# zivaCalculusExt

Allows you to perform calculus on numerical and boolean history grids in SkySpark.
zivaCalculusExt

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v1.8.0

## Overview

Welcome to SkySpark's Calculus Extension!

## zivaFindIntervals(hisGrid)

Find Intervals

• Return the ts, interval of a hisGrid
• Side Effects: Lose first ts of hisGrid
• Input: ts, val grid
• Output: Transmuted history grid of ts, interval

Cumulative Integral/Area under the Curve from Rectangle Method Approximation

• Supports a true History Grid with multiple V columns
• Should be exact for COV Points
• Side Effect: Data interpolated
• Input: ts, val*n grid where val*n can be multiple V columns with numbers and/or booleans
• Output: Transmuted history grid of ts, V*n columns

Cumulative Integral/Area under the Curve from Trapezoid Method Approximation

• Supports a true History Grid with multiple V columns
• Should be exact for Linear Points
• Side Effect: Data interpolated
• Input: ts, val*n grid where val*n can be multiple V columns with numbers and/or booleans
• Output: Transmuted history grid of ts, V*n columns

## zivaHisDelta(hisGrid)

Rolling Delta

• Supports a true History Grid with multiple V columns
• Side Effect: Data interpolated
• Input: ts, val*n grid where val*n can be multiple V columns with numbers
• Output: Transmuted history grid of ts, V*n columns
• Example: Get change between samples

## zivaHisDerivative(hisGrid)

Derivative

• Supports a true History Grid with multiple V columns
• Slope going to ts data-point is used as derivative of ts data-point
• Side Effects: Lose first ts of hisGrid; data interpolated
• Input: ts, val*n grid where val*n can be multiple V columns with numbers and/or booleans
• Output: Transmuted history grid of ts, V*n columns

## zivaHisRectIntegral(hisGrid)

Integral from Rectangle Method Approximation

• Supports a true History Grid with multiple V columns
• Should be exact for COV Points
• Side Effects: Lose first ts of hisGrid; data interpolated
• Input: ts, val*n grid where val*n can be multiple V columns with numbers and/or booleans
• Output: Transmuted history grid of ts, V*n columns

## zivaHisSum(hisGrid)

Rolling Sum

• Supports a true History Grid with multiple V columns
• Side Effect: Data interpolated
• Input: ts, val*n grid where val*n can be multiple V columns with numbers
• Output: Transmuted history grid of ts, V*n columns
• Example: Turn energy differentials to totalized values

## zivaHisTrapIntegral(hisGrid)

Integral from Trapezoid Method Approximation

• Supports a true History Grid with multiple V columns
• Should be exact for linear Points
• Side Effects: Lose first ts of hisGrid; data interpolated
• Input: ts, val*n grid where val*n can be multiple V columns with numbers and/or booleans
• Output: Transmuted history grid of ts, V*n columns

## zivaPreUnitFixer(value)

Function used to convert booleans and fix null units

• Fixes input units
• Inputs: Number or boolean
• Output: Number with units

## zivaPostUnitFixer(value)

Function used to fix time units in calculus functions.

• Fixes resultant units
• Inputs: Number with units
• Output: Number with clean units

## zivaHisZScore(hisGrid)

Get each ZScore of each cell of a hisGrid

• Supports a true History Grid with multiple V columns
• Side Effects: None
• Input: ts, v0 grid
• Output: Transmuted history grid of ts, v0 columns