src/numerical/slatec/fortran/dqawc.f

   1 *DECK DQAWC
   2       SUBROUTINE DQAWC (F, A, B, C, EPSABS, EPSREL, RESULT, ABSERR,
   3      +   NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
   4 C***BEGIN PROLOGUE  DQAWC
   5 C***PURPOSE  The routine calculates an approximation result to a
   6 C            Cauchy principal value I = INTEGRAL of F*W over (A,B)
   7 C            (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
   8 C            following claim for accuracy
   9 C            ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).
  10 C***LIBRARY   SLATEC (QUADPACK)
  11 C***CATEGORY  H2A2A1, J4
  12 C***TYPE      DOUBLE PRECISION (QAWC-S, DQAWC-D)
  13 C***KEYWORDS  AUTOMATIC INTEGRATOR, CAUCHY PRINCIPAL VALUE,
  14 C             CLENSHAW-CURTIS METHOD, GLOBALLY ADAPTIVE, QUADPACK,
  15 C             QUADRATURE, SPECIAL-PURPOSE
  16 C***AUTHOR  Piessens, Robert
  17 C             Applied Mathematics and Programming Division
  18 C             K. U. Leuven
  19 C           de Doncker, Elise
  20 C             Applied Mathematics and Programming Division
  21 C             K. U. Leuven
  22 C***DESCRIPTION
  23 C
  24 C        Computation of a Cauchy principal value
  25 C        Standard fortran subroutine
  26 C        Double precision version
  27 C
  28 C
  29 C        PARAMETERS
  30 C         ON ENTRY
  31 C            F      - Double precision
  32 C                     Function subprogram defining the integrand
  33 C                     Function F(X). The actual name for F needs to be
  34 C                     declared E X T E R N A L in the driver program.
  35 C
  36 C            A      - Double precision
  37 C                     Under limit of integration
  38 C
  39 C            B      - Double precision
  40 C                     Upper limit of integration
  41 C
  42 C            C      - Parameter in the weight function, C.NE.A, C.NE.B.
  43 C                     If C = A or C = B, the routine will end with
  44 C                     IER = 6 .
  45 C
  46 C            EPSABS - Double precision
  47 C                     Absolute accuracy requested
  48 C            EPSREL - Double precision
  49 C                     Relative accuracy requested
  50 C                     If  EPSABS.LE.0
  51 C                     and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
  52 C                     the routine will end with IER = 6.
  53 C
  54 C         ON RETURN
  55 C            RESULT - Double precision
  56 C                     Approximation to the integral
  57 C
  58 C            ABSERR - Double precision
  59 C                     Estimate or the modulus of the absolute error,
  60 C                     Which should equal or exceed ABS(I-RESULT)
  61 C
  62 C            NEVAL  - Integer
  63 C                     Number of integrand evaluations
  64 C
  65 C            IER    - Integer
  66 C                     IER = 0 Normal and reliable termination of the
  67 C                             routine. It is assumed that the requested
  68 C                             accuracy has been achieved.
  69 C                     IER.GT.0 Abnormal termination of the routine
  70 C                             the estimates for integral and error are
  71 C                             less reliable. It is assumed that the
  72 C                             requested accuracy has not been achieved.
  73 C            ERROR MESSAGES
  74 C                     IER = 1 Maximum number of subdivisions allowed
  75 C                             has been achieved. One can allow more sub-
  76 C                             divisions by increasing the value of LIMIT
  77 C                             (and taking the according dimension
  78 C                             adjustments into account). However, if
  79 C                             this yields no improvement it is advised
  80 C                             to analyze the integrand in order to
  81 C                             determine the integration difficulties.
  82 C                             If the position of a local difficulty
  83 C                             can be determined (e.g. SINGULARITY,
  84 C                             DISCONTINUITY within the interval) one
  85 C                             will probably gain from splitting up the
  86 C                             interval at this point and calling
  87 C                             appropriate integrators on the subranges.
  88 C                         = 2 The occurrence of roundoff error is detec-
  89 C                             ted, which prevents the requested
  90 C                             tolerance from being achieved.
  91 C                         = 3 Extremely bad integrand behaviour occurs
  92 C                             at some points of the integration
  93 C                             interval.
  94 C                         = 6 The input is invalid, because
  95 C                             C = A or C = B or
  96 C                             (EPSABS.LE.0 and
  97 C                              EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28))
  98 C                             or LIMIT.LT.1 or LENW.LT.LIMIT*4.
  99 C                             RESULT, ABSERR, NEVAL, LAST are set to
 100 C                             zero.  Except when LENW or LIMIT is
 101 C                             invalid, IWORK(1), WORK(LIMIT*2+1) and
 102 C                             WORK(LIMIT*3+1) are set to zero, WORK(1)
 103 C                             is set to A and WORK(LIMIT+1) to B.
 104 C
 105 C         DIMENSIONING PARAMETERS
 106 C            LIMIT - Integer
 107 C                    Dimensioning parameter for IWORK
 108 C                    LIMIT determines the maximum number of subintervals
 109 C                    in the partition of the given integration interval
 110 C                    (A,B), LIMIT.GE.1.
 111 C                    If LIMIT.LT.1, the routine will end with IER = 6.
 112 C
 113 C           LENW   - Integer
 114 C                    Dimensioning parameter for WORK
 115 C                    LENW must be at least LIMIT*4.
 116 C                    If LENW.LT.LIMIT*4, the routine will end with
 117 C                    IER = 6.
 118 C
 119 C            LAST  - Integer
 120 C                    On return, LAST equals the number of subintervals
 121 C                    produced in the subdivision process, which
 122 C                    determines the number of significant elements
 123 C                    actually in the WORK ARRAYS.
 124 C
 125 C         WORK ARRAYS
 126 C            IWORK - Integer
 127 C                    Vector of dimension at least LIMIT, the first K
 128 C                    elements of which contain pointers
 129 C                    to the error estimates over the subintervals,
 130 C                    such that WORK(LIMIT*3+IWORK(1)), ... ,
 131 C                    WORK(LIMIT*3+IWORK(K)) form a decreasing
 132 C                    sequence, with K = LAST if LAST.LE.(LIMIT/2+2),
 133 C                    and K = LIMIT+1-LAST otherwise
 134 C
 135 C            WORK  - Double precision
 136 C                    Vector of dimension at least LENW
 137 C                    On return
 138 C                    WORK(1), ..., WORK(LAST) contain the left
 139 C                     end points of the subintervals in the
 140 C                     partition of (A,B),
 141 C                    WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain
 142 C                     the right end points,
 143 C                    WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) contain
 144 C                     the integral approximations over the subintervals,
 145 C                    WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST)
 146 C                     contain the error estimates.
 147 C
 148 C***REFERENCES  (NONE)
 149 C***ROUTINES CALLED  DQAWCE, XERMSG
 150 C***REVISION HISTORY  (YYMMDD)
 151 C   800101  DATE WRITTEN
 152 C   890831  Modified array declarations.  (WRB)
 153 C   890831  REVISION DATE from Version 3.2
 154 C   891214  Prologue converted to Version 4.0 format.  (BAB)
 155 C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
 156 C***END PROLOGUE  DQAWC
 157 C
 158       DOUBLE PRECISION A,ABSERR,B,C,EPSABS,EPSREL,F,RESULT,WORK
 159       INTEGER IER,IWORK,LAST,LENW,LIMIT,LVL,L1,L2,L3,NEVAL
 160 C
 161       DIMENSION IWORK(*),WORK(*)
 162 C
 163       EXTERNAL F
 164 C
 165 C         CHECK VALIDITY OF LIMIT AND LENW.
 166 C
 167 C***FIRST EXECUTABLE STATEMENT  DQAWC
 168       IER = 6
 169       NEVAL = 0
 170       LAST = 0
 171       RESULT = 0.0D+00
 172       ABSERR = 0.0D+00
 173       IF(LIMIT.LT.1.OR.LENW.LT.LIMIT*4) GO TO 10
 174 C
 175 C         PREPARE CALL FOR DQAWCE.
 176 C
 177       L1 = LIMIT+1
 178       L2 = LIMIT+L1
 179       L3 = LIMIT+L2
 180       CALL DQAWCE(F,A,B,C,EPSABS,EPSREL,LIMIT,RESULT,ABSERR,NEVAL,IER,
 181      1  WORK(1),WORK(L1),WORK(L2),WORK(L3),IWORK,LAST)
 182 C
 183 C         CALL ERROR HANDLER IF NECESSARY.
 184 C
 185       LVL = 0
 186 10    IF(IER.EQ.6) LVL = 1
 187       IF (IER .NE. 0) CALL XERMSG ('SLATEC', 'DQAWC',
 188      +   'ABNORMAL RETURN', IER, LVL)
 189       RETURN
 190       END