power, .^
Elementwise power
Syntax
Description
C =
raises
each element of A
.^B
A
to the corresponding powers in
B
. The sizes of A
and
B
must be the same or be compatible.
If the sizes of A
and B
are compatible,
then the two arrays implicitly expand to match each other. For example, if one
of A
or B
is a scalar, then the scalar is
combined with each element of the other array. Also, vectors with different
orientations (one row vector and one column vector) implicitly expand to form a
matrix.
Examples
Square Each Element of Vector
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)
.
Row Vector to Power of Column Vector
Create a 1by2 row vector and a 3by1 column vector and raise the row vector to the power of the column vector.
a = [2 3]; b = (1:3)'; a.^b
ans = 3×2
2 3
4 9
8 27
The result is a 3by2 matrix, where each (i,j) element in the matrix is equal to a(j) .^ b(i)
:
$$\mathit{a}=\left[{\mathit{a}}_{1}\text{\hspace{0.17em}}{\mathit{a}}_{2}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{b}=\left[\begin{array}{c}{\mathit{b}}_{1}\\ {\mathit{b}}_{2}\\ {\mathit{b}}_{3}\end{array}\right],\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\text{\hspace{0.17em}}\mathit{a}\text{\hspace{0.17em}}.\u02c6\text{\hspace{0.17em}}\mathit{b}=\left[\begin{array}{cc}{{\mathit{a}}_{1}}^{{\mathit{b}}_{1}}& {{\mathit{a}}_{2}}^{{\mathit{b}}_{1}}\\ {{\mathit{a}}_{1}}^{{\mathit{b}}_{2}}& {{\mathit{a}}_{2}}^{{\mathit{b}}_{2}}\\ {{\mathit{a}}_{1}}^{{\mathit{b}}_{3}}& {{\mathit{a}}_{2}}^{{\mathit{b}}_{3}}\end{array}\right].$$
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
, the power
function returns complex results.
Use the nthroot
function to obtain the real roots.
C = nthroot(A,3)
C = 1
Input Arguments
A
, B
— Operands
scalars  vectors  matrices  multidimensional arrays
Operands, specified as scalars, vectors, matrices, or multidimensional
arrays. A
and B
must either be the
same size or have sizes that are compatible (for example,
A
is an M
byN
matrix and B
is a scalar or
1
byN
row vector). For more
information, see Compatible Array Sizes for Basic Operations.
Operands with an integer data type cannot be complex.
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  







Compatibility Considerations
Implicit expansion change affects arguments for operators
Behavior changed in R2016b
Starting in R2016b with the addition of implicit expansion, some combinations of arguments for basic operations that previously returned errors now produce results. For example, you previously could not add a row and a column vector, but those operands are now valid for addition. In other words, an expression like [1 2] + [1; 2]
previously returned a size mismatch error, but now it executes.
If your code uses elementwise operators and relies on the errors that MATLAB previously returned for mismatched sizes, particularly within a try
/catch
block, then your code might no longer catch those errors.
For more information on the required input sizes for basic array operations, see Compatible Array Sizes for Basic Operations.
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
andY
are real, butpower(X,Y)
is complex, simulation produces an error and generated code returnsNaN
. To get the complex result, make the input valueX
complex by passing incomplex(X)
. For example,power(complex(X),Y)
.When both
X
andY
are real, butX .^ Y
is complex, simulation produces an error and generated code returnsNaN
. To get the complex result, make the input valueX
complex by usingcomplex(X)
. For example,complex(X).^Y
.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:
When both
X
andY
are real, butpower(X,Y)
is complex, simulation produces an error and generated code returnsNaN
. To get the complex result, make the input valueX
complex by passing incomplex(X)
. For example,power(complex(X),Y)
.When both
X
andY
are real, butX .^ Y
is complex, simulation produces an error and generated code returnsNaN
. To get the complex result, make the input valueX
complex by usingcomplex(X)
. For example,complex(X).^Y
.Code generation does not support sparse matrix inputs for this function.
HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.
Both inputs must be scalar, and the exponent input, k
, must be
an integer.
ThreadBased Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports threadbased environments. For more information, see Run MATLAB Functions in ThreadBased Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
64bit 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).
See Also
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