Python API#

The functions described in the C API can be access using the Python lintegrate module provided with the library. These functions have a similar style to the SciPy quad() function.

logtrapz(f, x[, disable_checks=False, args=()])#

Given the natural logarithm f of some function g (i.e., f = log(g)), compute the natural logarithm of the integral of that function using the trapezium rule.

Parameters:

f (numpy.ndarray, list, or function handle) – A set of values of the logarithm of a function evaluated at points given by x, or a function handle of the log function to be evaluated.
x (numpy.ndarray, list, or float) – An array of values at which f has been evaluated, or is to be evaluated at. Or, provided f is also an array, a single value giving the spacing between evaluation points (if the function has been evaluated on an evenly spaced grid).
disable_checks (bool) – Set this to True to disable checks, such as making sure x values are in ascending order. Defaults to False.
args (tuple) – A tuple of any additional parameters required by the function f (to be unpacked within the function).

Returns:

The natural logarithm of the integral of the function

Return type:

float

lqng(func, a=0., b=0.[, args=(), epsabs=1.49e-8, epsrel=1.49e-8, intervals=None, nintervals=0, intervaltype='linear'])#

Python wrapper to the lintegration_qng() function. This will integrate exp(func), whilst staying in log-space to ensure numerical precision, using a non-adaptive procedure. It uses fixed Gauss-Kronrod-Patterson abscisae to sample the integrand at a maximum of 87 points (see gsl_integration_qng()).

Parameters:

func (function) – A callable Python function which returns the natural logarithm of the underlying function being integrated over.
a (float) – Lower limit of integration
b (float) – Upper limit of integration
args (tuple) –
Extra arguments to pass to func. These must be unpacked within func, e.g.:
```
def myfunc(x, args):
    y, z = args
    return x + y + z
```
epsabs (float) – The absolute error tolerance for the integral
epsrel (float) – The relative error tolerance for the integral
intervals (numpy.ndarray or list) – An array of values bounding intervals into which the integral will be split (this could be used, for example, if you have a very tightly peaked function and require small intervals around the peak).
nintervals (int) – If intervals is not given then split the range between a and b into nintervals intervals
intervaltype (str) – If splitting into nintervals intervals then choose whether to split the range in equal intervals in ‘linear’, ‘log’, or ‘log10’ space

Returns:

A tuple containing: the natural logarithm of the integral of exp(func), an estimate of the absolute error in the result, and the number of evaluations used in the integration

Return type:

tuple

lqag(func, a=0., b=0.[, args=(), epsabs=1.49e-8, epsrel=1.49e-8, limit=50, intkey=1, intervals=None, nintervals=0, intervaltype='linear'])#

Python wrapper to the lintegration_qag() function. This will integrate exp(func), whilst staying in log-space to ensure numerical precision, using a simple adaptive procedure (see gsl_integration_qag()).

Parameters:

func (function) – A callable Python function which returns the natural logarithm of the underlying function being integrated over.
a (float) – Lower limit of integration
b (float) – Upper limit of integration
args (tuple) –
Extra arguments to pass to func. These must be unpacked within func, e.g.:
```
def myfunc(x, args):
    y, z = args
    return x + y + z
```
epsabs (float) – The absolute error tolerance for the integral
epsrel (float) – The relative error tolerance for the integral
limit (int) – The maximum number of subintervals used in the integration
intkey (int) – A key given the integration rule following those for the gsl_integration_qag() function. This can be 1, 2, 3, 4, 5, or 6, corresponding to the 15, 21, 31, 41, 51 and 61 point Gauss-Kronrod rules respectively.
intervals (numpy.ndarray or list) – An array of values bounding intervals into which the integral will be split (this could be used, for example, if you have a very tightly peaked function and require small intervals around the peak).
nintervals (int) – If intervals is not given then split the range between a and b into nintervals intervals
intervaltype (str) – If splitting into nintervals intervals then choose whether to split the range in equal intervals in ‘linear’, ‘log’, or ‘log10’ space

Returns:

A tuple containing: the natural logarithm of the integral of exp(func) and an estimate of the absolute error in the result

Return type:

tuple

lcquad(func, a, b[, args=(), epsabs=1.49e-8, epsrel=1.49e-8, wsintervals=100, intervals=None, nintervals=0, intervaltype='linear'])#

Python wrapper to the lintegration_cquad() function. This will integrate exp(func), whilst staying in log-space to ensure numerical precision, using a doubly adaptive procedure (see gsl_integration_cquad()).

Parameters:

func (function) – A callable Python function which returns the natural logarithm of the underlying function being integrated over.
a (float) – Lower limit of integration
b (float) – Upper limit of integration
args (tuple) –
Extra arguments to pass to func. These must be unpacked within func, e.g.:
```
def myfunc(x, args):
    y, z = args
    return x + y + z
```
epsabs (float) – The absolute error tolerance for the integral
epsrel (float) – The relative error tolerance for the integral
wsintervals (int) – A sufficient number of subintervals for the integration (if the workspace is full the smallest intervals will be discarded)
intervals (numpy.ndarray or list) – An array of values bounding intervals into which the integral will be split (this could be used, for example, if you have a very tightly peaked function and require small intervals around the peak).
nintervals (int) – If intervals is not given then split the range between a and b into nintervals intervals
intervaltype (str) – If splitting into nintervals intervals then choose whether to split the range in equal intervals in ‘linear’, ‘log’, or ‘log10’ space

Returns:

A tuple containing: the natural logarithm of the integral of exp(func), an estimate of the absolute error in the result, and the number of evaluations used in the integration

Return type:

tuple