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Matlab Compatible Array Sizes

Compatible Array Sizes

Matlab Array

src: Compatible Array Sizes for Basic Operations

  • Most binary (two-input) operators and functions in MATLAB support arrays that have compatible sizes
  • Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are either the same or one of them is 1
    • Simplest cases:
      1. two array sizes are exactly the same
      2. one is a scalar
  • MATLAB implicitly expands arrays with compatible sizes to be the same size during the execution of the element-wise operation or function

2-D Inputs

Cases:

  • Two inputs which are exactly the same size
  • One input is a scalar
  • One input is a matrix, and the other is a column vector with the same number of rows
  • One input is a column vector, and the other is a row vector

Multidimensional Arrays

Every array in MATLAB has trailing dimensions of size 1. For multidimensional arrays, this means that a 3-4 matrix is the same as a matrix of size 3-4-1-1-1.

Examples:

  • One input is a matrix, and the other is a 3-D array with the same number of rows and columns.
  • One input is a matrix, and the other is a 3-D array, their dimensions are all either the same or one of them is 1

Empty Arrays

  • The rules are the same for empty arrays or arrays that have a dimension size of zero
    • rule: The size of the dimension that is not equal to 1 determines the size of the output
  • This means that dimensions with a size of zero must be paired with a dimension of size 1 or 0 in the other array, and that the output has a dimension size of 0 (for 0*1=1)
  • Example: size of is 3-0

Examples

To simplify vector-matrix operations, use implicit expansion with dimensional functions such as sum, mean, min, and others.

Subtract Vector from Matrix

>> A = magic(3)
A =
     8     1     6
     3     5     7
     4     9     2
>> C = mean(A)
C =
 
     5     5     5
>> A - C
ans =
     3    -4     1
    -2     0     2
    -1     4    -3

Add Row and Column Vector

Row and column vectors have compatible sizes, and when you perform an operation on them the result is a matrix.

>> a = [1:4]; b = [5:7]';
>> a + b
ans =
     6     7     8     9
     7     8     9    10
     8     9    10    11

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