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<html>
<head>
<title>
SUBPAK - A Utility Library
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SUBPAK <br> A Utility Library
</h1>
<hr>
<p>
<b>SUBPAK</b>
is a MATLAB library which
contains a number of utilities.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SUBPAK</b> is available in
<a href = "../../c_src/subpak/subpak.html">a C version</a> and
<a href = "../../cpp_src/subpak/subpak.html">a C++ version</a> and
<a href = "../../f77_src/subpak/subpak.html">a FORTRAN77 version</a> and
<a href = "../../f_src/subpak/subpak.html">a FORTRAN90 version</a> and
<a href = "../../m_src/subpak/subpak.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../m_src/c8lib/c8lib.html">
C8LIB</a>,
a MATLAB library which
implements certain elementary functions for "C8"
or double precision complex variables;
</p>
<p>
<a href = "../../m_src/cell/cell.html">
CELL</a>,
a MATLAB library which
defines a cell array, a generalization of an array which
can compactly store and retrieve vector or matrix data of
varying size, such as the rows of a triangular matrix.
</p>
<p>
<a href = "../../m_src/i4lib/i4lib.html">
I4LIB</a>,
a MATLAB library which
contains many utility routines, using "I4" or "single precision integer"
arithmetic.
</p>
<p>
<a href = "../../m_src/index/index.html">
INDEX</a>,
a MATLAB library which
converts a multidimensional vector index to a one-dimensional vector index;
it can handle zero and one based indexing schemes, as well as column major
and row major conventions.
</p>
<p>
<a href = "../../m_src/r8lib/r8lib.html">
R8LIB</a>,
a MATLAB library which
contains many utility routines, using "R8" or
"double precision real" arithmetic.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Milton Abramowitz, Irene Stegun,<br>
Handbook of Mathematical Functions,<br>
National Bureau of Standards, 1964,<br>
ISBN: 0-486-61272-4,<br>
LC: QA47.A34.
</li>
<li>
Book Industry Study Group,<br>
The Evolution in Product Identification:
Sunrise 2005 and the ISBN-13,<br>
<a href = "http://www.bisg.org/docs/The_Evolution_in_Product_ID.pdf">
http://www.bisg.org/docs/The_Evolution_in_Product_ID.pdf</a>
</li>
<li>
Thomas Cormen, Charles Leiserson, Ronald Rivest,<br>
Introduction to Algorithms,<br>
MIT Press, 2001,<br>
ISBN: 0262032937,<br>
LC: QA76.C662.
</li>
<li>
Donald Kreher, Douglas Simpson,<br>
Combinatorial Algorithms,<br>
CRC Press, 1998,<br>
ISBN: 0-8493-3988-X,<br>
LC: QA164.K73.
</li>
<li>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms for Computers and Calculators,<br>
Second Edition,<br>
Academic Press, 1978,<br>
ISBN: 0-12-519260-6,<br>
LC: QA164.N54.
</li>
<li>
Branch Rickey,<br>
Goodby to Some Old Baseball Ideas,<br>
Life Magazine,<br>
2 August 1954.
</li>
<li>
Alan Schwarz,<br>
Looking Beyond the Batting Average,<br>
The New York Times, <br>
Sunday, 1 August 2004.
</li>
<li>
Daniel Zwillinger, editor,<br>
CRC Standard Mathematical Tables and Formulae,<br>
30th Edition,<br>
CRC Press, 1996,<br>
ISBN: 0-8493-2479-3,<br>
LC: QA47.M315.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "angle_shift.m">angle_shift.m</a>,
shifts an angle to lie between BETA and BETA+2*PI.
</li>
<li>
<a href = "angle_shift_deg.m">angle_shift_deg.m</a>,
shifts an angle to lie between BETA and BETA+360.
</li>
<li>
<a href = "angle_to_rgb.m">angle_to_rgb.m</a>,
converts an angle to a color on the RGB hexagon.
</li>
<li>
<a href = "axis_limits.m">axis_limits.m</a>,
returns "nice" axis limits for a plot.
</li>
<li>
<a href = "bar_check.m">bar_check.m</a>,
computes the check digit for a bar code.
</li>
<li>
<a href = "bar_code.m">bar_code.m</a>,
constructs the 113 character bar code from 11 digits.
</li>
<li>
<a href = "bar_digit_code_left.m">bar_digit_code_left.m</a>,
returns the 7 character left bar code for a digit.
</li>
<li>
<a href = "bar_digit_code_right.m">bar_digit_code_right.m</a>,
returns the 7 character right bar code for a digit.
</li>
<li>
<a href = "bmi_english.m">bmi_english.m</a>,
computes the body mass index given English measurements.
</li>
<li>
<a href = "bmi_metric.m">bmi_metric.m</a>,
computes the body mass index given metric measurements.
</li>
<li>
<a href = "ch_cap.m">ch_cap.m</a>,
capitalizes a single character;
</li>
<li>
<a href = "ch_is_digit.m">ch_is_digit.m</a>,
determines if a character is a digit.
</li>
<li>
<a href = "ch_is_printable.m">ch_is_printable.m</a>,
determines if a character is printable.
</li>
<li>
<a href = "ch_swap.m">ch_swap.m</a>,
swaps two characters;
</li>
<li>
<a href = "ch_uniform.m">ch_uniform.m</a>,
returns a pseudorandom character.
</li>
<li>
<a href = "chvec_permute.m">chvec_permute.m</a>,
permutes a character vector.
</li>
<li>
<a href = "chvec_print.m">chvec_print.m</a>,
prints a character vector.
</li>
<li>
<a href = "chvec2_print.m">chvec2_print.m</a>,
prints a pair of character vectors.
</li>
<li>
<a href = "chvec_reverse.m">chvec_reverse.m</a>,
reverses the order of the entries of a character vector.
</li>
<li>
<a href = "cos_deg.m">
cos_deg.m</a>
returns the cosine of an angle given in degrees.
</li>
<li>
<a href = "degrees_to_radians.m">
degrees_to_radians.m</a>,
converts an angle measure from degrees to radians;
</li>
<li>
<a href = "e_constant.m">e_constant.m</a>,
returns the value of E.
</li>
<li>
<a href = "euler_constant.m">euler_constant.m</a>,
returns the value of the Euler-Mascheroni constant.
</li>
<li>
<a href = "fac_div.m">fac_div.m</a>,
divides two quantities represented as prime factors.
</li>
<li>
<a href = "fac_gcd.m">fac_gcd.m</a>,
finds the greatest common divisor of two quantities
represented as prime factors.
</li>
<li>
<a href = "fac_lcm.m">fac_lcm.m</a>,
finds the least common multiple of two quantities
represented as prime factors.
</li>
<li>
<a href = "fac_mul.m">fac_mul.m</a>,
multiplies two quantities represented as prime factors.
</li>
<li>
<a href = "fac_print.m">fac_print.m</a>,
prints a quantity represented as prime factors.
</li>
<li>
<a href = "fac_to_i4.m">fac_to_i4.m</a>,
converts a quantity represented as prime factors to an integer.
</li>
<li>
<a href = "fac_to_rat.m">fac_to_rat.m</a>,
converts a quantity represented as prime factors to a rational value.
</li>
<li>
<a href = "feet_to_meters.m">feet_to_meters.m</a>,
converts a measurement in feet to one in meters.
</li>
<li>
<a href = "gauss_sum.m">gauss_sum.m</a>,
evaluates a function which is the sum of Gaussians.
</li>
<li>
<a href = "get_seed.m">get_seed.m</a>,
returns a random seed for the random number generator.
</li>
<li>
<a href = "grid1.m">grid1.m</a>,
returns grid points between X1 and X2 in N dimensions.
</li>
<li>
<a href = "grid1n.m">grid1.m</a>,
returns a grid point between X1 and X2 in N dimensions.
</li>
<li>
<a href = "grid2.m">grid2.m</a>,
returns grid points between X1 and X2 in N dimensions.
</li>
<li>
<a href = "grid2n.m">grid2n.m</a>,
returns a grid point between X1 and X2 in N dimensions.
</li>
<li>
<a href = "grid3.m">grid3.m</a>,
returns an array of grid points between X1, X2 and X3 in N dimensions.
</li>
<li>
<a href = "grid3n.m">grid3n.m</a>,
returns one of the grid points between X1, X2 and X3 in N dimensions.
</li>
<li>
<a href = "grid4.m">grid4.m</a>,
computes a grid on the parallelogram set by X1, X2 and X3 in N space.
</li>
<li>
<a href = "grid4n.m">grid4n.m</a>,
computes on point from a grid on the parallelogram set
by X1, X2 and X3 in N space.
</li>
<li>
<a href = "i2vec_print.m">i2vec_print.m</a>,
prints a vector of pairs of integers;
</li>
<li>
<a href = "i3mat_flip_cols.m">i3mat_flip_cols.m</a>,
flips the columns in an I3MAT;
</li>
<li>
<a href = "i3mat_flip_rows.m">i3mat_flip_rows.m</a>,
flips the rows in an I3MAT;
</li>
<li>
<a href = "i4_log_10.m">i4_log_10.m</a>,
returns the integer part of the logarithm base 10 of an integer;
</li>
<li>
<a href = "i4_modp.m">i4_modp.m</a>,
returns the nonnegative remainder of integer division;
</li>
<li>
<a href = "i4_sign.m">i4_sign.m</a>,
returns the sign of an integer.
</li>
<li>
<a href = "i4_to_digits_decimal.m">i4_to_digits_decimal.m</a>,
determines the last N decimal digits of an integer;
</li>
<li>
<a href = "i4_to_fac.m">i4_to_fac.m</a>,
converts an integer into a product of prime factors;
</li>
<li>
<a href = "i4_to_isbn.m">i4_to_isbn.m</a>,
converts an I4 to its ISBN representation;
</li>
<li>
<a href = "i4_uniform.m">i4_uniform.m</a>,
returns a pseudorandom integer in a given range;
</li>
<li>
<a href = "i4int_to_r8int.m">
i4int_to_r8int.m</a>,
maps an I4 interval to an R8 interval;
</li>
<li>
<a href = "i4vec_min.m">i4vec_min.m</a>,
returns the minimum entry in an I4VEC;
</li>
<li>
<a href = "i4vec_permute.m">i4vec_permute.m</a>,
permutes an I4VEC in place;
</li>
<li>
<a href = "i4vec_print.m">i4vec_print.m</a>,
prints an I4VEC;
</li>
<li>
<a href = "i4vec_uniform.m">i4vec_uniform.m</a>,
returns a pseudorandom I4VEC in a given range;
</li>
<li>
<a href = "i8_btest.m">i8_btest.m</a>,
returns TRUE if bit POS of I is a 1;
</li>
<li>
<a href = "i8_xor.m">i8_xor.m</a>,
returns the exclusive OR of two integers;
</li>
<li>
<a href = "ij_next.m">
ij_next.m</a>,
returns the next matrix index;
</li>
<li>
<a href = "ij_next_gt.m">
ij_next_gt.m</a>,
returns the next matrix index, with the requirement that I < J;
</li>
<li>
<a href = "index_box2_next_2d.m">index_box2_next_2d.m</a>,
produces indices on the surface of a box in 2D.
</li>
<li>
<a href = "index_box2_next_3d.m">index_box2_next_3d.m</a>,
produces indices on the surface of a box in 3D.
</li>
<li>
<a href = "index1_col.m">index1_col.m</a>,
indexes a 1D array by columns.
</li>
<li>
<a href = "index1_row.m">index1_row.m</a>,
indexes a 1D array by rows.
</li>
<li>
<a href = "index2_col.m">index2_col.m</a>,
indexes a 2D array by columns.
</li>
<li>
<a href = "index2_row.m">index2_row.m</a>,
indexes a 2D array by rows.
</li>
<li>
<a href = "index3_col.m">index3_col.m</a>,
indexes a 3 array by columns.
</li>
<li>
<a href = "index3_row.m">index3_row.m</a>,
indexes a 3D array by rows.
</li>
<li>
<a href = "index4_col.m">index4_col.m</a>,
indexes a 4D array by columns.
</li>
<li>
<a href = "index4_row.m">index4_row.m</a>,
indexes a 4D array by rows.
</li>
<li>
<a href = "indexn_col.m">indexn_col.m</a>,
indexes an ND array by columns.
</li>
<li>
<a href = "indexn_row.m">indexn_row.m</a>,
indexes an ND array by rows.
</li>
<li>
<a href = "isbn_check.m">isbn_check.m</a>,
checks an ISBN for validity.
</li>
<li>
<a href = "isbn_to_i4.m">isbn_to_i4.m</a>,
converts an ISBN character to an I4.
</li>
<li>
<a href = "isbn_fill.m">isbn_fill.m</a>,
can fill in one missing character in an ISBN.
</li>
<li>
<a href = "l4mat_print.m">l4mat_print.m</a>,
prints an L4MAT;
</li>
<li>
<a href = "l4mat_print_some.m">l4mat_print_some.m</a>,
prints some of an L4MAT;
</li>
<li>
<a href = "l4mat_transpose_print.m">l4mat_transpose_print.m</a>,
prints an L4MAT, transposed;
</li>
<li>
<a href = "l4mat_transpose_print_some.m">l4mat_transpose_print_some.m</a>,
prints some of an L4MAT, transposed;
</li>
<li>
<a href = "l4vec_print.m">l4vec_print.m</a>,
prints a LVEC;
</li>
<li>
<a href = "lcm_12n.m">lcm_12n.m</a>,
computes the least common multiple of the integers 1 through N;
</li>
<li>
<a href = "pause_input.m">pause_input.m</a>,
waits until an input character is entered;
</li>
<li>
<a href = "perm_check.m">perm_check.m</a>,
checks that a vector represents a permutation;
</li>
<li>
<a href = "perm_cycle.m">perm_cycle.m</a>,
analyzes a permutation;
</li>
<li>
<a href = "perm_free.m">perm_free.m</a>,
reports the unused items in a partial permutation;
</li>
<li>
<a href = "perm_inverse.m">perm_inverse.m</a>,
computes the inverse of a permutation;
</li>
<li>
<a href = "perm_next.m">perm_next.m</a>,
computes all permutations of N things, one at a time;
</li>
<li>
<a href = "perm_print.m">perm_print.m</a>,
prints a permutation;
</li>
<li>
<a href = "perm_uniform.m">perm_uniform.m</a>,
selects a random permutation of N objects;
</li>
<li>
<a href = "pounds_to_kilograms.m">pounds_to_kilograms.m</a>,
converts a measurement in pounds to one in kilograms;
</li>
<li>
<a href = "prime.m">prime.m</a>,
returns the N-th prime number;
</li>
<li>
<a href = "prime_ge.m">prime_ge.m</a>,
returns the smallest prime greater than or equal to N;
</li>
<li>
<a href = "primer.m">primer.m</a>,
computes the prime numbers up to a given limit;
</li>
<li>
<a href = "r4_uniform_01.m">r4_uniform_01.m</a>,
returns a unit pseudorandom R4;
</li>
<li>
<a href = "r8_log_10.m">r8_log_10.m</a>,
returns the logarithm base 10 of an R8;
</li>
<li>
<a href = "r8_uniform.m">r8_uniform.m</a>,
returns a scaled pseudorandom R8;
</li>
<li>
<a href = "r8mat_print.m">r8mat_print.m</a>,
prints an R8MAT, with an optional title;
</li>
<li>
<a href = "r8mat_print_some.m">r8mat_print_some.m</a>,
prints some of an R8MAT;
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>,
prints the transpose of an R8MAT;
</li>
<li>
<a href = "r8mat_transpose_print_some.m">
r8mat_transpose_print_some.m</a>,
prints some of the transpose of an R8MAT;
</li>
<li>
<a href = "r8poly_order.m">r8poly_order.m</a>,
returns the order of a polynomial.
</li>
<li>
<a href = "r8poly_print.m">r8poly_print.m</a>,
prints a polynomial;
</li>
<li>
<a href = "r8vec_indicator.m">r8vec_indicator.m</a>,
sets an R8VEC to the indicator vector;
</li>
<li>
<a href = "r8vec_mean.m">r8vec_mean.m</a>,
returns the mean of an R8VEC;
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC;
</li>
<li>
<a href = "r8vec_variance.m">r8vec_variance.m</a>,
returns the variance of an R8VEC;
</li>
<li>
<a href = "radians_to_degrees.m">radians_to_degrees.m</a>,
converts an angle measure from radians to degrees;
</li>
<li>
<a href = "random_initialize.m">random_initialize.m</a>,
initializes the MATLAB random number generator;
</li>
<li>
<a href = "rat_factor.m">rat_factor.m</a>,
factors a rational value into a product of prime factors;
</li>
<li>
<a href = "roots_to_r8poly.m">roots_to_r8poly.m</a>,
converts polynomial roots to polynomial coefficients;
</li>
<li>
<a href = "roots_to_i4poly.m">roots_to_i4poly.m</a>,
converts polynomial roots to polynomial coefficients;
</li>
<li>
<a href = "s_cat.m">s_cat.m</a>,
concatenates two strings;
</li>
<li>
<a href = "s_eqi.m">s_eqi.m</a>,
compares two strings for equality, ignoring case and trailing blanks;
</li>
<li>
<a href = "s_len_trim.m">s_len_trim.m</a>,
returns the length of a character string to the last nonblank;
</li>
<li>
<a href = "s_swap.m">s_swap.m</a>,
swaps two strings;
</li>
<li>
<a href = "sin_deg.m">
sin_deg.m</a>
returns the sine of an angle given in degrees.
</li>
<li>
<a href = "sort_heap_external.m">sort_heap_external.m</a>,
external sorts a list of values into ascending order;
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a timestamp;
</li>
<li>
<a href = "tuple_next2.m">tuple_next2.m</a>,
computes the next element of an integer tuple space;
</li>
<li>
<a href = "tvec_bracket_even.m">tvec_bracket_even.m</a>,
computes evenly spaced angles between THETA1 and THETA2;
</li>
<li>
<a href = "tvec_bracket_even2.m">tvec_bracket_even2.m</a>,
computes evenly spaced angles between THETA1 and THETA2;
</li>
<li>
<a href = "tvec_bracket_even3.m">tvec_bracket_even3.m</a>,
computes evenly spaced angles between THETA1 and THETA2;
</li>
<li>
<a href = "tvec_even.m">tvec_even.m</a>,
computes evenly spaced angles between 0 and 2*PI;
</li>
<li>
<a href = "tvec_even2.m">tvec_even2.m</a>,
computes evenly spaced angles between 0 and 2*PI;
</li>
<li>
<a href = "tvec_even3.m">tvec_even3.m</a>,
computes evenly spaced angles between 0 and 2*PI;
</li>
<li>
<a href = "upc_check_digit.m">upc_check_digit.m</a>,
returns the check digit of a UPC;
</li>
<li>
<a href = "versine_pulse.m">versine_pulse.m</a>,
adds a versine pulse to a constant.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "subpak_test.m">subpak_test.m</a>,
runs all the tests;
</li>
<li>
<a href = "subpak_test_output.txt">subpak_test_output.txt</a>,
the output file;
</li>
<li>
<a href = "subpak_test01.m">subpak_test01.m</a>,
tests ANGLE_SHIFT;
</li>
<li>
<a href = "subpak_test02.m">subpak_test02.m</a>,
tests ANGLE_SHIFT_DEG;
</li>
<li>
<a href = "subpak_test03.m">subpak_test03.m</a>,
tests ANGLE_TO_RGB;
</li>
<li>
<a href = "subpak_test04.m">subpak_test04.m</a>,
tests AXIS_LIMITS;
</li>
<li>
<a href = "subpak_test05.m">subpak_test05.m</a>,
tests AXIS_LIMITS;
</li>
<li>
<a href = "subpak_test06.m">subpak_test06.m</a>,
tests BAR_CHECK, BAR_CODE, BAR_DIGIT_CODE_LEFT and
BAR_DIGIT_CODE_RIGHT.
</li>
<li>
<a href = "subpak_test07.m">subpak_test07.m</a>,
tests BMI_ENGLISH;
</li>
<li>
<a href = "subpak_test08.m">subpak_test08.m</a>,
tests FAC_DIV, FAC_GCD, FAC_LCM, FAC_MUL, FAC_TO_I4, and I4_TO_FAC.
</li>
<li>
<a href = "subpak_test09.m">subpak_test09.m</a>,
tests GAUSS_SUM;
</li>
<li>
<a href = "subpak_test10.m">subpak_test10.m</a>,
tests GET_SEED;
</li>
<li>
<a href = "subpak_test11.m">subpak_test11.m</a>,
tests GRID1;
</li>
<li>
<a href = "subpak_test12.m">subpak_test12.m</a>,
tests GRID1N;
</li>
<li>
<a href = "subpak_test13.m">subpak_test13.m</a>,
tests GRID2;
</li>
<li>
<a href = "subpak_test14.m">subpak_test14.m</a>,
tests GRID2N;
</li>
<li>
<a href = "subpak_test15.m">subpak_test15.m</a>,
tests GRID3;
</li>
<li>
<a href = "subpak_test16.m">subpak_test16.m</a>,
tests GRID3N;
</li>
<li>
<a href = "subpak_test17.m">subpak_test17.m</a>,
tests GRID4;
</li>
<li>
<a href = "subpak_test18.m">subpak_test18.m</a>,
tests GRID4N.
</li>
<li>
<a href = "subpak_test19.m">subpak_test19.m</a>,
tests INDEX1_COL, INDEX1_ROW, and related functions.
</li>
<li>
<a href = "subpak_test20.m">subpak_test20.m</a>,
tests ISBN_CHECK.
</li>
<li>
<a href = "subpak_test21.m">subpak_test21.m</a>,
tests ISBN_FILL.
</li>
<li>
<a href = "subpak_test22.m">subpak_test22.m</a>,
tests LCM_12N.
</li>
<li>
<a href = "subpak_test225.m">subpak_test225.m</a>,
tests L4MAT_PRINT.
</li>
<li>
<a href = "subpak_test24.m">subpak_test24.m</a>,
tests PERM_INVERSE;
</li>
<li>
<a href = "subpak_test25.m">subpak_test25.m</a>,
tests PRIME_GE;
</li>
<li>
<a href = "subpak_test26.m">subpak_test26.m</a>,
tests RANDOM_INITIALIZE.
</li>
<li>
<a href = "subpak_test27.m">subpak_test27.m</a>,
tests RAND.
</li>
<li>
<a href = "subpak_test28.m">subpak_test28.m</a>,
tests RAND.
</li>
<li>
<a href = "subpak_test29.m">subpak_test29.m</a>,
tests RAT_FACTOR.
</li>
<li>
<a href = "subpak_test30.m">subpak_test30.m</a>,
tests ROOTS_TO_R8POLY.
</li>
<li>
<a href = "subpak_test31.m">subpak_test31.m</a>,
tests SORT_HEAP_EXTERNAL;
</li>
<li>
<a href = "subpak_test32.m">subpak_test32.m</a>,
tests TVEC_EVEN, TVEC_EVEN2, TVEC_EVEN3;
</li>
<li>
<a href = "subpak_test33.m">subpak_test33.m</a>,
tests TVEC_BRACKET_EVEN, TVEC_BRACKET_EVEN2, TVEC_BRACKET_EVEN3;
</li>
<li>
<a href = "subpak_test34.m">subpak_test34.m</a>,
tests UPC_CHECK_DIGIT;
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 03 November 2011.
</i>
<!-- John Burkardt -->
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