Integrate y along the given axis using the simpson's rule. The integration happens in sequence along elements of x.

Options

• :axis - Axis along which to integrate. The default value is -1.

• :keep_axis (boolean/0) - If set to true, the axis which is reduced is kept. The default value is false.

• :even - If set to :avg, the average of the first and last interval is used in the integration. If set to :first, the first interval is used in the integration. If set to :last, the last interval is used in the integration. The default value is :avg.

Examples

iex> y = Nx.tensor([1, 2, 3])
iex> x = Nx.tensor([4, 5, 6])
iex> Scholar.Integrate.simpson(y, x)
#Nx.Tensor<
  f32
  4.0
>

iex> y = Nx.tensor([[0, 1, 2], [3, 4, 5]])
iex> x = Nx.tensor([[1, 2, 3], [1, 2, 3]])
iex> Scholar.Integrate.simpson(y, x)
#Nx.Tensor<
  f32[2]
  [2.0, 8.0]
>

iex> y = Nx.tensor([[0, 1, 2], [3, 4, 5]])
iex> x = Nx.tensor([[1, 1, 1], [2, 2, 2]])
iex> Scholar.Integrate.simpson(y, x, axis: 0)
#Nx.Tensor<
  f32[3]
  [1.5, 2.5, 3.5]
>

Integrate y along the given axis using the composite trapezoidal rule.

This is a simplified version of trapezoidal/3 that assumes x is a uniform tensor along axis with step size equal to dx.

Options

• :axis - Axis along which to integrate. The default value is -1.

• :keep_axis (boolean/0) - If set to true, the axis which is reduced is kept. The default value is false.

• :even - If set to :avg, the average of the first and last interval is used in the integration. If set to :first, the first interval is used in the integration. If set to :last, the last interval is used in the integration. The default value is :avg.

• :dx - The spacing between samples. The default value is 1.0.

Examples

iex> y = Nx.tensor([1, 2, 3])
iex> Scholar.Integrate.simpson_uniform(y)
#Nx.Tensor<
  f32
  4.0
>

iex> y = Nx.tensor([1, 2, 3])
iex> Scholar.Integrate.simpson_uniform(y, dx: 2)
#Nx.Tensor<
  f32
  8.0
>

iex> y = Nx.tensor([[0, 1, 2], [3, 4, 5]])
iex> Scholar.Integrate.simpson_uniform(y, dx: 2, axis: 0)
#Nx.Tensor<
  f32[3]
  [3.0, 5.0, 7.0]
>

Integrate y along the given axis using the composite trapezoidal rule. The integration happens in sequence along elements of x.

Options

• :axis - Axis along which to integrate. The default value is -1.

• :keep_axis (boolean/0) - If set to true, the axis which is reduced is kept. The default value is false.

Examples

iex> y = Nx.tensor([1, 2, 3])
iex> x = Nx.tensor([4, 5, 6])
iex> Scholar.Integrate.trapezoidal(y, x)
#Nx.Tensor<
  f32
  4.0
>

iex> y = Nx.tensor([[0, 1, 2], [3, 4, 5]])
iex> x = Nx.tensor([[1, 2, 3], [1, 2, 3]])
iex> Scholar.Integrate.trapezoidal(y, x)
#Nx.Tensor<
  f32[2]
  [2.0, 8.0]
>

iex> y = Nx.tensor([[0, 1, 2], [3, 4, 5]])
iex> x = Nx.tensor([[1, 1, 1], [2, 2, 2]])
iex> Scholar.Integrate.trapezoidal(y, x, axis: 0)
#Nx.Tensor<
  f32[3]
  [1.5, 2.5, 3.5]
>

Integrate y along the given axis using the composite trapezoidal rule.

This is a simplified version of trapezoidal/3 that assumes x is a uniform tensor along axis with step size equal to dx.

Options

• :axis - Axis along which to integrate. The default value is -1.

• :keep_axis (boolean/0) - If set to true, the axis which is reduced is kept. The default value is false.

• :dx - The spacing between samples. The default value is 1.0.

Examples

iex> y = Nx.tensor([1, 2, 3])
iex> Scholar.Integrate.trapezoidal_uniform(y)
#Nx.Tensor<
  f32
  4.0
>

iex> y = Nx.tensor([1, 2, 3])
iex> Scholar.Integrate.trapezoidal_uniform(y, dx: 2)
#Nx.Tensor<
  f32
  8.0
>

iex> y = Nx.tensor([[0, 1, 2], [3, 4, 5]])
iex> Scholar.Integrate.trapezoidal_uniform(y, dx: 2, axis: 0)
#Nx.Tensor<
  f32[3]
  [3.0, 5.0, 7.0]
>