Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
Here is an example from the IMSL library of mathematical functions. The function DGEFS (which solves a set of linear equations) has 105 lines of comments and 60 lines of program instructions.
SUBROUTINE DGEFS (A, LDA, N, V, ITASK, IND, WORK, IWORK)
C***BEGIN PROLOGUE DGEFS
C***PURPOSE Solve a general system of linear equations.
C***LIBRARY SLATEC
C***CATEGORY D2A1
C***TYPE DOUBLE PRECISION (SGEFS-S, DGEFS-D, CGEFS-C)
C***KEYWORDS COMPLEX LINEAR EQUATIONS, GENERAL MATRIX,
C GENERAL SYSTEM OF LINEAR EQUATIONS
C***AUTHOR Voorhees, E. A., (LANL)
C***DESCRIPTION
C
C Subroutine DGEFS solves a general NxN system of double
C precision linear equations using LINPACK subroutines DGECO
C and DGESL. That is, if A is an NxN double precision matrix
C and if X and B are double precision N-vectors, then DGEFS
C solves the equation
C
C A*X=B.
C
C The matrix A is first factored into upper and lower tri-
C angular matrices U and L using partial pivoting. These
C factors and the pivoting information are used to find the
C solution vector X. An approximate condition number is
C calculated to provide a rough estimate of the number of
C digits of accuracy in the computed solution.
C
C If the equation A*X=B is to be solved for more than one vector
C B, the factoring of A does not need to be performed again and
C the option to only solve (ITASK.GT.1) will be faster for
C the succeeding solutions. In this case, the contents of A,
C LDA, N and IWORK must not have been altered by the user follow-
C ing factorization (ITASK=1). IND will not be changed by DGEFS
C in this case.
C
C Argument Description ***
C
C A DOUBLE PRECISION(LDA,N)
C on entry, the doubly subscripted array with dimension
C (LDA,N) which contains the coefficient matrix.
C on return, an upper triangular matrix U and the
C multipliers necessary to construct a matrix L
C so that A=L*U.
C LDA INTEGER
C the leading dimension of the array A. LDA must be great-
C er than or equal to N. (terminal error message IND=-1)
C N INTEGER
C the order of the matrix A. The first N elements of
C the array A are the elements of the first column of
C the matrix A. N must be greater than or equal to 1.
C (terminal error message IND=-2)
C V DOUBLE PRECISION(N)
C on entry, the singly subscripted array(vector) of di-
C mension N which contains the right hand side B of a
C system of simultaneous linear equations A*X=B.
C on return, V contains the solution vector, X .
C ITASK INTEGER
C If ITASK=1, the matrix A is factored and then the
C linear equation is solved.
C If ITASK .GT. 1, the equation is solved using the existing
C factored matrix A and IWORK.
C If ITASK .LT. 1, then terminal error message IND=-3 is
C printed.
C IND INTEGER
C GT. 0 IND is a rough estimate of the number of digits
C of accuracy in the solution, X.
C LT. 0 see error message corresponding to IND below.
C WORK DOUBLE PRECISION(N)
C a singly subscripted array of dimension at least N.
C IWORK INTEGER(N)
C a singly subscripted array of dimension at least N.
C
C Error Messages Printed ***
C
C IND=-1 terminal N is greater than LDA.
C IND=-2 terminal N is less than 1.
C IND=-3 terminal ITASK is less than 1.
C IND=-4 terminal The matrix A is computationally singular.
C A solution has not been computed.
C IND=-10 warning The solution has no apparent significance.
C The solution may be inaccurate or the matrix
C A may be poorly scaled.
C
C Note- The above terminal(*fatal*) error messages are
C designed to be handled by XERMSG in which
C LEVEL=1 (recoverable) and IFLAG=2 . LEVEL=0
C for warning error messages from XERMSG. Unless
C the user provides otherwise, an error message
C will be printed followed by an abort.
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED D1MACH, DGECO, DGESL, XERMSG
C***REVISION HISTORY (YYMMDD)
C 800326 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 900510 Convert XERRWV calls to XERMSG calls. (RWC)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DGEFS
C
the Fortran code starts here ....
An example from a C program I wrote: about 53 lines of comments and description, followed by about 60 lines of program instructions.
/************************************************************************ ** * ROUTINE: atMatchLists * * DESCRIPTION: * Given 2 lists of s_star structures, * which have ALREADY been transformed so that the "x" * and "y" coordinates of each list are close to each other * (i.e. matching items from each list have very similar "x" and "y") * this routine attempts to find all instances of matching items * from the 2 lists. * * We consider a "match" to be the closest coincidence of centers * which are within "radius" pixels of each other. * * Use a slow, but sure, algorithm. * * We will match objects from A --> B. It is possible to have several * As that match to the same B: * * A1 -> B5 and A2 -> B5 * * This function finds such multiple-match items and deletes all but * the closest of the matches. * * place the elems of A that are matches into output list J * B that are matches into output list K * A that are not matches into output list L * B that are not matches into output list M * * * RETURN: * SH_SUCCESS if all goes well * SH_GENERIC_ERROR if an error occurs * * */ int atMatchLists ( int numA, /* I: number of stars in list A */ s_star *listA, /* I: first input list of items to be matched */ int numB, /* I: number of stars in list B */ s_star *listB, /* I: second list of items to be matched */ double radius, /* I: maximum radius for items to be a match */ char *basename /* I: base of filenames used to store the */ /* output; extension indicates which */ /* .mtA items from A that matched */ /* .mtB items from B that matched */ /* .unA items from A that didn't match */ /* .unB items from A that didn't match */ ) code starts here ...
I worked on a project which involved writing thousands of lines of code, broken up into over 50 files. In one of those files was this function, which is supposed to invert a matrix. It took quite a while for me to figure out what was going on, and how to use the routine. Grrrrr.
/************************************************************************** * * * inverts a symmetric routine * * * **************************************************************************/ /* Return 1 for success, 0 for failure */ #include/* Prototype definition */ #include "mtLstsq.h" int syminv(double *a, double *b, int dimension, double *pvrow, double *pvcol, int *use) code starts here ....