line_integrals, a FORTRAN77 code which returns the exact value of the integral of any monomial along the length of the unit monomial in 1D.
The length of the unit line in 1D is defined by
0 <= x <= 1
The integrands are all of the form
f(x) = x^e
where the exponent is a nonnegative integer.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
line_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
ball_integrals, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
CIRCLE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.
CUBE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
DISK_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
HYPERBALL_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.
HYPERCUBE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.
HYPERSPHERE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.
LINE_FEKETE_RULE, a FORTRAN77 library which approximates the location of Fekete points in an interval [A,B]. A family of sets of Fekete points, indexed by size N, represents an excellent choice for defining a polynomial interpolant.
LINE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.
LINE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a line segment in 1D.
LINE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D.
LINE_NCC_RULE, a FORTRAN77 library which computes a Newton Cotes Closed (NCC) quadrature rule for the line, that is, for an interval of the form [A,B], using equally spaced points which include the endpoints.
LINE_NCO_RULE, a FORTRAN77 library which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
POLYGON_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
PYRAMID_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
SIMPLEX_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.
SPHERE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
SQUARE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.
TETRAHEDRON_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
TRIANGLE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
WEDGE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.