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Text File  |  1985-11-29  |  3KB  |  93 lines
  1. C
  2. C     ..................................................................
  3. C
  4. C        SUBROUTINE DQH32
  5. C
  6. C        PURPOSE
  7. C           TO COMPUTE INTEGRAL(EXP(-X*X)*FCT(X), SUMMED OVER X FROM
  8. C                               -INFINITY TO +INFINITY).
  9. C
  10. C        USAGE
  11. C           CALL DQH32 (FCT,Y)
  12. C           PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT
  13. C
  14. C        DESCRIPTION OF PARAMETERS
  15. C           FCT    - THE NAME OF AN EXTERNAL DOUBLE PRECISION FUNCTION
  16. C                    SUBPROGRAM USED.
  17. C           Y      - THE RESULTING DOUBLE PRECISION INTEGRAL VALUE.
  18. C
  19. C        REMARKS
  20. C           NONE
  21. C
  22. C        SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
  23. C           THE EXTERNAL DOUBLE PRECISION FUNCTION SUBPROGRAM FCT(X)
  24. C           MUST BE FURNISHED BY THE USER.
  25. C
  26. C        METHOD
  27. C           EVALUATION IS DONE BY MEANS OF 32-POINT GAUSSIAN-HERMITE
  28. C           QUADRATURE FORMULA, WHICH INTEGRATES EXACTLY WHENEVER
  29. C           FCT(X) IS A POLYNOMIAL UP TO DEGREE 63.
  30. C           FOR REFERENCE, SEE
  31. C           SHAO/CHEN/FRANK, TABLES OF ZEROS AND GAUSSIAN WEIGHTS OF
  32. C           CERTAIN ASSOCIATED LAGUERRE POLYNOMIALS AND THE RELATED
  33. C           GENERALIZED HERMITE POLYNOMIALS, IBM TECHNICAL REPORT
  34. C           TR00.1100 (MARCH 1964), PP.213-214.
  35. C
  36. C     ..................................................................
  37. C
  38.       SUBROUTINE DQH32(FCT,Y)
  39. C
  40. C
  41.       DOUBLE PRECISION X,Y,Z,FCT
  42. C
  43.       X=.71258139098307276D1
  44.       Z=-X
  45.       Y=.7310676427384162D-22*(FCT(X)+FCT(Z))
  46.       X=.64094981492696604D1
  47.       Z=-X
  48.       Y=Y+.9231736536518292D-18*(FCT(X)+FCT(Z))
  49.       X=.58122259495159138D1
  50.       Z=-X
  51.       Y=Y+.11973440170928487D-14*(FCT(X)+FCT(Z))
  52.       X=.52755509865158801D1
  53.       Z=-X
  54.       Y=Y+.42150102113264476D-12*(FCT(X)+FCT(Z))
  55.       X=.47771645035025964D1
  56.       Z=-X
  57.       Y=Y+.59332914633966386D-10*(FCT(X)+FCT(Z))
  58.       X=.43055479533511984D1
  59.       Z=-X
  60.       Y=Y+.40988321647708966D-8*(FCT(X)+FCT(Z))
  61.       X=.38537554854714446D1
  62.       Z=-X
  63.       Y=Y+.15741677925455940D-6*(FCT(X)+FCT(Z))
  64.       X=.34171674928185707D1
  65.       Z=-X
  66.       Y=Y+.36505851295623761D-5*(FCT(X)+FCT(Z))
  67.       X=.29924908250023742D1
  68.       Z=-X
  69.       Y=Y+.54165840618199826D-4*(FCT(X)+FCT(Z))
  70.       X=.25772495377323175D1
  71.       Z=-X
  72.       Y=Y+.53626836552797205D-3*(FCT(X)+FCT(Z))
  73.       X=.21694991836061122D1
  74.       Z=-X
  75.       Y=Y+.36548903266544281D-2*(FCT(X)+FCT(Z))
  76.       X=.17676541094632016D1
  77.       Z=-X
  78.       Y=Y+.17553428831573430D-1*(FCT(X)+FCT(Z))
  79.       X=.13703764109528718D1
  80.       Z=-X
  81.       Y=Y+.60458130955912614D-1*(FCT(X)+FCT(Z))
  82.       X=.9765004635896828D0
  83.       Z=-X
  84.       Y=Y+.15126973407664248D0*(FCT(X)+FCT(Z))
  85.       X=.58497876543593245D0
  86.       Z=-X
  87.       Y=Y+.27745814230252990D0*(FCT(X)+FCT(Z))
  88.       X=.19484074156939933D0
  89.       Z=-X
  90.       Y=Y+.37523835259280239D0*(FCT(X)+FCT(Z))
  91.       RETURN
  92.       END
  93.