Understanding Array Shapes

In Openmadness, the shape of an array defines its dimensions and structure. It's like a blueprint that describes how your data is organized in space.

What is Shape?

The shape property returns an array where each element represents the size of a dimension:

For a 1D array (vector): shape is [length]
For a 2D array (matrix): shape is [rows, columns]
For a 3D array (cube): shape is [depth, rows, columns]

Examples

1D Array (Vector)

const temperatures = om.array([72, 75, 68, 71, 69]);
console.log("Temperatures shape:", temperatures.shape); // Output: [5]
// A single dimension with 5 elements

2D Array (Matrix)

const monthlyRevenue = om.array([
  [45000, 52000, 49000], // Q1 revenue for 3 products
  [48000, 51000, 47000], // Q2 revenue for 3 products
  [50000, 53000, 51000], // Q3 revenue for 3 products
]);
console.log("Monthly Revenue shape:", monthlyRevenue.shape); // Output: [3, 3]
// 3 rows and 3 columns

3D Array (Cube)

const yearlyData = om.array([
  // Year 1
  [
    [10, 20, 30], // Product A, regions 1-3
    [15, 25, 35], // Product B, regions 1-3
  ],
  // Year 2
  [
    [12, 22, 32], // Product A, regions 1-3
    [17, 27, 37], // Product B, regions 1-3
  ],
]);
console.log("Yearly Data shape:", yearlyData.shape); // Output: [2, 2, 3]
// 2 years, 2 products, 3 regions

Why Shapes Matter

Understanding shapes is essential because:

Operation Compatibility: Many operations require arrays with compatible shapes
Broadcasting: OpenMadness can automatically expand smaller arrays to match larger ones
Performance: Knowing your data's shape helps optimize memory usage and computation

Reshaping Arrays

You can transform an array's shape while preserving its data using the reshape() method:

import om from "openmadness";

const data = om.array([1, 2, 3, 4, 5, 6]);
console.log("Original shape:", data.shape); // Output: [6]

const reshaped = data.reshape([2, 3]);
console.log("Reshaped data:", reshaped.data);
// Output: [[1, 2, 3], [4, 5, 6]]
console.log("New shape:", reshaped.shape); // Output: [2, 3]

Remember

When reshaping, the total number of elements must remain the same (2×3=6 in the example above).