2D interpolation (interp2d, griddata) in SciPy - Mini Project: Build & Apply

2D Interpolation with interp2d and griddata

📖 Scenario: You have temperature readings from a few weather stations scattered in a small area. You want to estimate the temperature at other points between these stations to create a smooth temperature map.

🎯 Goal: Build a Python program that uses scipy.interpolate.interp2d and scipy.interpolate.griddata to estimate temperatures at new points based on given scattered data.

📋 What You'll Learn

Create arrays for known x and y coordinates and their temperature values

Set up a grid of new points where temperature will be estimated

Use interp2d to interpolate temperature on the grid

Use griddata to interpolate temperature on the grid

Print the interpolated temperature arrays

💡 Why This Matters

🌍 Real World

Weather forecasting and environmental monitoring often require estimating values at locations where no direct measurements exist. 2D interpolation helps create smooth maps from scattered sensor data.

💼 Career

Data scientists and analysts use interpolation techniques to fill missing data, create heatmaps, and prepare data for machine learning models in fields like meteorology, agriculture, and urban planning.

1

Create known data points

Create three NumPy arrays called x, y, and temp with these exact values: x = [0, 1, 2, 0, 1, 2], y = [0, 0, 0, 1, 1, 1], and temp = [30, 32, 34, 28, 29, 31].

SciPy

# Create arrays x, y, and temp with given values
# Your code here

Hint

Use np.array to create arrays for x, y, and temp.

2

Create grid points for interpolation

Create two 1D NumPy arrays called xi and yi using np.linspace to generate 5 points each from 0 to 2 for xi and from 0 to 1 for yi.

SciPy

import numpy as np

x = np.array([0, 1, 2, 0, 1, 2])
y = np.array([0, 0, 0, 1, 1, 1])
temp = np.array([30, 32, 34, 28, 29, 31])

# Create xi and yi arrays with 5 points each
# Your code here

Hint

Use np.linspace(start, stop, num_points) to create evenly spaced points.

3

Interpolate temperatures using interp2d and griddata

Import interp2d and griddata from scipy.interpolate. Use interp2d with x, y, and temp to create a function f_interp2d. Then use f_interp2d with xi and yi to get temp_interp2d. Also, create a 2D grid with np.meshgrid from xi and yi. Use griddata with points from x and y, values temp, and the grid points to get temp_griddata.

SciPy

import numpy as np

x = np.array([0, 1, 2, 0, 1, 2])
y = np.array([0, 0, 0, 1, 1, 1])
temp = np.array([30, 32, 34, 28, 29, 31])

xi = np.linspace(0, 2, 5)
yi = np.linspace(0, 1, 5)

# Import interp2d and griddata
# Create f_interp2d function
# Use f_interp2d with xi and yi to get temp_interp2d
# Create grid with np.meshgrid
# Use griddata to get temp_griddata
# Your code here

Hint

Use interp2d to create an interpolation function and call it with xi and yi. Use np.meshgrid to create grid points for griddata.

4

Print the interpolated temperature arrays

Print the arrays temp_interp2d and temp_griddata using two separate print statements.

SciPy

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

x = np.array([0, 1, 2, 0, 1, 2])
y = np.array([0, 0, 0, 1, 1, 1])
temp = np.array([30, 32, 34, 28, 29, 31])

xi = np.linspace(0, 2, 5)
yi = np.linspace(0, 1, 5)

f_interp2d = interp2d(x, y, temp, kind='linear')
temp_interp2d = f_interp2d(xi, yi)

X_grid, Y_grid = np.meshgrid(xi, yi)
points = np.column_stack((x, y))
temp_griddata = griddata(points, temp, (X_grid, Y_grid), method='linear')

# Print temp_interp2d and temp_griddata
# Your code here

Hint

Use print(temp_interp2d) and print(temp_griddata) to show the 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