[−][src]Trait ndarray_stats::SummaryStatisticsExt

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

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

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

    pub 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;

    pub 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;

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

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

    pub fn weighted_var(
        &self, 
        weights: &Self, 
        ddof: A
    ) -> Result<A, MultiInputError>
    where
        A: AddAssign + Float + FromPrimitive;

    pub fn weighted_std(
        &self, 
        weights: &Self, 
        ddof: A
    ) -> Result<A, MultiInputError>
    where
        A: AddAssign + Float + FromPrimitive;

    pub fn weighted_var_axis(
        &self, 
        axis: Axis, 
        weights: &ArrayBase<S, Ix1>, 
        ddof: A
    ) -> Result<Array<A, D::Smaller>, MultiInputError>
    where
        A: AddAssign + Float + FromPrimitive,
        D: RemoveAxis;

    pub fn weighted_std_axis(
        &self, 
        axis: Axis, 
        weights: &ArrayBase<S, Ix1>, 
        ddof: A
    ) -> Result<Array<A, D::Smaller>, MultiInputError>
    where
        A: AddAssign + Float + FromPrimitive,
        D: RemoveAxis;

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

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

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

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

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

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

Required methods

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

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.

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

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

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

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

pub 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, [src]

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

pub 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, [src]

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

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

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.

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

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.

pub fn weighted_var(
    &self,
    weights: &Self,
    ddof: A
) -> Result<A, MultiInputError> where
    A: AddAssign + Float + FromPrimitive, [src]

Return weighted variance of all elements in the array.

The weighted variance is computed using the West, D. H. D. incremental algorithm. Equivalent to var_axis if the weights are normalized.

The parameter ddof specifies the "delta degrees of freedom". For example, to calculate the population variance, use ddof = 0, or to calculate the sample variance, use ddof = 1.

Panics if ddof is less than zero or greater than one, or if axis is out of bounds, or if A::from_usize() fails for zero or one.

pub fn weighted_std(
    &self,
    weights: &Self,
    ddof: A
) -> Result<A, MultiInputError> where
    A: AddAssign + Float + FromPrimitive, [src]

Return weighted standard deviation of all elements in the array.

The weighted standard deviation is computed using the West, D. H. D. incremental algorithm. Equivalent to var_axis if the weights are normalized.

The parameter ddof specifies the "delta degrees of freedom". For example, to calculate the population variance, use ddof = 0, or to calculate the sample variance, use ddof = 1.

Panics if ddof is less than zero or greater than one, or if axis is out of bounds, or if A::from_usize() fails for zero or one.

pub fn weighted_var_axis(
    &self,
    axis: Axis,
    weights: &ArrayBase<S, Ix1>,
    ddof: A
) -> Result<Array<A, D::Smaller>, MultiInputError> where
    A: AddAssign + Float + FromPrimitive,
    D: RemoveAxis, [src]

Return weighted variance along axis.

The weighted variance is computed using the West, D. H. D. incremental algorithm. Equivalent to var_axis if the weights are normalized.

The parameter ddof specifies the "delta degrees of freedom". For example, to calculate the population variance, use ddof = 0, or to calculate the sample variance, use ddof = 1.

Panics if ddof is less than zero or greater than one, or if axis is out of bounds, or if A::from_usize() fails for zero or one.

pub fn weighted_std_axis(
    &self,
    axis: Axis,
    weights: &ArrayBase<S, Ix1>,
    ddof: A
) -> Result<Array<A, D::Smaller>, MultiInputError> where
    A: AddAssign + Float + FromPrimitive,
    D: RemoveAxis, [src]

Return weighted standard deviation along axis.

The weighted standard deviation is computed using the West, D. H. D. incremental algorithm. Equivalent to var_axis if the weights are normalized.

The parameter ddof specifies the "delta degrees of freedom". For example, to calculate the population variance, use ddof = 0, or to calculate the sample variance, use ddof = 1.

Panics if ddof is less than zero or greater than one, or if axis is out of bounds, or if A::from_usize() fails for zero or one.

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

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.

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

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.

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

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.

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

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.

pub fn __private__(&self, _: PrivateMarker)[src]

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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