log1p

Compute natural logarithm of 1+X accurately for small X

Syntax

Y = log1p(X)

Description

Y = log1p(X) computes the natural logarithm log(1+X) for each element in array X without explicitly computing 1+X. If X < -1, then Y is complex. This function is more accurate for small real values in X because it compensates for the round-off error in 1+X.

Examples

Natural Logarithm of 1+X for Small X

Compare the accuracy of log(1+X) and log1p(X).

Create a vector of small real values.

X = [-1e-16 1e-15 2e-14]

X = 1×3
10-13 ×

   -0.0010    0.0100    0.2000

Calculate the natural logarithm of 1+X using the log function.

Y = log(1+X)

Y = 1×3
10-13 ×

   -0.0011    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 the natural logarithm of 1+X using the log1p function.

Y = log1p(X)

Y = 1×3
10-13 ×

   -0.0010    0.0100    0.2000

In this case, where log1p(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 log1p 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.

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 log1p function supports GPU array input with these usage notes and limitations:

• If the output of the function running on the GPU can be complex, then you must explicitly specify its input arguments as complex. For more information, see Work with Complex Numbers on a GPU (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

R2023a: Perform calculations directly on tables and timetables

The log1p 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.