From numpy to ONNX

Converting a scikit-learn pipeline is easy when the pipeline contains only pieces implemented in scikit-learn associated to a converter in sklearn-onnx. Outside this scenario, the conversion usually requires to write custom code either directly with onnx operators, either by writing a custom converter. This tutorial addresses a specific scenario involving an instance of FunctionTransformer.

Translation problem

The following pipeline cannot be converted into ONNX when using the first examples of sklearn-onnx tutorial.


import numpy
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import FunctionTransformer, StandardScaler
from skl2onnx import to_onnx

log_scale_transformer = make_pipeline(
    FunctionTransformer(numpy.log, validate=False),

X = numpy.random.random((5, 2))

# Conversion to ONNX
    onx = to_onnx(log_scale_transformer, X)
except (RuntimeError, TypeError) as e:


    [[ 0.274  0.221]
     [ 0.663 -0.387]
     [-1.96   0.469]
     [ 0.264  1.354]
     [ 0.758 -1.658]]
    FunctionTransformer is not supported unless the transform function is of type <class 'numpy.ufunc'> wrapped with onnxnumpy.

The first step is a FunctionTransformer with a custom function written with numpy functions. The pipeline can be converted only if the function given to this object as argument can be converted into ONNX. Even if function numpy.log does exist in ONNX specifications (see ONNX Log), this problem is equivalent to a translation from a language, Python, to another one, ONNX.

Translating numpy to ONNX

The first approach was to use module ast to convert a function into a syntax tree and then try to convert every node into ONNX to obtain an equivalent ONNX graph.

mlprodict implements function translate_fct2onnx which converts the code of a function written with numpy and scipy into an ONNX graph.

The kernel ExpSineSquared is used by sklearn.gaussian_process.GaussianProcessRegressor and its conversion is required to convert the model. The first step is to write a standalone function which relies on scipy or numpy and which produces the same results. The second step calls this function to produces the ONNX graph.


import numpy
from scipy.spatial.distance import squareform, pdist
from sklearn.gaussian_process.kernels import ExpSineSquared
from mlprodict.onnx_tools.onnx_grammar import translate_fct2onnx
from mlprodict.onnx_tools.onnx_grammar.onnx_translation import (
    squareform_pdist, py_make_float_array)
from mlprodict.onnxrt import OnnxInference

# The function to convert into ONNX.

def kernel_call_ynone(X, length_scale=1.2, periodicity=1.1,

    # squareform(pdist(X, ...)) in one function.
    dists = squareform_pdist(X, metric='euclidean')

    # Function starting with 'py_' --> must not be converted into ONNX.
    t_pi = py_make_float_array(pi)
    t_periodicity = py_make_float_array(periodicity)

    # This operator must be converted into ONNX.
    arg = dists / t_periodicity * t_pi
    sin_of_arg = numpy.sin(arg)

    t_2 = py_make_float_array(2)
    t__2 = py_make_float_array(-2)

    t_length_scale = py_make_float_array(length_scale)

    K = numpy.exp((sin_of_arg / t_length_scale) ** t_2 * t__2)
    return K

# This function is equivalent to the following kernel.
kernel = ExpSineSquared(length_scale=1.2, periodicity=1.1)

x = numpy.array([[1, 2], [3, 4]], dtype=float)

# Checks that the new function and the kernel are the same.
exp = kernel(x, None)
got = kernel_call_ynone(x)

print("numpy function:")

# Converts the numpy function into an ONNX function.
fct_onnx = translate_fct2onnx(kernel_call_ynone, cpl=True,

# Calls the ONNX function to produce the ONNX algebric function.
# See below.
onnx_model = fct_onnx('X')

# Calls the ONNX algebric function to produce the ONNX graph.
inputs = {'X': x.astype(numpy.float32)}
onnx_g = onnx_model.to_onnx(inputs, target_opset=12)

# Creates a python runtime associated to the ONNX function.
oinf = OnnxInference(onnx_g)

# Compute the prediction with the python runtime.
res =
print("ONNX output:")

# Displays the code of the algebric function.
print("Function code:")
print(translate_fct2onnx(kernel_call_ynone, output_names=['Z']))


    [[1.    0.267]
     [0.267 1.   ]]
    numpy function:
    [[1.    0.267]
     [0.267 1.   ]]
    Traceback (most recent call last):
      File "somewhere/workspace/mlprodict/mlprodict_UT_39_std/_doc/sphinxdoc/", line 64, in <module>
        onnx_g = onnx_model.to_onnx(inputs, target_opset=12)
      File "somewhere/workspace/mlprodict/mlprodict_UT_39_std/_venv/lib/python3.9/site-packages/skl2onnx/algebra/", line 882, in to_onnx
        raise RuntimeError(
    RuntimeError: target_opset=12 is lower than the version=14 requested for this node 'OnnxIdentity'.

The output of function translate_fct2onnx is not an ONNX graph but the code of a function which produces an ONNX graph. That’s why the function is called twice. The first call compiles the code and a returns a new python function. The second call starts all over but returns the code instead of its compiled version.

This approach has two drawback. The first one is not every function can be converted into ONNX. That does not mean the algorithm could not be implemented with ONNX operator. The second drawback is discrepencies. They should be minimal but still could happen between a numpy and ONNX implementations.

From ONNX to Python

The Python Runtime can be optimized by generating custom python code and dynamically compile it. OnnxInference computes predictions based on an ONNX graph with a python runtime or onnxruntime. Method to_python goes further by converting the ONNX graph into a standalone python code. All operators may not be implemented.

Another tool is implemented in and converts an ONNX graph into a python code which produces this graph.

Numpy API for ONNX

This approach fixes the two issues mentioned above. The goal is write a code using the same function as numpy offers but executed by an ONNX runtime. The full API is described at Complete Numpy API for ONNX and introduced here. This section is developped in notebook numpyapionnxrst and Numpy to ONNX: Create ONNX graphs with an API similar to numpy.