* * $Id$ * * $Log$ * Revision 1.1.1.1 1996/04/01 15:02:20 mclareni * Mathlib gen * * #include "gen/pilot.h" SUBROUTINE DFUNFT(SUB,K,M,N,NX,NC,X,Y,SY,A,AL,AU,MODE,EPS,MAXIT, + IPRT,MFR,IAFR,PHI,DPHI,COV,STD,W,NERROR) #include "gen/imp64.inc" DIMENSION X(*),Y(*),SY(*) DIMENSION A(*),AL(*),AU(*),DPHI(*),IAFR(*) DIMENSION COV(NC,*),STD(*) DIMENSION W(*) EXTERNAL SUB *********************************************************************** * LEAMAX, VERSION: 15.03.1993 *********************************************************************** * * DFUNFT IS THE STEERING ROUTINE FOR NONLINEAR LEAST-SQUARES FITTING. * * SUBROUTINE CALLED: D501L1 * * * THE CONSTANTS, VARIABLES AND ARRAYS HAVE THE FOLLOWING MEANING. * * SUB NAME OF USER-SUPPLIED SUBROUTINE SUBPROGRAM, DECLARED * EXTERNAL IN THE CALLING PROGRAM. THIS SUBPROGRAM MUST PROVIDE * THE VALUES OF THE FUNCTION AND, IF MODE=1, THE VALUES OF THE * DERIVATIVES (SEE EXAMPLE) . * K (INTEGER) DIMENSION OF A SINGLE DATA POINT (OBSERVATION) X . * M (INTEGER) NUMBER OF DATA POINTS (OBSERVATIONS) . * N (INTEGER) NUMBER OF UNKNOWN PARAMETERS A. * NX (INTEGER) DECLARED FIRST DIMENSION OF ARRAY X IN THE * CALLING PROGRAM, WITH NX .GE. K . * NC (INTEGER) DECLARED FIRST DIMENSION OF ARRAY COV IN THE * CALLING PROGRAM, WITH NC .GE. N . * X (DOUBLE PRECISION) TWO-DIMENSIONAL ARRAY OF DIMENSION (NX,M). * ON ENTRY, X MUST CONTAIN THE DATA SET (X(I)) (THE I-TH * COLUMN OF X BELONGS TO THE DATA POINT X(I), I=1,...,M). * Y (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH M , * CONTAINS THE DATA SET (Y(I)) ON ENTRY. * SY (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH M , * CONTAINS THE WEIGTHS (SIGMA(I)) OF THE DATA POINTS ON ENTRY. * A (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH N . * ON ENTRY, A MUST CONTAIN THE STARTING VALUES OF THE UNKNOWN * PARAMETERS FOR THE LEVENBERG-MARQUARDT ALGORITHM. * ON EXIT, A CONTAINS AN APPROXIMATION OF THE MINIMUM POINT. * AL (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH N . * ON ENTRY, AL MUST CONTAIN THE LOWER BOUNDS OF A . * AU (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH N . * ON ENTRY, AU MUST CONTAIN THE UPPER BOUNDS OF A . * MODE (INTEGER) * = 0: THE DERIVATIVE IS COMPUTED NUMERICALLY. * = 1: THE DERIVATIVE HAS TO BE EVALUATED IN SUBPROGRAM SUB . * EPS (DOUBLE PRECISION) USER-SUPPLIED TOLERANCE USED TO CONTROL * THE TERMINATION CRITERION. EPS SHOULD BE CHOSEN ACCORDING * TO THE ACCURACY REQUIRED BY THE UNDERLYING PROBLEM AND TO * THE MACHINE ACCURACY ALSO (RECOMMENDED VALUE ON ENTRY: * 1D-6 ... 1D-12 ). * MAXIT (INTEGER) MAXIMUM PERMITTED NUMBER OF ITERATIONS. * IPRT (INTEGER) PRINTING CONTROL. G * = 0 : NO PRINTING OF INTERMEDIATE RESULTS * = +/- L : PRINTING OF INTERMEDIATE RESULTS AT EVERY ABS(L)-TH * ITERATION; IF IPRT < 0, PRINTING OF ALL INPUT * PARAMETERS OF DSUMSQ IN ADDITION. * MFR (INTEGER) ON EXIT, MFR CONTAINS THE NUMBER OF FREE VARIABLES * AT THE SOLUTION POINT. * IAFR (INTEGER) ONE-DIMENSIONAL ARRAY OF LENGTH 2 * N , USED AS * WORKING SPACE. ON EXIT, THE FIRST MFR ELEMENTS OF IAFR * CONTAIN THE INDICES OF THE FREE VARIABLES AT THE SOLUTION * POINT. * PHI (DOUBLE PRECISION) ON EXIT, PHI CONTAINS THE VALUE OF THE * OBJECTIVE FUNCTION AT THE MINIMUM POINT. * DPHI (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH N . * ON EXIT, DPHI CONTAINS THE DERIVATIVES OF THE OBJECTIVE * FUNCTION WITH RESPECT TO A (THE GRADIENT) AT THE LAST * ITERATION POINT. * COV (DOUBLE PRECISION) TWO-DIMENSIONAL ARRAY OF DIMENSION (NC,N). * ON EXIT, COV CONTAINS AN APPROXIMATION TO THE COVARIANCE * MATRIX. * STD (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH N . * ON EXIT, STD CONTAINS APPROXIMATIONS TO THE STANDARD * DEVIATIONS OF THE MODEL PARAMETER ESTIMATORS. * W (DOUBLE PRECISION) ONE-DIMENSIONAL ARRAY OF LENGTH * 9*N+4*M+2*M*N+3*N*N , USED AS WORKING SPACE. * NERROR (INTEGER) ERROR INDICATOR. ON EXIT: * = 0: NO ERROR OR WARNING DETECTED. * = 1: AT LEAST ONE OF THE CONSTANTS K, M, N, NX, NC, MAXIT IS * ILLEGAL OR AT LEAST FOR ONE J THE RELATION * AL(J) .LE. AU(J) IS NOT TRUE. * = 2: THE MAXIMUM NUMBER MAXIT OF ITERATIONS HAS BEEN * REACHED. * = 3: THE OBJECTIVE FUNCTION PHI OR ITS DERIVATIVE IS NOT * DEFINED FOR THE CURRENT VALUES OF THE UNKNOWN * PARAMETER VECTOR A. * = 4: THE ROUTINES DGEQPF , DORMQR , DTRTRS OF THE LINEAR * ALGEBRA PACKAGE LAPACK (F001) WERE UNABLE TO SOLVE * THE LINEAR LEAST SQUARES PROBLEMS * OR THE ROUTINE DSINV (F012) WAS UNABLE TO COMPUTE THE * COVARIANCE MATRIX . * ************************************************************************* * * THE FOLLOWING SUBROUTINE IS A SIMPLE EXAMPLE FOR SUB. * * SUBROUTINE SUB (K,X,N,A,F,DF,MODE,NERROR) * IMPLICIT DOUBLE PRECISION (A-H,O-Z) * DIMENSION A(*),X(*),DF(*) * * NERROR=0 * T=X(2)*A(2)+X(3)*A(3) * IF (T .EQ. 0) THEN * NERROR=1 * RETURN * ENDIF * * F=A(1)+X(1)/T * * IF(MODE .EQ. 0) RETURN * DF(1)=1 * DF(2)=-X(1)*X(2)/T**2 * DF(3)=-X(1)*X(3)/T**2 * RETURN * END * ************************************************************************* M1=1 M2=M1+N M3=M2+N M4=M3+N M5=M4+N M6=M5+2*M M7=M6+3*N M8=M7+N M9=M8+M+N MA=M9+(N+M)*N MB=MA+N*N MC=MB+N*N MD=MC+M CALL D501L1('DFUNFT',SUB,K,M,X,NX,Y,SY,MODE,EPS,MAXIT, 1 IPRT,N,A,AL,AU,PHI,DPHI,IAFR,MFR,COV,NC,STD, 2 W(M1),W(M2),W(M3),W(M4),W(M5),W(M6),W(M7),W(M8), 3 W(M9),W(MA),W(MB),W(MC),W(MD),IAFR(N+1),NERROR) RETURN END