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# Directory Listing of Routines

# projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum

- CROSS_SPEC
  This function estimates the power cross-spectrum of two vectors.
- DIMENSION
  This function returns the dimension of an array. It returns 0
- FILTER
  This function returns a smoothed version of the input vector.
- FILTER_WINDOW
  This function returns a desired filter window of desired width.
- PLUS
  This function returns 1 if the input is positive, 0 otherwise.
- TEST_CROSS_SPEC

# Routine Descriptions

## CROSS_SPEC

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     NAME:
     cross_spec

     PURPOSE:
     This function estimates the power cross-spectrum of two vectors.

     CATEGORY:
     Time Series Analysis

     CALLING SEQUENCE:
     Result = cross_spec(Y1, Y2)

     INPUTS:
     Y1:  A floating point vector of the same length as Y2.
     Y2:  A floating point vector of the same length as Y1.

     OPTIONAL INPUTS:
     -
     DELTAT, WIDTH, WINDOW

     KEYWORD PARAMETERS:
     AMPLITUDE:  Returns the amplitude component of the cross-spectrum.
     AUTOSPEC1:  Returns the auto-spectrum of Y1.
     AUTOSPEC2:  Returns the auto-spectrum of Y2.
     COHERENCY:  Returns the coherency of Y1 and Y2.
     DELTAT:  The time interval between values in the input vectors.
     DOUBLE:  If set the calculations are performed in double precision
       arithmetic.  The default is single precision.
     FREQ:  Returns the frequency values corresponding to the output
       cross-spectrum.
     PHASE:  Returns the phase component of the cross-spectrum, in radians.
       Positive values mean that Y1 is leading Y2 at that frequency.
     WIDTH:  The width, of type integer, of the smoothing window to be used
       by FILTER.pro.  If not given then no smoothing is performed.
     WINDOW:  A string containing the name of the smoothing window to be
       used by FILTER.pro.  Smoothing is only performed if WIDTH is
       given.

     OUTPUTS:
     Result:  Returns the cross-spectrum.
     AMPLITUDE, AUTOSPEC1, AUTOSPEC2, COHERENCY, FREQ, PHASE

     USES:
     FILTER.pro

     PROCEDURE:
     This function uses the FFT function to estimate the spectra.

     EXAMPLE:
     Create two time series of a periodic signal of period 23 and phase
     difference pi/2.  Add a pinch of noise.
       y1 = sin(6.28*findgen(1000)/23.)+0.1*randomn(1, 1000)
       y2 = sin(6.28*(findgen(1000)/23.-0.25)) $
           +0.1*randomn(2, 1000)
     Estimate the cross-spectrum.
       result = cross_spec(y1, y2, amplitude=amplitude, phase=phase, freq=freq)
     The amplitude power spectrum should have a peak at freq=1./23., and
     the phase at that frequency should be 0.5.

    CODE:
     A. Shinbori, 30/09/2011.

    MODIFICATIONS:
     A. Shinbori, 30/10/2011

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

(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/cross_spec.pro)

## DIMENSION

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     NAME:
     dimension

     PURPOSE:
     This function returns the dimension of an array.  It returns 0
     if the input variable is scalar.

     CATEGORY:
     Array

     CALLING SEQUENCE:
     Result = DIMENSION(Inarray)

     INPUTS:
     Inarray:  A scalar or array of any type.

     OUTPUTS:
     Result:  The dimension of Inarray.  Returns 0 if scalar.

     PROCEDURE:
     This function runs the IDL function SIZE.

     EXAMPLE:
     Define a 3*4-element array.
       x = findgen(3,4)
     Calculate the dimension of x.
       result = dimension(x)

    MODIFICATIONS:
     A. Shinbori, 30/10/2011

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

(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/dimension.pro)

## FILTER

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     NAME:
     filter

     PURPOSE:
     This function returns a smoothed version of the input vector.

     CATEGORY:
     Time Series Analysis

     CALLING SEQUENCE:
     Result = FILTER( Vector, [Width], [Window] )

     INPUTS:
     Vector:  An vector of type floating point and length N.

     OPTIONAL INPUTS:
     Width:  The width, of type integer, of the smoothing window.
     Window:  A string containing the name of the smoothing window to
       return.  Options are 'boxcar', 'gaussian', 'hanning',
       'triangle'.  The default is a boxcar window.

     KEYWORD PARAMETERS:
     BOXCAR:  Sets the smoothing window to a boxcar filter.  This is
       the default.  If set to a value, it replaces Width.
     EDGE_TRUNCATE:  Set this keyword to apply the smoothing to all points.
       If the neighbourhood around a point includes a point outside
       the array, the nearest edge point is used to compute the
       smoothed result.  If EDGE_TRUNCATE is not set, the points near
       the end are replaced with NaNs.
     FILTER:  A vector containing the filter window to use.  This overrides
       the window requested in the Window input.  This also returns
       the filter after use.
     NAN:  Set this keyword to ignore NaN values in the input array,
       provided there is at least one defined value nearby.  The
       default is to return NaNs wherever they occur.
     NO_NAN:  Obsolete version of NAN keyword retained for compatibility
       but no longer used.
     START_INDEX:  The location of the centre of the window for the first
       averaged output value, in units of Vector indices.  Values must
       be greater than 0.  The default is 0.
     STEP:  An integer defining the step size for window translation, in
       units of Vector indices.  The default is 1.
     TRIANGLE:  Sets the smoothing window to a triangle filter.  The default
       is a boxcar filter.  If set to a value, it replaces Width.
     WRAP_EDGES:  If set, the vector is treated as being cyclic and the
       ends are joined together when smoothing.

     OUTPUTS:
     Result:  Returns the smoothed version of Vector.

     USES:
     dimension.pro
     filter_window.pro
     plus.pro

     PROCEDURE:
     This function manually convolves the input vector with the filter.

     EXAMPLE:
           Create a vector of daily data and a sinusoid for a year.
       x = randomn( seed, 365 ) + sin( 6.28 * findgen( 365 ) / 365. )
     Smooth x with a boxcar filter of 7 days, wrapping the edges together.
       result = filter( x, 7, 'boxcar', /wrap_edges )

    CODE:
     A. Shinbori, 30/09/2011.

    MODIFICATIONS:
     A. Shinbori, 30/10/2011

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

(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/filter.pro)

## FILTER_WINDOW

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     NAME:
     filter_window

     PURPOSE:
     This function returns a desired filter window of desired width.

     CATEGORY:
     Time Series Analysis

     CALLING SEQUENCE:
     Result = filter_window([Width],[Window])

     OPTIONAL INPUTS:
     Width:  The width of the filter window, of type integer.
     Window:  A string containing the name of the smoothing window to
       return.  Options are 'boxcar', 'gaussian', 'hanning',
       'triangle'.  The default is a boxcar window.

     KEYWORD PARAMETERS:
     BOXCAR:  Sets the output to a boxcar window.  This is the default.
       If set to a value, it replaces Width (obsolete option).
     DIMENSION:  The dimension of the filter, of type integer.  The default
       is 1.
     TRIANGLE:  Sets the output to a triangle window.  The default is a
       boxcar window. If set to a value, it replaces Width (obsolete
       option).

     OUTPUTS:
     Result:  Returns the desired filter window.

     PROCEDURE:
     This function builds a filter of the desired shape and width, and then
     normalises it.

     EXAMPLE:
     Define a two dimensional boxcar window of width 5.
       result = filter_window( 5, 'boxcar', dimension=2 )
     result should be a 5x5 matrix with 0.04 for all entries.

    CODE:
     A. Shinbori, 30/09/2011.

    MODIFICATIONS:
     A. Shinbori, 30/10/2011

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

(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/filter_window.pro)

## PLUS

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     NAME:
     plus

     PURPOSE:
     This function returns 1 if the input is positive, 0 otherwise.

     CATEGORY:
     Mathematics

     CALLING SEQUENCE:
     Result = PLUS( Y )

     INPUTS:
     Y:  A scalar or array of type integer or floating point.

     OUTPUTS:
     Result:  Returns 1 if Y is positive, 0 otherwise.

     PROCEDURE:
     This function determines whether Y is greater than 0.

     EXAMPLE:
     Determine if 3 is positive.
       result = plus( 3 )

    CODE:
     A. Shinbori, 30/09/2011.

    MODIFICATIONS:
     A. Shinbori, 30/10/2011

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

(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/plus.pro)

## TEST_CROSS_SPEC

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    PROCEDURE: TEST_CROSS_SPEC.PRO
        A sample crib sheet that explains how to use the "cross_spec.pro"
        procedure. You can run this crib sheet.
        Or alternatively compile and run using the command:
            .run test_cross_spec

    Written by: A. Shinbori,  May 01, 2013
    Last Updated: A. Shinbori,  May 01, 2013

(See projects/iugonet/tools/statistical_package/coherence_analysis/cross_spectrum/test_cross_spec.pro)