# CUBE_INTEGRALS Integrals Over the Interior of the Unit Cube in 3D

CUBE_INTEGRALS is a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

The interior of the unit cube in 3D is defined by

```        0 <= X <= 1,
0 <= Y <= 1,
0 <= Z <= 1.
```

The integrands are all of the form

```        f(x,y,z) = x^e1 * y^e2 * z^e3.
```
where the exponents are nonnegative integers.

### Languages:

CUBE_INTEGRALS is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

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_ARBQ_RULE, a FORTRAN77 library which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.

CUBE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

CUBE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a cube in 3D.

CUBE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate the integral of a function 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_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the length of the unit line 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.

### List of Routines:

• CUBE01_MONOMIAL_INTEGRAL: integral over interior of unit cube in 3D.
• CUBE01_SAMPLE samples the interior of the unit cube in 3D.
• CUBE01_VOLUME: volume of the unit cube in 3D.
• I4VEC_UNIFORM_AB returns a scaled pseudorandom I4VEC.
• MONOMIAL_VALUE evaluates a monomial.
• R8MAT_UNIFORM_01 fills an R8MAT with unit pseudorandom numbers.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.

Last revised on 18 January 2014.