expm1

Compute exp(X)-1 accurately for small X

Syntax

Y = expm1(X)

Description

Y = expm1(X) computes exp(X)-1 for each element in array X. This function is more accurate for small real values in X because it compensates for the round-off error in exp(X).

Examples

Calculate exp(X)-1 Accurately for Small X

Compare the accuracy of exp(X)-1 and expm1(X).

Create a vector of small real values.

X = [-1e-17 1e-15 2e-14]

X = 1×3
10-13 ×

   -0.0001    0.0100    0.2000

Calculate exp(X)-1 using the exp function.

Y = exp(X)-1

Y = 1×3
10-13 ×

         0    0.0111    0.1998

The results can be zeros or have large relative errors. For example, Y(2) is not close to X(2), which is 1e-15.

Y(2)

ans = 
1.1102e-15

Calculate exp(X)-1 using the expm1 function.

Y = expm1(X)

Y = 1×3
10-13 ×

   -0.0001    0.0100    0.2000

In this case, where expm1(X) is approximately X, the results are more accurate. For example, Y(2) is now close to X(2), which is 1e-15.

Y(2)

ans = 
1.0000e-15

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 expm1 function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The expm1 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 expm1 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™.

The expm1 function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2023a: Perform calculations directly on tables and timetables

The expm1 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.