Arithmetics

The following arithmetic operations are supported:

Symbol	Name
+	Addition
-	Subtraction
*	Multiplication
/	Division
**	Exponentiation

These operations are used as ordinary arithmetical operators:

signal_1 + signal_2

Note on missing values: When performing arithmetic operations between signals, if any of the signals is missing data for certain dates, the result will not include data points on those dates.

Alternative approach: To handle missing data more gracefully, you can use the concat function followed by aggregation instead of direct arithmetic operations:

# Instead of:
signal1 + signal2
# Use:
concat([signal1, signal2]).sum()

# Instead of:
signal1 - signal2
# Use:
concat([signal1, -signal2]).sum()

This approach concatenates the signals and then applies an aggregation function (like sum()) that can handle missing values by skipping them rather than producing missing values.

weighted_sum(signal_1, signal_2, ..., signal_n, weights=[w_1, w_2,...w_3], nan_when_missing=False, normalize=True)

This function provides a method for handling weighted sums with possible missing values. When the signals have numerical values for a given time the value of weighted_sum is

w_1*signal_1 + w_2*signal_2 + … + w_n*signal_n.

When some signals are not numbers, the weighted sum is taken over only the signals with numerical values.

Parameters:

• signal_j – For j=1, 2, …, n, the signals which are combined.

• weights – When a list of n numerical weights is supplied this is the weights in the sum. When no weights are supplied it is assumed that w_j=1.

• nan_when_missing – If one of the signals have a missing value (NaN) the value of the sum is set to missing (NaN) if nan_when_missing=True, otherwise the missing values are skipped in the sum.

• normalize – If normalize=True the weights w_j are normalized so that the active weights sum to 1.

Example:

Combining card transaction data from multiple countries as a weighted average:

weighted_sum(UK_Spend, Germany_Spend, France_Spend, Italy_Spend, Spain_Spend, weights=[0.35, 0.35, 0.15, 0.1, 0.05])

signal.log()

Calculate the natural logarithm of the signal.

signal.exp()

Apply the exponential function to the signal.

For each value in the original signal, the result is calculated as the base of the natural logarithm, e ≈ 2.71, raised to the power of the original value.

signal.abs()

Calculate the absolute values of the signal.

signal.sign()

Calculate the sign of the signal values.

For each value in the original signal, the sign is +1 if the original value is positive, -1 if the original value is negative, and 0 if the original value is 0.