C2Functions know how to keep track of the first and second derivatives of functions, and to use this information in, for example, C2Function.find_root() and C2Function.partial_integrals() to allow much more efficient solutions to problems for which the general solution may be expensive.
The two primary classes are C2Function which represents an unevaluated function and its derivatives, and InterpolatingFunction which represent a cubic spline of provided data.
C2Functions can be combined with unary operators (nested/composed functions) or binary operators (+-*/ etc.)
Note that if SciPy is available, the C2Functions package will adopt useful bits from it to speed things up, but is otherwise not dependent on it.
Developed by Marcus H. Mendenhall, Vanderbilt University Keck Free Electron Laser Center, Nashville, TN USA
email: mendenhall@users.sourceforge.net
Work supported by the US DoD MFEL program under grant FA9550-04-1-0045
Classes | |
| class | C2Exception |
| Our own exception class. More... | |
| class | RangeError |
| Raised if an abscissa is out of range. More... | |
| class | C2NakedFunction |
| Raised if the base class C2Function is called without a valid value_with_derivatives(). More... | |
| class | C2Function |
| Provides support for the entire C2Function hierarchy. More... | |
| class | C2ScaledFunction |
| Create a function which is a simple scalar multiple of the parent. More... | |
| class | C2Constant |
| Create a function which is a constant. More... | |
| class | _fC2sin |
| Create a function which is the sine. Use the singleton C2Functions.C2sin to access this. More... | |
| class | _fC2cos |
| Create a function which is the cosine. Use the singleton C2Functions.C2cos to access this. More... | |
| class | _fC2log |
| Create a function which is the natural log. Use the singleton C2Functions.C2log to access this. More... | |
| class | _fC2exp |
| Create a function which is the e^x. Use the singleton C2Functions.C2exp to access this. More... | |
| class | _fC2sqrt |
| Create a function which is the square root. Use the singleton C2Functions.C2sqrt to access this. More... | |
| class | C2ScaledRecip |
| Create a function which is the scale /x. Use the singleton C2Functions.C2recip to access this as 1/x. More... | |
| class | _fC2identity |
| Create a function which is x. Use the singleton C2Functions.C2identity to access this. More... | |
| class | C2Linear |
| Create a function which is (x - x0)*slope + y0. More... | |
| class | C2Quadratic |
| Create a function which is a *(x - x0)**2 + b *(x - x0) + c. More... | |
| class | C2PowerLaw |
| Create a function which is ax**b. More... | |
| class | C2Polynomial |
| Create a function which is c0 + c1 (x-x0) + c2 (x-x0)^2 + ... More... | |
| class | C2ComposedFunction |
| create a composed function outer(inner(...)). The functions can either be unbound class names or class instances More... | |
| class | C2BinaryFunction |
| abstract class to create a binary function f (operator) g More... | |
| class | C2Sum |
| class to create function f + g More... | |
| class | C2Diff |
| class to create function f - g More... | |
| class | C2Product |
| class to create function f * g More... | |
| class | C2Ratio |
| class to create function f / g More... | |
| class | C2Power |
| class to create function f ** g with optimization if g is a constant More... | |
| class | InterpolatingFunction |
| the parent class for various interpolators. Does untransformed cubic splines by default. More... | |
| class | LogLinInterpolatingFunction |
| An InterpolatingFunction which stores log(x) vs. y. More... | |
| class | LinLogInterpolatingFunction |
| An InterpolatingFunction which stores x vs. log(y). More... | |
| class | LogLogInterpolatingFunction |
| An InterpolatingFunction which stores log(x) vs. log(y). More... | |
| class | AccumulatedHistogram |
| class | LogLogAccumulatedHistogram |
| class | InverseIntegratedDensity |
| class | LinLogInverseIntegratedDensity |
| class | C2InverseFunction |
| class | C2ConnectorFunction |
| class | C2LHopitalRatio |
Functions | |
| def | native |
| def | _spline |
| solve for the spline coefficients y'' | |
| def | _spline_extension |
| compute the correct coefficients and insert them to allow spline extrapolation | |
| def | _splint |
| compute the interpolated value for a set of spline coefficients and either a scalar x or an array of x values | |
| def | _identity |
| def | _one |
| def | _zero |
| def | _recip |
| def | _mrecip2 |
| def | _myexp |
| def | _mylog |
| def | LinearInterpolatingGrid |
| legacy... | |
| def | LogLogInterpolatingGrid |
| legacy... | |
| def | as |
| def | bessj |
| def | bessj_adaptive |
Variables | |
| string | _rcsid = "$Id: C2Functions.py,v 1.66 2007/11/21 16:18:00 mendenhall Exp $" |
| _numeric_float = _numeric.float64 | |
| tuple | C2sin = _fC2sin() |
| a pre-constructed singleton | |
| tuple | C2cos = _fC2cos() |
| a pre-constructed singleton | |
| tuple | C2log = _fC2log() |
| a pre-constructed singleton | |
| tuple | C2exp = _fC2exp() |
| a pre-constructed singleton | |
| tuple | C2sqrt = _fC2sqrt() |
| a pre-constructed singleton | |
| tuple | C2recip = C2ScaledRecip() |
| a pre-constructed singleton for 1/x | |
| tuple | C2identity = _fC2identity() |
| a pre-constructed singleton identity | |
| _has_linalg = True | |
| LogConversions = _mylog,_recip,_mrecip2,_myexp | |
| tuple | ag = ag1LinearInterpolatingGrid(1, 1.0,4) |
| tuple | ag13 = (ag1*ag1) |
| tuple | fn = C2sin(C2sqrt(ag1*ag1*ag1)) |
| tuple | x1 = fn.find_root(0.0, 1.35128, 0.1, 0.995, trace=True) |
| float | x = 0.1 |
| tuple | sna = C2sin(C2PowerLaw(1,2)) |
| tuple | xg = _numeric.array(range(sample), _numeric_float) |
| tuple | partials = sna.partial_integrals(xg) |
| tuple | sumsum = sum(partials) |
| tuple | yg = sna(xg) |
| tuple | simp = sum(sna.partial_integrals(xg, derivs=1)) |
| float | exact = 0.804776489343756110 |
| int | pc = 3 |
| tuple | b = math.exp(lv) |
| tuple | np = int(pc*b) |
| tuple | g = _numeric.array(range(np), _numeric_float) |
| tuple | v0 = C2recip.partial_integrals(g, allow_recursion=False) |
| n0 = C2recip.total_func_evals | |
| tuple | v1 |
| n1 = C2recip.total_func_evals | |
| tuple | v2 |
| n2 = C2recip.total_func_evals | |
| tuple | v3 |
| n3 = C2recip.total_func_evals | |
| tuple | yy = _numeric.exp(-xg[:-1]*xg[:-1]) |
| tuple | ah = AccumulatedHistogram(xg[::-1], yy[::-1], normalize=True) |
| tuple | ahi = AccumulatedHistogram(xg, yy, normalize=True, inverse_function=True) |
| tuple | xv = _numeric.array([1.5**(0.1*i) for i in range(100)]) |
| tuple | yv = _numeric.array([x**(-4)+0.25*x**(-3) for x in xv]) |
| tuple | f |
| tuple | f0 = C2PowerLaw(1., -4) |
| tuple | pp = f0.partial_integrals(_numeric.array(range(11), _numeric_float)*0.1 + 20) |
| list | energies = [float(2**(0.5*n)) for n in range(41)] |
| list | spect = [10000.0/(e*e) for e in energies] |
| list | e0 = energies[-1] |
| list | e1 = energies[0] |
| tuple | pf = LinLogInverseIntegratedDensity(energies[::-1], spect[::-1]) |
| tuple | r = (0.025*i) |
| tuple | mma = (e0*e1) |
| tuple | grid = (0., 3., 6., 9., 12.) |
| tuple | v = fn.GetSamplingGrid(xmin,xmax) |
| tuple | sn = fn.NormalizedFunction(0., math.pi) |
| tuple | gn = fn.SquareNormalizedFunction(0., 4.0*math.pi) |
| fn2 = fn*fn | |
| gn2 = gn*gn | |
| tuple | myexp = _fC2exp() |
| tuple | a = C2InverseFunction(myexp) |
1.5.4