#include "cdflib.h" void dstinv(double *zsmall,double *zbig,double *zabsst, double *zrelst,double *zstpmu,double *zabsto, double *zrelto) /* ********************************************************************** void dstinv(double *zsmall,double *zbig,double *zabsst, double *zrelst,double *zstpmu,double *zabsto, double *zrelto) Double Precision - SeT INverse finder - Reverse Communication Function Concise Description - Given a monotone function F finds X such that F(X) = Y. Uses Reverse communication -- see invr. This routine sets quantities needed by INVR. More Precise Description of INVR - F must be a monotone function, the results of QMFINV are otherwise undefined. QINCR must be .TRUE. if F is non- decreasing and .FALSE. if F is non-increasing. QMFINV will return .TRUE. if and only if F(SMALL) and F(BIG) bracket Y, i. e., QINCR is .TRUE. and F(SMALL).LE.Y.LE.F(BIG) or QINCR is .FALSE. and F(BIG).LE.Y.LE.F(SMALL) if QMFINV returns .TRUE., then the X returned satisfies the following condition. let TOL(X) = MAX(ABSTOL,RELTOL*ABS(X)) then if QINCR is .TRUE., F(X-TOL(X)) .LE. Y .LE. F(X+TOL(X)) and if QINCR is .FALSE. F(X-TOL(X)) .GE. Y .GE. F(X+TOL(X)) Arguments SMALL --> The left endpoint of the interval to be searched for a solution. SMALL is DOUBLE PRECISION BIG --> The right endpoint of the interval to be searched for a solution. BIG is DOUBLE PRECISION ABSSTP, RELSTP --> The initial step size in the search is MAX(ABSSTP,RELSTP*ABS(X)). See algorithm. ABSSTP is DOUBLE PRECISION RELSTP is DOUBLE PRECISION STPMUL --> When a step doesn't bound the zero, the step size is multiplied by STPMUL and another step taken. A popular value is 2.0 DOUBLE PRECISION STPMUL ABSTOL, RELTOL --> Two numbers that determine the accuracy of the solution. See function for a precise definition. ABSTOL is DOUBLE PRECISION RELTOL is DOUBLE PRECISION Method Compares F(X) with Y for the input value of X then uses QINCR to determine whether to step left or right to bound the desired x. the initial step size is MAX(ABSSTP,RELSTP*ABS(S)) for the input value of X. Iteratively steps right or left until it bounds X. At each step which doesn't bound X, the step size is doubled. The routine is careful never to step beyond SMALL or BIG. If it hasn't bounded X at SMALL or BIG, QMFINV returns .FALSE. after setting QLEFT and QHI. If X is successfully bounded then Algorithm R of the paper 'Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function' by J. C. P. Bus and T. J. Dekker in ACM Transactions on Mathematical Software, Volume 1, No. 4 page 330 (DEC. '75) is employed to find the zero of the function F(X)-Y. This is routine QRZERO. ********************************************************************** */ { E0000(1,NULL,NULL,NULL,NULL,NULL,zabsst,zabsto,zbig,zrelst,zrelto,zsmall, zstpmu); } /* END */