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Specify behavior of statistical reductions over the empty set #262

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Merged
merged 5 commits into from
Sep 15, 2021
Merged

Specify behavior of statistical reductions over the empty set #262

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cf28806
Specify `mean` behavior when provided a 0D array
kgryte Sep 13, 2021
0168a1f
Specify `prod` behavior when provided a 0D array
kgryte Sep 13, 2021
8e7a73c
Specify `sum` behavior when provided a 0D array
kgryte Sep 13, 2021
9229e97
Rephrase special cases and add special cases for other stats reductions
kgryte Sep 13, 2021
12415cb
Add guidance for min and max when `x` is 0D
kgryte Sep 13, 2021
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38 changes: 38 additions & 0 deletions spec/API_specification/statistical_functions.md
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Expand Up @@ -20,6 +20,10 @@ A conforming implementation of the array API standard must provide and support t

Calculates the maximum value of the input array `x`.

```{note}
When the number of elements over which to compute the maximum value is zero, the maximum value is implementation-defined. Specification-compliant libraries may choose to error, return a sentinel value (e.g., if `x` is a floating-point input array, return `NaN`), or return the minimum possible value for the input array `x` data type (e.g., if `x` is a floating-point array, return `-infinity`).
```

#### Parameters

- **x**: _<array>_
Expand All @@ -45,6 +49,12 @@ Calculates the maximum value of the input array `x`.

Calculates the arithmetic mean of the input array `x`.

#### Special Cases

For a floating-point input array `x`, let `N` equal the number of elements over which to compute the arithmetic mean and

- if `N` is `0`, the arithmetic mean is `NaN`.

#### Parameters

- **x**: _<array>_
Expand All @@ -70,6 +80,10 @@ Calculates the arithmetic mean of the input array `x`.

Calculates the minimum value of the input array `x`.

```{note}
When the number of elements over which to compute the minimum value is zero, the minimum value is implementation-defined. Specification-compliant libraries may choose to error, return a sentinel value (e.g., if `x` is a floating-point input array, return `NaN`), or return the maximum possible value for the input array `x` data type (e.g., if `x` is a floating-point array, return `+infinity`).
```

#### Parameters

- **x**: _<array>_
Expand All @@ -95,6 +109,12 @@ Calculates the minimum value of the input array `x`.

Calculates the product of input array `x` elements.

#### Special Cases

For an input array `x`, let `N` equal the number of elements over which to compute the product and

- if `N` is `0`, the product is `1` (i.e., the empty product).

#### Parameters

- **x**: _<array>_
Expand All @@ -120,6 +140,12 @@ Calculates the product of input array `x` elements.

Calculates the standard deviation of the input array `x`.

#### Special Cases

For a floating-point input array `x`, let `N` equal the number of elements over which to compute the standard deviation and

- if `N - correction` is less than or equal to `0`, the standard deviation is `NaN`.

#### Parameters

- **x**: _<array>_
Expand Down Expand Up @@ -149,6 +175,12 @@ Calculates the standard deviation of the input array `x`.

Calculates the sum of the input array `x`.

#### Special Cases

For an input array `x`, let `N` equal the number of elements over which to compute the sum and

- if `N` is `0`, the sum is `0` (i.e., the empty sum).

#### Parameters

- **x**: _<array>_
Expand All @@ -174,6 +206,12 @@ Calculates the sum of the input array `x`.

Calculates the variance of the input array `x`.

#### Special Cases

For a floating-point input array `x`, let `N` equal the number of elements over which to compute the variance and

- if `N - correction` is less than or equal to `0`, the variance is `NaN`.

#### Parameters

- **x**: _<array>_
Expand Down