1 | ;+ |
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2 | ; |
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3 | ; @file_comments |
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4 | ; |
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5 | ; |
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6 | ; @categories |
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7 | ; Statistics |
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8 | ; |
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9 | ; @param X {in}{required} |
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10 | ; An 2 dimension Array [nx,ny] |
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11 | ; |
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12 | ; @param LAG {in}{required} |
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13 | ; 2-element vector, in the intervals [-(nx-2), (nx-2)],[-(ny-2), (ny-2)], |
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14 | ; of type integer that specifies the absolute distance(s) between |
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15 | ; indexed elements of X. |
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16 | ; |
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17 | ; @keyword ZERO2NAN |
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18 | ; |
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19 | ; @keyword DOUBLE |
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20 | ; If set to a non-zero value, computations are done in double precision arithmetic. |
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21 | ; |
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22 | ; @history |
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23 | ; 28/2/2000 Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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24 | ; Based on the A_CORRELATE procedure of IDL |
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25 | ; |
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26 | ; @version |
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27 | ; $Id$ |
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28 | ; |
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29 | ;- |
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30 | ; |
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31 | FUNCTION auto_cov2d, x, lag, DOUBLE = double, ZERO2NAN = zero2nan |
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32 | ; |
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33 | compile_opt idl2, strictarrsubs |
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34 | ; |
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35 | XDim = SIZE(X, /dimensions) |
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36 | nx = XDim[0] |
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37 | ny = XDim[1] |
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38 | ;Sample autocovariance function |
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39 | Xmean = TOTAL(X, Double = Double) / (1.*nx*ny) |
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40 | ; |
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41 | res = TOTAL( (X[0:nx-1-lag[0], 0:ny-1-lag[1]] - Xmean) * $ |
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42 | (X[lag[0]:nx-1, lag[1]:ny-1] - Xmean) $ |
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43 | , Double = Double ) |
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44 | if keyword_set(zero2nan) AND res EQ 0 then res = !values.f_nan |
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45 | RETURN, res |
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46 | |
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47 | END |
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48 | ;+ |
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49 | ; |
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50 | ; @file_comments |
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51 | ; This function computes the autocorrelation Px(K,L) or |
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52 | ; autocovariance Rx(K,L) of a sample population X[nx,ny] as a |
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53 | ; function of the lag (K,L). |
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54 | ; |
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55 | ; @categories |
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56 | ; Statistics |
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57 | ; |
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58 | ; @param X {in}{required} |
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59 | ; An 2 dimension Array [nx,ny] |
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60 | ; |
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61 | ; @param LAG {in}{required} |
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62 | ; 2-element vector, in the intervals [-(nx-2), (nx-2)],[-(ny-2), (ny-2)], |
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63 | ; of type integer that specifies the absolute distance(s) between |
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64 | ; indexed elements of X. |
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65 | ; |
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66 | ; @keyword COVARIANCE |
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67 | ; If set to a non-zero value, the sample autocovariance is computed. |
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68 | ; |
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69 | ; @keyword DOUBLE |
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70 | ; If set to a non-zero value, computations are done in double precision arithmetic. |
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71 | ; |
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72 | ; @history |
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73 | ; 28/2/2000 Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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74 | ; Based on the A_CORRELATE procedure of IDL |
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75 | ; |
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76 | ; @version |
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77 | ; $Id$ |
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78 | ; |
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79 | ;- |
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80 | ; |
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81 | FUNCTION a_correlate2d, x, lag, COVARIANCE = covariance, DOUBLE = double |
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82 | ; |
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83 | compile_opt idl2, strictarrsubs |
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84 | ; |
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85 | |
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86 | ;Compute the sample-autocorrelation or autocovariance of (Xt, Xt+l) |
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87 | ;as a function of the lag (l). |
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88 | |
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89 | ON_ERROR, 2 |
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90 | |
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91 | XDim = SIZE(X, /dimensions) |
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92 | XNDim = SIZE(X, /n_dimensions) |
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93 | nx = XDim[0] |
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94 | ny = XDim[1] |
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95 | if XNDim NE 2 then $ |
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96 | ras = report("X array must contain 2 dimensions.") |
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97 | ;Check length. |
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98 | if nx lt 2 then $ |
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99 | ras = report("first dimension of X array must contain 2 or more elements.") |
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100 | if ny lt 2 then $ |
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101 | ras = report("second dimension of X array must contain 2 or more elements.") |
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102 | if n_elements(Lag) NE 2 THEN $ |
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103 | ras = report("Lag array must contain 2 elements.") |
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104 | |
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105 | ;If the DOUBLE keyword is not set then the internal precision and |
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106 | ;result are identical to the type of input. |
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107 | if N_ELEMENTS(Double) eq 0 then $ |
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108 | Double = (SIZE(X, /type) eq 5) |
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109 | |
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110 | if KEYWORD_SET(Covariance) eq 0 then begin ;Compute Autocorrelation. |
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111 | Auto = Auto_Cov2d(X, ABS(Lag), Double = Double) / $ |
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112 | Auto_Cov2d(X, [0L, 0L], Double = Double, /zero2nan) |
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113 | endif else begin ;Compute Autocovariance. |
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114 | Auto = Auto_Cov2d(X, ABS(Lag), Double = Double) / n_elements(X) |
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115 | endelse |
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116 | |
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117 | if Double eq 0 then RETURN, FLOAT(Auto) else $ |
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118 | RETURN, Auto |
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119 | |
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120 | END |
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