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Combining Fujitsu COBOL 3.0, PowerCOBOL 3.0, Silverfrost FTN95, and Numerical Recipes:
The Art of Scientific Computing1 (Statistics Analysis) - FORTRAN Files

(This page also contains information for combining Digital Mars D, Free Pascal, and Lazarus
programs with the same Silverfrost FTN95 Numerical Recipes subroutines)

It is highly recommended that a FORTRAN subroutine called either directly or indirectly by a COBOL program does not perform any user I/O.
It is highly recommended that a FORTRAN subroutine called either directly or indirectly by a D command line program does not perform any floating point output.
When calling FORTRAN intrinsic floating point functions, it is highly recommended to pass a single argument and not an expression;
passing an expression may be interpreted as passing a complex variable.

Statistics Analysis - FORTRAN Files is designed, like MATHPROC.FOR, to provide computational support for a main program as a dynamic link library (dll)
of numerical subprograms.  So far, these subprograms have been called by a COBOL GUI program, D command console programs (which do not seem to be very
robust for some reason), D GUI programs, Free Pascal programs, Lazarus (Delphi compatible) GUI program, and FORTRAN command console programs.

Statistics Analysis - FORTRAN Files is a collection of subprograms and functions for analyzing Moments of a Distribution (mean, deviation, etc.) and supporting
functions (sorting, finding minimum and maximum, point smoothing, etc.).  A single FORTRAN source file, STTSTCS.FOR, is used.  It contains over 30
subroutines and functions, many of which are from Numerical Recipes; several functions and subroutines are from other sources; some were developed by me.
Only those used by the various programs documented on this web site are detailed here.

Fourteen of these subprograms are called by a COBOL Windows program, a D command line program, a D Windows program, a D .dll, a Free Pascal GUI program
(compiled in {$MODE DELPHI}), and/or a Lazarus program, demonstrating the versatility of FORTRAN.  The original Numerical Recipes FORTRAN source is
unavailable for download from this page; it is available at Older Numerical Recipes book editions:

ISORT (used internally to sort the statistical data points Integer array); Published as SORT in Numerical Recipes (STTSTCS.FOR also contains an enhanced
version of Numerical Recipes' SORT3, called RSORT3, for sorting REAL*4 arrays; the original Numerical Recipes (1986) FORTRAN defaulted to IMPLICIT ALL;
this implementation uses IMPLICIT NONE and separate programs for INTEGER*2 and REAL*4 arrays;
both ISORT and RSORT3 use Heap Sort; was necessary
to modify both; also for highly unsorted data, may be required to call RSORT3 twice; these could be language/compiler/processor issues as well as algorithm
IMDIAN1 (called first; calls ISORT and finds the median, or middle value of an Integer array; half the values in the array are less than the median, half are greater);
Published as MDIAN1 in Numerical Recipes, modified for Integer arrays (Numerical Recipes' MDIAN2, included in STTSTCS.FOR, can be used for REAL*4 arrays).
SUMMATION (used internally to summarize the Integer array data points, from www.chem.ualberta.ca);
IMOMENT (calls SUMMATION and computes, as REALs, the Integer array average, standard deviation, etc.); Published as MOMENT in Numerical Recipes
(STTSTCS.FOR includes Numerical Recipes' AVEVAR to compute the same information for REAL*4 arrays).
IMODE (finds most common Integer array data point);
CRANK (calls ISORT and ranks the Integer array data points); Published as CRANK in Numerical Recipes
NROOT (used internally by GEOMEAN; used externally by Free Pascal Windows program proot to compute the Nth root of X);
GEOMEAN (computes the Integer array's geometric mean using NROOT);
HARMONICMEAN (computes the Integer array's harmonic mean);

Subprograms called by both D .dll dnrprocs.dll (function nScale (...)) and Lazarus program ST95DLPH unit stunit1 (indirectly2 via Free Pascal .dll
nrlazrs.dll procedure rMoment (...)):

D12R3MINMAX (finds the minimum and maximum values in a REAL*4 array); user written

Subprograms called by Lazarus program ST95DLPH unit stunit1 (indirectly2 via Free Pascal rMoment (...)):

AVEVAR (computes average, average deviation, standard deviation, variance of a REAL*4 array)

MDIAN2 (finds the median, or middle value of an unsorted REAL*4 array)

COBOL (and D) called FORTRAN subroutines:
IMDIAN1, IMOMENT, and IMODE are called directly by the COBOL main program STF95COB, D main program dstat, or the D main program winstat.  Only the subroutine statement and variable declarations are shown to prevent a possible intellectual property violation, since the original FORTRAN source code is published (with the exception of IMODE and NROOT).

      Comparison of mean, median and mode

ISORT (used internally), IMDIAN1, and IMOMENT are modified Integer versions from Numerical Recipes: The Art of Scientific Computing; IMODE has been added and is not a part of Numerical Recipes.  Also added another variable, IERR, to the parameter list; IERR is a returned error code.3

IMOMENT Subroutine Header
data points, stored as an Integer array IDATA(i)
number of data points N
average (mean) AVE  = (∑IDATA(i))  ∕  N
average deviation ADEV = (∑ | IDATA(i) - AVE | )  ∕  N
variance VAR = ( ∑ ( IDATA(i) - AVE )2)  ∕  (N - 1)
standard deviation (σ - 2nd moment of a distribution) SDEV =  VAR 
skewness (3rd moment of a distribution) SKEW = ∑ ( IDATA(i) - AVE )3 ∕  ( N*SDEV3 )
kurtosis (4th moment of a distribution) CURT = { ∑ ( ( IDATA(i) - AVE ) )4 }  ∕  (N*VAR2) - 3
(-3 causes CURT=0 for normal distribution)
error code IERR (initialized to zero; set to non-zero value if an error occurs)
The original Numerical Recipes (1986) FORTRAN source code did not have elaborate error checking.  As an example, added the code snippet at right to IMOMENT to check that the passed number of data points exceeds zero.  The calling program then checks IERR.EQ.0, indicating success.  As can be seen, most of the SUBROUTINEs include IERR. Error Code Processing
Two possible causes for an N<=0 error would be a bug or corrupted data.  This error checking allows a program to exit gracefully instead of crashing or hanging if an error occurs.  Often times hackers will attempt to bounds violate or buffer overflow a program to get into protected memory.

IERR.NE.0 does not always mean an error condition.  For example, in both QUADROOT and CUBCROOT IERR=105 indicates that one of the roots is imaginary and requires additional processing.

Have since added another argument, NUMVALS - Number Unique Values, between MODE_CNT and IERR to the parameter list.  Link to download the source is at the above left.

D called FORTRAN subprograms:
These three subroutines are called directly by the D Windows program winstat.

CRANK is a modified Integer version from Numerical Recipes: The Art of Scientific Computing, added another variable, IERR, to the parameter list; IERR is a returned error code; CRANK produces an ascending ranking of the array elements.

(NROOT is an implementation of an algorithm at gmplib.org and is called internally by GEOMEAN, externally by Pascal Windows program proot);

GEOMEAN and HARMONICMEAN are from the textbook FORTRAN For Scientists & Engineers, 2nd Edition, 1995
Note that the function NROOT is declared as a variable. This is required since sttstcs.for is compiled with IMPLICIT NONE
(Project, Properties, Compiler Options, Language, set global IMPLICIT NONE).

     GEO = N  IDATA(1)*IDATA(2)*⋯*IDATA(N) 
HARMONICMEAN function declaration      HARM = 1 ∕ { (1 ∕ IDATA(1)) + (1 ∕ IDATA(2)) + ⋯ + (1 ∕ IDATA(N)) }

D .dll and Lazarus unit called FORTRAN subroutine:
D12R3MINMAX, shown at right, is a simple subroutine to find the minimum and maximum values in an unsorted REAL array R.

It is called by the D float function nScale (...) in module dnrprocs.  nScale (...) then uses RMIN and RMAX (adjusting RMIN or RMAX to zero, if required) to produce a scaling factor for plotting points.

nScale scales array R into an INTEGER*2 output points array for plotting (the reason for adjusting RMIN or RMAX to zero, so the output points array extends to the axis).

D12R3MINMAX is also called indirectly by Lazarus program ST95DLPH unit stunit1 using nrlazrs procedure rMoment (...).

REAL array R is dynamically dimensioned (or dimensioned with variable bounds) for N elements.  In nScale array R is statically dimensioned for 1024 elements, in ST95DLPH 300 elements.  This does not produce any errors in DMD D 2.0, Free Pascal, or Lazarus.

N must be <= dimension size in calling program. Do not use variable bounds dimensioning for matrices.
Subroutine D12R3MINMAX (...)

Another example of IERR being used as a returned error code. 0 indicates success.

Lazarus units called FORTRAN subroutines via Object Pascal Library nrlazrs:
MDIAN2 (...) finds the middle value of a Real Array X of N elements; while it does not sort the array, it is more complicated and may not be as precise under certain conditions.
AVEVAR (...) computes the average, avg deviation, std deviation, and variance of a Real Array RCDATA of N elements.

Both MDIAN2 (...) and AVEVAR (...), as well as D12R3MINMAX, are called by Free Pascal Library nrlazrs (FORTRAN Numerical Recipes - Lazarus Interface) procedure rMoment (...).  rMoment (...), called by Lazarus program ST95DLPH unit stunit1, also calculates skewness and kurtosis.

AVEVAR (...) uses the same average, average deviation, variance, and standard deviation equations as IMOMENT (...) above.
AVEVAR (...) is also called by nrlazrs procedure rCoorelation (...) to compute the correlation r of two distributions.
nrlazrs procedure indxSort (...), used to sort parallel arrays by building an index table4, calls RSORT3 (...) and SAVECOPY (...)5 in sttstcs.dllRSORT3 (...) calls INDEXX (...) and SAVECOPY (...).

INDEXX (...) (not shown; p. 233 of Numerical Recipes 1986) builds the index table IORDER;
SAVECOPY (...) resequences the array(s) according to the index table.

modified SUBROUTINE RSORT3 (...) header
To call RSORT3 (...) with fewer than three arrays, simply pass the same array multiple times; RSORT3 (...) was modified to ignore it when ND < 3 (code snippet at right). calling SAVECOPY (...)
When called from a non-FORTRAN program, parameters N and ND must be Integer variables; when called from a FORTRAN program, N and ND can be Integer constants.

SAVECOPY (...) was written by removing repetitive code from the original SORT3 (...) and placing it in its own subroutine.  The repetitive code in SORT3 (...) was then replaced by a call to SAVECOPY (...).  SAVECOPY (...) also contains a secondary entry point, RAZERO (...).

indxSort (...) is called by Lazarus program ST95DLPH unit stunit1 and by the applications shown in Lazarus Tab Sheets and Lazarus Body Tubes Sub-forms.
SAVECOPY (...) is also called by wmath (Simulated Annealing; IORDER is the configuration table)

Project Properties, Compiling, Linking, Import Library
Project Properties:

Stored in file sttstcs.ftn95p; contains the settings shown at right.

Plato3 Project Explorer     Plato3 Project Menu

Before compiling, check the Project, Properties, Compiler Options, Miscellaneous are set as shown.

Verify Project, Set Target is DLL.

Compile normally using the Silverfrost FTN95 compiler using Build, Build.
Plato3 Property Pages, Miscellanious Compiler Options


First, STTSTCS.OBJ must be linked as STTSTCS.DLL and STTSTCS.LIB.

Later on, STTSTCS.LIB must be linked by the MicroSoft linker used by Fujitsu COBOL (creating STF95COB.EXE)
OR the Digital Mars implib utility (file bup.zip) (creating D executables).

Prior to linking, verify that Export all is enabled.

Link STTSTCS.DLL as a normal .dll using Silverfrost SLINK

Depending on the setting of Project Target (modifiable thru Project, Set Target), this is done automatically when compiling.
Plato3 Property Pages, Linker Options

.LIB file (STTSTCS.LIB import library):

For Fujitsu COBOL main programs (STF95COB.EXE):
The MicroSoft linker used by Fujitsu COBOL requires a .lib file (library file).  The Silverfrost SLINK is compatible with the MicroSoft linker.

After building the .dll, build the STTSTCS.LIB import library file:
click Project, Set Target
click the LIB radio button
click OK

click Build, Build

For Free Pascal and Lazarus Main Programs:
sttstcs.lib is not needed, so can skip this step
For program development systems compatible with the Microsoft Linker:
Plato3 Project Menu, Set Target

For Digital Mars D main programs:
Digital Mars compilers use a different object and library file format than Microsoft's 32 bit tools (the .dll's produced are compatible).  Therefore, for Digital Mars D main programs need to use the implib utility (file bup.zip) to create the import library (STTSTCS.LIB) from the dynamic link library (STTSTCS.DLL).

WARNING - Be Careful Not To Overwrite Your Silverfrost SLINK Generated Import Library.

After creating STTSTCS.DLL with Silverfrost SLINK, open a Command Prompt (or MS-DOS box) and type
implib sttstcs.lib sttstcs.dll
It is NOT necessary to do this with the Silverfrost salflibc.lib.  Do this only with user written .dll's called directly by the D executable and whose object and library file format is incompatible with Digital Mars.

Only need to recreate sttstcs.lib when SUBROUTINE declarations changes (change in number or type of arguments, adding or removing subroutines from the .dll, etc.)
For Digital Mars D compatible programs:

Win7 Command Prompt - building sttstcs.lib
(Be sure to use the D2 32-bit Command Prompt for compatibility with the CheckMate Win32 configuration)

1. Press, William H., Brian P. Flannery, Saul A Teukolsky, and William T. Vetterling (1986).  Numerical Recipes: The Art of
Scientific Computing
. New York:Press Syndicate of the University of Cambridge.
A student version (in English) of Numerical Recipes In 'C': The Art Of Scientific Computing, Second Edition, © 1988-1992 is
available from the University of Trieste at no cost.

2. Called via a stand-alone Free Pascal .dll.   Possibly related to a known Windows problem, calling direct may produce an Access
Violation Exception.  However, when called via a Free Pascal Library procedure, no exceptions are produced.  In either case, no
data corruption occurred, calculated results were correct.  When attempting to call a D .dll directly/indirectly from a Lazarus
application, a floating point error occurs.  Suspect the error occurs in the D .dll  DllMain function, not the called D function;
possibly modifying the DllMain function for C calls may work.  This was not necessary for Object Pascal calling D.

3. The variable IERR (or iErr) is used throughout the applications on this web site.  Each error condition / location is given a
unique non-zero value, even among unrelated applications (for example, COBOL calling FORTRAN Numerical Recipes and
Lazarus/Pascal/Fortran Center of Pressure).
4. Indexing is different from Ranking.  Multiple array elements may have the same ranking; each array element has its own unique index.
5. The indxSort (...) calls are conditional on passed arguments.  See source code.

Any and all © copyrights, ™ ® trademarks, or other intellectual property (IP) mentioned here are the property of their respective owners.  No infringment is intended.
If you suspect infringement occurred, please contact me at hp3000guru@yahoo.com, fully describing.
Thanks to By Cmglee (Own work) [CC BY-SA 3.0 or GFDL], via Wikimedia Commons,
gmplib.org, and Scientific Psychic for image, algorithm, and html code.

The source code files available for download on these pages are enhanced and tested periodically - check for revised versions.

Page best viewed with Mozilla FireFox 3.6.13 (or higher; PC Win32;  Ubuntu Linux - line spacing may be off), Safari 5.1.7, and Google Chrome Version 40.0.2214.94 (or higher) - Internet Explorer may not display or link correctly.

NOTE - Later versions of Fujitsu PowerCOBOL may be better equipped for calling FORTRAN subroutines.

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