ó Vc@sçddlmZmZmZmZddlmZmZmZddl m Z m Z ddl j ZddlZddlZddlZddl Z ddlZddlmZm Z ddlmZdddd d d d d „ZdS(i˙˙˙˙(texptcostlinspacet zeros_like(teulertheuntrk4(tsqrttpiN(tsinR(Rs5(1/(sigma*sqrt(2*pi)))*exp(-((t-mu)**2)/(2*sigma**2))gà?s [-1.5,2.5]RidtNoc%sddlm}m}m} m} m} m} m} m}|dƒ}t |ƒ}t |ƒ\}}t |ƒ}|||ƒ}|||ƒ}|||ƒ}||||‰| |g|ƒ}| |g|ƒ}| |g|ƒ}| |gˆƒ‰t j |||dƒ}‡fd†}t j ||ƒ||ƒ||ƒgƒ}||||ƒ}|dd…df}t j |ƒ}d}x(|D] }||ƒ||<|d}qW|dkrÏtjƒd GHntjƒg}tj||d ƒtj||d ƒd }d }|j|ƒ|j|ƒtjdƒtjdƒtjdƒtj|dddtƒddlm} | ƒ}!tj|!ddƒ|!jdƒddl}"|"j|!jƒƒ}#| ƒ}!tj|!ddƒ|!jdƒd|!jƒjdƒd}$t|$dƒ}$|#S(sFunction that solves the equation f + f''*f + f''' = RHS numerically with different ODEsolvers with use of the method of manufactured solution. The necesary Right hand side (RHS) is calculated from the differential equation by choosing/manufacturing a wanted solution. The differentiations are performed with use of the sympolic python module sympy. In this case the chosen solution f=Expression is set default to be a normal distribution. In order to be able to handle various functions f/Ekspression on various domains and with different solvers, filled in on a form on a webpage the arguments "Expression", "Domain" and "solver" are of type str. and are evaluated into python expressions with use of the eval() function. The default values of the arguments are automatically filled into the form of "view.html" file. Args: Expression(str): the manufactured solution sigma(float): standard deviation mu(float): mean value Domain(str): the computational domain solver(str): the chosen ODEsolver Nsteps(int): the number of timesteps erase(str): erase previous plot (Yes/No) Returns: figdata_png(string): the plot of (t, fnumeric) and (t, fanalytic) encoded with BytesIo to the fed into html file i˙˙˙˙(tsymbolstdifft integratetRationaltlambdifyRR RtticsItj|ƒ}|d|dˆ|ƒ|d|d|dg|(|S(sË Function that returns the dfn/dt of the differential equation f + f''*f + f''' = RHS as a system of 1st order equation; f = f1 f1' = f2 f2' = f3 f3' = RHS - f1 - f2*f3 Args: y(array): solutian array [f1, f2, f3] at time t t(time): current time Returns: yout(array): differantiation array [f1', f2', f3'] at time t iii(tnpR(tyRtyout(tRHS(s‚/Users/fredrikeikelandfossan/Documents/git/tkt4140_digital_compendium/digital_compendium/chapter1/src-ch1/Flask_app_MMS/compute.pytfunc;s6NitYesthellotgsr--t fanalytictfnumericsNormal distributionsf(t)tloctbesttframeon(tBytesIOtformattpngtsvgss"0