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dnconv

  1. C DNCONV    SOURCE    BP208322  20/02/06    21:15:22     10512          
  2. c-----------------------------------------------------------------------
  3. c\BeginDoc
  4. c
  5. c\Name: dnconv
  6. c
  7. c\Description:
  8. c  Convergence testing for the nonsymmetric Arnoldi eigenvalue routine.
  9. c
  10. c\Usage:
  11. c  call dnconv
  12. c     ( N, RITZR, RITZI, BOUNDS, TOL, NCONV )
  13. c
  14. c\Arguments
  15. c  N       Integer.  (INPUT)
  16. c          Number of Ritz values to check for convergence.
  17. c
  18. c  RITZR,  Double precision arrays of length N.  (INPUT)
  19. c  RITZI   Real and imaginary parts of the Ritz values to be checked
  20. c          for convergence.
  21.  
  22. c  BOUNDS  Double precision array of length N.  (INPUT)
  23. c          Ritz estimates for the Ritz values in RITZR and RITZI.
  24. c
  25. c  TOL     Double precision scalar.  (INPUT)
  26. c          Desired backward error for a Ritz value to be considered
  27. c          "converged".
  28. c
  29. c  NCONV   Integer scalar.  (OUTPUT)
  30. c          Number of "converged" Ritz values.
  31. c
  32. c\EndDoc
  33. c
  34. c-----------------------------------------------------------------------
  35. c
  36. c\BeginLib
  37. c
  38. c\Local variables:
  39. c     xxxxxx  real
  40. c
  41. c\Routines called:
  42. c     arscnd  ARPACK utility routine for timing. -> deleted by BP in 2020
  43. c     dlamch  LAPACK routine that determines machine constants.
  44. c     dlapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
  45. c
  46. c\Author
  47. c     Danny Sorensen               Phuong Vu
  48. c     Richard Lehoucq              CRPC / Rice University
  49. c     Dept. of Computational &     Houston, Texas
  50. c     Applied Mathematics
  51. c     Rice University
  52. c     Houston, Texas
  53. c
  54. c\Revision history:
  55. c     xx/xx/92: Version ' 2.1'
  56. c
  57. c\SCCS Information: @(#)
  58. c FILE: nconv.F   SID: 2.3   DATE OF SID: 4/20/96   RELEASE: 2
  59. c
  60. c\Remarks
  61. c     1. xxxx
  62. c
  63. c\EndLib
  64. c
  65. c-----------------------------------------------------------------------
  66. c
  67.       subroutine dnconv (n, ritzr, ritzi, bounds, tol, nconv)
  68. c
  69. c     %----------------------------------------------------%
  70. c     | Include files for debugging and timing information |
  71. c -INC TARTRAK
  72. c     %----------------------------------------------------%
  73. c
  74. c
  75. c     %------------------%
  76. c     | Scalar Arguments |
  77. c     %------------------%
  78. c
  79.       integer    n, nconv
  80.       REAL*8
  81.      &           tol
  82. c
  83. c     %-----------------%
  84. c     | Array Arguments |
  85. c     %-----------------%
  86.  
  87.       REAL*8
  88.      &           ritzr(n), ritzi(n), bounds(n)
  89. c
  90. c     %---------------%
  91. c     | Local Scalars |
  92. c     %---------------%
  93. c
  94.       integer    i
  95.       REAL*8
  96.      &           temp, eps23
  97. c
  98. c     %--------------------%
  99. c     | External Functions |
  100. c     %--------------------%
  101. c
  102.       REAL*8
  104.       external   dlapy2, dlamch
  105.  
  106. c     %-----------------------%
  107. c     | Executable Statements |
  108. c     %-----------------------%
  109. c
  110. c     %-------------------------------------------------------------%
  111. c     | Convergence test: unlike in the symmetric code, I am not    |
  112. c     | using things like refined error bounds and gap condition    |
  113. c     | because I don't know the exact equivalent concept.          |
  114. c     |                                                             |
  115. c     | Instead the i-th Ritz value is considered "converged" when: |
  116. c     |                                                             |
  117. c     |     bounds(i) .le. ( TOL * | ritz | )                       |
  118. c     |                                                             |
  119. c     | for some appropriate choice of norm.                        |
  120. c     %-------------------------------------------------------------%
  121. c
  122. *      call arscnd (t0)
  123. c
  124. c     %---------------------------------%
  125. c     | Get machine dependent constant. |
  126. c     %---------------------------------%
  127. c
  128.       eps23 = dlamch('Epsilon-Machine')
  129.       eps23 = eps23**(2.0D+0 / 3.0D+0)
  130. c
  131.       nconv  = 0
  132.       do 20 i = 1, n
  133.          temp = max( eps23, dlapy2( ritzr(i), ritzi(i) ) )
  134.          if (bounds(i) .le. tol*temp)   nconv = nconv + 1
  135.    20 continue
  136. c
  137. *      call arscnd (t1)
  138. c       tnconv = tnconv + (t1 - t0)
  139. c
  140.       return
  141. c
  142. c     %---------------%
  143. c     | End of dnconv |
  144. c     %---------------%
  145. c
  146.       end
  147.  
  148.  
  149.  

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