SUBPAK
A Utility Library
SUBPAK
is a FORTRAN77 library which
contains many utility routines.
SUBPAK contains routines for
a variety of tasks, including the greatest common divisor of two
integers, searching, sorting, range, and unique elements of vectors,
determinants and inverses of small matrices, and all the primes
less than 10,000.
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:
C4LIB,
a FORTRAN77 library which
implements certain elementary functions for "C4" or
single precision complex variables;
C8LIB,
a FORTRAN77 library which
implements certain elementary functions for "C8" or
double precision complex variables;
I4LIB,
a FORTRAN77 library which
contains many utility routines, using "I4" or "single precision integer"
arithmetic.
I8LIB,
a FORTRAN77 library which
contains many utility routines, using "I8" or "double precision integer"
arithmetic.
INDEX,
a FORTRAN77 library which
converts a multidimensional vector index to a onedimensional vector index;
it can handle zero and one based indexing schemes, as well as column major
and row major conventions.
R4LIB,
a FORTRAN77 library which
contains many utility routines, using "R4" or
"single precision real" arithmetic.
R8LIB,
a FORTRAN77 library which
contains many utility routines, using "R8" or
"double precision real" arithmetic.
Reference:

Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0486612724,
LC: QA47.A34.

Book Industry Study Group,
The Evolution in Product Identification:
Sunrise 2005 and the ISBN13,
http://www.bisg.org/docs/The_Evolution_in_Product_ID.pdf

Thomas Cormen, Charles Leiserson, Ronald Rivest,
Introduction to Algorithms,
MIT Press, 2001,
ISBN: 0262032937,
LC: QA76.C662.

Donald Kreher, Douglas Simpson,
Combinatorial Algorithms,
CRC Press, 1998,
ISBN: 084933988X,
LC: QA164.K73.

Peter Lewis, Allen Goodman, James Miller,
A PseudoRandom Number Generator for the System/360,
IBM Systems Journal,
Volume 8, 1969, pages 136143.

MILSTD 1753,
Fortran, DoD Supplement to American National Standard X3.91978,
November, 1978.

Albert Nijenhuis, Herbert Wilf,
Combinatorial Algorithms for Computers and Calculators,
Second Edition,
Academic Press, 1978,
ISBN: 0125192606,
LC: QA164.N54.

Branch Rickey,
Goodby to Some Old Baseball Ideas,
Life Magazine,
2 August 1954.

Alan Schwarz,
Looking Beyond the Batting Average,
The New York Times,
Sunday, 1 August 2004.

Daniel Zwillinger, editor,
CRC Standard Mathematical Tables and Formulae,
30th Edition,
CRC Press, 1996,
ISBN: 0849324793,
LC: QA47.M315.
Source Code:
Examples and Tests:
List of Routines:

ANGLE_SHIFT shifts angle ALPHA to lie between BETA and BETA+2PI.

ANGLE_SHIFT_DEG shifts angle ALPHA to lie between BETA and BETA+360.

ANGLE_TO_RGB returns a color on the perimeter of the color hexagon.

AXIS_LIMITS returns "nice" axis limits for a plot.

BAR_CHECK computes the check digit for a barcode.

BAR_CODE constructs the 113 character barcode from 11 digits.

BAR_DIGIT_CODE_LEFT returns the 7 character left bar code for a digit.

BAR_DIGIT_CODE_RIGHT returns the 7 character right bar code for a digit.

BMI_ENGLISH computes the body mass index given English measurements.

BMI_METRIC computes the body mass index given metric measurements.

CH_IS_DIGIT returns TRUE if a character is a decimal digit.

DEGREES_TO_RADIANS converts an angle measure from degrees to radians.

E_CONSTANT returns the value of E.

EULER_CONSTANT returns the value of the EulerMascheroni constant.

FAC_DIV divides two quantities represented as prime factors.

FAC_GCD finds the GCD of two products of prime factors.

FAC_LCM finds the LCM of two products of prime factors.

FAC_MUL multiplies two quantities represented as prime factors.

FAC_PRINT prints a product of prime factors.

FAC_TO_I4 converts a product of prime factors into an integer.

FAC_TO_RAT converts a prime factorization into a rational value.

FEET_TO_METERS converts a measurement in feet to meters.

GAUSS_SUM evaluates a function that is the sum of Gaussians.

GET_SEED returns a seed for the random number generator.

GET_UNIT returns a free FORTRAN unit number.

GRID1 finds grid points between X1 and X2 in N dimensions.

GRID1N finds the Ith grid point between X1 and X2 in N dimensions.

GRID2 computes grid points between X1 and X2 in N dimensions.

GRID2N computes one grid point between X1 and X2 in N dimensions.

GRID3 computes a grid on the parallelogram set by X1, X2 and X3 in N space.

GRID3N computes a parallelogram grid on 3 points in N dimensions.

GRID4 computes a grid on the parallelogram set by X1, X2 and X3 in N space.

GRID4N computes a single point on a parallelogram grid in N space.

I4_MODP returns the nonnegative remainder of integer division.

I4_SIGN evaluates the sign of an I4.

I4_SWAP switches two I4's.

I4_TO_DIGITS_DECIMAL determines the last N decimal digits of an I4.

I4_TO_FAC converts an I4 into a product of prime factors.

I4_TO_ISBN converts an I4 to an ISBN digit.

I4_UNIFORM returns a scaled pseudorandom I4.

I4VEC_INDICATOR sets an I4VEC to the indicator vector.

I4VEC_MIN computes the minimum element of an I4VEC.

I4VEC_PERMUTE permutes an I4VEC in place.

I4VEC_PRINT prints an I4VEC.

I4VEC_SUM returns the sum of the entries of an I4VEC.

I4VEC_UNIFORM returns a scaled pseudorandom I4VEC.

IJ_NEXT returns the next matrix index.

IJ_NEXT_GT returns the next matrix index, with the constraint that I < J.

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.

INDEX1_COL indexes a 1D vector by columns.

INDEX1_ROW indexes a 1D vector by rows.

INDEX2_COL indexes a 2D array by columns.

INDEX2_ROW indexes a 2D array by row.

INDEX3_COL indexes a 3D array by columns.

INDEX3_ROW indexes a 3D array by rows.

INDEX4_COL indexes a 4D array by columns.

INDEX4_ROW indexes a 4D array by rows.

INDEXN_COL indexes an ND array by columns.

INDEXN_ROW indexes an ND array by rows.

ISBN_CHECK checks an ISBN code.

ISBN_FILL fills in a missing digit in an ISBN code.

ISBN_TO_I4 converts an ISBN character into an integer.

ISET2_COMPARE compares two I2 sets.

ISET2_INDEX_INSERT_UNIQUE inserts unique values into an indexed sorted list.

ISET2_INDEX_SEARCH searches for an I2 set value in an indexed sorted list.

LCM_12N computes the least common multiple of the integers 1 through N.

LMAT_PRINT prints an LMAT.

LMAT_PRINT_SOME prints some of an LMAT.

LMAT_TRANSPOSE_PRINT prints an LMAT, transposed.

LMAT_TRANSPOSE_PRINT_SOME prints some of an LMAT, transposed.

LUHN_CHECK computes the Luhn checksum for a string of digits.

LVEC_PRINT prints an LVEC.

LVEC_PRINT_SOME prints "some" of an LVEC.

PERM_CHECK checks that a vector represents a permutation.

PERM_CYCLE analyzes a permutation.

PERM_FREE reports the unused items in a partial permutation.

PERM_INVERSE inverts a permutation "in place".

PERM_NEXT computes all of the permutations of N objects, one at a time.

PERM_PRINT prints a permutation.

PERM_UNIFORM selects a random permutation of N objects.

POUNDS_TO_KILOGRAMS converts a measurement in pounds to kilograms.

PRIME returns any of the first PRIME_MAX prime numbers.

PRIME_GE returns the smallest prime greater than or equal to N.

PRIMER computes the prime numbers up to a given limit.

R8_HUGE returns a "huge" R8.

R8_LOG_10 returns the logarithm base 10 of an R8.

R8_UNIFORM returns a scaled pseudorandom R8.

R8_UNIFORM_01 returns a unit pseudorandom R8.

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.

R8POLY_DEGREE returns the degree of a polynomial.

R8POLY_PRINT prints out a polynomial.

R8VEC_INDICATOR sets an R8VEC to the indicator vector.

R8VEC_MEAN returns the mean of an R8VEC.

R8VEC_PRINT prints an R8VEC.

R8VEC_VARIANCE returns the variance of an R8VEC.

RADIANS_TO_DEGREES converts an angle measure from radians to degrees.

RAT_FACTOR factors a rational value into a product of prime factors.

RICKEY evaluates Branch Rickey's baseball index.

ROOTS_TO_I4POLY converts polynomial roots to polynomial coefficients.

ROOTS_TO_R8POLY converts polynomial roots to polynomial coefficients.

S_LEN_TRIM returns the length of a string to the last nonblank.

SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.

TIMESTAMP prints out the current YMDHMS date as a timestamp.

TUPLE_NEXT2 computes the next element of an integer tuple space.

TVEC_EVEN computes evenly spaced angles between 0 and 2*PI.

TVEC_EVEN2 computes evenly spaced angles between 0 and 2*PI.

TVEC_EVEN3 computes evenly spaced angles between 0 and 2*PI.

TVEC_EVEN_BRACKET computes evenly spaced angles between THETA1 and THETA2.

TVEC_EVEN_BRACKET2 computes evenly spaced angles from THETA1 to THETA2.

TVEC_EVEN_BRACKET3 computes evenly spaced angles between THETA1 and THETA2.

UPC_CHECK_DIGIT returns the check digit of a UPC.

VERSINE_PULSE adds a versine pulse to a constant.
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the FORTRAN77 source codes.
Last revised on 03 November 2011.