Scientific Computing Using Python - PHYS:4905
Lecture #22 - Prof. Kaaret
Homework #16 is at the bottom of this page.
Squaring the circle
Numerical integration is the use of an algorithm to calculate the
value of a definite integral. It is also refereed to as quadrature,
which is a historical mathematical term that means calculating area
of a geometric shape by constructing a square with the same
area. The "quad" is the same root that leads us to use the
name quadratic for a polynomial in which the highest power
is a square. People have been working on quadrature since
Babylonian times. There is a papyrus from Egypt from around
1550 BC that states that "a circle's area stands to that of its
circumscribing square in the ratio 64/81". If you think
about this, it means that the Egyptians knew the value of π to an
accuracy of 0.6%.
Trapezium
We will consider the problem of finding an approximate numerical
value of the integral of a function f(x), the
integrand, over an interval [a, b],
We evaluate the function at n+1 points equally distributed
in [a, b]. The spacing between adjacent points
is then Δx = (b-a)/n. and the x-values
are xk = a +k Δx, where k
= 0, 1, ..., n.
A simple algorithm would be approximate each interval by a rectangle
with a width of Δx and a height equal to value of the
function at the left edge. This is called a left Riemann
sum. As you can see from the figure below. The left
Riemann sum is not a great way to calculate an integral. It
works if you make your bins fine enough (at the cost of more
computations), but it underestimates the integral in regions where
the function slope is positive and overestimates it where the slope
is negative. One could instead use a right Riemann sum, taking
the function value at the right edge, but it has the same issues,
only reversed.
A better thing to do is to use a trapeze. Oops, that's for the
circus. I meant a trapezium. The Trapezium is a tight
open cluster of stars in the heart of the Orion Nebula, named for
its four brightest stars.
![](data:image/png;base64,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)
Trapezium is also the word used in English outside North America to
denote a convex quadrilateral with at least one pair of parallel
sides. Most of us in this class call such an object a
trapezoid.
Trapezoids offer a more accurate way to estimate an integral.
The idea is that rather than draw a rectangle with a height set by
the function value at one edge, let's draw a trapezoid between the
two edges. For reasonably smooth functions, this often
provides a nice approximation to the function, and therefore a more
accurate estimate of its integral.
The area of a trapezoid is (a+b)h/2, where h is its height and a and
b are the lengths of the two sides.
We'll flip the trapezoid on its side, so that
.
The area of each trapezoid is then .
To calculate the integral, we sum the areas of all of the
trapezoids. For the first trapezoid, we'll have
When we add in the second one we get
Adding the third,
Note that we have to pay special attention to the first and last
points because they only contribute to one trapezoid while all of
the other points contribute to two.
Our approximation for the integral is then
Doing numerical integration this way is called using the trapezoid
rule and this formula is called the extended trapezoid rule.
We can write a Python function to do numerical integration via the
trapezoid rule using the following steps.
- Take as input, the name of the function to be integrated (f),
the endpoints of the interval of integration (a, b),
and the number of points to use (n).
- Create an array with xk values evenly
spaced from a to b.
- Evaluate the function at each xk value.
- Evaluate the sum in the equation above.
- Return the sum multiplied by the spacing between the points as
an estimate of the integral.
Thomas Simpson's rule
Approximating our function with trapezoids is nice, but it misses
sometimes, particularly if there is a maximum or minimum between our
x-values or the function has curvature. The trapezoid
rule approximates the integrand by drawing a line between adjacent
pairs of points. Instead, we could take adjacent triples of
points, draw a parabola through those three points, and integrate
that parabola analytically. This often does a better job as
nicely shown the figure below (drawn by Popletibus),
The formula for the area for one interval is
Note that if you substitute x0 = donut, x2
= beer, f(x)= Homer(x), you can re-write this
as Homer Simpson's rule,
To calculate the integral, we sum the integrals of all our little
parabolas. Note that we move by 2Δx each time so that
successive integration intervals don't overlap. The extended
Simpson's rule for calculating an integral is
The coefficients alternate between 4 and 2 all the way through the
middle of the sum. Note that n needs to be an even
number so that we have an odd number of terms in the sum.
The algorithm for doing integration via Simpson's rule is very
similar to that for the trapezoidal rule, but the sum is different.
Higher power?
You might ask, why stop at quadratic polynomials? There is a
Simpson's rule that uses cubic polynomials and the so-called
Newton–Cotes formulae allow any degree of polynomial. However,
one reaches diminishing returns because high order polynomials tend
to oscillate around the points they are drawn through and don't
actually provide better approximations. This is especially
true if the function has jumps, as seen in the figure below that
shows approximations to a step function with polynomials of 3rd,
5th, and 7th order and with the trapezoid rule. The trapezoid
rule clearly does a better job.
In general, numerical integration methods tend to work well for
smooth functions and poorly for functions with sharp features or
oscillations over scales close to the integration step size (Δx
in our discussions above). If your function has one or a few
discrete steps at known locations, then it is better to break the
integration up into pieces with edges at the step locations.
If your function oscillates, then you need to have at least
several integration bins within each oscillation period.
Adapt or perish
The accuracy of our estimation of the integral using either the
trapezoid rule or Simpson's rule is essentially set by the number of
grid points. More points means a smaller step size leading to
a better approximation of the function. The method don't
include a means to estimate the accuracy of the integration because
that depends on how well they approximate the function, which is
impossible to know precisely unless one can evaluate the integral
analytically, in which case one should do that rather than doing a
whole bunch of computations, or one evaluates the function at all
points in the integration interval, which would take an infinite
amount of time.
Usually, one estimates the accuracy by comparing the numerical
estimates obtained with different grid spacing. E.g. find the
integral using 1000 grid points, do it again with 2000 grid points,
and then take the absolute value of the difference as an estimate of
the accuracy. If the integrand is relatively smooth, so higher
order derivatives are not too large, then the accuracy of the
trapezoid rule scales with while
the accuracy of Simpson's rule scales with
.
You will check this in the homework assignment below.
In adaptive quadrature, the algorithm adjusts the grid to
obtain the desired accuracy. In simplest adaptive quadrature
algorithm, one
- Chooses an grid size and applies a method like the trapezoid
rule or Simpson's rule to estimate the integral. We'll
call the value of the integral I0.
- Divides the step size in half and repeats the numerical
integration. We'll call the new value of the integral I1.
- Checks if the desired accuracy has been reaches, specifically
check if abs(I1 - I0) <
itol*abs(I1), where itol is the
desired fractional accuracy. If we have reached the
desired accuracy, then we are done and we return I1.
If not, we set I0 = I1
and go back to step 2.
Such algorithms are called "globally" adaptive because they adjust
the whole grid. The trapezoidal rule and Simpson's rule are
particularly useful because we get to re-use all of the function
evaluations as we make the grid finer by dividing the step size in
half. The trapezoidal rule is particularly computationally
efficient because we don't even have to redo the sum over those
points.
becomes
We can simply add the old sum to the new sum with the new
points. We don't even have to keep the values from the
function evaluations on the coarser grid.
The disadvantage of globally adaptive quadrature is that the finer
grid spacings can become computationally expensive. In locally
adaptive quadrature, one breaks the interval into pieces and refines
the grid only for the pieces where the integral is not sufficiently
accurate. For example, one might
- Evaluate the integral in the intervals [a, (a+b)/2]
and [(a+b)/2, b], i.e. divide the original
interval in half, using a step size of Δx.
- Evaluate the integral in the same intervals using a step size
of Δx/2.
- For each of those intervals, check if we have reached the
desired accuracy using the same equation as in step 3 for global
quadrature. Note that if we achieve the desired fractional
accuracy in all intervals, then we will achieve it globally.
- For any interval where we have reached the desired accuracy,
stop and record the integral for that interval. For any
interval where we have not reached the desired accuracy, split
that interval into two pieces by going back to step 1 with a
and b set to the edges of that interval.
Some locally adaptive quadrature algorithms have an additional check
and stop if the global accuracy of the integral is good enough, i.e.
they add up the contributions from all of the pieces at each step
and stop if estimate of the total integral changes by less than itol
even if that accuracy hasn't been achieved for each individual
piece. This keeps the algorithm from throwing computational
resources into small pieces of the interval that are poorly behaved,
but don't make a large contribution to the total integral.
Locally adaptive quadrature is rather more complex to program than
globally adaptive quadrature. Most people don't even try, but
instead use a software package called QUADPACK that
was written in Fortran in the 1980s. There is a 300 page book
describing QUADPACK. Fortunately, the SciPy library includes
an interface to QUADPACK. The routine scipy.integrate.quad
uses locally adaptive quadrature to numerically integrate a
function, f(x), in a given interval (a, b),
to a specified relative accuracy epsrel, which is set by
default to 1.49e-08. It returns the value of the integral and
an estimate of the error. An example calling sequence is
from scipy.integrate import quad
integral, integral_err = quad(f, a, b)
The routine has many optional parameters and many more variables
that it can return that are described at its reference page https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html.
There is also a version to do double integrals of functions with two
variables, scipy.integrate.dblquad.
Homework #16
For HW #15, you will write Python code to perform numerical
integration via the trapezoid rule and Simpson's rule and evaluate
the accuracy of those routines. Please hand in your code
electronically.
Your code should have a function integrate_trapezoid that
does numerical integration using the trapezoid rule and takes as
input: the name of the function to be integrated (f), the
endpoints of the interval of integration (a, b), and
the number of points to use (n). Write this function
first and test it by integrating
over the interval [0, 10], which you should be able to check
analytically. Your code should have a similar function integrate_simpson
that does numerical integration using Simpson's rule.
In the main body of your script, define the function
g(x) = (1+cos(x)) * exp(-x/(2*pi))
First plot this function over the interval x = [0, 60].
Then write a loop that integrates this function in the interval [0,
60] using different values for the number of points,
where j = 6, ... 16. Do the integration using both the
trapezoid rule and Simpson's rule.
For each n, plot the error in the numerical integration,
which we will define as the absolute value of the difference between
numerically calculated integral and the analytically calculated
integral which is
versus the integration step size, Δx. You should do
this on a log-log scale. Think about what trends you
see. In particular, does the error for each method depend on
some power of Δx? Include a comment block at the end
of your code with some discussion of this.
This assignment is worth 50 points.