Class inte_transform (o2scl)

O2scl : Class List

template<class func_t, class def_inte_t, class fp_t = double>
class inte_transform : public o2scl::inte<func_t, double>

Integration using variable transformations for semi-infinite and infinite intervals.

Note

This class only works if the base integration type def_inte_t avoids evaluating the function at the left-hand end point.

Integration object

def_inte_t def_inte

Default integration object.

inline int set_inte(inte<internal_funct, fp_t> &i)

Set the base integration object to use.

inline virtual const char *type()

Return string denoting type (“inte_transform”)

Public Types

typedef std::function<fp_t(fp_t)> internal_funct

Internal function type based on floating-point type.

Public Functions

inline inte_transform()

inline virtual int integ_il_err(func_t &func, fp_t b, fp_t &res, fp_t &err)

Integrate function func from \( -\infty \) to b and place the result in res and the error in err.

This class uses the GSL approach, employing the transformation \( x = b - (1-t)/t \), and giving

\[ \int_{-\infty}^{b}~dx f(x) = \int_0^1~dt~f[b-(1-t)/t]/t^2 \]

inline virtual int integ_iu_err(func_t &func, fp_t a, fp_t &res, fp_t &err)

Integrate function func from a to \( \infty \) and place the result in res and the error in err.

This class uses the GSL approach, employing the transformation \( x = a + (1-t)/t \), and giving

\[ \int_a^{\infty}~dx f(x) = \int_0^1~dt~f[a+(1-t)/t]/t^2 \]

inline virtual int integ_i_err(func_t &func, fp_t &res, fp_t &err)

Integrate function func from \( -\infty \) to \( \infty \) and place the result in res and the error in err.

This class uses the GSL approach, employing the transformation \( x = (1-t)/t \), and giving

\[ \int_{-\infty}^{\infty}~dx f(x) = \int_0^1~dt~\left\{f[(1-t)/t] + f[-(1-t)/t]\right\}/t^2 \]

inline virtual int integ_err(func_t &func, fp_t a, fp_t b, fp_t &res, fp_t &err)

Integrate function func from a to b giving result res and error err.

The value given is a is ignored.

Protected Functions

inline virtual fp_t iu_transform(fp_t t)

Transform from \( t \in (0,1] \) to \( x \in [a,\infty) \).

inline virtual fp_t il_transform(fp_t t)

Transform from \( t \in (0,1] \) to \( x \in (-\infty,b] \).

inline virtual fp_t i_transform(fp_t t)

Transform from \( t \in (0,1] \) to \( x \in (-\infty,\infty) \).

inline virtual fp_t no_transform(fp_t t)

Transform from \( t \in (0,1] \) to \( x \in (-\infty,\infty) \).

Protected Attributes

func_t *user_func

A pointer to the user-specified function.

fp_t upper_limit

The upper limit.

fp_t lower_limit

The lower limit.

def_inte_t *it

The base integration object.

internal_funct fo_il

Function object.

internal_funct fo_iu

Function object.

internal_funct fo_i

Function object.

internal_funct fo_no

Function object.