Correlation (correlate) in SciPy - Step-by-Step Execution

Concept Flow - Correlation (correlate)

Input: Two sequences

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Choose mode: 'full', 'valid', 'same'

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Slide one sequence over the other

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Multiply overlapping elements

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Sum the products

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Store sum in output array

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Repeat for all valid shifts

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Return correlation array

Correlation slides one sequence over another, multiplies overlapping values, sums them, and stores results for each shift.

Execution Sample

SciPy

import numpy as np
from scipy.signal import correlate

x = np.array([1, 2, 3])
y = np.array([0, 1, 0.5])
result = correlate(x, y, mode='full')

Calculate full correlation of two small sequences x and y.

Execution Table

Step	Shift	Overlapping Elements (x, y)	Products	Sum	Output Array State
1	-2	(3,0)	3*0=0	0	[0]
2	-1	(2,0), (3,1)	2*0=0, 3*1=3	3	[0, 3]
3	0	(1,0), (2,1), (3,0.5)	1*0=0, 2*1=2, 3*0.5=1.5	3.5	[0, 3, 3.5]
4	1	(1,1), (2,0.5)	1*1=1, 2*0.5=1	2	[0, 3, 3.5, 2]
5	2	(1,0.5)	1*0.5=0.5	0.5	[0, 3, 3.5, 2, 0.5]

💡 All valid shifts processed; correlation array complete with length 5.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	Final
Shift	N/A	-2	-1	0	1	2	N/A
Output Array	[]	[0]	[0, 3]	[0, 3, 3.5]	[0, 3, 3.5, 2]	[0, 3, 3.5, 2, 0.5]	[0, 3, 3.5, 2, 0.5]

Key Moments - 2 Insights

Why does the output array length equal 5 for inputs of length 3?

Because mode='full' computes correlation at all shifts where sequences overlap at least partially, resulting in length = len(x) + len(y) - 1 = 3 + 3 - 1 = 5, as shown in execution_table rows 1-5.

Why is the first sum zero when shift is -2?

At shift -2, only the last element of x overlaps with the first element of y which is zero, so product is zero and sum is zero (execution_table row 1).

Visual Quiz - 3 Questions

Look at the execution table, what is the sum of products at shift 0?

A 2

B 3.5

C 3

D 0.5

💡 Hint

Check execution_table row 3 under 'Sum' column.

At which shift does the output array first get a non-zero value?

A -1

B -2

C 0

D 1

💡 Hint

Look at execution_table rows 1 and 2 for output values.

If mode was 'valid', how would the output array length change?

A It would be longer than 5

B It would be exactly 5

C It would be shorter than 5

D It would be zero length

💡 Hint

Recall 'valid' mode only includes full overlaps, so output length is smaller than full mode length.

Concept Snapshot

scipy.signal.correlate(x, y, mode='full')
- Slides y over x, multiplies overlapping elements, sums them
- mode='full' returns all overlaps (length = len(x)+len(y)-1)
- Output array shows correlation values at each shift
- Useful to find similarity or lag between sequences

Full Transcript

Correlation using scipy.signal.correlate takes two sequences and slides one over the other. At each shift, it multiplies overlapping elements and sums these products to produce a correlation value. The mode parameter controls which shifts are included. In 'full' mode, all partial overlaps are considered, resulting in an output array length equal to the sum of input lengths minus one. This process helps measure similarity or lag between sequences. The example traces each shift, showing overlapping elements, their products, and the cumulative output array building step-by-step.