Author: eudoxos
Date: 2009-01-17 23:26:54 +0100 (Sat, 17 Jan 2009)
New Revision: 1626
Added:
trunk/gui/py/linterpolation.py
Modified:
trunk/gui/SConscript
Log:
1. Add a few functions for integrating piecewise-linear functions in new module
yade.linterpolation
Modified: trunk/gui/SConscript
===================================================================
--- trunk/gui/SConscript 2009-01-15 05:17:58 UTC (rev 1625)
+++ trunk/gui/SConscript 2009-01-17 22:26:54 UTC (rev 1626)
@@ -79,6 +79,7 @@
env.File('runtime.py','py'),
env.File('ipython.py','py'),
env.File('plot.py','py'),
+ env.File('linterpolation.py','py'),
env.File('PythonTCPServer.py','py'),
])
Added: trunk/gui/py/linterpolation.py
===================================================================
--- trunk/gui/py/linterpolation.py 2009-01-15 05:17:58 UTC (rev 1625)
+++ trunk/gui/py/linterpolation.py 2009-01-17 22:26:54 UTC (rev 1626)
@@ -0,0 +1,97 @@
+# encoding: utf-8
+#
+# © 2009 Václav Šmilauer <[email protected]>
+#
+
+"""
+Module for rudimentary support of manipulation with piecewise-linear
+functions (which are usually interpolations of higher-order functions,
+whence the module name). Interpolation is always given as two lists
+of the same length, where the x-list must be increasing.
+
+Periodicity is supported by supposing that the interpolation
+can wrap from the last x-value to the first x-value (which
+should be 0 for meaningful results).
+
+Non-periodic interpolation can be converted to periodic one
+by padding the interpolation with constant head and tail using
+the sanitizeInterpolation function.
+
+There is a c++ template function for interpolating on such sequences in
+pkg/common/Engine/DeusExMachina/LinearInterpolate.hpp (stateful, therefore
+fast for sequential reads).
+
+TODO: Interpolating from within python is not (yet) supported.
+"""
+
+def revIntegrateLinear(I,x0,y0,x1,y1):
+ """Helper function, returns value of integral variable x for
+ linear function f passing through (x0,y0),(x1,y1) such that
+ 1. x∈[x0,x1]
+ 2. ∫_x0^x f dx=I
+ and raise exception if such number doesn't exist or the solution
+ is not unique (possible?)
+ """
+ from math import sqrt
+ dx,dy=x1-x0,y1-y0
+ if dy==0: # special case, degenerates to linear equation
+ return (x0*y0+I)/y0
+ a=dy/dx; b=2*(y0-x0*dy/dx); c=x0**2*dy/dx-2*x0*y0-2*I
+ det=b**2-4*a*c; assert(det>0)
+ p,q=(-b+sqrt(det))/(2*a),(-b-sqrt(det))/(2*a)
+ pOK,qOK=x0<=p<=x1,x0<=q<=x1
+ if pOK and qOK: raise ValueError("Both radices within interval!?")
+ if not pOK and not qOK: raise ValueError("No radix in given interval!")
+ return p if pOK else q
+
+def integral(x,y):
+ """Return integral of piecewise-linear function given by points
+ x0,x1,… and y0,y1,… """
+ assert(len(x)==len(y))
+ sum=0
+ for i in range(1,len(x)): sum+=(x[i]-x[i-1])*.5*(y[i]+y[i-1])
+ return sum
+
+def xFractionalFromIntegral(integral,x,y):
+ """Return x within range x0…xn such that ∫_x0^x f dx==integral.
+ Raises error if the integral value is not reached within the x-range.
+ """
+ sum=0
+ for i in range(1,len(x)):
+ diff=(x[i]-x[i-1])*.5*(y[i]+y[i-1])
+ if sum+diff>integral:
+ return
revIntegrateLinear(integral-sum,x[i-1],y[i-1],x[i],y[i])
+ else: sum+=diff
+ raise "Integral not reached within the interpolation range!"
+
+
+def xFromIntegral(integralValue,x,y):
+ """Return x such that ∫_x0^x f dx==integral.
+ x wraps around at xn. For meaningful results, therefore, x0 should == 0
"""
+ from math import floor
+ period=x[-1]-x[0]
+ periodIntegral=integral(x,y)
+ numPeriods=floor(integralValue/periodIntegral)
+
xFrac=xFractionalFromIntegral(integralValue-numPeriods*periodIntegral,x,y)
+ return period*numPeriods+xFrac
+
+def sanitizeInterpolation(x,y,x0,x1):
+ """Extends piecewise-linear function in such way that it spans at least
+ the x0…x1 interval, by adding constant padding at the beginning (using
y0)
+ and/or at the end (using y1) or not at all."""
+ xx,yy=[],[]
+ if x0<x[0]:
+ xx+=[x0]; yy+=[y[0]]
+ xx+=x; yy+=y
+ if x1>x[-1]:
+ xx+=[x1]; yy+=[y[-1]]
+ return xx,yy
+
+if __name__=="main":
+ xx,yy=sanitizeInterpolation([1,2,3],[1,1,2],0,4)
+ print xx,yy
+ print integral(xx,yy) # 5.5
+ print revIntegrateLinear(.625,1,1,2,2) # 1.5
+ print xFractionalFromIntegral(1.625,xx,yy) # 1.625
+ print xFractionalFromIntegral(2.625,xx,yy) # 2.5
+
_______________________________________________
Mailing list: https://launchpad.net/~yade-dev
Post to : [email protected]
Unsubscribe : https://launchpad.net/~yade-dev
More help : https://help.launchpad.net/ListHelp
