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# Directory Listing of Routines

# projects/iugonet/tools/statistical_package

- DIFFERENCE_TEST
- MANN_WHITNEY_TEST
  Test the difference for distributions between two data sets.
- NORMALITY_TEST
- S_TRANS
- TREND_TEST
  Test the trend of the data.
- UCHANGE_POINT_CHECKER
  Identify the change point of time-serise data.
- UCROSS_COR
  Calculate the cross correlation between two time-serise data
- UDATA_INTERPOLATION
  Perform the data interpolation for two time-serise data.
- UDIFFERENCE_TEST
  Perform the difference test for two pairs of time-series data sets and
- USPEC_COH
  Calculate the coherence and phase difference between two time-serise data.
- USTRANS_PWRSPC
  Calculate the local power spectrum for given time-series data and return the structure
- UTREND_TEST
  Test whether there is a significant trend of time-serise data or not.
- WELCH_TEST
  Test whether two pairs of average value of time series data is the same or.

# Routine Descriptions

## DIFFERENCE_TEST

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    Name:
    　　difference_test
    Purpose:
      平均値検定を行うプログラム。
      χ二乗検定によって正規分布との適合を検定する。
      どちらも正規分布に従う場合はWelch検定
      どちらかが正規分布に従わない場合はマンホイットニー検定のみを用いる。
    Syntax:
      difference_test,x,y,result,sl=**
    Keywords:
      result:検定結果を'0'：ウェルチ検定使用-判定は異,'1'：ウェルチ検定使用-判定は同,'2'：マンホイットニー-異,'3'：マンホイットニー-同、で返す
      sl:有意水準。指定しない場合はsl=0.05で検定。
      test_sel：行う検定を指定。'2'はマンホイットニー検定、'1'はウェルチ検定、'0'はχ二乗検定によって正規分布との適合を検定
      2012/12/13 改変　by 濵口

(See projects/iugonet/tools/statistical_package/difference_test.pro)

## MANN_WHITNEY_TEST

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    NAME:
      Mann_Whitney_test

    PURPOSE:
       Test the difference for distributions between two data sets.
       Distribution of the population does not matter.

    KEYWORDS:
      sl:significance level
         If you don't set sl, sl = 0.05
      mv:missing value
         If you don't set mv, mv = only NaN
      z:Statistical test value.
      Z0:Critical value of the standard normal distribution at significance level
      c:Comment

    NOTES:
      The output result is 3 or 2 if both distributions is same or different.

    CODE:
    R. Hamaguchi, 13/02/2012.

    MODIFICATIONS:
    A. Shinbori, 01/05/2013.
    A. Shinbori, 10/07/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/mann_whitney_test.pro)

## NORMALITY_TEST

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    NAME
     normality_test

    PURPOSE
     Test whether time-series data obey the normal distribution or not
     with the chi-square goodness-of-fit test.

    SYNTAX
     result=normality_test(x,sl=sl,mv=mv)

    KEYWORDS:
      x:Input data
      sl:Significant level
         The default is 0.05.
      mv:Missing value.
         If not set, only the NaN value is dealt with.

    NOTES:
      Output the value '0' if the input data obey the normal distribution and
      '1' if not obey.

    CODE:
    R. Hamaguchi, 13/02/2012.

    MODIFICATIONS:
    A. Shinbori, 01/05/2013.
    A. Shinbori, 10/07/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/normality_test.pro)

## S_TRANS

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    NAME:
    s_trans

    PURPOSE:
     Calculate the local power spectrum for given time-series data and return the structure
     which contains {st:, ph: freq:, time:} where st is the S Transform.

    SYNTAX:
     results = s_trans(time-series)

    KEYWOARDS:
     \help               explains all the keywords and parameters
     \verbose            flags errors and size
     \samplingrate       if set returns array of frequency
     \maxfreq
     \minfreq
     \freqsmplingrate
     \piecewisenumber    divides the time series, and passes back array
     \power              returns the power spectrum
     \abs                returns the absolute value spectrum
     \Rremoveedge        removes the edge with a 5% taper, and takes out least-sqares fit parabola

     Added a "mask out edges" keyword, which STs a line (ie st of edges) and thresholds the returned st matrix.
     The value of masked edges is the percent at which to  make the threshold default = 5 %.

     Added an EXAMPLE keyword, will display a time series and the amplitude of the ST to the current graphics device
     WARNING, will call !P.multi=0

    ===================== Modified hilbert transform ================================
    ;;;;;;;;;;;;;;;;;;;;
    +
     NAME:
      hilbert

     PURPOSE:
      Return a series that has all periodic terms shifted by 90 degrees.

    CODE:
     A. Shinbori, 04/06/2012.

    MODIFICATIONS:

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/s_trans.pro)

## TREND_TEST

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    NAME:
      trend_test
    PURPOSE:
      Test the trend of the data.
    SYNTAX:
      trend_test,y
    KEYWORDS:
        y:Input data
        Z:Statistical test value.
        sl:Significant level. The default is 0.05.

    CODE:
     R. Hamaguchi, 17/01/2013.

    MODIFICATIONS:
     A. Shinbori, 01/05/2013.
     A. Shinbori, 10/07/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/trend_test.pro)

## UCHANGE_POINT_CHECKER

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    NAME:
    uchange_point_checker

    PURPOSE:
    Identify the change point of time-serise data.

    SYNTAX:
    uchange_point_checker,vname1

    CODE:
    R. Hamaguchi, 17/01/2013.

    MODIFICATIONS:
    A. Shinbori, 08/05/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/uchange_point_checker.pro)

## UCROSS_COR

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    NAME:
    ucross_cor

    PURPOSE:
      Calculate the cross correlation between two time-serise data
      and perform a test of correlation.

    CALLING SEQUENCE:
     ucross_cor, vname1,vname2

    INPUT:
     vname1 = first tplot variable name
     vname2 = second tplot variable name

    OUTPUT:
     cross_cor = cross correlation between two time-serise data
     x_cor = auto correlation of the first tplot variable
     y_cor = auto correlation of the second tplot variable

    KEYWORDS:
      sl  = Significant level of correlation test.
      low_lag = lag time of left direction
      high_lag = lag time of right direction

    EXAMPLE:
      ucross_cor, tplot1, tplot2

    CODE:
    R. Hamaguchi, 15/01/2013.

    MODIFICATIONS:
    A. Shinbori, 31/01/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/ucross_cor.pro)

## UDATA_INTERPOLATION

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    NAME:
    udata_interpolation

    PURPOSE:
     Perform the data interpolation for two time-serise data.

    CALLING SEQUENCE:
     udata_interpolation, vname1,vname2

    INPUT:
     vname1 = first tplot variable name
     vname2 = second tplot variable name

    KEYWORDS:
      st_time0  = start time of data interpolation
      ed_time0 = end time of data interpolation
      reverse = exchange of two data sets
        If set, the data interplation is performed on the basis of time range of data2.
      set_interval = set up time interval to interplate the two data sets.
      If not set, the time interval is determined on the basis of the minimum interval
      in the two data sets.

    EXAMPLE:
       udata_interpolation, tplot1, tplot2

    CODE:
    R. Hamaguchi, 15/01/2013.

    MODIFICATIONS:
    A. Shinbori, 20/02/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2019-10-12 12:38:21 -0700 (Sat, 12 Oct 2019) $
     $LastChangedRevision: 27847 $
     $URL $

(See projects/iugonet/tools/statistical_package/udata_interpolation.pro)

## USPEC_COH

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    NAME:
    uspec_coh

    PURPOSE:
      Calculate the coherence and phase difference between two time-serise data.

    CALLING SEQUENCE:
     uspec_coh, vname1,vname2

    INPUT:
     vname1 = first tplot variable name
     vname2 = second tplot variable name

    OUTPUT:
     main_period = the period given the maximum coherence.

    KEYWORDS:
      deltat  = time interval of observation data
      width = the width of window function
        Default is 10.
      window = type of window function (hanning, boxcar, gaussian, triangle)
        Default is 'hanning' window.
      xsize = plot size of x direction. Default is 1400.
      ysize = plot size of y direction. Default is 700.

    EXAMPLE:
       uspec_coh, tplot1, tplot2

    CODE:
    R. Hamaguchi, 15/01/2013.

    MODIFICATIONS:
    A. Shinbori, 31/01/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/uspec_coh.pro)

## USTRANS_PWRSPC

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    PROCEDURE:
     ustrans_pwrspc, varname, newname = newname

    PURPOSE:
     Calculate the local power spectrum for given time-series data and return the structure
     which contains {st:, ph: freq:, time:} where st is the S Transform and
       store the tplot variable.

    INPUT:
     varname = variable passed to get_data, example - uts_mag_ccnv

    KEYWORDS:
     newname: set output variable name
     \help               explains all the keywords and parameters
     \verbose            flags errors and size
     \samplingrate       if set returns array of frequency
     \maxfreq            maximum frequency performing the S transform
     \minfreq            minimum frequency performing the S transform
     \freqsmplingrate    frequency interval
     \power              returns the power spectrum
     \abs                returns the absolute value spectrum
     \Rremoveedge        removes the edge with a 5% taper, and takes out least-sqares fit parabola

    HISTORY:
     14-aug-2012, Atsuki Shinbori
    $LastChangedBy: nikos $
    $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
    $LastChangedRevision: 25538 $
    $URL: svn+ssh://thmsvn@ambrosia.ssl.berkeley.edu/repos/spdsoft/trunk/projects/iugonet/tools/statistical_package/ustrans_pwrspc.pro $

(See projects/iugonet/tools/statistical_package/ustrans_pwrspc.pro)

## UTREND_TEST

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    NAME:
    utrend_test

    PURPOSE:
    Test whether there is a significant trend of time-serise data or not.

    SYNTAX:
    utrend_test,vname1,sl=sl

    KEYWORDS:
    sl:significant level (Default is 0.05)

    CODE:
    R. Hamaguchi, 17/01/2013.

    MODIFICATIONS:
    A. Shinbori, 01/05/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/utrend_test.pro)

## WELCH_TEST

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    NAME:
      welch_test
    PURPOSE:
      Test whether two pairs of average value of time series data is the same or.
      It is assumed that both distibutions of the data sets are normal distribution
      and have different variance.

    SYNTAX:
      result=Welch_test(x,y,sl=sl,mv=mv)

    KEYWORDS:
      sl:Significant level.
         The default is 0.05.
      mv:Missing value.
         If not set, Only the NaN value is dealt with.
      z:Statistical test value
      t_sl:Critical value of t-distribution in the significant level.

    NOTES:
      The test result is output as a value of 1 and 0 if the average value is the same
      and different, respectively.

    CODE:
     R. Hamaguchi, 13/12/2012.

    MODIFICATIONS:
     A. Shinbori, 01/05/2013.
     A. Shinbori, 10/07/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/welch_test.pro)

## UDIFFERENCE_TEST

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    NAME:
    　　udifference_test

    PURPOSE:
      Perform the difference test for two pairs of time-series data sets and
      test the fit of a normal distribution by χ-square test
      If both data sets obey the normal distribution, the Welch test is applied.
      If both data sets do not obey the normal distribution,
      only the Mann-Whitney test is used.

    SYNTAX:
      difference_test,vname1,vname2,sl=sl,test_sel=test_sel

    KEYWORDS:
      result:Test result.
             The values '0' and '1' mean that the judgement of the Welch test is different
             and same, respectively. Moreover, the values '2' and '3' mean that the judgement
             of the Mann-Whitney test is different and same, respectively.
      sl:Significant level.
         The default is 0.05.
      test_sel：Specify the test to be performed. The value '2' is the Mann-Whitney test,
               '1' is the Welch test, and '0' is to test the fit of a normal distribution
               by χ-square test

    CODE:
    R. Hamaguchi, 13/02/2012.

    MODIFICATIONS:
    A. Shinbori, 01/05/2013.
    A. Shinbori, 10/07/2013.

    ACKNOWLEDGEMENT:
     $LastChangedBy: nikos $
     $LastChangedDate: 2018-08-01 11:03:38 -0700 (Wed, 01 Aug 2018) $
     $LastChangedRevision: 25538 $
     $URL $

(See projects/iugonet/tools/statistical_package/udifference_test.pro)