[157] | 1 | ;+ |
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| 2 | ; @file_comments |
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| 3 | ; |
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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 XD |
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| 9 | ; |
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| 10 | ; |
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| 11 | ; @param YD |
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| 12 | ; |
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| 13 | ; |
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| 14 | ; @param M |
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| 15 | ; |
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| 16 | ; |
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| 17 | ; @param NT |
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| 18 | ; |
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| 19 | ; |
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| 20 | ; @param NDIM |
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| 21 | ; |
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| 22 | ; |
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| 23 | ; @keyword ZERO2NAN |
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| 24 | ; |
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| 25 | ; |
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| 26 | ; @keyword DOUBLE |
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| 27 | ; If set to a non-zero value, computations are done in |
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| 28 | ; double precision arithmetic. |
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| 29 | ; |
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| 30 | ; @examples |
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| 31 | ; |
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| 32 | ; |
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| 33 | ; @history |
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| 34 | ; |
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| 35 | ; |
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| 36 | ; @version |
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| 37 | ; $Id$ |
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| 38 | ; |
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| 39 | ;- |
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[163] | 40 | FUNCTION timecross_cov, Xd, Yd, M, nT, Ndim, Double = Double, ZERO2NAN = zero2nan |
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[150] | 41 | ;Sample cross covariance function. |
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| 42 | |
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| 43 | compile_opt hidden |
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[2] | 44 | ; |
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[150] | 45 | case Ndim OF |
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| 46 | 1:res = TOTAL(Xd[0:nT - M - 1L] * Yd[M:nT - 1L] $ |
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| 47 | , Double = Double) |
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| 48 | 2:res = TOTAL(Xd[*, 0:nT - M - 1L] * Yd[*, M:nT - 1L] $ |
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| 49 | , Ndim, Double = Double) |
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| 50 | 3:res = TOTAL(Xd[*, *, 0:nT - M - 1L] * Yd[*, *, M:nT - 1L] $ |
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| 51 | , Ndim, Double = Double) |
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| 52 | 4:res = TOTAL(Xd[*, *, *, 0:nT - M - 1L] * Yd[*, *, *, M:nT - 1L] $ |
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| 53 | , Ndim, Double = Double) |
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| 54 | ENDCASE |
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| 55 | if keyword_set(zero2nan) then begin |
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| 56 | zero = where(res EQ 0) |
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| 57 | if zero[0] NE -1 then res[zero] = !values.f_nan |
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| 58 | ENDIF |
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[2] | 59 | ; |
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[150] | 60 | RETURN, res |
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| 61 | |
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| 62 | END |
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| 63 | ;+ |
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| 64 | ; @file_comments |
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| 65 | ; This function computes the "time cross correlation" Pxy(L) or |
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| 66 | ; the "time cross covariance" between 2 arrays (this is some |
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| 67 | ; kind of c_correlate but for multidimenstionals arrays) as a |
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| 68 | ; function of the lag (L). |
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[2] | 69 | ; |
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[150] | 70 | ; @categories |
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[157] | 71 | ; Statistics |
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[2] | 72 | ; |
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[163] | 73 | ; @param X {in}{required}{type=array} |
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[150] | 74 | ; An Array which last dimension is the time dimension of |
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| 75 | ; size n, float or double. |
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[2] | 76 | ; |
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[163] | 77 | ; @param Y {in}{required}{type=array} |
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[150] | 78 | ; An Array which last dimension is the time dimension of |
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| 79 | ; size n, float or double. |
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[2] | 80 | ; |
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[163] | 81 | ; @param LAG {in}{required}{type=scalar or vector} |
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[150] | 82 | ; A scalar or n-element vector, in the interval [-(n-2), (n-2)], |
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| 83 | ; of type integer that specifies the absolute distance(s) between |
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| 84 | ; indexed elements of X. |
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[2] | 85 | ; |
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[150] | 86 | ; @keyword COVARIANCE |
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| 87 | ; If set to a non-zero value, the sample cross |
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| 88 | ; covariance is computed. |
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[2] | 89 | ; |
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[150] | 90 | ; @keyword DOUBLE |
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| 91 | ; If set to a non-zero value, computations are done in |
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| 92 | ; double precision arithmetic. |
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[2] | 93 | ; |
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[150] | 94 | ; @examples |
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| 95 | ; |
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[2] | 96 | ; Define two n-element sample populations. |
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| 97 | ; 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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| 98 | ; y = [2.31, 2.76, 3.02, 3.13, 3.72, 3.88, 3.97, 4.39, 4.34, 3.95] |
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| 99 | ; |
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| 100 | ; Compute the cross correlation of X and Y for LAG = -5, 0, 1, 5, 6, 7 |
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| 101 | ; lag = [-5, 0, 1, 5, 6, 7] |
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| 102 | ; result = c_timecorrelate(x, y, lag) |
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| 103 | ; |
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| 104 | ; The result should be: |
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| 105 | ; [-0.428246, 0.914755, 0.674547, -0.405140, -0.403100, -0.339685] |
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| 106 | ; |
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[150] | 107 | ; @history |
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[157] | 108 | ; - 01/03/2000 Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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[2] | 109 | ; Based on the C_CORRELATE procedure of IDL |
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[21] | 110 | ; - August 2003 Sebastien Masson |
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| 111 | ; update according to the update made in C_CORRELATE by |
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| 112 | ; W. Biagiotti and available in IDL 5.5 |
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[2] | 113 | ; |
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[150] | 114 | ; INTRODUCTION TO STATISTICAL TIME SERIES |
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| 115 | ; Wayne A. Fuller |
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| 116 | ; ISBN 0-471-28715-6 |
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[2] | 117 | ; |
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[150] | 118 | ; @version |
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| 119 | ; $Id$ |
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| 120 | ; |
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| 121 | ;- |
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[163] | 122 | FUNCTION c_timecorrelate, X, Y, Lag, Covariance = Covariance, Double = Double |
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[2] | 123 | |
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| 124 | ;Compute the sample cross correlation or cross covariance of |
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| 125 | ;(Xt, Xt+l) and (Yt, Yt+l) as a function of the lag (l). |
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| 126 | |
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| 127 | ON_ERROR, 2 |
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| 128 | |
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| 129 | xsize = SIZE(X) |
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| 130 | ysize = SIZE(Y) |
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| 131 | nt = float(xsize[xsize[0]]) |
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| 132 | NDim = xsize[0] |
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| 133 | |
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| 134 | if total(xsize[0:xsize[0]] NE ysize[0:ysize[0]]) NE 0 then $ |
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| 135 | MESSAGE, "X and Y arrays must have the same size and the same dimensions" |
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| 136 | |
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| 137 | ;Check length. |
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| 138 | if nt lt 2 then $ |
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| 139 | MESSAGE, "Time dimension of X and Y arrays must contain 2 or more elements." |
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| 140 | |
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| 141 | ;If the DOUBLE keyword is not set then the internal precision and |
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| 142 | ;result are identical to the type of input. |
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| 143 | if N_ELEMENTS(Double) eq 0 then $ |
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| 144 | Double = (Xsize[Xsize[0]+1] eq 5 or ysize[ysize[0]+1] eq 5) |
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| 145 | |
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| 146 | if n_elements(lag) EQ 0 then lag = 0 |
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| 147 | nLag = N_ELEMENTS(Lag) |
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| 148 | |
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[21] | 149 | ;Deviations |
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| 150 | if double then one = 1.0d ELSE one = 1.0 |
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| 151 | Ndim = size(X, /n_dimensions) |
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| 152 | Xd = TOTAL(X, Ndim, Double = Double) / nT |
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| 153 | Xd = X - Xd[*]#replicate(one, nT) |
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| 154 | Yd = TOTAL(Y, Ndim, Double = Double) / nT |
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| 155 | Yd = Y - Yd[*]#replicate(one, nT) |
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| 156 | |
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[2] | 157 | if nLag eq 1 then Lag = [Lag] ;Create a 1-element vector. |
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| 158 | |
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| 159 | case NDim of |
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[21] | 160 | 1:if Double eq 0 then Cross = FLTARR(nLag) else Cross = DBLARR(nLag) |
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| 161 | 2:if Double eq 0 then Cross = FLTARR(Xsize[1], nLag) else Cross = DBLARR(Xsize[1], nLag) |
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| 162 | 3:if Double eq 0 then Cross = FLTARR(Xsize[1], Xsize[2], nLag) $ |
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| 163 | else Cross = DBLARR(Xsize[1], Xsize[2], nLag) |
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| 164 | 4:if Double eq 0 then Cross = FLTARR(Xsize[1], Xsize[2], Xsize[3], nLag) $ |
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| 165 | else Cross = DBLARR(Xsize[1], Xsize[2], Xsize[3], nLag) |
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[2] | 166 | endcase |
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| 167 | |
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[21] | 168 | if KEYWORD_SET(Covariance) eq 0 then begin ;Compute Cross Crossation. |
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[2] | 169 | for k = 0, nLag-1 do begin |
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| 170 | if Lag[k] ge 0 then BEGIN |
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| 171 | case NDim of |
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[21] | 172 | 1: Cross[k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) |
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| 173 | 2: Cross[*, k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) |
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| 174 | 3: Cross[*, *, k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) |
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| 175 | 4: Cross[*, *, *, k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) |
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| 176 | endcase |
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[2] | 177 | ENDIF else BEGIN |
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| 178 | case NDim of |
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[21] | 179 | 1: Cross[k] = TimeCross_Cov(Yd, Xd, ABS(Lag[k]), nT, Ndim, Double = Double) |
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| 180 | 2: Cross[*, k] = TimeCross_Cov(Yd, Xd, ABS(Lag[k]), nT, Ndim, Double = Double) |
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| 181 | 3: Cross[*, *, k] = TimeCross_Cov(Yd, Xd, ABS(Lag[k]), nT, Ndim, Double = Double) |
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| 182 | 4: Cross[*, *, *, k] = TimeCross_Cov(Yd, Xd, ABS(Lag[k]), nT, Ndim, Double = Double) |
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| 183 | endcase |
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[2] | 184 | ENDELSE |
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[21] | 185 | ENDFOR |
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| 186 | div = sqrt(TimeCross_Cov(Xd, Xd, 0L, nT, Ndim, Double = Double, /zero2nan) * $ |
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| 187 | TimeCross_Cov(Yd, Yd, 0L, nT, Ndim, Double = Double, /zero2nan)) |
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| 188 | Cross = temporary(Cross)/((temporary(div))[*]#replicate(one, nLag)) |
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[2] | 189 | endif else begin ;Compute Cross Covariance. |
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| 190 | for k = 0, nLag-1 do begin |
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| 191 | if Lag[k] ge 0 then BEGIN |
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| 192 | case NDim of |
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[21] | 193 | 1: Cross[k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) / nT |
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| 194 | 2: Cross[*, k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) / nT |
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| 195 | 3: Cross[*, *, k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) / nT |
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| 196 | 4: Cross[*, *, *, k] = TimeCross_Cov(Xd, Yd, Lag[k], nT, Ndim, Double = Double) / nT |
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[2] | 197 | ENDCASE |
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| 198 | ENDIF else BEGIN |
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| 199 | case NDim of |
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[21] | 200 | 1: Cross[k] = TimeCross_Cov(yd, xd, ABS(Lag[k]), nT, Ndim, Double = Double) / nT |
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| 201 | 2: Cross[*, k] = TimeCross_Cov(yd, xd, ABS(Lag[k]), nT, Ndim, Double = Double) / nT |
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| 202 | 3: Cross[*, *, k] = TimeCross_Cov(yd, xd, ABS(Lag[k]), nT, Ndim, Double = Double) / nT |
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| 203 | 4: Cross[*, *, *, k] = TimeCross_Cov(yd, xd, ABS(Lag[k]), nT, Ndim, Double = Double) / nT |
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[2] | 204 | ENDCASE |
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| 205 | ENDELSE |
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| 206 | endfor |
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| 207 | endelse |
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| 208 | |
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[21] | 209 | if Double eq 0 then RETURN, FLOAT(Cross) else RETURN, Cross |
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[2] | 210 | |
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| 211 | END |
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| 212 | |
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