1 | ; $Id$ |
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2 | ; Copyright (c) 1995-1997, Research Systems, Inc. All rights reserved. |
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3 | ; Unauthorized reproduction prohibited. |
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4 | ;+ |
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5 | ; NAME: |
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6 | ; a2_correlate |
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7 | ; |
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8 | ; PURPOSE: |
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9 | ; This function computes the autocorrelation Px(L) or autocovariance |
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10 | ; Rx(L) of a sample population X as a function of the lag (L). |
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11 | ; |
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12 | ; CATEGORY: |
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13 | ; Statistics. |
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14 | ; |
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15 | ; CALLING SEQUENCE: |
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16 | ; Result = A_correlate(X, Lag) |
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17 | ; |
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18 | ; INPUTS: |
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19 | ; X: An n-element vector of type integer, float or double. |
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20 | ; |
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21 | ; LAG: A scalar or n-element vector, in the interval [-(n-2), (n-2)], |
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22 | ; of type integer that specifies the absolute distance(s) between |
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23 | ; indexed elements of X. |
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24 | ; |
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25 | ; KEYWORD PARAMETERS: |
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26 | ; COVARIANCE: If set to a non-zero value, the sample autocovariance |
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27 | ; is computed. |
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28 | ; |
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29 | ; DOUBLE: If set to a non-zero value, computations are done in |
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30 | ; double precision arithmetic. |
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31 | ; |
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32 | ; EXAMPLE |
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33 | ; Define an n-element sample population. |
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34 | ; x = [3.73, 3.67, 3.77, 3.83, 4.67, 5.87, 6.70, 6.97, 6.40, 5.57] |
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35 | ; |
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36 | ; Compute the autocorrelation of X for LAG = -3, 0, 1, 3, 4, 8 |
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37 | ; lag = [-3, 0, 1, 3, 4, 8] |
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38 | ; result = a_correlate(x, lag) |
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39 | ; |
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40 | ; The result should be: |
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41 | ; [0.0146185, 1.00000, 0.810879, 0.0146185, -0.325279, -0.151684] |
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42 | ; |
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43 | ; PROCEDURE: |
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44 | ; See computational formula published in IDL manual. |
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45 | ; |
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46 | ; REFERENCE: |
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47 | ; INTRODUCTION TO STATISTICAL TIME SERIES |
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48 | ; Wayne A. Fuller |
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49 | ; ISBN 0-471-28715-6 |
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50 | ; |
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51 | ; MODIFICATION HISTORY: |
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52 | ; Written by: GGS, RSI, October 1994 |
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53 | ; Modified: GGS, RSI, August 1995 |
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54 | ; Corrected a condition which excluded the last term of the |
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55 | ; time-series. |
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56 | ; Modified: GGS, RSI, April 1996 |
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57 | ; Simplified AUTO_COV function. Added DOUBLE keyword. |
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58 | ; Modified keyword checking and use of double precision. |
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59 | ; Modified: W. Biagiotti, Advanced Testing Technologies Inc., Hauppauge, NY, July 1997 |
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60 | ; Moved all constant calculations out of main loop for greatly |
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61 | ; reduced processing time. |
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62 | ; |
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63 | ; DISCLAIMER: This routine has been modified from its original form as it was |
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64 | ; supplied by Research Systems, Inc (RSI). As such, RSI is not responsible |
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65 | ; for any errors existing in this code. |
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66 | ;- |
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67 | |
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68 | FUNCTION Auto_Cov, X, M, nX, Double = Double |
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69 | |
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70 | COMMON data, Xmean |
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71 | |
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72 | ;Sample autocovariance function. |
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73 | RETURN, TOTAL((X[0:nX - M] - Xmean) * (X[M:nX] - Xmean), Double = Double) |
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74 | |
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75 | END |
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76 | |
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77 | FUNCTION a2_correlate, X, Lag, Covariance = Covariance, Double = Double |
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78 | |
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79 | COMMON data, Xmean |
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80 | |
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81 | ;Compute the sample-autocorrelation or autocovariance of (Xt, Xt+l) |
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82 | ;as a function of the lag (l). |
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83 | |
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84 | ON_ERROR, 2 |
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85 | |
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86 | TypeX = SIZE(X) |
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87 | nX = TypeX[TypeX[0]+2] |
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88 | |
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89 | ;Check length. |
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90 | if nX lt 2 then $ |
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91 | MESSAGE, "X array must contain 2 or more elements." |
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92 | |
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93 | ;If the DOUBLE keyword is not set then the internal precision and |
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94 | ;result are identical to the type of input. |
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95 | if N_ELEMENTS(Double) eq 0 then $ |
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96 | Double = (TypeX[TypeX[0]+1] eq 5) |
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97 | |
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98 | nLag = N_ELEMENTS(Lag) |
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99 | |
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100 | if nLag eq 1 then Lag = [Lag] ;Create a 1-element vector. |
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101 | |
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102 | if Double eq 0 then Auto = FLTARR(nLag) else Auto = DBLARR(nLag) |
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103 | |
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104 | ; Calculate constants OUTSIDE of main loop |
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105 | Xmean = TOTAL(X, Double = Double) / nX |
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106 | nX = nX - 1 ; Translate into last index (avoid redundancy) |
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107 | last_idx = nLag - 1 ; Last loop indice |
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108 | Lag = ABS(Lag) ; Calculate with vector ops |
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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 | |
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112 | for k = 0, last_idx do $ |
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113 | Auto[k] = Auto_Cov(X, Lag[k], nX, Double = Double) |
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114 | |
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115 | temp_Corr = Auto_Cov(X, 0L, nX, Double = Double) |
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116 | Auto = Auto / temp_Corr |
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117 | |
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118 | endif else begin ;Compute Autocovariance. |
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119 | for k = 0, last_idx do $ |
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120 | Auto[k] = Auto_Cov(X, Lag[k], nX, Double = Double) |
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121 | |
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122 | Auto = Auto / nX |
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123 | endelse |
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124 | |
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125 | if Double eq 0 then RETURN, FLOAT(Auto) else $ |
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126 | RETURN, Auto |
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127 | |
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128 | END |
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