<HTML><HEAD><TITLE>Manpage of HYBRJ_</TITLE> </HEAD><BODY> <H1>HYBRJ_</H1> Section: C Library Functions (3)<BR>Updated: March 8, 2002<BR><A HREF="#index">Index</A> <A HREF="index.html">Return to Main Contents</A><HR> <A NAME="lbAB"> </A> <H2>NAME</H2> hybrj_, hybrj1_ - find a zero of a system of nonlinear function <A NAME="lbAC"> </A> <H2>SYNOPSIS</H2> <B>#include <<A HREF="file:/usr/include/minpack.h">minpack.h</A>></B> <DL COMPACT> <DT> <B>void hybrj1_ (void (*</B><I>fcn</I><B>)(int *</B><I>n</I><B>,</B> <B>double *</B><I>x</I><B>,</B> <B>double *</B><I>fvec</I><B>,</B> <B>double *</B><I>fjec</I><B>,</B> <B>int *</B><I>ldfjac</I><B>,</B> <B>int *</B><I>iflag</I><B>),</B> <DL COMPACT><DT><DD> <B>int *</B><I>n</I><B>,</B> <B>double *</B><I>x</I><B>,</B> <B>double *</B><I>fvec</I><B>,</B> <B>double *</B><I>fjac</I><B>,</B> <DD> <B>int *</B><I>ldfjac</I><B>,</B> <DD> <B>double *</B><I>tol</I><B>,</B> <B>int *</B><I>info</I><B>,</B> <B>double *</B><I>wa</I><B>,</B> <B>int *</B><I>lwa</I><B>);</B> </DL> <P> <DT> <B>void hybrj_ (void (*</B><I>fcn</I><B>)(int *</B><I>n</I><B>,</B> <B>double *</B><I>x</I><B>,</B> <B>double *</B><I>fvec</I><B>,</B> <B>double *</B><I>fjec</I><B>,</B> <B>int *</B><I>ldfjac</I><B>,</B> <B>int *</B><I>iflag</I><B>),</B> <DL COMPACT><DT><DD> <B>int *</B><I>n</I><B>,</B> <B>double *</B><I>x</I><B>,</B> <B>double *</B><I>fvec</I><B>,</B> <B>double *</B><I>fjac</I><B>,</B> <DD> <B>int *</B><I>ldfjac</I><B>,</B> <DD> <B>double *</B><I>xtol</I><B>,</B> <B>int *</B><I>maxfev</I><B>,</B> <B>double *</B><I>diag</I><B>,</B> <B>int *</B><I>mode</I><B>,</B> <B>double *</B><I>factor</I><B>,</B> <B>int *</B><I>nprint</I><B>,</B> <B>int *</B><I>info</I><B>,</B> <B>int *</B><I>nfev</I><B>,</B> <DD> <B>int *</B><I>njev</I><B>,</B> <B>double *</B><I>r</I><B>,</B> <B>int *</B><I>lr</I><B>,</B> <B>double *</B><I>qtf</I><B>,</B> <DD> <B>double *</B><I>wa1</I><B>,</B> <B>double *</B><I>wa2</I><B>,</B> <B>double *</B><I>wa3</I><B>,</B> <B>double *</B><I>wa4</I><B>);</B> </DL> <DD> </DL> <A NAME="lbAD"> </A> <H2>DESCRIPTION</H2> <DD>The purpose of <B>hybrj_</B> is to find a zero of a system of <I>n</I> nonlinear functions in <I>n</I> variables by a modification of the Powell hybrid method. The user must provide a subroutine which calculates the functions and the Jacobian. <P> <B>hybrj1_</B> serves the same function but has a simplified calling sequence. <BR> <A NAME="lbAE"> </A> <H3>Language notes</H3> <B>hybrj_</B> and <B>hybrj1_</B> are written in FORTRAN. If calling from C, keep these points in mind: <DL COMPACT> <DT>Name mangling.<DD> With <B>g77</B> version 2.95 or 3.0, all the function names end in an underscore. This may change with future versions of <B>g77</B>. <DT>Compile with <B>g77</B>.<DD> Even if your program is all C code, you should link with <B>g77</B> so it will pull in the FORTRAN libraries automatically. It's easiest just to use <B>g77</B> to do all the compiling. (It handles C just fine.) <DT>Call by reference.<DD> All function parameters must be pointers. <DT>Column-major arrays.<DD> Suppose a function returns an array with 5 rows and 3 columns in an array <I>z</I> and in the call you have declared a leading dimension of 7. The FORTRAN and equivalent C references are: <P> <PRE> z(1,1) z[0] z(2,1) z[1] z(5,1) z[4] z(1,2) z[7] z(1,3) z[14] z(i,j) z[(i-1) + (j-1)*7] </PRE> </DL> <A NAME="lbAF"> </A> <H3>Parameters for both functions</H3> <I>fcn</I> is the name of the user-supplied subroutine which calculates the functions. In FORTRAN, <I>fcn</I> must be declared in an external statement in the user calling program, and should be written as follows: <P> <PRE> subroutine fcn(n,x,fvec,fjac,ldfjac,iflag) integer n,ldfjac,iflag double precision x(n),fvec(n),fjac(ldfjac,n) ---------- if iflag = 1 calculate the functions at x and return this vector in fvec. do not alter fjac. if iflag = 2 calculate the jacobian at x and return this matrix in fjac. do not alter fvec. --------- return end </PRE> <P> <P> In C, <I>fcn</I> should be written as follows: <P> <PRE> void fcn(int n, double *x, double *fvec, double *fjac, int *ldfjac, int *iflag) { /* if iflag = 1 calculate the functions at x and return this vector in fvec. do not alter fjac. if iflag = 2 calculate the jacobian at x and return this matrix in fjac. do not alter fvec. */ } </PRE> <P> The value of <I>iflag</I> should not be changed by <I>fcn</I> unless the user wants to terminate execution of hybrj_. In this case set <I>iflag</I> to a negative integer. <P> <I>n</I> is a positive integer input variable set to the number of functions and variables. <P> <I>x</I> is an array of length <I>n</I>. On input <I>x</I> must contain an initial estimate of the solution vector. On output <I>x</I> contains the final estimate of the solution vector. <P> <I>fjac</I> is an output <I>n</I> by <I>n</I> array which contains the orthogonal matrix q produced by the qr factorization of the final approximate jacobian. <P> <I>ldfjac</I> is a positive integer input variable not less than <I>n</I> which specifies the leading dimension of the array <I>fjac</I>. <P> <I>fvec</I> is an output array of length <I>n</I> which contains the functions evaluated at the output <I>x</I>. <BR> <A NAME="lbAG"> </A> <H3>Parameters for <B>hybrj1_</B></H3> <P> <I>tol</I> is a nonnegative input variable. Termination occurs when the algorithm estimates that the relative error between <I>x</I> and the solution is at most <I>tol</I>. <P> <I>info</I> is an integer output variable. If the user has terminated execution, <I>info</I> is set to the (negative) value of <I>iflag</I>. See description of <I>fcn</I>. Otherwise, <I>info</I> is set as follows. <P> <I>info</I> = 0 improper input parameters. <P> <I>info</I> = 1 algorithm estimates that the relative error <BR> between <I>x</I> and the solution is at most <I>tol</I>. <P> <I>info</I> = 2 number of calls to fcn has reached or exceeded <BR> 200*(<I>n</I>+1). <P> <I>info</I> = 3 <I>tol</I> is too small. No further improvement in <BR> the approximate solution <I>x</I> is possible. <P> <I>info</I> = 4 iteration is not making good progress. <P> <I>wa</I> is a work array of length <I>lwa</I>. <P> <I>lwa</I> is a positive integer input variable not less than (<I>n</I>*(3*<I>n</I>+13))/2. <BR> <A NAME="lbAH"> </A> <H3>Parameters for <B>hybrj_</B></H3> <P> <I>xtol</I> is a nonnegative input variable. Termination occurs when the relative error between two consecutive iterates is at most <I>xtol</I>. <P> <I>maxfev</I> is a positive integer input variable. Termination occurs when the number of calls to <I>fcn</I> is at least <I>maxfev</I> by the end of an iteration. <P> <I>diag</I> is an array of length <I>n</I>. If <I>mode</I> = 1 (see below), <I>diag</I> is internally set. If <I>mode</I> = 2, <I>diag</I> must contain positive entries that serve as multiplicative scale factors for the variables. <P> <I>mode</I> is an integer input variable. If <I>mode</I> = 1, the variables will be scaled internally. If <I>mode</I> = 2, the scaling is specified by the input <I>diag</I>. Other values of mode are equivalent to <I>mode</I> = 1. <P> <I>factor</I> is a positive input variable used in determining the initial step bound. This bound is set to the product of <I>factor</I> and the euclidean norm of diag*x if nonzero, or else to <I>factor</I> itself. In most cases factor should lie in the interval (.1,100.). 100. Is a generally recommended value. <P> <I>nprint</I> is an integer input variable that enables controlled printing of iterates if it is positive. In this case, <I>fcn</I> is called with <I>iflag</I> = 0 at the beginning of the first iteration and every nprint iterations thereafter and immediately prior to return, with <I>x</I> and <I>fvec</I> available for printing. If <I>nprint</I> is not positive, no special calls of <I>fcn</I> with <I>iflag</I> = 0 are made. <P> <I>info</I> is an integer output variable. If the user has terminated execution, <I>info</I> is set to the (negative) value of <I>iflag</I>. See description of <I>fcn</I>. Otherwise, <I>info</I> is set as follows. <P> <I>info</I> = 0 improper input parameters. <P> <I>info</I> = 1 relative error between two consecutive iterates <BR> is at most <I>xtol</I>. <P> <I>info</I> = 2 number of calls to <I>fcn</I> has reached or exceeded <BR> <I>maxfev</I>. <P> <I>info</I> = 3 <I>xtol</I> is too small. No further improvement in <BR> the approximate solution <I>x</I> is possible. <P> <I>info</I> = 4 iteration is not making good progress, as <BR> measured by the improvement from the last <BR> five jacobian evaluations. <P> <I>info</I> = 5 iteration is not making good progress, as <BR> measured by the improvement from the last <BR> ten iterations. <P> <I>nfev</I> is an integer output variable set to the number of calls to <I>fcn</I>. <P> <I>fjac</I> is an output <I>n</I> by <I>n</I> array which contains the orthogonal matrix <I>q</I> produced by the <I>qr</I> factorization of the final approximate jacobian. <P> <I>ldfjac</I> is a positive integer input variable not less than <I>n</I> which specifies the leading dimension of the array <I>fjac</I>. <P> <I>r</I> is an output array of length <I>lr</I> which contains the upper triangular matrix produced by the <I>qr</I> factorization of the final approximate Jacobian, stored rowwise. <P> <I>lr</I> is a positive integer input variable not less than (<I>n</I>*(<I>n</I>+1))/2. <P> <I>qtf</I> is an output array of length <I>n</I> which contains the vector (q transpose)*<I>fvec</I>. <P> <I>wa1</I>, <I>wa2</I>, <I>wa3</I>, and <I>wa4</I> are work arrays of length <I>n</I>. <P> <A NAME="lbAI"> </A> <H2>SEE ALSO</H2> <B><A HREF="hybrd_.html">hybrd</A></B>(3), <B><A HREF="hybrd_.html">hybrd1</A></B>(3). <BR> <P> <A NAME="lbAJ"> </A> <H2>AUTHORS</H2> Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More. <BR> This manual page was written by Jim Van Zandt <<A HREF="mailto:jrv@debian.org">jrv@debian.org</A>>, for the Debian GNU/Linux system (but may be used by others). <P> <HR> <A NAME="index"> </A><H2>Index</H2> <DL> <DT><A HREF="#lbAB">NAME</A><DD> <DT><A HREF="#lbAC">SYNOPSIS</A><DD> <DT><A HREF="#lbAD">DESCRIPTION</A><DD> <DL> <DT><A HREF="#lbAE">Language notes</A><DD> <DT><A HREF="#lbAF">Parameters for both functions</A><DD> <DT><A HREF="#lbAG">Parameters for <B>hybrj1_</B></A><DD> <DT><A HREF="#lbAH">Parameters for <B>hybrj_</B></A><DD> </DL> <DT><A HREF="#lbAI">SEE ALSO</A><DD> <DT><A HREF="#lbAJ">AUTHORS</A><DD> </DL> <HR> This document was created by <A HREF="index.html">man2html</A>, using the manual pages.<BR> Time: 10:19:50 GMT, April 20, 2007 </BODY> </HTML>