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- SIGN(a, b)
- bfgs(x, f, df, costTol=1e-10, gradTol=0.0001, maxIters=200, verbose=0, stepsize0=1, resetInterval=None)
Perform Broyden-Fletcher-Goldfarb-Shanno variant of
Davidson-Fletcher-Powell minimization.
Return value is the tuple (x,J(x),numIters)
- brent(ax, bx, cx, f, tol=1e-08, ITMAX=100, ZEPS=1e-10)
Find minimum bracketed by ax,bx,cx
return (xmin,f(xmin))
- conmin(x, f, df, costTol=1e-10, gradTol=0.0001, maxIters=200, stepsize=1, verbose=0)
conjugate gradient minimization of function f with gradient df, starting at
position x.
stepsize specifies initial stepsize to be taken
Return value is the tuple (x,J(x),numIters)
FIX: this routine makes unnecessary function calls.
- dot(...)
- linemin(func, p, xi, stepsize)
determine the minimum of func starting at point p, in the direction xi.
return (pf,pfmin,xif)
minimum position, fmin, and the actual displacement vector used
- mnbrak(ax, bx, func)
given function func, and given distinct initial points ax and bx, this
routine searches in the downhill direction *defined by the function as
evaluated at the initial points) and returns new points ax, bx, cx which
bracket a minimum of the function. Also returned are the function values
at the three points fa, fb and fc.
- norm(...)
- outerProd(x, y)
return the outer product matrix result of multiplying the vectors x and y
- simplex(func, x0, args=(), xtol=0.0001, ftol=0.0001, maxIters=None, maxfun=None, full_output=0, verbose=1, retall=0, callback=None)
Minimize a function using the downhill simplex algorithm.
:Parameters:
func : callable func(x,*args)
The objective function to be minimized.
x0 : ndarray
Initial guess.
args : tuple
Extra arguments passed to func, i.e. ``f(x,*args)``.
callback : callable
Called after each iteration, as callback(xk), where xk is the
current parameter vector.
:Returns: (xopt, {fopt, iter, funcalls, warnflag})
xopt : ndarray
Parameter that minimizes function.
fopt : float
Value of function at minimum: ``fopt = func(xopt)``.
iter : int
Number of iterations performed.
funcalls : int
Number of function calls made.
warnflag : int
1 : Maximum number of function evaluations made.
2 : Maximum number of iterations reached.
allvecs : list
Solution at each iteration.
*Other Parameters*:
xtol : float
Relative error in xopt acceptable for convergence.
ftol : number
Relative error in func(xopt) acceptable for convergence.
maxIters : int
Maximum number of iterations to perform.
maxfun : number
Maximum number of function evaluations to make.
full_output : bool
Set to True if fval and warnflag outputs are desired.
verbose : bool
Set to True to print convergence messages.
retall : bool
Set to True to return list of solutions at each iteration.
:Notes:
Uses a Nelder-Mead simplex algorithm to find the minimum of
function of one or more variables.
- wrap_function(function, args)
# the following routines are from scipy optimize.fmin
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