bsxfun

Apply element-wise operation to two arrays with implicit expansion enabled

Syntax

C = bsxfun(fun,A,B)

Description

C = bsxfun(fun,A,B) applies the element-wise binary operation specified by the function handle fun to arrays A and B.

Examples

Deviation of Matrix Elements from Column Mean

Subtract the column mean from the corresponding column elements of a matrix A. Then normalize by the standard deviation.

A = [1 2 10; 3 4 20; 9 6 15];
C = bsxfun(@minus, A, mean(A));
D = bsxfun(@rdivide, C, std(A))

D = 3×3

   -0.8006   -1.0000   -1.0000
   -0.3203         0    1.0000
    1.1209    1.0000         0

In MATLAB® R2016b and later, you can directly use operators instead of bsxfun, since the operators independently support implicit expansion of arrays with compatible sizes.

(A - mean(A))./std(A)

ans = 3×3

   -0.8006   -1.0000   -1.0000
   -0.3203         0    1.0000
    1.1209    1.0000         0

Compare Vector Elements

Compare the elements in a column vector and a row vector. The result is a matrix containing the comparison of each combination of elements from the vectors. An equivalent way to execute this operation is with A > B.

A = [8; 17; 20; 24]

A = 4×1

     8
    17
    20
    24

B = [0 10 21]

B = 1×3

     0    10    21

C = bsxfun(@gt,A,B)

C = 4x3 logical array

   1   0   0
   1   1   0
   1   1   0
   1   1   1

Expansion with Custom Function

Create a function handle that represents the function $$f(a,b)=a-e^b$$.

fun = @(a,b) a - exp(b);

Use bsxfun to apply the function to vectors a and b. The bsxfun function expands the vectors into matrices of the same size, which is an efficient way to evaluate fun for many combinations of the inputs.

a = 1:7;
b = pi*[0 1/4 1/3 1/2 2/3 3/4 1].';
C = bsxfun(fun,a,b)

C = 7×7

         0    1.0000    2.0000    3.0000    4.0000    5.0000    6.0000
   -1.1933   -0.1933    0.8067    1.8067    2.8067    3.8067    4.8067
   -1.8497   -0.8497    0.1503    1.1503    2.1503    3.1503    4.1503
   -3.8105   -2.8105   -1.8105   -0.8105    0.1895    1.1895    2.1895
   -7.1205   -6.1205   -5.1205   -4.1205   -3.1205   -2.1205   -1.1205
   -9.5507   -8.5507   -7.5507   -6.5507   -5.5507   -4.5507   -3.5507
  -22.1407  -21.1407  -20.1407  -19.1407  -18.1407  -17.1407  -16.1407

Input Arguments

fun — Binary function to apply

function handle

Binary function to apply, specified as a function handle. fun must be a binary (two-input) element-wise function of the form C = fun(A,B) that accepts arrays A and B with compatible sizes. For more information, see Compatible Array Sizes for Basic Operations. fun must support scalar expansion, such that if A or B is a scalar, then C is the result of applying the scalar to every element in the other input array.

In MATLAB^® R2016b and later, the built-in binary functions listed in this table independently support implicit expansion. With these functions, you can call the function or operator directly instead of using bsxfun. For example, you can replace C = bsxfun(@plus,A,B) with A+B.

Function	Symbol	Description
plus	+	Plus
minus	-	Minus
times	.*	Array multiply
rdivide	./	Right array divide
ldivide	.\	Left array divide
power	.^	Array power
eq	==	Equal
ne	~=	Not equal
gt	>	Greater than
ge	>=	Greater than or equal to
lt	<	Less than
le	<=	Less than or equal to
and	&	Element-wise logical AND
or	|	Element-wise logical OR
xor	N/A	Logical exclusive OR
max	N/A	Binary maximum
min	N/A	Binary minimum
mod	N/A	Modulus after division
rem	N/A	Remainder after division
atan2	N/A	Four-quadrant inverse tangent; result in radians
atan2d	N/A	Four-quadrant inverse tangent; result in degrees
hypot	N/A	Square root of sum of squares

Example: C = bsxfun(@plus,[1 2],[2; 3])

Data Types: function_handle

A,B — Input arrays

scalars | vectors | matrices | multidimensional arrays

Input arrays, specified as scalars, vectors, matrices, or multidimensional arrays. Inputs A and B must have compatible sizes. For more information, see Compatible Array Sizes for Basic Operations. Whenever a dimension of A or B is singleton (equal to one), bsxfun virtually replicates the array along that dimension to match the other array. In the case where a dimension of A or B is singleton, and the corresponding dimension in the other array is zero, bsxfun virtually diminishes the singleton dimension to zero.

Data Types: single | double | uint8 | uint16 | uint32 | uint64 | int8 | int16 | int32 | int64 | char | logical
Complex Number Support: Yes

Tips

• It is recommended that you replace most uses of bsxfun with direct calls to the functions and operators that support implicit expansion. Compared to using bsxfun, implicit expansion offers faster speed of execution, better memory usage, and improved readability of code. For more information, see Compatible Array Sizes for Basic Operations.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

The specified function must not rely on persistent variables.

For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Code generation does not support sparse matrix inputs for this function.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• Code generation does not support sparse matrix inputs for this function.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• See bsxfun in the Parallel Computing Toolbox™ documentation.

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).