Mercurial > octave-nkf
view libcruft/quadpack/dqagp.f @ 5537:12f1f74fa340
Added tag ss-2-9-4 for changeset f16c05db6250
author | jwe@segfault.lan |
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date | Fri, 01 Feb 2008 21:47:21 -0500 |
parents | 5b781670e9ee |
children |
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SUBROUTINE DQAGP(F,A,B,NPTS2,POINTS,EPSABS,EPSREL,RESULT,ABSERR, * NEVAL,IER,LENIW,LENW,LAST,IWORK,WORK) C***BEGIN PROLOGUE DQAGP C***DATE WRITTEN 800101 (YYMMDD) C***REVISION DATE 830518 (YYMMDD) C***CATEGORY NO. H2A2A1 C***KEYWORDS AUTOMATIC INTEGRATOR, GENERAL-PURPOSE, C SINGULARITIES AT USER SPECIFIED POINTS, C EXTRAPOLATION, GLOBALLY ADAPTIVE C***AUTHOR PIESSENS,ROBERT,APPL. MATH. & PROGR. DIV - K.U.LEUVEN C DE DONCKER,ELISE,APPL. MATH. & PROGR. DIV. - K.U.LEUVEN C***PURPOSE THE ROUTINE CALCULATES AN APPROXIMATION RESULT TO A GIVEN C DEFINITE INTEGRAL I = INTEGRAL OF F OVER (A,B), C HOPEFULLY SATISFYING FOLLOWING CLAIM FOR ACCURACY C BREAK POINTS OF THE INTEGRATION INTERVAL, WHERE LOCAL C DIFFICULTIES OF THE INTEGRAND MAY OCCUR (E.G. C SINGULARITIES, DISCONTINUITIES), ARE PROVIDED BY THE USER. C***DESCRIPTION C C COMPUTATION OF A DEFINITE INTEGRAL C STANDARD FORTRAN SUBROUTINE C DOUBLE PRECISION VERSION C C PARAMETERS C ON ENTRY C F - SUBROUTINE F(X,IERR,RESULT) DEFINING THE INTEGRAND C FUNCTION F(X). THE ACTUAL NAME FOR F NEEDS TO BE C DECLARED E X T E R N A L IN THE DRIVER PROGRAM. C C A - DOUBLE PRECISION C LOWER LIMIT OF INTEGRATION C C B - DOUBLE PRECISION C UPPER LIMIT OF INTEGRATION C C NPTS2 - INTEGER C NUMBER EQUAL TO TWO MORE THAN THE NUMBER OF C USER-SUPPLIED BREAK POINTS WITHIN THE INTEGRATION C RANGE, NPTS.GE.2. C IF NPTS2.LT.2, THE ROUTINE WILL END WITH IER = 6. C C POINTS - DOUBLE PRECISION C VECTOR OF DIMENSION NPTS2, THE FIRST (NPTS2-2) C ELEMENTS OF WHICH ARE THE USER PROVIDED BREAK C POINTS. IF THESE POINTS DO NOT CONSTITUTE AN C ASCENDING SEQUENCE THERE WILL BE AN AUTOMATIC C SORTING. C C EPSABS - DOUBLE PRECISION C ABSOLUTE ACCURACY REQUESTED C EPSREL - DOUBLE PRECISION C RELATIVE ACCURACY REQUESTED C IF EPSABS.LE.0 C AND EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28), C THE ROUTINE WILL END WITH IER = 6. C C ON RETURN C RESULT - DOUBLE PRECISION C APPROXIMATION TO THE INTEGRAL C C ABSERR - DOUBLE PRECISION C ESTIMATE OF THE MODULUS OF THE ABSOLUTE ERROR, C WHICH SHOULD EQUAL OR EXCEED ABS(I-RESULT) C C NEVAL - INTEGER C NUMBER OF INTEGRAND EVALUATIONS C C IER - INTEGER C IER = 0 NORMAL AND RELIABLE TERMINATION OF THE C ROUTINE. IT IS ASSUMED THAT THE REQUESTED C ACCURACY HAS BEEN ACHIEVED. C IER.GT.0 ABNORMAL TERMINATION OF THE ROUTINE. C THE ESTIMATES FOR INTEGRAL AND ERROR ARE C LESS RELIABLE. IT IS ASSUMED THAT THE C REQUESTED ACCURACY HAS NOT BEEN ACHIEVED. C ERROR MESSAGES C IER = 1 MAXIMUM NUMBER OF SUBDIVISIONS ALLOWED C HAS BEEN ACHIEVED. ONE CAN ALLOW MORE C SUBDIVISIONS BY INCREASING THE VALUE OF C LIMIT (AND TAKING THE ACCORDING DIMENSION C ADJUSTMENTS INTO ACCOUNT). HOWEVER, IF C THIS YIELDS NO IMPROVEMENT IT IS ADVISED C TO ANALYZE THE INTEGRAND IN ORDER TO C DETERMINE THE INTEGRATION DIFFICULTIES. IF C THE POSITION OF A LOCAL DIFFICULTY CAN BE C DETERMINED (I.E. SINGULARITY, C DISCONTINUITY WITHIN THE INTERVAL), IT C SHOULD BE SUPPLIED TO THE ROUTINE AS AN C ELEMENT OF THE VECTOR POINTS. IF NECESSARY C AN APPROPRIATE SPECIAL-PURPOSE INTEGRATOR C MUST BE USED, WHICH IS DESIGNED FOR C HANDLING THE TYPE OF DIFFICULTY INVOLVED. C = 2 THE OCCURRENCE OF ROUNDOFF ERROR IS C DETECTED, WHICH PREVENTS THE REQUESTED C TOLERANCE FROM BEING ACHIEVED. C THE ERROR MAY BE UNDER-ESTIMATED. C = 3 EXTREMELY BAD INTEGRAND BEHAVIOUR OCCURS C AT SOME POINTS OF THE INTEGRATION C INTERVAL. C = 4 THE ALGORITHM DOES NOT CONVERGE. C ROUNDOFF ERROR IS DETECTED IN THE C EXTRAPOLATION TABLE. C IT IS PRESUMED THAT THE REQUESTED C TOLERANCE CANNOT BE ACHIEVED, AND THAT C THE RETURNED RESULT IS THE BEST WHICH C CAN BE OBTAINED. C = 5 THE INTEGRAL IS PROBABLY DIVERGENT, OR C SLOWLY CONVERGENT. IT MUST BE NOTED THAT C DIVERGENCE CAN OCCUR WITH ANY OTHER VALUE C OF IER.GT.0. C = 6 THE INPUT IS INVALID BECAUSE C NPTS2.LT.2 OR C BREAK POINTS ARE SPECIFIED OUTSIDE C THE INTEGRATION RANGE OR C (EPSABS.LE.0 AND C EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28)) C RESULT, ABSERR, NEVAL, LAST ARE SET TO C ZERO. EXEPT WHEN LENIW OR LENW OR NPTS2 IS C INVALID, IWORK(1), IWORK(LIMIT+1), C WORK(LIMIT*2+1) AND WORK(LIMIT*3+1) C ARE SET TO ZERO. C WORK(1) IS SET TO A AND WORK(LIMIT+1) C TO B (WHERE LIMIT = (LENIW-NPTS2)/2). C C DIMENSIONING PARAMETERS C LENIW - INTEGER C DIMENSIONING PARAMETER FOR IWORK C LENIW DETERMINES LIMIT = (LENIW-NPTS2)/2, C WHICH IS THE MAXIMUM NUMBER OF SUBINTERVALS IN THE C PARTITION OF THE GIVEN INTEGRATION INTERVAL (A,B), C LENIW.GE.(3*NPTS2-2). C IF LENIW.LT.(3*NPTS2-2), THE ROUTINE WILL END WITH C IER = 6. C C LENW - INTEGER C DIMENSIONING PARAMETER FOR WORK C LENW MUST BE AT LEAST LENIW*2-NPTS2. C IF LENW.LT.LENIW*2-NPTS2, THE ROUTINE WILL END C WITH IER = 6. C C LAST - INTEGER C ON RETURN, LAST EQUALS THE NUMBER OF SUBINTERVALS C PRODUCED IN THE SUBDIVISION PROCESS, WHICH C DETERMINES THE NUMBER OF SIGNIFICANT ELEMENTS C ACTUALLY IN THE WORK ARRAYS. C C WORK ARRAYS C IWORK - INTEGER C VECTOR OF DIMENSION AT LEAST LENIW. ON RETURN, C THE FIRST K ELEMENTS OF WHICH CONTAIN C POINTERS TO THE ERROR ESTIMATES OVER THE C SUBINTERVALS, SUCH THAT WORK(LIMIT*3+IWORK(1)),..., C WORK(LIMIT*3+IWORK(K)) FORM A DECREASING C SEQUENCE, WITH K = LAST IF LAST.LE.(LIMIT/2+2), AND C K = LIMIT+1-LAST OTHERWISE C IWORK(LIMIT+1), ...,IWORK(LIMIT+LAST) CONTAIN THE C SUBDIVISION LEVELS OF THE SUBINTERVALS, I.E. C IF (AA,BB) IS A SUBINTERVAL OF (P1,P2) C WHERE P1 AS WELL AS P2 IS A USER-PROVIDED C BREAK POINT OR INTEGRATION LIMIT, THEN (AA,BB) HAS C LEVEL L IF ABS(BB-AA) = ABS(P2-P1)*2**(-L), C IWORK(LIMIT*2+1), ..., IWORK(LIMIT*2+NPTS2) HAVE C NO SIGNIFICANCE FOR THE USER, C NOTE THAT LIMIT = (LENIW-NPTS2)/2. C C WORK - DOUBLE PRECISION C VECTOR OF DIMENSION AT LEAST LENW C ON RETURN C WORK(1), ..., WORK(LAST) CONTAIN THE LEFT C END POINTS OF THE SUBINTERVALS IN THE C PARTITION OF (A,B), C WORK(LIMIT+1), ..., WORK(LIMIT+LAST) CONTAIN C THE RIGHT END POINTS, C WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) CONTAIN C THE INTEGRAL APPROXIMATIONS OVER THE SUBINTERVALS, C WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST) C CONTAIN THE CORRESPONDING ERROR ESTIMATES, C WORK(LIMIT*4+1), ..., WORK(LIMIT*4+NPTS2) C CONTAIN THE INTEGRATION LIMITS AND THE C BREAK POINTS SORTED IN AN ASCENDING SEQUENCE. C NOTE THAT LIMIT = (LENIW-NPTS2)/2. C C***REFERENCES (NONE) C***ROUTINES CALLED DQAGPE,XERROR C***END PROLOGUE DQAGP C DOUBLE PRECISION A,ABSERR,B,EPSABS,EPSREL,POINTS,RESULT,WORK INTEGER IER,IWORK,LAST,LENIW,LENW,LIMIT,LVL,L1,L2,L3,L4,NEVAL, * NPTS2 C DIMENSION IWORK(LENIW),POINTS(NPTS2),WORK(LENW) C EXTERNAL F C C CHECK VALIDITY OF LIMIT AND LENW. C C***FIRST EXECUTABLE STATEMENT DQAGP IER = 6 NEVAL = 0 LAST = 0 RESULT = 0.0D+00 ABSERR = 0.0D+00 IF(LENIW.LT.(3*NPTS2-2).OR.LENW.LT.(LENIW*2-NPTS2).OR.NPTS2.LT.2) * GO TO 10 C C PREPARE CALL FOR DQAGPE. C LIMIT = (LENIW-NPTS2)/2 L1 = LIMIT+1 L2 = LIMIT+L1 L3 = LIMIT+L2 L4 = LIMIT+L3 C CALL DQAGPE(F,A,B,NPTS2,POINTS,EPSABS,EPSREL,LIMIT,RESULT,ABSERR, * NEVAL,IER,WORK(1),WORK(L1),WORK(L2),WORK(L3),WORK(L4), * IWORK(1),IWORK(L1),IWORK(L2),LAST) C C CALL ERROR HANDLER IF NECESSARY. C LVL = 0 10 IF(IER.EQ.6) LVL = 1 IF(IER.GT.0) CALL XERROR('ABNORMAL RETURN FROM DQAGP',26,IER,LVL) RETURN END