IMSL_ERR_ABS, floaterr_abs (Input) Absolute accuracy desired. Default: where ɛ is the machine precision
IMSL_ERR_REL, floaterr_rel (Input) Relative accuracy desired. Default: where ɛ is the machine precision
IMSL_ERR_EST, float*err_est (Output) Address to store an estimate of the absolute value of the error.
IMSL_MAX_SUBINTER, intmax_subinter (Input) Number of subintervals allowed. Default: max_subinter = 500.
IMSL_N_SUBINTER, int*n_subinter (Output) Address to store the number of subintervals generated.
IMSL_N_EVALS, int*n_evals (Output) Address to store the number of evaluations of fcn.
IMSL_FCN_W_DATA, floatfcn(floatx, void*data), void*data (Input) User supplied function to be integrated, which also accepts a pointer to data that is supplied by the user. data is a pointer to the data to be passed to the user-supplied function. See the Introduction, Passing Data to User-Supplied Functions at the beginning of this manual for more details.
Description
The function imsl_f_int_fcn_inf is a special-purpose integrator that uses a globally adaptive scheme to reduce the absolute error. It initially transforms an infinite or semi-infinite interval into the finite interval [0, 1]. It then uses the same strategy as the function imsl_f_int_fcn_sing.
On some platforms, imsl_f_int_fcn_inf can evaluate the user-supplied function fcn in parallel. This is done only if the function imsl_omp_options is called to flag user-defined functions as thread-safe. A function is thread-safe if there are no dependencies between calls. Such dependencies are usually the result of writing to global or static variables.
The function imsl_f_int_fcn_inf is based on the subroutine QAGI by Piessens et al. (1983).
Examples
Example 1
The value of
is computed.
#include <imsl.h>
#include <stdio.h>
#include <math.h>
float fcn(float x);
int main()
{
float q, exact, pi;
pi = imsl_f_constant("pi", 0);
imsl_omp_options(
IMSL_SET_FUNCTIONS_THREAD_SAFE, 1,
0);
/* Evaluate the integral */
q = imsl_f_int_fcn_inf (fcn, 0.0,
IMSL_BOUND_INF,
0);
/* Print the result and the */
/* exact answer */
exact = -pi*log(10.)/20.;
printf("integral = %10.3f\nexact = %10.3f\n", q, exact);
}
float fcn(float x)
{
float z;
z = 10.*x;
return log(x)/(1+ z*z);
}
Output
integral = -0.362
exact = -0.362
Example 2
The value of
is again computed. The values of the actual and estimated error are printed as well. Note that these numbers are machine dependent. Furthermore, the error estimate is usually pessimistic. That is, the actual error is usually smaller than the error estimate, as in this example. The number of function evaluations also are printed.
#include <imsl.h>
#include <stdio.h>
#include <math.h>
float fcn(float x);
int main()
{
int n_evals;
float q, exact, err_est, exact_err, pi;
pi = imsl_f_constant("pi",
0);
imsl_omp_options(
IMSL_SET_FUNCTIONS_THREAD_SAFE, 1,
0);
/* Evaluate the integral */
q = imsl_f_int_fcn_inf (fcn, 0.0,
IMSL_BOUND_INF,
IMSL_ERR_EST, &err_est,
IMSL_N_EVALS, &n_evals,
0);
/* Print the result and the */
/* exact answer */
exact = -pi*log(10.)/20.;
exact_err = fabs(exact - q);
printf("integral = %10.3f\nexact = %10.3f\n", q, exact);
