Lyness-Kaganove benchmark

1 files changed, 41 insertions, 2 deletions

diff --git a/README.rst b/README.rst
index 12eba6d..838add1 100644
--- a/README.rst
+++ b/README.rst
@@ -1,9 +1,48 @@
 Vquad
 =====
 
-Vquad is a work-in-progress towards a general-purpose, robust, efficient, and parallel library for numerical integration.
+Vquad is a work-in-progress towards a general-purpose, robust, efficient, and
+parallel library for numerical integration.
 
 History
 -------
 
-Vquad is based on algorithm 4 from the article "Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants", Pedro Gonnet, ACM TOMS 37, 26 (2010).
+Vquad is based on algorithm 4 from the article "Increasing the Reliability of
+Adaptive Quadrature Using Explicit Interpolants", Pedro Gonnet, ACM TOMS 37,
+26 (2010).
+
+Usage example
+-------------
+
+```
+import numpy
+import vquad
+
+# Simple usage.
+igral, err = vquad.vquad(numpy.cos, -1, 1, rtol=1e-10)
+
+# Object interface.
+it = vquad.Vquad(numpy.cos, -1, 1)
+igral, err = it.improve_until(rtol=1e-10)
+
+# Evaluate interpolant.
+xs = numpy.linspace(-1, 1, 101)
+ys = it(xs)
+```
+
+Benachmarks and tests
+---------------------
+
+Vquad includes extensive tests and benchmarks.  The tests focus on verifying
+correctness and can be run with
+```
+python3 -m pytest -s
+```
+The `-s` shows some statistics that are gathered during the testing.
+
+The benchmarks take longer to run and allow to quantitatively compare the
+performance of the algorithm.  The benchmark is run by executing the vquad
+module.  To get help, run:
+```
+python3 -m vquad -h
+```