1 | ;+ |
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2 | ; |
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3 | ; @file_comments |
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4 | ; |
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5 | ; |
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6 | ; @categories |
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7 | ; Statistics |
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8 | ; |
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9 | ; @param X {in}{required}{type=array} |
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10 | ; An Array which last dimension is the time dimension so |
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11 | ; size n. |
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12 | ; |
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13 | ; |
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14 | ; @param NT |
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15 | ; |
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16 | ; |
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17 | ; @keyword DOUBLE |
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18 | ; If set to a non-zero value, computations are done in |
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19 | ; double precision arithmetic. |
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20 | ; |
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21 | ; @examples |
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22 | ; |
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23 | ; |
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24 | ; @history |
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25 | ; |
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26 | ; |
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27 | ; @version |
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28 | ; $Id: skewness_4d.pro 232 2007-03-20 16:59:36Z pinsard $ |
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29 | ; |
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30 | ;- |
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31 | FUNCTION Skewness_Num, X, nT, Double = Double, NAN = nan |
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32 | ; Compute the numerator of the skewness expression |
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33 | ; |
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34 | |
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35 | compile_opt idl2, strictarrsubs |
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36 | ; |
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37 | TimeDim = size(X, /n_dimensions) |
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38 | Xmean = NAN ? TOTAL(X, TimeDim, Double = Double, NAN = nan) / TOTAL(FINITE(X), TimeDim) : $ |
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39 | TOTAL(X, TimeDim, Double = Double) / nT |
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40 | one = double ? 1.0d : 1.0 |
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41 | Xmean = Xmean[*]#replicate(one, nT) |
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42 | res = TOTAL( (X-Xmean)^3, TimeDim, Double = Double, NAN = nan) |
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43 | |
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44 | RETURN, res |
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45 | |
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46 | END |
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47 | ;+ |
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48 | ; @file_comments |
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49 | ; Same function as SKEWNESS but accept array (until 4 |
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50 | ; dimension) for input and perform the skewness |
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51 | ; along the time dimension which must be the last |
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52 | ; one of the input array. |
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53 | ; |
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54 | ; @categories |
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55 | ; Statistics |
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56 | ; |
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57 | ; @param X {in}{required}{type=array} |
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58 | ; An Array which last dimension is the time dimension so |
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59 | ; size n. |
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60 | ; |
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61 | ; @keyword DOUBLE |
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62 | ; If set to a non-zero value, computations are done in |
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63 | ; double precision arithmetic. |
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64 | ; |
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65 | ; @examples |
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66 | ; |
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67 | ; @history |
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68 | ; 24/2/2000 Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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69 | ; |
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70 | ; Based on the a_timecorrelate procedure of IDL |
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71 | ; INTRODUCTION TO STATISTICAL TIME SERIES |
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72 | ; Wayne A. Fuller |
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73 | ; ISBN 0-471-28715-6 |
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74 | ; |
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75 | ; @version |
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76 | ; $Id: skewness_4d.pro 232 2007-03-20 16:59:36Z pinsard $ |
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77 | ; |
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78 | ;- |
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79 | |
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80 | FUNCTION skewness_4d, X, DOUBLE = Double, NVAL = nval |
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81 | ; |
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82 | compile_opt idl2, strictarrsubs |
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83 | ; |
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84 | ; Compute the skewness from 1d to 4d vectors |
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85 | @common |
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86 | |
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87 | ON_ERROR, 2 |
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88 | |
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89 | XDim = SIZE(X, /dimensions) |
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90 | XNDim = SIZE(X, /n_dimensions) |
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91 | nT = XDim[XNDim-1] |
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92 | |
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93 | ; Keyword NAN activated if needed |
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94 | ; Keyword NVAL not compulsory. |
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95 | |
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96 | NAN = ( (WHERE(FINITE(X) EQ 0 ))[0] NE -1 ) ? 1 : 0 |
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97 | ;We can retrieve the matrix of real lenghts of time-series |
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98 | nTreal = ( (WHERE(FINITE(X) EQ 0 ))[0] NE -1 ) ? TOTAL(FINITE(X), XNDim) : nT |
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99 | |
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100 | IF ARG_PRESENT(NVAL) THEN nval = nTreal |
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101 | |
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102 | ; Check length. |
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103 | IF (WHERE(nTreal LE 1))[0] NE -1 THEN $ |
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104 | MESSAGE, "Matrix of length of time-series must contain 2 or more elements" |
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105 | |
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106 | ; If the DOUBLE keyword is not set then the internal precision and |
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107 | ; result are identical to the type of input. |
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108 | type = SIZE(X, /TYPE) |
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109 | useDouble = (N_ELEMENTS(Double) eq 1) ? KEYWORD_SET(Double) : $ |
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110 | (type eq 5) |
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111 | |
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112 | ; Type of outputs according to the type of data input |
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113 | case XNDim of |
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114 | 1: Skew = useDouble ? DBLARR(1) : FLTARR(1) |
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115 | 2: Skew = useDouble ? DBLARR(XDim[0]) : FLTARR(XDim[0]) |
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116 | 3: Skew = useDouble ? DBLARR(XDim[0], XDim[1]) : FLTARR(XDim[0], XDim[1]) |
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117 | 4: Skew = useDouble ? DBLARR(XDim[0], XDim[1], XDim[2]) : FLTARR(XDim[0], XDim[1], XDim[2]) |
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118 | endcase |
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119 | ; Compute standard deviation |
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120 | ; nTreal might be a matrix |
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121 | std = a_timecorrelate(X, 0, /covariance) |
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122 | std = sqrt(std) |
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123 | zero = where(std EQ 0) |
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124 | |
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125 | if zero[0] NE -1 then STOP, $ |
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126 | 'Cannot compute skewness since there are zeros in the matrix of standard deviations !' |
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127 | |
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128 | ; Problem with high masked values (x^3 makes NaN when x is high) |
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129 | ; Threshold put on the values of the tab |
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130 | idx_std = WHERE (std GT 1.0e+10) |
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131 | X = X < 1.0e+10 |
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132 | std = std < 1.0e+10 |
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133 | |
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134 | ; Compute skewness |
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135 | Skew = Skewness_Num(X, nT, Double = useDouble, NAN = nan) / (nTreal*std^3) |
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136 | IF idx_std[0] NE -1 THEN Skew[idx_std] = valmask |
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137 | |
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138 | return, useDouble ? Skew : FLOAT(Skew) |
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139 | |
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140 | END |
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141 | |
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