cospi

Compute cos(X*pi) accurately

Syntax

Y = cospi(X)

Description

Y = cospi(X) computes cos(X*pi) without explicitly computing X*pi. This calculation is more accurate than cos(X*pi) because the floating-point value of pi is an approximation of π. In particular:

• For odd integers, cospi(n/2) is exactly zero.

• For integers, cospi(n) is +1 or -1.

Examples

Calculate Cosine of Multiples of π

Compare the accuracy of cospi(X) vs. cos(X*pi).

Create a vector of values.

X = [0 1/2 1 3/2 2];

Calculate the cosine of X*pi using the normal cos function.

Y = cos(X*pi)

Y = 1×5

    1.0000    0.0000   -1.0000   -0.0000    1.0000

The results contain small numerical errors due to the fact that pi is a floating-point approximation of the true value of $\pi$. For instance, Y(2) is not exactly zero even though $\cos \left(\frac{\pi }{2}\right)=0$.

Y(2)

ans = 
6.1232e-17

Use cospi to calculate the same values. In this case, the results are exact.

Z = cospi(X)

Z = 1×5

     1     0    -1     0     1

Z(2)

ans = 
0

Input Arguments

X — Input array

scalar | vector | matrix | multidimensional array | table | timetable

Input array, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

Data Types: single | double | table | timetable
Complex Number Support: Yes

Extended Capabilities

Tall Arrays

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

The cospi 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.

GPU Arrays

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

The cospi 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 in R2018b

R2023a: Perform calculations directly on tables and timetables

The cospi function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.