2D interpolation (interp2d, griddata) in SciPy - Step-by-Step Execution

Concept Flow - 2D interpolation (interp2d, griddata)

Start with scattered 2D points

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Choose interpolation method

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interp2d: grid-based

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Create interpolation function

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Input new points to estimate values

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Output interpolated values on new points

We start with scattered 2D data points, choose an interpolation method (interp2d or griddata), create an interpolation function, then input new points to get estimated values.

Execution Sample

SciPy

import numpy as np
from scipy.interpolate import interp2d, griddata

x = np.array([0, 1, 2])
y = np.array([0, 1, 2])
z = np.array([[0, 1, 4], [1, 2, 5], [4, 5, 8]])

f_interp2d = interp2d(x, y, z, kind='linear')
zi = f_interp2d(1.5, 1.5)

points = np.array([[0,0],[1,1],[2,2]])
values = np.array([0,2,8])
zi_griddata = griddata(points, values, (1.5,1.5), method='linear')

This code creates interpolation functions using interp2d and griddata, then estimates values at point (1.5, 1.5).

Execution Table

Step	Action	Input	Output/Result
1	Define x, y arrays	x=[0,1,2], y=[0,1,2]	Arrays created
2	Define z matrix	z=[[0,1,4],[1,2,5],[4,5,8]]	Matrix created
3	Create interp2d function	interp2d(x,y,z,kind='linear')	Function f_interp2d created
4	Call f_interp2d(1.5,1.5)	x=1.5, y=1.5	Interpolated value zi = 4.75
5	Define points and values for griddata	points=[[0,0],[1,1],[2,2]], values=[0,2,8]	Arrays created
6	Call griddata(points, values, (1.5,1.5), method='linear')	point=(1.5,1.5)	Interpolated value zi_griddata = 5.0
7	End	No more calls	Interpolation complete

💡 All interpolation steps completed, values estimated at (1.5,1.5)

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
x	undefined	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]
y	undefined	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]	[0,1,2]
z	undefined	undefined	[[0,1,4],[1,2,5],[4,5,8]]	[[0,1,4],[1,2,5],[4,5,8]]	[[0,1,4],[1,2,5],[4,5,8]]	[[0,1,4],[1,2,5],[4,5,8]]	[[0,1,4],[1,2,5],[4,5,8]]	[[0,1,4],[1,2,5],[4,5,8]]
f_interp2d	undefined	undefined	undefined	interp2d function	interp2d function	interp2d function	interp2d function	interp2d function
zi	undefined	undefined	undefined	undefined	4.75	4.75	4.75	4.75
points	undefined	undefined	undefined	undefined	undefined	[[0,0],[1,1],[2,2]]	[[0,0],[1,1],[2,2]]	[[0,0],[1,1],[2,2]]
values	undefined	undefined	undefined	undefined	undefined	[0,2,8]	[0,2,8]	[0,2,8]
zi_griddata	undefined	undefined	undefined	undefined	undefined	undefined	5.0	5.0

Key Moments - 3 Insights

Why does interp2d require grid data but griddata can handle scattered points?

interp2d needs x and y arrays to be sorted and form a grid (see Step 3 in execution_table), while griddata works directly with scattered points (Step 5). This is why griddata is more flexible for irregular data.

Why can the interpolated values from interp2d and griddata be different at (1.5, 1.5)?

interp2d uses the grid z values and linear interpolation on the grid (Step 4), while griddata uses the scattered points and their values (Step 6). Different input data and methods cause different results.

What happens if we input a point outside the original data range?

Both methods may return NaN or extrapolate poorly. This is because interpolation estimates values inside known data bounds (see exit_note). Extrapolation is not guaranteed.

Visual Quiz - 3 Questions

Look at the execution_table at Step 4, what is the interpolated value from interp2d at (1.5, 1.5)?

A Undefined

B 5.0

C 3.75

D 2.5

💡 Hint

Check the Output/Result column at Step 4 in execution_table.

At which step does griddata compute the interpolated value?

A Step 3

B Step 6

C Step 4

D Step 2

💡 Hint

Look for 'griddata' call and output in execution_table rows.

If we change the interpolation method in interp2d from 'linear' to 'cubic', what changes in the execution_table?

A Step 3 function creation fails

B Step 6 output value changes

C Step 4 output value changes

D No change at all

💡 Hint

interp2d function creation is at Step 3, output at Step 4 depends on method.

Concept Snapshot

2D Interpolation with interp2d and griddata:
- interp2d: for gridded data, creates a function f(x,y)
- griddata: for scattered points, interpolates at any point
- Both estimate values inside known data range
- Use kind='linear' or 'cubic' for smoothness
- Output: interpolated values at new points

Full Transcript

This visual execution shows how 2D interpolation works using scipy's interp2d and griddata. We start with known data points arranged either on a grid or scattered. interp2d requires grid data and creates a function to estimate values at new points. griddata works directly with scattered points and interpolates values at any location. We traced variable values and function calls step-by-step, showing how inputs transform into interpolated outputs. Key moments clarify differences between methods and common beginner questions. The quiz tests understanding of the interpolation steps and results.

Practice

1. What is the main difference between interp2d and griddata in SciPy for 2D interpolation?

easy

A. interp2d returns values directly; griddata returns a function.

B. interp2d works on regular grids; griddata works on scattered points.

C. interp2d only works for 1D data; griddata works for 2D data.

D. interp2d is faster than griddata in all cases.

Solution

1. Step 1: Understand interp2d usage

   interp2d requires data on a regular grid and returns an interpolation function.

2. Step 2: Understand griddata usage

   griddata works with scattered (irregular) points and returns interpolated values directly.

3. Final Answer:

   interp2d works on regular grids; griddata works on scattered points. -> Option B

4. Quick Check:

   Grid type difference = interp2d works on regular grids; griddata works on scattered points. [OK]

Hint: Remember: interp2d = grid, griddata = scattered points [OK]

Common Mistakes:

• Confusing which function returns a callable
• Thinking both require regular grids
• Assuming griddata returns a function

2. Which of the following is the correct way to create an interpolation function using interp2d with arrays x, y, and z?

easy

A. f = interp2d(z, x, y, kind='cubic')

B. f = interp2d(x, y)

C. f = interp2d(x, y, z, kind='linear')

D. f = interp2d(x, y, z, method='nearest')

Solution

1. Step 1: Check interp2d parameters

   interp2d requires x, y, and z arrays, plus optional kind for interpolation type.

2. Step 2: Validate option syntax

   f = interp2d(x, y, z, kind='linear') uses correct parameter order and valid kind argument. f = interp2d(z, x, y, kind='cubic') swaps parameters incorrectly. f = interp2d(x, y) misses z. f = interp2d(x, y, z, method='nearest') uses invalid method keyword.

3. Final Answer:

   f = interp2d(x, y, z, kind='linear') -> Option C

4. Quick Check:

   Correct parameters and keyword = f = interp2d(x, y, z, kind='linear') [OK]

Hint: Remember interp2d needs x, y, z arrays and 'kind' keyword [OK]

Common Mistakes:

• Swapping x, y, z order
• Using 'method' instead of 'kind'
• Omitting z array

3. What is the output of this code snippet?

import numpy as np
from scipy.interpolate import griddata
points = np.array([[0, 0], [1, 0], [0, 1]])
values = np.array([1, 2, 3])
xi = np.array([[0.5, 0.5]])
result = griddata(points, values, xi, method='linear')
print(result)

medium

A. [3.0]

B. [1.5]

C. [2.5]

D. [2.0]

Solution

1. Step 1: Understand input points and values

   Points are at (0,0)=1, (1,0)=2, (0,1)=3. We want value at (0.5,0.5).

2. Step 2: Apply linear interpolation

   Linear interpolation averages values weighted by distance. At (0.5,0.5), value is average of 1, 2, 3 weighted equally, resulting in 2.0.

3. Final Answer:

   [2.0] -> Option D

4. Quick Check:

   Linear interpolation at center = 2.0 [OK]

Hint: For triangle center, average vertex values linearly [OK]

Common Mistakes:

• Confusing method keyword
• Miscomputing weighted average
• Expecting a scalar instead of array

4. Identify the error in this code using interp2d:

import numpy as np
from scipy.interpolate import interp2d
x = np.array([0, 1, 2])
y = np.array([0, 1, 2])
z = np.array([1, 2, 3])
f = interp2d(x, y, z, kind='cubic')
print(f(1.5, 1.5))

medium

A. The shape of z does not match the grid defined by x and y.

B. The 'kind' parameter should be 'linear' instead of 'cubic'.

C. interp2d does not accept numpy arrays as input.

D. The function call f(1.5, 1.5) should be f([1.5], [1.5]).

Solution

1. Step 1: Check shapes of x, y, and z

   x and y have length 3 each, so z must be 3x3 grid (2D array), but z is 1D with length 3.

2. Step 2: Understand interp2d requirements

   interp2d expects z shape to be (len(y), len(x)) matching grid points. Mismatch causes error.

3. Final Answer:

   The shape of z does not match the grid defined by x and y. -> Option A

4. Quick Check:

   z shape must match x,y grid [OK]

Hint: z must be 2D array matching x and y grid sizes [OK]

Common Mistakes:

• Passing 1D z instead of 2D
• Ignoring shape mismatch errors
• Misusing function call syntax

5. You have scattered temperature data at points pts = np.array([[0,0],[1,0],[0,1],[1,1]]) with values temps = np.array([30, 32, 31, 29]). You want to estimate temperature on a regular 5x5 grid covering [0,1]x[0,1]. Which approach correctly achieves this?

hard

A. Use griddata with pts, temps, and the 5x5 grid points to get interpolated values.

B. Use interp2d directly with pts and temps arrays.

C. Use griddata but only with the corner points of the grid.

D. Use interp2d with a 1D array of temps and x, y coordinates.

Solution

1. Step 1: Identify data type

   Data points are scattered (not on a regular grid), so griddata is suitable.

2. Step 2: Create regular grid and interpolate

   Create 5x5 grid points with np.meshgrid and use griddata with pts and temps to get interpolated temperatures on grid.

3. Final Answer:

   Use griddata with pts, temps, and the 5x5 grid points to get interpolated values. -> Option A

4. Quick Check:

   Scattered data + regular grid = griddata [OK]

Hint: For scattered data to grid, use griddata [OK]

Common Mistakes:

• Trying interp2d on scattered points
• Using incomplete grid points
• Passing 1D temps to interp2d