:00,  2.97s/it]

N	8	16	32	64	100	128	200	256	400	512	1024
fct
numpy	0.007115	0.010029	0.015813	0.026288	0.038093	0.047181	0.070768	0.089044	0.136099	0.069048	0.136035
ort	0.000967	0.001449	0.002064	0.003559	0.005453	0.007038	0.009775	0.018565	0.029007	0.030170	0.064594
torch	0.176037	0.180110	0.178986	0.150199	0.194171	0.200485	0.205705	0.180152	0.221740	0.081667	0.124144

Reduction on a particular case RKR

(N, 64, 16, 16), axis=(0, 2, 3)

axes = (0, 2, 3)
df, piv, ax = benchmark_op(
    axes, shape_fct=lambda dim: (dim, 64, 16, 16))
dfs.append(df)
df.pivot("fct", "N", "average")

Out:

  0%|          | 0/11 [00:00<?, ?it/s]
  9%|9         | 1/11 [00:00<00:06,  1.48it/s]
 18%|#8        | 2/11 [00:01<00:07,  1.13it/s]
 27%|##7       | 3/11 [00:03<00:09,  1.18s/it]
 36%|###6      | 4/11 [00:05<00:09,  1.42s/it]
 45%|####5     | 5/11 [00:07<00:11,  1.95s/it]
 55%|#####4    | 6/11 [00:10<00:11,  2.27s/it]
 64%|######3   | 7/11 [00:14<00:10,  2.75s/it]
 73%|#######2  | 8/11 [00:18<00:09,  3.28s/it]
 82%|########1 | 9/11 [00:25<00:08,  4.16s/it]
 91%|######### | 10/11 [00:28<00:03,  3.80s/it]
100%|##########| 11/11 [00:33<00:00,  4.23s/it]
100%|##########| 11/11 [00:33<00:00,  3.02s/it]

N	8	16	32	64	100	128	200	256	400	512	1024
fct
numpy	0.002426	0.004902	0.008167	0.014676	0.021942	0.027749	0.042226	0.054067	0.082807	0.042922	0.084252
ort	0.001268	0.001938	0.003723	0.006287	0.009553	0.011422	0.018796	0.024808	0.040023	0.021918	0.040855
torch	0.059271	0.086945	0.122529	0.124595	0.203098	0.179521	0.205229	0.227056	0.271238	0.125010	0.177085

Reduction on a particular case RKRK

(8, 24, 48, N), axis=(0, 2)

axes = (0, 2)
df, piv, ax = benchmark_op(axes, shape_fct=lambda dim: (8, 24, 48, dim))
dfs.append(df)
df.pivot("fct", "N", "average")

Out:

  0%|          | 0/11 [00:00<?, ?it/s]
  9%|9         | 1/11 [00:01<00:19,  1.92s/it]
 18%|#8        | 2/11 [00:02<00:11,  1.23s/it]
 27%|##7       | 3/11 [00:04<00:10,  1.31s/it]
 36%|###6      | 4/11 [00:05<00:10,  1.47s/it]
 45%|####5     | 5/11 [00:07<00:10,  1.69s/it]
 55%|#####4    | 6/11 [00:10<00:09,  1.98s/it]
 64%|######3   | 7/11 [00:13<00:09,  2.41s/it]
 73%|#######2  | 8/11 [00:17<00:08,  2.94s/it]
 82%|########1 | 9/11 [00:23<00:07,  3.69s/it]
 91%|######### | 10/11 [00:26<00:03,  3.49s/it]
100%|##########| 11/11 [00:32<00:00,  4.51s/it]
100%|##########| 11/11 [00:32<00:00,  3.00s/it]

N	8	16	32	64	100	128	200	256	400	512	1024
fct
numpy	0.010435	0.012825	0.018634	0.028819	0.040265	0.049142	0.073128	0.090945	0.137708	0.069292	0.135588
ort	0.001459	0.002595	0.004599	0.008858	0.012105	0.017449	0.029198	0.043995	0.066525	0.081930	0.307510
torch	0.177319	0.053281	0.106080	0.114717	0.124100	0.149301	0.167036	0.195177	0.209823	0.088867	0.116373

Conclusion

Some of the configurations should be investigated. l-reducesum-problem1. The reduction on tensorflow in one dimension seems to be lazy.

merged = pandas.concat(dfs)
name = "reducemax"
merged.to_csv("plot_%s.csv" % name, index=False)
merged.to_excel("plot_%s.xlsx" % name, index=False)
plt.savefig("plot_%s.png" % name)

plt.show()

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