[157] | 1 | ;+ |
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[232] | 2 | ; |
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[157] | 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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[163] | 8 | ; @param X {in}{required}{type=array} |
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[242] | 9 | ; An array which last dimension is the time dimension so |
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[157] | 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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[335] | 18 | ; @keyword NAN |
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| 19 | ; |
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[157] | 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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[335] | 24 | ; @hidden |
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[157] | 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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[335] | 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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[114] | 32 | ; |
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| 33 | compile_opt idl2, strictarrsubs |
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| 34 | ; |
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[335] | 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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[2] | 37 | |
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[335] | 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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[2] | 64 | END |
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[150] | 65 | ;+ |
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[242] | 66 | ; |
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[150] | 67 | ; @file_comments |
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[327] | 68 | ; Same function as <proidl>A_CORRELATE</proidl> but accept array (until 4 |
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[150] | 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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[157] | 77 | ; Statistics |
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[150] | 78 | ; |
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[163] | 79 | ; @param X {in}{required}{type=array} |
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[242] | 80 | ; An array which last dimension is the time dimension so |
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[150] | 81 | ; size n. |
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| 82 | ; |
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[163] | 83 | ; @param LAG {in}{required}{type=scalar or vector} |
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[335] | 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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[150] | 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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[335] | 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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[150] | 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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[371] | 101 | ; |
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[335] | 102 | ; Define an n-element sample population. |
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[371] | 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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[150] | 104 | ; |
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[242] | 105 | ; Compute the autocorrelation of X for LAG = -3, 0, 1, 3, 4, 8 |
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[371] | 106 | ; IDL> lag = [-3, 0, 1, 3, 4, 8] |
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| 107 | ; IDL> result = a_correlate(x, lag) |
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[150] | 108 | ; |
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[242] | 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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[150] | 111 | ; |
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| 112 | ; @history |
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[157] | 113 | ; 24/2/2000 Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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[150] | 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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[335] | 124 | FUNCTION a_timecorrelate, x, lag, COVARIANCE=covariance, DOUBLE=double, NVAL = nval |
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[114] | 125 | ; |
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| 126 | compile_opt idl2, strictarrsubs |
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| 127 | ; |
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[2] | 128 | |
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[327] | 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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[2] | 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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[242] | 137 | |
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[335] | 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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[342] | 148 | IF (WHERE(nTreal GT 1))[0] EQ -1 THEN $ |
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[335] | 149 | MESSAGE, "Matrix of length of time-series must contain 2 or more elements" |
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| 150 | |
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[2] | 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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[335] | 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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[2] | 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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[335] | 161 | ; Type of outputs according to the type of data input |
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| 162 | |
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[2] | 163 | case XNDim of |
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[335] | 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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[2] | 168 | endcase |
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| 169 | |
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[335] | 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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[2] | 191 | |
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[335] | 192 | return, useDouble ? Auto : FLOAT(Auto) |
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[2] | 193 | |
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| 194 | END |
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