From 26c292bb6629bd14f349c4f27cad8986aa709779 Mon Sep 17 00:00:00 2001 From: wdaniau Date: Tue, 24 Nov 2009 16:33:40 +0000 Subject: [PATCH] Contribution de Sylvain : fonction e1 avec arguments complexes ze1 git-svn-id: https://lxsd.femto-st.fr/svn/fvn@55 b657c933-2333-4658-acf2-d3c7c2708721 --- doc/fvn.pdf | 4559 +++++++++++++++++++++++------------------------ doc/fvn.tex | 28 +- fvn_fnlib/Makefile | 2 +- fvn_fnlib/fvn_fnlib.f90 | 3 + fvn_fnlib/ze1.f90 | 53 + 5 files changed, 2347 insertions(+), 2298 deletions(-) create mode 100644 fvn_fnlib/ze1.f90 diff --git a/doc/fvn.pdf b/doc/fvn.pdf index 46900b5..74d7ea7 100644 --- a/doc/fvn.pdf +++ b/doc/fvn.pdf @@ -700,16 +700,13 @@ endobj << /S /GoTo /D [470 0 R /Fit ] >> endobj 508 0 obj << -/Length 1299 +/Length 1306 /Filter /FlateDecode >> stream -xZMs6Ẅ́ EGqyaO8]k-^0s Ы-`< 0OWmI,P0y>ׁIᰂ ichHMe?=i:K]B8bYK*:#&,FJНj{͐J퇮N[b1^&zWՁ:&*wfT27ZY.V೐@[yYj",`n$,z%1>Z@[QXKzY0=ڭ!Ǧ/tDa?S'Π33^ 9\oRZqwIu'i@5ȿT^hYrBѤSrkl@ATsp1v>] -әӜU-gHdrg -DM ->>Ea# -eVQ%1['K٬.{n^wf[|#*w@"y\1W]zO3HBY $8M4*KL5kOs5b-*D^Nz_b* mV:5B*7&y:*{kcѴٰ j#W/m3"Mwr 4YA.= -@?IZT=0eMRd)Y^xwdHvcSY;LU]ΒvSv-`-{]K,!$ lgy!bxz!qٻxvxUMgIwJoS6z_KRk4t|=CEښ3, ĺ%3*OunF֕-cp4˽7E[ yQgvzq^W&7*ܥ۳6kDiZ]0YccHgi! 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00000 n +0000289279 00000 n trailer -<< /Size 1049 -/Root 1047 0 R -/Info 1048 0 R -/ID [<64C7ED682C2886557EC7C1BDEBA687D5> <64C7ED682C2886557EC7C1BDEBA687D5>] >> +<< /Size 1048 +/Root 1046 0 R +/Info 1047 0 R +/ID [<6A4F94399634C79BFC1155F88E046203> <6A4F94399634C79BFC1155F88E046203>] >> startxref -287776 +289612 %%EOF diff --git a/doc/fvn.tex b/doc/fvn.tex index 10f839f..00beaea 100644 --- a/doc/fvn.tex +++ b/doc/fvn.tex @@ -66,10 +66,11 @@ This library has been initially written for the use of the ``Acoustic and micros Copyright, this License, and the Availability note are retained, and a notice that the code was modified is included. -\subsubsection*{Authors} -As of the day this manuel is written there's only one author of fvn :\newline -William Daniau\newline -william.daniau@femto-st.fr\newline +\subsubsection*{Authors and Contributors} +\begin{itemize} + \item William Daniau (william.daniau@femto-st.fr) + \item Sylvain Ballandras (sylvain.ballandras@femto-st.fr) +\end{itemize} \section{Naming scheme and convention} The naming scheme of the routines is as follow : @@ -1228,15 +1229,28 @@ Specific interfaces : \verb'ei,dei' e1(x) \end{verbatim} \begin{itemize} - \item x is a real + \item x is a real or complex \end{itemize} -This function evaluates the exponential integral for argument greater than 0 and the Cauchy principal value for argument less than 0. It is define by equation \ref{e1} for $x \neq 0$. +For a real argument, this function evaluates the exponential integral for argument greater than 0 and the Cauchy principal value for argument less than 0. It is define by equation \ref{e1} for $x \neq 0$. \begin{equation} \label{e1} e1(x)= \int _{x} ^\infty {e^{-t}\over t}dt \end{equation} -Specific interfaces : \verb'e1,de1' +For a complex argument, the notation in equation \ref{e1cplx} is used (Abramowitz and Stegun, p.228 \url{http://www.math.ucla.edu/~cbm/aands/page_228.htm}): +\begin{equation} +\label{e1cplx} + e1(z) = \int _{z} ^\infty {e^{-t}\over t}dt \textrm{~with~} \left| arg(z) \right| < \pi +\end{equation} +For positive values of real part of $z$, this can be written as in equation \ref{e1cplx_pos} : +\begin{equation} +\label{e1cplx_pos} + e1(z)= \int _{1} ^\infty {e^{-tz}\over t}dt \textrm{~with~} Re(z) > 0 +\end{equation} + + + +Specific interfaces : \verb'e1,de1,ze1' \subsubsection{ali} \begin{verbatim} diff --git a/fvn_fnlib/Makefile b/fvn_fnlib/Makefile index 6228e71..2cc35ef 100644 --- a/fvn_fnlib/Makefile +++ b/fvn_fnlib/Makefile @@ -61,7 +61,7 @@ zexprl.o zgamma.o zgamr.o zlbeta.o \ zlngam.o zlnrel.o zlog10.o zpsi.o \ zsinh.o ztanh.o ztan.o besyn.o \ besjn.o dbesyn.o dbesjn.o beskn.o \ -besin.o dbeskn.o dbesin.o +besin.o dbeskn.o dbesin.o ze1.o lib:$(objects) diff --git a/fvn_fnlib/fvn_fnlib.f90 b/fvn_fnlib/fvn_fnlib.f90 index b1dc808..cd09f59 100644 --- a/fvn_fnlib/fvn_fnlib.f90 +++ b/fvn_fnlib/fvn_fnlib.f90 @@ -282,6 +282,9 @@ interface e1 real(8) function de1(x) real(8) :: x end function de1 + complex(8) function ze1(x) + complex(8) :: x + end function end interface e1 !!!!!!!!!!!!!!! diff --git a/fvn_fnlib/ze1.f90 b/fvn_fnlib/ze1.f90 new file mode 100644 index 0000000..6a2d9e3 --- /dev/null +++ b/fvn_fnlib/ze1.f90 @@ -0,0 +1,53 @@ +function ze1(z) +! +! ==================================================== +! Purpose: Compute complex exponential integral E1(z) +! Input : z --- Argument of E1(z) +! Output: CE1 --- E1(z) +! ==================================================== +! +! Déclaration des variables en passage de paramètre +! +implicit none +complex(8), intent(in) :: z +complex(8) :: ze1 +! +! Déclaration des variables locales +! +integer(4) :: k +real(8) :: pi,el,x,a0 +complex(8) :: cr,ct0,ct +parameter(pi=3.141592653589793D0,el=0.5772156649015328D0) +! +! traitement en fonction des différents cas +! - Z nul entraîne E1 infini +! - module de Z inférieur à 10 ou 20 : formule log+gam+somme +! - module de Z supérieur à 10 ou 20 : formule asymptotique +! + x=dreal(z) + a0=cdabs(z) + if (a0==0.0D0) then + ze1 = dcmplx(1.0D+300,0.0D0) + else if ((a0 <= 10.D0).or.(x <= 0.D0.and.a0 <= 20.D0)) then + ze1 = dcmplx(1.0D0,0.0D0) + cr = dcmplx(1.0D0,0.0D0) + k=0 + do while (cdabs(cr)<=cdabs(ze1)*1.0D-15) + k = k+1 + cr = -cr*k*z/(k+1.0D0)**2 + ze1 = ze1+cr + end do + ze1 = -el-cdlog(z)+z*ze1 + else + ct0 = dcmplx(0.0D0,0.0D0) + do k=120,1,-1 + ct0 = k/(1.0D0+k/(z+ct0)) + end do + ct = 1.0D0/(z+ct0) + ze1 = cdexp(-z)*ct + if (x <= 0.D0.AND.dimag(z) == 0.0) ze1 = ze1-pi*dcmplx(0.D0,1.D0) + end if +! + return +end function + -- 2.16.4