[−][src]Trait ndarray_stats::SummaryStatisticsExt

pub trait SummaryStatisticsExt<A, S, D> where
    S: Data<Elem = A>,
    D: Dimension, {
    fn mean(&self) -> Result<A, EmptyInput>
    where
        A: Clone + FromPrimitive + Add<Output = A> + Div<Output = A> + Zero;

    fn weighted_mean(&self, weights: &Self) -> Result<A, MultiInputError>
    where
        A: Copy + Div<Output = A> + Mul<Output = A> + Zero;

    fn weighted_sum(&self, weights: &Self) -> Result<A, MultiInputError>
    where
        A: Copy + Mul<Output = A> + Zero;

    fn weighted_mean_axis(
        &self, 
        axis: Axis, 
        weights: &ArrayBase<S, Ix1>
    ) -> Result<Array<A, D::Smaller>, MultiInputError>
    where
        A: Copy + Div<Output = A> + Mul<Output = A> + Zero,
        D: RemoveAxis;

    fn weighted_sum_axis(
        &self, 
        axis: Axis, 
        weights: &ArrayBase<S, Ix1>
    ) -> Result<Array<A, D::Smaller>, MultiInputError>
    where
        A: Copy + Mul<Output = A> + Zero,
        D: RemoveAxis;

    fn harmonic_mean(&self) -> Result<A, EmptyInput>
    where
        A: Float + FromPrimitive;

    fn geometric_mean(&self) -> Result<A, EmptyInput>
    where
        A: Float + FromPrimitive;

    fn kurtosis(&self) -> Result<A, EmptyInput>
    where
        A: Float + FromPrimitive;

    fn skewness(&self) -> Result<A, EmptyInput>
    where
        A: Float + FromPrimitive;

    fn central_moment(&self, order: u16) -> Result<A, EmptyInput>
    where
        A: Float + FromPrimitive;

    fn central_moments(&self, order: u16) -> Result<Vec<A>, EmptyInput>
    where
        A: Float + FromPrimitive;

    fn __private__(&self, _: PrivateMarker);
}

Extension trait for ArrayBase providing methods to compute several summary statistics (e.g. mean, variance, etc.).

Required methods

fn mean(&self) -> Result<A, EmptyInput> where
    A: Clone + FromPrimitive + Add<Output = A> + Div<Output = A> + Zero, 

Returns the arithmetic mean x̅ of all elements in the array:

    1   n
x̅ = ―   ∑ xᵢ
    n  i=1

If the array is empty, Err(EmptyInput) is returned.

Panics if A::from_usize() fails to convert the number of elements in the array.

fn weighted_mean(&self, weights: &Self) -> Result<A, MultiInputError> where
    A: Copy + Div<Output = A> + Mul<Output = A> + Zero, 

Returns the [arithmetic weighted mean] x̅ of all elements in the array. Use weighted_sum if the weights are normalized (they sum up to 1.0).

      n
      ∑ wᵢxᵢ
     i=1
x̅ = ―――――――――
       n
       ∑ wᵢ
      i=1

Panics if division by zero panics for type A.

The following errors may be returned:

  • MultiInputError::EmptyInput if self is empty
  • MultiInputError::ShapeMismatch if self and weights don't have the same shape

[arithmetic weighted mean] https://en.wikipedia.org/wiki/Weighted_arithmetic_mean

fn weighted_sum(&self, weights: &Self) -> Result<A, MultiInputError> where
    A: Copy + Mul<Output = A> + Zero, 

Returns the weighted sum of all elements in the array, that is, the dot product of the arrays self and weights. Equivalent to weighted_mean if the weights are normalized.

     n
x̅ =  ∑ wᵢxᵢ
    i=1

The following errors may be returned:

  • MultiInputError::ShapeMismatch if self and weights don't have the same shape

fn weighted_mean_axis(
    &self,
    axis: Axis,
    weights: &ArrayBase<S, Ix1>
) -> Result<Array<A, D::Smaller>, MultiInputError> where
    A: Copy + Div<Output = A> + Mul<Output = A> + Zero,
    D: RemoveAxis, 

Returns the [arithmetic weighted mean] x̅ along axis. Use weighted_mean_axis if the weights are normalized.

      n
      ∑ wᵢxᵢ
     i=1
x̅ = ―――――――――
       n
       ∑ wᵢ
      i=1

Panics if axis is out of bounds.

The following errors may be returned:

  • MultiInputError::EmptyInput if self is empty
  • MultiInputError::ShapeMismatch if self length along axis is not equal to weights length

[arithmetic weighted mean] https://en.wikipedia.org/wiki/Weighted_arithmetic_mean

fn weighted_sum_axis(
    &self,
    axis: Axis,
    weights: &ArrayBase<S, Ix1>
) -> Result<Array<A, D::Smaller>, MultiInputError> where
    A: Copy + Mul<Output = A> + Zero,
    D: RemoveAxis, 

Returns the weighted sum along axis, that is, the dot product of weights and each lane of self along axis. Equivalent to weighted_mean_axis if the weights are normalized.

     n
x̅ =  ∑ wᵢxᵢ
    i=1

Panics if axis is out of bounds.

The following errors may be returned

  • MultiInputError::ShapeMismatch if self and weights don't have the same shape

fn harmonic_mean(&self) -> Result<A, EmptyInput> where
    A: Float + FromPrimitive, 

Returns the harmonic mean HM(X) of all elements in the array:

          ⎛ n     ⎞⁻¹
HM(X) = n ⎜ ∑ xᵢ⁻¹⎟
          ⎝i=1    ⎠

If the array is empty, Err(EmptyInput) is returned.

Panics if A::from_usize() fails to convert the number of elements in the array.

fn geometric_mean(&self) -> Result<A, EmptyInput> where
    A: Float + FromPrimitive, 

Returns the geometric mean GM(X) of all elements in the array:

        ⎛ n   ⎞¹⁄ₙ
GM(X) = ⎜ ∏ xᵢ⎟
        ⎝i=1  ⎠

If the array is empty, Err(EmptyInput) is returned.

Panics if A::from_usize() fails to convert the number of elements in the array.

fn kurtosis(&self) -> Result<A, EmptyInput> where
    A: Float + FromPrimitive, 

Returns the kurtosis Kurt[X] of all elements in the array:

Kurt[X] = μ₄ / σ⁴

where μ₄ is the fourth central moment and σ is the standard deviation of the elements in the array.

This is sometimes referred to as Pearson's kurtosis. Fisher's kurtosis can be computed by subtracting 3 from Pearson's kurtosis.

If the array is empty, Err(EmptyInput) is returned.

Panics if A::from_usize() fails to convert the number of elements in the array.

fn skewness(&self) -> Result<A, EmptyInput> where
    A: Float + FromPrimitive, 

Returns the Pearson's moment coefficient of skewness γ₁ of all elements in the array:

γ₁ = μ₃ / σ³

where μ₃ is the third central moment and σ is the standard deviation of the elements in the array.

If the array is empty, Err(EmptyInput) is returned.

Panics if A::from_usize() fails to convert the number of elements in the array.

fn central_moment(&self, order: u16) -> Result<A, EmptyInput> where
    A: Float + FromPrimitive, 

Returns the p-th central moment of all elements in the array, μₚ:

     1  n
μₚ = ―  ∑ (xᵢ-x̅)ᵖ
     n i=1

If the array is empty, Err(EmptyInput) is returned.

The p-th central moment is computed using a corrected two-pass algorithm (see Section 3.5 in Pébay et al., 2016). Complexity is O(np) when n >> p, p > 1.

Panics if A::from_usize() fails to convert the number of elements in the array or if order overflows i32.

fn central_moments(&self, order: u16) -> Result<Vec<A>, EmptyInput> where
    A: Float + FromPrimitive, 

Returns the first p central moments of all elements in the array, see central moment for more details.

If the array is empty, Err(EmptyInput) is returned.

This method reuses the intermediate steps for the k-th moment to compute the (k+1)-th, being thus more efficient than repeated calls to central moment if the computation of central moments of multiple orders is required.

Panics if A::from_usize() fails to convert the number of elements in the array or if order overflows i32.

fn __private__(&self, _: PrivateMarker)

This method makes this trait impossible to implement outside of ndarray-stats so that we can freely add new methods, etc., to this trait without breaking changes.

We don't anticipate any other crates needing to implement this trait, but if you do have such a use-case, please let us know.

Warning This method is not considered part of the public API, and client code should not rely on it being present. It may be removed in a non-breaking release.

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Implementations on Foreign Types

impl<A, S, D> SummaryStatisticsExt<A, S, D> for ArrayBase<S, D> where
    S: Data<Elem = A>,
    D: Dimension, [src]

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Implementors

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