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00000 n +0000278320 00000 n trailer -<< /Size 933 -/Root 931 0 R -/Info 932 0 R -/ID [ ] >> +<< /Size 1013 +/Root 1011 0 R +/Info 1012 0 R +/ID [ ] >> startxref -242556 +278652 %%EOF diff --git a/doc/fvn.tex b/doc/fvn.tex index b4bccb4..98faac9 100644 --- a/doc/fvn.tex +++ b/doc/fvn.tex @@ -300,7 +300,7 @@ end program \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 type of the left hand side. No generic interface for this one. +This function return the identity matrix of rank n, in the specified type. No generic interface for this one. @@ -585,7 +585,7 @@ Results are plotted on figure \ref{akima} \section{Least square polynomial} -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 sgelss (dgelss), which solve this problem using singular value decomposition. +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} call fvn_lspoly(np,x,y,deg,coeff,status) @@ -848,7 +848,7 @@ end function \section{Special functions} -Specials functions are available in fvn by using an implementation of fnlib \url{http://www.netlib.org/fn}. 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. The double complex versions of the routines are not present in the web version of fnlib, so these have been added, but not intensely tested. +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. \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 : @@ -1533,12 +1533,47 @@ bsj1(x)=J_1(x)={1 \over \pi} \int _0 ^\pi cos(x sin(\theta)-\theta) d\theta Specific interfaces : \verb'besj1,dbesj1' +\subsubsection{bsjn} +\begin{verbatim} + bsjn(n,x,factor,big) +\end{verbatim} +\begin{itemize} + \item n is an integer + \item x is a real + \item factor is an optional integer + \item big is an optional real +\end{itemize} +This function evaluates Bessel function of the first kind of order n (plotted in figure \ref{besseljnfamily}). These functions satisfy the recurrent relation \ref {bsjn}. +\begin{equation} + \label{bsjn} +J_{n+1}(x)={{2n}\over x} J_n(x) - J_{n-1}(x) +\end{equation} +This relation is directly used in upward direction to compute $J_n(x)$ for $x>n$. However it is unstable for $x0 -\end{equation} %\begin{equation} -% \left{\begin{array}{ll} -% Ai(x) & \textrm{~if~}x\leq0 \\ -% e^{{2\over3}x^{3\over2}}Ai(x) & \textrm{~if~}x>0 -%\end{array}\right. -%\label{aie} +% \label{aie} +%aie(x)=Ai(x) \textrm{~if~}x\leq0 \qquad \qquad aie(x)=e^{{2\over3}x^{3\over2}}Ai(x)\rm{~if~}x>0 %\end{equation} +\begin{equation} +\label{aie} + aie(x)=\left\{\begin{array}{ll} + Ai(x) & \textrm{~if~}x\leq0 \\ + e^{{2\over3}x^{3\over2}}Ai(x) & \textrm{~if~}x>0 +\end{array}\right. +\end{equation} Specific interfaces : \verb'aie,daie' @@ -1788,9 +1918,16 @@ Specific interfaces : \verb'aie,daie' \item x is a real \end{itemize} This function evaluates the exponentially scaled Airy function of the second kind defined in equation \ref{bie}. +%\begin{equation} +% \label{bie} +%bie(x)=Bi(x)\textrm{~if~}x\leq0 \qquad \qquad bie(x)=e^{-{2\over3}x^{3\over2}}Bi(x)\rm{~if~}x>0 +%\end{equation} \begin{equation} \label{bie} -bie(x)=Bi(x)\textrm{~if~}x\leq0 \qquad \qquad bie(x)=e^{-{2\over3}x^{3\over2}}Bi(x)\rm{~if~}x>0 +bie(x)=\left\{\begin{array}{ll} +Bi(x) & \textrm{~if~}x\leq0 \\ +e^{-{2\over3}x^{3\over2}}Bi(x) & \textrm{~if~}x>0 +\end{array}\right. \end{equation} Specific interfaces : \verb'bie,dbie' @@ -1803,11 +1940,19 @@ Specific interfaces : \verb'bie,dbie' \item x is a real \end{itemize} This function evaluates the exponentially scaled derivative of the Airy function as defined in equation \ref{aide}. +%\begin{equation} +% \label{aide} +%aie(x)=Ai^\prime(x) \textrm{~if~}x\leq0 \qquad \qquad aie(x)=e^{{2\over3}x^{3\over2}}Ai^\prime(x)\rm{~if~}x>0 +%\end{equation} \begin{equation} \label{aide} -aie(x)=Ai^\prime(x) \textrm{~if~}x\leq0 \qquad \qquad aie(x)=e^{{2\over3}x^{3\over2}}Ai^\prime(x)\rm{~if~}x>0 +aide(x)=\left\{\begin{array}{ll} +Ai^\prime(x) & \textrm{~if~}x\leq0 \\ +e^{{2\over3}x^{3\over2}}Ai^\prime(x) & \textrm{~if~}x>0 +\end{array}\right. \end{equation} + Specific interfaces : \verb'aide,daide' @@ -1821,7 +1966,10 @@ Specific interfaces : \verb'aide,daide' This function evaluates the exponentially scaled derivative of the Airy function of the second kind as defined in equation \ref{bide}. \begin{equation} \label{bide} -bie(x)=Bi^\prime(x)\textrm{~if~}x\leq0 \qquad \qquad bie(x)=e^{-{2\over3}x^{3\over2}}Bi^\prime(x)\rm{~if~}x>0 +bie(x)=\left\{\begin{array}{ll} +Bi^\prime(x) & \textrm{~if~}x\leq0 \\ +e^{-{2\over3}x^{3\over2}}Bi^\prime(x) & \textrm{~if~}x>0 +\end{array}\right. \end{equation} Specific interfaces : \verb'bide,dbide'