np.linspace() for evenly spaced arrays in NumPy - Step-by-Step Execution

Concept Flow - np.linspace() for evenly spaced arrays

Start with start, stop, num

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Calculate step size = (stop - start) / (num - 1)

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Generate array elements: start + i * step for i in 0 to num-1

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Return evenly spaced array

np.linspace() takes start, stop, and number of points, then calculates equal steps and creates an array with those points.

Execution Sample

NumPy

import numpy as np
arr = np.linspace(0, 10, 5)
print(arr)

Creates an array of 5 numbers evenly spaced from 0 to 10.

Execution Table

Step	i (index)	Calculation	Value	Array so far
1	0	0 + 0 * 2.5	0.0	[0.0]
2	1	0 + 1 * 2.5	2.5	[0.0, 2.5]
3	2	0 + 2 * 2.5	5.0	[0.0, 2.5, 5.0]
4	3	0 + 3 * 2.5	7.5	[0.0, 2.5, 5.0, 7.5]
5	4	0 + 4 * 2.5	10.0	[0.0, 2.5, 5.0, 7.5, 10.0]
6	-	All points generated	-	[0.0, 2.5, 5.0, 7.5, 10.0]

💡 All 5 points generated, array complete.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
i	N/A	0	1	2	3	4	N/A
step	N/A	2.5	2.5	2.5	2.5	2.5	2.5
value	N/A	0.0	2.5	5.0	7.5	10.0	10.0
array	[]	[0.0]	[0.0, 2.5]	[0.0, 2.5, 5.0]	[0.0, 2.5, 5.0, 7.5]	[0.0, 2.5, 5.0, 7.5, 10.0]	[0.0, 2.5, 5.0, 7.5, 10.0]

Key Moments - 3 Insights

Why does np.linspace include the stop value in the array?

Because np.linspace divides the interval into (num-1) equal steps and includes both start and stop points, as shown in execution_table rows 1 and 5.

What happens if num is 1 in np.linspace(start, stop, num)?

The array will contain only the start value, since no steps are needed. This is different from a range and is not shown here but follows the same logic.

Why is the step size calculated as (stop - start) / (num - 1)?

Because to get num points including start and stop, we need (num-1) intervals between them, as explained in concept_flow and shown in the step calculation in execution_table.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value at i=3?

A 5.0

B 7.5

C 10.0

D 2.5

💡 Hint

Check the row where i=3 in the execution_table to see the calculated value.

At which step does the array reach its final length?

A Step 6

B Step 4

C Step 5

D Step 3

💡 Hint

Look at the 'Array so far' column in execution_table to see when the array has 5 elements.

If num was changed to 3, what would the step size be?

A 5.0

B 3.3

C 10.0

D 2.5

💡 Hint

Use the formula step = (stop - start) / (num - 1) with stop=10, start=0, num=3.

Concept Snapshot

np.linspace(start, stop, num)
Creates num evenly spaced points from start to stop inclusive.
Step size = (stop - start) / (num - 1).
Returns a numpy array with these points.
Useful for smooth ranges including the end value.

Full Transcript

np.linspace() is a function in numpy that creates an array of evenly spaced numbers between a start and stop value. You give it three inputs: start, stop, and how many points you want. It calculates the step size by dividing the distance between start and stop by one less than the number of points. Then it creates each point by adding multiples of the step size to the start. The result is an array that includes both the start and stop values, spaced evenly. This is different from functions like range() which exclude the stop value. For example, np.linspace(0, 10, 5) creates [0.0, 2.5, 5.0, 7.5, 10.0]. This method is very useful when you want a smooth set of points for plotting or calculations.