MATLAB Vectorization

Vectorization

Vectorization is the practice of performing operations on entire vectors or arrays at once instead of processing individual elements one at a time with a loop.

Vectorized Computation

Vectorized computation is the use of MATLAB's array-based operations to perform the same calculation across multiple data elements efficiently.

Element-Wise Operation

An element-wise operation performs a calculation independently on corresponding elements of arrays. MATLAB commonly indicates element-wise operations using a dot, such as .*, ./, and .^.

Matrix Operation vs. Element-Wise Operation

A matrix operation follows the mathematical rules of matrix algebra, while an element-wise operation performs the calculation independently on corresponding array elements. Example: A * B performs matrix multiplication, while A .* B performs element-wise multiplication.

Element-Wise Division (./)

The ./ operator divides corresponding elements of arrays individually. Example: A ./ B divides each element of A by the corresponding element of B.

Logical Array

A logical array is an array whose elements contain logical values true or false, often produced by applying a condition to an array. Example: A > 5 produces true wherever an element of A is greater than 5.

Logical Indexing

Logical indexing is a MATLAB technique that uses a logical array to directly select or modify elements for which a condition is true. Example: A(A > 5) returns the elements of A that are greater than 5.

Logical Mask

A logical mask is a logical array used to identify which elements of another array should be selected, modified, or analyzed. Example: mask = A > 5; creates a mask whose true positions identify qualifying elements of A.

Multiple Logical Conditions

Multiple logical conditions combine two or more conditions to select data satisfying a more specific set of requirements. Example: A(A > 5 & A < 10) selects elements greater than 5 and less than 10.

if Statement

An if statement executes a block of MATLAB code only when its specified condition evaluates to true. Example: if x > 0, y = sqrt(x); end

elseif Clause

An elseif clause tests an additional condition when the preceding if or elseif condition is false. Example: if x > 0, y = 1; elseif x == 0, y = 0; end

else Clause

An else clause executes a block of code when none of the preceding conditions in an if statement are true. Example: if x >= 0, y = 1; else, y = -1; end

for Loop

A for loop repeatedly executes a block of MATLAB code for each value in a specified sequence. Example: for k = 1:10, y(k) = k^2; end

while Loop

A while loop repeatedly executes a block of MATLAB code as long as its specified condition remains true. Example: while x < 10, x = x + 1; end

Preallocation

Preallocation is the practice of creating an array at its required final size before repeatedly assigning values to its elements. Example: y = zeros(1,100); before filling y inside a loop. This can improve performance by preventing MATLAB from repeatedly resizing the array.

Vectorization vs. Looping

Vectorization performs an operation directly on an entire array, while looping processes elements through repeated iterations. Example: y = x.^2; is a vectorized alternative to individually squaring each element of x with a loop.