BINS
Order, Sort and Search Data using Bins

BINS is a FORTRAN90 library, using double precision arithmetic, which can sort data into order, or lump it into bins, or select an item of particular rank, or find the unique elements in a list.

Related Data and Programs:

BINS is also available in a C++ version.

SUBPAK is a FORTRAN90 library which contains many routines for sorting and searching data.

Reference:

1. Jon Bentley, Bruce Weide, Andrew Yao,
   Optimal Expected Time Algorithms for Closest Point Problems,
   ACM Transactions on Mathematical Software,
   Volume 6, Number 4, December 1980, pages 563-580.
2. Thomas Cormen, Charles Leiserson, Ronald Rivest,
   Introduction to Algorithms,
   MIT Press, 2001,
   ISBN: 0262032937,
   LC: QA76.C662.
3. Barry Joe,
   GEOMPACK - a software package for the generation of meshes using geometric algorithms,
   Advances in Engineering Software,
   Volume 13, pages 325-331, 1991.
4. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.

Source Code:

• bins.f90, the source code.
• bins.csh, commands to compile the source code.

Examples and Tests:

• bins_prb.f90, a sample calling program.
• bins_prb.csh, commands to compile and run the sample program.
• bins_prb_output.txt, the output file.

List of Routines:

• BIN_SEARCH_ONE_2D searches one cell in a 2D array of bins.
• BIN_TO_R8_EVEN returns the limits for a given "bin" in [A,B].
• BIN_TO_R8_EVEN2 returns the limits for a given "bin" in [A,B].
• BIN_TO_R82_EVEN returns the limits for a given R82 "bin" in [A,B].
• BIN_TO_R82_EVEN2 returns the limits for a given D82 "bin" in [A,B].
• BIN_TO_R82_EVEN3 returns the limits for a given R82 "bin" in [A,B].
• BIN_TO_R83_EVEN2 returns the limits for a given R83 "bin" in [A,B].
• BIN_TO_R83_EVEN3 returns the limits for a given R83 "bin" in [A,B].
• BIN_TO_R8VEC_EVEN3 returns the limits for a given R8VEC "bin" in [A,B].
• DIAEDG chooses a diagonal edge.
• DTRIS2 constructs a Delaunay triangulation of 2D vertices.
• GET_SEED returns a seed for the random number generator.
• I4_MODP returns the nonnegative remainder of integer division.
• I4_SWAP switches two integer values.
• I4_WRAP forces an integer to lie between given limits by wrapping.
• I4MAT_PRINT prints an integer matrix.
• I4MAT_PRINT_SOME prints some of an integer matrix.
• I4MAT_TRANSPOSE_PRINT prints an IMAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an integer matrix.
• INDEX_BOX2_NEXT_2D produces indices on the surface of a box in 2D.
• INDEX_BOX2_NEXT_3D produces indices on the surface of a box in 3D.
• I4VEC_HEAP_D reorders an I4VEC into a descending heap.
• I4VEC_INDICATOR sets an I4VEC to the indicator vector.
• I4VEC_PRINT prints an I4VEC.
• I4VEC_SORT_HEAP_A ascending sorts an I4VEC using heap sort.
• I4VEC_UNIQUE finds the number of unique elements in a sorted I4VEC.
• I4VEC2_COMPARE compares pairs of integers stored in two vectors.
• I4VEC2_SORT_A ascending sorts a vector of pairs of integers.
• I4VEC2_UNIQUE keeps the unique elements in a array of pairs of integers.
• LRLINE determines where a point lies in relation to a directed line.
• PERM_INV inverts a permutation "in place".
• POINTS_NEAREST_POINT_BINS_2D finds the nearest point to a given point in 2D.
• POINTS_NEAREST_POINT_BINS_2D_2 finds the nearest point to a given point in 2D.
• POINTS_NEAREST_POINT_BINS_2D_3 finds the nearest point to a given point in 2D.
• POINTS_NEAREST_POINT_DEL_2D: nearest neighbor in a Delaunay triangulation.
• POINTS_NEAREST_POINT_NAIVE_2D finds the nearest point to a given point in 2D.
• POINTS_NEAREST_POINT_NAIVE_3D finds the nearest point to a given point in 3D.
• POINTS_NEAREST_POINTS_BINS_2D finds the nearest point to given points in 2D.
• POINTS_NEAREST_POINTS_BINS_2D_2 finds the nearest point to given points in 2D.
• POINTS_NEAREST_POINTS_BINS_2D_3 finds the nearest point to given points in 2D.
• POINTS_NEAREST_POINTS_BINS_2D_4 finds the nearest point to given points in 2D.
• POINTS_NEAREST_POINTS_BINS_3D_2 finds the nearest point to given points in 3D.
• POINTS_NEAREST_POINTS_BINS_3D_3 finds the nearest point to given points in 3D.
• POINTS_NEAREST_POINTS_NAIVE_2D finds the nearest point to given points in 2D.
• POINTS_NEAREST_POINTS_NAIVE_3D finds the nearest point to given points in 3D.
• POINTS_NEAREST_POINT_NAIVE_ND finds the nearest point to a given point in ND.
• R8_TO_BIN_EVEN determines the appropriate "bin" for C in [A,B].
• R8_TO_BIN_EVEN2 determines the appropriate "bin" for C in [A,B].
• R8_TO_BIN_UNEVEN places X in one of several unevenly spaced bins.
• R8_UNIFORM returns a scaled pseudorandom R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R82_UNIFORM returns a random R82 value in a given range.
• R82_TO_BIN_EVEN determines the appropriate "bin" for an R82 value.
• R82_TO_BIN_EVEN2 determines the appropriate "bin" for an R82 value.
• R82_TO_BIN_EVEN3 determines the appropriate "bin" for an R82 value.
• R82VEC_BIN_EVEN bins an R82VEC into evenly spaced bins.
• R82VEC_BIN_EVEN2 bins an R82VEC into evenly spaced bins.
• R82VEC_BIN_EVEN3 bins an R82VEC into evenly spaced bins.
• R82VEC_BINNED_REORDER reorders a binned R82 data vector.
• R82VEC_BINNED_REORDER2 reorders a binned R82VEC.
• R82VEC_BINNED_SORT_A sorts each bin of a binned R82VEC.
• R82VEC_BINNED_SORT_A2 sorts each bin of a binned R82VEC.
• R82VEC_PART_QUICK_A reorders an R82VEC as part of a quick sort.
• R82VEC_PERMUTE permutes an R82VEC in place.
• R82VEC_PRINT prints an R82VEC.
• R82VEC_UNIFORM returns a random R82VEC in a given range.
• R82VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an R82VEC.
• R82VEC_SORT_QUICK_A ascending sorts an R82VEC using quick sort.
• R83_TO_BIN_EVEN2 determines the appropriate "bin" for an R83 value.
• R83_TO_BIN_EVEN3 determines the appropriate "bin" for an R83 value.
• R83VEC_BIN_EVEN2 bins an R83VEC into evenly spaced bins.
• R83VEC_BIN_EVEN3 bins an R83 array into evenly spaced bins.
• R83VEC_BINNED_REORDER reorders a binned R83 data vector.
• R83VEC_BINNED_REORDER2 reorders a binned R83 data vector.
• R83VEC_BINNED_SORT_A sorts each bin of a binned R83VEC.
• R83VEC_BINNED_SORT_A2 sorts each bin of an R83 binned data vector.
• R83VEC_PART_QUICK_A reorders an R83VEC as part of a quick sort.
• R83VEC_PRINT prints an R83VEC.
• R83VEC_UNIFORM returns a random R83VEC in a given range.
• R83VEC_SORT_QUICK_A ascending sorts an R83VEC using quick sort.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8VEC_BIN bins an R8VEC, returning the population of each bin.
• R8VEC_BIN_EVEN bins an R8VEC into evenly spaced bins.
• R8VEC_BINNED_REORDER reorders a binned R8VEC.
• R8VEC_BINNED_SORT_A ascending sorts a binned reordered R8VEC.
• R8VEC_BRACKET searches a sorted array for successive brackets of a value.
• R8VEC_EQ is true if every pair of entries in two vectors is equal.
• R8VEC_GT == ( A1 > A2 ) for real vectors.
• R8VEC_LT == ( A1 < A2 ) for real vectors.
• R8VEC_PART_QUICK_A reorders an R8VEC as part of a quick sort.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_SORT_QUICK_A ascending sorts an R8VEC using quick sort.
• R8VEC_SWAP swaps the entries of two real vectors.
• R8VEC_TO_BIN_EVEN3 determines the appropriate "bin" for an R8VEC.
• R8VEC_UNIFORM returns a random R8VEC in a given range.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• SWAPEC swaps diagonal edges until all triangles are Delaunay.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.
• TRIANGLE_AREA_2D computes the area of a triangle in 2D.
• TRIANGLE_SAMPLE_2D returns a random point in a triangle.
• TRIANGULATION_NABE_NODES determines the neighbors of triangulation nodes.
• TRIANGULATION_PRINT prints out information defining a Delaunay triangulation.
• TRIANGULATION_SAMPLE_2D returns random points in a triangulation.
• TUPLE_NEXT2 computes the next element of an integer tuple space.
• VBEDG determines which boundary edges are visible to a point.

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