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How do you make a linear vector in MATLAB?

Published in MATLAB Vectors 2 mins read

You can create a linear vector (a vector with evenly spaced elements) in MATLAB using the linspace function.

Here's a breakdown of how to use linspace:

% Create a row vector with 100 elements between 0 and 1 (inclusive).
y = linspace(0, 1);

% Create a row vector with n elements between x1 and x2 (inclusive).
y = linspace(x1, x2, n);

Explanation

  • linspace(x1, x2): This creates a row vector containing 100 evenly spaced points between x1 (the starting value) and x2 (the ending value). The default number of points is 100 if not specified.

  • linspace(x1, x2, n): This creates a row vector containing n evenly spaced points between x1 and x2.

    • x1: The first element of the vector.
    • x2: The last element of the vector.
    • n: The number of elements in the vector.

    The spacing between the points is calculated as (x2 - x1) / (n - 1).

Examples

  1. Creating a vector from 1 to 10 with 5 elements:

    vector1 = linspace(1, 10, 5)
% Output: vector1 = [1.0000, 3.2500, 5.5000, 7.7500, 10.0000]

  2. Creating a vector from 0 to pi with 50 elements:

    vector2 = linspace(0, pi, 50)
% Output: A 1x50 vector with values from 0 to pi.

  3. Using the default 100 points:

    vector3 = linspace(0, 5)
% Output: A 1x100 vector with values from 0 to 5.

Important Considerations

  • The linspace function always includes both the starting value (x1) and the ending value (x2) in the resulting vector.

  • If n is 1, then the vector contains only the value x1.

  • If x1 and x2 are complex, then linspace generates evenly spaced complex numbers.

Alternatives

While linspace is the most direct approach, you can also create a linear vector using the colon operator (:) and specify the increment:

x = 1:2:10 % Start at 1, increment by 2, and end at or before 10
%Output: x = [1 3 5 7 9]

However, the colon operator requires specifying the increment, and it might not always guarantee the inclusion of the exact end value like linspace does. Therefore, linspace is generally preferred for creating precise linearly spaced vectors.

In summary, linspace provides a straightforward and reliable way to generate linear vectors in MATLAB, allowing you to control the start, end, and number of points in the vector.

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