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# 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
################################################################################
# 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
################################################################################
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
# 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.
# 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)
# 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)
# 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)
# FUNCTION:
# Compute ramp:
result = (x-a) * Heaviside(x-a)
# Return Value:
result
}
################################################################################
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