git-svn-id: https://lxsd.femto-st.fr/svn/fvn@45 b657c933-2333-4658-acf2-d3c7c2708721

daniau
1 parent 410c0dfaf8
Showing 15 changed files with 1377 additions and 1290 deletions Side-by-side Diff
doc/fvn.pdf
doc/fvn.tex
fvn_test/test_akima.f90
fvn_test/test_det.f90
fvn_test/test_integ.f90
fvn_test/test_inter1d.f90
fvn_test/test_inter2d.f90
fvn_test/test_inter3d.f90
fvn_test/test_lsp.f90
fvn_test/test_matcon.f90
fvn_test/test_matev.f90
fvn_test/test_matinv.f90
fvn_test/test_muller.f90
fvn_test/test_operators.f90
fvn_test/test_sparse.f90
@@ -29,7 +29,7 @@
  
 \section{Whatis fvn,license}
 \subsection{Whatis fvn}
-fvn is a Fortran95 mathematical library/module. It provides various usefull subroutine covering linear algebra, numerical integration, least square polynomial, spline interpolation, zero finding, special functions etc.
+fvn is a Fortran95 mathematical library with several modules. It provides various usefull subroutine covering linear algebra, numerical integration, least square polynomial, spline interpolation, zero finding, special functions etc.
  
 Most of the work for linear algebra is done by interfacing Lapack \url{http://www.netlib.org/lapack} which means that Lapack and Blas \url{http://www.netlib.org/blas} must be available on your system for linking fvn. If you use an AMD microprocessor, the good idea is to use ACML ( AMD Core Math Library \url{http://developer.amd.com/acml.jsp} which contains an optimized Blas/Lapack.
  
  
@@ -87,10 +87,14 @@
  
 For each routine, there is a generic interface (simply remove \verb'_*' in the name), so using the specific routine is not mandatory.
  
+
+There's a general module called ``\verb'fvn''' that include all fvn submodules. So whatever part of the library is used in the program a ``\verb'use fvn''' will be sufficient instead of specifying the specific module.
+
 \section{Linear algebra}
 The linear algebra routines of fvn are an interface to lapack, which make it easier to use.
 \subsection{Matrix inversion}
 \begin{verbatim}
+Module : use fvn_linear
 call fvn_matinv(d,a,inva,status)
 \end{verbatim}
 \begin{itemize}
@@ -103,7 +107,7 @@
 \subsubsection*{Example}
 \begin{verbatim}
 program inv
- use fvn 
+ use fvn_linear
  implicit none
  
  real(8),dimension(3,3) :: a,inva
@@ -124,6 +128,7 @@
  
 \subsection{Matrix determinants}
 \begin{verbatim}
+Module : use fvn_linear
 det=fvn_det(d,a,status)
 \end{verbatim}
 \begin{itemize}
@@ -135,7 +140,7 @@
 \subsubsection*{Example}
 \begin{verbatim}
 program det
- use fvn 
+ use fvn_linear
  implicit none
  
  real(8),dimension(3,3) :: a
@@ -157,6 +162,7 @@
  
 \subsection{Matrix condition}
 \begin{verbatim}
+Module : use fvn_linear
 call fvn_matcon(d,a,rcond,status)
 \end{verbatim}
 \begin{itemize}
@@ -181,7 +187,7 @@
 \subsubsection*{Example}
 \begin{verbatim}
 program cond
- use fvn 
+ use fvn_linear
  implicit none
  
  real(8),dimension(3,3) :: a
@@ -202,6 +208,7 @@
  
 \subsection{Eigenvalues/Eigenvectors}
 \begin{verbatim}
+Module : use fvn_linear
 call fvn_matev(d,a,evala,eveca,status)
 \end{verbatim}
 \begin{itemize}
  
@@ -212,10 +219,11 @@
  \item status (out) is an optional integer equal to zero if something went wrong
 \end{itemize}
  
+
 \subsubsection*{Example}
 \begin{verbatim}
 program eigen
- use fvn 
+ use fvn_linear
  implicit none
  
  real(8),dimension(3,3) :: a
@@ -249,6 +257,7 @@
 The provided routines solves the equation $Ax=B$ where A is sparse and given in its triplet form.
  
 \begin{verbatim}
+Module : fvn_sparse
 call fvn_sparse_solve(n,nz,T,Ti,Tj,B,x,status)
 \end{verbatim}
 \begin{itemize}
  
@@ -262,11 +271,12 @@
  \item status (out) is an integer which contain non-zero is something went wrong
 \end{itemize}
  
+
 \subsubsection*{Example}
 \begin{verbatim}
 program test_sparse
  
- use fvn
+ use fvn_sparse
  implicit none
  
  integer(8), parameter :: nz=12
@@ -292,7 +302,7 @@
  
 program test_sparse
  
-use fvn
+use fvn_sparse
 implicit none
  
 integer(4), parameter :: nz=12
  
  
@@ -320,15 +330,20 @@
  
 \subsection{Identity matrix}
 \begin{verbatim}
+ Module : use fvn_linear
  I=fvn_*_ident(n)     (*=s,d,c,z)
 \end{verbatim}
 \begin{itemize}
  \item n (in) is an integer equal to the matrix rank
 \end{itemize}
+
 This function return the identity matrix of rank n, in the specified type. No generic interface for this one.
  
 \subsection{Operators}
 fvn defines some linear operators similar to those defined in IMSL\textregistered (\url{http://www.vni.com/products/imsl/}), that can be used for matrix operations.
+\begin{verbatim}
+ Module : use fvn_linear
+\end{verbatim}
  
 \subsubsection{Unary operators}
 \paragraph{.i.}
@@ -403,6 +418,7 @@
 fvn provide function for interpolating values of a tabulated function of 1, 2 or 3 variables, for both single and double precision.
 \subsubsection{One variable function}
 \begin{verbatim}
+ Module : use fvn_interpol
  value=fvn_quad_interpol(x,n,xdata,ydata)
 \end{verbatim}
 \begin{itemize}
@@ -417,7 +433,7 @@
 \begin{verbatim}
 program inter1d
  
-use fvn
+use fvn_interpol
 implicit none
  
 integer(kind=4),parameter :: ndata=33
@@ -454,6 +470,7 @@
  
 \subsubsection{Two variables function}
 \begin{verbatim}
+Module : use fvn_interpol
 value=fvn_quad_2d_interpol(x,y,nx,xdata,ny,ydata,zdata)
 \end{verbatim}
 \begin{itemize}
@@ -471,7 +488,7 @@
  
 \begin{verbatim}
 program inter2d
-use fvn
+use fvn_interpol
 implicit none
  
 integer(kind=4),parameter  :: nx=21,ny=42
@@ -513,6 +530,7 @@
  
 \subsubsection{Three variables function}
 \begin{verbatim}
+ Module : use fvn_interpol
 value=fvn_quad_3d_interpol(x,y,z,nx,xdata,ny,ydata,nz,zdata,tdata)
 \end{verbatim}
 \begin{itemize}
@@ -531,7 +549,7 @@
 \paragraph*{Example}
 \begin{verbatim}
 program inter3d
-use fvn
+use fvn_interpol
  
 implicit none
  
@@ -579,6 +597,7 @@
 \subsubsection{Utility procedure}
 fvn provides a simple utility procedure to locate the interval in which a value is located in an increasingly ordered array.
 \begin{verbatim}
+Module : use fvn_interpol
 call fvn_find_interval(x,i,xdata,n)
 \end{verbatim}
 \begin{itemize}
@@ -595,6 +614,7 @@
 fvn provides Akima spline interpolation and evaluation for both single and double precision real.
 \subsubsection{Interpolation}
 \begin{verbatim}
+Module : use fvn_interpol
 call fvn_akima(n,x,y,br,co)
 \end{verbatim}
 \begin{itemize}
@@ -606,6 +626,7 @@
  
 \subsubsection{Evaluation}
 \begin{verbatim}
+Module : use fvn_interpol
 y=fvn_spline_eval(x,n,br,co)
 \end{verbatim}
 \begin{itemize}
@@ -621,7 +642,7 @@
  
 \begin{verbatim}
 program akima
- use fvn
+ use fvn_interpol
  implicit none
  
  integer :: nbpoints,nppoints,i
@@ -681,6 +702,7 @@
 fvn provide a function to find a least square polynomial of a given degree, for real in single or double precision. It is performed using Lapack subroutine sgels (dgels), which solve this problem.
  
 \begin{verbatim}
+Module : use fvn_linear
 call fvn_lspoly(np,x,y,deg,coeff,status)
 \end{verbatim}
 \begin{itemize}
@@ -695,7 +717,7 @@
 Here's a simple example : we've got 13 measurement points and we want to find the least square degree 3 polynomial for these points :
 \begin{verbatim}
  program lsp
- use fvn
+ use fvn_linear
  implicit none
  
  integer,parameter :: npoints=13,deg=3
@@ -760,6 +782,7 @@
 fvn provide a routine for finding zeros of a complex function using Muller algorithm (only for double complex type). It is based on a version provided on the web by Hans D Mittelmann \url{http://plato.asu.edu/ftp/other\_software/muller.f}.
  
 \begin{verbatim}
+ Module : use fvn_misc
  call fvn_muller(f,eps,eps1,kn,nguess,n,x,itmax,infer,ier)
 \end{verbatim}
 \begin{itemize}
@@ -780,7 +803,7 @@
 Example to find the ten roots of $x^{10}-1$
 \begin{verbatim}
  program muller
- use fvn
+ use fvn_misc
  implicit none
  
  integer :: i,info
@@ -811,6 +834,7 @@
 \subsection{Gauss Legendre Abscissas and Weigth}
 This subroutine was inspired by Numerical Recipes routine gauleg.
 \begin{verbatim}
+Module : use fvn_integ
 call fvn_gauss_legendre(n,qx,qw)
 \end{verbatim}
 \begin{itemize}
@@ -822,6 +846,7 @@
  
 \subsection{Gauss Legendre Numerical Integration}
 \begin{verbatim}
+Module : use fvn_integ
 call fvn_gl_integ(f,a,b,n,res)
 \end{verbatim}
 \begin{itemize}
@@ -836,6 +861,7 @@
 This kind of numerical integration is an iterative procedure which try to achieve a given precision.
 \subsubsection{Numerical integration of a one variable function}
 \begin{verbatim}
+Module : use fvn_integ
 call fvn_integ_1_gk(f,a,b,epsabs,epsrel,key,res,abserr,ier,limit)
 \end{verbatim}
 This routine evaluate the integral of function f as in equation \ref{intsple}
@@ -875,6 +901,7 @@
  
 \subsubsection{Numerical integration of a two variable function}
 \begin{verbatim}
+Module : use fvn_integ
 call fvn_integ_2_gk(f,a,b,g,h,epsabs,epsrel,key,res,abserr,ier,limit)
 \end{verbatim}
 This function evaluate the integral of a function f(x,y) as defined in equation \ref{intdble}. The parameters of same name as in the previous paragraph have exactly the same function and behaviour thus only what differs is decribed here
@@ -891,7 +918,7 @@
 \subsubsection*{Example}
 \begin{verbatim}
 program integ
- use fvn
+ use fvn_integ
  implicit none
  
  real(8), external :: f1,f2,g,h
  
@@ -943,8 +970,12 @@
 \section{Special functions}
 Specials functions are available in fvn by using an implementation of fnlib \url{http://www.netlib.org/fn} with some additions. This can be used separatly from the rest of fvn by using the module \verb'fvn_fnlib' and linking the library \verb'libfvn_fnlib.a' . The module provides a generic interfaces to all the routines. Specific names of the routines are given in the description.
  
+\begin{verbatim}
+ Module : use fvn_fnlib
+\end{verbatim}
+
 \paragraph{Important Note}
-Due to the addition of fnlib to fvn, some functions that were in fvn and are redondant will be removed from fvn, so update your code now and replace them with the fnlib version. These are listed here after :
+Due to the addition of fnlib to fvn, some functions that were in fvn and are redondant are now removed from fvn, so update your code now and replace them with the fnlib version. These are listed here after :
 \begin{itemize}
  \item \verb'fvn_z_acos' replaced by \verb'acos'
  \item \verb'fvn_z_asin' replaced by \verb'asin'
 program akima
- use fvn
+ use fvn_interpol
  implicit none
  integer :: nbpoints,nppoints,i
  real(8),dimension(:),allocatable :: x_d,y_d,breakpoints_d
 program test_det
-use fvn
+use fvn_linear
 implicit none
 real(8),dimension(3,3) :: a
 real(8) :: deta
 program integ
- use fvn
+ use fvn_integ
  implicit none
  real(8), external :: f1,f2,g,h
  real(8) :: a,b,epsabs,epsrel,abserr,res
 program inter1d
-use fvn
+use fvn_interpol
 implicit none
 integer(kind=4),parameter :: ndata=33
 integer(kind=4) :: i,nout
 program inter2d
-use fvn
+use fvn_interpol
 implicit none
 integer(kind=4),parameter :: nx=21,ny=42
 integer(kind=4) :: i,j
 program test_inter3d
-use fvn
+use fvn_interpol
 implicit none
 integer(kind=4),parameter :: nx=21,ny=42,nz=18
 integer(kind=4) :: i,j,k
 program lsp
-use fvn
+use fvn_linear
 implicit none
 integer,parameter :: npoints=13,deg=3
  integer :: status,i
 program test_matcon
-use fvn
+use fvn_linear
 implicit none
 real(8),dimension(3,3) :: a
 real(8) :: rcond
 program test_matev
-use fvn
+use fvn_linear
 implicit none
 real(8),dimension(3,3) :: a
 complex(8),dimension(3) :: evala
 program test_matinv
-use fvn
+use fvn_linear
 implicit none
 integer(4), parameter :: n=3
 integer(4) :: status,i
 program muller
-use fvn
+use fvn_misc
 implicit none
 integer :: i,info
 complex(8),dimension(10) :: roots
 program test_matinv
-use fvn
+use fvn_linear
 implicit none
  
 integer, parameter :: n=3
 program test_sparse
-use fvn
+use fvn_sparse
 implicit none
 integer(4), parameter :: nz=12
 integer(4), parameter :: n=5
...	...	@@ -29,7 +29,7 @@
29	29
30	30	\section{Whatis fvn,license}
31	31	\subsection{Whatis fvn}
32		-fvn is a Fortran95 mathematical library/module. It provides various usefull subroutine covering linear algebra, numerical integration, least square polynomial, spline interpolation, zero finding, special functions etc.
	32	+fvn is a Fortran95 mathematical library with several modules. It provides various usefull subroutine covering linear algebra, numerical integration, least square polynomial, spline interpolation, zero finding, special functions etc.
33	33
34	34	Most of the work for linear algebra is done by interfacing Lapack \url{http://www.netlib.org/lapack} which means that Lapack and Blas \url{http://www.netlib.org/blas} must be available on your system for linking fvn. If you use an AMD microprocessor, the good idea is to use ACML ( AMD Core Math Library \url{http://developer.amd.com/acml.jsp} which contains an optimized Blas/Lapack.
35	35
36	36
...	...	@@ -87,10 +87,14 @@
87	87
88	88	For each routine, there is a generic interface (simply remove \verb'_*' in the name), so using the specific routine is not mandatory.
89	89
	90	+
	91	+There's a general module called ``\verb'fvn''' that include all fvn submodules. So whatever part of the library is used in the program a ``\verb'use fvn''' will be sufficient instead of specifying the specific module.
	92	+
90	93	\section{Linear algebra}
91	94	The linear algebra routines of fvn are an interface to lapack, which make it easier to use.
92	95	\subsection{Matrix inversion}
93	96	\begin{verbatim}
	97	+Module : use fvn_linear
94	98	call fvn_matinv(d,a,inva,status)
95	99	\end{verbatim}
96	100	\begin{itemize}
...	...	@@ -103,7 +107,7 @@
103	107	\subsubsection*{Example}
104	108	\begin{verbatim}
105	109	program inv
106		- use fvn
	110	+ use fvn_linear
107	111	implicit none
108	112
109	113	real(8),dimension(3,3) :: a,inva
...	...	@@ -124,6 +128,7 @@
124	128
125	129	\subsection{Matrix determinants}
126	130	\begin{verbatim}
	131	+Module : use fvn_linear
127	132	det=fvn_det(d,a,status)
128	133	\end{verbatim}
129	134	\begin{itemize}
...	...	@@ -135,7 +140,7 @@
135	140	\subsubsection*{Example}
136	141	\begin{verbatim}
137	142	program det
138		- use fvn
	143	+ use fvn_linear
139	144	implicit none
140	145
141	146	real(8),dimension(3,3) :: a
...	...	@@ -157,6 +162,7 @@
157	162
158	163	\subsection{Matrix condition}
159	164	\begin{verbatim}
	165	+Module : use fvn_linear
160	166	call fvn_matcon(d,a,rcond,status)
161	167	\end{verbatim}
162	168	\begin{itemize}
...	...	@@ -181,7 +187,7 @@
181	187	\subsubsection*{Example}
182	188	\begin{verbatim}
183	189	program cond
184		- use fvn
	190	+ use fvn_linear
185	191	implicit none
186	192
187	193	real(8),dimension(3,3) :: a
...	...	@@ -202,6 +208,7 @@
202	208
203	209	\subsection{Eigenvalues/Eigenvectors}
204	210	\begin{verbatim}
	211	+Module : use fvn_linear
205	212	call fvn_matev(d,a,evala,eveca,status)
206	213	\end{verbatim}
207	214	\begin{itemize}
208	215
...	...	@@ -212,10 +219,11 @@
212	219	\item status (out) is an optional integer equal to zero if something went wrong
213	220	\end{itemize}
214	221
	222	+
215	223	\subsubsection*{Example}
216	224	\begin{verbatim}
217	225	program eigen
218		- use fvn
	226	+ use fvn_linear
219	227	implicit none
220	228
221	229	real(8),dimension(3,3) :: a
...	...	@@ -249,6 +257,7 @@
249	257	The provided routines solves the equation $Ax=B$ where A is sparse and given in its triplet form.
250	258
251	259	\begin{verbatim}
	260	+Module : fvn_sparse
252	261	call fvn_sparse_solve(n,nz,T,Ti,Tj,B,x,status)
253	262	\end{verbatim}
254	263	\begin{itemize}
255	264
...	...	@@ -262,11 +271,12 @@
262	271	\item status (out) is an integer which contain non-zero is something went wrong
263	272	\end{itemize}
264	273
	274	+
265	275	\subsubsection*{Example}
266	276	\begin{verbatim}
267	277	program test_sparse
268	278
269		- use fvn
	279	+ use fvn_sparse
270	280	implicit none
271	281
272	282	integer(8), parameter :: nz=12
...	...	@@ -292,7 +302,7 @@
292	302
293	303	program test_sparse
294	304
295		-use fvn
	305	+use fvn_sparse
296	306	implicit none
297	307
298	308	integer(4), parameter :: nz=12
299	309
300	310
...	...	@@ -320,15 +330,20 @@
320	330
321	331	\subsection{Identity matrix}
322	332	\begin{verbatim}
	333	+ Module : use fvn_linear
323	334	I=fvn__ident(n) (=s,d,c,z)
324	335	\end{verbatim}
325	336	\begin{itemize}
326	337	\item n (in) is an integer equal to the matrix rank
327	338	\end{itemize}
	339	+
328	340	This function return the identity matrix of rank n, in the specified type. No generic interface for this one.
329	341
330	342	\subsection{Operators}
331	343	fvn defines some linear operators similar to those defined in IMSL\textregistered (\url{http://www.vni.com/products/imsl/}), that can be used for matrix operations.
	344	+\begin{verbatim}
	345	+ Module : use fvn_linear
	346	+\end{verbatim}
332	347
333	348	\subsubsection{Unary operators}
334	349	\paragraph{.i.}
...	...	@@ -403,6 +418,7 @@
403	418	fvn provide function for interpolating values of a tabulated function of 1, 2 or 3 variables, for both single and double precision.
404	419	\subsubsection{One variable function}
405	420	\begin{verbatim}
	421	+ Module : use fvn_interpol
406	422	value=fvn_quad_interpol(x,n,xdata,ydata)
407	423	\end{verbatim}
408	424	\begin{itemize}
...	...	@@ -417,7 +433,7 @@
417	433	\begin{verbatim}
418	434	program inter1d
419	435
420		-use fvn
	436	+use fvn_interpol
421	437	implicit none
422	438
423	439	integer(kind=4),parameter :: ndata=33
...	...	@@ -454,6 +470,7 @@
454	470
455	471	\subsubsection{Two variables function}
456	472	\begin{verbatim}
	473	+Module : use fvn_interpol
457	474	value=fvn_quad_2d_interpol(x,y,nx,xdata,ny,ydata,zdata)
458	475	\end{verbatim}
459	476	\begin{itemize}
...	...	@@ -471,7 +488,7 @@
471	488
472	489	\begin{verbatim}
473	490	program inter2d
474		-use fvn
	491	+use fvn_interpol
475	492	implicit none
476	493
477	494	integer(kind=4),parameter :: nx=21,ny=42
...	...	@@ -513,6 +530,7 @@
513	530
514	531	\subsubsection{Three variables function}
515	532	\begin{verbatim}
	533	+ Module : use fvn_interpol
516	534	value=fvn_quad_3d_interpol(x,y,z,nx,xdata,ny,ydata,nz,zdata,tdata)
517	535	\end{verbatim}
518	536	\begin{itemize}
...	...	@@ -531,7 +549,7 @@
531	549	\paragraph*{Example}
532	550	\begin{verbatim}
533	551	program inter3d
534		-use fvn
	552	+use fvn_interpol
535	553
536	554	implicit none
537	555
...	...	@@ -579,6 +597,7 @@
579	597	\subsubsection{Utility procedure}
580	598	fvn provides a simple utility procedure to locate the interval in which a value is located in an increasingly ordered array.
581	599	\begin{verbatim}
	600	+Module : use fvn_interpol
582	601	call fvn_find_interval(x,i,xdata,n)
583	602	\end{verbatim}
584	603	\begin{itemize}
...	...	@@ -595,6 +614,7 @@
595	614	fvn provides Akima spline interpolation and evaluation for both single and double precision real.
596	615	\subsubsection{Interpolation}
597	616	\begin{verbatim}
	617	+Module : use fvn_interpol
598	618	call fvn_akima(n,x,y,br,co)
599	619	\end{verbatim}
600	620	\begin{itemize}
...	...	@@ -606,6 +626,7 @@
606	626
607	627	\subsubsection{Evaluation}
608	628	\begin{verbatim}
	629	+Module : use fvn_interpol
609	630	y=fvn_spline_eval(x,n,br,co)
610	631	\end{verbatim}
611	632	\begin{itemize}
...	...	@@ -621,7 +642,7 @@
621	642
622	643	\begin{verbatim}
623	644	program akima
624		- use fvn
	645	+ use fvn_interpol
625	646	implicit none
626	647
627	648	integer :: nbpoints,nppoints,i
...	...	@@ -681,6 +702,7 @@
681	702	fvn provide a function to find a least square polynomial of a given degree, for real in single or double precision. It is performed using Lapack subroutine sgels (dgels), which solve this problem.
682	703
683	704	\begin{verbatim}
	705	+Module : use fvn_linear
684	706	call fvn_lspoly(np,x,y,deg,coeff,status)
685	707	\end{verbatim}
686	708	\begin{itemize}
...	...	@@ -695,7 +717,7 @@
695	717	Here's a simple example : we've got 13 measurement points and we want to find the least square degree 3 polynomial for these points :
696	718	\begin{verbatim}
697	719	program lsp
698		- use fvn
	720	+ use fvn_linear
699	721	implicit none
700	722
701	723	integer,parameter :: npoints=13,deg=3
...	...	@@ -760,6 +782,7 @@
760	782	fvn provide a routine for finding zeros of a complex function using Muller algorithm (only for double complex type). It is based on a version provided on the web by Hans D Mittelmann \url{http://plato.asu.edu/ftp/other\_software/muller.f}.
761	783
762	784	\begin{verbatim}
	785	+ Module : use fvn_misc
763	786	call fvn_muller(f,eps,eps1,kn,nguess,n,x,itmax,infer,ier)
764	787	\end{verbatim}
765	788	\begin{itemize}
...	...	@@ -780,7 +803,7 @@
780	803	Example to find the ten roots of $x^{10}-1$
781	804	\begin{verbatim}
782	805	program muller
783		- use fvn
	806	+ use fvn_misc
784	807	implicit none
785	808
786	809	integer :: i,info
...	...	@@ -811,6 +834,7 @@
811	834	\subsection{Gauss Legendre Abscissas and Weigth}
812	835	This subroutine was inspired by Numerical Recipes routine gauleg.
813	836	\begin{verbatim}
	837	+Module : use fvn_integ
814	838	call fvn_gauss_legendre(n,qx,qw)
815	839	\end{verbatim}
816	840	\begin{itemize}
...	...	@@ -822,6 +846,7 @@
822	846
823	847	\subsection{Gauss Legendre Numerical Integration}
824	848	\begin{verbatim}
	849	+Module : use fvn_integ
825	850	call fvn_gl_integ(f,a,b,n,res)
826	851	\end{verbatim}
827	852	\begin{itemize}
...	...	@@ -836,6 +861,7 @@
836	861	This kind of numerical integration is an iterative procedure which try to achieve a given precision.
837	862	\subsubsection{Numerical integration of a one variable function}
838	863	\begin{verbatim}
	864	+Module : use fvn_integ
839	865	call fvn_integ_1_gk(f,a,b,epsabs,epsrel,key,res,abserr,ier,limit)
840	866	\end{verbatim}
841	867	This routine evaluate the integral of function f as in equation \ref{intsple}
...	...	@@ -875,6 +901,7 @@
875	901
876	902	\subsubsection{Numerical integration of a two variable function}
877	903	\begin{verbatim}
	904	+Module : use fvn_integ
878	905	call fvn_integ_2_gk(f,a,b,g,h,epsabs,epsrel,key,res,abserr,ier,limit)
879	906	\end{verbatim}
880	907	This function evaluate the integral of a function f(x,y) as defined in equation \ref{intdble}. The parameters of same name as in the previous paragraph have exactly the same function and behaviour thus only what differs is decribed here
...	...	@@ -891,7 +918,7 @@
891	918	\subsubsection*{Example}
892	919	\begin{verbatim}
893	920	program integ
894		- use fvn
	921	+ use fvn_integ
895	922	implicit none
896	923
897	924	real(8), external :: f1,f2,g,h
898	925
...	...	@@ -943,8 +970,12 @@
943	970	\section{Special functions}
944	971	Specials functions are available in fvn by using an implementation of fnlib \url{http://www.netlib.org/fn} with some additions. This can be used separatly from the rest of fvn by using the module \verb'fvn_fnlib' and linking the library \verb'libfvn_fnlib.a' . The module provides a generic interfaces to all the routines. Specific names of the routines are given in the description.
945	972
	973	+\begin{verbatim}
	974	+ Module : use fvn_fnlib
	975	+\end{verbatim}
	976	+
946	977	\paragraph{Important Note}
947		-Due to the addition of fnlib to fvn, some functions that were in fvn and are redondant will be removed from fvn, so update your code now and replace them with the fnlib version. These are listed here after :
	978	+Due to the addition of fnlib to fvn, some functions that were in fvn and are redondant are now removed from fvn, so update your code now and replace them with the fnlib version. These are listed here after :
948	979	\begin{itemize}
949	980	\item \verb'fvn_z_acos' replaced by \verb'acos'
950	981	\item \verb'fvn_z_asin' replaced by \verb'asin'
1	1	program test_det
2		-use fvn
	2	+use fvn_linear
3	3	implicit none
4	4	real(8),dimension(3,3) :: a
5	5	real(8) :: deta
1	1	program test_inter3d
2		-use fvn
	2	+use fvn_interpol
3	3	implicit none
4	4	integer(kind=4),parameter :: nx=21,ny=42,nz=18
5	5	integer(kind=4) :: i,j,k
1	1	program test_matcon
2		-use fvn
	2	+use fvn_linear
3	3	implicit none
4	4	real(8),dimension(3,3) :: a
5	5	real(8) :: rcond
1	1	program test_matev
2		-use fvn
	2	+use fvn_linear
3	3	implicit none
4	4	real(8),dimension(3,3) :: a
5	5	complex(8),dimension(3) :: evala
1	1	program test_matinv
2		-use fvn
	2	+use fvn_linear
3	3	implicit none
4	4	integer(4), parameter :: n=3
5	5	integer(4) :: status,i
1	1	program muller
2		-use fvn
	2	+use fvn_misc
3	3	implicit none
4	4	integer :: i,info
5	5	complex(8),dimension(10) :: roots