scipy.integrate.dblquad¶
- scipy.integrate.dblquad(func, a, b, gfun, hfun, args=(), epsabs=1.49e-08, epsrel=1.49e-08)[source]¶
Compute a double integral.
Return the double (definite) integral of
func(y, x)
fromx = a..b
andy = gfun(x)..hfun(x)
.- Parameters
- funccallable
A Python function or method of at least two variables: y must be the first argument and x the second argument.
- a, bfloat
The limits of integration in x: a < b
- gfuncallable or float
The lower boundary curve in y which is a function taking a single floating point argument (x) and returning a floating point result or a float indicating a constant boundary curve.
- hfuncallable or float
The upper boundary curve in y (same requirements as gfun).
- argssequence, optional
Extra arguments to pass to func.
- epsabsfloat, optional
Absolute tolerance passed directly to the inner 1-D quadrature integration. Default is 1.49e-8. dblquad` tries to obtain an accuracy of
abs(i-result) <= max(epsabs, epsrel*abs(i))
wherei
= inner integral offunc(y, x)
fromgfun(x)
tohfun(x)
, andresult
is the numerical approximation. See epsrel below.- epsrelfloat, optional
Relative tolerance of the inner 1-D integrals. Default is 1.49e-8. If
epsabs <= 0
, epsrel must be greater than both 5e-29 and50 * (machine epsilon)
. See epsabs above.
- Returns
- yfloat
The resultant integral.
- abserrfloat
An estimate of the error.
See also
quad
single integral
tplquad
triple integral
nquad
N-dimensional integrals
fixed_quad
fixed-order Gaussian quadrature
quadrature
adaptive Gaussian quadrature
odeint
ODE integrator
ode
ODE integrator
simpson
integrator for sampled data
romb
integrator for sampled data
scipy.special
for coefficients and roots of orthogonal polynomials
Examples
Compute the double integral of
x * y**2
over the boxx
ranging from 0 to 2 andy
ranging from 0 to 1.>>> from scipy import integrate >>> f = lambda y, x: x*y**2 >>> integrate.dblquad(f, 0, 2, lambda x: 0, lambda x: 1) (0.6666666666666667, 7.401486830834377e-15)