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gradient#

ivy.gradient(x, /, *, spacing=1, edge_order=1, axis=None)[source]#

Calculate gradient of x with respect to (w.r.t.) spacing.

Parameters:

  • x (Union[Array, NativeArray]) – input array representing outcomes of the function

  • spacing (Union[int, list, tuple], default: 1) – if not given, indices of x will be used if scalar indices of x will be scaled with this value if array gradient of x w.r.t. spacing

  • edge_order (int, default: 1) – 1 or 2, for ‘frist order’ and ‘second order’ estimation of boundary values of gradient respectively. Note: jax supports edge_order=1 case only

  • axis (Optional[Union[int, list, tuple]], default: None) – dimension(s) to approximate the gradient over by default partial gradient is computed in every dimension

Return type:

Union[Array, List[Array]]

Returns:

ret – Array with values computed from gradient function from inputs

Examples

>>> spacing = (ivy.array([-2., -1., 1., 4.]),)
>>> x = ivy.array([4., 1., 1., 16.], )
>>> ivy.gradient(x, spacing=spacing)
ivy.array([-3., -2.,  2.,  5.])

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x)
[ivy.array([[ 9., 18., 36., 72.],
   [ 9., 18., 36., 72.]]), ivy.array([[ 1. ,  1.5,  3. ,  4. ],
   [10. , 15. , 30. , 40. ]])]

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x, spacing=2.0)
[ivy.array([[ 4.5,  9. , 18. , 36. ],
   [ 4.5,  9. , 18. , 36. ]]), ivy.array([[ 0.5 ,  0.75,  1.5 ,  2.  ],
   [ 5.  ,  7.5 , 15.  , 20.  ]])]

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x, axis=1)
ivy.array([[ 1. ,  1.5,  3. ,  4. ],
   [10. , 15. , 30. , 40. ]])

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x, spacing=[3., 2.])
[ivy.array([[ 3.,  6., 12., 24.],
   [ 3.,  6., 12., 24.]]), ivy.array([[ 0.5 ,  0.75,  1.5 ,  2.  ],
   [ 5.  ,  7.5 , 15.  , 20.  ]])]

>>> spacing = (ivy.array([0, 2]), ivy.array([0, 3, 6, 9]))
>>> ivy.gradient(x, spacing=spacing)
[ivy.array([[ 4.5,  9. , 18. , 36. ],
   [ 4.5,  9. , 18. , 36. ]]), ivy.array([[ 0.33333333, 0.5,  1., 1.33333333],
   [ 3.33333333,  5.        , 10.        , 13.33333333]])]
Array.gradient(self, /, *, spacing=1, edge_order=1, axis=None)[source]#

Calculate gradient of x with respect to (w.r.t.) spacing.

Parameters:

  • self (Union[Array, NativeArray]) – input array representing outcomes of the function

  • spacing (Union[int, list, tuple], default: 1) – if not given, indices of x will be used if scalar indices of x will be scaled with this value if array gradient of x w.r.t. spacing

  • edge_order (int, default: 1) – 1 or 2, for ‘first order’ and ‘second order’ estimation of boundary values of gradient respectively. Note: jax supports edge_order=1 case only

  • axis (Optional[Union[int, list, tuple]], default: None) – dimension(s) to approximate the gradient over by default partial gradient is computed in every dimension

Return type:

Union[Array, List[Array]]

Returns:

ret – Array with values computed from gradient function from inputs

Examples

>>> spacing = (ivy.array([-2., -1., 1., 4.]),)
>>> x = ivy.array([4., 1., 1., 16.], )
>>> ivy.gradient(x, spacing=spacing)
ivy.array([-3., -2.,  2.,  5.])

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x)
[ivy.array([[ 9., 18., 36., 72.],
   [ 9., 18., 36., 72.]]), ivy.array([[ 1. ,  1.5,  3. ,  4. ],
   [10. , 15. , 30. , 40. ]])]

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x, spacing=2.0)
[ivy.array([[ 4.5,  9. , 18. , 36. ],
   [ 4.5,  9. , 18. , 36. ]]), ivy.array([[ 0.5 ,  0.75,  1.5 ,  2.  ],
   [ 5.  ,  7.5 , 15.  , 20.  ]])]

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x, axis=1)
ivy.array([[ 1. ,  1.5,  3. ,  4. ],
   [10. , 15. , 30. , 40. ]])

>>> x = ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]])
>>> ivy.gradient(x, spacing=[3., 2.])
[ivy.array([[ 3.,  6., 12., 24.],
   [ 3.,  6., 12., 24.]]), ivy.array([[ 0.5 ,  0.75,  1.5 ,  2.  ],
   [ 5.  ,  7.5 , 15.  , 20.  ]])]

>>> spacing = (ivy.array([0, 2]), ivy.array([0, 3, 6, 9]))
>>> ivy.gradient(x, spacing=spacing)
[ivy.array([[ 4.5,  9. , 18. , 36. ],
   [ 4.5,  9. , 18. , 36. ]]), ivy.array([[ 0.33333333,  0.5,  1., 1.33333333],
   [ 3.33333333,  5.        , 10.        , 13.33333333]])]
Container.gradient(self, /, *, spacing=1, edge_order=1, axis=None)[source]#

Calculate gradient of x with respect to (w.r.t.) spacing.

Parameters:

  • x – input array representing outcomes of the function spacing if not given, indices of x will be used if scalar indices of x will be scaled with this value if array gradient of x w.r.t. spacing

  • edge_order (Union[int, Container], default: 1) – 1 or 2, for ‘frist order’ and ‘second order’ estimation of boundary values of gradient respectively.

  • axis (Optional[Union[int, list, tuple, Container]], default: None) – dimension(s) to approximate the gradient over. By default, partial gradient is computed in every dimension

Return type:

Container

Returns:

ret – Array with values computed from gradient function from inputs

Examples

>>> coordinates = ivy.Container(
>>>     a=(ivy.array([-2., -1., 1., 4.]),),
>>>     b=(ivy.array([2., 1., -1., -4.]),)
>>> )
>>> values = ivy.Container(
>>>     a=ivy.array([4., 1., 1., 16.]),
>>>     b=ivy.array([4., 1., 1., 16.])
>>> )
>>> ivy.gradient(values, spacing=coordinates)
{
    a: ivy.array([-3., -2., 2., 5.]),
    b: ivy.array([3., 2., -2., -5.])
}

>>> values = ivy.Container(
>>>     a=ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]]),
>>>     b=ivy.array([[-1, -2, -4, -8], [-10, -20, -40, -80]])
>>> )
>>> ivy.gradient(values)
[{
    a: ivy.array([[9., 18., 36., 72.],
                  [9., 18., 36., 72.]]),
    b: ivy.array([[-9., -18., -36., -72.],
                  [-9., -18., -36., -72.]])
}, {
    a: ivy.array([[1., 1.5, 3., 4.],
                  [10., 15., 30., 40.]]),
    b: ivy.array([[-1., -1.5, -3., -4.],
                  [-10., -15., -30., -40.]])
}]

>>> values = ivy.Container(
>>>     a=ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]]),
>>>     b=ivy.array([[-1, -2, -4, -8], [-10, -20, -40, -80]])
>>> )
>>> ivy.gradient(values, spacing=2.0)
[{
    a: ivy.array([[4.5, 9., 18., 36.],
                  [4.5, 9., 18., 36.]]),
    b: ivy.array([[-4.5, -9., -18., -36.],
                  [-4.5, -9., -18., -36.]])
}, {
    a: ivy.array([[0.5, 0.75, 1.5, 2.],
                  [5., 7.5, 15., 20.]]),
    b: ivy.array([[-0.5, -0.75, -1.5, -2.],
                  [-5., -7.5, -15., -20.]])
}]

>>> values = ivy.Container(
>>>     a=ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]]),
>>>     b=ivy.array([[-1, -2, -4, -8], [-10, -20, -40, -80]])
>>> )
>>> ivy.gradient(values, axis=1)
{
    a: ivy.array([[1., 1.5, 3., 4.],
                  [10., 15., 30., 40.]]),
    b: ivy.array([[-1., -1.5, -3., -4.],
                  [-10., -15., -30., -40.]])
}

>>> values = ivy.Container(
>>>     a=ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]]),
>>>     b=ivy.array([[-1, -2, -4, -8], [-10, -20, -40, -80]])
>>> )
>>> ivy.gradient(values, spacing = [3., 2.])
[{
    a: ivy.array([[3., 6., 12., 24.],
                  [3., 6., 12., 24.]]),
    b: ivy.array([[-3., -6., -12., -24.],
                  [-3., -6., -12., -24.]])
}, {
    a: ivy.array([[0.5, 0.75, 1.5, 2.],
                  [5., 7.5, 15., 20.]]),
    b: ivy.array([[-0.5, -0.75, -1.5, -2.],
                  [-5., -7.5, -15., -20.]])
}]

>>> coords = ivy.Container(
>>>    a=(ivy.array([0, 2]), ivy.array([0, 3, 6, 9])),
>>>    b=(ivy.array([0, -2]), ivy.array([0, -3, -6, -9]))
>>>)
>>> values = ivy.Container(
>>>     a=ivy.array([[1, 2, 4, 8], [10, 20, 40, 80]]),
>>>     b=ivy.array([[-1, -2, -4, -8], [-10, -20, -40, -80]])
>>>)
>>> ivy.gradient(values, spacing = coords)
[{
    a: ivy.array([[4.5, 9., 18., 36.],
                  [4.5, 9., 18., 36.]]),
    b: ivy.array([[4.5, 9., 18., 36.],
                  [4.5, 9., 18., 36.]])
}, {
    a: ivy.array([[0.33333333, 0.5, 1., 1.33333333],
                  [3.33333333, 5., 10., 13.33333333]]),
    b: ivy.array([[0.33333333, 0.5, 1., 1.33333333],
                  [3.33333333, 5., 10., 13.33333333]])
}]
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