LINE_INTEGRALS
Integrals Along the Length of the Unit Line in 1D

LINE_INTEGRALS is a C library 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
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

LINE_INTEGRALS is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BALL_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.

CIRCLE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.

CUBE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

DISK01_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.

HYPERBALL_INTEGRALS, a C 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 C 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 C 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 C 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 C library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

LINE_GRID, a C library which computes a grid of points over the interior of a line segment in 1D.

LINE_MONTE_CARLO, a C 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 C 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 C 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 C library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

PYRAMID_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

SIMPLEX_INTEGRALS, a C 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 C library which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.

SQUARE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.

TETRAHEDRON_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TRIANGLE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.

WEDGE_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

Source Code:

• line_integrals.c, the source code.
• line_integrals.h, the include file.

Examples and Tests:

• line_integrals_test.c, a sample calling program.
• line_integrals_test.txt, the output file.

List of Routines:

• LINE01_LENGTH: length of the unit line in 1D.
• LINE01_MONOMIAL_INTEGRAL: monomial integral over the unit line in 1D.
• LINE01_SAMPLE samples the unit line in 1D.
• MONOMIAL_VALUE_1D evaluates a monomial in 1D.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C source codes.