SciPyPackages/Integrate - SciPy wiki dump

scipy.integrate

The package scipy.integrate does two things: integration (or quadrature), and solving differential equations.

Quadrature functions

quadrature(func, a, b, args=(), tol=1.5e-8, maxiter=50): Integrate func from a to b using Gaussian quadrature with absolute tolerance tol. args is extra arguments to pass to func, and maxiter is the maximum number of iterations. Returns (val, err), where val is the Gaussian quadrature approximation, and err is the difference between the last two estimates of the integral.
romberg(function, a, b, tol=1.48e-8, show=0, divmax=10): Romberg integration of a callable function or method.
dblquad(func, a, b, gfun, hfun, args=(), epsabs=1.5e-8, epsrel=1.5e-8): Compute the double (definite) integral of func(y,x,*args) from x=a..b and y=gfun(x)..hfun(x). Returns (val, err).
tplquad(func, a, b, gfun, hfun, qfun, rfun, args=(), epsabs=1.5e-8, epsrel=1.5e-8): Compute the triple (definite) integral of func(z,y,x,*args) from x=a..b, y=gfun(x)..hfun(x), and z=qfun(x,y)..rfun(x,y). Returns (val, err).
quad(func, a, b, args=(), full_output=0, epsabs=1.49e-8, epsrel=1.49e-8, limit=50, points=None, weight=None, wvar=None, wopts=None, maxp1=50, limlst=50): Computes an integral using a technique from the Fortan library QUADPACK. The function is integrated from a to b. Run scipy.integrate.quad_explain() for more information on the more esoteric inputs and outputs.

Differential Equations

ode, odeint.

odeint(func, y0, t, args=(), Dfun=None, col_deriv=0, full_output=0, ml=None, mu=None, rtol=None, atol=None, tcrit=None, h0=0.0, hmax=0.0, hmin=0.0, ixpr=0, mxstep=0, mxhnil=0, mxordn=12, mxords=5, printmessg=0)

Integrate a system of ordinary differential equations.
```
#class right

inline:odeint2.png
```
```
   1 from scipy import *
   2 from pylab import *
   3 deriv = lambda y,t : array([y[1],-y[0]])
   4 # Integration parameters
   5 start=0
   6 end=10
   7 numsteps=10000
   8 time=linspace(start,end,numsteps)
   9 from scipy import integrate
  10 y0=array([0.0005,0.2])
  11 y=integrate.odeint(deriv,y0,time)
  12 plot(time,y[:,0])
  13 show()
```

Another example of numerical integration of ODEs is given by "Integrating Lokta-Volterra equations with SciPy".

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