SUBPAK
A Utility Library

SUBPAK is a MATLAB library which contains a number of utilities.

Licensing:

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

Languages:

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

Related Programs:

C8LIB, a MATLAB library which implements certain elementary functions for "C8" or double precision complex variables;

CELL, 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.

I4LIB, a MATLAB library which contains many utility routines, using "I4" or "single precision integer" arithmetic.

INDEX, 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.

R8LIB, a MATLAB library which contains many utility routines, using "R8" or "double precision real" arithmetic.

Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Book Industry Study Group,
   The Evolution in Product Identification: Sunrise 2005 and the ISBN-13,
   http://www.bisg.org/docs/The_Evolution_in_Product_ID.pdf
3. Thomas Cormen, Charles Leiserson, Ronald Rivest,
   Introduction to Algorithms,
   MIT Press, 2001,
   ISBN: 0262032937,
   LC: QA76.C662.
4. Donald Kreher, Douglas Simpson,
   Combinatorial Algorithms,
   CRC Press, 1998,
   ISBN: 0-8493-3988-X,
   LC: QA164.K73.
5. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.
6. Branch Rickey,
   Goodby to Some Old Baseball Ideas,
   Life Magazine,
   2 August 1954.
7. Alan Schwarz,
   Looking Beyond the Batting Average,
   The New York Times,
   Sunday, 1 August 2004.
8. Daniel Zwillinger, editor,
   CRC Standard Mathematical Tables and Formulae,
   30th Edition,
   CRC Press, 1996,
   ISBN: 0-8493-2479-3,
   LC: QA47.M315.

Source Code:

• angle_shift.m, shifts an angle to lie between BETA and BETA+2*PI.
• angle_shift_deg.m, shifts an angle to lie between BETA and BETA+360.
• angle_to_rgb.m, converts an angle to a color on the RGB hexagon.
• axis_limits.m, returns "nice" axis limits for a plot.
• bar_check.m, computes the check digit for a bar code.
• bar_code.m, constructs the 113 character bar code from 11 digits.
• bar_digit_code_left.m, returns the 7 character left bar code for a digit.
• bar_digit_code_right.m, returns the 7 character right bar code for a digit.
• bmi_english.m, computes the body mass index given English measurements.
• bmi_metric.m, computes the body mass index given metric measurements.
• ch_cap.m, capitalizes a single character;
• ch_is_digit.m, determines if a character is a digit.
• ch_is_printable.m, determines if a character is printable.
• ch_swap.m, swaps two characters;
• ch_uniform.m, returns a pseudorandom character.
• chvec_permute.m, permutes a character vector.
• chvec_print.m, prints a character vector.
• chvec2_print.m, prints a pair of character vectors.
• chvec_reverse.m, reverses the order of the entries of a character vector.
• cos_deg.m returns the cosine of an angle given in degrees.
• degrees_to_radians.m, converts an angle measure from degrees to radians;
• e_constant.m, returns the value of E.
• euler_constant.m, returns the value of the Euler-Mascheroni constant.
• fac_div.m, divides two quantities represented as prime factors.
• fac_gcd.m, finds the greatest common divisor of two quantities represented as prime factors.
• fac_lcm.m, finds the least common multiple of two quantities represented as prime factors.
• fac_mul.m, multiplies two quantities represented as prime factors.
• fac_print.m, prints a quantity represented as prime factors.
• fac_to_i4.m, converts a quantity represented as prime factors to an integer.
• fac_to_rat.m, converts a quantity represented as prime factors to a rational value.
• feet_to_meters.m, converts a measurement in feet to one in meters.
• gauss_sum.m, evaluates a function which is the sum of Gaussians.
• get_seed.m, returns a random seed for the random number generator.
• grid1.m, returns grid points between X1 and X2 in N dimensions.
• grid1.m, returns a grid point between X1 and X2 in N dimensions.
• grid2.m, returns grid points between X1 and X2 in N dimensions.
• grid2n.m, returns a grid point between X1 and X2 in N dimensions.
• grid3.m, returns an array of grid points between X1, X2 and X3 in N dimensions.
• grid3n.m, returns one of the grid points between X1, X2 and X3 in N dimensions.
• grid4.m, computes a grid on the parallelogram set by X1, X2 and X3 in N space.
• grid4n.m, computes on point from a grid on the parallelogram set by X1, X2 and X3 in N space.
• i2vec_print.m, prints a vector of pairs of integers;
• i3mat_flip_cols.m, flips the columns in an I3MAT;
• i3mat_flip_rows.m, flips the rows in an I3MAT;
• i4_log_10.m, returns the integer part of the logarithm base 10 of an integer;
• i4_modp.m, returns the nonnegative remainder of integer division;
• i4_sign.m, returns the sign of an integer.
• i4_to_digits_decimal.m, determines the last N decimal digits of an integer;
• i4_to_fac.m, converts an integer into a product of prime factors;
• i4_to_isbn.m, converts an I4 to its ISBN representation;
• i4_uniform.m, returns a pseudorandom integer in a given range;
• i4int_to_r8int.m, maps an I4 interval to an R8 interval;
• i4vec_min.m, returns the minimum entry in an I4VEC;
• i4vec_permute.m, permutes an I4VEC in place;
• i4vec_print.m, prints an I4VEC;
• i4vec_uniform.m, returns a pseudorandom I4VEC in a given range;
• i8_btest.m, returns TRUE if bit POS of I is a 1;
• i8_xor.m, returns the exclusive OR of two integers;
• ij_next.m, returns the next matrix index;
• ij_next_gt.m, returns the next matrix index, with the requirement that I < J;
• index_box2_next_2d.m, produces indices on the surface of a box in 2D.
• index_box2_next_3d.m, produces indices on the surface of a box in 3D.
• index1_col.m, indexes a 1D array by columns.
• index1_row.m, indexes a 1D array by rows.
• index2_col.m, indexes a 2D array by columns.
• index2_row.m, indexes a 2D array by rows.
• index3_col.m, indexes a 3 array by columns.
• index3_row.m, indexes a 3D array by rows.
• index4_col.m, indexes a 4D array by columns.
• index4_row.m, indexes a 4D array by rows.
• indexn_col.m, indexes an ND array by columns.
• indexn_row.m, indexes an ND array by rows.
• isbn_check.m, checks an ISBN for validity.
• isbn_to_i4.m, converts an ISBN character to an I4.
• isbn_fill.m, can fill in one missing character in an ISBN.
• lcm_12n.m, computes the least common multiple of the integers 1 through N;
• lmat_print.m, prints an LMAT;
• lmat_print_some.m, prints some of an LMAT;
• lmat_transpose_print.m, prints an LMAT, transposed;
• lmat_transpose_print_some.m, prints some of an LMAT, transposed;
• lvec_print.m, prints a LVEC;
• pause_input.m, waits until an input character is entered;
• perm_check.m, checks that a vector represents a permutation;
• perm_cycle.m, analyzes a permutation;
• perm_free.m, reports the unused items in a partial permutation;
• perm_inverse.m, computes the inverse of a permutation;
• perm_next.m, computes all permutations of N things, one at a time;
• perm_print.m, prints a permutation;
• perm_uniform.m, selects a random permutation of N objects;
• pounds_to_kilograms.m, converts a measurement in pounds to one in kilograms;
• prime.m, returns the N-th prime number;
• prime_ge.m, returns the smallest prime greater than or equal to N;
• primer.m, computes the prime numbers up to a given limit;
• r4_uniform_01.m, returns a unit pseudorandom R4;
• r8_log_10.m, returns the logarithm base 10 of an R8;
• r8_uniform.m, returns a scaled pseudorandom R8;
• r8mat_print.m, prints an R8MAT, with an optional title;
• r8mat_print_some.m, prints some of an R8MAT;
• r8mat_transpose_print.m, prints the transpose of an R8MAT;
• r8mat_transpose_print_some.m, prints some of the transpose of an R8MAT;
• r8poly_order.m, returns the order of a polynomial.
• r8poly_print.m, prints a polynomial;
• r8vec_indicator.m, sets an R8VEC to the indicator vector;
• r8vec_mean.m, returns the mean of an R8VEC;
• r8vec_print.m, prints an R8VEC;
• r8vec_variance.m, returns the variance of an R8VEC;
• radians_to_degrees.m, converts an angle measure from radians to degrees;
• random_initialize.m, initializes the MATLAB random number generator;
• rat_factor.m, factors a rational value into a product of prime factors;
• roots_to_r8poly.m, converts polynomial roots to polynomial coefficients;
• roots_to_i4poly.m, converts polynomial roots to polynomial coefficients;
• s_cat.m, concatenates two strings;
• s_eqi.m, compares two strings for equality, ignoring case and trailing blanks;
• s_len_trim.m, returns the length of a character string to the last nonblank;
• s_swap.m, swaps two strings;
• sin_deg.m returns the sine of an angle given in degrees.
• sort_heap_external.m, external sorts a list of values into ascending order;
• timestamp.m, prints the current YMDHMS date as a timestamp;
• tuple_next2.m, computes the next element of an integer tuple space;
• tvec_bracket_even.m, computes evenly spaced angles between THETA1 and THETA2;
• tvec_bracket_even2.m, computes evenly spaced angles between THETA1 and THETA2;
• tvec_bracket_even3.m, computes evenly spaced angles between THETA1 and THETA2;
• tvec_even.m, computes evenly spaced angles between 0 and 2*PI;
• tvec_even2.m, computes evenly spaced angles between 0 and 2*PI;
• tvec_even3.m, computes evenly spaced angles between 0 and 2*PI;
• upc_check_digit.m, returns the check digit of a UPC;
• versine_pulse.m, adds a versine pulse to a constant.

Examples and Tests:

• subpak_test.m, runs all the tests;
• subpak_test_output.txt, the output file;
• subpak_test01.m, tests ANGLE_SHIFT;
• subpak_test02.m, tests ANGLE_SHIFT_DEG;
• subpak_test03.m, tests ANGLE_TO_RGB;
• subpak_test04.m, tests AXIS_LIMITS;
• subpak_test05.m, tests AXIS_LIMITS;
• subpak_test06.m, tests BAR_CHECK, BAR_CODE, BAR_DIGIT_CODE_LEFT and BAR_DIGIT_CODE_RIGHT.
• subpak_test07.m, tests BMI_ENGLISH;
• subpak_test08.m, tests FAC_DIV, FAC_GCD, FAC_LCM, FAC_MUL, FAC_TO_I4, and I4_TO_FAC.
• subpak_test09.m, tests GAUSS_SUM;
• subpak_test10.m, tests GET_SEED;
• subpak_test11.m, tests GRID1;
• subpak_test12.m, tests GRID1N;
• subpak_test13.m, tests GRID2;
• subpak_test14.m, tests GRID2N;
• subpak_test15.m, tests GRID3;
• subpak_test16.m, tests GRID3N;
• subpak_test17.m, tests GRID4;
• subpak_test18.m, tests GRID4N.
• subpak_test19.m, tests INDEX1_COL, INDEX1_ROW, and related functions.
• subpak_test20.m, tests ISBN_CHECK.
• subpak_test21.m, tests ISBN_FILL.
• subpak_test22.m, tests LCM_12N.
• subpak_test225.m, tests LMAT_PRINT.
• subpak_test24.m, tests PERM_INVERSE;
• subpak_test25.m, tests PRIME_GE;
• subpak_test26.m, tests RANDOM_INITIALIZE.
• subpak_test27.m, tests RAND.
• subpak_test28.m, tests RAND.
• subpak_test29.m, tests RAT_FACTOR.
• subpak_test30.m, tests ROOTS_TO_R8POLY.
• subpak_test31.m, tests SORT_HEAP_EXTERNAL;
• subpak_test32.m, tests TVEC_EVEN, TVEC_EVEN2, TVEC_EVEN3;
• subpak_test33.m, tests TVEC_BRACKET_EVEN, TVEC_BRACKET_EVEN2, TVEC_BRACKET_EVEN3;
• subpak_test34.m, tests UPC_CHECK_DIGIT;

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