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rfft1b

  1. C RFFT1B    SOURCE    BP208322  18/10/08    21:15:17     9952           
  2. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
  3. C
  4. C   FFTPACK 5.1 
  5. C
  6. C   Authors:  Paul N. Swarztrauber and Richard A. Valent
  7. C
  8. c  FFTPACK 5.1 routine RFFT1F computes the one-dimensional Fourier 
  9. c  transform of a periodic sequence within a real array.  This  
  10. c  is referred to as the BACKWARD transform or Fourier analysis, 
  11. c  transforming the sequence from SPECTRAL to PHYSICAL space.
  12. c 
  13. c  
  14. c  This transform is normalized since a call to RFFT1F followed
  15. c  by a call to RFFT1B (or vice-versa) reproduces the original
  16. c  array subject to algorithmic constraints, roundoff error, etc.
  17. c  
  18. c  Input Arguments
  19. c  
  20. c  N       Integer length of the sequence to be transformed.  The 
  21. c          transform is most efficient when N is a product of 
  22. c          small primes.
  23. c  
  24. c  INC     Integer increment between the locations, in array R,
  25. c          of two consecutive elements within the sequence.
  26. c  
  27. c  R       Real array of length LENR containing the sequence to be 
  28. c          transformed.
  29. c  
  30. c  LENR    Integer dimension of R array.  LENR must be at least 
  31. c          INC*(N-1) + 1.
  32. c 
  33. c  WSAVE   Real work array of length LENSAV.  WSAVE's contents must 
  34. c          be initialized with a call to subroutine RFFT1I before the 
  35. c          first call to routine RFFT1F or RFFT1B for a given transform
  36. c          length N. 
  37. c 
  38. c 
  39. c  LENSAV  Integer dimension of WSAVE array.  LENSAV must be at least 
  40. c          N + INT(LOG (REAL(N))/LOG(2.)) +4.
  41. c 
  42. c 
  43. c  WORK    Real work array of dimension LENWRK.
  44. c  
  45. c  LENWRK  Integer dimension of WORK array.  LENWRK must be at N.
  46. c 
  47. c 
  48. c  Output Arguments
  49. c  
  50. c   R      Real output array R.  For purposes of exposition, 
  51. c          assume R's range of indices is given by 
  52. c          R(0:(N-1)*INC).
  53. c  
  54. c          Then
  55. c  
  56. c                         N-1
  57. c          R(0) =         SUM  R(N1*INC)/N
  58. c                         N1=0
  59. c  
  60. c          If N is even, set NH=N/2-1; if N is odd set NH=(N-1)/2;
  61. c          then for J=1,...,NH
  62. c  
  63. c            R((2*J-1)*INC) = 
  64. c  
  65. c                      N-1
  66. c                   2.*SUM  (R(N1*INC)*COS(J*N1*2*PI/N)/N
  67. c                     N1=0
  68. c  
  69. c           and
  70. c  
  71. c             R(2*J*INC) = 
  72. c  
  73. c                      N-1
  74. c                   2.*SUM  (R(N1*INC)*SIN(J*N1*2*PI/N)/N
  75. c                     N1=0
  76. c  
  77. c           Also if N is even then
  78. c  
  79. c             R((N-1)*INC) = 
  80. c  
  81. c                      N-1
  82. c                      SUM  (-1)**N1*R(N1*INC)/N
  83. c                      N1=0
  84. c  
  85. c  
  86. c  IER     Integer error return
  87. c          =  0 successful exit
  88. c          =  1 input parameter LENR   not big enough
  89. c          =  2 input parameter LENSAV not big enough
  90. c          =  3 input parameter LENWRK not big enough
  91. c 
  92. c 
  93. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
  94.  
  95.       SUBROUTINE RFFT1B ( N, INC, R, LENR, WSAVE, LENSAV,
  96.      1                  WORK, LENWRK, IER)
  97.       IMPLICIT INTEGER(I-N)
  98.       IMPLICIT REAL*8(A-H,O-Z)
  99.       INTEGER  N, INC, LENR, LENSAV, LENWRK, IER
  100.       REAL*8   R(LENR), WSAVE(LENSAV)     ,WORK(LENWRK)
  101. C
  102.       IER = 0
  103. C
  104.       IF (LENR .LT. INC*(N-1) + 1) THEN
  105.         IER = 1
  106. c         CALL XERFFT ('RFFT1B ', 6)
  107.         call erreur(5)
  108.       ELSEIF (LENSAV .LT. N + INT(LOG(REAL(N))/LOG(2.)) +4) THEN
  109.         IER = 2
  110. c         CALL XERFFT ('RFFT1B ', 8)
  111.         call erreur(5)
  112.       ELSEIF (LENWRK .LT. N) THEN
  113.         IER = 3
  114. c         CALL XERFFT ('RFFT1B ', 10)
  115.         call erreur(5)
  116.       ENDIF
  117. C
  118.       IF (N .EQ. 1) RETURN
  119. C
  120.       CALL RFFTB1 (N,INC,R,WORK,WSAVE,WSAVE(N+1))
  121.       RETURN
  122.       END
  123.  
  124.  
  125.  

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