beta
Beta function
Syntax
Description
returns the beta function
evaluated at the elements of B
= beta(Z
,W
)Z
and W
. Both
Z
and W
must be real and nonnegative.
Examples
Compute Beta Function for Integer Arguments
Compute the beta function for integer arguments and . Based on the definition, the beta function can be calculated as
.
Set the output format to rational to show the results as ratios of integers.
format rat
B = beta((1:10)',3)
B = 1/3 1/12 1/30 1/60 1/105 1/168 1/252 1/360 1/495 1/660
Plot Beta Function
Calculate the beta function for = 0.05, 0.1, 0.2, and 1 within the interval . Loop over values of , evaluate the function at each one, and assign each result to a row of B
.
Z = [0.05 0.1 0.2 1]; W = 0:0.05:10; B = zeros(4,201); for i = 1:4 B(i,:) = beta(Z(i),W); end
Plot all of the beta functions in the same figure.
plot(W,B) grid on legend('$z = 0.05$','$z = 0.1$','$z = 0.2$','$z = 1$','interpreter','latex') title('Beta function for $z = 0.05, 0.1, 0.2$, and $1$','interpreter','latex') xlabel('$w$','interpreter','latex') ylabel('$B(z,w)$','interpreter','latex')
Input Arguments
Z
— Input array
scalar | vector | matrix | multidimensional array
Input array, specified as a scalar, vector, matrix, or multidimensional array. The
elements of Z
must be real and nonnegative. Z
and
W
must be the same size, or else one of them must be a
scalar.
Data Types: single
| double
W
— Input array
scalar | vector | matrix | multidimensional array
Input array, specified as a scalar, vector, matrix, or multidimensional array. The
elements of W
must be real and nonnegative. Z
and
W
must be the same size, or else one of them must be a scalar.
If
Z
orW
is equal to 0, the beta function returnsInf
.If
Z
andW
are both 0, the beta function returnsNaN
.
Data Types: single
| double
More About
Beta Function
The beta function is defined by
The term is the gamma function
References
[1] Olver, F. W. J., A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, and B. V. Saunders, eds., Chapter 5.12 Beta Function, NIST Digital Library of Mathematical Functions, Release 1.0.22, Mar. 15, 2018.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
The
beta
function fully supports tall arrays. For more information,
see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The beta
function
fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray
(Parallel Computing Toolbox). 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 R2006a
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