[2] | 1 | ;+ |
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| 2 | ; NAME: |
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| 3 | ; A_CORRELATE2d |
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| 4 | ; |
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| 5 | ; PURPOSE: |
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| 6 | ; |
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| 7 | ; This function computes the autocorrelation Px(K,L) or |
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| 8 | ; autocovariance Rx(K,L) of a sample population X[nx,ny] as a |
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| 9 | ; function of the lag (K,L). |
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| 10 | ; |
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| 11 | ; CATEGORY: |
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| 12 | ; Statistics. |
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| 13 | ; |
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| 14 | ; CALLING SEQUENCE: |
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| 15 | ; Result = a_correlate2d(X, Lag) |
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| 16 | ; |
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| 17 | ; INPUTS: |
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| 18 | ; X: an 2 dimension Array [nx,ny] |
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| 19 | ; |
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| 20 | ; LAG: 2-element vector, in the intervals [-(nx-2), (nx-2)],[-(ny-2), (ny-2)], |
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| 21 | ; of type integer that specifies the absolute distance(s) between |
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| 22 | ; indexed elements of X. |
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| 23 | ; |
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| 24 | ; KEYWORD PARAMETERS: |
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| 25 | ; COVARIANCE: If set to a non-zero value, the sample autocovariance |
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| 26 | ; is computed. |
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| 27 | ; |
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| 28 | ; DOUBLE: If set to a non-zero value, computations are done in |
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| 29 | ; double precision arithmetic. |
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| 30 | ; |
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| 31 | ; EXAMPLE: |
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| 32 | ; |
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| 33 | ; PROCEDURE: |
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| 34 | ; |
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| 35 | ; |
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| 36 | ; nx-k-1 ny-l-1 |
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| 37 | ; sigma sigma (X[i,j]-Xmean)(X[i+k,j+l]-Ymean) |
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| 38 | ; i=0 j=0 |
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| 39 | ; correlation(X,[k,l])=------------------------------------------------------ |
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| 40 | ; nx-1 ny-1 |
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| 41 | ; sigma sigma (X[i,j]-Xmean)^2) |
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| 42 | ; i=0 j=0 |
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| 43 | ; |
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| 44 | ; |
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| 45 | ; nx-k-1 ny-l-1 |
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| 46 | ; sigma sigma (X[i,j]-Xmean)(Y[i+k,j+l]-Ymean) |
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| 47 | ; i=0 j=0 |
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| 48 | ; covariance(X,[k,l])=------------------------------------------------------ |
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| 49 | ; nx*ny |
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| 50 | ; |
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| 51 | ; Where Xmean is the mens of the sample population |
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| 52 | ; x=(x[0,0],x[1,0],...,x[nx-1,ny-1]). |
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| 53 | ; |
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| 54 | ; |
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| 55 | ; REFERENCE: |
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| 56 | ; |
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| 57 | ; MODIFICATION HISTORY: |
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| 58 | ; 28/2/2000 Sebastien Masson (smasson@lodyc.jussieu.fr) |
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| 59 | ; Based on the A_CORRELATE procedure of IDL |
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| 60 | ;- |
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| 61 | |
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| 62 | FUNCTION Auto_Cov2d, X, Lag, Double = Double, zero2nan = zero2nan |
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| 63 | XDim = SIZE(X, /dimensions) |
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| 64 | nx = XDim[0] |
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| 65 | ny = XDim[1] |
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| 66 | ;Sample autocovariance function |
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| 67 | Xmean = TOTAL(X, Double = Double) / (1.*nx*ny) |
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| 68 | ; |
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| 69 | res = TOTAL( (X[0:nx-1-lag[0], 0:ny-1-lag[1]] - Xmean) * $ |
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| 70 | (X[lag[0]:nx-1, lag[1]:ny-1] - Xmean) $ |
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| 71 | , Double = Double ) |
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| 72 | if keyword_set(zero2nan) AND res EQ 0 then res = !values.f_nan |
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| 73 | RETURN, res |
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| 74 | |
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| 75 | END |
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| 76 | |
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| 77 | FUNCTION A_Correlate2d, X, Lag, Covariance = Covariance, Double = Double |
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| 78 | |
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| 79 | ;Compute the sample-autocorrelation or autocovariance of (Xt, Xt+l) |
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| 80 | ;as a function of the lag (l). |
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| 81 | |
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| 82 | ON_ERROR, 2 |
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| 83 | |
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| 84 | XDim = SIZE(X, /dimensions) |
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| 85 | XNDim = SIZE(X, /n_dimensions) |
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| 86 | nx = XDim[0] |
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| 87 | ny = XDim[1] |
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| 88 | if XNDim NE 2 then $ |
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| 89 | MESSAGE, "X array must contain 2 dimensions." |
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| 90 | ;Check length. |
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| 91 | if nx lt 2 then $ |
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| 92 | MESSAGE, "first dimension of X array must contain 2 or more elements." |
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| 93 | if ny lt 2 then $ |
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| 94 | MESSAGE, "second dimension of X array must contain 2 or more elements." |
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| 95 | if n_elements(Lag) NE 2 THEN $ |
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| 96 | MESSAGE, "Lag array must contain 2 elements." |
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| 97 | |
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| 98 | ;If the DOUBLE keyword is not set then the internal precision and |
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| 99 | ;result are identical to the type of input. |
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| 100 | if N_ELEMENTS(Double) eq 0 then $ |
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| 101 | Double = (SIZE(X, /type) eq 5) |
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| 102 | |
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| 103 | if KEYWORD_SET(Covariance) eq 0 then begin ;Compute Autocorrelation. |
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| 104 | Auto = Auto_Cov2d(X, ABS(Lag), Double = Double) / $ |
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| 105 | Auto_Cov2d(X, [0L, 0L], Double = Double, /zero2nan) |
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| 106 | endif else begin ;Compute Autocovariance. |
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| 107 | Auto = Auto_Cov2d(X, ABS(Lag), Double = Double) / n_elements(X) |
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| 108 | endelse |
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| 109 | |
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| 110 | if Double eq 0 then RETURN, FLOAT(Auto) else $ |
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| 111 | RETURN, Auto |
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| 112 | |
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| 113 | END |
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