NuMFor 9f2ab49 (2024-04-08)
Numerical (Modern) Fortran. Library for Simple Numerical computing
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qaws Interface Reference

Subroutine qaws estimates integrals with algebraico-logarithmic endpoint singularities given by the weight function $ W(x) $. More...

Detailed Description

Subroutine qaws estimates integrals with algebraico-logarithmic endpoint singularities given by the weight function $ W(x) $.

\[ I= \int_{a}^{b} f(x) W(x) dx \]

Parameters
[in]fThe function to integrate
[in]a(real) lower limit of integration
[in]b(real) upper limit of integration
[in]alfa(real) parameter of the weight function
[in]beta(real) parameter of the weight function
[in]flgw(integer) flag indicating the kind of weight function used:
  • flgw = 1 $ \Rightarrow W(x) = (x-a)^\alpha (b-x)^\beta $
  • flgw = 2 $ \Rightarrow W(x) = (x-a)^\alpha (b-x)^\beta \log(x-a) $
  • flgw = 3 $ \Rightarrow W(x) = (x-a)^\alpha (b-x)^\beta \log(b-x) $
  • flgw = 4 $ \Rightarrow W(x) = (x-a)^\alpha (b-x)^\beta \log(x-a) \log(b-x) $
[in]args(real, array, optional) extra arguments (if needed) to be passed to the function f
[out]IntVal(same kind as f) Approximation to integral
[in]epsabs(real, optional) Absolute accuracy requested. Default = 1.e-7
[in]epsrel(real, optional) Relative accuracy requested. Default = 1.e-5
[out]abserr(real, optional) Estimation of absolute error achieved
[out]neval(integer, optional) Number of function evaluations performed
[out]ier(integer, optional) Error code
[in,out]info(optional) Information and workspace. Must be of type d_qp_extra for integration of real functions and of type c_qp_extra for integration of complex functions.

Example:

real(dp) :: Integ1
real(dp) :: alfa, beta
integer :: flgw
alfa = 0._dp
beta = 0._dp
flgw = 2 ! weight function => log(x-a)^alfa = log(x)
! fquad458 = 1/(1 + \ln(x)^{2})^{2}
call qaws(fquad458, zero, 1._dp, alfa, beta, flgw, integ1)
print "(A)", 'integrate(log(x)/(1 + ln(x)^{2})^{2}, 0, 1) = '//str(integ1)
! integrate(log(x)/(1 + ln(x)^{2})^{2}, 0, 1) = -0.1892750041577
The documentation for this interface was generated from the following file: