1 | ;+ |
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2 | ; |
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3 | ; @file_comments |
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4 | ; |
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5 | ; @categories |
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6 | ; Statistics |
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7 | ; |
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8 | ; @param X {in}{required}{type=array} |
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9 | ; An array which last dimension is the time dimension so |
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10 | ; size n. |
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11 | ; |
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12 | ; @param M |
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13 | ; |
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14 | ; @param NT |
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15 | ; |
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16 | ; @keyword ZERO2NAN |
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17 | ; |
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18 | ; @keyword NAN |
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19 | ; |
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20 | ; @keyword DOUBLE |
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21 | ; If set to a non-zero value, computations are done in |
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22 | ; double precision arithmetic. |
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23 | ; |
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24 | ; @hidden |
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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 | FUNCTION timeauto_cov, x, m, nt, DOUBLE=double, ZERO2NAN=zero2nan, NAN = nan |
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31 | ;Sample autocovariance function |
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32 | ; |
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33 | compile_opt idl2, strictarrsubs |
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34 | ; |
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35 | IF NAN AND M GE 1 THEN $ |
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36 | STOP, 'Warning : lagged autocorrelation is not possible at the moment for time-series with NaN !!!' |
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37 | |
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38 | TimeDim = size(X, /n_dimensions) |
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39 | Xmean = NAN ? TOTAL(X, TimeDim, Double = Double, NAN = nan) / TOTAL(FINITE(X), TimeDim) : $ |
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40 | TOTAL(X, TimeDim, Double = Double) / nT |
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41 | one = double ? 1.0d : 1.0 |
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42 | Xmean = Xmean[*]#replicate(one, nT - M) |
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43 | |
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44 | ; Time-series with NaN : only for Lag = 0 |
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45 | case TimeDim of |
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46 | 1:res = TOTAL((X[0:nT - M - 1L] - Xmean) * (X[M:nT - 1L] - Xmean), $ |
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47 | TimeDim, Double = Double, NAN = nan) |
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48 | 2:res = TOTAL((X[*, 0:nT - M - 1L] - Xmean) * $ |
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49 | (X[*, M:nT - 1L] - Xmean[*]) $ |
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50 | , TimeDim, Double = Double, NAN = nan) |
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51 | 3:res = TOTAL((X[*, *, 0:nT - M - 1L] - Xmean[*, *]) * $ |
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52 | (X[*, *, M:nT - 1L] - Xmean) $ |
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53 | , TimeDim, Double = Double, NAN = nan) |
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54 | 4:res = TOTAL((X[*, *, *, 0:nT - M - 1L] - Xmean) * $ |
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55 | (X[*, *, *, M:nT - 1L] - Xmean) $ |
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56 | , TimeDim, Double = Double, NAN = nan) |
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57 | ENDCASE |
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58 | if keyword_set(zero2nan) then begin |
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59 | zero = where(res EQ 0) |
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60 | if zero[0] NE -1 then res[zero] = !values.f_nan |
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61 | endif |
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62 | RETURN, res |
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63 | |
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64 | END |
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65 | ;+ |
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66 | ; |
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67 | ; @file_comments |
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68 | ; Same function as <proidl>A_CORRELATE</proidl> but accept array (until 4 |
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69 | ; dimension) for input and do the autocorrelation or the |
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70 | ; autocovariance along the time dimension which must be the last |
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71 | ; one of the input array. |
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72 | ; |
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73 | ; This function computes the autocorrelation Px(L) or autocovariance |
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74 | ; Rx(L) of a sample population X as a function of the lag (L). |
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75 | ; |
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76 | ; @categories |
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77 | ; Statistics |
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78 | ; |
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79 | ; @param X {in}{required}{type=array} |
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80 | ; An array which last dimension is the time dimension so |
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81 | ; size n. |
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82 | ; |
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83 | ; @param LAG {in}{required}{type=scalar or vector} |
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84 | ; A scalar or n-element vector, in the interval [-(n-2), (n-2)], |
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85 | ; of type integer that specifies the absolute distance(s) between |
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86 | ; indexed elements of X. |
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87 | ; |
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88 | ; @keyword COVARIANCE |
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89 | ; If set to a non-zero value, the sample autocovariance |
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90 | ; is computed. |
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91 | ; |
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92 | ; @keyword NVAL |
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93 | ; A named variable that, on exit, contains the number of valid |
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94 | ; observations (not NAN) |
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95 | ; |
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96 | ; @keyword DOUBLE |
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97 | ; If set to a non-zero value, computations are done in |
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98 | ; double precision arithmetic. |
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99 | ; |
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100 | ; @examples |
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101 | ; |
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102 | ; Define an n-element sample population. |
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103 | ; IDL> 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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104 | ; |
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105 | ; Compute the autocorrelation of X for LAG = -3, 0, 1, 3, 4, 8 |
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106 | ; IDL> lag = [-3, 0, 1, 3, 4, 8] |
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107 | ; IDL> result = a_correlate(x, lag) |
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108 | ; |
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109 | ; The result should be: |
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110 | ; [0.0146185, 1.00000, 0.810879, 0.0146185, -0.325279, -0.151684] |
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111 | ; |
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112 | ; @history |
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113 | ; 24/2/2000 Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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114 | ; |
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115 | ; Based on the A_CORRELATE procedure of IDL |
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116 | ; INTRODUCTION TO STATISTICAL TIME SERIES |
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117 | ; Wayne A. Fuller |
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118 | ; ISBN 0-471-28715-6 |
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119 | ; |
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120 | ; @version |
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121 | ; $Id$ |
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122 | ; |
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123 | ;- |
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124 | FUNCTION a_timecorrelate, x, lag, COVARIANCE=covariance, DOUBLE=double, NVAL = nval |
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125 | ; |
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126 | compile_opt idl2, strictarrsubs |
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127 | ; |
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128 | |
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129 | ; Compute the sample-autocorrelation or autocovariance of (Xt, Xt+l) |
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130 | ; as a function of the lag (l). |
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131 | |
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132 | ON_ERROR, 2 |
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133 | |
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134 | XDim = SIZE(X, /dimensions) |
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135 | XNDim = SIZE(X, /n_dimensions) |
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136 | nT = XDim[XNDim-1] |
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137 | |
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138 | ; Keyword NAN activated if needed for TimeAuto_Cov function |
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139 | ; Keyword NVAL not compulsory. |
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140 | |
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141 | NAN = ( (WHERE(FINITE(X) EQ 0 ))[0] NE -1 ) ? 1 : 0 |
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142 | ;We can retrieve the matrix of real lenghts of time-series |
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143 | nTreal = ( (WHERE(FINITE(X) EQ 0 ))[0] NE -1 ) ? TOTAL(FINITE(X), XNDim) : nT |
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144 | |
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145 | IF ARG_PRESENT(NVAL) THEN nval = nTreal |
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146 | |
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147 | ;Check length. |
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148 | IF (WHERE(nTreal GT 1))[0] EQ -1 THEN $ |
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149 | MESSAGE, "Matrix of length of time-series must contain 2 or more elements" |
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150 | |
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151 | ;If the DOUBLE keyword is not set then the internal precision and |
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152 | ;result are identical to the type of input. |
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153 | type = SIZE(X, /TYPE) |
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154 | useDouble = (N_ELEMENTS(Double) eq 1) ? KEYWORD_SET(Double) : (type eq 5) |
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155 | |
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156 | if n_elements(lag) EQ 0 then lag = 0 |
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157 | nLag = N_ELEMENTS(Lag) |
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158 | |
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159 | if nLag eq 1 then Lag = [Lag] ;Create a 1-element vector. |
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160 | |
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161 | ; Type of outputs according to the type of data input |
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162 | |
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163 | case XNDim of |
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164 | 1: Auto = useDouble ? DBLARR(nLag) : FLTARR(nLag) |
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165 | 2: Auto = useDouble ? DBLARR(XDim[0], nLag) : FLTARR(XDim[0], nLag) |
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166 | 3: Auto = useDouble ? DBLARR(XDim[0], XDim[1], nLag) : FLTARR(XDim[0], XDim[1], nLag) |
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167 | 4: Auto = useDouble ? DBLARR(XDim[0], XDim[1], XDim[2], nLag) : FLTARR(XDim[0], XDim[1], XDim[2], nLag) |
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168 | endcase |
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169 | |
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170 | ; Compute lagged autocorrelation or autocovariance (no NaN) |
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171 | FOR k = 0, nLag-1 DO BEGIN |
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172 | case XNDim of |
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173 | 1: BEGIN |
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174 | Auto[k] = TimeAuto_Cov(X, ABS(Lag[k]), nT, Double = useDouble, NAN = nan) / $ |
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175 | ( KEYWORD_SET(Covariance) ? nTreal : TimeAuto_Cov(X, 0L, nT, Double = useDouble, /zero2nan, NAN = nan) ) |
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176 | END |
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177 | 2: BEGIN |
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178 | Auto[*, k] = TimeAuto_Cov(X, ABS(Lag[k]), nT, Double = useDouble, NAN = nan) / $ |
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179 | ( KEYWORD_SET(Covariance) ? nTreal : TimeAuto_Cov(X, 0L, nT, Double = useDouble, /zero2nan, NAN = nan) ) |
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180 | END |
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181 | 3: BEGIN |
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182 | Auto[*, *, k] = TimeAuto_Cov(X, ABS(Lag[k]), nT, Double = useDouble, NAN = nan) / $ |
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183 | ( KEYWORD_SET(Covariance) ? nTreal : TimeAuto_Cov(X, 0L, nT, Double = useDouble, /zero2nan, NAN = nan) ) |
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184 | END |
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185 | 4: BEGIN |
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186 | Auto[*, *, *, k] = TimeAuto_Cov(X, ABS(Lag[k]), nT, Double = useDouble, NAN = nan) / $ |
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187 | ( KEYWORD_SET(Covariance) ? nTreal : TimeAuto_Cov(X, 0L, nT, Double = useDouble, /zero2nan, NAN = nan) ) |
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188 | END |
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189 | ENDCASE |
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190 | ENDFOR |
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191 | |
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192 | return, useDouble ? Auto : FLOAT(Auto) |
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193 | |
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194 | END |
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