📄 hybrj_.html
字号:
<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 modificationof the Powell hybrid method. The user must provide asubroutine which calculates the functions. The Jacobian isthen calculated by a forward-difference approximation.<P><B>hybrj1_</B> serves the same function but has a simplified callingsequence.<BR><A NAME="lbAE"> </A><H3>Language notes</H3><B>hybrj_</B> and <B>hybrj1_</B> are written in FORTRAN. If calling fromC, 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 anunderscore. 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 easiestjust 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 anarray <I>z</I> and in the call you have declared a leading dimension of7. 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 calculatesthe functions. In FORTRAN, <I>fcn</I> must be declared in an externalstatement in the user calling program, and should be written asfollows:<P><PRE>subroutine fcn(n,x,fvec,fjac,ldfjac,iflag)integer n,ldfjac,iflagdouble precision x(n),fvec(n),fjac(ldfjac,n)----------if iflag = 1 calculate the functions at x andreturn this vector in fvec. do not alter fjac.if iflag = 2 calculate the jacobian at x andreturn this matrix in fjac. do not alter fvec.---------returnend</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> unlessthe 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 numberof functions and variables.<P><I>x</I> is an array of length <I>n</I>. On input <I>x</I> must containan 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 theorthogonal matrix q produced by the qr factorizationof 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 containsthe 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 occurswhen the algorithm estimates that the relative errorbetween <I>x</I> and the solution is at most <I>tol</I>.<P><I>info</I> is an integer output variable. If the user hasterminated 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. Terminationoccurs when the relative error between two consecutiveiterates is at most <I>xtol</I>.<P><I>maxfev</I> is a positive integer input variable. Terminationoccurs 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 (seebelow), <I>diag</I> is internally set. If <I>mode</I> = 2, <I>diag</I>must contain positive entries that serve asmultiplicative scale factors for the variables.<P><I>mode</I> is an integer input variable. If <I>mode</I> = 1, thevariables will be scaled internally. If <I>mode</I> = 2,the scaling is specified by the input <I>diag</I>. Othervalues of mode are equivalent to <I>mode</I> = 1.<P><I>factor</I> is a positive input variable used in determining theinitial step bound. This bound is set to the product of<I>factor</I> and the euclidean norm of diag*x if nonzero, or elseto <I>factor</I> itself. In most cases factor should lie in theinterval (.1,100.). 100. Is a generally recommended value.<P><I>nprint</I> is an integer input variable that enables controlledprinting of iterates if it is positive. In this case,<I>fcn</I> is called with <I>iflag</I> = 0 at the beginning of the firstiteration and every nprint iterations thereafter andimmediately prior to return, with <I>x</I> and <I>fvec</I> availablefor printing. If <I>nprint</I> is not positive, no special callsof <I>fcn</I> with <I>iflag</I> = 0 are made.<P><I>info</I> is an integer output variable. If the user hasterminated 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 ofcalls to <I>fcn</I>.<P><I>fjac</I> is an output <I>n</I> by <I>n</I> array which contains theorthogonal matrix <I>q</I> produced by the <I>qr</I> factorizationof 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 theupper triangular matrix produced by the <I>qr</I> factorizationof 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 containsthe 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>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -