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APT SUBROUTINE ONE-LINE SUMMARIES

Author:  Arthur L. Edwards (email:  xenopsbird@comcast.net).

Updated:  2006 July 7 13:00.

The APT Library currently contains over 300 subroutines, ranging from
basic low-level vector procedures to the higher-level Monte Carlo sampling
and geometric methods needed for Monte Carlo tracking of particles or beams
of matter or energy in 1-D, 2-D or 3-D geometries.

To find a subroutine for a particular task, look up any of the key words
describing the task in the appendix "APT SUBROUTINE KEY WORDS".
To find any other subroutines required for use of a particular subroutine,
see the appendix "APT SUBROUTINE LINKS".

One-line summaries are given below, alphabetically by subroutine name,
grouped into the six general categories below:

Physical and chemical constants
Geometry
Monte Carlo sampling (geometric)
Monte Carlo sampling (numerical)
Mathematics and statistics
Data manipulation
Bit and character manipulation (machine independent)
Precision and round-off error control
Error procedures

PHYSICAL AND CHEMICAL CONSTANTS

A modern (1999) self-consistent set of values of the fundamental constants
of physics and chemistry is provided in subroutines aptconl (180 values in
cm-g-sh-jerk-kev units), and aptconm (217 values in SI units).

aptconl  Find 1999 values of specified fundamental constants in cm-g-sh-keV.
aptconm  Find 1999 values of specified fundamental constants in SI units.

GEOMETRY

The geometry group consists of the Monte Carlo (geometric) group,
and the subroutines summarized below, including coordinate transformations;
translation, rotation, reflection and inversion operations; vector operations;
consideration of geometric objects, including points, lines, curves,
planes and quadric surfaces, and their interrelationships; and much more.
Many procedures are available in 1-D, 2-D and 3-D forms, in rectangular,
cylindrical and spherical coordinate systems, and in forms to process scalar
data and array data.

aptacct  Find points on a trajectory with time-dependent acceleration.
aptafac  Find all unexponentiated factors of an integer.
aptaxis  Find the principal axes, center and type of a quadric surface.
aptbanc  Find the bisectors of angles in a major plane.
aptbang  Find the bisectors of angles in 3-D space.
aptbrkn  Find if point is in a brick, local coordinates, distances.
aptbrkp  Find point with given local coordinates in a brick.
aptbrkv  Find coordinates, edge lengths, areas, volume of a brick.
aptcang  Find an angle in degrees, grads, radians, arc deg, min, sec.
aptcinc  Find the intersection between 2 circles in a major plane.
aptcirc  Find the circle through three points in a major plane.
aptcirk  Find the radii and centers of 2 circles tangent to 3 tangent circles.
aptcirl  Find the center of a circle tangent to two tangent circles.
aptcirp  Find the circle through three points in 3-D space.
aptcirt  Find the radii of two circles tangent to three tangent circles.
aptclis  Find equation of a cylinder with a given axis and radius.
aptcnis  Find equation of a cone on a major axis, given two points.
aptcniz  Find equation of a cone on the z axis, given two points.
aptcois  Find equation of a cone on a major axis, given vertex and angle.
aptcris  Find extreme curvatures at a point on a quadric surfaces.
aptcsys  Transform coordinates - Cartesian, cylindrical, spherical.
aptcsyv  Transform coordinates and vectors - Cartesian, cyl, spherical.
aptcube  Generate a cube centered on the origin.
aptcycy  Find axial and surface distances between two circular cylinders.
aptcyis  Find equation of a cylinder on a major axis, given the radius.
aptdirt  Find all unique directions between groups of points.
aptdist  Find distance and direction between two points, any coordinates.
aptdode  Generate a regular dodecahedron centered on the origin.
aptelis  Find equation of ellipsoid on major axis, given center, two pts.
aptesis  Find equation of ellipsoid at origin, given three semiaxes.
aptetrl  Find local coordinates of points in tetrahedrons.
aptetrn  Find if point is in a tetrahedron, distances, local coordinates.
aptetru  Find unit vector at specified angles from two other vectors.
aptetrv  Find line at specified angles from two other lines.
aptetrw  Find point with given vertex weights in tetrahedron, quadrangle.
aptfdqc  Find local coordinates of points in quadrangles.
apticos  Generate a regular icosahedron centered on the origin.
aptil08  Tile a unit sphere with triangles:  8, 32, 128, 512, ...
aptil12  Tile a unit sphere with triangles:  60, 240, 960, ...
aptil20  Tile a unit sphere with triangles:  20, 80, 320, ...
aptintq  Find proximal or intersection points of two quadric surfaces.
aptinvc  Invert coordinates in a major plane.
aptinvp  Invert coordinates in xyz space.
aptlnic  Find intersection of a line with a circle in a major plane.
aptlnlc  Find intersection of 2 lines in a major plane.
aptlnln  Find the minimum distance between 2 lines in xyz space.
aptlnpl  Find intersection of a line with a plane.
aptlntr  Find intersection of a line with a plane through three points.
aptmopv  Operate on vectors with a 3 by 3 matrix operator.
aptmove  Move a point a specified distance and direction, any coord sys.
aptmovs  Move a point a specified distance and direction, spherical.
aptmvcy  Move a point a specified distance and direction, cylindrical.
aptocta  Generate a regular octahedron centered on the origin.
aptparb  Find points on a parabolic (linearly accelerated) trajectory.
aptparh  Find initial velocity for a parabolic trajectory to hit a point.
aptparl  Find proximal points of a parabolic trajectory with a line.
aptparp  Find intersections of a parabolic trajectory with a plane.
aptparq  Find intersections of parabolic trajectory with quadric surface.
aptpars  Find proximal points of a parabolic trajectory with a point.
aptpart  Find parabolic trajectory for one to three points and times.
aptparx  Find quadric surface equation extrema on parabolic trajectory.
aptpblc  Find the line perpendicularly bisecting a line in a plane.
aptpbln  Find the plane perpendicularly bisecting a line in xyz space.
aptpent  Subdivide a regular pentagon into 5 triangles, on a sphere.
aptperc  Project points onto a perspective view line in a major plane.
aptpers  Project points onto a perspective view plane in xyz space.
aptpfac  Find all prime factors of an integer, and Euler's totient function.
aptpfit  Find the equation of a plane through three points.
aptplcy  Find intersection/distance of a plane and a circular cylinder.
aptplis  Find intersection of a major plane with a quadric surface.
aptplpl  Find the line of intersection of two planes, or their distance.
aptplqu  Find intersection/distance of a plane and a quadric surface.
aptplsp  Find the circle of intersection of a plane and a sphere.
aptpolc  Generate any regular polygon in a major plane.
aptpoly  Generate any regular polygon in xyz space.
aptprcy  Project a set of points onto a cylinder in xyz space (options).
aptprim  Find prime numbers and irreducible proportion geometric factors.
aptproc  Project a set of points radially onto a circle in a major plane.
aptprop  Project a set of points normally onto a plane in xyz space.
aptpros  Project a set of points radially onto a sphere in xyz space.
aptprsp  Project a set of points onto a sphere in xyz space (options).
aptptlc  Find the distance from a point to a line in a major plane.
aptptln  Find the distance from a point to a line in xyz space.
aptptpl  Find the distance from a point to a plane, and the near point.
aptqdic  Find the distances from a point to the edges of a quadrangle.
aptqexc  Find the extrema of a quadric curve in a major plane.
aptqexv  Find any extrema of a quadric surface in a specified direction.
aptqext  Find any x, y, z extrema, type and center of a quadric surface.
aptqfdc  Find the local coordinates of points in a quadrangle.
aptqfit  Find the quadric surface through nine points.
aptqhyp  Find the quadric surface through edges and center of a quadrangle.
aptqinc  Find if a point is in a quadrangle in a major plane, distances.
aptqnor  Find a quadric surface normal vector and tangent plane at a point.
aptqper  Find a quadric surface two quadric surface families are orthogonal on.
aptqprr  Find a proximal point on a quadric surface using steepest ascent.
aptqprt  Find a proximal point on a quadric surface using random trials.
aptquad  Find the distance from a point to a nonplanar quadrangle.
aptqupr  Project a quadric surface in a specified direction.
aptqupt  Find extreme and axis intercept points on a quadric surface.
aptquwt  Find the point with given local coordinates in a quadrangle.
aptqvac  Find the shapes and vertex areas of a set of planar quadrangles.
aptqval  Find the value of a quadric surface function at a specified point.
aptrabc  Find lines that cut a triangle into two equal areas and perimeters.
aptradv  Project a set of points onto a view factor plane in xyz space.
aptrcab  Find result of aptrcut for a single vertex of a triangle.
aptrcut  Find lines that cut a triangle into two equal areas and perimeters.
aptrefc  Reflect a direction vector from a line, all in a major plane.
aptrefl  Reflect a direction vector from a plane perp to a major plane.
aptrefq  Analyze a reflection operator, to find the plane.
aptrefs  Reflect points or direction vectors from a specified plane.
aptrext  Given small triangle from aptrcut, find all original triangles.
aptrich  Find if three edge lengths can form a real triangle.
aptripc  Find the local coordinates of a point in a major plane triangle.
aptripl  Find the local coordinates of a point in an xyz space triangle.
aptripp  Find equilateral projection of triangle with specified vertices.
aptripq  Find a triple point of three quadric surfaces.
aptripr  Find equilateral projection of triangle with specified edges.
aptrips  Find the scalar triple product of three vectors.
aptript  Find the distance from a triangle to a point in xyz space.
aptripv  Find the vector triple product of three vectors.
aptrkcl  Find the intersection of a linear track with a 1-D cylinder.
aptrkcy  Find the intersection of a linear track with a z-r cone.
aptrkis  Find the intersection of a linear track with a quadric surface.
aptrklc  Find the intersection of a linear track with a line in a plane.
aptrkpl  Find the intersection of a linear track with a plane.
aptrkrl  Find the intersection of a linear track with a 1-D sphere.
aptrksl  Find the intersection of a linear track with a major plane.
aptrloc  Find point with given vertex weights in a major plane triangle.
aptrlop  Find point with given vertex weights in an xyz space triangle.
aptrois  Find new equation coefficients for transformed quadric surface.
aptrota  Find the rotation operator for a specified axis, angle.
aptrotc  Rotate vectors in a major plane by a specified angle.
aptrotp  Find the rotation operator to make a plane parallel to another.
aptrotq  Analyze a rotation operator to find the axis, angle.
aptrots  Find the operator for 3 rotations around the major axes.
aptrott  Find the operator to rotate a plane and vector onto another.
aptrotv  Find the operator to rotate a vector onto another vector.
aptsclc  Linearly scale a set of points or vectors in a major plane.
aptscll  Linearly scale a set of points or vectors in xyz space.
aptsclr  Cylindrically scale a set of points or vectors in xyz space.
aptsclu  Uniformly scale a set of points or vectors in xyz space.
aptspcy  Find distance between a sphere and a circular cylinder.
aptspha  Find the sphere centered on an axis, and through two points.
aptsphk  Find the radii and centers of 2 spheres tangent to 4 tangent spheres.
aptsphl  Find the center of a sphere tangent to three tangent spheres.
aptsphp  Find the sphere with its surface through four specified points.
aptspht  Find the radii of two spheres tangent to four tangent spheres.
aptspsp  Find the circle of intersection between two spheres.
aptsver  Find the Steiner vertex of a triangle.
apttetd  Find the volume and centroid of a tetrahedron in xyz space.
apttetr  Generate a regular tetrahedron centered on the origin.
apttinc  Find if a point is in a triangle in a major plane, distances.
apttrac  Translate the origin to a specified point in a major plane.
apttran  Translate the origin to a specified point in xyz space.
apttric  Find the edge lengths, area, centroid of a major plane triangle.
apttrid  Find the edge lengths, area, centroid of an xyz space triangle.
apttrig  Find general geometric data for an xyz space triangle.
apttrip  Find the distance from a point to a triangular surface, more.
apttris  Find new equation coefficients for translated quadric surface.
aptvadc  Find a vector sum with specified coefficients, in a major plane.
aptvadd  Find a vector sum with specified coefficients.
aptvanc  Find the angle between two vectors in a major plane.
aptvang  Find the cosine of the angle between two vectors.
aptvaxb  Find a vector product and its magnitude.  Parallel?.
aptvaxc  Find vector product of two major plane vectors.  Parallel?.
aptvcvc  Project a vector onto another vector in a major plane.
aptvdic  Find the direction vector between two points in a major plane.
aptvdil  Find the distance between two points on a major axis.
aptvdis  Find a vector difference.  Coincidence?.
aptvdoc  Find scalar product of two major plane vectors.  Orthogonal?
aptvdos  Find a scalar product of two vectors.  (1+ 2nd.)  Orthogonal?.
aptvdot  Find a scalar product of two vectors.  (1+ pairs.)  Orthogonal?.
aptvpap  Find vector components parallel and perp to another vector.
aptvplc  Find the vector perpendicular to a line, all in a major plane.
aptvpln  Find the vector normal to a plane specified by three points.
aptvplp  Project a vector onto a plane in xyz space.
aptvsuc  Find the weighted sum of two vectors in a major plane.
aptvsum  Find the weighted sum of two vectors.
aptvuac  Find magnitude, replace a major plane vector with unit vector.
aptvubc  Find magnitude, unit vector for a vector in a major plane.
aptvuna  Find magnitude, replace a vector with a unit vector.
aptvunb  Find magnitude, unit vector for a vector.
aptvunz  Find magnitude, replace a vector with a unit vector (scalar).
aptvusz  Find magnitude, unit vector for a vector (scalar version).
aptvxuc  Find magnitude, unit vector product of two major plane vectors.
aptvxun  Find magnitude, unit vector product of two vectors.
aptwhis  Find side, distance for a point near a quadric surface.
aptwist  Twist points around an axis depending on axial position.
aptwirl  Twist points around an axis depending or radial position.

MONTE CARLO SAMPLING (GEOMETRIC)

The Monte Carlo (geometric) group contains the subroutines summarized below.

aptbrks  Randomly sample points in a brick (coordinate volume).
aptetrp  Randomly sample points in a tetrahedron.
aptlocd  Randomly sample points on an annular disk.
aptlocs  Randomly sample points in a spherical annulus.
aptlocy  Randomly sample points in a cylindrical annulus.
aptqloc  Randomly sample points in a planar quadrangle or triangle.
aptscad  Randomly sample planar vectors from a uniform PDF.
aptscan  Randomly sample 3-D unit vectors at a fixed angle from an axis.
aptscap  Randomly sample 3-D unit vectors from a cosine-power PDF.
aptscar  Randomly sample 3-D vectors, cosine-power in spherical sector.
aptscat  Randomly sample 3-D unit vectors from a uniform PDF.
aptscav  Randomly sample 3-D unit vectors from cosine-power PDFs.
aptscaz  Randomly sample a 3-D unit vector at a fixed angle from an axis.
aptsciz  Randomly sample a 3-D unit vector from a uniform PDF.
aptscma  Randomly sample 3-D unit vectors at fixed angle from major axis.
aptscmz  Randomly sample 3-D unit vector at fixed angle from major axis.
aptscns  Randomly sample points on a frustrum of a right circular cone.
aptscnv  Randomly sample points in a frustrum of a right circular cone.
aptspar  Randomly sample points in a parallelopiped or parallelogram.
apttloc  Randomly sample points in a triangle in a major plane.
apttlod  Randomly sample points in a triangle in 3-D space.

MONTE CARLO SAMPLING (NUMERICAL)

The Monte Carlo (numerical) group contains the subroutines summarized below.

aptalin  Find the aliased bins for a piecewise linear tabulated PDF.
aptalsb  Randomly sample bins from an aliased tabulated PDF.
aptalsh  Randomly sample values from a set of specified bins, uniform.
aptalsl  Randomly sample values from a set of specified bins, linear.
aptalst  Randomly sample bins in packed aliased PDFs, one PDF per sample.
aptcump  Find the cumulative PDF for a histogram or piecewise linear PDF.
aptcums  Randomly sample bins from a cumulative PDF.
aptcumt  Randomly sample bins in packed CPDFs, one CPDF per sample.
apteqin  Find equal-probability bin indices for a piecewise linear PDF.
apteqsb  Randomly sample bins from an array of equally probable bins.
apteqxn  Find equal-probability bins for a piecewise linear PDF.
apteqxs  Randomly sample values from a set of equal-probability bins.
aptexpl  Randomly sample values from one or more limited exponential PDFs.
aptexps  Randomly sample values from one or more exponential PDFs.
aptmaxw  Randomly sample values from a relativistic Maxwellian PDF.
aptnorm  Randomly sample values from one or more Normal PDFs.
aptrand  Randomly reorder an array.
aptrans  Randomly sample values from an array, without replacement.
aptrfps  Randomly sample a value from a range of values (floating-point).
aptrfpt  Randomly sample values, with any degree of striation (fl-pt).
aptrins  Randomly sample a value from a range of values (integer).
aptrint  Randomly sample values, with any degree of striation (integers).
aptslid  Randomly sample values from a linear PDF.
aptsliv  Randomly sample one value from each linear PDF.
aptspod  Randomly sample values on an interval from a power-law PDF.
aptxnup  Randomly sample frequencies from a Planck or Wien PDF.

MONTE CARLO SAMPLING (BIT AND CHARACTER)

aptbitr  Randomly sample bits and put into part of a machine word.
aptchrn  Randomly sample characters and put into a character string.

MATHEMATICS AND STATISTICS

Most of the mathematics and statistics subroutines have unique features
to control round-off errors.
aptpfab

aptbadd  Add two big integers (one digit per word, any number base).
aptbasb  Find the value of a big integer in a specified number base.
aptbase  Find the value of a decimal number in a specified number base.
aptbcat  Concatenate the digits of two nonzero big integers.
aptbdiv  Divide one big integer by another in a specified number base.
aptbexp  Find the exponential function of a big integer.
aptbfac  Find the factorial function of a big integer.
aptbmul  Multiply two big integers (one digit per word, any number base).
aptbpac  Find the number of perm's and comb's using big integers.
aptbpow  Find a power of a big integer (one digit per word).
aptbrtn  Find a root of a big integer (one digit per word).
aptbsub  Find the difference beween two big integers (one digit per word).
aptbsum  Find the count of each digit in a big integer, any number base).
aptbtod  Find the integer, floating point and log values for a big integer.
aptcmad  Find the greatest common divisor and least common multiple.
aptcofr  Find the continued fraction, convergents, sums for a given value.
aptcofv  Find the convergents, partial sums of a continued fraction.
aptcomf  Find the number of combinations of N things taken M at a time.
aptcomg  Find the number of ways a group can be separated into smaller groups.
aptcrtr  Find remainders for an integer, given integer divisors.
aptcrts  Find the solution to a Chinese Remainder Theorum problem.
aptcubs  Find the real and complex roots of a cubic polynomial equation.
aptdet3  Find the determinant of a 3x3 matrix.
aptdet4  Find the determinant of a 4x4 matrix.
aptdtob  Find the big integer for a specified decimal integer, any number base.
aptfact  Find the factorial function of an integer.
aptftob  Find the big integer for a specified decimal floating point value.
aptgrat  Find ratio of geometric series given first term, sum, length.
aptiris  Find the integer plus reciprocal integer series for a decimal number.
aptltob  Find the big integer for a the log10 of a decimal floating point value.
aptmean  Find mean value and standard deviation of a set of values.
aptmord  Find order, multiplicative inverse of an integer in modular arithmetic.
aptmprd  Find the matrix product of two n by n matrices.
aptnewt  Find a real root of a polynomial using Newtonian iteration.
aptperf  Find the number of permutations of N things taken M at a time.
aptpfab  Find all prime factors of a big integer (one digit per word).
aptpfac  Find all prime factors of an integer, and Euler's totient function.
aptpfft  Find all prime factors of a factorial function.
aptpole  Find the values of a polynomial equation for a set of arguments.
aptpolf  Factor a real root out of a polynomial equation.
aptpolr  Find real roots, extrema and infl pts of a polynomial equation.
aptprim  Find prime numbers and irreducible proportion geometric factors.
aptqrts  Find the real or complex roots of a quadratic equation.
aptqrtv  Find the real or complex roots of a set of quadratic equations.
aptquar  Find the real and complex roots of a quartic polynomial equation.
aptsolv  Solve linear equation sets, invert matrices.
aptsudo  Solve a Sudoku puzzle.
aptsudp  Find permitted digits for solving a Sudoku puzzle.
aptsudu  Find duplicate characters in Sudoku puzzle row, column or box.
aptsudx  Do bookkeeping for solving a Sudoku puzzle.

DATA MANIPULATION

The data manipulation subroutines allow a variety of operations on
data, of use in many applications.

aptcomb  Generate all combinations of N things taken M at a time.
aptdeld  Reduce a table to rows with unique values in specified columns.
aptintp  Interpolate or extrapolate with two points, linear or log axes.
aptlook  Table look-up, any interval, ascending or desc, binary search.
aptmnlg  Find positive values and indices of min and max of an array.
aptmnmx  Find values and indices of minimum and maximum of an array.
aptperm  Generate all permutations of N things taken M at a time.
aptsorm  Sort two or more columns of a 2-D array, any direction, mode.
aptsort  Sort one column of a 1-D or 2-D array, any direction, mode.
aptword  Find if machine words are between two specified limits, any mode.

BIT AND CHARACTER MANIPULATION (MACHINE INDEPENDENT)

The bit and character manipulation subroutines allow parsing of input
data, working with file names, formatting output data, and many other tasks.
Two additional subroutines, aptbitr and aptchrn, in the Monte Carlo sampling
group, allow random sampling of bits and characters.

aptatob  Copy digits 0-9 in a character string into separate words.
aptbitb  Do Boolean operations on bits of machine words.
aptbite  Expand bits from machine words into a type integer*1 array.
aptbitf  Find a bit string in a machine word.
aptbitm  Move a bit string from one machine word to another.
aptbitp  Contract bits from a type integer*1 array into machine words.
aptbits  Shift bits right or left in a machine word, wrap-around or pull.
aptblsq  Reduce multiple blanks to a single blank in a character string.
aptchai  Translate octal, decimal or hexadecimal characters into integer.
aptchap  Separate a character string into data fields, translate.
aptchfp  Find a character string in another character string.
aptchfs  Find a delimited character string in another character string.
aptchia  Translate integer into octal, decimal or hexadecimal characters.
aptchin  Increment or decrement a character string, with carry.
aptchip  Find and replace non-graphic characters in a character string.
aptchmv  Move a character string from one character array to another.
aptchrp  Replace individual characters in a character string.
aptchsq  Squeeze a character out of a string, right-fill with blanks.
aptchtp  Translate a character string into integer and/or floating-point.
aptfbrk  Find a delimited character string in another character string.
aptffip  Read and crack free-field input lines into symbols, by mode.
apthexa  Translate a decimal number into a hexadecimal string.
apthexd  Translate a hexadecimal string into a decimal number.
aptquot  Find a delimited character string,  with escaped delimiters.
aptrmbl  Remove leading and/or trailing blanks from a character string.
aptsuba  Combine a stem and an ASCII subscript into a character string.
aptsubb  Combine a stem and ASCII subscripts into a character string.
aptsubi  Combine a stem and integer subscripts into a character string.
aptsubm  Translate a character string into a variable and subscripts, more.
aptsubr  Translate a character string into a variable and a subscript.
aptsubs  Translate a character string into a variable and a subscript, more.

PRECISION AND ROUND-OFF ERROR CONTROL

A number of techniques are needed to control or eliminate the
effects of round-off error due to the finite number of bits of precision
available on computers, especially to get correct and unambiguous answers
to such important geometric questions as whether geometric objects are
coincident, colinear, coplanar, parallel, perpendicular or tangent, within
the uncertainty due to round-off error, and to avoid producing meaningless
results that may later require special handling and testing to prevent major
errors or program crashes.  The following subroutines provide methods in
addition to those built into most APT subroutines.

aptfdad  Apply limits to a fractional distance.
aptfdav  Apply limits to a set of fractional distances.
aptnint  Round off a value to an integer multiple of a factor, if close enough.
aptrnds  Round off a value to a relative or absolute precision.
aptvlic  Impose lower limits on components of a vector in a major plane.
aptvlim  Impose lower limits on the components of a vector.
aptvtoc  Impose limits on the components of a vector in a major plane.
aptvtol  Impose limits on the components of a vector.

STANDARD ERROR PROCEDURE

An error procedure subroutine is provided to test the error flag
returned by another subroutine, write a message to specified output units,
providing information about the source of the error, and then to either
return or terminate the run, as specified by the user.

aptnerr  Test error flag, write messages to output files, and return or exit.

UCRL-WEB-209832
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