power, .^

Element-wise power

Syntax

C = A.^B

C = power(A,B)

Description

C = A.^B raises each element of A to the corresponding power in B.

C = power(A,B) is an alternate way to execute A.^B, but is rarely used. It enables operator overloading for classes.

Examples

Square Each Element of Vector

Create a vector, A, and square each element.

A = 1:5;
C = A.^2

C = 1×5

     1     4     9    16    25

Find Inverse of Each Matrix Element

Create a matrix, A, and take the inverse of each element.

A = [1 2 3; 4 5 6; 7 8 9];
C = A.^-1

C = 3×3

    1.0000    0.5000    0.3333
    0.2500    0.2000    0.1667
    0.1429    0.1250    0.1111

An inversion of the elements is not equal to the inverse of the matrix, which is instead written A^-1 or inv(A).

Find Roots of Number

Calculate the roots of -1 to the 1/3 power.

A = -1;
B = 1/3;
C = A.^B

C = 0.5000 + 0.8660i

For negative base A and noninteger B, if abs(B) is less than 1, the power function returns the complex roots of A.

Use the nthroot function to obtain the real roots.

C = nthroot(A,3)

C = -1

Input Arguments

A — Base

scalar | vector | matrix | multidimensional array

Base, specified as a scalar, vector, matrix, or multidimensional array. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

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

B — Exponent

scalar | vector | matrix | multidimensional array

Exponent, specified as a scalar, vector, matrix, or multidimensional array. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

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

More About

IEEE Compliance

For real inputs, power has a few behaviors that differ from those recommended in the IEEE^®-754 Standard.

	MATLAB®	IEEE
power(1,NaN)	NaN	1
power(NaN,0)	NaN	1

Extended Capabilities

Tall Arrays

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

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

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

Usage notes and limitations:

• When both X and Y are real, but power(X,Y) is complex, simulation produces an error and generated code returns NaN. To get the complex result, make the input value X complex by passing in complex(X). For example, power(complex(X),Y).

• When both X and Y are real, but X .^ Y is complex, simulation produces an error and generated code returns NaN. To get the complex result, make the input value X complex by using complex(X). For example, complex(X).^Y.

• 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:

• 64-bit integers are not supported.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

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).