interp1d for 1D interpolation in SciPy - Step-by-Step Execution

Concept Flow - interp1d for 1D interpolation

Start with known points (x, y)

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Create interp1d function

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Input new x values

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interp1d calculates interpolated y

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Output interpolated y values

We start with known data points, create an interpolation function, input new x values, and get interpolated y values.

Execution Sample

SciPy

from scipy.interpolate import interp1d
x = [0, 1, 2]
y = [0, 1, 4]
f = interp1d(x, y)
new_x = [0.5, 1.5]
result = f(new_x)

This code creates an interpolation function from points (0,0), (1,1), (2,4) and finds y values at 0.5 and 1.5.

Execution Table

Step	Action	Input	Process	Output
1	Define known points	x=[0,1,2], y=[0,1,4]	Store points for interpolation	Points stored
2	Create interp1d function	x, y	Build linear interpolation function	Function f created
3	Input new x values	new_x=[0.5,1.5]	Pass new_x to f	Calculate interpolated y
4	Calculate y at 0.5	0.5	Linear interpolate between (0,0) and (1,1)	0.5
5	Calculate y at 1.5	1.5	Linear interpolate between (1,1) and (2,4)	2.5
6	Return result	new_x	Collect interpolated values	[0.5, 2.5]

💡 All new_x values processed, interpolation complete

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 6
x	undefined	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]
y	undefined	[0,1,4]	[0,1,4]	[0,1,4]	[0,1,4]
f	undefined	undefined	interp1d function	interp1d function	interp1d function
new_x	undefined	undefined	undefined	[0.5,1.5]	[0.5,1.5]
result	undefined	undefined	undefined	undefined	[0.5, 2.5]

Key Moments - 2 Insights

Why does interp1d only work between the known x points?

interp1d by default does linear interpolation only within the range of x. Outside this range, it cannot estimate values unless specified. See execution_table steps 4 and 5 where interpolation happens between known points.

What happens if new_x contains a value exactly equal to a known x?

interp1d returns the exact y value for that x without interpolation. This is because the function matches the known point directly, as shown in execution_table step 4 for x=0.5 (between points) and would be direct if x=1.

Visual Quiz - 3 Questions

Look at the execution_table, what is the interpolated y value at new_x=1.5?

A 2.5

B 1.5

C 3.0

D 4.0

💡 Hint

Check step 5 in execution_table where y at 1.5 is calculated.

According to variable_tracker, what is the value of 'result' after step 6?

A [0, 1]

B [1.0, 4.0]

C [0.5, 2.5]

D undefined

💡 Hint

Look at the 'result' row under 'After Step 6' in variable_tracker.

If we add new_x=3 to the input, what will happen by default?

A interp1d will extrapolate and give a value

B interp1d will raise an error

C interp1d will return NaN

D interp1d will ignore the value

💡 Hint

interp1d by default does not extrapolate beyond known x; see key_moments about interpolation range.

Concept Snapshot

interp1d creates a function for 1D interpolation
Input: known x and y points
Output: interpolated y for new x values
Default: linear interpolation within x range
Outside range: raises error unless allowed
Use f(new_x) to get interpolated results

Full Transcript

We start with known data points x and y. Then we create an interpolation function f using interp1d. When we input new x values, the function calculates y values by linear interpolation between the known points. For example, at x=0.5, y is 0.5, and at x=1.5, y is 2.5. The function only works within the range of known x values by default. If a new x is outside this range, an error occurs unless extrapolation is enabled. The result is an array of interpolated y values corresponding to the new x inputs.