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View of /pkg/fEcofin/R/3F-HeavisideFunction.R

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Revision 1235 - (download) (annotate)
Tue Feb 27 22:19:33 2007 UTC (7 years, 4 months ago) by wuertz
File size: 6285 byte(s)
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General 
# Public License along with this library; if not, write to the 
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston, 
# MA  02111-1307  USA

# Copyrights (C)
# for this R-port: 
#   1999 - 2007, Diethelm Wuertz, GPL
#   Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
#   info@rmetrics.org
#   www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
#   see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
#   see Rmetrics's copyright file


################################################################################
# FUNCTION:             HEAVISIDE AND RELATED FUNCTIONS:
#  Heaviside             Computes Heaviside unit step function
#  Sign                  Another signum function
#  Delta                 Computes delta function
#  Boxcar                Computes boxcar function
#  Ramp                  Computes ramp function
#  .heavisideSlider      Displays Heaviside and related functions
################################################################################


Heaviside = 
function(x, a = 0) 
{   # A function implemented by Diethelm Wuertz

    # Description:
    #   Computes the Heaviside or unit step function.
    
    # Arguments:
    #   x - a numeric vector.
    #   a - the location of the break.
    
    # Details:
    #   The Heaviside step function is 1 for x>a, 1/2 for x=a,
    #   and 0 for x<a.
    
    # Notes:
    #   Heaviside Unit Step Function and Related Functions
    #   See:  http://mathworld.wolfram.com/HeavisideStepFunction.html
    #   Note: sign(x) is part of R's base package
    
    # Changes:
    #
    
    # FUNCTION:
    
    # Compute H:
    result = (sign(x-a) + 1)/2
    
    # Return Value:
    result
}


# ------------------------------------------------------------------------------


Sign =
function(x, a = 0) 
{   # A function implemented by Diethelm Wuertz

    # Description:
    #   Computes the (modofied) Sign function.
    
    # Arguments:
    #   x - a numeric vector.
    #   a - the location of the break.
    
    # Details:
    #   The Sign function is 1 for x>a, 0 for x=a,
    #   and -1 for x<a.
    
    # Changes:
    #
    
    # FUNCTION:
    
    # Compute Sign:
    result = sign(x-a)
    
    # Return Value:
    result
}


# ------------------------------------------------------------------------------


Delta = 
function(x, a = 0) 
{   # A function implemented by Diethelm Wuertz

    # Description:
    #   Computes the delta function.
    
    # Arguments:
    #   x - a numeric vector.
    #   a - the location of the break.
    
    # Details:
    #   The delta function is defined as: delta(x) = d/dx Heaviside(x-a)
    
    # Changes:
    #
    
    # FUNCTION:
    
    # Compute delta:
    result = 1/sign(abs(x-a))-1
    
    # Return Value:
    result
}


# ------------------------------------------------------------------------------


Boxcar =
function(x, a = 0.5) 
{   # A function implemented by Diethelm Wuertz

    # Description:
    #   Computes the boxcar function.
    
    # Arguments:
    #   x - a numeric vector.
    #   a - the location of the break.
    
    # Details:
    #   The boxcar function is defined as: 
    #       Pi(x) = Heaviside(x+a) - Heaviside(x-a)
    
    # Changes:
    #
    
    # FUNCTION:
    
    # Compute boxcar:
    result = Heaviside(x-a) - Heaviside(x+a)
    
    # Return Value:
    result
}


# ------------------------------------------------------------------------------


Ramp =
function(x, a = 0) 
{   # A function implemented by Diethelm Wuertz

    # Description:
    #   Computes the ramp function.
    
    # Arguments:
    #   x - a numeric vector.
    #   a - the location of the break.
    
    # Details:
    #   The ramp function is defined as: R(x)= (x-a)*Heaviside(x-a)
    
    # Changes:
    #
    
    # FUNCTION:
    
    # Compute ramp:
    result = (x-a) * Heaviside(x-a)
    
    # Return Value:
    result
}


# ------------------------------------------------------------------------------


.heavisideSlider =
function()
{   # A function implemented by Diethelm Wuertz

    # Description
    #   Displays Heaviside and related functions
    
    # Changes:
    #
    
    # FUNCTION:
    
    # Internal Function:
    refresh.code = function(...)
    {
        # Sliders:
        a = .sliderMenu(no = 1)
        by = .sliderMenu(no = 2)
        
        # Frame:
        par(mfrow = c(2, 2), cex = 0.7)
        
        # FGN TimeSeries:
        x = seq(-10, 10, by = by)
        H  = Heaviside(x, a)
        Sign  = Sign(x, a)
        Delta  = Delta(x, a)
        Boxcar  = Boxcar(x, a)
        Ramp  = Ramp(x, a)
        plot(x, H, type = "b", ylim = c(-1, 1), 
            col = "steelblue", pch = 19)
        title(main = paste("Heaviside | a =", a))
        grid()
        plot(x, Sign, type = "b", ylim = c(-1, 1), 
            col = "steelblue", pch = 19)
        title(main = paste("Sign | a =", a))
        grid()
        plot(x, Boxcar, type = "b", ylim = c(-1, 1), 
            col = "steelblue", pch = 19)
        title(main = paste("Boxcar | a =", a))
        grid()
        plot(x, Ramp, type = "b", 
            col = "steelblue", pch = 19)
        title(main = paste("Ramp | a =", a))
        grid()
        
        # Reset Frame:
        par(mfrow = c(1, 1), cex = 0.7)
    }
  
    # Open Slider Menu:
    .sliderMenu(refresh.code,
       names =       c(  "a", "by"),
       minima =      c(  -10,  0.1),
       maxima =      c(   10,  1.0),
       resolutions = c(  0.1,  0.1),
       starts =      c(    0,  0.2))
}


################################################################################


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