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#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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from typing import List
import numpy as np
from maxframe import opcodes
from maxframe.serialization.serializables import Float64Field, Int8Field, KeyField
from maxframe.tensor.core import TensorOrder
from maxframe.tensor.datasource import tensor as astensor
from maxframe.tensor.operators import TensorOperator, TensorOperatorMixin
from maxframe.tensor.utils import validate_axis
from maxframe.typing_ import EntityType
class TensorTrapezoid(TensorOperator, TensorOperatorMixin):
_op_type_ = opcodes.TRAPEZOID
y = KeyField("y")
x = KeyField("x")
dx = Float64Field("dx")
axis = Int8Field("axis")
@classmethod
def _set_inputs(cls, op: "TensorTrapezoid", inputs: List[EntityType]):
super()._set_inputs(op, inputs)
op.y = op._inputs[0]
if op.x is not None:
op.x = op._inputs[-1]
def __call__(self, y, x=None):
inputs = [y]
order = y.order
if x is not None:
x = astensor(x)
inputs.append(x)
if x.order == TensorOrder.C_ORDER:
order = TensorOrder.C_ORDER
shape = tuple(s for ax, s in enumerate(y.shape) if ax != self.axis)
dtype = np.trapz(np.empty(1, dtype=y.dtype)).dtype
return self.new_tensor(inputs, shape=shape, dtype=dtype, order=order)
[docs]
def trapezoid(y, x=None, dx=1.0, axis=-1):
"""
Integrate along the given axis using the composite trapezoidal rule.
Integrate `y` (`x`) along given axis.
Parameters
----------
y : array_like
Input tensor to integrate.
x : array_like, optional
The sample points corresponding to the `y` values. If `x` is None,
the sample points are assumed to be evenly spaced `dx` apart. The
default is None.
dx : scalar, optional
The spacing between sample points when `x` is None. The default is 1.
axis : int, optional
The axis along which to integrate.
Returns
-------
trapezoid : float
Definite integral as approximated by trapezoidal rule.
See Also
--------
sum, cumsum
Notes
-----
Image [2]_ illustrates trapezoidal rule -- y-axis locations of points
will be taken from `y` tensor, by default x-axis distances between
points will be 1.0, alternatively they can be provided with `x` tensor
or with `dx` scalar. Return value will be equal to combined area under
the red lines.
References
----------
.. [1] Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule
.. [2] Illustration image:
https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png
Examples
--------
>>> import maxframe.tensor as mt
>>> mt.trapezoid([1,2,3]).execute()
4.0
>>> mt.trapezoid([1,2,3], x=[4,6,8]).execute()
8.0
>>> mt.trapezoid([1,2,3], dx=2).execute()
8.0
>>> a = mt.arange(6).reshape(2, 3)
>>> a.execute()
array([[0, 1, 2],
[3, 4, 5]])
>>> mt.trapezoid(a, axis=0).execute()
array([1.5, 2.5, 3.5])
>>> mt.trapezoid(a, axis=1).execute()
array([2., 8.])
"""
y = astensor(y)
axis = validate_axis(y.ndim, axis)
op = TensorTrapezoid(y=y, x=x, dx=dx, axis=axis)
return op(y, x=x)