atoti.array module¶

atoti.array.len(measure)¶

Return a measure equal to the number of elements of the passed array measure.

Return type: Measure

atoti.array.max(measure)¶

Return a measure equal to the maximum element of the passed array measure.

The max of an empty array is None.

Return type: Measure

atoti.array.mean(measure)¶

Return a measure equal to the mean of all the elements of the passed array measure.

The mean of an empty array is 0.

Return type: Measure

atoti.array.min(measure)¶

Return a measure equal to the minimum element of the passed array measure.

The min of an empty array is None.

Return type: Measure

atoti.array.n_greatest(measure, n)¶

Return an array measure containing the n greatest elements of the passed array measure.

Return type: Measure

atoti.array.n_greatest_indices(measure, n)¶

Return an array measure containing the indices of the n greatest elements of the passed array measure.

Example

The following example creates a measure that returns the 3 greatest indices of an array:

m["array"] = [ 400, 200, 100, 500, 300]
m["3 greatest indices"] = atoti.array.n_greatest_indices(m["array"], 3)

This measure will return [3, 0, 4] because the greatest values are 500 at index 3, then 400 at index 0 and 300 at index 4.

Return type: Measure

atoti.array.n_lowest(measure, n)¶

Return an array measure containing the n lowest elements of the passed array measure.

Return type: Measure

atoti.array.n_lowest_indices(measure, n)¶

Return an array measure containing the indices of the n lowest elements of the passed array measure.

Example

The following example creates a measure that returns the 3 lowest indices of an array:

m["array"] = [ 400, 200, 100, 500, 300]
m["3 lowest indices"] = atoti.array.n_lowest_indices(m["array"], 3)

This measure will return [2, 1, 4] because the lowest values are 100 at index 2, then 200 at index 1 and 300 at index 4.

Return type: Measure

atoti.array.negative_values(measure)¶

Return a measure where all the elements > 0 of the passed array measure are replaced by 0.

Return type: Measure

atoti.array.nth_greatest(measure, n)¶

Return a measure equal to the n-th greatest element of the passed array measure.

Return type: Measure

atoti.array.nth_lowest(measure, n)¶

Return a measure equal to the n-th lowest element of the passed array measure.

Return type: Measure

atoti.array.positive_values(measure)¶

Return a measure where all the elements < 0 of the passed array measure are replaced by 0.

Return type: Measure

atoti.array.prefix_sum(measure)¶

Return a measure equal to the sum of the previous elements in the passed array measure.

Example

If an array has the following values: [2.0, 1.0, 0.0, 3.0], the returned array will be: [2.0, 3.0, 3.0, 6.0].

Return type: Measure

atoti.array.prod(measure)¶

Return a measure equal to the product of all the elements of the passed array measure.

The product of an empty array is 1.

Return type: Measure

atoti.array.quantile(measure, q, *, mode='inc', interpolation='linear')¶

Return a measure equal to the requested quantile of the elements of the passed array measure.

Here is how to obtain the same behaviour as these standard quantile calculation methods:

R-1: mode="centered" and interpolation="lower"
R-2: mode="centered" and interpolation="midpoint"
R-3: mode="simple" and interpolation="nearest"
R-4: mode="simple" and interpolation="linear"
R-5: mode="centered" and interpolation="linear"
R-6 (similar to Excel’s PERCENTILE.EXC): mode="exc" and interpolation="linear"
R-7 (similar to Excel’s PERCENTILE.INC): mode="inc" and interpolation="linear"
R-8 and R-9 are not supported

The formulae given for the calculation of the quantile index assume a 1-based indexing system.

Parameters

measure (Measure) – The measure to get the quantile of.
q (Union[float, Measure]) – The quantile to take. Must be between 0 and 1. For instance, 0.95 is the 95th percentile and 0.5 is the median.
mode (Literal[‘simple’, ‘centered’, ‘inc’, ‘exc’]) –
The method used to calculate the index of the quantile. Available options are, when searching for the q quantile of a vector X:
- simple: len(X) * q
- centered: len(X) * q + 0.5
- exc: (len(X) + 1) * q
- inc: (len(X) - 1) * q + 1
interpolation (Literal[‘linear’, ‘higher’, ‘lower’, ‘nearest’, ‘midpoint’]) –
If the quantile index is not an integer, the interpolation decides what value is returned. The different options are, considering a quantile index k with i < k < j for a sorted vector X:
- linear: v = X[i] + (X[j] - X[i]) * (k - i)
- lowest: v = X[i]
- highest: v = X[j]
- nearest: v = X[i] or v = X[j] depending on which of i or j is closest to k
- midpoint: v = (X[i] + X[j]) / 2

Return type

Measure

atoti.array.quantile_index(measure, q, *, mode='inc', interpolation='lower')¶

Return a measure equal to the index of requested quantile of the elements of the passed array measure.

Parameters

measure (Measure) – The measure to get the quantile of.
q (Union[float, Measure]) – The quantile to take. Must be between 0 and 1. For instance, 0.95 is the 95th percentile and 0.5 is the median.
mode (Literal[‘simple’, ‘centered’, ‘inc’, ‘exc’]) –
The method used to calculate the index of the quantile. Available options are, when searching for the q quantile of a vector X:
- simple: len(X) * q
- centered: len(X) * q + 0.5
- exc: (len(X) + 1) * q
- inc: (len(X) - 1) * q + 1
interpolation (Literal[‘higher’, ‘lower’, ‘nearest’]) –
If the quantile index is not an integer, the interpolation decides what value is returned. The different options are, considering a quantile index k with i < k < j for the original vector X and the sorted vector Y:
- lowest: the index in X of Y[i]
- highest: the index in X of Y[j]
- nearest: the index in X of Y[i] or Y[j] depending on which of i or j is closest to k

Return type

Measure

atoti.array.sort(measure, *, ascending=True)¶

Return an array measure with the elements of the passed array measure sorted.

Parameters

measure (Measure) – The array measure to sort.
ascending (bool) – When set to False, the first value will be the greatest.

Return type

Measure

atoti.array.std(measure, *, mode='sample')¶

Return a measure equal to the standard deviation of the elements of the passed array measure.

Parameters

measure (Measure) – The measure to get the standard deviation of.
mode (Literal[‘sample’, ‘population’]) –
One of the supported modes:
- The sample standard deviation, similar to Excel’s STDEV.S, is \(\sqrt{\frac{\sum_{i=0}^{n} (X_i - m)^{2}}{n - 1}}\) where m is the sample mean and n the size of the sample. Use this mode if the data represents a sample of the population.
- The population standard deviation, similar to Excel’s STDEV.P is \(\sqrt{\frac{\sum_{i=0}^{n}(X_i - m)^{2}}{n}}\) where m is the mean of the Xi elements and n the size of the population. Use this mode if the data represents the entire population.

Return type

Measure

atoti.array.sum(measure)¶

Return a measure equal to the sum of all the elements of the passed array measure.

The sum of an empty array is 0.

Return type: Measure

atoti.array.var(measure, *, mode='sample')¶

Return a measure equal to the variance of the elements of the passed array measure.

Parameters

measure (Measure) – The measure to get the variance of.
mode (Literal[‘sample’, ‘population’]) –
One of the supported modes:
- The sample variance, similar to Excel’s VAR.S, is \(\frac{\sum_{i=0}^{n} (X_i - m)^{2}}{n - 1}\) where m is the sample mean and n the size of the sample. Use this mode if the data represents a sample of the population.
- The population variance, similar to Excel’s VAR.P is \(\frac{\sum_{i=0}^{n}(X_i - m)^{2}}{n}\) where m is the mean of the Xi elements and n the size of the population. Use this mode if the data represents the entire population.

Return type

Measure