[Scipy-svn] r2219 - in trunk/Lib: integrate interpolate optimize
scipy-svn at scipy.org
scipy-svn at scipy.org
Sat Sep 23 17:56:54 EDT 2006
Author: rkern
Date: 2006-09-23 16:56:21 -0500 (Sat, 23 Sep 2006)
New Revision: 2219
Modified:
trunk/Lib/integrate/ode.py
trunk/Lib/integrate/odepack.py
trunk/Lib/integrate/quadpack.py
trunk/Lib/integrate/quadrature.py
trunk/Lib/interpolate/fitpack.py
trunk/Lib/interpolate/fitpack2.py
trunk/Lib/interpolate/info.py
trunk/Lib/optimize/anneal.py
trunk/Lib/optimize/cobyla.py
trunk/Lib/optimize/lbfgsb.py
trunk/Lib/optimize/minpack.py
trunk/Lib/optimize/optimize.py
trunk/Lib/optimize/tnc.py
trunk/Lib/optimize/zeros.py
Log:
Add cross-reference information to docstrings.
Modified: trunk/Lib/integrate/ode.py
===================================================================
--- trunk/Lib/integrate/ode.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/integrate/ode.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -118,6 +118,10 @@
return <f(t,y)>
def jac(t,y[,arg1,..]):
return <df/dy(t,y)>
+
+See also:
+ odeint - an integrator with a simpler interface based on lsoda from ODEPACK
+ quad - for finding the area under a curve
"""
def __init__(self,f,jac=None):
Modified: trunk/Lib/integrate/odepack.py
===================================================================
--- trunk/Lib/integrate/odepack.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/integrate/odepack.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -108,6 +108,9 @@
mxordn -- maximum order to be allowed for the nonstiff (Adams) method.
mxords -- maximum order to be allowed for the stiff (BDF) method.
+ See also:
+ ode - a more object-oriented integrator based on VODE
+ quad - for finding the area under a curve
"""
if ml is None:
Modified: trunk/Lib/integrate/quadpack.py
===================================================================
--- trunk/Lib/integrate/quadpack.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/integrate/quadpack.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -174,6 +174,13 @@
wopts -- Optional input for reusing Chebyshev moments.
maxp1 -- An upper bound on the number of Chebyshev moments.
+ See also:
+ dblquad, tplquad - double and triple integrals
+ fixed_quad - fixed-order Gaussian quadrature
+ quadrature - adaptive Gaussian quadrature
+ odeint, ode - ODE integrators
+ simps, trapz, romb - integrators for sampled data
+ scipy.special - for coefficients and roots of orthogonal polynomials
"""
if type(args) != type(()): args = (args,)
if (weight is None):
@@ -332,6 +339,14 @@
y -- the resultant integral.
abserr -- an estimate of the error.
+ See also:
+ quad - single integral
+ tplquad - triple integral
+ fixed_quad - fixed-order Gaussian quadrature
+ quadrature - adaptive Gaussian quadrature
+ odeint, ode - ODE integrators
+ simps, trapz, romb - integrators for sampled data
+ scipy.special - for coefficients and roots of orthogonal polynomials
"""
return quad(_infunc,a,b,(func,gfun,hfun,args),epsabs=epsabs,epsrel=epsrel)
@@ -372,5 +387,13 @@
y -- the resultant integral.
abserr -- an estimate of the error.
+ See also:
+ quad - single integral
+ dblquad - double integral
+ fixed_quad - fixed-order Gaussian quadrature
+ quadrature - adaptive Gaussian quadrature
+ odeint, ode - ODE integrators
+ simps, trapz, romb - integrators for sampled data
+ scipy.special - for coefficients and roots of orthogonal polynomials
"""
return dblquad(_infunc2,a,b,gfun,hfun,(func,qfun,rfun,args),epsabs=epsabs,epsrel=epsrel)
Modified: trunk/Lib/integrate/quadrature.py
===================================================================
--- trunk/Lib/integrate/quadrature.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/integrate/quadrature.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -29,11 +29,19 @@
val -- Gaussian quadrature approximation to the integral.
+ See also:
+
+ quad - adaptive quadrature using QUADPACK
+ dblquad, tplquad - double and triple integrals
+ romberg - adaptive Romberg quadrature
+ quadrature - adaptive Gaussian quadrature
+ romb, simps, trapz - integrators for sampled data
+ cumtrapz - cumulative integration for sampled data
+ ode, odeint - ODE integrators
"""
[x,w] = p_roots(n)
x = real(x)
- ainf, binf = map(isinf,(a,b))
- if ainf or binf:
+ ainf, binf = map(isinf,(a,b)) if ainf or binf:
raise ValueError, "Gaussian quadrature is only available for " \
"finite limits."
y = (b-a)*(x+1)/2.0 + a
@@ -83,6 +91,15 @@
val -- Gaussian quadrature approximation (within tolerance) to integral.
err -- Difference between last two estimates of the integral.
+ See also:
+
+ romberg - adaptive Romberg quadrature
+ fixed_quad - fixed-order Gaussian quadrature
+ quad - adaptive quadrature using QUADPACK
+ dblquad, tplquad - double and triple integrals
+ romb, simps, trapz - integrators for sampled data
+ cumtrapz - cumulative integration for sampled data
+ ode, odeint - ODE integrators
"""
err = 100.0
val = err
@@ -108,6 +125,17 @@
"""Cumulatively integrate y(x) using samples along the given axis
and the composite trapezoidal rule. If x is None, spacing given by dx
is assumed.
+
+ See also:
+
+ quad - adaptive quadrature using QUADPACK
+ romberg - adaptive Romberg quadrature
+ quadrature - adaptive Gaussian quadrature
+ fixed_quad - fixed-order Gaussian quadrature
+ dblquad, tplquad - double and triple integrals
+ romb, trapz - integrators for sampled data
+ cumtrapz - cumulative integration for sampled data
+ ode, odeint - ODE integrators
"""
y = asarray(y)
if x is None:
@@ -172,6 +200,17 @@
exact if the function is a polynomial of order 3 or less. If
the samples are not equally spaced, then the result is exact only
if the function is a polynomial of order 2 or less.
+
+ See also:
+
+ quad - adaptive quadrature using QUADPACK
+ romberg - adaptive Romberg quadrature
+ quadrature - adaptive Gaussian quadrature
+ fixed_quad - fixed-order Gaussian quadrature
+ dblquad, tplquad - double and triple integrals
+ romb, trapz - integrators for sampled data
+ cumtrapz - cumulative integration for sampled data
+ ode, odeint - ODE integrators
"""
y = asarray(y)
nd = len(y.shape)
@@ -231,6 +270,17 @@
"""Uses Romberg integration to integrate y(x) using N samples
along the given axis which are assumed equally spaced with distance dx.
The number of samples must be 1 + a non-negative power of two: N=2**k + 1
+
+ See also:
+
+ quad - adaptive quadrature using QUADPACK
+ romberg - adaptive Romberg quadrature
+ quadrature - adaptive Gaussian quadrature
+ fixed_quad - fixed-order Gaussian quadrature
+ dblquad, tplquad - double and triple integrals
+ simps, trapz - integrators for sampled data
+ cumtrapz - cumulative integration for sampled data
+ ode, odeint - ODE integrators
"""
y = asarray(y)
nd = len(y.shape)
@@ -361,6 +411,16 @@
the triangular array of the intermediate results will be printed.
If |vec_func| is True (default is False), then |function| is
assumed to support vector arguments.
+
+ See also:
+
+ quad - adaptive quadrature using QUADPACK
+ quadrature - adaptive Gaussian quadrature
+ fixed_quad - fixed-order Gaussian quadrature
+ dblquad, tplquad - double and triple integrals
+ romb, simps, trapz - integrators for sampled data
+ cumtrapz - cumulative integration for sampled data
+ ode, odeint - ODE integrators
"""
if isinf(a) or isinf(b):
raise ValueError("Romberg integration only available for finite limits.")
Modified: trunk/Lib/interpolate/fitpack.py
===================================================================
--- trunk/Lib/interpolate/fitpack.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/interpolate/fitpack.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -1,8 +1,8 @@
#!/usr/bin/env python
"""
fitpack (dierckx in netlib) --- A Python-C wrapper to FITPACK (by P. Dierckx).
- FITPACK is a collection of FORTRAN programs for CURVE and SURFACE
- FITTING with SPLINES and TENSOR PRODUCT SPLINES.
+ FITPACK is a collection of FORTRAN programs for curve and surface
+ fitting with splines and tensor product splines.
See
http://www.cs.kuleuven.ac.be/cwis/research/nalag/research/topics/fitpack.html
@@ -28,8 +28,8 @@
For bivariate splines: profil, regrid, parsur, surev
"""
-__all__ = ['splrep', 'splprep', 'splev', 'splint', 'sproot',
- 'spalde', 'bisplrep', 'bisplev']
+__all__ = ['splrep', 'splprep', 'splev', 'splint', 'sproot', 'spalde',
+ 'bisplrep', 'bisplev']
__version__ = "$Revision$"[10:-1]
import _fitpack
from numpy import atleast_1d, array, ones, zeros, sqrt, ravel, transpose, \
@@ -166,6 +166,12 @@
Remarks:
SEE splev for evaluation of the spline and its derivatives.
+
+ See also:
+ splrep, splev, sproot, spalde, splint - evaluation, roots, integral
+ bisplrep, bisplev - bivariate splines
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
if task<=0:
_parcur_cache = {'t': array([],float), 'wrk': array([],float),
@@ -319,6 +325,11 @@
y2 = splev(x2, tck)
plot(x, y, 'o', x2, y2)
+ See also:
+ splprep, splev, sproot, spalde, splint - evaluation, roots, integral
+ bisplrep, bisplev - bivariate splines
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
if task<=0:
_curfit_cache = {}
@@ -414,6 +425,12 @@
y -- an array of values representing the spline function or curve.
If tck was returned from splrep, then this is a list of arrays
representing the curve in N-dimensional space.
+
+ See also:
+ splprep, splrep, sproot, spalde, splint - evaluation, roots, integral
+ bisplrep, bisplev - bivariate splines
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
t,c,k=tck
try:
@@ -449,6 +466,12 @@
wrk -- An array containing the integrals of the normalized B-splines defined
on the set of knots.
+
+ See also:
+ splprep, splrep, sproot, spalde, splev - evaluation, roots, integral
+ bisplrep, bisplev - bivariate splines
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
t,c,k=tck
try: c[0][0];return _ntlist(map(lambda c,a=a,b=b,t=t,k=k:splint(a,b,[t,c,k]),c))
@@ -475,6 +498,12 @@
Outputs: (zeros, )
zeros -- An array giving the roots of the spline.
+
+ See also:
+ splprep, splrep, splint, spalde, splev - evaluation, roots, integral
+ bisplrep, bisplev - bivariate splines
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
t,c,k=tck
if k==4: t=t[1:-1]
@@ -510,6 +539,12 @@
results -- An array (or a list of arrays) containing all derivatives
up to order k inclusive for each point x.
+
+ See also:
+ splprep, splrep, splint, sproot, splev - evaluation, roots, integral
+ bisplrep, bisplev - bivariate splines
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
t,c,k=tck
try:
@@ -588,6 +623,11 @@
SEE bisplev to evaluate the value of the B-spline given its tck
representation.
+
+ See also:
+ splprep, splrep, splint, sproot, splev - evaluation, roots, integral
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
x,y,z=map(myasarray,[x,y,z])
x,y,z=map(ravel,[x,y,z]) # ensure 1-d arrays.
@@ -686,6 +726,15 @@
vals -- The B-pline or its derivative evaluated over the set formed by
the cross-product of x and y.
+
+ Remarks:
+
+ SEE bisprep to generate the tck representation.
+
+ See also:
+ splprep, splrep, splint, sproot, splev - evaluation, roots, integral
+ UnivariateSpline, BivariateSpline - an alternative wrapping
+ of the FITPACK functions
"""
tx,ty,c,kx,ky=tck
if not (0<=dx<kx): raise ValueError,"0<=dx=%d<kx=%d must hold"%(dx,kx)
Modified: trunk/Lib/interpolate/fitpack2.py
===================================================================
--- trunk/Lib/interpolate/fitpack2.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/interpolate/fitpack2.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -53,6 +53,13 @@
""" Univariate spline s(x) of degree k on the interval
[xb,xe] calculated from a given set of data points
(x,y).
+
+ Can include least-squares fitting.
+
+ See also:
+
+ splrep, splev, sproot, spint, spalde - an older wrapping of FITPACK
+ BivariateSpline - a similar class for bivariate spline interpolation
"""
def __init__(self, x, y, w=None, bbox = [None]*2, k=3, s=None):
@@ -195,7 +202,8 @@
raise NotImplementedError,'finding roots unsupported for non-cubic splines'
class InterpolatedUnivariateSpline(UnivariateSpline):
- """ Interpolated univariate spline approximation."""
+ """ Interpolated univariate spline approximation. Identical to UnivariateSpline with less error checking."""
+
def __init__(self, x, y, w=None, bbox = [None]*2, k=3):
"""
Input:
@@ -215,7 +223,7 @@
self._reset_class()
class LSQUnivariateSpline(UnivariateSpline):
- """ Weighted least-squares univariate spline approximation."""
+ """ Weighted least-squares univariate spline approximation. Appears to be identical to UnivariateSpline with more error checking."""
def __init__(self, x, y, t, w=None, bbox = [None]*2, k=3):
"""
@@ -296,6 +304,15 @@
""" Bivariate spline s(x,y) of degrees kx and ky on the rectangle
[xb,xe] x [yb, ye] calculated from a given set of data points
(x,y,z).
+
+ See also:
+
+ bisplrep, bisplev - an older wrapping of FITPACK
+ UnivariateSpline - a similar class for univariate spline interpolation
+ SmoothUnivariateSpline - to create a BivariateSpline through the
+ given points
+ LSQUnivariateSpline - to create a BivariateSpline using weighted
+ least-squares fitting
"""
def get_residual(self):
@@ -324,8 +341,16 @@
raise NotImplementedError
class SmoothBivariateSpline(BivariateSpline):
- """ Smooth bivariate spline approximation."""
+ """ Smooth bivariate spline approximation.
+ See also:
+
+ bisplrep, bisplev - an older wrapping of FITPACK
+ UnivariateSpline - a similar class for univariate spline interpolation
+ LSQUnivariateSpline - to create a BivariateSpline using weighted
+ least-squares fitting
+ """
+
def __init__(self, x, y, z, w=None,
bbox = [None]*4, kx=3, ky=3, s=None, eps=None):
"""
@@ -364,7 +389,14 @@
class LSQBivariateSpline(BivariateSpline):
""" Weighted least-squares spline approximation.
+ See also:
+
+ bisplrep, bisplev - an older wrapping of FITPACK
+ UnivariateSpline - a similar class for univariate spline interpolation
+ SmoothUnivariateSpline - to create a BivariateSpline through the
+ given points
"""
+
def __init__(self, x, y, z, tx, ty, w=None,
bbox = [None]*4,
kx=3, ky=3, eps=None):
Modified: trunk/Lib/interpolate/info.py
===================================================================
--- trunk/Lib/interpolate/info.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/interpolate/info.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -13,10 +13,23 @@
bisplrep -- find bivariate smoothing spline representation.
bisplev -- evaluate bivariate smoothing spline.
+ UnivariateSpline -- A more recent, object-oriented wrapper;
+ finds a (possibly smoothed) interpolating
+ spline.
+ InterpolatedUnivariateSpline
+ LSQUnivariateSpline
+ BivariateSpline -- A more recent, object-oriented wrapper;
+ finds a interpolating spline for a
+ bivariate function.
+
+ SmoothBivariateSpline
+
Interpolation Class
interp1d -- Create a class whose instances can linearly interpolate
- to compute unknown values.
+ to compute unknown values of a univariate function.
+ interp2d -- Create a class whose instances can interpolate
+ to compute unknown values of a bivariate function.
"""
postpone_import = 1
Modified: trunk/Lib/optimize/anneal.py
===================================================================
--- trunk/Lib/optimize/anneal.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/optimize/anneal.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -181,6 +181,26 @@
feval -- Number of function evaluations
iters -- Number of cooling iterations
accept -- Number of tests accepted.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
x0 = asarray(x0)
lower = asarray(lower)
Modified: trunk/Lib/optimize/cobyla.py
===================================================================
--- trunk/Lib/optimize/cobyla.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/optimize/cobyla.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -45,6 +45,25 @@
x -- the minimum
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
err = "cons must be a sequence of callable functions or a single"\
" callable function."
Modified: trunk/Lib/optimize/lbfgsb.py
===================================================================
--- trunk/Lib/optimize/lbfgsb.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/optimize/lbfgsb.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -117,6 +117,26 @@
* C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B,
FORTRAN routines for large scale bound constrained optimization (1997),
ACM Transactions on Mathematical Software, Vol 23, Num. 4, pp. 550 - 560.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
n = len(x0)
Modified: trunk/Lib/optimize/minpack.py
===================================================================
--- trunk/Lib/optimize/minpack.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/optimize/minpack.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -86,6 +86,25 @@
"fsolve" is a wrapper around MINPACK's hybrd and hybrj algorithms.
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
x0 = atleast_1d(x0)
n = len(x0)
@@ -188,8 +207,7 @@
magnitude. Column j of p is column ipvt(j)
of the identity matrix.
'qtf' : the vector (transpose(q) * fvec).
- mesg -- a string message giving information about the cause of
- failure.
+ mesg -- a string message giving information about the cause of failure.
ier -- an integer flag. If it is equal to 1 the solution was
found. If it is not equal to 1, the solution was not
found and the following message gives more information.
@@ -218,6 +236,25 @@
"leastsq" is a wrapper around MINPACK's lmdif and lmder algorithms.
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
x0 = atleast_1d(x0)
n = len(x0)
@@ -313,6 +350,26 @@
fprime is the derivative of the function. If not given, the
Secant method is used.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
if fprime is not None:
@@ -353,6 +410,26 @@
def fixed_point(func, x0, args=(), xtol=1e-10, maxiter=500):
"""Given a function of one variable and a starting point, find a
fixed-point of the function: i.e. where func(x)=x.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
p0 = x0
@@ -374,6 +451,26 @@
def bisection(func, a, b, args=(), xtol=1e-10, maxiter=400):
"""Bisection root-finding method. Given a function and an interval with
func(a) * func(b) < 0, find the root between a and b.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
i = 1
eva = func(a,*args)
Modified: trunk/Lib/optimize/optimize.py
===================================================================
--- trunk/Lib/optimize/optimize.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/optimize/optimize.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -134,6 +134,25 @@
disp -- non-zero to print convergence messages.
retall -- non-zero to return list of solutions at each iteration
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
fcalls, func = wrap_function(func, args)
x0 = asfarray(x0)
@@ -613,6 +632,26 @@
and warnflag in addition to xopt.
disp -- print convergence message if non-zero.
retall -- return a list of results at each iteration if non-zero
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
x0 = asarray(x0)
if maxiter is None:
@@ -757,6 +796,26 @@
and warnflag in addition to xopt.
disp -- print convergence message if non-zero.
retall -- return a list of results at each iteration if True
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
x0 = asarray(x0)
if maxiter is None:
@@ -906,6 +965,25 @@
provided, then the hessian product will be approximated using finite
differences on fprime.
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
x0 = asarray(x0)
fcalls, f = wrap_function(f, args)
@@ -1043,6 +1121,26 @@
ierr -- An error flag (0 if converged, 1 if maximum number of
function calls reached).
numfunc -- The number of function calls.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
if x1 > x2:
@@ -1169,6 +1267,26 @@
Uses inverse parabolic interpolation when possible to speed up convergence
of golden section method.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
_mintol = 1.0e-11
_cg = 0.3819660
@@ -1267,6 +1385,26 @@
(see bracket)
Uses analog of bisection method to decrease the bracketed interval.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
if brack is None:
xa,xb,xc,fa,fb,fc,funcalls = bracket(func, args=args)
@@ -1433,6 +1571,25 @@
disp -- non-zero to print convergence messages.
retall -- non-zero to return a list of the solution at each iteration
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
# we need to use a mutable object here that we can update in the
# wrapper function
@@ -1557,6 +1714,26 @@
grid -- tuple with same length as x0 representing the
evaluation grid
Jout -- Function values over grid: Jout = func(*grid)
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
N = len(ranges)
if N > 40:
Modified: trunk/Lib/optimize/tnc.py
===================================================================
--- trunk/Lib/optimize/tnc.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/optimize/tnc.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -54,6 +54,7 @@
}
HUGE_VAL=1e500 # No standard representation of Infinity in Python 2.3.3
+ # FIXME: can we use inf now that we have numpy and IEEE floats?
EINVAL = -2 # Invalid parameters (n<1)
INFEASIBLE = -1 # Infeasible (low > up)
@@ -149,6 +150,26 @@
x : the solution (a list of floats)
nfeval : the number of function evaluations
rc : return code (corresponding message in optimize.tnc.RCSTRINGS)
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
n = len(x0)
Modified: trunk/Lib/optimize/zeros.py
===================================================================
--- trunk/Lib/optimize/zeros.py 2006-09-23 11:47:47 UTC (rev 2218)
+++ trunk/Lib/optimize/zeros.py 2006-09-23 21:56:21 UTC (rev 2219)
@@ -70,6 +70,26 @@
is the root, and r is a RootResults object containing information
about the convergence. In particular, r.converged is True if the
the routine converged.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
if type(args) != type(()) :
args = (args,)
@@ -113,6 +133,26 @@
is the root, and r is a RootResults object containing information
about the convergence. In particular, r.converged is True if the
the routine converged.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
if type(args) != type(()) :
args = (args,)
@@ -157,6 +197,26 @@
is the root, and r is a RootResults object containing information
about the convergence. In particular, r.converged is True if the
the routine converged.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
if type(args) != type(()) :
args = (args,)
@@ -201,6 +261,26 @@
is the root, and r is a RootResults object containing information
about the convergence. In particular, r.converged is True if the
the routine converged.
+
+ See also:
+
+ fmin, fmin_powell, fmin_cg,
+ fmin_bfgs, fmin_ncg -- multivariate local optimizers
+ leastsq -- nonlinear least squares minimizer
+
+ fmin_l_bfgs_b, fmin_tnc,
+ fmin_cobyla -- constrained multivariate optimizers
+
+ anneal, brute -- global optimizers
+
+ fminbound, brent, golden, bracket -- local scalar minimizers
+
+ fsolve -- n-dimenstional root-finding
+
+ brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
+
+ fixed_point -- scalar fixed-point finder
+
"""
if type(args) != type(()) :
args = (args,)
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