Package 'deformula'

deformula: Integration of One-Dimensional Functions with Double Exponential Formulas

Description

Numerical quadrature of functions of one variable over a finite or infinite interval with double exponential formulas.

Author(s)

Maintainer: Hiroyuki Okamura [email protected] (ORCID)

See Also

Useful links:

• https://github.com/okamumu/deformula/

• Report bugs at https://github.com/okamumu/deformula/issues

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Integration of one-dimensional functions over finite interval with the double exponential formula.

Description

Numerical quadrature of functions of one variable over (lower, upper) with the double exponential formula.

Usage

deformula.moneone(
  f,
  lower,
  upper,
  ...,
  zero.eps = 1e-12,
  rel.tol = 1e-08,
  start.divisions = 8,
  max.iter = 12
)

Arguments

f	An R function taking a numeric first argument.
lower	The lower limit of integration.
upper	The upper limit of integration.
...	Additional arguments to be passed to ‘f’.
zero.eps	A threshold value to be zero.
rel.tol	A relative accuracy requested.
start.divisions	An integer. The initial number of subintervals.
max.iter	An integer for the maximum number of iterations to increase subintervals.

Value

A list with components;

value	A value for integral.
x	A vector of subintervals.
w	A vector of weights.
t	A vector of subintervals for trapezoid integral.
h	A value of subinterval.
message	OK or a string for the error message.

Examples

f <- function(x, a) exp(-a*x)
deformula.moneone(f, 0, 1, a=0.1)

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Integration of one-dimensional functions over infinite interval with the double exponential formula.

Description

Numerical quadrature of functions of one variable over [0, infinity) with the double exponential formula.

Usage

deformula.zeroinf(
  f,
  ...,
  zero.eps = 1e-12,
  rel.tol = 1e-08,
  start.divisions = 8,
  max.iter = 12
)

Arguments

f	An R function taking a numeric first argument.
...	Additional arguments to be passed to ‘f’.
zero.eps	A threshold value to be zero.
rel.tol	A relative accuracy requested.
start.divisions	An integer. The initial number of subintervals.
max.iter	An integer for the maximum number of iterations to increase subintervals.

Value

A list with components;

value	A value for integral.
x	A vector of subintervals.
w	A vector of weights.
t	A vector of subintervals for trapezoid integral.
h	A value of subinterval.
message	OK or a string for the error message.

Examples

f <- function(x, a) exp(-a*x)
deformula.zeroinf(f, a=0.1)

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