[Wien] Understanding the subroutine in SRC_lapw1/RINT13.f

[Laurence Marks]

You are correct about what rint13.f does. It is a Simpson integrations
using equal spacing (from the logarithm of the radial mesh). It is not
written in the most clear code, you may want to compare it to charge*.f
elsewhere which is cleaner.

N.B., in parts of the code charge*.f has been changed to a numerically more
stable integral, mainly lapw[0-2].

---
Professor Laurence Marks
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else has thought", Albert Szent-Gyorgi
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On May 24, 2017 08:25, "Dara Goldar" <dara.goldar at gmail.com> wrote:

Dear Wien2k-team

I am currently implementing a program that will compute the overlap between
various (L)APW(+lo) eigenfunctions extracted from Wien2k-simulations. As I
understand, the subroutine RINT13 computes the radial integral over
two-component radial functions on an exponential mesh, which is why I've
spent some time now studying it.

There is one thing in particular about the code that I'm not able to make
sense of. I've scissored out the code and attached it to this e-mail in
case you have a newer version.

-------------------------- code from RINT13.F ----------------------------
59        GOTO 10
60   20 CONTINUE
61        P1 = RNOT*(C1*A(1)*X(1) + C2*B(1)*Y(1))
62        P2 = R1*(C1*A(J1)*X(J1) + C2*B(J1)*Y(J1))
63        S = 2*Z2 + 4*Z4 + R*(C1*A(J)*X(J) + C2*B(J)*Y(J)) + P2
64        S = (DX*S+P1)/3.0D+0
65        IF (J1 .GT. 1) S = S + 0.5D+0*DX*(P1+P2)
66!
67        RETURN
-------------------------- end code from RINT13.F -------------------------

On line 64, why is P1 not multiplied with DX? All other contributions to S
are multiplied with DX, so I see no reason why P1 on line 64 shouldn't be.
Apart from that, the code makes sense to me.

With regards
Dara Goldar, Master's student
NTNU/ Norwegian Defence Establishment
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