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QuickStart Samples

Piecewise Curves QuickStart Sample (IronPython)

Illustrates working with piecewise constant and piecewise linear curves using classes from the Extreme.Mathematics.Curves namespace in IronPython.

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import numerics

from System import Array

# The piecewise curve classes reside in the 
# Extreme.Mathematics.Curves namespace.
from Extreme.Mathematics.Curves import *
from Extreme.Mathematics import *

# Illustrates the use of the PiecewiseConstantCurve and
# PiecewiseLinearCurve classes.

# A piecewise curve is a curve that has a different definition
# on subintervals of its domain.
# 
# This QuickStart Sample illustrates constant and linear piecewise
# curves, which - as the name suggest - are constant or linear
# on each interval.
#
# For an example of cubic splines, see the CubicSplines QuickStart 
# Sample.
#

# 
# Piecewise constants
#

# All piecewise curves inherit from the PiecewiseCurve class.
# Piecewise constant curves are implemented by the
# PiecewiseConstantCurve class. It has three constructors.

# The first constructor takes two double arrays as parameters.
# These contain the x and y values of the data points:
xValues = Array[float]([1, 2, 3, 4, 5, 6])
yValues = Array[float]([1, 3, 4, 3, 4, 2])
constant1 = PiecewiseConstantCurve(xValues, yValues)

# The second constructor takes two Vector objects, containing the
# x and y-values of the data points:
xVector = Vector.Create(xValues)
yVector = Vector.Create(yValues)
constant2 = PiecewiseConstantCurve(xVector, yVector)

# The third constructor only takes one parameter: an array of
# Point structures that represent the data point.
dataPoints = Array[Point]([Point(1, 1), Point(2, 3), Point(3, 4), Point(4, 3), Point(5, 4), Point(6, 2) ])
constant3 = PiecewiseConstantCurve(dataPoints)

#
# Curve Parameters
#

# The shape of any curve is determined by a set of parameters.
# These parameters can be retrieved and set through the
# Parameters collection. The number of parameters for a curve 
# is given by this collection's Count property.
#
# Piecewise constant curves have 2n parameters, where n is the number of
# data points. The first n parameters are the x-values. The next
# n parameters are the y-values.

print "constant1.Parameters.Count =", constant1.Parameters.Count
# Parameters can easily be retrieved:
print "constant1.Parameters[0] =", constant1.Parameters[0]
# Parameters can also be set:
constant1.Parameters[0] = 1

#
# Curve Methods
#

# The ValueAt method returns the y value of the
# curve at the specified x value:
print "constant1.ValueAt(2.4) =", constant1.ValueAt(2.4)

# The SlopeAt method returns the slope of the curve
# a the specified x value:
print "constant1.SlopeAt(2.4) =", constant1.SlopeAt(2.4)
# The slope at the data points is Double.NaN if the value of the constant
# is different on either side of the data point:
print "constant1.SlopeAt(2) =", constant1.SlopeAt(2)

# Piecewise constant curves do not have a defined derivative. 
# The GetDerivative method returns a GeneralCurve:
derivative = constant1.GetDerivative()
print "Type of derivative:", derivative.GetType().ToString()
print "derivative(2.4) =", derivative.ValueAt(2.4)

# You can get a Line that is the tangent to a curve
# at a specified x value using the TangentAt method:
tangent = constant1.TangentAt(2.4)
print "Slope of tangent line at 2.4 =", tangent.Slope

# The integral of a piecewise constant curve can be calculated exactly. 
print "Integral of constant1 between 1.4 and 4.6 =", constant1.Integral(1.4, 4.6)


# 
# Piecewise linear curves
#

# Piecewise linear curves are used for linear interpolation
# between data points. They are implemented by the
# PiecewiseLinearCurve class. It has three constructors, # similar to the constructors for the PiecewiseLinearCurve
# class..These constructors create the linear interpolating
# curve between the data points.

# The first constructor takes two double arrays as parameters.
# These contain the x and y values of the data points:
xValues2 = Array[float]([ 1, 2, 3, 4, 5, 6 ])
yValues2 = Array[float]([1, 3, 4, 3, 4, 2 ])
line1 = PiecewiseLinearCurve(xValues2, yValues2)

# The second constructor takes two Vector objects, containing the
# x and y-values of the data points:
xVector2 = Vector.Create(xValues2)
yVector2 = Vector.Create(yValues2)
line2 = PiecewiseLinearCurve(xVector2, yVector2)

# The third constructor only takes one parameter: an array of
# Point structures that represent the data point.
dataPoints2 = Array[Point]([ \
    Point(1, 1), Point(2, 3), Point(3, 4), \
    Point(4, 3), Point(5, 4), Point(6, 2) ])
line3 = PiecewiseLinearCurve(dataPoints)

#
# Curve Parameters
#

# Piecewise linear curves have 2n parameters, where n is the number of
# data points. The first n parameters are the x-values. The next
# n parameters are the y-values.

print "line1.Parameters.Count =", line1.Parameters.Count
# Parameters can easily be retrieved:
print "line1.Parameters[0] =", line1.Parameters[0]
# Parameters can also be set:
line1.Parameters[0] = 1

#
# Curve Methods
#

# The ValueAt method returns the y value of the
# curve at the specified x value:
print "line1.ValueAt(2.4) =", line1.ValueAt(2.4)

# The SlopeAt method returns the slope of the curve
# a the specified x value:
print "line1.SlopeAt(2.4) =", line1.SlopeAt(2.4)
# The slope at the data points is Double.NaN if the slope of the line
# is different on either side of the data point:
print "line1.SlopeAt(2) =", line1.SlopeAt(2)

# Piecewise line curves do not have a defined derivative. 
# The GetDerivative method returns a GeneralCurve:
derivative = line1.GetDerivative()
print "Type of derivative:", derivative.GetType().ToString()
print "derivative(2.4) =", derivative.ValueAt(2.4)

# You can get a Line that is the tangent to a curve
# at a specified x value using the TangentAt method:
tangent = line1.TangentAt(2.4)
print "Slope of tangent line at 2.4 =", tangent.Slope

# The integral of a piecewise line curve can be calculated exactly. 
print "Integral of line1 between 1.4 and 4.6 =", line1.Integral(1.4, 4.6)