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\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 @@ In the following description of subroutines parameters, input parameters are fol 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 @@ call fvn_matinv(d,a,inva,status) \subsubsection*{Example} \begin{verbatim} program inv - use fvn + use fvn_linear implicit none real(8),dimension(3,3) :: a,inva @@ -124,6 +128,7 @@ end program \subsection{Matrix determinants} \begin{verbatim} +Module : use fvn_linear det=fvn_det(d,a,status) \end{verbatim} \begin{itemize} @@ -135,7 +140,7 @@ det=fvn_det(d,a,status) \subsubsection*{Example} \begin{verbatim} program det - use fvn + use fvn_linear implicit none real(8),dimension(3,3) :: a @@ -157,6 +162,7 @@ end program \subsection{Matrix condition} \begin{verbatim} +Module : use fvn_linear call fvn_matcon(d,a,rcond,status) \end{verbatim} \begin{itemize} @@ -181,7 +187,7 @@ The 1-norm itself is defined as the maximum value of the columns absolute values \subsubsection*{Example} \begin{verbatim} program cond - use fvn + use fvn_linear implicit none real(8),dimension(3,3) :: a @@ -202,6 +208,7 @@ end program \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 @@ call fvn_matev(d,a,evala,eveca,status) \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 @@ By interfacing Tim Davis's SuiteSparse from university of Florida \url{http://ww 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 @@ call fvn_sparse_solve(n,nz,T,Ti,Tj,B,x,status) \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 @@ end program program test_sparse -use fvn +use fvn_sparse implicit none integer(4), parameter :: nz=12 @@ -320,15 +330,20 @@ end program \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 @@ This operator gives the matrix product of thee first operand and the conjugate t 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 @@ x must be within the range of xdata to actually perform an interpolation, otherw \begin{verbatim} program inter1d -use fvn +use fvn_interpol implicit none integer(kind=4),parameter :: ndata=33 @@ -454,6 +470,7 @@ end program \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 @@ xdata and ydata must be strictly increasingly ordered. \begin{verbatim} program inter2d -use fvn +use fvn_interpol implicit none integer(kind=4),parameter :: nx=21,ny=42 @@ -513,6 +530,7 @@ end program \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 @@ xdata, ydata and zdata must be strictly increasingly ordered. \paragraph*{Example} \begin{verbatim} program inter3d -use fvn +use fvn_interpol implicit none @@ -579,6 +597,7 @@ end program \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 @@ The resulting integer i is as : $xdata(i) <= x < xdata(i+1)$. If $x < xdata(1)$ 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 @@ call fvn_akima(n,x,y,br,co) \subsubsection{Evaluation} \begin{verbatim} +Module : use fvn_interpol y=fvn_spline_eval(x,n,br,co) \end{verbatim} \begin{itemize} @@ -621,7 +642,7 @@ One can see that the interpolation is very efficient even with only 30 points. O \begin{verbatim} program akima - use fvn + use fvn_interpol implicit none integer :: nbpoints,nppoints,i @@ -681,6 +702,7 @@ Results are plotted on figure \ref{akima} 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 @@ call fvn_lspoly(np,x,y,deg,coeff,status) 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 @@ The results are plotted on figure \ref{lsp} . 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 @@ This subroutine always returns the last approximation for root j in x(j). if the 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 @@ Using an integrated slightly modified version of quadpack \url{http://www.netlib \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 @@ This subroutine computes n Gauss-Legendre abscissas and weigths \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 function is a simple Gauss Legendre integration subroutine, which evaluate 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 @@ This routine evaluate the integral of function f as in equation \ref{intsple} \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 @@ This function evaluate the integral of a function f(x,y) as defined in equation \subsubsection*{Example} \begin{verbatim} program integ - use fvn + use fvn_integ implicit none real(8), external :: f1,f2,g,h @@ -943,8 +970,12 @@ end function \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' diff --git a/fvn_test/test_akima.f90 b/fvn_test/test_akima.f90 index b075706..8849845 100644 --- a/fvn_test/test_akima.f90 +++ b/fvn_test/test_akima.f90 @@ -1,5 +1,5 @@ program akima - use fvn + use fvn_interpol implicit none integer :: nbpoints,nppoints,i real(8),dimension(:),allocatable :: x_d,y_d,breakpoints_d diff --git a/fvn_test/test_det.f90 b/fvn_test/test_det.f90 index 376c520..0feadd1 100644 --- a/fvn_test/test_det.f90 +++ b/fvn_test/test_det.f90 @@ -1,5 +1,5 @@ program test_det -use fvn +use fvn_linear implicit none real(8),dimension(3,3) :: a real(8) :: deta diff --git a/fvn_test/test_integ.f90 b/fvn_test/test_integ.f90 index 383feda..5b68dfb 100644 --- a/fvn_test/test_integ.f90 +++ b/fvn_test/test_integ.f90 @@ -1,5 +1,5 @@ program integ - use fvn + use fvn_integ implicit none real(8), external :: f1,f2,g,h real(8) :: a,b,epsabs,epsrel,abserr,res diff --git a/fvn_test/test_inter1d.f90 b/fvn_test/test_inter1d.f90 index a1f0a08..9f6fa6f 100644 --- a/fvn_test/test_inter1d.f90 +++ b/fvn_test/test_inter1d.f90 @@ -1,5 +1,5 @@ program inter1d -use fvn +use fvn_interpol implicit none integer(kind=4),parameter :: ndata=33 integer(kind=4) :: i,nout diff --git a/fvn_test/test_inter2d.f90 b/fvn_test/test_inter2d.f90 index a8bc359..c01cd71 100644 --- a/fvn_test/test_inter2d.f90 +++ b/fvn_test/test_inter2d.f90 @@ -1,5 +1,5 @@ program inter2d -use fvn +use fvn_interpol implicit none integer(kind=4),parameter :: nx=21,ny=42 integer(kind=4) :: i,j diff --git a/fvn_test/test_inter3d.f90 b/fvn_test/test_inter3d.f90 index e00ade6..a8af391 100644 --- a/fvn_test/test_inter3d.f90 +++ b/fvn_test/test_inter3d.f90 @@ -1,5 +1,5 @@ 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 diff --git a/fvn_test/test_lsp.f90 b/fvn_test/test_lsp.f90 index 42922d7..ca10298 100644 --- a/fvn_test/test_lsp.f90 +++ b/fvn_test/test_lsp.f90 @@ -1,5 +1,5 @@ program lsp -use fvn +use fvn_linear implicit none integer,parameter :: npoints=13,deg=3 integer :: status,i diff --git a/fvn_test/test_matcon.f90 b/fvn_test/test_matcon.f90 index cc956fb..f25659b 100644 --- a/fvn_test/test_matcon.f90 +++ b/fvn_test/test_matcon.f90 @@ -1,5 +1,5 @@ program test_matcon -use fvn +use fvn_linear implicit none real(8),dimension(3,3) :: a real(8) :: rcond diff --git a/fvn_test/test_matev.f90 b/fvn_test/test_matev.f90 index 982a1e4..b292314 100644 --- a/fvn_test/test_matev.f90 +++ b/fvn_test/test_matev.f90 @@ -1,5 +1,5 @@ program test_matev -use fvn +use fvn_linear implicit none real(8),dimension(3,3) :: a complex(8),dimension(3) :: evala diff --git a/fvn_test/test_matinv.f90 b/fvn_test/test_matinv.f90 index e493a53..0e6353d 100644 --- a/fvn_test/test_matinv.f90 +++ b/fvn_test/test_matinv.f90 @@ -1,5 +1,5 @@ program test_matinv -use fvn +use fvn_linear implicit none integer(4), parameter :: n=3 integer(4) :: status,i diff --git a/fvn_test/test_muller.f90 b/fvn_test/test_muller.f90 index f0bfcc4..963f3c6 100644 --- a/fvn_test/test_muller.f90 +++ b/fvn_test/test_muller.f90 @@ -1,5 +1,5 @@ program muller -use fvn +use fvn_misc implicit none integer :: i,info complex(8),dimension(10) :: roots diff --git a/fvn_test/test_operators.f90 b/fvn_test/test_operators.f90 index d9ed67a..cb4c71c 100644 --- a/fvn_test/test_operators.f90 +++ b/fvn_test/test_operators.f90 @@ -1,5 +1,5 @@ program test_matinv -use fvn +use fvn_linear implicit none integer, parameter :: n=3 diff --git a/fvn_test/test_sparse.f90 b/fvn_test/test_sparse.f90 index 7f34a87..3efb586 100644 --- a/fvn_test/test_sparse.f90 +++ b/fvn_test/test_sparse.f90 @@ -1,5 +1,5 @@ program test_sparse -use fvn +use fvn_sparse implicit none integer(4), parameter :: nz=12 integer(4), parameter :: n=5