fintech-algorithms
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Units, Dimensions, Scale, and Normalization

Install and import#

bash
npm install fintech-algorithms
ts
import { unitsDimensionsScaleAndNormalization } from "fintech-algorithms/foundations/mathematical-language-and-quantitative-reasoning/units-dimensions-scale-and-normalization";

Signature#

unitsDimensionsScaleAndNormalization(input)

Rescales a series by subtracting an offset and dividing by a scale, so numbers recorded in one unit can be compared on a common footing.

Parameters#

NameTypeNotes
inputD00InputA plain object. Every F01 topic first reads values, which must be a non-empty array of finite numbers, and validates it before any per-topic branch runs. This topic then reads offset and scale, both coerced with Number, and sourceUnit, which is passed through untouched as a label.

Returns#

{ normalized: number[]; sourceUnit: unknown; targetUnit: string }

normalized holds (value - offset) / scale for each entry in input order. sourceUnit is echoed back from the input and targetUnit is always the fixed label scaled units.

Errors#

  • When input is not a plain object — throws TypeError
  • When values is missing, empty, or not an array — throws RangeError
  • When values contains a value that is not a finite number — throws RangeError
  • When scale is zero — throws RangeError

Complexity: time O(n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

input
{
  "values": [1, 2, 3, 4, 5],
  "startingCash": 1000,
  "inflows": 250,
  "outflows": 120,
  "slope": 2,
  "intercept": 1,
  "part": 25,
  "whole": 200,
  "elapsed": 5,
  "old": 4.5,
  "new": 4.75,
  "base": 16,
  "exponent": 0.5,
  "a": 2
}

Showing 14 of 28 fields.

Call#

unitsDimensionsScaleAndNormalization(input)

Returns#

object with 2 fields: normalized, sourceUnit

{
  "normalized": [0, 0.5, 1, 1.5, 2],
  "sourceUnit": "SAR millions"
}

Diagrams#

Units, Dimensions, Scale, and Normalization — concept anatomy
Units, Dimensions, Scale, and Normalization — lesson map
Units, Dimensions, Scale, and Normalization — mistake contrast

Calculation flow#

Units, Dimensions, Scale, and Normalization — four-part map 
flowchart LR
    A["Name the input"] --> B["Apply: base amount = displayed amount × scale; per-unit amount = base amount / count"]
    B --> C["Check units and boundary"]
    C --> D["Explain the output"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

  • The International System of Units (SI Brochure), 9th edition — Bureau International des Poids et Mesures
  • NIST/SEMATECH e-Handbook of Statistical Methods — NIST/SEMATECH
  • Author-derived and synthetic boundary

The rest of the Mathematical Language and Quantitative Reasoning family#