HYPERCUBE_GRID
Grid of Points Inside a Hypercube in M Dimensions

HYPERCUBE_GRID is a FORTRAN77 library which generates a grid of points over the interior of a hypercube in M dimensions.

The M-dimensional hypercube is the set of points (X(1),X(2),...,X(M)) such that:

         A(I) <= X(I) <= B(I)
       

For each dimension I, a set of parameters is input:

• NS(I), the number of points along the I-th coordinate direction;
• A(I), B(I), the left and right endpoints of the I-th coordinate.
• C(I), one of 5 choices for centering the grid in the I-th coordinate.

The centering options allow the user to control the centering of the equally spaced points. This is easiest to illustrate if we look at a 1 dimensional case and assume A = 0 and B = 1. Then, using NS = 4, the centering options will produce 4 equally spaced points as follows:

• 1: 0, 1/3, 2/3, 1 (include endpoints)
• 2: 1/5, 2/5, 3/5, 4/5 (do not include endpoints)
• 3: 0, 1/4, 2/4, 3/4 (do not include right endpoint)
• 4: 1/4, 2/4, 3/4, 1 (do not include left endpoint)
• 5: 1/8, 3/8, 5/8, 7/8 (half spacing at the ends)

Licensing:

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

Languages:

HYPERCUBE_GRID 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_GRID, a FORTRAN77 library which computes a grid of points over the interior of a ball in 3D.

CIRCLE_ARC_GRID, a FORTRAN77 program which computes a grid of points over the length of a circular arc in 2D;

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

DISK_GRID, a FORTRAN77 library which computes a grid of points over the interior of a disk in 2D.

ELLIPSE_GRID, a FORTRAN77 library which computes a grid of points over the interior of an ellipse in 2D.

ELLIPSOID_GRID, a FORTRAN77 library which computes grid points over the interior of an ellipsoid in 3D.

HYPERCUBE_EXACTNESS, a FORTRAN77 program which measures the monomial exactness of an M-dimensional quadrature rule over the interior of the unit hypercube in M dimensions.

LINE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a line segment in 1D.

PYRAMID_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit pyramid in 3D.

SIMPLEX_GRID, a FORTRAN77 library which generates a grid of points over the interior of a simplex in M dimensions.

SPHERE_GRID, a FORTRAN77 library which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, on the surface of the unit sphere in 3D.

SQUARE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a square in 2D.

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

TRIANGLE_GRID, a FORTRAN77 library which computes a grid of points over the interior of a triangle in 2D.

WEDGE_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit wedge in 3D.

Source Code:

• hypercube_grid.f, the source code.
• hypercube_grid.sh, BASH commands to compile the source code.

Examples and Tests:

• hypercube_grid_prb.f, a sample calling program.
• hypercube_grid_prb.sh, BASH commands to compile and run the sample program.
• hypercube_grid_prb_output.txt, the output file.

List of Routines:

• HYPERCUBE_GRID: grid points over the interior of a hypercube in M dimensions.
• I4VEC_PRODUCT returns the product of the entries of an I4VEC.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8VEC_DIRECT_PRODUCT creates a direct product of R8VEC's.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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