Using Python's sympy module to express a complicated function -


how can symbolically express following equation using python's sympy module, such later find second derivative , therefore compute hessian matrix?

the function

enter image description here

what i've tried: 

import sympy nc,ns,tc,ysc,theta,theta_star,t,dt,sigma_s,measured,simulated=sympy.symbols(' nc ns tc ysc theta theta_star t dt sigma_s  measured simulated ') chi=(1/2*nc*ns) * sympy.mpmath.nsum(   1 / tc *  sympy.integrate(  ((simulated - measured)  /  sigma_s )    **2) , (t,0,tc))

the error: 

  file "c:\anaconda1\lib\site-packages\sympy\concrete\expr_with_limits.py", line 358, in __new__     "specify dummy variables %s" % function)  valueerror: specify dummy variables (-measured + simulated)**2/sigma_s**2

don't use sympy.mpmath.nsum. mpmath functions numerical calculations only. represent sum symbolically, use sympy.sum. works this

in [3]: sum(f(x), (x, 0, n)) out[3]:   n  ___  ╲   ╲   f(x)   ╱  ╱  ‾‾‾ x = 0

secondly, sympy has told explicitly when 1 variable depends on another. i'm unclear s , c in equation. if variables, should create symbols s , c. importantly, t needs variable, , things depend on t need functions like

thetastar, t = symbols('thetastar t') y_sc = function('y')

and use 

y_sc(thetastar, t)

(if s , c supposed variables well, should use y = function('y') , y(s, c, thetastar, t)).


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