# Namespace Normalization¶

namespace normalization

Functions

af::array decimalScalingNorm(af::array tss)

Normalizes the given time series according to its maximum value and adjusts each value within the range (-1, 1).

Return
af::array An array with the same dimensions as tss, whose values (time series in dimension 0) have been normalized by dividing each number by 10^j, where j is the number of integer digits of the max number in the time series.
Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.

void decimalScalingNormInPlace(af::array &tss)

Same as decimalScalingNorm, but it performs the operation in place, without allocating further memory.

Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.

af::array maxMinNorm(af::array tss, double high = 1.0, double low = 0.0, double epsilon = 0.00000001)

Normalizes the given time series according to its minimum and maximum value and adjusts each value within the range [low, high].

Return
af::array An array with the same dimensions as tss, whose values (time series in dimension 0) have been normalized by maximum and minimum values, and scaled as per high and low parameters.
Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.
• high: Maximum final value (Defaults to 1.0).
• low: Minimum final value (Defaults to 0.0).
• epsilon: Safeguard for constant (or near constant) time series as the operation implies a unit scale operation between min and max values in the tss.

void maxMinNormInPlace(af::array &tss, double high = 1.0, double low = 0.0, double epsilon = 0.00000001)

Same as maxMinNorm, but it performs the operation in place, without allocating further memory.

Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.
• high: Maximum final value (Defaults to 1.0).
• low: Minimum final value (Defaults to 0.0).
• epsilon: Safeguard for constant (or near constant) time series as the operation implies a unit scale operation between min and max values in the tss.

af::array meanNorm(af::array tss)

Normalizes the given time series according to its maximum-minimum value and its mean. It follows the following formulae:

$\acute{x} = \frac{x - mean(x)}{max(x) - min(x)}.$

Return
af::array An array with the same dimensions as tss, whose values (time series in dimension 0) have been normalized by substracting the mean from each number and dividing each number by $$max(x) - min(x)$$, in the time series.
Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.

void meanNormInPlace(af::array &tss)

Normalizes the given time series according to its maximum-minimum value and its mean. It follows the following formulae:

$\acute{x} = \frac{x - mean(x)}{max(x) - min(x)}.$

Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.

af::array znorm(af::array tss, double epsilon = 0.00000001)

Calculates a new set of timeseries with zero mean and standard deviation one.

Return
af::array With the same dimensions as tss where the time series have been adjusted for zero mean and one as standard deviation.
Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.
• epsilon: Minimum standard deviation to consider. It acts as a gatekeeper for those time series that may be constant or near constant.

void znormInPlace(af::array &tss, double epsilon = 0.00000001)

Adjusts the time series in the given input and performs z-norm inplace (without allocating further memory).

Parameters
• tss: Expects an input array whose dimension zero is the length of the time series (all the same) and dimension one indicates the number of time series.
• epsilon: Minimum standard deviation to consider. It acts as a gatekeeper for those time series that may be constant or near constant.