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
Raise Table to Power of Another Table
Since R2023a
Create two tables and raise the first table to the power of the second. The row names (if present in both) and variable names must be the same, but do not need to be in the same orders. Rows and variables of the output are in the same orders as the first input.
A = table([1;2],[3;4],VariableNames=["V1","V2"],RowNames=["R1","R2"])
A=2×2 table
V1 V2
__ __
R1 1 3
R2 2 4
B = table([4;2],[3;1],VariableNames=["V2","V1"],RowNames=["R2","R1"])
B=2×2 table
V2 V1
__ __
R2 4 3
R1 2 1
C = A .^ B
C=2×2 table
V1 V2
__ ___
R1 1 9
R2 8 256
Input Arguments
A
, B
— Operands
scalars  vectors  matrices  multidimensional arrays  tables  timetables
Operands, specified as scalars, vectors, matrices, multidimensional
arrays, tables, or timetables. 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.
Inputs that are tables or timetables must meet the following conditions: (since R2023a)
If an input is a table or timetable, then all its variables must have data types that support the operation.
If only one input is a table or timetable, then the other input must be a numeric or logical array.
If both inputs are tables or timetables, then:
Both inputs must have the same size, or one of them must be a onerow table.
Both inputs must have variables with the same names. However, the variables in each input can be in a different order.
If both inputs are tables and they both have row names, then their row names must be the same. However, the row names in each input can be in a different order.
If both inputs are timetables, then their row times must be the same. However, the row times in each input can be in a different order.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 logical
 char
 table
 timetable
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  







Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
The
power
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 VHDL, Verilog and SystemVerilog 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™.
The power
function
supports GPU array input with these usage notes and limitations:
64bit integers are not supported.
If base
A
or exponentB
are sparse,B
must be a scalar.
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).
Version History
Introduced before R2006aR2023a: Perform operations directly on tables and timetables
The power
operator supports operations directly on tables and
timetables without indexing to access their variables. All variables must have data types
that support the operation. For more information, see Direct Calculations on Tables and Timetables.
R2016b: Implicit expansion change affects arguments for operators
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.
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