I'm relatively new to using Python to fit my data, so please excuse my lack of programming finesse. I have, however, been unable to find a solution to the errors my current curve fitting attempts are throwing. I believe these errors are due to my model function's complex dependence on one of the two variable parameters (namely, Kd). I would appreciate insight regarding what specifically is causing this problem and how I may adjust my definition or fitting package to avoid it. Minimal working example to follow:

```
# Import libraries
import scipy as scipy
from scipy import stats
import numpy as np
from scipy.optimize import curve_fit

np.set_printoptions(precision=4)
ConcSyringeTotal = 9.5 ## total monomer concentration in the syringe [M]tot, in mM
Vinj = 10 ## volume injected in each injection, in uL
Vinit = 1250 ## volume of solvent initially in the sample cell, in uL
Vcell = 1000 ## cell volume, in uL (only the heat change within this volume is measured)
Injections = np.arange(2.00,26.00,1.00)
print Injections
Energy = np.array([136.953, 105.119, 84.414, 69.373, 60.898, 52.813, 46.187, 39.653, 33.894, 29.975, 27.315, 24.200, 21.643, 19.080, 16.158, 13.454, 13.218, 11.568, 10.742, 9.547, 8.693, 7.334, 6.111, 4.741])
print Energy

def DimerDissociation(injection, Kd, DHd): ## a dimer dissociation model for an ITC dilution experiment
    ## returns the heat flow (y-data, in ucal) per injection (x-data, unitless)
    ## fit for the dissociation constant (Kd, in mM = mmol/L, umol/mL, nmol/uL) 
    ## and the enthalpy of dissociation (DHd, in ucal/nmol = kcal/mol)
    ##
    ## concentration (in mM) of the free monomer in the cell after equilibration of the i-th injection
    VolumeAdded = 6+(injection-1)*Vinj ## in uL
    VolumeTotal = Vinit + VolumeAdded ## in uL
    CellTotal = ConcSyringeTotal*VolumeAdded ## Total in the cell after the i-th injection, in nmol
    ConcCellTotal = CellTotal/VolumeTotal ## Total concentration in the cell after the i-th injection, in mM
    ConcCellMonomer_roots =  np.roots([1, Kd/2, -Kd*ConcCellTotal/2]) 
    ConcCellMonomer_real = ConcCellMonomer_roots.real[abs(ConcCellMonomer_roots.imag)<1e-5]
    ConcCellMonomer_positive = ConcCellMonomer_real[ConcCellMonomer_real>0]
    ConcCellMonomer = ConcCellMonomer_positive[ConcCellMonomer_positive<ConcCellTotal]
    ##
    ## concentration (in mM) of the free monomer in the syringe
    ConcSyringeMonomer_roots =  np.roots([1, Kd/2, -Kd*ConcSyringeTotal/2]) 
    ConcSyringeMonomer_real = ConcSyringeMonomer_roots.real[abs(ConcSyringeMonomer_roots.imag)<1e-5]
    ConcSyringeMonomer_positive = ConcSyringeMonomer_real[ConcSyringeMonomer_real>0]
    ConcSyringeMonomer = ConcSyringeMonomer_positive[ConcSyringeMonomer_positive<ConcSyringeTotal]
    ## nmol of the free monomer injected from the syringe
    SyringeMonomerInjected = Vinj*ConcSyringeMonomer[0]
    ##
    ## concentration (in mM) of the free monomer in the cell before the i-th injection
    VolumeAddedPre = 6+(injection-2)*Vinj
    VolumeTotalPre = Vinit + VolumeAddedPre
    CellTotalPre = ConcSyringeTotal*VolumeAddedPre
    ConcCellTotalPre = CellTotalPre/VolumeTotalPre
    ConcCellMonomerPre_roots =  np.roots([1, Kd/2, -Kd*ConcCellTotalPre/2]) 
    ConcCellMonomerPre_real = ConcCellMonomerPre_roots.real[abs(ConcCellMonomerPre_roots.imag)<1e-5]
    ConcCellMonomerPre_positive = ConcCellMonomerPre_real[ConcCellMonomerPre_real>0]
    ConcCellMonomerPre = ConcCellMonomerPre_positive[ConcCellMonomerPre_positive<ConcCellTotalPre]
    ## nmol of the free monomer in the cell before the i-th injection
    CellMonomerPre = VolumeTotalPre*ConcCellMonomerPre[0]
    ##
    ## concentration of the free monomer before equilibration of the i-th injection, in mM
    ConcCellMonomerBefore = (CellMonomerPre+SyringeMonomerInjected)/VolumeAdded
    ## concentration of the free monomer after equilibration of the i-th injection, in mM
    ConcCellMonomerAfter = ConcCellMonomer[0]
    ## change in concentration of the free monomer over the equilibration of the i-th injection, in mM
    ConcCellMonomerChange = ConcCellMonomerAfter - ConcCellMonomerBefore
    ##
    return Vcell*DHd*ConcCellMonomerChange
DimerDissociation_opt, DimerDissociation_cov = curve_fit(DimerDissociation, Injections, Energy, p0=[0.4,10])
DimerDissociation_stdev = np.sqrt(np.diag(DimerDissociation_cov))
print "optimized parameters:", DimerDissociation_opt
print "covariance matrix:", DimerDissociation_cov
print "standard deviation of fit parameters:", DimerDissociation_stdev

```

And the associated error:

```
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-38-b5ef2361feed> in <module>()
     52     ##
     53     return Vcell*DHd*ConcCellMonomerChange
---> 54 DimerDissociation_opt, DimerDissociation_cov = curve_fit(DimerDissociation, Injections, Energy, p0=[0.4,10])
     55 DimerDissociation_stdev = np.sqrt(np.diag(DimerDissociation_cov))
     56 print "optimized parameters:", DimerDissociation_opt

//anaconda/lib/python2.7/site-packages/scipy/optimize/minpack.pyc in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, **kw)
    553     # Remove full_output from kw, otherwise we're passing it in twice.
    554     return_full = kw.pop('full_output', False)
--> 555     res = leastsq(func, p0, args=args, full_output=1, **kw)
    556     (popt, pcov, infodict, errmsg, ier) = res
    557 

//anaconda/lib/python2.7/site-packages/scipy/optimize/minpack.pyc in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
    367     if not isinstance(args, tuple):
    368         args = (args,)
--> 369     shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
    370     m = shape[0]
    371     if n > m:

//anaconda/lib/python2.7/site-packages/scipy/optimize/minpack.pyc in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
     18 def _check_func(checker, argname, thefunc, x0, args, numinputs,
     19                 output_shape=None):
---> 20     res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
     21     if (output_shape is not None) and (shape(res) != output_shape):
     22         if (output_shape[0] != 1):

//anaconda/lib/python2.7/site-packages/scipy/optimize/minpack.pyc in _general_function(params, xdata, ydata, function)
    443 
    444 def _general_function(params, xdata, ydata, function):
--> 445     return function(xdata, *params) - ydata
    446 
    447 

<ipython-input-38-b5ef2361feed> in DimerDissociation(injection, Kd, DHd)
     19     CellTotal = ConcSyringeTotal*VolumeAdded ## Total in the cell after the i-th injection, in nmol
     20     ConcCellTotal = CellTotal/VolumeTotal ## Total concentration in the cell after the i-th injection, in mM
---> 21     ConcCellMonomer_roots =  np.roots([1, Kd/2, -Kd*ConcCellTotal/2])
     22     ConcCellMonomer_real = ConcCellMonomer_roots.real[abs(ConcCellMonomer_roots.imag)<1e-5]
     23     ConcCellMonomer_positive = ConcCellMonomer_real[ConcCellMonomer_real>0]

//anaconda/lib/python2.7/site-packages/numpy/lib/polynomial.pyc in roots(p)
    199     """
    200     # If input is scalar, this makes it an array
--> 201     p = atleast_1d(p)
    202     if len(p.shape) != 1:
    203         raise ValueError("Input must be a rank-1 array.")

//anaconda/lib/python2.7/site-packages/numpy/core/shape_base.pyc in atleast_1d(*arys)
     47     res = []
     48     for ary in arys:
---> 49         ary = asanyarray(ary)
     50         if len(ary.shape) == 0 :
     51             result = ary.reshape(1)

//anaconda/lib/python2.7/site-packages/numpy/core/numeric.pyc in asanyarray(a, dtype, order)
    512 
    513     """
--> 514     return array(a, dtype, copy=False, order=order, subok=True)
    515 
    516 def ascontiguousarray(a, dtype=None):

ValueError: setting an array element with a sequence.

```