base (version 3.3)

log: Logarithms and Exponentials

Description

log computes logarithms, by default natural logarithms, log10 computes common (i.e., base 10) logarithms, and log2 computes binary (i.e., base 2) logarithms. The general form log(x, base) computes logarithms with base base.

log1p(x) computes $log(1+x)$ accurately also for $|x| << 1$.

exp computes the exponential function.

expm1(x) computes $exp(x) - 1$ accurately also for $|x| << 1$.

Usage

log(x, base = exp(1))
logb(x, base = exp(1))
log10(x)
log2(x)
log1p(x)
exp(x)
expm1(x)

Arguments

x

a numeric or complex vector.

base

a positive or complex number: the base with respect to which logarithms are computed. Defaults to $e$=exp(1).

Value

A vector of the same length as x containing the transformed values. log(0) gives -Inf, and log(x) for negative values of x is NaN. exp(-Inf) is 0.For complex inputs to the log functions, the value is a complex number with imaginary part in the range [-\pi, \pi][-pi, pi]: which end of the range is used might be platform-specific.

S4 methods

exp, expm1, log, log10, log2 and log1p are S4 generic and are members of the Math group generic. Note that this means that the S4 generic for log has a signature with only one argument, x, but that base can be passed to methods (but will not be used for method selection). On the other hand, if you only set a method for the Math group generic then base argument of log will be ignored for your class.

Source

log1p and expm1 may be taken from the operating system, but if not available there then they are based on the Fortran subroutine dlnrel by W. Fullerton of Los Alamos Scientific Laboratory (see http://www.netlib.org/slatec/fnlib/dlnrel.f and (for small x) a single Newton step for the solution of log1p(y) = x respectively.

Details

All except logb are generic functions: methods can be defined for them individually or via the Math group generic.

log10 and log2 are only convenience wrappers, but logs to bases 10 and 2 (whether computed via log or the wrappers) will be computed more efficiently and accurately where supported by the OS. Methods can be set for them individually (and otherwise methods for log will be used).

logb is a wrapper for log for compatibility with S. If (S3 or S4) methods are set for log they will be dispatched. Do not set S4 methods on logb itself.

All except log are primitive functions.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole. (for log, log10 and exp.)

Chambers, J. M. (1998) Programming with Data. A Guide to the S Language. Springer. (for logb.)

See Also

Trig, sqrt, Arithmetic.

Examples

log(exp(3))
log10(1e7) # = 7

x <- 10^-(1+2*1:9)
cbind(x, log(1+x), log1p(x), exp(x)-1, expm1(x))