EINT

Numerically integrate data employing the extrapolation method.

• make,
• gcc, and
• gfortran.

make
sudo make install PREFIX=/usr/local

Default installation in /usr/local. Installs:

• eint: executable program which processes CSV data to compute integrals numerically,
• libeint.so: shared library providing the functions extrapolation_float, and extrapolation_double;
• EINT_C.h: C header file for libeint.so, and
• EINT_F.h: Fortran header file for libeint.so.

sudo make uninstall PREFIX=/usr/local

cp profiles/parallel.make Makefile

EINT computes integrals of the form

$$ I = \frac{1}{b-a}\int_{a}^{b}f(x)dx, $$

using the extrapolation (a.k.a. Romberg integration) method. We assume that the $[a, b]$ interval is discretised as

$$ x \to x_i = a + (b-a)\frac{i-1}{N-1} = a + (i-1)h : i\in[1, N], $$

and that the array of values $\{f(x_i): i\in[1, N]\}$ is known. We call $N$ the number of discretisation points, and $h$ the "step size". EINT returns the integral $I$ after entering the array of values $\{f(x_i)\}$.

The accuracy of the method depends on $N$. Given a prime factorisation of $N-1$, $N-1 = 2^{n_2}3^{n_3}\cdots$, the extrapolation method can be applied with an arbitrary prime base $p$. If $p^{n_p}$ is a factor of $N-1$, then the expected accuracy of the result will be $\mathcal{O}(h^{2n_p})$.

After installation, the manual page is available

man eint

Additional resources, use cases and examples can be found in the example/ directory.

Compute $\int_0^1 dx\; x$ using $N = 5$.

echo "0.0 0.25 0.5 0.75 1.0" | eint -t

pre-commit install

fypp src/EINT_Core.fypp src/EINT_Core.F90
fypp src/Prime_Factors.fypp src/Prime_Factors.F90

make test

firefox test/report/index.html

code test/report/valgrind_s_run.log
code test/report/valgrind_p_run.log

make static_analysis
code test/static_analysis_reports/*.rpt