Interpolation (interp1) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of interp1 with linear method

What is the output of the following MATLAB code snippet?

MATLAB

x = [1 2 3 4 5];
y = [10 20 30 40 50];
xi = 2.5;
yi = interp1(x, y, xi, 'linear');
disp(yi);

A 25

B 20

C 30

D Error: Undefined function or variable 'interp1'

💡 Hint

Linear interpolation finds the value halfway between y(2) and y(3).

The value at xi=2.5 is halfway between y(2)=20 and y(3)=30, so the output is 25.

❓ Predict Output

intermediate

Output of interp1 with 'nearest' method

What will be the output of this MATLAB code?

MATLAB

x = [0 1 2 3 4];
y = [0 10 20 30 40];
xi = 2.7;
yi = interp1(x, y, xi, 'nearest');
disp(yi);

A 30

B 27

C 20

D Error: Input data must be strictly increasing

💡 Hint

Nearest method picks the y value of the closest x point.

2.7 is closer to 3 than 2, so yi = y(4) = 30.

❓ Predict Output

advanced

interp1 with 'spline' method output

What is the output of this MATLAB code snippet?

MATLAB

x = [1 2 3 4];
y = [1 4 9 16];
xi = 2.5;
yi = interp1(x, y, xi, 'spline');
disp(round(yi,2));

A 8.50

B 7.25

C 6.56

D Error: Method 'spline' not supported

💡 Hint

Spline interpolation fits a smooth curve through points.

The spline interpolation at 2.5 gives approximately 6.56 after rounding.

❓ Predict Output

advanced

interp1 with extrapolation option

What is the output of this MATLAB code?

MATLAB

x = [1 2 3];
y = [2 4 6];
xi = 4;
yi = interp1(x, y, xi, 'linear', 'extrap');
disp(yi);

A 6

B 8

C NaN

D Error: Extrapolation not allowed

💡 Hint

Extrapolation extends the linear trend beyond known points.

Linear extrapolation beyond x=3 gives yi=8 at x=4.

🧠 Conceptual

expert

Error type from invalid interp1 input

What error does MATLAB produce when calling interp1 with non-monotonic x vector like this? x = [1 3 2 4]; y = [10 30 20 40]; xi = 2.5; interp1(x, y, xi);

A No error, returns interpolated value.

B Error using interp1: Y must be a vector of the same length as X.

C Error using interp1: XI must be within the range of X.

D Error using interp1: X must be strictly monotonic increasing or decreasing.

💡 Hint

interp1 requires x to be sorted strictly increasing or decreasing.

The x vector is not strictly monotonic, so interp1 throws an error about monotonicity.

Practice

1. What does the MATLAB function interp1 do?

easy

A. It calculates the derivative of a function.

B. It sorts a vector in ascending order.

C. It estimates intermediate values between known data points.

D. It plots data points on a graph.

Solution

1. Step 1: Understand the purpose of interpolation

   Interpolation is used to estimate values between known data points.

2. Step 2: Identify the role of interp1

   interp1 in MATLAB performs 1D interpolation to find intermediate values.

3. Final Answer:

   It estimates intermediate values between known data points. -> Option C

4. Quick Check:

   Interpolation = estimating values [OK]

Hint: Remember: interp1 fills gaps between points [OK]

Common Mistakes:

• Confusing interpolation with sorting
• Thinking interp1 calculates derivatives
• Assuming interp1 creates plots

2. Which of the following is the correct syntax to interpolate the value at x = 2.5 using vectors x and y in MATLAB?

easy

A. interp1(x, y, 2.5)

B. interp1(y, x, 2.5)

C. interp1(2.5, x, y)

D. interp1(x, 2.5, y)

Solution

1. Step 1: Recall interp1 function syntax

   The syntax is interp1(x, y, xi) where x and y are known points, xi is query point.

2. Step 2: Match the correct order of arguments

   interp1(x, y, 2.5) uses interp1(x, y, 2.5), which matches the syntax correctly.

3. Final Answer:

   interp1(x, y, 2.5) -> Option A

4. Quick Check:

   interp1(x, y, xi) = correct syntax [OK]

Hint: Remember: interp1(x, y, xi) order matters [OK]

Common Mistakes:

• Swapping x and y vectors
• Putting query point before vectors
• Using wrong argument order

3. Given x = [1 2 3 4] and y = [10 20 30 40], what is the output of interp1(x, y, 2.5) in MATLAB?

medium

A. Error

B. 20

C. 30

D. 25

Solution

1. Step 1: Understand linear interpolation between points

   At x=2, y=20 and at x=3, y=30. For x=2.5, interpolate linearly.

2. Step 2: Calculate interpolated value

   Value = 20 + (2.5-2)*(30-20)/(3-2) = 20 + 0.5*10 = 25.

3. Final Answer:

   25 -> Option D

4. Quick Check:

   Linear interp at 2.5 = 25 [OK]

Hint: Linear interp averages between neighbors [OK]

Common Mistakes:

• Choosing nearest point value instead of interpolating
• Confusing x and y values
• Expecting an error for valid input

4. What is wrong with this MATLAB code snippet?

x = [1 2 3];
y = [10 20];
interp1(x, y, 2)

medium

A. Vectors x and y have different lengths causing an error.

B. The query point 2 is outside the range of x.

C. interp1 requires y to be a matrix, not a vector.

D. The syntax of interp1 is incorrect.

Solution

1. Step 1: Check vector lengths

   Vector x has length 3, y has length 2; they must be equal for interp1.

2. Step 2: Identify error cause

   Different lengths cause MATLAB to throw an error when calling interp1.

3. Final Answer:

   Vectors x and y have different lengths causing an error. -> Option A

4. Quick Check:

   Equal vector lengths needed [OK]

Hint: Check x and y lengths match before interp1 [OK]

Common Mistakes:

• Ignoring vector length mismatch
• Thinking query point must be outside range
• Assuming interp1 needs matrix y

5. You have temperature data temp = [15 18 21 24] measured at times time = [0 3 6 9] hours. How would you find the temperature at 4.5 hours using cubic interpolation in MATLAB?

hard

A. interp1(time, temp, 4.5)

B. interp1(time, temp, 4.5, 'cubic')

C. interp1(time, temp, 4.5, 'linear')

D. interp1(temp, time, 4.5, 'cubic')

Solution

1. Step 1: Identify correct argument order and method

   Syntax is interp1(x, y, xi, method). Here x=time, y=temp, xi=4.5, method='cubic'.

2. Step 2: Choose cubic interpolation

   interp1(time, temp, 4.5, 'cubic') uses 'cubic' method correctly for smooth interpolation.

3. Final Answer:

   interp1(time, temp, 4.5, 'cubic') -> Option B

4. Quick Check:

   Use 'cubic' for smooth interp [OK]

Hint: Use 'cubic' as 4th argument for smooth interp [OK]

Common Mistakes:

• Swapping time and temp vectors
• Using default linear instead of cubic
• Omitting interpolation method argument