Proceedings_of_the_Meeting_of_the_Western_Region_of_COMMON_196512 Proceedings Of The Meeting Western Region COMMON 196512
Proceedings_of_the_Meeting_of_the_Western_Region_of_COMMON_196512 Proceedings_of_the_Meeting_of_the_Western_Region_of_COMMON_196512
User Manual: Proceedings_of_the_Meeting_of_the_Western_Region_of_COMMON_196512
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PROCEEDmGS
OF THE MEETING
OF
~
WESTERN REGION
OF COMMON
The International Hotel
Los Angeles, California.
December 6, 7, and 8, 1965
r:neW.tI.neMtTlf*ttT7!msr
Table of Contents
o
0
Program Agenda
Registration Roster
Civil Engineering Panel
Snobol 3
An Interpretive Input Routine for Linear Programming
1620 SPS and SPS ll-D Object Deck Modifier
Cleartran
Automonitor
Anthropology and the Teaching of Programming
The 1620 for Simulation in a Biomedical Environment
Pert/CPM
Critical Path Method Scheduling
Project Planning and Control
Solution of a Problem in Heat Transfer
Some Applications of Cracovians
MRl Plotter Subroutines
iii
vi
1
9
17
49
54
66
79
85
96
101
146
164
166
216
'·,,1
.I'.. J
ii
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PROGRAM AGENDA
MONDAY, DECEMBER 6
8:00
Late Registration
General Session
9:00
Welcome
IBM Announcements
Sound Off - Bob White
10:00
Coffee
10:.30
Sound Ofr (contd.)
11:.30
Converting from the 1620 to System .360 - The
1620Compat&bility Feature for Model.30 by
H. Elmer and H. Weber (IBM)
12:00
Lunch
Session A
1:15
Civil Engineering Panel
Richard Wainer, Chairman
James W. Hunter
Frank Julian
James Nugent
George Taylor
Robert Olson and others
Session B
SNOBOL .3, A List Processing Language for the
IBM 1620 by David L. Wilson
2:15
Easy LP by D. J. Aigner
2:40
1620 SPS-II and SPS II-D Object neck Modifier by
Betty M. Ear10ugher
,3:00
Coffee
Coffee
3:30
Civil Engineering Panel (contd.)
The Omnimetrics Operating System by
Marvin Rubinstein
4: 30
5:00
C1eartran by Francis W. Winn
New User Meeting
Paul Bickford
TUESDAY. DECEMBER 7
Session A
Session B
Session C
Education Panel
George R. Jaffray, Chairman
Carl Feingold (arrived late)
John A. Ferling
Fernando Figueroa
Charles B. Kinzek
William G. Lane
PERT and CPM Panel (see
abstracts)
Gaylord Baker, Chairman
10:00
Coffee
Coffee
Coffee
10:30
Panel (contd.)
Panel (contd.)
Tutorial (contd.)
ll:oo
Automonitor for 1620 Machine Language
by John Rettenmayer
Solution of a Problem in Heat
Transfer by James C. Caslin,
H. E. Fettis, and John W.
Goresh
11:20
Anthropology and Progranmdng by
Herman B. Weissman
Computer Design of High Velocity
Duct System· by Ralph Vandiver
11:50
The 1620 for Simulation in a Bic-Medical Same Applications of Cracovians
Environment by I. R. Neilsen and
by Marco T. Rincon B.
James J. Horning
8:30
M. Lopez
Marvin Rubinstein
Dave Stadlman
12:00
Expanding the CapabilitY' of
Plotter Software bY'
Dean Lawrence
Use of a 1620 at a Solar
Observatory by Robert L. Shutt
12:10
12:35
2:00
()
Advanced Monitor Tutorial Bert Madsen
A class':.in how MONITOR is
constructed and how to make
modifications
Lunch
Lunch
Lunch
Tour to Jet Propulsion Laboratory
Tour
Tour
~
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WEDNESDAY. DECEMBER 8
General Session - Eli Katz
8:30
PLl Tutorial - John Harris
10:00
Corfee
10:30
1130 Computer bY' Paul Manikowski
11:00
Sound
12:00
Luncheon
orr
Speaker:
Subject:
Response - Bob White
Fred Greenberger
The Fnture of the Free Standing
Small· Computer
Session A
Session B
1:45
Tutorial - 1130-1800 Programming Paul Manikowski
Tutorial - 360 Programming Systems - JaY' Michtom
3:00
Coffee
Co free
3:30
Tutorial (contd.)
Tutorial (contd.)
1965 COMMON CONFERENCE - REGISTRATION
AIGNER, D.J.
ALLEN, ROBERT C.
AMMERMAN, THOMAS W.
BACON, RICHARD P.
BAUER, EDWARD G.
BELDNER, RUDYARD
BERRY, J. DOUGLASS
BICKFORD, PAUL A.
BIRD, FRANK
BOLES, JAMES N.
BROWNE, PAUL
BRUCE, J.W.
BRYANT, JACK K.
BURNS, BRUCE A.
BUSCHMAN, W.O.
CA INSKI, RAY
CARROLL, LANE L.
CHAMBERLAIN, D.L.
CLARK, CHARLES L.
CORTOPASSI, ANDREW
COTTON, BILL
CRABTREE, S. JAMES
CURIEL, ROBERT
DABE, RODNEY G.
DAHLEN, JAMES W.
DICKSON, THOMAS R.
DIEHR, PAULA
DOUGHERTY, DANIEL J.
EARLOUGHER, BETTY M.
ELMER, HANS
ELY, DEAN E.
EMERSON, JOHN T
FAGG, PETER
FERLING, JOHN A.
FETTIS, HENRY E.
GU INN, JOHN R.
HALL, OMER D.
HECKMAN, A. R.
HOLT, JOHN
HORTON, MURIEL MRS
HUNTER, JAMES W.
HUSSAIN, KHATEEB M.
HUTZLER, R. H.
ISMCMAN, DAVID
JACKSON, LARRY D.
JAFFRAY, GEORGE
JOHNSTON, T. S.
JULIAN, F. B.
KATZ, ELI
KI SH I, HIRO KO
UNIVERSITY OF ILLINOIS
3342
UNIVERSITY OF VICTORIA
7044
PITTSBURGH PLATE GLASS CO.
5195
SAN DIEGO STATE COLLEGE
5142
SAN DIEGO STATE COLLEGE
5142
LA DEPT OF WATER AND POWER
5181
GANNETT FLEMING CORDDRY/CARPENTER 1009
OKLAHOMA STATE UNIVERSITY
SACRAMENTO PEAK OBSERVATORY
5053
UNIVERSITY OF CALIF.,BERKELEY
5076
UNION RESEARCH CENTER
5077
OFFC OF SURVEYOR/ROAD COMM,SAN DIEGO
LA DEPT. OF COUNT ENGR.
5018
US AIR FORCE, COLORADO SPRINGS
1029
CALIF. STATE POLYTECHNIC COLLEGE, SAN LUIS OBISPO
PUBLIC SERVICE CO. OF NEW MEXICO
SAN DIEGO STATE COLLEGE
5142
OFFC OF SURVEYOR/ROAD COMM,SAN DIEGO
CALIF STATE COLLEGE, LA
5185
US BUREAU OF RECLAMATION
5096
METAL STRUCTURES CORP
5208
SUNDSTRAND AVIATION, ROCKFORD, ILL.
INFORMATION SYSTEMS CO.
5174
CONSOER, TOWNSEND + ASSOC.
3334
US ARMY CORPS OF ENGINEERS
5186
ORANGE COAST COLLEGE
5212
ITT FEDERAL LABS
5227
HAWAIIAN SUGAR PLANTERS ASSOC.
5030
STANFORD ELECTRONICS LAB
5123
IBM, ENOl COTT
FRANKLIN ELECTRIC CO., INC.
1432
FRESNO STATE COLLEGE
5241
IBM, POUGHKEEPSIE
CLAREMONT MENS COLLEGE
5033
AERONAUTICAL RES. LAB
3024
TEXAS COLLEGE OF ARTS/INDUSTRIES
5104
LA COUNTY FLOOD CONTROL DISTRICT
5141
QUINTON ENGINEERS, LTD.
5054
NORTH AMERICAN AVIATION, INC.
5149
JET PROPULSION LAB
5019
LA COUNTY
5018
CALIF STATE COLLEGE, FULLERTON
CONSULTANT - LOS ANGELES
QU I NTON ENG I NEERS, LTO.
5054
COLORADO STATE UNIVERSITY
LOS ANGELES VALLEY COLLEGE
TEXAS TECHNOLOGICAL COLLEGE
5143
OFFC OF SURVEYOR /ROAD COMM, SAN 0 I EGO
LA DEPT. OF WATER AND POWER
5181
WESTERN DATA PROC CENTER/UCLA
5215
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KLEIN, SEYMOUR
LAHNERS, ELAINE L.
LANE, WI LL IAM G.
LAWRENCE, DEAN
LINSDAY, THOMAS H.
LITTRELL, ROBERT T.
MAGWIRE, CRAIG
MAN I KOWSKI, PAUL
MARTINEZ, JESS
MATTHEWS, E.L.
MAUDLIN, CHARLES E.
MCCOLLUM, PAUL A.
MCFARLAND, ALBERT
MCMI LLAN, FRANK
MCMENAMIN, JOSEPH L.
MILLIGAN, PERCY L.
MOFFITT, ROBERT D.
MYLIUS, WILLIAM G. JR.
NEAL, KENNETH L.
NORRIS, BOYD C.
OLSON, ROBERT
PAQU I N, NANCY
POTTS, W.W.
PRESTON, SPENCER V.
RANDALL, ROBERT F.
REDLACK, HERBERT C.
RE I CH, CARL T.
RICHARDS, THOMAS C.
RINCON, MARCO TULlO
ROCKWEL L, BILL
ROEDER, GEORGE L.
RUBINSTEIN, MARVIN
SAMSON, STEPHEN L.
SARKISIAN, HARRY
SCHANDUA, EMIL J.
SCHRADER, LUANA MRS.
SHUTT, ROBERT L.
STEINHILBER, J. R.
TAYLOR, GEORGE I.
TOWN, GEORGE G.
TUCK, MICHAEL R.
UTLEY, BRIAN
VANCE, GARRY
VANDIVER, RALPH JR.
VAURS, SANDRA
WA INER, RI CHARD
WALKER, CHARLES S.
WEISSMAN, HERMAN B.
WHITE, ROBERT R.
WILSON, DAVID L.
WILSON, G.W.
WINDMEYER, WALTER C.
WINN, FRANCIS W.
WOODWORTH, JAMES A.
LA CITY TRAFFIC DEPT.
VETERANS ADMIN. HOSPITAL
3055
CHICO STATE COLLEGE
5190
MIDWEST RESEARCH INST.
3180
VENTURA COLLEGE
5243
CALIF. STATE COLLEGE, LONG BEACH
5198
UNIVERSITY OF NEVADA
5038
I BM, LA
OMN IMETR I CS
5172
IBM, SAN JOSE, CALIF.
UNIVERSITY OF OKLAHOMA, NORMAN, OKLA.
OKLAHOMA STATE UNIVERSITY
3158
SAN DIEGO STATE COLLEGE
5142
FRESNO STATE COLLEGE
5241
GROSSMONT COLLEGE
5145
SOUTHERN UNIVERSITY
1339
NORTH PACIFIC DIV.-CORPS OF ENGRGS 5085
THE RUST ENGINEERING CO.
1164
US ARMY CORP OF ENGR
5248
US BUREAU OF RECLAMATION
5096
LA DEPT OF WATER AND POWER
5181
US PUBLIC HEALTH SERVICE
1118
OFFC OF SURVEYOR/ROAD COMM,SAN DIEGO
SAN DIEGO STATE COLLEGE
5142
AUSTIN COLLEGE
5252
SACRAMENTO STATE COLLEGE
MONTEREY PENINSULA COLLEGE
5152
VENTURA COLLEGE
5243
UNIVERSIDAD DEL ZULIA, VENEZUELA
8027
SAN DIEGO STATE COLLEGE
5142
US AIR FORCE, COLORADO SPRINGS
1029
OMNIMETRICS
5172
US ATOMIC ENERGY COMM
1258
HUMBOLDT STATE COLLEGE
ST. EDWARDS UNIV.
5228
CALIFORNIA STATE COLLEGE,HAYWARD
5105
SACRAMENTO PEAK OBSERVATORY
5053
ITT FEDERAL LABS
5227
LA COUNTY FLOOD CONTROL DISTRICT
5141
SEATTLE UNIVERSITY
5219
ARGONNE NATIONAL LAB
1273
IBM, SAN JOSE
UNIVERSITY OF NEVADA
5038
BENHAM-BLAIR AND AFFILIATES, OKLAHOMA CI TY
SAN JOSE STATE COLLEGE
5121
5009
DEPT OF PUBLIC WORKS, LA
ARIZONA STATE UNIV.
5199
UNIVERSITY OF ILLINOIS
LA DEPT. OF WATER AND POWER
5181
UNIVERSITY OF WISCONSIN
t~ASSMAN CONST. CO., KANSAS CITY, MO. 3378
DOW CHEMI CAL CO.
5155
COMPUTER LANGUAGE RESEARCH, DALLAS 5148
DOW CHEMI CAL CO
5155
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19&5 COMMON CONFERENCE - REGISTRATION
\
AIGNER, D.J.
UNIVERSITY OF ILLINOIS
ALLEN, ROBERT C.
UNIVERSITY OF VICTORIA
AMMERMAN, THOMAS W. PITTSBURGH PLATE GLASS CO.
BACON, RICHARD P. SAN DIEGO STATE COllEGE
BAUER, EDWARD G.
SAN DIEGO STATE COLLEGE
BELDNER, RUDYARD
lA DEPT. OF WATER AND POWER
BERRY, J. DOUGLASS GANNETT FlEMI NG CORDDRY /CARPENTER
BICKFORD, PAUL A. OKLA. STATE U. TECHNICAL INSTITUTE
BIRD, FRANK
SACRAMENTO PEAK OBSERVATORY
BOLES, JAMES N.
UNIVERSITY OF CALIFORNIA, BERKELEY
BROWNE, PAUL
UNION OIL RESEARCH CENTER
BRUCE, J. W.
OFFC OF SURVEYOR/ROAD COMMISSION
BRYANT, JACK K.
LA DEPT. OF COUNTY ENGR.
BURNS, BRUCE A.
US AIR FORCE
BUSCHMAN, W.O.
CALIF. STATE POLYTECHNIC COLLEGE
CAINSKI, RAY
PUBLIC SERVICE CO. OF NEW MEXICO
CARROLL, LANE L.
SAN DIEGO STATE COLLEGE
CHAMBERLAIN, D.l. OFFC OF SURVEYOR/ROAD COMMISSION
CLARK, CHARLES L. CALIF STATE COLLEGE AT LA
CORTOPASSI, ANDREW US BUREAU OF RECLAMATION
COTTON, BILL
METAL STRUCTURES CORP.
CRABTREE, S. JAMES SUNDSTRAND AV IATION
CURIEL, ROBERT
INFORMATION SYSTEMS CO.
DABE, RODNEY G.
CONSOER, TOWNSEND + ASSOC.
DAHLEN, JAMES W.
US ARMY CORPS OF ENGINEERS
DICKSON, THOMAS R. ORANGE COAST COLLEGE
DIEHR, PAULA
ITT FEDERAL LABS
DOUGHERTY,DANIEl J.HAWAIIAN SUGAR PLANTERS ASSOC.
EARLOUGHER,BETTY M. STANFORD ELECTRONICS LAB
ELMER, HANS
IBM
ELY, DEAN E.
FRANKLIN ELECTRIC CO., INC.
EMERSON, JOHN T.
FRESNO STATE COLLEGE
FAGG, PETER
IBM
FERLING, JOHN A.
CLAREMONT MENS COLLEGE
FETTIS, HENRY E.
AERONAUTICAL RES. lAB
GUINN, JOHN R.
TEXAS COLLEGE OF ARTS/INDUSTRIES
HALL, OMER D.
LA COUNTY FLOOD CONTROL DI STRI CT
HECKMAN, A.R.
QUINTON ENGINEERS, lTD.
HOLT, JOHN
NORTH AMERICAN AVIATION, INC.
HORTON,MURIEl
JET PROPULSION LAB
HUNTER, JAMES W.
LA COUNTY ENGR.
HUSSAIN, KHATEEB M.CALIF STATE COLLEGE AT FULLERTON
HUTZLER, R.H.
CONSULTANT - lOS ANGELES
ISAACMAN, DAVID
QUINTON ENGINEERS, lTD.
JACKSON, LARRY D. COLORADO STATE UN IVERS I TY
JAFFRAY, GEORGE
lOS ANGELES VALLEY COLLEGE
JOHNSTON, T.S.
TEXAS TECHNOLOGICAL COLLEGE
JUL IAN, F.B.
OFFC OF SURVEYOR/ROAD COM~1I SS ION
KATZ, ELI
lA DEPT. OF WATER AND POWER
KI SH I, HIRO KO
WES TERN DA TA PROC CEN TER /UCLA
o
URBANA, ILLINOIS
VICTORIA,B.C.,CANADA
CORPUS CHRISTI, TEXAS
SAN DIEGO, CALIF.
SAN DIEGO, CALIF.
lOS ANGELES, CALIF.
HARRI SBURG, PENNA.
OKLAHOMA CITY, OKLA.
SUNSPOT, NEW MEXICO
BERKELEY, CALIF.
BREA, CALIF.
SAN DIEGO, CALIF.
LOS ANGELES, CALIF.
COLORADO SPRINGS,COLO.
SAN LUIS OBISPO,CALIF.
NEW MEXICO
SAN DIEGO, CALIF.
SAN DIEGO, CALIF.
LOS ANGELES, CALIF.
SACRAMENTO, CALIF.
GRAPEVINE, TEXAS
ROCKFORD, I LL I NO IS
tf\,
LOS ANGELES, CALIF.
V
CHICAGO, ILLINOIS
SEATTLE, WASHINGTON
COSTA MESA, CAL IF.
SAN FERNANDO, CALIF.
HONOlULU,HAWAII
STANFORD, CALI F.
ENDICOTT, NEW YORK
BLUFFTON, INDIANA
FRESNO, CALIF.
POUGHKEEPSIE1NEW YORK
CLAREMONT, CALIF.
W-PATTERSON AFB, OHIO
KINGSVILLE, TEXAS
LOS ANGELES, CAL IF.
LOS ANGELES, CALIF.
LOS ANGELES, CALIF.
PASADENA, CALIF.
LOS ANGELES, CALIF.
FULLERTON, CALIF.
lOS ANGELES, CALIF.
LOS ANGELES, CALIF.
FORT COlL I NS, COLORADO
VAN NUYS, CALIF.
lUBBOCK, TEXAS
SAN DI EGO, CAL IF.
LOS ANGELES, CALIF.
LOS ANGE LES, CAL IF.
I
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KLEIN, SEYMOUR
LA CITY TRAFFIC DEPT.
LAHNERS, ELAINE L. VETERANS ADMIN. HOSPITAL
LANE, WILLIAM G.
CHICO STATE COLLEGE
LAWRENCE, DEAN
MIDWEST RESEARCH INST.
LINSDAY, THOMAS H. VENTURA COLLEGE
LITTRELL, ROBERT T.CALIF STATE COLLEGE AT LONG BEACH
MAGWIRE, CRAIG
UNIVERSITY OF NEVADA
MAN I KOWSKI ,PAUL
IBM WESTERN REGION
MARTINEZ, JESS
OMNIMETRICS
MA TTH EW S, E. L •
IBM
MAUDLIN, CHARLES E.UNIVERSITY OF OKLAHOMA
MCCOLLUM, PAUL A. OKLAHOMA STATE UNIVERSITY
MCFARLAND, ALBERT SAN DIEGO STATE COLLEGE
MCMILLAN, FRANK
FRESNO STATE COLLEGE
MCMENAMIN,JOSEPH L.GROSSMONT COLLEGE
MILLIGAN, PERCY L. SOUTHERN UNIVERSITY
MOFFITT, ROBERT D. NORTH PACIFIC DIV-CORPS OF ENGRS
MYLIUS, WILLIAM G. THE RUST ENGINEERING CO.
NEAL, KENNETH L.
US ARMY CORPS OF ENGR
NORRIS, BOYD C.
US BUREAU OF RECLAMATION
OLSON, ROBERT
LA DEPT OF WATER A~D POWER
PAQUIN, NANCY
US PUBLIC HEALTH SERVICE
POTTS, W.W.
OFFC OF SURVEYOR/ROAD COMMISSION
PRESTON, SPENCER V.SAN DIEGO STATE COLLEGE
RANDALL, ROBERT F. AUSTIN COLLEGE
REDLACK, HERBERT C.SACRAMENTO STATE COLLEGE
REICH, CARL T.
MONTEREY PENINSULA COLLEGE
RICHARDS, THOMAS C.VENTURA COLLEGE
RINCON,MARCO TULlO UNIVERSIDAD DEL ZULIA
ROCKWELL, BILL
SAN DIEGO STATE COLLEGE
ROEDER GEORGE L. US AIR FORCE
RUBINstEIN, MARVIN OMNIMETRICS
SAMSON, STEPHEN L. US ATOMIC ENERGY COMM.
SARKISIAN, HARRY
HUMBOLDT STATE COLLEGE
SCHANDUA, EMIL J. ST. EDWARDS UNIVERSITY
SCHRADER, LUANA
CALIF STATE COLLEGE AT HAYWARD
SHUTT, ROBERT L.
SACRAMENTO PEAK OBSERVATORY
STEINHILBER, J.R. ITT FEDERAL LABS
TAYLOR, GEORGE I. LA COUNTY FLOOD CONTROL DISTRICT
TOWN, GEORGE G.
SEATTLE UNIVERSITY
TUCK, MICHAEL R.
ARGONNE NATIONAL LAB
UTLEY, BRIAN
IBM
VANCE, GARRY
UNIVERSITY OF NEVADA
VANDIVER RALPH JR.BENHAM-BLAIR AND AFFILIATES
VAURS. SANDRA
SAN JOSE STATE COLLEGE
WAINER, RICHARD
DEPT OF PUBLIC WORKS
WALKER, CHARLES S. ARIZONA STATE UNIVERSITY
WEISSMAN,HERMAN B. UNIVERSITY OF ILLINOIS
WHITE, ROBERT R.
LA DEPT OF WATER AND POWER
WILSON, DAV 10 L.
UN I VERS I TY OF WI SCONS IN·
WILSON, G.W.
MASSMAN CONST. CO.
WINDMEYER,WALTER C.DOW CHEMICAL CO.
WINN, FRANCIS W.
COMPUTER LANGUAGE RES~ARCH
WOODWORTH, JAMES A.DOW CHEMICAL DO.
===
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LOS ANGELES, CALIF.
OMAHA, NEBRASKA
CH I CO, CA LIF.
KANSAS CITY, MISSOURI
VENTURA, CALIF.
LONG BEACH, CALIF.
RENO, NEVADA
LOS ANGELES, CALIF.
LOS ANGELES, CALIF.
SAN JOSE, CALIF.
NORMAN, OKLAHOMA
STILLWATER, OKLAHOMA
SAN DIEGO, CALIF.
FRESNO, CALIF.
EL tAJON, CALIFORNIA
BATON ROUGELLOUISIANA
PORTLAND,ORt.GON
BIRMINGHAM,ALABAMA
SEATTLE, WASHINGTON
SACRAMENTO, CALIF.
LOS ANGELES, CALIF.
ROCKVILLE,MARYLAND
SAN DIEGO, CALIF.
SAN DIEGO, CALIF.
SHERMAN, TEXAS
SACRAMENTO, CALIF.
MON TEREY, CAL IF.
VENTURA, CALIF.
MARACAIBO, VENEZUELA
SAN DIEGO CALIF.
COLORADO SPRINGS,COLO.
LOS ANGELES, CALIF.
NEW"YORK,NEW YORK
AR CA TA, CA LIF.
AUSTIN, TEXAS
HAYWARD, CALIF.
SUNSPOT, NEW MEXICO
SAN FERNANDO,CALIF.
LOS ANGELES, CALIF.
SEATTLE, CALIF.
IDAHO FALLS, IDAHO
SAN JOSE, CALIF.
RENO, NEVADA
OKLAHOMA CITY,OKLA.
SAN JOSE, CALIF.
LOS ANGELES~ CALIF.
TEMPE, ARIZuNA
URBANA, I LLI NO IS
LOS ANGELES, CALIF.
MILWAUKEE,WISCONSIN
KANSAS CITY, MISSOURI
HOUSTON, TEXAS
DALLAS, TEXAS
HOUSTON, TEXAS
- _____ . __ ... __ ... @.4i¥!4.k,Q,o¥#J.Ji.tJ.I.'A.,;.,
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Introduction to Civil Engineering Panel by Richard \'Jainer,
Assistant Division Engineer, Coordinating Division, Bureau of
Engineering of the City of Los Angeles.
The speakers on this panel, with the exception of
Mr. Julian of San Diego, are from the Data Processing Committee of
the Los Angeles Chapter of the American Public Works Association.
About four years ago when the various governmental agencies in the
area started to become computer oriented, informal meetings were
held.
To give a more official stature to the group, we requested
recognition from the Los Angeles Chapter of the American Fubllc
Works Association and for the last three years we have been
recognized as a working committee of this organization.
At tne outset, workshop meetings were fairly frequent to
share oup experience and to prevent duplication of effort.
As
programs have been completed and familiarity with their usage
obtained, the need for frequency of meetings has diminished and now
meetings are held quarterly.
The Panel today will present information on some of the
applications developing and problems encountered in the area of
acceptance of computer technology in Municipal Engineering.
IfJilliam Reader, Structural Engineer, Bridge and Structural
Division, Bureau of Engineering, City of Los Angeles.
~Ilr.
I want to discuss a method for the design of reinforced
concrete multiple box structures.
to develop
The slope deflection method used
the general algebraic equations is applicable to wide
variety of structures though the loading conditions used are those
found in conditions approximating underground and
loading.
unsymetr~cal
Through the use of tabular design methods and computer
,
-2-
developed tables, the coefficients of maximum stress conditions
()
are determined.
Fixed end moments are applied to each member and composite
moment diagram is developed.
Superpositioned moments are applied
to balance the fixed end moments.
The algebraic slope deflection
equations are then reduced.
From these simplified algebraic equations, the computer
(1620 Modell, 20 K) was used to develop
to simplify the designer's work.
tables of coefficients
The advantages of this method are:
1.
Time savings and reduction of errors over previous
2.
An increase in visualization of effect of changes on
methods.
final configuration.
3.
Facilitate the development of more economical design.
C
Jim Nugent, Technical Service Supervisor Advance Planning Section,
County of Los Angeles Road Department.
The County Road Department has developed and refined the
classic problem of earth work into a neat package of both tabular
output and graphic display using an 8K 1401.
This program reduces to a minlmum the computational
demands of the' Engineer'stlme and frees him to evaluate the results
and ,attempt better solutions.
The steps in establishing the economics of an earthwork
design by the manual method are traditional:
Alignment, both'
vertical and horizantal, is established by the Engineer; the cross
sections are plotted and the template is superimposed; quantities
,are calculated from planimetered cross sections; and finally, the
results are analyzed to determine the economics of the assumed
2.
o
f'"
-3-
alignments.
Often at this point, an entire reprocessing must be
done to arrive at a better solution.
Average Engineers' time for
this manual processing is in the range of 65 hours per mile of
roadvllay.
Through the application of new techniques, the cross
section data is prepared photogrametrically, a trial alignment is
made, and the information processed by our 1401 system.
Cross
sections and profiles are plotted by the 1403 at the rate of about
12 sections per minute, considerably faster than most line plotters.
When the cross sections were plotted by a service bureau, the cost
was about two dollars per section as compared to our current estimate
of above ten cents a section.
This rapid and economic method allows for the establishment
C',
of the most economic deSign.
It is now feasible to try several
alignments or further refine a selected alignment to produce the
minimum construction cost design.
The computer time required for
the automated method is about 20 minutes per mile including plotting.
«..Tim Runder:
Associate Civil Engineer, Office of the County Engineer,
County of Los Angeles.
Oneof the typical problems ,of municipal Sanitatlon Des:tgn
iq the investigation of a sewer network.
The flows, capacity,
hydraulic grades and total flow at an outlet for a network are
analyzed by the computer freeing the engineer of the relativel:!
routine arithmetrical computations requtred.
The program dev810pes a model of the system based on
o
conduit size) land use" manhole numbers, drainage areas and slopes.
This data, combined with actual measured data at control pOint.s,
-------------_
.._=:._m,::8"LZ'!mi"J,.,,,mII!;:.;,,'!i!'!,,S,,,,,,,",,,,,,",,,,,P'!'!llI!,_
.. """
... 4¢2&C!lI!'I
___ ._~_._~~.Iw,ii'!.ii\,a~¥Mi!!l!\li,".i2~,.,,...i""".
_4#_.,"""",""--""""""'I..". .
..
j"'.,."'•..:"~"".:,!,!.""'-.-.".~
;.--~--:"""""-~~,
0","\
,I
produces a tabular output of
I\ tabular output 1.s also
pe~8ent
~roc~uced
of capacity beinz
Sho1~lin3
ut:!,l~zed.
T,'h2t rea.ches have exceeded
capacity 2nd are in need of replacement.
'As the program now operates on our 20K
three pass processing program.
number3~
it is a
syste~,
The first program 3ccepts the manhole
land use, p5pe parameters and drainage areas and computes
the theoretical capacity of
the pa3s I output plus
t~e
measu~ed
capac:tty being utilj_zed.
network elements.
data to develop
Pass 2 accepts
the percent
o~
Pass 3 developef:. the formal O'Lltput,
replacement schedules, and estimated cost.
It is e3timated that,the cost saving realized over former
methods is about 50 percent.
In addition, once the basic data file
has been established it becomes
econom~cally
feasible to provide
estimates of how zoning changes or new connections would affect the
existing system.
This method could be amplified to dover other
gravity flow systems such as storm drains and water supply.
Frank B. Julian, Program Developement Engineer, Office of the County
Road Commlssioner~ County of ' San Diego.
When I was requested to appear on this panel, my first
idea was to speak about our 1620 earthwork program.
After further
thought, I changed my mind, but not because of a conflict with
Mr. Nugent's presentation.
The decision was based on a certain
aspect of our program that presents problems familiar to most
organizations.
The documentation for input format is good" but due
to lack of capacity, certain data checks are not made.
When these
conditions arise, naturally the program blows and the only one
that knows where and how to correct It 1s the programmer
himse'lf:~
"'eMMhltlnrrtt!e'tlt1t1emt*uwrllS'fS
-5-
Though the action of the computer can be reasonably
anticipated, the human reaction is completely unpredictable.
When
we first installed the 1620 computer about four years ago, we had
the green eye-shade and sleeve garter types that were still not too
sure of the ability of a slide'rule.
As a consequence, no doors
were broken down by the crushing hoard wanting to use the beast.
Interest has been stimulated 'through familiarization classes and
allowlng them to write programs.
The biggest selling point, though,
has been short turn around time on data submitted.
At one end of the scale are those, and
m~
are
guilty~
who enjoy wrlting a program, no matter how trivial, without a real
understanding or interest in how much it costs.
C
of
th~_s
A singular example
is the processor manipulators and program modifiers striving
to save micro-seconds.
This is fun but not really productive.
At the opposj.te extreme is the man who is afraid that the
computer, like an
expend~ble
item of supplies, will be used up.
keeps looking for the great applications.
He
Trivial applications,
though productive and economically justified, are not of sufficient
challenge to warrant implimentation.
He over studies applications
hoping the requestor will give up and go away.
As we discuss the various odd computer types-, the last one
to touch on is the non-documenting prograIDt"'TIer who, four years later
can not figure out his criptic notes on the edge of a sheet 9f
paper.
o
Use the ability of the processor to handle comment cards,
the next man who has to pick up the
grateful.
progra~
will be eternally
------.-----..•
-.~~.
-6-
I am sure that these types are not unJque to our
organization, every installation has its share.
1'Je
can all try to do
j.8
The only thing
o
to place the computer 1.n lte) proper
prospective and pay more attention to the people who make up the
organ:t za tion.
Robert Olson, Water Works Engineer, Los Angeles Department of Water
and Power.
I want to discuss a program for the flow distribution and
head losses in a water distribution system on a 1620-60K system.
Capacity of the program is 600 lines, 600 junctions and 175 loops.
The .solution is by means of the Hardy--r]ross method of successive
itter3tions.
Input data is pipe parameters, roughness factors,
inflows, outflows, and elevations of junctions.
The method of solution is to prepare a schematic of the
network.
skippi~3
The loops are
any
assumed for
num~c·~s.
e~ch
line.
nu~bered
o
in an arbitrary fashion but not
Starting with loop 1 a direction of flow is
Then each line is numbered.
Each junction
is numbered with junction #1 being a point of known hydraulic grade.
On each line place the length, diameter End friction factor.
Quantities of inflow and take-outs are shown and a check made to be
sure that outflows are the same as
~nflows.
The program uses nine
dlfferent types of data cards fop such information as jdentification,
pipe numbers, parameters, number of itterations, junction numbers,
and loop definit1_bns.
Output is in three parts.
Part 1 is an optional output
showing unbalanced heads at junctions after each itteration.
Second
output is line data showing flo,,\[ and head less in feet per 1000 feet.
Output 3 is the hydraulic grade line elevations and pressure head
at each junction.
0
h!f'bihils',drIWttlW'{'!!iI'l!.hii'ij,mrrnrm'
3?P
-7-
o
George Taylor Jr., Associ2te Civil Engineer, Data Processing Section,
Los An3eles County Flood Control District.
The Los Zngeles County Flood Control District has modified
tll.e IBr·1-S0GO-l 'system from the original type"t,\}riter output to card
output for offline listing because our workload required several
hours of typing each day.
Our workload has been running about
150% utilization.
Mr. Ramsdale of IBr.1 and r1r. LebovJ of the Los .A.ngeles
Road Department have assisted j.n
14}~J
&
~ounty
further modificat1on to use the
Printer d.irectly as the output device, by direct rr.achine lan-
Guage patches which change the output dev:i.ce code from 04 to 09
and control the carriage skipping.
Had the COGO I System been compiled in FORTRAN with Format,
o
it would have been possible to change the subroutine linkage address
from type. to Punch, since both statements
comp~_le
a3 follo\'Js:
BT to the type or punch routine with the Format address,
BTM to the £,ill routine with each variable i.n turn except
the last followed, by a BTM to the completion routine with
the last variable.
The BT to the output routine could be changed by changing
the linkage address every time it occured in a program.
A simple
SPS program was used to do this to one of our condensed program
decks.
Fortran without Format compiles a type statement as
follov-ls:
BT to a RCTY routine \,'-lith the first variable, BT to a
TBTY routine for each variable.
The Punch statement, however,
o
7
.'''''.::::',£. ",;,;,,,,,, ,; 5""",,,,,,
,
tI
-8-
compi.les as follows:
BT to a fill routine for each variable, followed by a
c;'
BT to the output routine.
This necessitated completely recompiling the COGO I
System, changing all of the Type statements to Punch statements.
A couple of 'the plug decks require executing them before punching
\.
the plug.
This was dorie by manually branching directly to the
proper statement number, the location of which was found by searching
the symbol table.
A further modification is being made in the eOGO I Monitor
for checking the sequence numbers of the plugs decks as they are read
(our 1622 Automatically shuffles the decks as they are read),
automatically skipping to a new sheet when a character appears in
column 80 of a data card, and to pack more than four variables into
the output area similar to MIT's DTM system to simulate the original
typewriter output format.
g
-_._ ...- ' -
......
_
..
_--
""_.
-
._-.
--.-~-.-..
..'-
-
-----_._-
o
'YuINiIW'f'!t'ftrrerr
SNOBOL 3, A List Processing Language
For the IBM 1620
I.
Ge'nerfll Comperison--List Processing vs. Fortran.
A list processing l~nguage is designed to work with ALPHABETIC
rether then numeric date ~s is FORTRAN. One would never consider
writing B multiple correlation in SNOBOL. On the other hand, one
could write programs in SNOBOL to:
1.
Columnize an article for a newspaner. That is, set up
the print so that the left and right margins are even
and, if necessary~ decide where to hyphenate words.
2.
Read in a Fortran-like eYnression, take its analytic
derivative, and put out a Fortran-like expression, which,
when evaluated, will give the derivative.
Both of the above anplications would be very difficult to
nrogramin FORTRAN or SPS.'
II.
o
Acknowledgement.
SNOBOL was first implemented for the IBM 7090 by D.J. Farker,
R.E. Griswold, and I.p.polonsky at Bell Labs, Holndel, New Jersey.
There was an article written by them on SNOBOL 1 in the January 1964
issue of the Journal of the Association for Com~uting Machinery
called "SNOBOL, A String Manipulation Language.
III.
Direction of Implementation.
The purpose of the implementation is educational. We want
to be able to tell our students what a list processing language is
all about. As a result, this imnlementation is rather slow.
Practical progr~ms for production runs generally invo~ve a change of
card format involving about 'four SNOBOL statements.
~or example~, recently we ran a job with a group of address
cards which had the last name first. The problem was to switch
the last names down to the end. This involved a four card program in SNOBOL •
. The '9rogram has been submitted to the 1620 Users Group Library. They have not yet finished p,rocessing it, but they have
given it a temporary P.l.D. number of D3l82.
IV.
o
Data Structure--String and String Name.
The basic data structure of SNOBOL .is the string. 'A string
contains from 0 to 5000 ordered alphabetic, numeric, blank, or
snecial characters. Each string has a name which is from-l to 80
alphabetic or numeric characters including the special characters
of' period and record mark. The string is needed s'o that the
SNOBOL progrBm can refer to the string; much like a variable name
in FORTRAN.
q
"J;="A::JU::":,:,J,:~:,,,,,,,,,,,,,,,,;g,,,
. MI,
SNOBOL 3 continued
v.
PAGE 2
SNOBOL Statement Construction.
The SNOBOt'statement consists of five parts:
LABEL
STRING
@@
Statement
Label
Reference
String
Match
Specification
=
/S(LABEL)
Construction
Specification
o
Go to
Specification
Except for the End Statement, S~OBOL has just one statement
type. The purpose of the separate parts of the statement is as
follows:
1.
Sta·tement Label. A statement label must meet the same
requirements 8S a string name~ eycent that it must begin
with a letter or digit. The statement label is needed
for reference from other statements very much like statement numbers in FORTRAN. Like FORTRAN', where the statement
number is optionBl~ so is the statement label in SNOBOL.
Stetement labels must begin in col. 1 if present, otherwise col. 1 is left blank. The rest of the statement is
in 'free format in the sense that wherever a space is
required~ more than 6ne cen be used.
1
4.
.
2.
Reference String Name. This gives the string which will
be worked on for this statement. This is the only nert
of the statement which cannot be eliminated.
-
3.
MBtch Suecification: This snecifies that which some
substring in the reference string must match. In this
case, the match snecification has just one element: @ @.
This is e literal string, which is suecified by its contents surrounded by @ signs. Thus, in this case, we are
looking for a blank somewhere in the string named STRING.
The match scen is generally left to right, and the interpreter will take the first match it comes to. Since
strings which contain @ signs cannot be specified by 8
literal, a special string QUOTE is supplied which contains
just one @ sign. Notice that if there are no blanks in
the string named STRING, the match "fails."
Construction Specification: This specifies what the substring
which is matched is to be changed to in the reference
string. This part of the statement is separated from the
match specification by an equal sign.' If the match speci~
fication is not included, the whole reference string is
changed to. whet is suecified. If the construction specification is omitted, then the. reference string is left
unchanged. If the match wes unsuccessful, then the construction specification is ignored and the reference
string is left unGhanged. In this case., if a space
is found in the string named STRING, it will be replaced
by a record mark specified by @~.
10
(;
o
ipwiliwmihii::iw'-'f !-',j--u--!tt'w:nWlii55
I
SNOBOL 3 continued
5.
PAGE 3
Go to Specification. This specifies the next statement
to be executed. If the part is omitted, the next sequential ins~ruction in the program is executed. The
slash preceded by a blank and follol~Ted "by a non-blank
character identifies the go ito specif1ca~1on. Parentheses enclose
the name of the next statement to be executed. ~This
name can be constructed if desired in
/S(LABEL)
:~he S indicates a "conditiona.l1j go to!': vo to. LABEL. i~ a.nd --only
1f the match was successful. A oranch on fa1Iure 1S
indicated by an F. Here the failure branch is not
specified. ,Therefore, the next sequential instruction
will be executed on a failure.
Since LABEL is the statement label of ,this statement, the
interpreter will loop through the statement, until all
blanks are replaced by record marks in the string named
STRING.
Notice ,that if the statement is modified to
LABEL STRING @ @
all the spaces in string will be deleted. This is one
of the first things ~one in any FORTRAN compiler.
0 ,'
I
= /S(LABEL)
,,~
VI.
Radix Sort Explanation.
The sample program (see inserted listing)which I am going to
go through involves alphabetizing words using the radix sort
technique. The technique is simply that used when one orders
cards on a card sorter. For example, say one wanted to sort the
following number into numeric order:
2297
2147
2293
2143
2197
2193
2243
2247.
One would first sort on the last column.
ginal order is preserved):
o
(In case of ties ori-
2293
2143
2193
2243
2297
2147
2197'
2247.
Then one would ',S)rt on the second last col\Ulln:
/I
.
------------lIIIIUIIIi=_iJA_a:=Il'I'!t£,,:,e,""""'~~~----,.--. . _._
....•
..4. ..•.
4 1I1!IIl
___._.4!¥:;il!J!i!!ll~~.a~".H-'T,----"·p....
- · -_ _ _"=~·"I!·=·-,-"". ;r'!····,::L.. -:.-.~.. -.. _~ ...:.' .
SNOBOL 3 continued
PAGE·
4
2143
2243
2147
2247
2293
2297
2197.
Now
the last
digit is
which is
o
the numbers are once again out of order with respect to
digit. However, on the cards where the second last
the same, the cards are in order by the last digit,
just what we want. Sorting on the third last digit gets:
2143
2147
2193
2197
2243
2247
.2293
2297.
Since the first digits are all the same, an extra sort on
the first digit will yield the same result. Notice that the
numbers are now in order.
listin
VII.
on a card by card basis.
o
,l#XEQ SNOBOL
This card would appear only on those machines which operate
under a MONITOR system. Otherwise, it should be omitted.
BEGIN SYSPIT *SIZE* @ @
SYSPIT is a special string :for the SYStemi's peripheral I.nput
Tape. On this interpreter this means the card reader. Whenever
SYSPIT appears, one card is read and its contents are put into
a string of length 80. There is no construction or go to specification in this statement.
*SIZE* is what is known as a filler. It can be matched with
as many characters from the re:ference string as necessary to
permit the rest of the match speci:fication to match. If the match
is successful, then the contents of SIZE are replaced by those
characters against which the filler was matched. A filler may
match a null string (string of length zero). I:f a :filler is the
:first element in a match speci:fication list, then, as is this one,
it is matched starting with the first character o:f the reference
string; if it is the last elemeni; the character it is matched
against is extended to the last character of the reference string.
In this case, *SIZE* @ @ is being matched against the first
input card which· is a 9 followed by blanks. The @ @ will match
the blank in col. 2 and SIZE will be filled with the 9. The
/2
o
!!wltilr:jfe"j'''erWl'5rr
SNOBOL 3 continued
o
PAGE 5
purpose of the statement is to read in the maximum number of'
letters in the word to be sorted or, looking at it another way,
the number of columns to be sorted on.
START SYSPIT *WORDS* @ @
/F(LO)
This statement is very much like the preceding one, only
the names have been changed and a failure exit ha.s been added.
In this case, WORDS will be filled with ARMY, TEST, GLOBAL, etc.
LIST = LIST WORDS / (START)
Since the match sp~cification is missing, the entire string
is set equal to the construction specifications. Here the construction specification consists of two elements LIST and WORDS.
The contents of the two strings are combined with all of the
chara.cters in LIST preceding all of the character in WORDS. The
results are stored in LIST. Notice that the first time through
the string,LIST is used before it has been defined. This perfectly legal. Any undefined string is taken as being nUll.
Then the program goes back to START and reads the next card
whose contents~ up to the first blank,are stored in WORDS. The
contents of WORDS is then added onto the contents of ~IST~
Once again we go back to start. However, this time the card read
doesn't have a blank. The contents of WORDS is left unchanged
and control transfers to LO.
o
LO SYSPOT
=
@ THE LIST TO BE ALPHABETIZED IS - @LIST
SYSPOT is a special symbol for SYStem's Peripheral Output
Tape. In the case it's the typewriter, or, if you have a pr.inter,
the 1443 printer. There is also SYSPPT (SYStem's Peripheral
Punch Tape), which is the card punch. Every time SYSPOT (or
SYSPPT) appears in a statement, its contents are outputted once
the statement completed. This statement will type out
THE LIST TO BE ALPHABETIZED ISfollowed by the contents of LIST.
SYSPOT
= VOID
This prints a blank line since void is empty, being undefined.
Ll ALPHABET
= @ABCDEFGHIJKLMNOPQRSTUVWXYZ@
This statement put the alphabet into ALPHABET. In the context of the program, the statement actually defines the collating
sequence to be used. The definit'ion is completely independent of
the natural machine collating sequence.
o
L2
SIZE
=
SIZE
'@1@
Arithmetic is permitted between two strings whose content
are purely numeric. Both strings are decoded into ten-~igit
numbers; the arithmetic operation (+J-,*,/,or **) is carried out
and the results are recoded as a string. Negative numbers are
coded with a minus in: 'front,' all preceding zeros are d,ronped,
except if the result is zero the resulting string is ,@O@. .
Special provision has been made to avoid coding a negative zero.
Here SIZE, which was 9, is decremented to 8. SIZE contains the
number of letters in a word to be ignored before the column we
are now sorting on.
13
===:,2Z1":',,,.,.(.
'~"",.,,,,,,,,
.
__
-
n.
__
.........
k.,!...·. ~,JJgf¥,:'!*¥g:gs
'I
il
I
1
SNOBOL 3 continued
PAGE 6
SIZE
:@-@
/S (FIN)
This statement asks if there is a minus sign in SIZE. Eventually SIZE will be decremented to the point where it contains
a minus one, in which case this statement will transfer to FIN.
For the time being, the match will fail and wefll go on.
o
L3
LIST *WORD* @,@
=
/F(L5)
Everything up to the first comma in LIST is put into 1tIORD
and the substring of LIST which was matched, including the comma,
will be set equal to the null string. That is, this particular
work will be deleted from LIST. IF LIST HAS NO MORE IN IT, then
the match fails and the program transfers to L5.
~'rORD *HEAD/SIZE*
*PIT/@l@*
/F(L4)
HEAD/SIZE denotes a "fixed len~th filler." In this case,
HEAD can only be filled 'with -the - num-ber of' characters specified' by the
numeric string SIZE. Likewise, PIT can only be filled by one
character, which happens to be the character we are sorting on.
If the vTord is too small, the contents of HEAD and PIT are left
unchanged and the program transfers to L4.
$ PIT
= $PIT ~oJORD @,@ / (L3)
The $indicates indirect addressing. The contents of PIT
are to be used as a string name. If PIT contains @K@, then it is
the string name K that we are dealing with. Almost all restrictions on string names and statement labels are removed when
indirect addressing is used. In this case, say we are sorting
on the fourth letter of the work TENSOR. Then @TENSOR,@ would
be added onto the string name S. These strings with one character
names are being viewed as pockets in a sorter are. After this
statement is done, it transfers beck to L3 to pick off the next
word from LIST.
0
L4
BIN
=
BIN WORD @,@
/(L3)
BIN is used to store those words which are too short to be
sorted at this time. Control is then transferred back to L3'
to take the next word off of LIST.
L5
BIN *LIST* =
Now that all the words have been distributed among the
"pockets," tha.t is strings with one character names, we must collect
the words back into LIST in collating sequence. This statement
does two things:
1.
Moves what is in BIN, that is, those words too short for
sorting on this column, into LIST.
2.
Set BIN equal to the null string.
This is done since the arbitrary filler LIST will match with
the entire string BIN because it is both the first and last
element in the match specification.
o
,ji'i"f'tKtllrl!t5',,'·-n'3
~NOBOL
PAGE 7
3 continued
16
ALPHABET *PIT/@l@* = /F(ll),
This statement put into PIT the next "pocket' to be put
back into LIST. This letter is then deleted from the string
named ALPHABET. If the list of letters in ALPHABET ha.s been
exhausted, control is transferred back to L1. At L1 the contents
of ALPHABET are restored, SIZE is decremented again, and the sort
continues on the next column.
LIST = LIST
$PIT
Add the words in the "pocket" onto LIST.
$PIT =
/(L6)
Set the "pocket" equal to the null string and transfer back
to L6 to get the name of the next "pocket."
FIN SYSPOT= @ THE ALPHABETIZED LIST IS - @ IJIST
After the sort is complete, that is~ SIZE also-reaches a
minus one, this statement types the alphabetized list.
c'
END
BEGIN
This statement performed the functions of both the END and
STOP statement on FORTRAN. It indicates to physical end of the
source deck for the interpreter. If control is transferred to
it, either by a branch to END or, as in this case, by being
executed as the next sequential instruction, execution of the
program is ended. BEGIN is the statement label of the first instruction to be executed in the program. If this name is omitted,
execution starts with:' the first ~tatement, as in FORTRAN.
VIII.
Other Features.
The language has several other features:
Recursive Functions
Balanced (with respect to parentheses) Fillers
Back Referencing (if the contents in a Filler match further
down)
Tracing Capabilities (sense switch 1)
Memory Dump (on a control card).
NO/~ ~
b~I:IJ e
SNI!3tfL
hCl- ~
bee n
a e c- ej:J·i e cL
e.I/I1MftV //6r?u~J
U IJd e
o
/5'
£=:::=:::5='::':. ".3,;, ,.
*" 4-
r-
-6- h e..
**XEQ SNOBOL
o
BEGIN
SYSPIT
,;':S I ZE,;':
@ @
STAnT
SYSPIT
';':~JO RDS,;':
@ @
LIST
=
SYSPOT
= @THE LIST TO BE I\LPHABET I ZED
LO
SYSPOT
LIST VlORDS
=
=
Ll
ALPHABET
L2
SIZE
=
SIZE
@-@
L3
L4
@ LIST
IS -
VIOD
@A8CDEFGi-11 J
SIZE -
KLf.ll'lOPQRSTUV~vXYZ@
@l@
/S(FIN)
/F(LS)
\jOHD
*HEAD/SIZE*
SPIT
=
$PIT
/F(L4)
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An
Input Routine
for Linear Programming
~nterpretive
D. J. Aigner
University of Illinois
1.
Introduction
The LP system to be described below derived from a need to. make available
to business and economics students with essentially no programming background a set
of easy-to-use codes for various tools in the fields of operations research and
statistical analysis.
While as a general proposition it would seem that business schools are
requiring increased mathematical and statistical sophistication on the part of
students (as reflected in their curricula), a basic introduction to digital
4[:\
machines, required of all undergraduates, is not yet such a general reality.
When
such a course is a requirement in these curricula it will likely become of lesser
importance - indeed, more difficult to justify economically the effort required in
many cases to produce truly simple input codes fcr students' use, such as the one
which is the subject of this note.
Of course the programming model, whether it be of linear or non-linear
form, and as one of a number of such examples, finds application in fields other
than business and economics.
Thus viewed in a more global perspective· the central
University computing facilities, at least in the short run, should be
co~cerned,
if
not committed. to providing a basic kit of popular tools which is easily accessible
to the unsophisticated user.
This last statement is not an apology for the existence
of such people, but rather a judgment based on an observation of reality.
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17
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The
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educational process does not merely apply to the person who is listed as a student
in the University records, but to his teachers as well.
And while we usuaJ.ly
J
speak of pedagogy as a teacher to student causal relation, it may as well be applied
across disciplines on a teacher to teacher basis, and, as is becoming', 'more apparent,
the learning
process~especially
with regard to computer applications in "virgin"
areas, also takes the form of a student to teacher feedback.
lihile this introduction may not seem appropos. the more technical content to follow, it does establish, if its basic premise is agreed on, a justification for the cost of preparing rather complex (from a coding standpoint) I/O
routines for many well-used tools of analysis.
At Illinois the premise in question is accepted, with the result that an
integrated set of 37 programs for statistical techniques, matrix editing and manipulations, data transformation, and certain operations research tools has been
produced; the programs are available individuaJ.ly or in combination through a
single data input routine.
This package, designated SSUPAC, is presently stored
on the 7094 disk file and may be obtained by the user via the main operating
system just as he would any compiler.
The linear programming code in SSUPAC, written originally by Glenn
Rosbrook of the University's Statistical Service Unit, is unique not for reason
that the code is superior in efficiency, generality, or flexibility to other
codes, but because of its input routine.
calculation
~urposes,
Indeed, any LP code could be used for
receiving its input from this routine.
The input code has
aJ.so been adapted as ALPS, A Linear Programming'System on the College of Business
Administration's 1620, and is used primarily as a pedagogical device for students
in operations research courses.
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2.
Description of the Routine
The ....
concept upon which ALPS is based is quite simple: to produce
?' ";
a code for linear programming which requires input of the simplest form, but
is general-' enough to allow a variety' of data modes (mixed perhaps), has very few
restrictions for card punching, and will itself take care of adding slack or artificial variables where necessary.
The result produced in attempting to meet these
goals takes the form of an algebraic statement of the LP problem, e.g.
Maximize
(or minimize)
Subject to
.
amlxl + am2 x2 + •••• + am:n xn ~
o
x.?:
~
b
m
i = 1, •..• , n
0
translated ver batim onto punched cards" except for the non-negative restrictions.
For example, the problem
Subject to
4XI +6x2 + 3x3 = 24.5
Xl +
1.5x2 + 3X3 < 12
< 12
could be inputed to ALPS as:
MAXIMIZE ~
=
• 5X(1)
+ 6X(2) - 5)«3),
SUBJECT TO
o
CONSTRAINT (1) 4X(1) + 6X(2) + 3X(3) = 24.5)
CONSTRAINT (2) X( I) + 1. 5EOOX( 2) + 5X( 3 ) IE 12,
CONSTRAINT (3) 3X(1) + X(2) IE 12, END
4£.:::.,,'"'$''',.,,;, ..•.,,4,..,
- 4 -
Basically, the routine keys off the beginning letter of each statement,
M, S, C, or E to determine the type of statement: "M" for the objective function
(maximize or minimize), "s" for any editorial statement, ftC 11 for a oonstraint (
statement, and "E" for the end of problem statement.
In the objective and con-
straint statements an ending comma signals termination of the statement • Editorial
statements can be used anywhere in the input, and statements may be punched anywhere on the card or cards necessary; continuation is automatic until the terminating cmmna is found and all blanks are ignored.
Coefficients may take on ibur "modes": integer as in 3X(1), Fortran "F"
format as in .5X(I), floating as in 1.5EOOX(2), and no coefficient as in X(l),
which is interpreted as lX(l).
There are no restrictions on mixing modes in any
Forms of the -constraint inequations are indicated by IE (~), GE @),
statement.
and E or =.
o
Identical comments as above apply to the mode representation of the
constraint constants.
As presently written, ALPS does error checking in the statements for
invalid characters, integer subscripts, beginning letters and ending commas
(where applicable) for all statements, etc.
Also included is a capacity check
for the maximum matrix size allowed, which of course varies according to the
particular machine at hand.
ALPS prepares a data matrix from the above input by adding necessary
slack and artificial variables with appropriate weights for the objective function, provides an initial basiS, and, if required, transforms a minimization
problem into a maximization problem as input to any LP solver.
cess is outlined in Figure 1.-
The basic pro-
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- 5 -
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3.
Coordination with a Solution Routine
Bootstrapping the output of ALPS to a given
obviously dependent in form on the hardvrare at hand.
calc~lation
routine is
For small equipment without
peripheral storage devices the most efficient method for coordination likely
would be to prepare the data matrix (size determined by the solution routine and
the hardware) in high-order memory and load the solving routine directly after
ALPS puts the matrix into its proper addresses.
With less imposing memory limi-
tations, or possession of disk or tape storage, the coordination problem could
be handled in a variety of ways, depending on the maximum problem size desired.
As presently written ALPS requires approximately 7,200 BCD positions
plus the output data matrix* or about 1,000 words plus on a Boolean machine.
Input statements are processed individually, then immediately translated into
4[)
their appropriate locations in the data matrix.
Both operating versions at Illinois use a Fortran-coded revised simplex
algoritlun for computation.
*
Or matrices, depending on the algorithm used.
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Adaptations for the 1620
ALPS is now used:h conjunctj.on vlith a mag tape 1620, where the data
matrix is outputed from ALPS to tape, the Fortran-coded LP solver is read into
memory, and finally the (lata matrix j_s returned to memory from tape.
A disk-
oriented 1620 could be utilized in the same fashion, so that, no intermediate
output neeo. be hancl1ed.
For a strictly card-orienteo. machine, it is possible to alleviate
intermediate handling problems also, by preparing the data matrix in addresses
appropriate to a given solution routine, and then loading the solution routine
C"
,
over ALPS.
The basic modifications necessary to accomplish this consist of the
"./~
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folloving (references refer to SPS source listing):
Change
To
17
EXIT
H
18
RWT2
remove
18 - 19
l'ECH+6, NUM
through
TFM
RNCD
B
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MES2 DAC 38
21
BOX DSB 10, 21"
CONTRI DSB 10, 74"
CONST DSB 10,
21
BLAST DC
1;
1575"
These locations must have
their addresses set so as
to place the arrays in
their corresponding sol~tion
l'outine locations
Can be set to correspond
to given memory capacity
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The Fortran code used at present with ALPS is :Listed on pp. 22-21~.
On
a 40K machine the maximum matrix size (coefficients plus constraint constants) is
n + m ~ 1551t vTith the normal significance levels f
=
8, k = 5, maximum problem
size being dependent upon the number of IE's and GE f S included.
The maximum
problem size of 71.~ variables and 21 constraints could only occur if all constraints
","ere equalities.
Of course there are l-rays, given tapes or disks, to increase
problem size by some
this.
I1
p ing_pong" method, but our user I s requirements hardly Jus~ify
It is also difficult to justify using the 1620 for large LP problems given
that one has tlVO large-scale machines available for ger.l.eral use.
A copy of the user's information sheet for
AJ~S
is also included to
show examples of input and output for the LP package.
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COMPACTION ROUTINE. AT STORE. ADOR GIVES RECORD MARK POSITION
CF ROUT
RCTY
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AM CNUM.I0
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BNE *-36
TFM AODR.STCOL
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START TFM COLM.STCOL
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B
*+24
AM EX.I,tO
CF FLAG
AM AT. 1
AM COUNT,2
TRY
B
PERIODAM COUNT. I
TO WORK.-COUNT
TOM WORK - I • O. 1 1
CM WORK,O.IO. SEE IF NUMBER IS THRU
BE SERVE
* COUND PUT IN CHECK FOR PERIOD. AM AT RHS OF THING STARTING W/ BLANK
SM COUNT. 1
SF FLAG2
PERIOD-24
B
MINUS SF MINUS
PERIOD-24
B
MINUSESF MINUSE
AM COUNT.2'
E
SF E
TOM WORK - 1 • O. I 1
TO WORK.-COUNT
CM WORK.l.10.SEE !F A PLUS SIGN
BE E
CM WORK.2,10,SEE IF A MINUS SIGN
BE MINUSE
AM COUNT. I
TO WORK-I.-COUNT
AM COUNT.2
TO WORK,-COUNT
SF 1Af0RK-1
BNF *+24.MINUSE
SF WORK
EX,WORK
A
SERVE SF EX-I
SF EX-9
CF EX-2
BNF *~24,MINUS
SF EX-2
TFM *+18.FORM-31
TOM FORM-31.0 •• TO SET TO ZERO
AM *-6.1
CM *-18.FORM-2
BNE *-36
* FOR I-CONVERSION
33
•
rti:W.e&+ittjitlli:iiiN'·W·!!!·'HftWe'flmS
-17-
0
0·
".,'"
BNF *+24.E
BB
BNF *+24.FLAG2
BB
AM COUNT2.1
COUNT2 IS ON RHS OF FIRST NO.
*
TF PLACE.COUNTI
PLACE.COUNT2
S
TFM ADDR.O
SM PLACE.2
AM ADDR.l
CM PLACE.O
BH *-36
SF ADDR-l
TF EX.ADDR
BB
END ROUTINE
*
NOP
END
BNF BRND.ROUT., IF ERRORS EXIST, EXIT
EXIT
BRND TFM PLACE1,CREC,~,PLACEl CHECKS FOP C-CONDITION
TFM J,O ••• INDICATES USE OF EXTRA COLUMNS
TFM SLIP.CONTRt
MM SAVE,lO.10
SF 95
A
SLIP,99
MM SAVE1.tO.l0
SF 95
A
SLIP.99 •• SLIP IS BELOW ADDITIONAL COLUMN
TFM JJ.O
TFM 1.0
FOR I MATRIX. PLACE3
*
TF PLACE3.SAVE
A
PLACE3. t
MM PL ACE 3, 1 0 , 1 0
SF 95
TF PLACE3.99
1.750,9
MM
SF 95
PLACE3,99
A
AM PLACE3,CONST
LOOP BNF RECK.-PLACEI
*
GE ROUTINE
TFL -PLACE3.NEGONE
TFL -SLIP.LGNEG
AM SLIP,10
*
FOR EXTRA COLUMNS. PLACE2
TF PLACE2.SAVE
PLACE2.SAVEl
A
PLACE2.J
A
MM PLACE2.10.10
SF 95
TF PLACE2.99
1.750,9
MM
SF 95
PLACE2.99
A
AM PLACE2.CONST
TFL .-PLACE2.0 NE
AM J.l
INCRE •••• TO INCREMENT PLACE 1 AND 3 AND I
B
RECK BNR NONE.-PLACEI
-la-
* LE ROUTINE
TFL -PLACE3.0NE
INCRE
B
NONE TFL -PLACE3.0NE
TF EQOINN. I
EQOWN.SAVE
A
MM EQOWN.I0.I0
SF 95
TF EQOINN.99
AM EQDWN.CONTRI
TFL -EQDINN.LGNEG
I•1
INCRE AM
AM PLACE1.1
AM PLACE3.760
SAVE1.1
C
BNE LOOP
PUT BOX AWAY AT END OF CONSTRAINTS
*
TFM PLACE! .BOX
TF PLACE2.SAVE
A
PLACE2.SAVEI
A
PLACE2.J
MM PLACE2. 10, 10
SF 9?
TF PLACE2,99
AM PLACE2.CONST
TFM 1',0
NIFTY TFL -PLACE2.-Pt...ACEl
AM PLACE 1, 10
AM PLACE2,7!50
AM
I•I
SAVEl,!
C
BNE NIFTY
TF SUB. SAVE
SUB.SAVEI
A
SUB.J
A
RWT2
TFM TRT+6,NUM+30
TRT
TFM NUM+30.0
CM TRT+6.NUM+160
BE *+36
AM TRT+6,!5
TRT
B
TF NUM+4 , SUB
TF NUM+9,SAVEl
TF NUM+14,SAVE
CF NUM
CF NUM+S
CF NUM+10
TF NUM+80.RMARt<
TFM YECH+6.NUM
BTM WRfTE,o
TO SLIP.CONST-9
TO CONST-9.RMARt<
TFM YECH+6.CONTRI-9
BTM WRITE,O
TO CONST-9.SLIP
SF CONST-9
TFM YECH+6.CONST-9
8TM WRITE,O
RWT2
EXIT
3 S'-----_ .. _'"._-
-_._-----_.---.---
-----
--~--~
-._----
-
------"------ ..
_-
0
0
~
0
\
r
-19-
o
-
H
DC 5,0
WRITE TFM CD,5,10
TFM COUNT,S,10
BV *+12
CTI2
YECH WNT20
BNWC*+14
BKT242000
SM COUNT.l,10
BNZ WRITE+2~
RCTY
WATYMESI
EFT2
SM CO,1,10
BNZ WRITE+12
RCTY
WATYMES2
H
MESI
MES2
NOt
ERR2
ERR4
ERRS
ERR6
N07'
0
ERR7
ERRS
MES4
MESS
MES6
MESIO
MES12
ROUT
ERRl1
ERRIO
o
B
WRITE
DAC 17.TAPE WRITE CHECK'
DAC 3S,PUT NEW TAPE OF TWO, THEN PRESS START'
DAC 4S,USED MORE THAN FIVE CARDS FOR ONE SPECIFICATION'
DAC 29, INVALID CHARACTER IN A NUMBER
DAC 1,'
DAC 33,FIRST LETTER NOT A C. M, E, OR S'
DAC 18.INVALID SUBSCRIPT'
DAC 47,TWO SUBSCRIPTS ARE EQUAL IN OBJECTIVE FUNCTION'
RCTY
IAIATYERR7
8TM ROUT.O.I0
B
AGAIN
DAC38,NO +. -. GE. LE. :, OR E AFTER AN XCI)
DAC 1,'
DAC 37.CONSTRAINT NUMBER IS GREATER THAN 21'
DAC 41.A COMMA DOES NOT TERMINATE THE END OF A C
DAC 36,ONSTRAINT OR THE OBJECTIVE FUNCTION'
DAC 25.COLUMN 80 IS NOT A BLANK'
DAC 25,ERROR IS IN CARD NUMBER ,
DAC 35.ERRORS NOT CHECKED IN CARD NUMBER ,
DAC 45.A COMMA IS BEFORE THE END OF A SPECIFICATION'
DC 5.0
RCTY
IAIATYMES6
WNTYCDSAVE-3
SF ROUT
RCTY
RCTY
BB
WATVMES5
BTM ROUT.O.I0
TF STCOL+ 15S, RMARK
TFM STCOL-2,O.10
WACDSTCOL-2
B
AGAIN
\NATV MES4
SM COSAVE.l
BTM ROUT.O.IO
AM CDSAVE.l
CM IAIORK.45.10,SEE IF AN END CARD
BE END
3G
m.2..,Z!.,...,..__.u.,",
} ..
.;;,o;.%#'''A .. # ..;.,p-,..
4 ._--,.- ...... . M·
~'
I
-20WATYMESIO
WNTYCDSAVE-3
RCTY
AGAIN
B
DC 2.0
STCOL DAC 5.00000
DC 50.0
DC 50.0
DC 50.0
RMARK DC
2.'
DC 8.10000000
ONE
DC 2.01
DC 8.-50000000
LGNEG DC 2.06
CNUM DC 5.0
DC 5.0
CD
DC 5.0
t
5.0
DC
J
FINAL DC 5.0
5.0
PLACEIDC
PLACE2DC 5.0
PLACE3DC 5.0
SLIP DC 5.0
EQDWN DC 5.0
COUNTIDC 5.0 •• MOVING ADDRESS OF NUMBER
5.0 •• ADDRESS OF BEGINNING OF NUMBER
COUNT2DC
COUNT3DC
5.0
CDSAVEDC 5.0
1• t
DC
AT
DC 5.0
DC 5.0
JJ
5.0
PLACE DC
ADDR DC 5.0
COLM DC 5.0
COUNT DC 5.0
DC 8.0
EX
DC
2.0
WORK DC
2.KO
NUM
DAC 3.000
DC 50.0
DC 50.0
50.0
DC
DC 50.0
DC 50.0
DC 50.0
DC 50.0
DC 50.0
DC 50.0
50.0
DC
DC 50.0
DC 50.0
DC 50.0
50.0
DC
DC 50.0
DC 50.0
DC 8.0
ZERO DC
2.-99
DC 8.-10000000
NEGONEDC 2.01
OVERLPDSC 50.0
DC 32.0
0
0
0
I
t.
I
-21-
0
DSB lO.2l •• FOR PLACEMENT OF NUMBER FOLLOWING C-CONDITIONS
DSC 2l.0.,FOR PLACEMENT OF CONSTRAINT CONDITIONS
DC 5.0
SAVE DC 5.0
DC 5.0
SUB
SAVEl DC 5.0 •• FOR THE NUMBER OF CONSTRAINTS
CONTRIDSB lO.74 •• FOR STORAGE OF MAX-MIN VECTOR
CONST DSB lO.1575,.FOR STORAGE OF CONSTRAINT MATRIX
BLAST DC
1,'
DEND402
BOX
CREC
o
o
3f
1t,\'tU!)ii.i)•..ii#.l.LL •.Jill1..d!l'L..'fu.,.••.".',"
-22-
C
C
1111
1 199
1188
61
65
62
68
40
75
88
1160
1 169
1 165
161
165
162
168
1222
1220
1221
175
188
1270
DIMENSION BC75.21).C(21).N(21).ZSTAR(75).PC74)
COMMON Nl
COMMON B
MAXIMUM NUMBER OF CONSTRAINTS IS 21
NUMBER OF VARIABLES ALLOWED = 74-NUMBER OF CONSTRAINTS USED-NO. OF
READ INPUT TAPE 2.51.NCOL.NROW.NVAR
READ TAPE 2.P
PUNCH 101
READ TAPE 2.B
NT=O
I F CNT ) 1 1 a8. 1 188. 1 1 99
PUNCH 1 1 0
LL=O
NN=NCOL +
2 = 0.0
L2
1
IFCNN-8)62.62.65
LL = LL+8
GO TO 68
LL=LL+NN
Z = 1.0
PUNCH 20.(~.~=L2.LL)
DO 40 I=I.NROW
PUNCH 25.I.CB(~.I).~=L2.LL)
IF (Z-I.0) 75.88.88
NN=NN-8
L2 = L2+8
GO TO 61
IFf NT) 1169.1169,1160
PUNCH 111
GO TO 1165
PUNCH 103
LL=O
NN=NCOL
2=0
L2=1
r F ( NN-8) 1 62. 162. 165
LL=LL+8
GO TO 168
LL=LL+NN
Z=I.
PUNCH 20,C~.~=L2.LL)
1=1
IFCNT) 1220,1220.1222
PUNCH 25.I,(ZSTAR(~),~=L2,LL)
GO TO 1221
PUNCH 25,I,CP(~).~=L2.LL)
IFCZ-l.)175,188.188
NN=NN-8
L2=L2+8
GO TO 161
IFCNT) 1270,1270,399
NN=NVAR+l
11=0
DO 1 ~=NN.NCOL
00 1 1 1 ,NROW
o
GE'S
=
=
IFCBC~.I)-I.)1.9,1
9/ 1 I:: I 1 + 1
;\1(11)=,,)
CCII)=P(~)
CONTINUE
j
i""
o
o
Nl=O
1501 1..1..=0
1=1
z=O.
1..2=1
NN=11
IFCN1)1502.1502.1503
1502 PUNCH 104
GO TO 961
1503 PUNCH 105
961 JF(NN-8>962.962.965
965 LL=LL+8
GO TO 968
962 LL=LL+NN
Z=l.
968 IF(Nl)1504.1504,1505
1504 PUNCH 20.(J.J=L2,LL)
PUNCH 29.(NeJ),J=L2,LL)
GO TO 1506
1505 PUNCH 20.CJ.J=L2.LL)
PUNCH 25,I.CCCJ),J=L2,LL)
1506 NN=NN-8
L2=L2+8
IFCZ-l.)961.988,988
988 IFCNl)1507.t507,1508
1507 Nl=1
GO TO 1501
1508 Ll=NCOL+l
200 00 203 1=I.NCOL
ZSTARC I )=-P( I)
DO 203 J=1.NROW
203 ZSTAR(I)=ZSTAR(I)+ceJ)*BCI,J)
C
OPTIMALITY CHECK AND SIMPLEX CRITERION
400 FLAG=O
SMALL=O
DO 404 1=1, NCOL
IFCZSTAR(I»402,404.404
402 FLAG=l.
IF(ZSTARCI)-SMALL)403,404,404
403 SMALL=ZSTARCI)
IN=I
404 CONTINUE
IF(FLAG)900.900.405
C
APPLY SIMPLEX CRITERION II
405 SMALL=9.E35
DO 409 I=1,NROW
IFCBCIN.I»409,409,408
408 QUOT=BCLt,I)/BeIN,I)
IFCQUOT -SMALL)411.410,409
411 IN=I
SMALL=QUOT
GO TO .409
410 IF (BCIN,I)-B(IN,JN»409,409.411
409 CONTINUE
IFCSMALL-9.E35)500,407,407
407 PUNCH 1001
GO TO 9089
C NORMALIZE EQUATIONS WRT ENTERING VARIABLE
500 DO 501 J=l.Ll
501 ZSTAR(J)=BeJ,JN)/BCIN.JN)
DO 502 I=l.NROIAI
,"' ..02- ~-n-¥--*'-.-.~-.-" ... @:;:i!f¥4Ufl@jiii%$U.m:W.f.EFrM ,
-24-
o
PROD = B ( IN. I )
DO 502 J= 1.LI
502 B(J.I,=BCJ.()-ZSTARCJ)*PROD
DO 503 J=l.LI
503 BCJ.JN)=Z5TAR(J)
CCJN)=PCIN)
N(JN)=IN
GO TO 200
C OUTPUl
900 NT=1
GO TO 1111
399 PUNCH 1 12
Z=O.
DO 909 l-l.NROW
P(21)=Be~1.1)*C(I)
Z=Z+p(21)
909 PUNCH 120.
N(ll.BCLl.t).CCt).PC21)
PUNCH 113.Z
JJ3 FORMAT C27HSOPTIMAL FUNCTIONAL VALUE =
• Ft4.4 )
120 FORMATCSX.15.6X.F14.4.9X.FI4.4.2X.FJ4.4'
110 FORMAT (17HlSOLUTION MATRIX
)
111 FORMATe35H20PPORTUNTIY COSTS OR SHADO~ PRICES
It2 FORMATCt4H5VARtABLE USED.8X.8HQUANTITV'10X.13HCONTRIB./UNIT.
111X.SHVA~UE)
1001
51
lOS
104
103
29
25
20
101
9089
FORMATeJ9H5S0LUTION UNBOUNDED)
FORMAT(315)
FORMAT(6H5COSTS )
FORMAT(16H5BASIS VARIABLES'
FORMAT(30H2CONTRIBUTtON ePROFIT OR COST)
FORMATeSX.SI14/1H9.26X.3I14)
FORMAT CIX.I3.2X.5F14.4/1H9.27X.3F14.4)
FORMAT (lHO.3X.SI14/1H9.25X.3114)
FORMATe 13HOMATRIX CHECK)
END
o
o
C'\
,"~I
*****************
I.
[I.
A LINEAR PROGRAMING SYSTEM (ALPS)
*************************
GENERAL INFORMATION
THE FUNCTION OF LINEAR PROGRAMING IS TO' OPTIMIZE A LINEAR OBJECTIVE
FUNCTION SUBJECT TO LINEAR CONSTRAINTS.
FOR A DISCUSSION OF PROCEDURES
AND INTERPRETATIONS SEE CHURCHMAN. ACKOFF. ARNOFF. INTRODUCTION TO
OPERATIONS RESEARCH' NEW YORK. WILEY. 1961. OR ANY GENREALLY ACCEPTED
TEXT ON THE SUBJECT.
THIS PROGRAM USES THE GENERAL SIMPLEX METHOD.
TO PRINT THE PUNCHED OUTPUT ON THE IBM 407. USE THE OUTPUT BOARD WITH
SWITCHES ONE AND TWO DOWN (FOR FORMAT CONTROL).
STATEMENTS (IN ORDER)
A.
CALL CARDS
1.
$$JOB
COLUMNS 1-5
6
7-12
13
14-33
34
35-38
39
40-42
43
44-45
o
2.
B.
$$JOB
B (BLANK)
10 NO •• STAFF. FAC, OR JOB NUMBER
B
NAME, LAST NAME FIRST (USE A COMMA)
B
COURSE NAME ABBREVIATION OR GENL IF NON-CLASS WORK
8
COURSE
NUMBER.
IF ANY
B
SECTION.
46
47~48
B
49-80
B
IF ANY. RIGHT JUSTIFIED
PROBLEM NUMBER.
IF ANY. RIGHT JUSTIFIED
$$ALPS
( I N COLUMNS 1 -6 )
OBJECTIVE FUNCTION
1.
PUNCH MAXIMIZE OR MINIMIZE' FOLLOWED BY YOUR FAVORITE FUNCTIONAL
NAME (OPTIONAL). AND THEN PUNCH AN EQUAL SIGN (:). FOLLOWED BY THE
FUNCTION. AS SHOWN IN THE EXAMPLES.
IT IS NEAT BUT NOT NECESSARY
TO BEGIN PUNCHING IN COLUMN 1.
ALL BLANKS ARE IGNORED.
2.
FOLLOW IT WITH A COMMA.
USE NO MORE THAN FIVE CARDS.
C.
'SUBJECT TO THE FOLLOWING- IS OPTIONAL.
ACTUALLY, EDITORIAL COMMENTS
MAY BE PLACED ANYWHERE BETWEEN SPECIFICATIONS (AFTER $$ALPS) BY SIMPLY
HAVING AN S AS THE FIRST CHARACTER.
D.
CONSTRAINTS
1.
IT IS NEAT BUT NOT NECESSARY TO START IN COLUMN 1.
2.
PUT THE CONSTRAINT NUMBER IN PARENTHESIS FOLLOWING THE WORD
'CONSTRAINT'. THEN WRITE THE CONSTRAINT FUNCTION, FOLLOWED BY ONE OF
THE SYMBOLS OF EQUALITY OR INEQUALITY.
(A) LE MEANS LESS THAN OR EQUAL TO
(B) GE MEANS GREATER THAN OR EQUAL TO
ec) E OR
MEANS EQUAL TO
3.
THEN WRITE THE CONSTRAINING FUNCTIONAL VALUE, IN ANY FORM
ACCEPTABLE TO A COEFFICIENT (SEE BELOW), FOLLOWED BY A COMMA.
=
o
E.
-END' STATEMENT. PUNCHED IN ANY COLUMN. SIGNALS THE END OF DATA COMPILATION AND INITIATES EXECUTION.
tJ2
I ,,,,,,au.$!-,.
...".,.4¥L.. ,
li~. i
I
I
III.
RESTRICTIONS
A.
THE MAXIMUM NUMBER OF CONSTRAINTS IS 21.
o
B.
THE NUMBER OF VARIABLES ALLOWED (NOT INCLUDING SLACK OR ARTIFICIAL
VARIABLES) IS BETWEEN 32 AND 74.
TO BE MORE SPECIFIC. IT IS 74 MINUS THE
NUMBER OF CONSTRAINTS USED MINUS THE NUMBER OF CONSTRAINTS USING THE
NOTATION 'GE' (MEANING GREATER THAN OR EQUAL TO).
THE FORMULA IS. USING
NOTATION VERBALIZED IN THE LAST SENTENCE.
v
= 74
-
C'S -
GEtS.
C.
ONE SPECIFICATION (A CONSTRAINT OR THE OBJECTIVE FUNCTION) MUST NOT
BE WRITTEN ON MORE THAN FIVE (5) CARDS.
D.
A COMMA MUST FOLLOW EACH SPECIFICATION.
THE END STATEMENT AND
COMMENT STATEMENTS (BEGINNING WITH AN s) 09 NOT REQUIRE THE TERMINATING
COMMA.
E.
WRITE NOTHING IN COLUMN 80.
F.
USE OF NUMBERS FOR COEFFICIENTS--FOUR MODES POSSIBLE. AND THEY MAY ALL
BE USED IN ANY ONE SPECIFICATION.
1. FIXED POINT MODE (AN INTEGER)
2.
FLOATING POINT MODE (YOU SUPPLY THE DECIMAL POINT)
3.
NO NUMBER IN FRONT OF AN X SIGNIFIES A I, E.G •• X(25) IS
INTERPRETED AS lX(25)
4.
EXPONENTIAL MODE
A.
NOT RECOMMENDED BECAUSE THE COEFFICIENTS SHOULD BE BETWEEN
1 AND 1.0.000. SAY. FOR ACCURATE RESULTS.
IF THE COEFFICIENTS ARE
NOT IN THIS RANGE. A SCALE FACTOR SHOULD BE USED BEFORE PUNCHING.
B.
MAY USE FIXED OR FLOATING MANTISSA.
C.
FOLLOW IT WITH AN E. THEN A MINUS OR PLUS SIGN (OPTIONAL).
AND THEN A TWO DIGIT EXPONENT.
D.
EXAMPLE-- 22E03 IS INTERPRETED AS 22.000.00
0,
'
G.
SUBSCRIPTS ARE PUT IN PARENTHESES FOLLOWING THE 'X'.
THEY MUST NOT
CONTAIN A DECIMAL POINT. AND ARE. OF COURSE, ONE OR TWO DIGITS IN LENGTH.
IV.
ERROR STATEMENTS
A.
ALPS HAS A LIMITED CAPACITY TO CHECK FOR ERRORS.
THE MATRIX CHECK
SHOULD ALWAYS BE VISUALLY COMPARED WITH YOUR INPUT DATA TO INSURE ACCURACY
OF THE RESULTS.
THE ERROR STATEMENTS ARE SELF-EXPLANITORY.
ALL ERRORS
EXCEPT THE FIRST TWO INHIBIT EXECUTION.
THE MONITOR IS CALLED AFTER
ALL CARDS ARE CHECKED FOR ERRORS.
ONLY THE FIRST ERROR IN EACH CARD IS
USUALLY GIVEN.
B.
THEY ARE-TAPE WRITE CHECK
PUT NEW TAPE ON TWO. THEN PRESS START
USED MORE THAN FIVE CARDS FOR ONE SPECIFICATION
INVALID CHARACTER IN A NUMBER
FIRST LETTER NOT A C. M. E. OR S
INVALID SUBSCRIPT
TWO SUBSCRIPTS ARE EQUAL IN OBJECTIVE FUNCTION
NO +. -. GE. LE.
OR E AFTER AN XCI)
A COMMA DOES NOT TERMINATE THE END OF A CONSTRAINT OR THE OBJECTIVE
FUNCTION
ERRORS NOT CHECKED IN CARD NUMBER XXXX
=.
o
I
l''''
-'2.7-
o
COLUMN eo IS NOT' A BLANK
CONSTRAINT NUMBER IS GREATER THAN 21
A COMMA IS BEFORE THE END OF A SPECIFICATION
C.
TYPED WITH EACH ERROR STATEMENT EXCEPT THE FIRST TWO IS
ERROR IS IN CARD NUMBER XXXX
(ALL CARDS ARE COUNTED.)
v.
EXAMPLE INPUTS
SSJOB STAFF CASSIDY,HENRY
SSALPS
MAXIMIXE
.5X(I) + 6X(2) + 5X(3)
•
SUBJECT TO THE FOLLOWING CONSTRAINTS.
CONSTRAINT (1) 4X(I) + 6X(2) + 3X(3)
LE 24
CONSTRAINT (2)
XCI) + 1.5X(2) + 3 X(3) LE 12
CONSTRAINT (3)
3X( 1) + X(2) LE 12
S AN EDITORIA~ STATEMENT
END PROBLEM
=
SSJOB FAC
ABLE. B.
SSALPS
MAXIMIZE IT ONE TIME = 2EOOX(I) +3 X (2).
5 AN EDITORIAL STATEMENT
CONSTRAINT (5)-X(2) GE -3
CONSTRAINT (4 ) x ( 1,) LE 3 •
CONSTRAINT (3) X ( 1 ) +5X(2) GE4.
CONSTRAINT (2 ) 6EOO X ( 1 ) +2EOOX(2) GE +S'
CONSTRAINT ( 1 ) X ( 1 ) + X(2) LE4 •
END
•
SSJOB STAFF SMITH. HARRY
SSALPS
MINIMIZE THE FUNCTION
5.30X(1)+4.90X(2)+4.40X(3)+5.10X(4)+7.00X(5)+6X(6)
+5.70X(7)+5.20X(S)+5.eOX(9)+6.70X(lO)+7.00X(11)+S.OOX('12)+6.30X(13)
+5.90X(14'+5.40X(15)+6.10X(16).
SUBJECT TO THE FOLLOWING
CONSTRAINT(l) lX(1)+lX(2)+lX(3t+1X(4)LE13.
CONSTRAINT(2~ lX(5)+lX(6)+lX(7)+lX(S)LE10.
CONSTRAINT(3) 1X(9)+lX( lO)+IX( 11 )+lX( 12)LES.
CONS TRA I NT ( 4) 1 X ( 13) + 1 X ( 14) + 1 X ( 15) + 1 X ( 16) LE4.
CONSTRAINT(5) lX(I)+lX(S)+lX(9)+lX(13)=10.3.
CONSTRAINT(6) lX(2)+lX(6)+lX(lO)+lX(14)=7.1.
CONSTRAINT(7) lX(3)+lX(7)+lX(11)+lX(lS)=6.2.
S
E:OITORIAL STATEMENT--AS IF I HAD ANYTHING TO EDITORIALIZE
CONSTRAINT(~) lX(4)+lX(S)+IXCI2)+IX(16)=9.1.
END OF PROBLEM
=
o
Z 42-,.,
.. ,-,,._ "., _.Q......
_ :;::E4@4A¢A¢;;;;aallM¥
.Q_"";_n
I
VI.
EXAMPLE OUTPUT
MINIMIZE THE FUNCTION = 5.30XCl)+4.90XC2)+4.40XC3)+5.10X(4)+7.00XCS)+6X(6)
+S.70X(7)+5.20XCS)+S.SOX(9)+6.70X(10)+7.00XCll)+S.00X(12)+6.30X(13)
+S.90X(14)+S.40X(15)+6.10X(16).
SU8JECT TO THE FOLLOWING
CONSTRAINT(l) lX(1)+lX(2)+lXC3)+lX(4)LE13.
CONSTRAINT(2) lX(S)+lXC6)+lXC7)+lXCS)LElO.
CONSTRAINT(3) lX(9)+lX(10)+lXCll)+lXC12)LES.
CONSTRAINT(4) lXCI3)+lXCI4)+lX(lS)+lXCI6)LE4.
CONSTRAINT(S) lX(1)+IX(S)+lXC9)+lX(13):10.3.
CONSTRAINT(6) lX(2)+lX(6)+lX(10)+IXC14)=7.1.
CONSTRAINT(7) lX(3)+lXC7)+lXCIl)+IX(lS)=6.2.
S
EDITORIAL STATEMENT--AS IF I HAD ANYTHING TO EDITORIALIZE
CONSTRAINT(S) lX(4)+lX(S)+lXC12)+lXCI6)=9.1.
END OF PROBLEM
MATRIX CHECK
4
5
6
7
8
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
2
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
3
1.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
4
1.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
S
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
6
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
7
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
2
3
4
5
6
7
8
9
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
10
0.0000
.0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
11
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
12
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
13
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
14
p.OOOO
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
15
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
16
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
17
t.OOOO
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
18
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
19
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
0.0000
20
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
21
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
22
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
23
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
24
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
1.0000
2
3
~,
0'.
~
t
2
3
4
5
6
7
S
8
0
-
--
--
I
I\:)
(X),
I
25
13.0000
10.0000
8.0000
4.0000
10.3000
7.1000
6.2000
9.1000
2
3
4
5
6
7
~
8
0
0
o
o
o
CONTRIBUTION (PROFIT OR COST)
3
-4.4000
4
-5.1000
5
-7.0000
6
-6.0000
7
-5.7000
8
-5.2000
-5.3000
2
-4.9000
9
-5.8000
10
-6.7000
11
-7.0000
12
-8.0000
13
-6.3000
14
-5.9000
15
-5.4000
16
-6.1000
17
0.0000
18
0.0000
19
0.0000
20
0.0000
21
-500000.0000
22
-500000.0000
23
-500000.0000
24
-500000.0000
I
I\)
BASIS VARIABLES
1
17
-t:...
~
2
18
3
19
4
20
5
21
COSTS
0.0000
2
0.0000
3
0.0000
4
0.0000
5
-500000.0000
6
22
6
-500000.0000
7
23
7
-500000.0000
8
24
8
-500000.0000
~
I
,i
"I
-30-
,I
'!
00000000
00000000
COOOOOOOOO
00000000
00000000
00000000
1000000000
-00000000
0 0 0 0 0 0 0 ....
0 .... 0 - 0 0 0 -
•0
•0
•0
•0
• -•
o• • 0
00000000
00000000
U100000000
00000000
I"looooogoo
· . . ... . . · ... . ...
I
00000000
00000000
""'00000000
00000000
• ....• 0
• -• 0• ....• -• 0•
• • • • • • • •
00000000
00000000
.00000000
C\l00000000
00000000
00000000
NOOOOO
00
- 0 0 0 0 .... - 0
•0
• 0
• •0
• -• -•0•
00000000
000(,)0000
1000000000
00000000
00000000
00000000
.q00000000
00000000
00000000
00000000
C\l00000000
C\l00000000
0 .... 0 - 0 - 0 0
00000-00
000-0-00
00000000
00000000
U100000000
00000000
MOOOOOOOO
00000000
00000000
00000000
00000000
00000000
C\l00000000
0 - ........ 0 0
000--00
00000000
00000000
.q00000000
00000000
00000000
00000000
C\l00000000
00000000
I
I
• • • • • • • •
I
• • • • • • • •
,
• • • • • • • •
•
· . . . . . . . · . . . . . . . · ...... .
I
00000000
00
--00
o
00000000
00000000
000000000
C\l00000000
· . . . . .. . · . .. .. . . · .. . . . . .
.... 0 .... 0 - 0 ....
•
•
--0
• •
00000000
00000000
00000000
00000000
000000-0
00-0-0-0
00000000
00000000
C\l00000000
00000000
OOOOOOCOO
00000000
00000000
00000000
CDOOOOOOOO
00000000
-0000000
-0-0-000
0-000000
()\OOOOOOOO
00000000
00000000
00000000
00000000
00000000
""'00000000
00000000
00-00000
.... 0 0 - 0 - 0 0
· .... .. .
0:
00000000
00000000
O\OOOOOQOO
00000000
00000000
00000000
MOOOOOOOO
00000000
· . . . . . .. · . .. ... .
X
000-0000
00000000
00000000
-00000000
00000000
• • • • • • • •
0000-000
•
00000000
00000000
• •••••••
•
· ...... .
t-
• •••••••
-00
-0--
I
,
· .. ... ..
• • • • • • • •
•
00000000
00000000
U100000000
C\lInO\Oqr}IOC\I-
........
q
CO-C\lC\lIOCJI
o
~
~
Z
o
I
"
t~
.... C\lM.qU1IO,....CO
..J
o
en
'17
-C\lMqU1IO,....CO
I
..
o
o
o
OPPQRTUNTIV COSTS OR SHADOW PRICES
:3
2
9
20
14
:3
8
.9000
11
2.1000
12
3.3000
13
0.0000
14
0.0000
15
0.0000
16
.9000
0.0000
10
1.3000
17
1.0000
18
0.0000
19
.5000
20
0.0000
21
499993.7000
22
499994.1000
23
499994.6000
24
499994.8000
QUANTI TV
4.5000
.9000
8.0000
1.4000
2.3000
2.6000
6.2000
9.1000
OPTIMAL FUNCTIONAL VALUE
VII.
0.0000
0.0000
VARIABLE USED
18
7
.3000
0.0000
9
h,
-..,,'-.,
6
.1000
.7000
0.0000
2
5
8
4
=
CONTRIB./UNIT
-4.9000
0.0000
-5.8000
0.0000
-5.3000
-5.9000
-4.4000
-5.2000
VALUE
-22.0500
0.0000
-46.4000
0.0000
-12.1900
-15.3400
-27.2800
-47.3200
-170.5800
PROGRAMED BV HENRV CASSIDV, AIDED BV BILL PETEFISH, AUG. 6, 1965
&
,
~
:1
:'' '/
I
o
I
I
I
--I
I
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- - - - - - - - - - - - - - - - - - - - - - - - - -------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
F#@#:iti:fr.t::'tJJ.eWiDrW·TC--
o
1620 SPS and SPS II-D
Object Deck Modifier
()
Betty M. Ear10ugher
Stanford Electronics
La.borator~es
Stanford University
December 6, 1965
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1620 SPS and SPS II-D Object Deck Modifier
I'm sure most of us have had the experience of writ1nK and
as SPS program on the 1620.
debu~K1na
Typically, the process goes as follows:
1.
Write and key punch the SPS source program.
2.
Arrange for computer time.
2 or 3 hours will be needed for a
moderately long program.
3.
Load the assembler deck.
This takes 2-3 minutes.
4.
Load the source program and execute Pass I of the assembly
5.
Load the source program again, execute Pass II of ,the assembly,
and get an object deck punched.
6.
Load the object deck into core.
7.
Find a bug or bugs.
These may occur in object deck patches, if
o
any have been made in the deck.
8.
If the change necessary to correct the bug is minor, punch a
patch card to correct it.
Also, if large portions of the .program
were not destroyed by the error, patch in core and continue
debugging.
Otherwise, it may ·be necessary to reload the object
deck, or even to re-assemble.
With a disk file and Monitor, the process is made somewhat easier by bypassing
the tedious loading of the assembler.
Even so, debugging is a frustrating
procedure, and not the least of these frustrations can be the errors made
in correcting the errors in the original program.
When a bug is found, a correction can often be made in the object
deck, avoiding the assembly process.
This is done by punching a patch card,
which is loaded over the erroneous instructions or data when the object deck
---~'--'--'-
__
._.
._----
o
I
i''''
2
o
is loaded.
When patching a program, the address at which the correction is
being made and the correction itself usually must be typed
twice-~once
enter the correction into core and once to punch a patch card.
0 ..
maa~
in a
flUfftbOl'
to
Errors can
or piaces' in t;his process--
I.
Typing the address at which the change is to be made.
2.'
Typing the change.
3.
Punching the change in a patch card.
4.
Punching the address in a patch card.
5.
In the card assembler, computing and punching the address at which
the change ends.
6.
Keeping track of which change goes with which patch card.
This catalogue of errors may sound exaggerated, but after 3 or 4
hours on the computer, it is possible to make any or all of these errors
o
in any given correction.
A few years ago, a student in the Electrical Engineering Department of
Stanford University wrote a program which prevents the person debugging
anSPS program from making four of the six errors mentioned above.
program is called the 1620 SPS Object Deck Modifier, or DECK
M~D
This
for short.
It was originally written to be operated with the card assembler, and was
revised when SPS II-D under Monitor I became
avail~ble.
Let me describe the program with reference to 'the SPS II card assembly
system; modifications necessary for other versions of SPS are minor.
DECK
M~D
is loaded after the object program is in core.
,a message is typed giving the two sense. sWitch functions/used.
During loading,
DECK
M~D
requires 1000 digits of storage, and usually resides in/the upper 1000 digits
o
,of' core.·, The first instruction 1's then at 19000, 39000, or 59000, depending
,":-
. ,f
". L'$lffl!!_
3
on the core size available, so one can easily remembe'r the starting address.
To use DECK
M~D,
execute a branch to the starting address.
o
The type-
writer carriage will return and the program will wait for an entry from the
typewriter.
The address at which the modification is to be made ,should be,typed.
This address is the lowest memory address (high order digit of the modification).
-It need not be a 5-digit number--the program will supply leading zeroes.
Rls
When
is depressed, the typewriter will space over and wait for entry of the
actual modification.
Up to 61 digits of numeric information may be entered;
record marks are allowed only as the last digit.
When
Rls
is again depressed,
a 3-digit sequence number is typed to identify the change and a patch card
is punched in the proper format with the sequence number just typed.
After
the patch card is punched, the patch is transmitted as a record to the,
appropriate place in memory.
until DECK
M~D
The sequence number will not be reset to 000
is reloaded--thus there will be no duplicate sequence numbers
in a series of modifications.
As long as the patch cards are kept in order,
there is no difficulty in making patches on top of patches ..
Two program switches are used by DECK
error-correction procedure.
M~D.
Switch 4 is for the typical
(Turn the switch on after a typing error is made,
hit RIS, and the information may be re-entered.)
Switch 3 is used to provide a return to the program being debugged.
It may be turned on whenever the typewriter is awaiting data entry (either
an address or a modification).
The words "00 TO" will be typed, and the
typewriter will await entry of an address to which a branch is to be made.
Rls
(Again, this need not be a 5-digit number.)
When
is depressed, a branch
to the address just typed will be executed.
The patch cards are usually
allowed to accumulate in,the punch hopperuntll the object program is to be
o
4
reloaded, at which time, they are placed in front of the seventh card from
the end in the object deck.
Operation of DECK
M~D
is essentially the same for SPS II-D (disk SPS) •
A modiftgatton ma1 have 67 diGits, witD
character.
no reQord marks
8ZQQpt AA
All patch cards are punched in absolute f.ormat, so DECK
the lAst
M~D
may
not be used to patch relocatable SPS (e.g. subroutines written to be used
with a
F~RTRAN
main program).
Patch cards are placed in front of the second
card from the end of the object deck.
The deck is self-loading, rather than
stored on the disk, to avoid the possibility of destroying a part of core
"by calling the Monitor.
: disk in core-image format
Of course, it would load faster if stored on the
J
and this can certainly be done if memory below
2402 is never used by the programmer.
o
In summary, the 1620 SPS Object Deck Modifier provides a way to avoid
the most common errors associated with correcting errors in a
program~
by
.' automatically punching patch cards at the same time a correction is made to
a program in memory.
This program will be available from the 1620 Program Library in the near
future.
·0
,t
Until then, I will be happy to supply copies of the source decks.
I
!II
I
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ABSTRACT
CLEARTRAN is a system for compiling FORTRAN statements to
yield an object program having maximum efficiency. The object program
generaJlyoccupies less than one-half the core space and usually executes
twice as fast as the MONITOR n system. Programs. involving substantial
an10unts of subscripted variables may execute in as little as one tenth the
usual time.
'
'-Infinite" 'programs may he compiled by virtue of "instant" linkage
. from disk and the use of optional advanced language concepts •
. "My 1620 can draw circles around your 1620" aptly describes the
. Format capability. Equations can be "plotted" on the printer. Information
can be extracted from a card read or a card may be re-read by any Format
number. Complete printer control is available with FORMAT statements.
Printing of the results of one problem may be obtained while computing the
next set of answers •
. Error analyses are exceedingly thorough ~;.t both the compile ~d
execution. stage •. For example, unidentified variables, and out-of-range
subscripts are called out at ,both compile .and execute ti..-.rne. The object
program seldom blows ,up during execution. A tract routine is available
for presentation of both ,the name of the var,iableand its v8J\ue as calculated.
o
CLEARTRAN VERBS
o
IF)
. INTEGER
,'PAGE
BRANCH BACK
. PAUSE
CALL
. PERFORM'
EXIT
INTERRUPTPRINT
PUNCH
LINK
PDUMP
READ'
REAL·
COMMON·
CONTINUE
REC·ORD
. DEFINE
RELEASE
ADDRESSES
CARD IMAGE
. DISK
ERROR MESSAGE'·
DISK ADDRESS'
PRINT SKIp·
FAST LOG
. PRINT ROUNDING
. RETURN
SIZE
STA.RT
ROUTINE
DIMENSION
SET
'DO
STACK'
DO BACK
STOP
END
STORE
.
EQUIVALENCE
,.ADDRESSES
'CONSTANTS
FETCH
. ·FIND
NAMES
SU·BROUTINE
FORMA.T
.·.TAG
FUNCTION
TRA.C'E
GO TO
HOLD
PRIN'I\ TYPE, PUNCH
CARD IMAGE
·OFF
ERROR.MESSAGE . TYPE ..
. ZIP
PRINT SKIP
PRINT ROUND1NG
ACCEPT
AS~IGN
o
--
-
.. -
..
_----------
-~.
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~
IN-LINE ROUTINE
A group of FORTRAN statelnents prefac~d by ROUTINE is defined
c.u:; an in-line routine. The routine is given a name with up to six alphanun,eric characteristics" the first of which nlust be alphabetic. A routine
is normally entered by 'means of the PERFORM command and the normal
exit is by BRANCH BACK.
The PERFORM command generates a BTM.(branch and transmit
inlmediate) type of instruction,.witll t.he return address being carried to
the routine for use when a BRANCH BACK instruction is encountered. If
thE~ PERFORM command includes a statement number, the BRANCH BACK
will be to the address of the statement number specified; otherwise, the
return address will be that of the statement following PERFORM.
o
The data and variables used in a routine are identical to those of a
mainline program. A routine may be located anywhere in the program except within the confines of another routine. The normal exit from a routine
is by the BRANCH BACK command, of which several may be used if desired.
A direct entry to any numbered statement of the routine may be used. In
--,
this event, dhe BRANCH BAGK exit address from the routine will be that
specified by the PERFORM command last used to enter the routine. .
The' address of a routine may be stored in a subscripted array by
the STORE ADDRESSES command. This makes it possible to PERFORM
. a computed address" e. g., PERFORM RUTEN(J).
While within a routine,' one may PERFORM other routines provided
the chain of addresses required to return to the mainline program is not
broken. If there is a need to break the chain, the address of the ROUTINE
where the break is to occur may be saved by including the name o'f the
routine as the third operand of the PERFORM command.
By this. mean.s, one may perform a ROUTINE from within tne routine
itself, ',if desired. Examples are illustrated in the sample programs...·
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". A4ik4i,C4,MQ.'; ,.\. .....·.(24.\ 4·.. J.
.;£.. g«$.,4. __
_, DEFINI
ON OF VARIABLES AND ASSIGNMENT OF ADDRESSES
A varia Ie is "defined" if it is' encountered to the left of an equal
sign, in a READ, ACCEPT or FETCH stat~ment, or in one of the
following: COMM N; DIMENSION, EQUIVA:LENCE, INTEGER, REAL,
STACK.
o
DIMBNSION
The DIMENSION statenlcnt is used to define· the size and the number of words in an array. The nunlber of subscripts which may be used is
not limited. to three. The length of the fields in an array can be made
different from normal by placing an intergal number in fron't of each elenlent of the list. The minim.um length field is two. There is no maximum
. litnit to the length of the field; however, the prnctica11imit for use in
conjUnction with printer comlnands is 288.
COMMON
This command is identical to IBM's.
STACK
'. The STACK command is the opposite of COMMON; i. e., 'the variables in the list are assigned sequentially ascending addresses, while those
in COMMON have descending addresses. A dirnensioned variable can be
equivalenced to the first element of a list previously stacked making it
possible, thereby,· to refer to the list- as an array. The STACK command
is especially convenient for use in conjunction with the deferred PRINT
command described later.
o
TAG
If it is desire d to dete rmine all the positions in a program where
reference to a particular variable is made, the TA.G command may be
used. Up to five variables may be tagged at one time; e. g.,
TA.G, V, VOICE, A20,. I, YOU
REAL
.
This verb defines a variable as a floating point type even though
the initial letter might be I, J i K, L, MorN. .
INTEGER
This command defines a variable as a fixed point type even if. the
initial letter is other than I, J, K, L, M or N.
-57
- - - - - , - - ... _ - - - - - - - - - - - ---
o
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FIELD LENGTH
As with the DIMENSION command, the length of a variable can be
changed from the normal length hy placing a number immediately after the
STACK, REAL or INTEGER conlmands.
ALTERNA TE DIMENSIONING
The list in the COMMON, STACK" REAL or INTEGER commands
can be subscripted as in a DIMENSION statement if the variable is to be
din1ensioned. (The variable lnust not then appear in a DIMENSION statement. )
STORE
The STORE command may be used to store at compile time three
types of data: addresses, fixed or floating constants with sign, or'ialphanumeric data. The name of the field where the data are to be stored in
core is the first element of the list; the remaining elements are stored in
first and successively higher addresses.
ASSIGN
o
This command may be used to move addresses in core at object
time.
DEFINE
The DEFINE ADDRESSES command may be used to specify indirect
addresses where the actual address of a subroutine" routine, statement
number, constant" etc., may be found. This command is very useful for
a communication link between two programs which may be in core simultaneously.
TRACE
The commands TRACE PRINT, TRACE TYPE" TRACE PUNCH, ar:td:
TRACE OFF may be used to follow the path of a problem through a program.'
The TRA CE PRINT statement calls in a relocatable subroutine which prints
the name of the variable on the lefthand side of the eqll:al sign in 'each arithmetic statement, together with its numerical value. Three variables and
their values are printed on each line. Switch 4 activates the TRA.CE· subroutine at .object time.
CA.LL INTERRUPT
o
The CA.LL INTERRUPT statement resuits in storage on disk of the
core immage of the program and data, together withthe address at which ,
the intert;'upt occurred. The CALL INTERRUPT command may be selected·
!j?"
sac..
.-t,~"",--
"rh._
_. _"h
.,,;;;;4.0 (AUd.,-
--- -- . '-
'..
g ...:
by program calculations or by 1urning on a programmed sense switch.
The
program maybe restored and execution continued by loading a single
INTERRUPT RESTART card. If data remain to be read, the last card
read, together with cards not yet read, should be set aside for reloadin,g.
Obviously, data stored by RECORD commands may be lost unless the disk
pack is set aside.
o
PRINTER D1JMP
If it is desired to dump the contents of core on the printer during
the execution of a program" one may use the following command:
CALL PDUMP (Nl, N2)
NJ. and N2 may be absolute addresses or they may be the names of variables.
CALL PDUMP pulls in a disk utility program which prints core between the
lirnits specified, with 100 digits per line grouped by tens" with core addresses
conveniently shown. Control returns to the program after execution.
, ZIP
The ZIP statement used irnmediately preceding a 00 will speed up
the evaluation of arithmetic expressions involving subscripted variables.
The conditions where ZIP nlay be used are:
1. Indexing must be unde r DO loop control only.
2. Each arithmetic statement must be complete without
having to use more than one continuati~n c~rd~ __ 11_
3. DO's may be nested not more than ~ deep. \fVV\.~
·4. The number of subscripted words may not exceed 20.
(The above limits are tentative. )
. Example:
ZIP
11 00 3 J=l, 10
12 DO 3 K=3, 5
13 00· 3 'L=l# JIM, 2
1 A(J) = A(J) + B(J, K# L) +A.B(I)
IF (C(J 1 KI L) - 50. )2, 31 2
2; C(J ,KI L) = D(J, K+l, L-l) +F +A(J)
:3 CONTINUE
<
,I
. ;J ..( ..
,
~,
,\.
..
~'l'/
Note t~ere are "four subscripted "words" in the above, under ZIP ,
control.·A(J) is one word, B(J 1 KI L)I C(J 1 K, L) and D(J, K+ 1, L-1) are the'
others. Each word m.ust consist of notmore than 12 characters including,
the two parenth·eses. AB(I) is not a "word" because its indexl I, is not"
. ....
under 00 control.
.
,
'
'
Another ZIP could be used after statement·.No. 3. The DO's must
have numerical starts· and numerical increments •. The DO's may have variable
upper limits.; i.·e. ~ JIM in statement 13.
o
o
I/O FEATURES'
The input or output achieved by execution of' conventional I/O FORTH.AN statements is identical to that from IBM compilers. Cerlain addi- .
tional features are available, as follows:
1.
2.
3.
4.
5.
6.
7•
B.
9.
10.
11.
B~TYPE,
G-TYPE, andJ-TYPE FORMAT
ALPHABETIC SUBSTITUTION IN E &F OUTPUT
AUTOMA.TIC E & F ROUNDING
AUTOMATIC PA.GE SKIP
CARD IMAGE REREAD
. DEFERRED PRINTING
FORMAT OVERRIDE
NON FORMAT READ
PLOTTER SIMULA TION
PLUS SIGN (+) SPACE IGNORE
COMPLETE PRINTER CONTROL
B- TYPE FORMA T
o
B-type words (B for Beta) can be read or written with a non- standard'
length designated by the FORMAT statement. The length may be a single
character, Bl, or up to BOcharacters for reading the entire card, BBO, or
B144 for printing 144 characters. The variable where such a word is stored
normally is dimensioned so as to have its word length equivalent to that used
in the FORMAT. For example B1 words could be read into a dimensioned
variable with a word length of at least 2. B80 words should be read into
fields which are at least 160 digits long.
A single B-type character is stored as two digits in core, the left
one of which is flagged. If stored in a standard fixed-point field of four digits,
. only the two positions to the right side of the four are used. When printing or' .
ptulching such a word, by a B-type FORMA.T which is identical in length to
that used to read the word, conventional output is obtained. However, if the
length designated by the FORMAT statement used to read the word is less
than the length used in output, the character will be positioned incorrectly
by the difference in the two lengths. This can be corrected by changing the
. output FORMA.T statement so that the .two lengths are equal, using X-type .:
FORMAT to make up the differences where required for spacing purposes~ .
G-TYPE FORMA.T
o
.
This is identical to F-type FOR~.AT except that the first blank follow~"
ing the field is considered as a decimal. G-type FORMAT is normally ,used .
.for reading o n l y . '
. .
.
" 2W --''''''"
*-a.ijM.YR.';;;;;!. ..
-!
.
.
.
-
,.,*. . . ,.
.•
J-TYPE FORM.AT
This is identical to I -type FORMAT except that the first blank to
the right of the field terminates reading. This permits left-justified,
fixed-point fields.
o
ALPHABETIC SUBSTITUTION IN E & F OUTPUT
On occasions it may be desirable to substitute a short word or
blanks in place of an E or F output field. This can be done by setting:the
floating-point variable to be listed equal to a special alphabetic field.! The
two leftmost characters of the alphabetic field inust be the decimal point
equivalent (03). The decimal point is not printed but the alphabetic characters·.which represent the remaining portion of the word will be printed.
A.s an illustration,
IF (A) 2, 1, 2
1 A = WORD (1)
2 PRINT 100, A
100 FORMAT (FlO. 0)
STORE NAMES (WORD(l), .. <-NONE, •
, • ALL)
7\
will cause the word NONE to be printed if A. were zero at the IF statement.
Blanks would be printed if A were set equal to WORD(2)·and the word ALL
would be printed if set equal to WORD(3).
A.UTOMATIC E & F ROUNDING
Rounding of E and F output is automatic. If automatic rounding is
not desired, it can be bypassed by the com~and: ·HOLD ROUNDING; and
restored later if desired by: RELEASE ROUNDING .
. AUTOMA TIC PAGE SKIP
A skip to a new page is automatic when the bottom line of the page
is sensed (printer indicator 34). This feature can be eliminated by the
command: HOLD SKIP (and restored by RELEASE SKIP). This might be
desirable when using plotter simulation, or when page skip is under program
control.
'
CARD IMAGE REREA,D
The usual READ statement with a FORMAT number will cause a
new card to be read and data extracted therefrom in accordance with the
FORMAT specifications. It is possible to "read" the same card again, '"
using dlfferentFORMAT statements if.desired. by two different methods:
(P(
o
1.
2.
o
Place an X (for extra) after the FORMAT number
in the READ statement.
Use the command, lIOLD CARD IM1\GE, followed
by a conventional {-{,gAD statement.
The latter causes a one-time sldp of the nornJal procedure whereby a new
card is read for each READ statelnent, making it possible to reread the
last read card. 'The HOLD CAR,D IMAGE comrnand can be nullified by the
command RELEASE CARD IMAGE.
DEFERRED PRINTING
Some problems require that all or almost all of the calculations
be completed prior to doing any output. With CLEARTRA.N it is possible
to print the results ·of one set of calculations while calculating the following
set. By this means, printing and calculations can go on simultaneously
with a considerable savings in time. Deferred output can be obtained by
placing the letter "s" (for Save) after the FORl'/[AT number of an output
statement; e. g., PRINT 102S, List. This command will be ignored at object'
time prior to execution of a SA VE command.
o
The output commands utilizing this feature can be placed at selected·····.
positions in the mainline of the program where recycling does not occur.
Alternately, all PRINT S commands can be placed in a ROUTINE using a computed GO TO to execute successive statements. The ROUTINE could be
executed by randomly placed PERFORM statements. When used in a
ROUTINE, the "printer busy" indicator should be tested to save time (if the
printer is busy an immediate exit from the ROUTINE should be made.)
The SA,VE (V1, V2) commands result in a transfer of that portion of
core image lying between the address of variable VI and variable V2 to a
safe place in memory. This includes V1, but not V2. The variables to be
listed by S type output commands should be in contiguous memory locations
for the least space requirements. The. ST ACK or COMMON commands are
used to achieve the desired order. All the variables to be listed should be
in either COMMON or STACK, but not part in one and part in the other.
The deferred output command can be made to list current values
if a zero i~used in a SA.VE statement; i. e. ,SA.VE (0). The original status.
can be restored by using a negative number in a SA,VE statement; e. g.,
SAVE (-1).
...;
..
FORMA.T OVERRJDE
The list of an 110 statement is under control of the specifications'
set up in the FORMAT statement. This normally requires that the number
items in a subscripted list be identical to the "repeat" number of the· .
corresponding ele~ent in the FORMA.T statement.
"
of
o
au..,..,. _._
."""'n."
, .....
,;;;;;;;;1I(¥)$1,,4,)2):;.;", ;-".-¥.~.-. ·1·. ·..:.
,". -,
.•.:
'!
WithCLEARTRAN, an I/O list may involve subscripts using a
variable index. The corresponding "repeat" number of the FORMAT.
specification should be greater than the maxilnum' possible value of the
index(99 is tops). If the repeat number happens to be less than the index
variable,. FORMAT control will pass to the next element of the FORMAT
o
statement~
NON FORM.A TREAD
The preparation of input data to be read under FORMAT control
requires extra care to insure proper positioning of data on the punched
card. This problem can be circumvented by using the REA D statement
without a FORMAT number. Data of the E, F, 1 and A type can be read
without a FORMAT number. One or several spaces are used to separate
data fields. All 80 columns of a card may be used. A relocatable library
subroutine ·examines the input data and discriminates between E, F, I or
A data. The F-type conversion results from a decimal point in a numeric
data field. The E-type results if a decimal point and the letter E are fotmd.
The I-type is generated when there is no decimal point in a numeric field.
The A:-type is obtained if none of the above conditions are met.
An "input error" is called out if the variable being read is in the'
wrong ·mode. The unread portion of the card is typed and a BRANCH TO
the program starting address occurs.
One card may contain information which is read by several READ.
statements. After all the fields on a card are read, the next item on a
list will cause a new card to be read, even if the item is ~ the middle of
a list. A record mark in column one of a card calls EXIT.
PLOTTER SIMULA.TTON
The SET command is identical to the PRINT command with the
exception that printi~g does not occur. The SET c.ommand is normally used
to build an image which is to be held in position for additional modifications •.
If an X follows the FORMAT nUlnber of a SET command, "extra" informa.
tion can be placed' in the image without destruction of information previouslyi~·.
placed (except' that which is overlaid). By this means, it is· possible to
"
build up a complex line of information which is to be printed after all the
information is in place.
The X specification in a FORMA.T statement is used to position or . . :
space adjacent fields. In CLEA.RTRA.N one may use the X specification ~
followed by a fixed point variable in parenthesis; e. g., X(Nl).· This.
.
specification ,will result ina number of spaces equal to the value of the
fixed point variable Nl.
.
o
!I,.,
!
o
One may use the space supress character (+) in column one to
p:rlnt one set of characters on top cf another. This character should be .
erased (lHO) prior to the final PRINT command.
After a line of data is in position, it is printed by a PRINT command,.,
the FORMA.T number of which is followed by the letter X.
'
~
The ~irst 80 characters of an image ca..l1 be punched by placing the
letter X after the FORMAT nUITlber of ptulch statement.
A program to illustrate these features is attached. This program
plots three equations, coordinate grids, and prints alphabetic information
simultaneously. Another prC!gram "draws" a picture of a heat exchanger
tubesheet.
PLUS SIGN (+) SPACE IGNORE
. It is not necessary to provide space for. the plus sign when printing
or ptUlching. This makes it possible to put additional information on a card
when punching, or to pack E or F fields adjacent to other fields when printing.An error may occur if the E or F fields are n'egative, since space must
be provided for the minus sign. .
....
COMPLETE PRINTER CONTROL
A complete set of printer controls is available with CLEARTRAN.
The following is a list of the printer controls which are achieved by placing
a Hollirith character in column one:
Before Printing
+ Space supress
J one space
K two spaces
L' three spaces
:. 1 skip to channel 1
2 skip to channel 2
3"·'-' skip to channel 3
4 skip to channel 4
5 skip to channel· 5
6 .skip to channel 6
7 .skip to channel 7
8 skip to channel 8
.. 9 skip to chamle 1 9
= skip to channel 11
@ skip to' channel 12
0
After Printing:
S
T
A.
B
one space
~wo spaces
skip
skip
C skip
D skip
E skip
.F skip
G skip
H skip
I skip
skip
)
skip
to channel 1
to channel 2
to channel 3
to channel' 4
to· channel 5
to charinel 6
to channel 7
to channel 8
to channel 9
to channel 11
to channel 12
(Any other character may result in a runaway carriage. )
.(p '/
u
. . . .,.,_........._" ..~ ... ;;am;;m4JR.Ag
j
"',' -
••
.Q.AM· -
FQ.RMAT stutementEI with mUltiple. slashes which are executed
only by PRINT commands a re automatically cOtnpiled so as to take advantage of fast printer spacing msofar as possible.
0·"·
j,
The "printer busy" indicator (35) can be sensed by use of the
statement: IF (SENSE SWITCII 35) Nl, N2. A BRANCH TO statement Nl
occurs if the indicator is on (buffer is unavailable for loading); N2 if off
(buffer can be loaded).
Similarly, 33, 34 and 25 can be used to sense respectively channel
9, channel 12 , and printer check indicator on the. 1443.
o
o
AUT 0 M 0 NIT 0 R
FOR
IBM
THE
162 0
Presented At The
WESTERH REGION WINTER
{\flEETIHG OF CONllJ.ON
o
December 7, 1965
By
John W. Rettenmayer
western Data Processing center
405 Hi1gard Ave.
o
Los Angeles, California 90024
1
The WDPC 1620 Automonitor was written at the Western Data
/
Processing Center, which is. a part of the Graduate School of
Business Administration at UCLA.
'.'
0·
,
I
It was written to serve as a
debugging aid to the students in BA 113, an introductory course
in data processing.
This class usually has from 60 to 80 students,
so any debugging which requires manual operation at the console
is extremely inconvenient to other students and greatly increases
the confusion from too many students milling around awaiting their
turn on the machine.
(The 1620 lab is an open-shop arrangement.)
The WDPC Automonitor is used for debugging student-written
1620 machine language programs.
Instead of being executed directly,
the student's program is executed one instruction at a time, with
each instruction and its memory address being printed out just before
it is executed.
As long as the Automonitor is in control, the trac-
ing may be turned on or off to enable the operator to trace selected
portions of the student's program, or all of it.
For example,
tracing may be desired only after a certain point in the program
has been reached, that point being indicated by a particular value
being printed.
At that point switch 1 may be turned on and the in-
structions will be traced from then until switch 1 is turned off
again.
This selection process may be repeated as often as needed.
The students are given only two constraints: (1) their programs
must start at location 5000, and (2) they may not use any memory
positions lower than 5000 because that area is reserved for the
loader program and the Automonitor.
To increase the throughput of
the system, the students' machine language programs are run under
the Monitor I System.
This
req~ires
that the student program
return control to Monitor upon successful execution.
If execution
o
I"
i
W6,r-*,nseeU--'tf"-e"ml'!
••
2
4()
is not completed successfully, then the operator must manually
branch to Monitor (using a 4900796 instruction).
In order to
allow stacking of jobs, the student cannot test for last card,
as is usually done to signal the processing of the last data
card.
Therefore, each student ,is also required to test for a
trailer card having a record mark in column 1.
The Monitor I
end-of-job card does nicely for this purpose.
As Lmplied above, the 1620 configuration at WDPC includes a
1311 disk storage drive and a Monitor I System.
We also have 40K
of core storage, and, although it has no bearing upon the use of
the Automonitor, a 1627 plotter.
OPERATING
C'
PRO C E D 'u R E
Student's deck setup:
~~COLD
START
FFPAUSE
(for stacked input)
~#XEQSMACHLG
(Student's machine language program,
punched one instruction per card.)
(blank card -- to separate program from data)
(data for student's program)
If tracing will be desired during any part of the user's
program execution, switch 2 should be turned on before the word
EXECUTION is typed on the console typewriter.
:) 0
Then turning switch
1 o'n at any time will cause tracing to begin, and turning switch
1 off will stop the trace printout.
. ....,U:M#.4Q\iUiW(M ,-.-
.,..)¥
3
LOADER PROGRAH
I~CHLG
o
(a listing of which follows later) is the program
which loads the student's program.
MACHLG is stored on the disk
in the regular way, with an associated DIM entry, and is called
into core and executed by the ""XEQSMonitor Control Card.
The
functions performed by MACIILG are the following.
First, it loads from the, disk into core 37,000 digits, starting at location 3000 and ending with 39999.
These 37,000 digits
are obtained from one cylinder of the disk, which contains 20,000
digits, so that part of the cylinder is used twice.
(We have re-
defined the disk storage so that cylinder 0 is not a part of the
disc's working storage, but is available for MACHLG to use.
Other
installations may wish to obtain the cylinder in some other way,
and shoulQ change the instructions in imCHLG accordingly.)
The
first 14 sectors of the cylinder contain the Automonitor program;
therefore it is loaded with its starting address being 3000.
The
rest of the cylinder contains only zeroes which are used to effectively clear core from the end of the Automonitor to location 39999.
Locations 0 - 2999 are not cleared since they contain the arithmeticCtables, part of the Monitor Supervisor routine, and MACHLG
itself.
Second, r4ACHLG ,loads the student's program, starting at
location 5000.
MACHLG loads each instruction; i.e. the first
12 digits of each card, into successively higher memory positions
until it detects a card with a blank in 90lumn 1, sl.gnifying that
the entire program has been lOaded.
Third, control is transferred to the instruction at 3000,
o
tl!
r
I
which is the first instruction of the Automonitor.
4
o
AUTOr-10NITOR OPERATION
The following description is brief and perhaps confusing;
please refer to the program listing for better understanding.
The Automonitor first interrogates Switch 2 to see if tracing is or will be desired.
If not, control is transferred to the
student's program and that program executed directly.
If Switch
2 is on, then the student's program will not be executed directly,
but will be simulated by the Automonitor in the following manner.
First, the Automonitor copies the student's first instruction
into an area within the Automonitor program, which will be referred to as the simulation registero
(Actually the instruction is
copied into two areas -- one for execution and the other for outputting the instruction.)
(j)
If the instruction is not a branch in-
struction, it will be executed directly in the simulation register.
Since this register in imbedded in the
Automon~tor
program,
con-
trol will remain in the Automonitor after execution of the instruction.
Then the next sequential instruction of the student's
program is treated by the same process.
If the instruction is a branch, then the actual execution of
that instruction, even in the simulation register, would cause
control to be transferred to the student's program and the Automonitor would then be inoperable.
Therefore, that branch instruction
must be simulated in such a way that the next instruction operated
upon by the Automonitor is the correct one.
That is, if a branch
were called for by the conditions of the machine, then the instruction
at the branch address must be the next one fetched ahd treated.
~o
I
If a branch were not called for, then we want to take the next
5
sequential instruction after the unsuccessful branch instruction.
~
This is done by carrying out the appropriate tests, for conditional
branches, and modifying the 'next instruction address' (ADDR)
accordingly.
TRACING
If at any time the user wants to have his program traced as
it is simulated by the Automonitor, he only has to turn on switch
1.
This will cause the address of each instruction and the
instruction itself to be printed.
If switch 3 is on, the trace
will be punched on cards; if it is off, the trace will be printed
on the console typewriter.
Which option is chosen depends, of
course, on the demand for operating time and the availability and
convenience of listing equipment.
(The punched output will have
the instruction address and the instruction separated by one zero
(~
."".J
~I
,'II.
instead of blanks since alphameric mode is not used.)
If it is definitely known that a trace will not be needed,
then switch 2 should be off initially so that the user's program
will be executed directly instead of being simulated.
However,
on short student programs the added time used by the Automonitor
is insignificant, so one need not worry about accidentally leaving
switch 2 on.
RESTRICTIONS
By their nature, operation codes 07, 17 and 27 cannot, to my
knowledge, by simulated since to do so would require accessing
the hardware registers.
Also, the Automonitor will not handle
any compare operation, since the Automonitor itself makes a great
many comparisons and, as it now stands, would probably destroy
'71
o
6
o
the indicator set by the user's compare operation before his
branch-on-condition instruction would be simulated.
It is pos-
sible to rewrite the Automonitor to handle compares, but the
compare instruction is rarely used by beginning students, so we
have not done so.
For the same reason of infrequent use the
branch-no-indicator instruction (op code 47) has not been included either, although to do so would simply be a matter of
following the logic of OP46 (see listing of Automonitor).
The WDPC Automonitor could be elaborated upon to a considerable
extent to achieve a sophisticated tool for debugging 1620 machine
language programs.
However, it was the opinion of the author that
such a tool would serve to defeat the purpose for which the student
is taught machine language.
That purpose is primarily to acquaint
him with the basic level operations of the computer, and much of
that acquaintance comes from manual debugging, i.e. experience.
However, a minimal automonitor is helpful in those cases where
j
the lab assistant must help the student debug -- formerly by
manually stepping through the program at the console.
Each section of the Automonitor program delineated by the
lines of asterisks is self-contained and has no particular physical relationship to the other sections.
The 'B
FLAG' instruction
just before the section labelled 'FLAG' seems to be a superfluous
instruction, but it was left in the code in order to preserve
this modularity.
Extensions to the Automonitor can be easily made,
if desired, by following the pattern of the present sections.
o
It
is recommended that the modularity be retained since it clarifies
the flow of the program to a considerable degree.
72-
o
7
ACKNOt1LEDGEI1ENTS
~ACHLG
was originally \'lritten and implemented by George
H.
Schoenherr, who was in charge of the '1620 installation at WDPC
and is now an employee of IBH at San Jose.
Sally Ann and Susan
Gulick did a considerable amount of debugging of the Automonitor
after the first rough version was written.
Their work was done
as an extracurricular project for BA 113, and is much appreciated.
The author and the WDPC staff would appreciate any comments
and would particularly like to receive information on extensions
and modifications that are made to the Automonitoro
**JOB 5
**:J:XE
*EXECUTION
BOOZER, G.l.
BA 113 PROGRAMMING PROBLEM NO.1
QSt~ACH lG
rT2150
0-0355"
~920tj"
T0020(f
fl0000
,.OOO~
~2005
0-199"5
END OF JOB
The above execution of the student's program was with switch
2 off. It will now be run again with both switch 1 and 2 on,
but switch 1 will be turned off after the second answer is obtained.
**JOB 5
**
o
BOOZER, G.l.
BA 113 PROGRAMMING PROBLEM NO.1
:J::J:XEQSMACHLG
EXECUTION
0-5000
0"5012
0"5036
el5048
a'5060
361500100500
450503615001
321500100000
261206015005
361500100500
~5072 321500100000
a" 50 84 261206515005
a" 50 96 321206600000
0"5108 22 t 207012070
~5120
321207100000
l) 51 3 2 221 207 51 207 5
0"5144 211207012060
5"5156 211207012065
0-5160 460532401400
0'5180· 251500600400
05192 261500512070
(5'5204 340000000102
~5216
3A1500100100 ~2150
()035C'
"9920C)
T0020C)
Tlooeo
!ooo(r
o
02005 '
cr1995cONDITION CODE NOT RECOGNIZED
END OF JOB
;;;www
mas .",Q _.... ,.0, .. _ .~.~ •...•..__._.
• . . . . .tMA41~.~.;JIiI,.;~
;.;..
.42., .. ?.. 4T4 ....-
., ..
'::i
1
o
**JOB 5
**SPS 5
*LIST TYPEWRITER
10 NUMBER0842
*NAMEfviA CH LG
*STORE CORE IMAGE
~c
START
SK
RON
FIELD,00701
FIE LO, 00702
SK
VELO,00701
RON VE LD, 0070 2
CARD
RNCD IMAGE
SF
IMAGE
CM
IMAGE + 1,00,10
CF
IMAGE
BE
3000
TRANS TO
PROG, H~AGE, 67
AM
TRANS + 11,01,7
AM
PROG,01,7
CM
TRANS + l',IMAGE + 12,7
BE
RESTOR
B
TRANS
RESTOR TFM TRANS + l',IMAGE,7
B
CARD
FIELD DDA ,1,00000,200,03000
VELD
ODA
,1,00030,170,23000
PROG
IfvlAGE
OSA 5000
DSS 00
DENO START
02402
02414
02426
02438
02450
02462
02474
024f16
02498
02510
02522
02534
02546
02558
02570
o258 2
02594
02606
02612
02615
02620
02626
02629
02638
02639
02402
34 02606 00701
36 02606 00702
34 02620 00701
36 02620 00702
36 02639 00500
32 02639 00000
14 02640 0000'0
33 02639 00000
46 03000 01200
25 0263B 0-2639
11 02521 00001
11 02638 ~0001
14 02521 ()2651
46 02582 01200
49 02510 00000
16 02521 0" 263 9
49 02450 00000
00006 10'0000
00003 200
00005 a3000
00006 100030
00003 f70
00005 23000
00005 ~5000
00080
Ol
END OF ASSEt·iB LV •
02720 CORE POSITIONS REQUIRED
00022 STATEMENTS PROCESSED
OK LOADED MACHLG (1042 10"4600lr040"2402cr2402:f:
END OF JOB
0
7-r)
1
AUTOMONITOR
o
OORG
FIRST '. TFM
TFM
START BC2
B
'r****,b't*,'dr
CLEAR S
TO
TO
TO
AM
AM
AM
AM
C
BH
TFM
TFM
C,)
"
'0
BNC1
BC3
PRINT RCTY
WNTY
3000"
DEFI~E ORIGIN
03000
ADDR, 5000,7, I NIT IAL IZE ADDR
~3000
ADDR1,5000,7, INITIALIZE ADDRl
03012
CLEAR", IF SW 2 IS ON, BRANCH TO CLEAR
03024
03036
SOOO",BRANCH TO 5000
CLEAR RECORD MARK
WNCD ADORl-4
TO
AOOR1+1,INST+12"
B
FLAG
SF
CM
BNH
Ct1
BE
CM
BE
'eM
BE
CM
BE
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ANTHROPOLOGY AND THE TEACHING OF PROGRAMMING
Presented at Western Region Winter Meeting of COMMON, December 7, 1965,
Los Angeles, California.
This discussion, since what I have to say could not be considered
a "paper" will be mainly narrative in nature.
Let me introduce myself as neither a programming expert nor as an
anthropologist.
The title of this talk carne about due to an unimaginative
attempt to call it something.
I am, in fact, a physicist in charge of a
computational group, trapped into spending part of my time as an administrator.
I am involved in a small amount of research in atomic and molecular
spectra and structure.
I teach a course combining quantum mechanics, atomic
and molecular physics.
Usually when a course is given we concern ourselves with the
winners~
those who pass--and consider the losers as somehow deficient and incapable.
But I believe we must look more carefully at the losers in programming
courses.
Somehow the "miracles" of computing have been greatly overdrama-
tized, and we are all guilty.
administrations?
sort.
How else do we get money from tight fisted
Well and good, a lot of people believe things of this
Especially students--especially some of the foreign students.
The consideration of attitudes came up in the careful examination of
the types of students who were dropping Mathematics 195, Introduction of
Automatic Digital Computing--and their reasons.
o
71
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Mathematics 195 is required of all engineering students at Illinois,
and may be taken after .having had differential cal,culus.
It became obvious
o
that foreign students were having considerable difficulty, much more than'
native born, although there had not been much distinction between these two
groups in their mathematics grades.
More than once, a section would lose
every foreign student; only occasionally would a foreign student last
through to complete the course.
As far as native born students are concerned, the ability to pass the
course seemed to be, in very general terms, only a function of intelligence
as evidenced by grades.
Good students do well, poor students do poorly.
Now and then an otherwise average scholar does very well because something
seems to click.
However, the foreign student
who has been doing average,
or perhaps even better than average, work in his other courses, would be in
trouble in the programming course.
What and why?
For several reasons this is not a trivial problem.
o
Let us look at
some aspects of possible answers, which hopefully might lead to better ways
of dealing with the problem.
1.
Are we overtraining foreign students?
Are the skills and experience
he is acquiring not applicable when he returns to his native country?
Does
the student know this and is this why he is negligent in his learning?
Some people are becoming analytical and critical, and think that this may be
the case.
Have we alienated these graduates from the manpower and techniques
of his own country, replacing them with skills and tools that are not
available?
There is no point in saying what ought to be available; we must
deal with what is.
Are we right in demanding a skill that cannot;-be applied?
The facts are that there are now 80,000 foreign students in this country,
most of whom are studying in scientific and engineering fields.
;Fe
·If we require
o
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that th~y learn useless techniques, upon returning to their native lands
they become estranged from their own people.
In such an instance, unfor-
tunately education has become a destructive influence.
This need not and
should not be.
2.
system?
Let us consider our system of enumeration.
Well, let us look at Roman engineering:
Coliseum, and aqueducts that still function.
Is it the only "useful"
roads, forts, arches, the
All done with an awkward I,
II, III, IV, etc., and look at this
LXXXI
Try that on your 1620, 1800 or 360.
III
We are decimalized almost everywhere
in the world, but should we be, to coin an expression, binarized or
octalized?
o
I would like to learn more about learning arithmetic.
Because
most of us learned by counting objects, apples and bananas, long before we
learned to abstract "numberness".
In some societies this " numberness" is
prone to have associated ideas which I shall touch on later.
3.
Is there a cultural and ethnic antipathy to our objectives? Let me
quote:
o
-non-literate peoples are capable, under the pressing conditions
of necessity, of doing their utmost with their minds to solve
some practical problem in a scientific manner. Most of the
scientific processes involved are of a practical nature, and
there is little time or inclination for science for science's
sake. The latter activity does not appear until the development of highly sophisticated societies like Hellenic Greece.
This is but yesterday in the history of human time. Because
the Greeks were an aristocratic society based on slavery, they,
who had so much of the necessary theoretical knowledge at their
disposal, virtually failed to apply it. Machines were unnecessary since slaves could do all the work. The Greeks were
interested in ideas--in brains--not in drains. The refuse of
civilization could be disposed of by slaves, but only those
with the necessary leisure could create and maintain that
civilization. The Greeks developed the greatest ideas in the
humanities and the sciences that the world has ever known, and
probably the fewest inventions of a mechanical kind. -Not that
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Problem solution in real-time has not been an important
requirement in our work to date. It has, in fact, been a real
advantage to be able to slow down certain physiological processes
for the convenience of the observer.
APPLICATIONS
o
Much of our simulation work involves the PACTOLUS system
described by Robert Brennan of IBM, San Jose, at the 1964 Fall
Joint Computer Conference. PACTOLUS is one of the so-called
"analog-oriented languages." It allows the 1620 to be progranuned
much like an analog computer: i.e. by the preparation of block
diagram and a "wiring list." Many function blocks are available
in PACTOLUS. The key element is a numerical integrator, which
allows the use of this system to solve differential equations.
Even a digitally-oriented person usually finds it relatively
easy to go from a set of differential equations to a block diagram
to a PACTOLUS coding sheet with initial conditions, and perhaps
1/2 hour after being given the problem have the problem on the
computer. The computer prints on one sheet the system configuration, the initial conditions and parameters, and the time and
output controls. Any of these can be selected for modification at
any time by turning on various sense switches.
Three models on which we have worked will be used to illustrate typical applications:
KIDNEY MODEL:
The time-course of radioactive tracers injected into the
circulatory system can be monitored at various body sites. The
radioisotope rhenogram is widely used in evaluating kidney function,
but no adequate mathematical model exists for evaluating the curves
that are generated by monitoring the radioactivity at kidneys, bladder,
and other locations of interest. We are currently working on the
development of such a model. A first and rudimentary version began
with a so-called two-c!avity open compartment system. Such a system
can be described by a set of three simultaneous differential equations.
(See Figure II) The programming time to get this simple model running
on the computer was only a few minutes. Many physiological problems
can be similarly cons;idered in terms of such multi-compartment
analysis and)the ease of programming in PACTOLUS and the ready
evaluation of the model through inspection of the solutions in
graphical form on the CRT are a great convenience.
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TWO-COMPARTMENT KIDNEY MODEL
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NERVE MODEL:
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A great variety of structures and processes make up the nervous
system. One obviously important and all-pervasive phenomenon is
the action potential by which information is transmitted along the
membrane separating the solution within from that without. The
resting nerve is characterized by ionic concentrations within and
without which, operating across the membrane conductance, determine
the potential of the solution within the nerve in relation to that
outside (typically -80 mV). When stimulated., the nerve .. fires" or
depolarizes. Actually the potential reverses with the inside going
to perhaps +40 mV. This depolarization "spike", or action potential,
then propogates along the nerve fiber. Hodgkin and Huxleyl proposed
the model shown in Figure 3 for the situation occuring at the bounding membrane.
Implementing this model is not without challenge. We are not
completely satisfied with the pr.esent version.
(see Figure 4) The
model is straightforward (and uninteresting) except for the nonlinear conductances shown in series with the ionic ·'batteries".
The values of these conductances have been shown by Hodgkin and
Huxley to be complicated functions of the time-history of cell
voltage. Without the graphical output and interactive capabilities
of our present computer system it is doubtful that a working model
on the 1620 would have been achieved at all. Further trial and
error adjustment of tl;1e functions and parameters is needed to moore
accurately match the behavior of a real nerve.
HEART MODEL:
There are two limitations of PACTOLUS that we feel tend to
somewhat restrict its usefulness-. Digital computer users tend to
feel rather keenly the somewhat arbitrary restriction to analoglike 3-input block notation and tend to feel that future software
should accept differential equations directly as input--perhaps in
a FORTRAN-like format--whileperserving the man-machine interactiveness which is the strong point of PACTOLUS.
The second is that a special-purpose system such as PACTOLUS _
is almost inherently somewhat limited in its capability of producing
polished, well-labelled outputs such as are typically needed in the
use of already well-developed models.
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lHodgkin, A. L. and Huxley, A. F.;J. Physiol. 117, p 500 (1952)
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The Lorna Linda University Heart Model falls into this category.
It was a model of proven usefulness as a research tool before conversion to the 1620 was even attempted. Due to the demands of internal
logical structure, and output requirements, this model has been
written and maintained bin the FORTRAN Language.
Computer analysis of electrocardiograms has received much
attention. The clinical cardiologist has typically attempted
diagnosis on the basis of the so-called scalar electrocardiogram.
Leads are attached to the body at various sites and the scalar
electrocardiogram is then simply a plot of the voltage between a
pair of these leads as a function of time. With the concept of
orthogonal leads it becomes possible to think of these voltages as
components of an electric vector which changes in magnitude and
direction as the depolarization wave sweeps over the heart in a
cycle. The figure traced in space by the tip of this vector (or
the projection of this figure on a given plane) is then called the
vectorcardiogram.
We now have a computer model which will generate vector (or
scalar) cardiograms which look like those generated by a human
patient.
In developing our computer model we consider a heart divided
into 20 segments. As the depolarizion wave sweeps over the heart
it passes through a given segment thereby creating an equivalent
electric vector. The time course of these twenty vectors is given
as twenty functions with their directions specified by their direction cosines. The vector sum of these 20 segment vectors taken at
each moment of time then specifies a single equivalent vector which
is regarded as generating the vectorcardiogram. The model was
first programmed for the analog computer2 but the 1620 version has
been much more successful not only because of greater freedom in
specifying the 20 functions but also because of the ability of the
digital computer to process the output in useful ways to provide
a more meaningful display.
We shall restrict our discussion to techniques by which we have
tried to enhance the usefulness of the graphical output of this model.
The typical electro-cardiogram EKG of yesterday and today
consists of a polygraph output of from 6 - 12 essentially periodic
traces of voltages obtained from leads placed at various points on
the body. 12 lines are the basic output of the Heart Model and
correspond to one period of each of 12 scalar leads. These can be
2 Selvester, R. H., Collier, C. R. and Pearson, R. B.;
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Circulation,
Vol. xxxI, January 1965.
o
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used to compare the output of the model with traditional EKG's.
Two loops, the projections on a horizontal and frontal plane of
the 3-dimensional loop, present the same amount of information as
the scalar lines, but relationships are much more easily seen.
The use of color permits us to readily compare abnormal cases
with the normal ones. Shifts in the vector loops are often detected
much more easily than the corresponding changes in the scalar leads.
Our next thought was "if going from l-dimension to 2-dimensions
in our presentation increases the digestibility of information so
much, what about 3-d?" We don't have a 3-d plotter yet. What we
do have is a series of programs which prepare left-and right-eye
views from 3-d coordinates for use with an old-fashioned stereoscope. The 3-d effect so produced can be startingly good.
We are in the process of debugging the programs and the
photographic techniques for the preparation of full-color, 3-d,
animated motion pictures of vector-cardiograms, using data from
either the model or from patients. Right now, the program is ahead
of our photographic technique. When both operate to our satisfaction
we plan to prepare movies to be used in medical education.
o
o
CONCLUSION
We are reminded of a remark by Professor Culler when asked how
the time-sharing system at UC, Santa Barbara compares with other
such systems. He responded that "one comparison that could be made
is that the Santa Barbara system is a member of a class of systems
which exist-as opposed to a much larger class of systems which
people talk about." Remote terminals and graphical display devices
are rapidly becoming available for a variety of computer systems and
the on-line concept is one which is supposedly going to revolutionize the world of computers in the near future. Meanwhile our system
exists and we are on-line. The economics of the system are such
that we can allow sign1f1cant blocks of user time with the operator
interacting with the computer as he observes on the CRT display the
effects of his parameter and programming manipulation. The needed
element of high-speed CRT display was developed and could be duplicated by other users with a modest expenditure of time and money.
o
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PERT / CPM
PRACTICAL APPLICATIONS AND A LOOK TO THE FUTURE
PRACTICAL APPLICATIONS
I am very pleased for the opportunity to participate in this conference. And, particularly on this subject.
I feel, as do the other members on the panel that techniques like
PERT (Program Evaluation and Review Techniques) and C. P. M.
(Critical Path Method) have great potential.
Up until the last couple of years, references to PERT/CPM were associated with large defense programs or large construction projects. NOw, we find that there is an awakening on the part of
management to the potential of these teChniques. These techniques
(particularly C.P.M.) are now being used in all types of construction (large and small), in the field of education, equipment maintenance, accounting and auditing, data processing, and many others.
As a matter of fact, the use of these techniques have spread to so
many new fields that I have heard hints to the effect that the
notorious t'English Train Robbery" was so well planned, scheduled,
and carried out that the culprits must have used C.P.M.
o
Before getting into details on npractical Applications" let us review various techniques now used in Project Management.
We have PERT, CPM, GANTT CHARTS, CHECK CHARTS, HUNCH, HABIT, /
INTUITION. If we were to list them in order of use, they would
most likely fall in the following sequence: ----1.
2.
. 3.
4.
5.
Hunch, Habit, Intuition
Gantt Charts
Check Charts
CPM (Trend toward Activity Oriented systems)
PERT (Defense Industry uses, bu~ technique being
modified)
,
.
You know, businesses a.re now too complex and costly to operate as
they were in the "good old days.tI And yet,' we Btill find many
being run by habit. That is, there is ~ formal planning.
We continuously hear and read of projects being late for one reason
or another. Some part or material not delivered, some equipm~nt or
manpower not available, request for budget approp~iationoverlooked.
Hurry and wait, crash program, work overtime, seems to be the standard practice. And, we realize these delays and conditi.ons might
have been averted had there been any real planning.
o
I recently heard of two computer installations that had to be delayed. One was delayed because the site was not ready, the other
because systems and programming for the conversion were not started
in time.
1
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I
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There will always be delays beyond the control of a manager, but
think of the times that the project could have gone smoothly had
there been planning; that is: both strategic and operational
planning.
~
I am sure you have heard of the Polaris Submarine and Missile pro-
ject,and the project being completed two years ahead of schedule
using the new PERT technique. Also, of Dupont and others using
C o PIo1l and saving time and money on maintenance of equipment and
on construction projects.
But let us discuss some smaller applications of C.P.M. Some that
have benefited both the company and the person who developed the
network.
Following are some examples of such C.P.M. applications:
I.
A young engineer became interested in PERT/CPM and took a
course on the technique. His supervisor heard of his interest and assigned him to develop a network for the
"Puddingstone Dam. Maintenance Project."
Show Chart No. I.
II.
young man working in the construction industry took a
course on C.P.M. technique for a term project. He developed
a network on a "60,000 sq. ft. Warehouse" that his company
planned to build. He showed the network to his superintendent. He was so ~pressed that the company actually used
the network for scheduling and controlling the project.
A
~
Show Chart He. II.
III.
A Police Sergeant applied the C.P.M. technique to a pro-
gram for "overhauling and installation of radios on motorcycles." He developed the network and computed the total
time manually.' It proved the value of formal planning
and scheduling. It also pointed out that the project eould
not possibly be completed by the scheduled (direct date)
using the manpower prov.ioed.
The Sergeant's superior officers were 80 impressed with the
advantages of this technique over others in use that they
are recommending that other officers learn PERT and C.P.M.
techniques.
Show Chart No. III.
IV.
Executive Secretary took an interest and learned the
fundamentals of PERT and C.P.M. She developed a network
on "merging two departments." Her boss, a vice president,
was so iMpressed that he assigned her to develop C.P.M.
networks on "opening a European Plant."
An
Show Chart Io. IV.
She now has a new title "Pert Analyst."
17
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There a.re many applications . I eould'mention: mountain cabins,
apartments;paiRtlng buildings, D.P. applications and installations.,and so" forth. Yoti can see that youdCi:> not have to look
far .. forpractical applications.·· Any:project which meets the
cri taris.: space.,. people, departments, .cri tical schedules, tight
budgets, and interrelated or dependent tasks.
H
Projects that call for good planning, scheduling and control.
o
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11
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Western Region
Winter Meeting of Common
Gaylord L. Baker
PERT / CPM
o
PRACTICAL APPLICATIONS AND A LOOK TO THE FUTURE
TO THE FtJ'l'URE
-A LOOK -----
1.
Unfortunately, none of us have a cr~stal Ball. Nor do we have
the psychic or prognostic ability 0 Jean-nIXon. As a matter
af fact, most of us have trouble predicting what our wives or
children are going to do next.
But as fa.r as business is concerned, if we study the past,
what's happening right now, we can see trends. It doesn't
take a very astute person to evaluate the technological advances
made in science and engineering in the last 30 years: our space
program, telev.1sion, surgery on eyes and heart, nuclear power.
And of course we must recognize the advances made in computer
technology as almost unbelievable.
What about the Future? We can expect some amazing progress with
lazers, witn-itomic power, electronic miniturization, and in the
use of computers.
2.
What about management? Have we made much advancement? . Certainly
not comparable to science and engineering. Oh, we are using computers and some other improved office equipment, but there are
so many managers operating by habit; by trial and error.
()
They say there is a trend towards the use of mathematics and
the computer by management.
3.
Future for Management. No question, there will be wider and
expandealUse
PERT and CPM and, no doubt, with technical improvement. Remember, the primary function of management is
PLANNING and PERT andCPM Forces Planning. That is, both strategic and operational.
or
STRATEGIC PLANNING:
A clear definition of objectives
Scope of project defined
Directed dates and authority
Imposed conditions
Laws and legal provisions
Approvals
Financial and Budget Controls
Resource limits and Company Policy
OPERATIONAL PLANNING
What we must do
Logical sequence of performance
Interrelationships and Dependencies (one task to another)
The things we use: manpower, material, equipment, etc.
11
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Another thing, there will be more of ,a, common understanding
between· ·those ·in the ,financial end· (Controller.s ,-Budget "Of-··,
ficers, Boards, those controlling the finances) and those
doing the project--whether the project would be construction,
sales, training~Data Processing, scientific, engineering, or
any of the many new fields.
Each will be able to visually see the CONDITION OF THE PROJECT in terms of:
What has to be done
When and how long
What has been done
What is being done
What has yet to be done
Also, ~ to date
In closing, a few years ago I was out at UCLA doing a Resource
Simulation Study on the 1620. I noticed a young fellow in the
corner and assumed that he was the son of one in our GR. He
looked about fifteen. He sat down beside me. I asked, "Waiting
for dad?" "No, waiting to test PROG." This took me by surprise
and I asked, "Prog. 1401?" "No, but 1410." I asked, uhowold?"
He said, ntwelve years. u
0"
You know, we live in a competitive society and to advance and to
keep ahead of these young students we have to not only have experience, but to keep abreast of new ideas and techniques. Like
PERT and CPM.
,~
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THE DEPARTl\1ENT OF WATER AND POWER IS
o
CRITICAL PATH METHOD SCHEDULING PROGRAM FOR
THE IBM 1620 DATA PROCESSING SYSTEN
CADS MK III
(Construction and Design Scheduling Mark III)
Raymond C. Burt, Robert C. Burt and Marciano Lopez
Department of Water and Power
Los Angeles, California
ACKNOWLEDGMENT
The authors wish to aclmowledge the assistance given
by Mr. L. O. Schmidt, formerly with the Department of Water
and Power, Mr. J. T. Au, and Mr. B. H. Kawaguchi, in the
programming and analysis of the Department's CADS scheduling
system.
4:)
INTRODUCTION
This paper is a discussion of the Critical Path Method
of scheduling hereafter referred to as CADS now in use by the
Department of Water and Power, City of Los Angeles, for the
scheduling of design, construction, material procurement,
equipment maintenance, and preliminary operations of steam plants,
large bulk power substations, Water System projects, and a nuclear
plant.
CADS may be described as an automated method of
scheduling complex projects on digital computers.
l\1ore than
that, it is a logical approach to project scheduling, organization
and planning in detail.
o
/ () /
The various methods of computer scheduling (see
appendix, page AI) presently available have been developed out
o
of a need for a logical method to analyze the relationship
between thousands of activities which go into large manufacturing
and construction projects.
WHY IS CADS NEEDED?
CADS plays an important role in the Department's design
and construction for several reasons, as follows:
1.
In order to supply sufficient detail for the
establishment of target dates for such items as material
procurement, engineering, preparation of drawings, orderly
installation of equipment and so forth, it is necessary to
schedule and coordinate several thousand jobs or activities.
2.
Since there are over 100 design, construction, and
o
material procurement groups in a major project team, a standard
scheduling and coordination technique administered by a central
authority is required.
3.
Because of the vastness of the projects and the
continual need for updating schedules, high sgeed scheduling
techniques are required tq prevent delays in obtaining vital
information.
4.
A method is desired which enables the scheduler or
engineer to pinpoint, in advance and with sufficient scope, the
areas of difficulty and to take corrective action months in
advance instead of after the difficulty has been encountered.
2
o
/
5.
c:;
A
techniqu~
is
de~ired
which enables a scheduler
,or engineer to describe a project in regard to its many
dependent activities or jobs, with the required start and finish
dates of the project, and which then automatically adjusts the
resulting schedule by making time corrections on critical jobs
to produce a final schedule meeting the original requirements
specified.
6.
Finally, a technique or method is required which
enables the. scheduler or engineer to see the effect of a
slippage of anyone job or activity in a project with regard to
the overall project target date.
With regard to the last point above, it has been
assumed in the past that there are certain key items or
activities in a large project, such as the placement of a main
4()
power transformer or the arrival of a turbine spindle, which
could be used to measure the progress of a project and indicate
project completion date slippage .
. Another assumption in the past was that only the
large or key items in a project need be scheduled and that
everything else would automatically fall in place.
these assumptions are false.
Both of
The two weeks late arrival of
reinforcing steel for a transformer foundation can delay a project
just as long and can be just as serious a problem as the two
weeks late arrival of the transformer to be installed on the
foundation.
3
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HOW IS CADS USED IN THE DEPARTMENT?
The Department's version of CPM scheduling is called
CADS.
CADS, which stands for Construction and Design
o
Scheduling, has been used in the scheduling and the coordination
of all design, material procurement, construction and testing
activities needed to build three large bulk power substations,
Receiving Stations S, P, and T, in the Los Angeles area.
Two
of these stations, RS-S and RS-T, are conventional, aboveground
138 KV to 34.5 KV Substations with ultimate capacities of 400 MVA
each.
RS-P is a 230 KV to 34.5 KV underground station, (in the
downtown area of Los Angeles) with an initially installed transformer
capacity of 320 MVA.
All phases of the projects such as site
selection, engineering, drafting, management approval, material
procurement, construction, testing, and energizing of the stations
are scheduled in detail to answer inquiries and problems of the
following types:
An electrical design engineer needs to know when a
set of detailed structural drawings will be ready in order to
know when he can start design of an electrical equipment
installation.
A land division officer wonders whether a two weeks
delay in obtaining a parcel of land will be acceptable.
A member of engineering management is considering
whether or not enough time is left to request a change in system
design.
4
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A chief draftsman flooded with a deluge of drafting
jobs must assign the order in which the jobs are to be done.
A specification writer is faced with deciding what
delivery date will be satisfactory approximately two years from
now.
Noting the tremendous expense tOQay for construction
equipment rental and wages, a project engineer has the problem
of deciding the exact day on which to begin construction in
order to meet the project completion time and at the same time
minimize cost.
These problems, and many more, can be answered
by CADS.
A typical receiving station schedule for the type of
stations indicated above consists of approximately 2500 jobs or
o
activities.
Portions of a typical receiving station schedule
are shown in the appendix of this paper.
These comouter listings
will be explained later.
In conjunction with the scheduling of large receiving
stations, it was necessary to schedule the transmission and
underground engineering and construction of the lines and cables
entering the stations.
The other main application of CADS in the Department
has been the scheduling of construction and preliminary operation
activities of Units 1, 2 and 3 at the Departmentts new Haynes
Steam Plant.
These units will produce 230 MW each.
The
construction of these units not only involves the coordination
and scheduling of the Departmentts own construction groups, but
o
5
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I
also that of the various contractors responsible for the boilers,
turbines, tank erections, and so forth.
To date only the
construction and preliminary operation activities have been
o
scheduled by CADS for the above units.
One of the extra dividends accrued in going to
computer scheduling, and in particular to CADS, was the increased
understanding and knowledge of the detailed activities, with
their interrelationships, required in building a plant.
The
benefits from this one point alone have made the program highly
desirable and successful.
The last major point pertains to the manner in which
the CPM or CADS automated scheduling program was implemented
within the Department.
The computer program was developed at the suggestion
of several Department senior engineers concerned with the
coordinating and scheduling of large projects.
o
The original
programming group consisted of engineers, having previous plant
design experience and familiar with computers.
In the latter part of 1960, much time was spent in
researching available publications, principally those concerning
the Navy's PERT Program.
After analyzing the Department's needs
and the programs then available, it was .decided to write an
entirely new program having the input and output features that
the Department required.
The engineers, who wrote the computer orogram,
6
o
I
I
1.1
- - - - - - - - - - - - - - - - - - - - - - - - -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
F":~T
prepared, with the help of the Station Design Engineers, the
first receiving station schedule data.
The first steam plant
schedule data were prepared by the preliminary operation,
construction and scheduling engineers because of their greater
familiarity with steam plant construction activities.
The
task of originating, organizing, operating and implementing
computer schedules for all projects is now done by the
Department's Design and Construction Division staff engineering
schedulers, who have historically been charged with the
responsibility for coordinating and scheduling.
The original
computer programming group now serves in a consulting capacity.
WHAT CAN CADS DO THAT CONVENTIONAL SCHEDULING TECHNIQUES CANNOT?
As was pOinted out above, CADS or CPM can analyze
thousands of detailed activities, as to their correct time
relations.
Using conventional bar chart techniques, it is
physically impossible and impractical to correctly relate
several thousand activities according to calendar dates, to type
or print and proof complete schedules for distribution at
regular intervals within a satisfactory period of time, much
less examine the critical and subcritical paths for areas of
possible trouble.
With former conventional techniques, only the major
equipment and construction activities could be scheduled,
therefore not providing sufficient detail to indicate problem
areas.
In addition, independent schedules for design,
7
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construction, and material procurement were made by various
subsection schedulers in order to aid their engineering groups.
This resulted in conflicting schedules, each in different
degrees of updating.
o
CADS can update, print, proof, and ready
a complete detailed schedule for distribution in a matter of
minutes after the need for a change has been recognized.
Lastly, CADS, through its automatic rescheduling features,
can adjust a schedule through its ability to find the critical
areas or paths, modify certain time estimates, and recast a
schedule iteratively until specific project requirements are
met.
HOW DOES CADS COMMUNICATE OR PORTRAY ITS INFORMATION TO THE
SCHEDULER AND/OR ENGINEER?
The advent of high speed, large storage digital
computers, with the ability to output information at the rate
o
of 600 lines per minute and with up to 132 characters on a line,
has provided a temptation for programmers to output too much
information for humans to digest.
To be certain, management,
design engineers, clerks, and construction people need detailed
scheduling information because they work with details.
It is
the day-to-day decisions, such as which jobs are to be performed
next, how many people are needed on the design staff during the
next year, and can part of a group be rotated to new assignments,
that plague management.
With the ability to provide detailed
8
o
information and while still recognizing the frailty of human
OJ
beings in digesting large amounts of data, the specifications
for the CADS output format were devised.
A person reading a schedule is usually concerned with
the details which pertain to his group only.
For instance,
the supervisor of a group of electrical draftsmen is concerned
with jobs which require electrical drafting and not with the
number of plumbers needed on a
~articular
date.
Hence, the
schedule output is divided into summaries according to actual
Department design and construction groups.
A partial list of
groups in the Department given individual summary printouts
from the CADS schedule may be found in the appendix, nage A4.
A supervisor is concerned with decisions such as when .jobs
o
assigned to his group should be started and finished" how many
men should be employed on each, which jobs can be started
early, is overtime required, and are the prerequisites to starting
a job available (key drawings, engineering calculations, sketches,
and so on).
A supervisor therefore needs an individual summary
for his group which contains the above information.
The two typical approaches can be made when examining a
summa~J
schedule.
The first type of inquiry might be as follows:
Has a particular job been completed yet?
And the second tyPe:
Which jobs should be started, finished, or active
today?
9
o
:1
The first type of inquiry requires an alphabetical
listing of activities by summary, while the second requires a
chronological listing of activities by
summa~T.
o
The CADS
output format includes both types of listings for each summary.
In addition, it is convenient to have the outout format for
each summary in both tabular and graphical forms.
The
alphabetical listing of activities is printed in tabular form
and the chronological listing 1s orinted in graphical form
(bar chart) for each individual group summary.
In order to discuss the output formats, samnles of
which are included in the
appendix~
it is first necessary to
define the terms activity, related (prerequisite) activity,
critical path, slack time, normal and critical time, and normal
and critical manpower.
An activity can be either a task performed or an elapse
of time.
o
Examples of tasks performed are engineering studies,
drafting, installations, and testing.
of time is the curing of concrete.
An example of an elapse
Before most activities can
be started, certain prerequisite activities must be completed
first.
These prerequisite activities are known as related
activities.
As an example', the curing of a concrete foundation
is the related activity to the activity of placing a transformer
on that foundation.
To further illustrate the term related
activity, the placing of the transformer on the foundation is
a related activity to the activity of connecting the transformer
10
o
/10
ri:
to the station bus work. "
o
The remaining terms can best be described with the
aid of a diagram.
On page A5 of the appendix a simplified
schedule has been diagrammed (both names and time estimates
are arbrltrary and are intended only to illustrate
terminology and the manner in which CADS schedules).
The
diagram shows the relationship of activities to each other with
regard to the sequence in which the activities must be performed.
A real time scale is included at the right of the page.
On the
side of the page labeled pass 1, the activities TRANSFORMER
FINAL ASSElvfBLY and I'RANSFORMER WIRING CONNECTION are both shown
as requiring the related activl ty TRANSFORf,mR PLACEMENT;
however, since the activi ty TRANSFORMER FINAL ASSEl\1BLY req1.)ires
more time to perform than the activity TRANSFORJVTER WIRING
CI
CONNECTION, the related activity TRANSFORMER PLACEMENT m"ust be
" completed earlier than what is required for the activity
TRANSFORMER \vIRING CONNECTION..
The time re')resented by the
dash line on the diagram is known as slack time.
The tnterval
between having all the related activitIes complete and the
latest posslblestarting date for an activity is defined as the
slack time of the activity.
~lIRING
For the act:lv;.t:l TRANSPORfiIER
CONNECTION,the slack time referring to the tIme scale
is one day.
A oath is comprised of two or more activities
worked in series.
The activi ties TRANSFO?tflIER TEST, TRANS~ORrI[ER
FINAL ASSEf1BLY , TRANSFORMER PLACEl\1ENT and TRANSFORMER DELIVERY
11
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4A,J4i"·riAn';;;:,AMU:;;:m====.....
form a path.
Another path is defined by the activities
TRANSFORMER TEST, TRANSFORMER WIRING CONNECTION,. TRANSFORMER
PLACEMENT and TRANSFORMER DELIVERY.
It is noticed that some
of the same activities occurred in the second oath as were in
the
o
In the first uath there exists no slack time.
f~rst ~ath.
The activity TRANSFORMER WIRING CONNECTION has slack time in
the second path.
The critical path is the longest nath in
time and contains no slack time.
For the ryass
1
diagram,
the critical path consists of TRANSFORMER TEST, TRANSFORMER
FINAL ASSEMBLY, TRANSFORMER PLACEMENT, TRANSFORMER FOUNDATION
CONCRETE CURE, TRANSFORMER FOUNDATION FORM STRIP, TRANSFORr·1ER
FOUNDATION CONCRETE POUR, and TRANSFORMER FOUNDATION FORr1
INSTALLATION.
Although the critical path is the longest ryath
in the project, it dictates the shortest time in which the
project may be completed.
Only when
activiti~s
in the critical
path have their time shortened or are worked in parallel rather
()~
than in series can the nroject time be reduced.
Since in most cases the sequence in which activities
are performed cannot be changed (a concrete foundation must cure
before placing
eq1.~ipment
unon it) the common way to shorten a
project is to shorten the allowable time to Derform each activity
in the critical path.
This can be accomolished by placing more
manpower on the activity or by working more than one shift ner
day.
Activities are therefore given two time estimates, normal
and critical.
The normal estimate is given as the time and
number of men normally allowed to
accom~lish
a given activity.
I?
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_nn'!",i·-
The critical estimate is based unon the time and number of men
required to perform an activity when a oro.1ect must be
completed in minimum time.
For most activities the critical
time estimate will be smaller than the normal estimate, and
the critical number of men estimate larger than the normal
estimate.
For some activities the normal and critical
estimates will be the same (i.e. concrete cure).
If the left side of page A5 of the
a~Dendix
is again
referred to, a number nair can be observed directly below the
name of each activity.
The number on the left side of the
slash (/) represents the normal days estimate, and the number
on the right the critical days estimate.
If the activities
represented by the diagram were scheduled by CADS using normal
(
estimates, the pass 1 schedule output would appear as shown
'\.. \
",'
on the left side of the page.
Should the time required to comnlete
this work be greater than acceptable, CADS wpuld attemnt to
reschedule as shown f'or pas~ ~~e ;Dass " schedvle was obtained
by replacing the normal es~ate'with the cri.tical estlmate for
each activity appearing in the critical path of pass 1,
(transformer test, final assembly, placement, fovndation concrete
cure, form stri'!J and form installation), and rescheduling.
Again
if the pass? schedule requires too many days to comnlete, the
activities aonearing in the critical oath of pass
?,
(rack area
backfill, grounding mat installation., and rack area excavation)
would have their normal estimates renlaced with critical
13
o
113
estimates by the CADS program.
With these changes a new
schedule is output as shown under pass 3, page A6.
This
recycling process continues until the schedule is shortened
. _"
0
to an acceptable time or until all the activities appearing
in the critical path obtained in the new pass were
previously reduced to their critical estimates in an earlier
pass or until the number of passes equals the limit for the
maximum allowable number of passes (which can be set by the
individual scheduling with the CADS program).
In order to describe some of the output features of
CADS, the following definitions and explanations are made.
Activity Index Number.
This is a computer generated
activity identification number, which 1s unique for each
particular activity.
This activity number is assigned when all
activities are sorted, alphamerically by summary, during
proceSSing.
The activity index number will normally change for
subsequent schedule recasting.
o
It is usually used in locating
a specific· activity when the schedule outputs are being
examined.
File Number.
This is an arbitrarily chosen activity
identification number assigned by the scheduler, and is used for
identifying an activity external to the computer.
This number
does not change for subsequent schedule recasting and is
therefore useful for activity data modifications.
14
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The output features of CADS are:
o
Summary - Activity Table.
This table is printed as the
first item in the schedule and lists all the summary numbers and
summary names used, with the number of activities assigned to each
summary.
The heading contains the date at which the schedule is
made, the ,project name, and the page number.
Next, listed in
numerically ascending order are the summary numbers with their
respective sununary names and assigned activities (see appendix,
page All).
Critical - Path Table.
This table provides a list
of all activities in the critical path for the specified pass
number.
The heading shows the date at which the schedule is
made, the name of the project, the pass and the page number.
Next, a total indicates the number of activities comprising
the critical path, as well as the number of working days for
the -critical path.
If the computer generated schedule does not
terminate within the required completion time period, a message
is printed out showing the pass number and the number of working
days by which the schedule "OVershoots" the project completion
date.
In addition to the activity name, the index number, file
number and time estimate are also listed.
The critical path
activities are arranged so that activitie"s occurring towards the
beginning of the project are listed first.
(See appendix, pages
AI2-Al3) •
If rescheduling occurs, then subsequent critical-path
tables will be printed for each pass.
o
15
/I~L)
"•.•.•.•••___....... _. __ .•.__ ._.____________.. ____.. _ _ _ _ _ ._._. _______...._.. __..__..._._...___........_..... __.__......._._ .. ___.......________..._.._.•_ •••. _._. _ _
Alphabe-tic'Schedule.
~_~~~._"
•• " •. --,,=..
~~~~,_
..
~~.---'-_._
.. c_.. _._"'.. _
.. __ ..
The alphabetIc schedule
alphameric~al1y li~sts' all:activlt1es" with their related activities,
0
for'each·sUmrnary. 'The heading "includes the 'date at' which the
schedule i's'made, the name or' the project,- the summary name" the
pass nUmber, arid the page number.
Information 'included for each
ac-tivlty i11. thi,s schedule is the activity
i~dex
number, the
activi·ty name, the file ninnber, the normal time and manpower
estimate·s, the critical time and inanpow'er estimates" the computed,.
if not initially estimated, total man-hour requirements, the slack
time, the start date, and the finish date.
Information pertaining
to related activities is indented. -Time and manpower estimates
actUally used in the schedule are marked with an asterisk.
Any
activity previously completed or finished will be indicated by
the word IICompleted" in the start and finish columns.
(See
appendix,-pages A14-A16).
({)
Chronological (Bar Chart) Schedule.
The graphical
type of schedule lists activities chronologically by starting
da..tefor 'each summary.
The heading includes the date at which
the schedule is made, the name of the project, the summa~
name" and :the . page number.
The maximum period for Wh~
scheduling information can be provided on one 'page is four months.
In addition to the activity name, the activity manpower requirement
and slack time: are also shown.
Near the top of the page, the
months "and years under consideration are indicated.
lines show actual calendar work days.
The next two
'A)'eekends and holidays are
16
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I
I
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omitted.
c
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.'.~': ;!
The first line, is the first digit" or tet;l,s', position of
the calendar day" and the second line is the second.. digit or
units position of the calendar day.
The "XiS" span. :the time
interval during which the activity is to be perforroed.
A
ttc n
occurring on the last calendar day of a pageindica1;es that the
nX" sequence is continued into a subsequent time.period.
Therefore"
the same activity will occur on another page of the schedule.
An activity which has been completed will not appear in.the
chronological schedule.
At the end of the list of a summary containing all
activities for a specific time interval" usually four months"
a "total manpower requirements" chart is printed.
The values
indicate the total number of men required by the group represented,
in the summary" for any particular date during the ,interval.
The first, second, and third lines indicate the hundreds, tells,
and units positions, respectively, of the manpower,value.
(See appendix, pages A17-A18).
HOW DOES THE SCHEDULER AND/OR ENGINEER DESCRIBE THE PROJECT TO .
THE CADS SYSTEM?
The schematic approach (arrow diagramming) for
collecting schedule data for the CADS program was avoided because
of the difficulties in showing the sequence relationships
between activities, and because of the limited number of
activities which can be shown on a'single sheet of paper.
The collection of data for a project schedule is
17
~O
Ii 7
begun by examining the finished product and asking the
que'stions:
Which components make up the finished product,
and what is the last activity performed on each of these
components before they are declared complete?
This initial list of activities is called the endof-project activity list.
It is not necessary to include in
this list any activity which is a prerequisite to any other
activity.
Each end-of-project activity is then examined to
determine its innnediate prerequisite activities.
Then the
immediate prerequisite activities to the activities preceding
the end-of-project activities are sought, etc.
The activities
which must immediately precede an activity are called that
activity's related activities.
((It)
The order of performance of activities (starting
~V
',,-
I
with a particular end-of-project activity) for most
installations 1s as shown below.
Indented activities are
related (immediate prerequisites) to the non-indented
activity directly above.
COMPONENT TEST
OOMPONENT INSTALLATION
COMPONENT INSTALLATION
COMPONENT MATERIAL DELIVERY
COMPONENT INSTALLATION DRAvlING REVIEW BY
CONSTRUCTION
COMPONENT AREA PREPARATION
COMPONENT MATERIAL DELIVERY
COMPONENT BID AWARD TO DELIVERY TIME
18
t
01
Ilf
o
COMPONENT BID AWARD TO DELIVERY TIME
COMPONENT AWARD OF CONTRACT, APPROVAL
COMPONENT AWARD OF CONTRACT, APPROVAL
COMPONENT BID EVALUATIONS
COMPONENT BID EVALUATIONS
COMPONENT BID ADVERTISEMENT TIME
COMPONENT BID ADVERTISEMENT TIME
COMPONENT SPECIFICATION APPROVAL
COMPONENT SPECIFICATION APPROVAL
COMPONENT SPECIFICATION PREPARATION
COMPONENT SPECIFICATION PREPARATION
(The prerequisite of preparing any specification
is generally the engineering of some key
drawing (i.e., one line wiring design
eqUipment, or structural steel~ and/or the
preparation of an authorization.)
COMPONENT INSTALLATION DRAWING REVIEW BY
CONSTRUCTION
COMPONENT INSTALLATION DRAWING APPROVAL
o
COMPONENT INSTALLATION DRAWING APPROVAL
COMPONENT INSTALLATION DRAWING REVIEW BY DESIGN
ENGINEERING
COMPONENT INSTALLATION DRAWING REVIEW BY DESIGN
ENGINEERING
COMPONENT INSTALLATION DRAWING DRAFTING CHECK
COMPONENT INSTALLATION DRAWING DRAFTING CHECK
COMPONENT INSTALLATION DRAFTING
COMPONENT INSTALLATION DRAFTING
. COMPONENT INSTALLATION DESIGN ENGINEERING
COMPONENT INSTALLATION DESIGN ENGINEERING
(The prerequisite of engineering varies. It can
be one or all of the following: authorization
prepared, other engineering complete, other
drawings ~repared, and manufacturer's drawing
prepared. )
COMPONENT AREA PREPARATION
(e.g. installation of equipment board, erection
of a building, concrete cure, etc.)
o
19
1/9
The collection of data as shown in the above section
for a proje9t schedule 1s accomplished by describing in order
starting with the end-of-project q.ctivities, step by step, the
activities necessary for the construction of a project.
o
Once
the construction phase of the data·collection has been completed
far enough to require the delivery of material or drawings,
the steps for material procurement and obtaining drawings are
almost always the same for each item in most organizations.
After the data breakdown has been decided, time
estimates are given to each activity.
The time estimate is
based on how long it will take to complete a given activity
if all of its related (or prerequisite) activities are completed
first.
The time estimate can be given in working days with the
manpower (number of men) estimate optional or as a total manhour estimate with the manpower estimate required.
If an
activity has previously been completed, that information can
o
also be entered.
The above data collection method is based on the
following hypotheses:
A group or person charged with the
responsibility for performing a given activity (particularly
if the activity is similar to one performed previously) can
reasonably answer at least two questions about the activity.
First, what is needed (related or prerequisite activity list)
before the activity can be started?
Second, if everything
that is needed to start the activity is available, how long
20
o
/2CJ
o
will it take to perform the activity?
Once each activity making up the project has been defined
(given a time estimate and a relateq activity list) and
keypunched on IBM cards, the scheduler only needs to specify the
starting date (normally today) and the target date for the
project.
This information, together with the project title,
sununary names (all on IBM cards) and the CADS program are all
that is necessary for running the program on the IBM-1620
computer and obtaining a schedule.
Some of the characteristics of the CADS program are as
follows:
If an activity is not listed as a related activity to
any other activity, it will become an end-of-project activity
0)
and have a completion date.equal to that of the coml?letlon date
of the entire project.
If an activity is listed as a related activity of
several other activities, its completion date will precede the
starting date of the earliest starting activity requiring it as
a related activity.
Every related activity must appear as a defined
activity.
CADS places the begin date of all activities as close
to the end-of-project date as possible within the limits set by
the activity time estimates and thelr.prerequisites.
In the process of collecting data for a project schedule,
one might wonder how fine of a data breakdown is necessary.
o
21
/.2/
The
answer to this question is that the detailed breakdown of data
should be made fine enough to allow time estimates to be made
without having to estimate dead time for each activity.
Dead
o
time as referred to here means the time wasted on an activity,
stopped because of lack of information and/or material
necessary to complete the activity.
If the input data is
collected in sufficient detail, each activity's related
(prerequisite) activities are scheduled to be completed before
the activity requiring them is scheduled to be started.
Thus,
assunling reasonably accurate data and an adherence to schedule
dates, the situation where an activity could have been completed
earlier had it only been known that it was needed by a certain
date can be prevented.
Again, as a defense against the argument that too
much data just confuses the schedule and makes it impossible
to follow, it must be pointed out that the individual groups
o
performing the activities are given individual summary schedules
containing only the activities aSSigned to their particular
group and not the entire schedule output.
Furthermore, once
the data collected for a project schedule has been,thoroughly
checked out and the target date established, it is not necessary
for management to try to follow the entire schedule output.
Management, in order to keep watch over a project,
needs to know whether or not the schedule is being adhered to.
Schedulers and coordinators also need this information in order
22
o
/22..
'r;eJ!!.m;ffitF'M. "anITmnr;-;;
an
to know if a schedule needs to be updated.
o
This can be
accomplished by having the schedulers collect periodically
(i.e., monthly) from the individual groups the progress of all
activities completed, active or started during the month.
The
number of activities completed, active or started during the
month is very small.
The number of these activities which are
not progressing according to the schedule is even smaller.
Therefore, with an effective reporting system, management needs
only to be concerned with a few activities during any month.
To further simplify the problem when one or more
activities deviate appreciably from the schedule, the updated
~
data can be automatically rescheduled by the CADS program in a
matter of minutes.
The· CADS program adjusts the schedule
through,its ability to find the critical path, modify the
()
critical path activity time estimates, and recast a schedule
iteratively until the project is brought back to the original
target date.
The steps taken by the program to adjust the
schedule are printed out in concise form.
CADS updates prints,
proofs and readies the complete, detailed schedule for
distribution automatically.
WHAT ARE THE SUPPORTING SYSTEMS AND ERROR CHECKING FEATUP£S
OF THE
SYSTEIvl?
Since the Department has an IBM 1620 computer, several
programs have been written f'or the machine which provide a
convenient method f'or CADS data preparation and checking.
23
o
/2-3
One
program of this type can generate prerequisite activities in
a sequence for input to the CADS program when given certain
o
specific activities whose sequence or trace is a }mown or
fixed procedure in the Department.
Three commonly used
sequences are drawing, specification, and bill of material
preparation.
Given an equipment delivery because of formal bid
or bill of material requisition, or a drawing delivery, this
program will generate activities in the proper sequence
to and including engineering.
dOl\~
Other programs can delete,
change, or list specific cards in a CADS data file.
In order
to provide a rapid method for producing data for similar
proJects programs have been written which will reproduce and
renumber CADS input data files.
A 1620 program is also available which will generate
block diagrams of the project showing the activity relationships.
~
This program uses the CADS input data to generate these diagrams.
Some error checking features have been developed in
the CADS computer program in order to facilitate data debugging.
One feature provides a check on activities which have either
not been defined or have been improperly defined.
When this
occurs, a message "Found no J num for---------------tr, is
printed out.
Another common error is feedback.
Feedback is
an improperly defined relationship between two or more activities.
When this occurs two or more activities are prerequisites of
24
o
/2,/
I,
ET,ran -rr1tJfftflU!!:tWIm
each other, either directly or indirectly.
c:;
Feedback is noted
when a list of affected activities is printed out with no
subsequent schedule information.
A sub-program has been
written which will handle the feedback-affected activities and
produce a list of activities showing the paths which are
directly involved in the feedback.
As can be seen, these
features provide means by which data handling and correction
can be reduced to a minimum.
EDUCATION REQUIREMENTS FOR Ir.JIPLEMENTING CADS
The problem in securing and training personnel to
implement an automated scheduling program deserves conunent.
As was stated above, the original programming and schedule
preparation was carried out by special studies engineers
()\
familiar with
computers~
but the staff scheduling engineers
who now run the system had little or no knowledge of computers.
The engineering scheduling personnel have been sent to short
computer orientation and training sessions to acquire basic
operating knowledge.
In addition, good success has been
obtained from brief training periods of clerical help in a
step-by-step process over a period of months.
In
the operation
of any computing system, the main key to success is finding
interested, careful personnel.
Since the special studies group provides consulting
service when difficult or unusual circumstances are encountered,
little knowledge is required by the schedulers concerning the
operating characteristics of the IBM 1620 which is used for
o
25
the major portion of the Department's automated scheduling program.
EQUIPMENT
A typical 1500 activity CADS schedule requires about
two hours of IBM 1620 time.
o
In addition to the IBM 1620,
another computer, the IBM 1401, is used for report writing.
These two machines are available within the Department.
Also,
the Department has a well-equipped card tabulating section,
which provides services for reproducing, sorting, collating, and
other preliminary card handling procedures for CADS.
FUTURE
Planned modifications and additions for the CADS
system are as follows:
1.
The inclusion of job or activity cost data with
the aim of developing a program which would schedule a project
for a minimum overall cost.
2.
The establishment of an automated division-wide
o
manpower allocation system for scheduling of major projects
simultaneously.
3.
The inclusion of features for special job progress
reports, to be provided for management use.
CONCLUSIONS
The Department has applied an automated scheduling
system to the task of scheduling and coordinating the deSign
and construction of several large substations and to the
ta~k
/
I
26
o
/2G
o
of scheduling and coordinating the construction and preliminary
operations of several large steam generating units currently
under construction.
This scheduling system has been operating
successfully since the early part of 1961 and is now an
integral part of the Design and Construction Division's operations.
o
27
/27
Critical Path and PERT
BIBLIOGRAPHY
1961-1962
o
1.
Berman, H~ Try critical path method to cut turnaround
time 20 percent. -HYdrocarbon Processing and Petroleum Refiner, 41:135-8, January 1962.
2.
Builders bone up on critical path at MIT. *Eng1neer1ng
- News-Record, 168:19-20, June 28, 1962.
3.
CPM enthusiasts claim bonus benef1ts. *Engineer1ng-NewsRecord, 169:42-44, August 9, 1962.
4.
Cabell, C. P. Integrated programming; simplified version
of PERT. Plant Engineering 16:106-12, September 1962.
5.
Christensen, B. M. Network models for project scheduling.
Machine Design, 34:114-18, May 10, 1962 - 34:173-7,
May 24, 1962; 34:132-8, June 7, 1962; 3 4:155-604
June 21, 1962; 34:105-11, July 5, 1962; 34:136- 0,
July 19, 1962.
May 10: Planning phase--initial steps in setting
up network models with special emphasis on crit1calpath method. May 24: Preliminary schedule phase.
June 7: Advanced scheduling phase; determining
critical points; choosing schedule. June 21: First
steps in working our samples project. July 5: Computer routines for planning and scheduling problems of
any practical size. July 19: Establishing specific
plan of implementation.
6.
Cosinuke, W. Critical-path technique for planning and
scheduling. *Chemica1 Engineering, 69:113-18, June 25,
1962.
7.
Critical path method; new tool for job management.
ing News-Record, 166:25-7, January 26, 1961.
8.
Driessnack, H. H. PERT on c-14l.
5:32-5, August 1962.
9.
Eisner, H. Generalized network approach to the planning and
scheduling of a research project; PERT technique.
Operations Research, 10:115-25, January 1962.
0,
*Engineer-
Aerospace Management,
10. Glaser, L. B. Critical path planning and scheduling;
application to engineering and construction. Chemical
Engineering Progress, 57:60-5, November 1961.
*Magazine titles marked with an asterisk may be found in the
Department library
Al
o
iWE
iT
-2-
11. Hawthorne, R.
o
Pert and pep; useful tools or t1mewasters?
Space/Aeronautics, 36:56-8, August 1961.
12. Healy,
T~ L.
Activity subdivision and PERT probability
statements. Operations Research, 9:341-50, MayJune, 1961.
13. Huish, H. A. Keeping critical path up-to-date is no problem
with a computer. *Plant Management and Engineering,
24:15-19, April 1962.
14. Industry borrows control tool that's closing missle gap.
*Iron Age, 190:62-4, July 5, 1962...
.
15. Kast, W. G.
Critical path method ideal tool for plant
construction. Hydrocarbon Processing and Petroleum
Refiner, 41:123-30, February 1962.
16. Kelley, J. E.
Critical-path planning and scheduling:
Mathematical basis. Operations Research, 9:29-320,
May-June 1961.
17. Kruse, M. E.
Streamline your maintenance planning with
critical path scheduling. *Plant management and
Engineering, 23:49-51, December 1961.
o
18. Loeber, N. C. PERT for small projects.
34:134-9, October 25, 1962.
Machine DeSign,
19. Lundenheimer, E. L.
Use critical path method to plan
complex projects. *Power Engineering 66:37-40,
September 1962.
20. Lynch, C. J.
Plan projects scientifically with criticalpath scheduling. *Product Engineering, 34:92-6,
September 18, 1961.
21. Martin, N. M.
Critical-path method expedites IBM projects.
*Engineering NeWS-Record, 169:34-6, July 5, 1962.
22. Mauehly, J. W. Critical-path scheduling. * Chemical
Engineering, 69:139-54, April 16, 1962.
23. Meyers, R. E.
Critical path scheduling as applied to
refinery turn-aroundsj abstract. Chemical Engineering Progress, 58:104, July 1962
*See Footnote on page AI.
A2
o
r
,-ir·
','1
.,1
!
-324.
Pearlman, J. Engineering program planning and control
through use of PERT. Institute of Radio Engineers.
Transactions on Engineering Management, EM-7:125-34,
December 1960.
25.
Reeves,E. Critical-path speeds refinery revamp.
Canadian Chemical Processing, 44:74-6+, October 1960.
26.
Schureman, L. R. 'Critical path' as job scheduling and
control aid. Roads and Streets, 105:66-8, 70,
June 1962.
/
27.
Stagg, G. W. et ale PERT schedules manpower.
World, 158:36-7, July 30, 1962.
28.
Stegber, C. B. Scheduli~ projects by critical path.
*Electronics, 3S;S6-7,March 2, 1962.
29.
Steinfield, R. C. Critical path saves time and money.
*Chemica1 Engineering, 67:148, 150-2, November 28,
1960.
30.
Whalen, J. M. Adding performance control to cost control.
National Association of Accountants. Bulletin, 43:6774, August 1962.
31.
Young, L. H. Now_ industry schedules by computer; PERT
(Project evaluation and review technique) on critical
path method (CPM). Control Engineering, 9:16-18,
January 1962.
32.
Proceedings of the Seventh Annual Engineering and Operations
Workshop, American Public Power ASSOCiation, Phoenix
Arizona, January 1963.
33.
Proceedings of the AIPE-ASME Plant Engineering Conference,
Los Angeles, California April 1964
o
*Electrical
*See Footnote on Page Al
A3
o
nr'
mrrrure,mrteet11i"
SUMMARY INDEX
O
'i,,I
o
o
1 STA.DES.SEC.R.S. ELECT. GRP.
2 STA.DES.SEC. ELECT. SPEC. GRP.
3 MANAGEMENT
4 STA.DES.SEC. R.S. MECH. GRP.
5 ADM. &ENG. SERV. SEC. ELECT. DRFTG.
6 ADM.&ENG.SERV.SEC.ELECT.CHECK
7 ADM.&ENG.SERV.SEC.MECH.DRFTG.
8 ADM.&ENG.SERV.SEC.MECH.CHECK
9 ADM. &ENG. SERV. SEC. CIVIL DRFTG.
10 ADM.&ENG.SERV.SEC.CIVIL CHECK
11 ADM. &ENG. SERV. SEC. STRUC. &ARC. DRFTG.
12 ADM.&ENG.SERV.SEC.STRUC.&ARC.CHECK
13 ADM.&ENG.SERV.SEC.STRUC.GRP.
14 ADM.&ENG.SERV.SEC.ARCHITECH GRP.
15 ADM.&ENG.SERV.SEC. CIVIL GRP.
16 STA. PRELIM. ENG. & APPR.
1 7 LAND DIVISION
18 TRANS.&DIST. UNDERGROUND CONST.
19 TRANS.&DIST. SEC. UNDERGROUND DES.
20 PROJECT MATERIAL DELIVERY
21 CONTRACT WORK
22 CONSTRUCTION DRAWINGS
23 FORMWORK
24 CONCRETE PLACEMENT
25 PLUMBER
26 EXCAVATION & GRADING
28 ELECTRICAL INSTALLATION
,29 MATERIAL PROCUREMENT
30 SPECIFICATIONS OFFICE
31 ELECTRICAL TEST
32 NONSENSE
33 CONSTRUCTION FACILITIES
34 FOREIGN DRAWINGS
35 STA.DES.SEC. LIGHTING GRP.
36 STA.DES.SEC. SPECIFICATIONS
37 COMMUNICATIONS
38 LANDSCAPING
39 SURVEY AND SOIL TEST
40 RELAY & OSCILLOGRAPH GRPS.
41 TRANS. & DIST. SEC. SPECIFICATIONS
42 ADM.&ENG.SERV.SEC. STRUCT. SPEC.
43 ADM.&ENG.SERV.SEC.CIVIL SPEC.
44 LATHING AND PLASTERING
45 MECHANICAL INSTALLATION
46 PIPING INSTALLATION
A4
/3/
47 SCAFFOLDING
48 SANDBLAST & PAINTING
49 MECH. INSTR. INST.
50 ELECT. INSTR. INST.
51 FORM & PLACE REINFORCING STEEL
52 WELDING
53 CHIPPING & GROUTING
54 BACKFILL
56 PROTECTIVE COATING
57 STEEL FABRICATION & ERECTION
58 PRELIM.OPER.
59 BRICKMASON
60 LABORERS
61 ELECT. DESIGN. GRP. 1 (ROF)
62 ELECT. DESIGN GRP. 2 ~RWE~
63 ELECT. DESIGN GRP. 3 HLH
64 ELECT. DESIGN GRP. 4 CAE
65 STEAM DESIGN BOILER GRP.
66 STEAM DESIGN ROT.EQUIP.&HT.
EXCH. GRP.
67 STEAM DESIGN INSTRUMENT GRP.
68 STEAM DESIGN EQUIP LAYOUT GRP.
69 STEAM DESIGN PIPING GRP.
70 STEAM DESIGN NUCLEAR GRP.
71 STEAM DESIGN NUCLEAR STAFF.GRP.
72 ELEe. MECH. & HELPERS
73 CARPENTER & PILE BUCKS
74 MILLWRIGHTS
75 PIPE FITTERS
76 BOILER MAKERS
77 IRON WORKERS
78 REINFORCING STEEL WORKERS
79 EQUIPMENT OPERATOR
80 STA.DES.MECHANICAL GRP.
81 CEMENT FINISHERS
82 STRUCTURAL ~NSTALLATION
0
PASS 2
PASS
END
END
TRANSFORMER
TEST
2/1
TRANSFORMER
TEST
RACK AREA
BACKFILL
2/1
TRANSFORMER
FINAL
ASSEMBLY
TRANSFORMER
FINAL
ASSEMBLY
RACK
AREA
BACKFILL
TRANSFORMER
WIRING
CONNECTION
TRANSFORMER
WIRING
CONNECTION
4/2
5/3
TRANSFORMER
PLACEMENT
GROUNDING
MAT
INSTALLATION
GROUNDING
MAT
INSTALLATION
10/6
TRANSFORMER
FOUNDATION
CONCRETE
CURE
TRANSFORMER
FOUNDATION
CONCRETE
CURE
TRANSFORME
DELIVERY
4/4
TRANSFORMER
DELIVERY
9/4
TRANSFORME
FOWNDATION
FJ M STRIP
I I
TRANSFORMER
FOUNDATION
CONCRETE /
POUR
I I
:::i
TRANSFORMER
FOUNDATION
FORM STRIP
TRANSFORMER
FOUNDATION
CONCRETE POUR
4/3
TRANSFORMER
FOUNDATION
FORM
INSTALLATION
W
-
TRANSFORMER
FOUNDATION
FORM
INSTALLATION
RACK AREA
EXCAVATION
0
RACK
AREA
EXCAVATION
START FOR PASS 2
4/2
START FOR PASS I
FIG. AS
MULTI- PASS SCHEDULE COMPRESSION
0
/3'2.;..
0
PASS 2
PASS 3
END
END
TRANSFORMER
TEST
TRANSFORMER
FINAL
ASSEMBLY
TRANSFORMER
TEST
RACK
AREA
BACKFILL
TRANSFORMER
FINAL
ASSEMBLY
TRANSFOflMER
WJRING
CONNECTION
RACK
AREA
BACKFILL
TRANSFORMER
WIRING
CONNECTION
GROUNDING
MAT
INSTALLATION
TRANSFORMER
PLACEMENT
TRANSFORMER
PLACEMENT
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MAT
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TRANSFORMER
FOUNDATION
CONCRETE
CURE
0
TRANSFORMER
DELIVERY
TRANSFORMER
FOUNDATION
CONCRETE
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RACK
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lJJ
~
TRANSFORMER
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FOUNDATION
FORM
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TRANSFORMER
FOUNDATION
fORM
INSTALLATION
RACK
AREA
EXCAVATION
START FOR· PASS 3
START FOR PASS 2
o
FIG. AS
MULTI-PASS SCHEDULE COMPRESSION
/.3
~3
o~
END
II
PAINT
10
TEST
I
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I
9
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4
TEST (2 DAYS)
INSTALL
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3
INSTALL
2
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INSTALL
ERECT
INSTALL' (5 DAYS)
PAINT (I DAY)
INSTALL
START
o
ERECT '( I DAY)
FIG. A 7
GRAPHICAL REPRESENTATION OF CADS SCHEDULING TECHNIQUE (BASED ON ACTIVITY TIME
AND PREREQUISITE LIST)
o
l.31
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TARGET DATE
END
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FIG. A 8
MATERIAL
SCHEDULE WITH CRITICAL PATH TIME EQUAL 10 fOTA'L AVAILABLE PROJECT TIME
o
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81
NUCL&RAOIOLOGICAL lNSTR
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89
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90
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..
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.
SUMMAR! NAME
SUMMARY NUM8ER
...........
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CADS MARK II SCHEDULE FO __ MALI.BtI NUCLeAR
1.1.965
u~n
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~
CRt TICAL ·;PAlTH
3' ACTIVITIES COMPRISE THE CRITICAL PATtf T.OTALING 1395 WCRKING DAYS
PAS5 NO.
1 SCHEDULE OVERSHOOTS DESIRED PROJECT CtlMPLEUQN DATE tY
lNOEX NO.
"-....
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>
......
ACTIVITY
NA~e
14 WORKING DAYS
FltE NO.
DAYS
46,
AEC PUBLIC HEARING REOONVENES
5'0044
15
)46
TIME SPACER.CP EFF TO PUB HRNG
51001t5
104
466
CONSTRUCTION PERMIT EffECT1VE
510046
1
604
SIGN weST CONTRACT FOR sew ENG
510039
1
464
AUTHORIZE TITLE 1 ENGINEERING
51001e0
66
585
Stw CONTAIN STRUCTURE OESIGN
5100ltl
S5
410
D8l
5~0042
66
1t69
DBl L(NER PLATE FA8RICATION
510043
132
576
RX CONTA STRUC FOUN MAT IN
510001
44
540
REACCONTASTRU BOT DBL LINER IN
510003
55
665
REACCONTA 80T LINER FR£ON TEST
570004
6
543
REACONTAVRTDBlLNRtPOPCRNCONCIN
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66
552
REACT CONTA INTEAIORCONC PH8IN
510013
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lINER~81 D
TO PURCHASE ORDR
52
I
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REACTOR CRANE IN
610017
U
539
REACCONTADMED8lLNRtPOPCRNCONIN
510014
198
667
REACT CONTA FREON TEST
510015
11
51t5
REACT AUX SYS EQ & PPG PHA IN
530002
154
666
REACT CONTA AIR TEST
510032
11
519
RC PPG HANGERS LOOPA PH8 iN
5.0018
33
531
RCPPGFIT'WELDtPRECLEANLOOPAPH8
5G0015
33
521t
RCP MTR LOOP A IN
5G0007
6
514
RC PPG COLD SPRINGtFINML WELD
510001t
55
664
RC SYSTEM FILL , COLD FLUSH
500053
6
663
RC SYS INITIAL HYDRO TEST
500054
6
623
THERM INSULA FIELD JOINtS 'IN a
500003
6.
658
NUCl SYSTEMS HOT fUNtT TESTING
650003
22
1
PAGe· 1
~u..
CADS MARK II SCHEOUL~FO~ ~AL'~_~,NUC~eA~ U~I.!.. 1
it 1965
IN()EX
NO.
ACTIVITY NAME
REMOV~,~" HO ~L~~N ,
6ift8
1t6t
"tUSH S:V_S
,. CORE LOAP,IHG ~ ,ASSEMBLY
~V TOP INTERNALS IN
51'
66~..,_R'I H~.. !~. 2 '.F.INAL HYDRQ T·E~T_ ..
660006
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U
.80001
11
1.0009
U
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6
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I,HlTllL CRlTlClLe 0 PWRTESTING
65000Z
19
STEAM
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STEAM BLOW
......
.
...
..
28005'-
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~'2
~
DAYS
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..
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"
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650
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~
PASS
-._.
TIME
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CADS MARK II SCHEDULE FOA MALlBU NUCLEAR UNIT 1
It 1965
PASS
ELECTRICAL tNSTAllATION
aPREREQutSITE ACTIVITIES ARE INDENTEOa
INDEX NO.
252
FILE NO.
0~0030
ISOLATED PHASE 22KV 8US IN
69
ISOLATED PHAse 22KV BUS OL
252
ISOLATED PH 22KV BUS SUPPORTIN
0~0028
"-
>-
258
~
START DATE
FINISH DATE
-l-~-
I'1.-
22 MAy 1910
66-
0-
66
o
Q
o
, JUN 1970
10·
4-
9
~
320
o
29 JUL 1970
11 AUG 1970
MTR HTR DISTR EQUIP 'INCwtR
040131
NijCSERVICE£CONTROl HOUSE CONST
010199
MTR HTR DISTR PNL DL
04013$
77
MTR HTR RELAY CABINET Ot
040139
18
MTR HTR RELAYS DL
040140
79
MTR HTR SUPPLY TRANSF OL
040141
22-
0-
22
o
o
o
2q JUL 1~10
27 AUG 1910
NSC BLDG CABLE RISER IN
040056
NUCSERVIce£CONTROL HOUSE CONST
010199
80
N6C BLDG CABLE RISER MATL Dt
040051
10-
o.
10
o
o
o
14 AUG 1969
27 AUG 1969
NSC BLDG CABLE TRAY SVS IN
040050
NUCSERVICE&CONTROL HOUSE CaNST
010199
N&C BLDG CABLE TRAY DL
'81
040051
33·
o.
33
o
°
o
14 JUL 1969
27 AUG 1969
NSC 8LDG GRO GRIOtELECTROOE IN
040044
184
N6C 8lDG CABLE VAULT IN
010200
82
NSC 8LDG GRO CRIOtElECTROOE OL
040045
5·
O.
5
Q
Q
o
23 SfP 1968
27 SfP 19.8
10-
0-
10
a
°
o
21 JUL 1969
1 AUG 1969
22*
0*
22
o
o
o
4 AUG 1969
3 SEP 19691,
NSC BLDG TERM RM CABLE TRAV IN
040054
N~CSERVICE&CONTROl HOUSE CONST
010199
NSC BLDG TeRM RM CABLE TRAY OL
040055
22*
o.
22
o
o
o
" AUG 1969
3
NSC BLDG TEST eIRC PlSEQIN&WIR
040060
NUCSERVIceiCONTROl HOUSE CONST
010199
86
N5C BLDG TEST elRC PL&EQ Ol
040061
33*
o.
:33
a
o
a
14 JUL 1910
27 AUG 1970
1'-laT
NSf BLDG VAULT CABLE TRAY SYIN
0"0052
NUCSERVICetCoNTROl House CaNST
010199
,184
NSC BLDG CABLE VAULT IN
010200
81
NSC BLDG VAULT CA8LE TRAY OL
040053
22*
0-
22
o
o
o
27 JAN 1910
26 FEB 1970
J'
LUBe OIL PMP MTR CNDSWJR IN
lUIE OIL PMPtReSERVOIR tNSTL
Nse
185
83
260
259
84
261
185
85
040031
040029
040030
0~023e
180007
LIGHTING CONDUIT IN
040046
NueSERVIce£CONTROl HOUSE CaNST
010199
NSC BLDG LIGHTING CONDUIT DL
040047
8LD~
Nse BLDG LIGHTING INtWIR
NSC BLDG LIGHTING CONDUIT IN
NSC BLDG lIGHTING EQUIP OL
040048
-185
NSC
264
185
CAe~E
TERMINAL EQ IN£WIR
040064
NUCSERVICE£CONTROL HOUSE CaNST
010199
~ JUN Bi10
~
SEP 1970
,
-j-
1-
I:
f.
I
!
t:
040046
040049
185
263
SL~CK
o
259
2.2
DAyS
o
185
~
TOTAL
MANHRS
o
-185
257
CRITICAL
DAYS
~eN
10
185
76
'-..,
N{!RMAL
DAY'S
MEN
0-
160
256
-- - l'
10-
2-54
255
I
a-INDICATES ESTIMATe USEDa
ISOLATED PM 22KY BUS SUPPORT IN
lSOl_TEO PH 22KV BUS SUPPORTDl
68
253
ACTIVITY NAl1e
----PAGE-----28.00~
---------1.-
1
I.,
J'
I
I'
I
f
I
II,
se P
1969
1-
I
111
22*
0*
22
o
o
a
27 JAN 1970
26 FEB 1970
f·
I
f~
~--------------------------------------------------------------------,-
JU~
1, 1965
CADS MARK II SCHEOULE FOR MALIBU HUCLEAR UNiT 1
E~eCTR1CAL
88
2"
266
>
270
I-'
\]1
~
040208
O~
t40~MAL
~EN
DAYS
CRll ICAl
CAYS
MEN
TOTAL
MAN~RS
15-
o.
15
o
o
580022
PRESSURIZER ~TR fA CTLSPWR WIR
"160 BLDG VAULT CABLe TRAV SYIN
NSO BLDG TERM ~M CA8LE TRAY IN
NSC IlDG CABLE RISER IN
ZS6
CABLE TUNNEL CABLE TRAY IN
217
NSO OASLE TERMINAL EO IN&WJR
261t
0~0199
DAVS
SLACK
o
41t-
0-
44
o
o
Q
15-
O.
15
o
o
952
10-
O·
10
o
o
o
Olt0052
040054
040056
040058
Olt0061t
500058
PR~SSURIIER
IN
PRIMARYCONTA ELEe $ERV FA IN
1
1
t'
11
iNSTALLATION
START DATE
FINISH DATE
II
12 MAR 1969
tw
I'
20 FEB 1969
Olt0209
020030
263
261
13 MAR 1969
13
MA~
1969
23 APR 1969
13
~A~
1969
12 MAR
191~
27 FEB
191~
fi
I
la
I'
I
I
I
I
II
I
i
510031t
1-
0*
1
o
o
1114
12 MAR
197~
12 MAR 1970
I!
I'
PWR CONTROL RELIEF VALVE IN'WI
0"0172
O~Ol73
PWR CONTROL RELIEF VALVE Ea DL
10-
0*
10
o
o
o
14 AUG 1970
21 AUG 1970
93
10*
0*
10
a
o
o
27 FEB 1970
12 MAR 1910
263
261
256
211
261t
521t
00\0181
REACT COOL PP1A FA CTl&PWR WIR
Olt0052
NSC BLDG VAULT CABLE TRAY SVIN
040054
NSC BLDG TERM RM CABLE TRAY IN
040056
NSC BLDG CABLE RISER IN
Olt0058
CASLE TUNNeL CABLE TRAV IN
040061t
NSC CASLE TERMINAL EQ IN&WIR
500007
Rep MTR LOOP A IN
REACT COOL PP1B FA CTL&PWR wIR
RCP MTR LOOP 8 IN
0~0182
10*
0*
10
o
o
187
27 FEB 1970
12 MAR 1970
525
REACT COOL PPIC FA CTl&PWR WIR
RCP MTR LOOP C IN
Olt0183
10*
0-
10
o
o
155
27 FeB 1970
12 MAR 1970
526
REACT COOL PPID FA CTl&PWR WIR
RCP MfR lOOP 0 IN
040184
10*
0-
10
a
o
77
21 FES U70
12 MAR 1970
527
I(
SAFETYINJ PP MTRIA CTL&PWR WIR
SAFETY INJECTION PMP 1A INSTl
0~0189
10*
o.
10.
o
o
36
• MAY 1970
15 MAY 1970
586
l~
SAFETVINJ PP MTR1B CTl&PWR WIR
SAFElY INJECTION PMP 16 INSTl
040190
10*
0-
10
o
o
36
~ MAY 1910
15 ~AY 1970
581
I(
SAFfTYINJ PP MTRIC CTLtPWR WIR
040191
10*
o.
10
o
o
36
• MAY 1970
1S MAY 1970
22*
0-
22
o
o
o
17 APR 1969
271
212
213
CON IN
BLDG lIGHt CdN
8l0GGGUARD House CONST
PAGWOe UTILITY SERVICE FA IN
509
'f:.:
OF~
ll~HT
28.005
Olt0065
Olt0210
OFPCCEGGUARD BLDG LIGHT IN'WIR
040208
OFFICe&'YARD BLDG LIGHt CON tN
0402U
92
OFfICE&GUARD BLDG LIGHT EQ DL
269
...........
BLDG
QfFICEGGUA~O
PAGE
265
2.67
268
Nle CA8LE TERMINAL EQ OL
QFFiteCG~ARD
91
164
FILE NO.
ACTIVITY NAME
1
a-INDICATES ES'IMA1E USEDa
ap«E«saUUITE ACTIV IT us ARE INDENTEDa
.UUJ E,)( NO,.,
PASS
274
275
216
211
588
278
It 11
SAFETY INJECTION PMP
Ie
500021t
53000l
5)0002
530003
040204
~
h,
If
500031t
SHoPtWR€HSe B LIGHT CONDUIT IN
SHOP&WREH5E SUPERSTRUCTURE IN
In
I,
5000lt5
INSTl
I
1~
MAY 1969
020006
I~'
I(
i-I
I
I(
Iy~
__ ._____ ., __ .____.____. _ _ _ _. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .J...._
o
e
o
o
o
,JUt
-
1.196'
CADS "ARK II SCHEDULE
o
F~R
.
MAlleu
NUCLEAR
•..
....
U~IT
1
. . ._- - .......
PASS
'
..
1 ----.---._--_.-._----PAGE 28.006
-
ELECTRICAL tNSTALlATION
aPREREQutSITE
ACTIVITIES ARE- INOENTiDD
- -..
------ .. -- ...• _........
INOEl( NO.
100
279
6HOf'WR6HSE BLDG LIGHT tN'WIA
nll -"------SflOPCWREHSf! 8 LIGHT C{JffllUlT'lff
281
282
105
108
---_.
..
FILE NO.
SH8P'WHEHSE B tiGHt CONDUIT Ol
,101
210
---~
ACTIVITY NAMI
040205
01t0206
SHOPCWHEHSE 8LDG LIGHT EQ OL
STATOR 'OOLING SYSTeM INCWIR
S~ATOR COOLING SYS EQUIP OL
040015
-STE." n"PINSTR.cCONTROl 'INIWl
040170
STEAM TEMP INS1RCCONTROL EQ Ol
,284
'-.
~
\..J\i
C\
286
217
28B
IN6~RUMeNT'C~NTRbL
INCWIR
TURS INSTRUMENT'CONTROl EQ Dt.
0"'0005
lUAS-GEN CASlE TRAY liYS IN
TURBPlT ELEV 35 CONC DeCK IN
TURB~GeN CABLE TRAY DL
01t0040
119
TUR8GENGRD GRID4ELECTR'OD:E IN
TURBGEN GRO GR1DCELECTROOe Dl
00\001t2
TUR81NE REGULATING CAB tNeWIA,
GENERATOR MAJO. PARts OL
040021
62
12'1
41lt
'fURSPL,T ILOG UGtiTlNG IN,'WIR
TURBPLT 8LOG LtGHT CONDUIT IN
:122
TURBPlT 8LOG L1GHT EQUIP OL
289
355
125
,290
130
291
185
131
132
TUR8PLT GRDGRtO IN
TURBPLT eJ UNWATERING SY$ IN
TUABPLT GROGRIO Dl
VARO
185
133
CONDUIT~MANHOLe
SYSTEM t~
YARD CONDUIT DUCT MATL DL
3'.
o.
3,3
0
0
4~.
04f
4~'
D-
O
30'e
It*
21
4
It It-
0-
44
66-
Oli
31e
33
0
01,0001
040038
040036
040039
040222
000006
Olt0225
0"'0214
FINISH DATE
22 JUL 1910
4 SEP 1910
19~
11 JUN U7G
11 AUG 1910'
960
0
17 JUL 1910
27 AUG 1970
0
0
0
29 JUN 1910
27 MIG 1970
66
(I
0
0
26 MAV 1969
27 AUG 1961f
o.
33
0
0
0
2' JUL 1968
10 SEP 1968-
22,-
o·
22
(]
0
31
20 JUl 1970
18 AUG 1970
75'.
0-
75
0
0
0
22 JAN 1910
1 MAY 1970
180-
O.
180
0
0
(I
8 MAV 1910
22JAtc 1911
15.
0-
15
0
0
0
15 FEe 1968
7 MAR 1968
192-
o.
792
0
0
0
II MAY 1961
15 Jut 1910
22e
0-
23
0
0
0
8 JAN 1970
6 FEB 1970
3-
Oe
~
0
0
0
2 FEB 1910
" FEB 1910
0"'0215
DC BA~T CHARGER lA IN£WIR
040147
NUCSERVICe'CONTROL HOUSE CONST
010199
125V DC BATT C~ARGER 1A&18 DL
01t0149
0
START CATE
SUCK
0
04001t3
120V INS1A SUPPLY PltEQ IN&WIR
040 13It
NUCSERVIce&CONTROl HOUSE CONST
010199
120V INSTR SUPPLY Pl&EQ OL
040135
120V INSTRSUPAUTOTRANSFERSW Dl
040136
125~
292
010113
040041
TURe9LT BLDG LIG~T CONDUIT IN
040036
lURePLT ILBG LtGHT CONDUIT Dl
01t0031
TURePLT SUPERSfR WAllSCROOF IN
110039
281
0-
DAVS
! JUl 1969
-,-,
040004
TOTAL
MAHHfU
3'.
._
..... -._- -
040111
,192
118
.285
>....
lURI
CR111CAL
MEN
DA'S
19 "AY 1969
040016
TUR8 INsrrR WIR-TUR8 TERMCAI!I IN
01t0239
TURa INSTR WIR-TUR8 TEAMCAaOL
04Q21t0
,U8
lURe T&RMINAl CA8 INSTL
110015
112
NORMAL
DAYS
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0"40204 '
040207
111
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Date
CRITICAL PATH/COSTING/GRAPHIC PLOT SYSTEM
Project Rooster pump Station
INPUT FORM
. s
By~Omnjmetnc
I
""'-
~
~
J
. : ; Q;
c:~~
JOB DESCRIPTION
o,,!C
Zo.
Est.
Cost
Code!
Onto
Code!
Onto
Code!
Onto
Code!
Onto
Code! SRT! Job
No.
Onto
~ost
«I
CQ'tS
_0
CO
L--:od~
1
1
19
1
15
. 5 SUBMIT ELECT MA TLS
2
1·
.
Ii SURMIl" PLRr. MA l"LS
3
1
12
9
1
,1
c:; STTRMT1' PATN1'
C~R
l'
+ SAMPLES
4 SUBMIT PRE-FAB MET BLDGS D
1
2
4
'3
Ii SURMTT CONC MA 1'I~C; +MIY
1
1
c
2
2 MORTI .T7. ~
2000
1
,
4
2 r.R A n~
4000
5
1
2
3
1 SURVEY
5
_4
7
1 1'R ENCH FOO1'TNCtS
1000
1000
5
1
1
6
3
4
o RESTRAIN
3000
4
2
6
~
7
n CUT + STUB-UP PIPE MAIN
6
~
6
7
10
9
n~.C:::
ST7.~
5
6
6
3
8
I
9
10
2
11
12
CtOVT OK
1
1 PROCURE
1
4 GOVT OK
14
2
c:; GOVT OK
1~
15
c:; GOVT OK
12
13
Ii CtOVT OK
16
17
7
8
8
11
10
11
15
3 FORM + PLACE
5 CURE
10 PROCURE + DELIVER
9
13
i
7
20
16
19
1
-
Time
EST
-~
38
40
6500
5
3
"nn
27000
6
2
1
2
46
6
2
IE
19
20
51
56
6J
66~
71
75
79
(1
....
I
Date
'
/t
:!
CRITICAL PATH/COSTING/GRAPHIC PLOT SYSTEM
1/
I
Project
,
By
I
"'~'
l>J
INPUT FORM
/;
II
I:;~
Time
EST
J
13
11
16
20 .
21
g~~
JOB DESCRIPTION
~~:
Est •.
Cost
+ DELIVER
lC PROCURE + DELIVER
,~ PROCURE + DELIVER
C
17
PROCURE
Code!
Onto
Code/
Onto
Code!
Onto
Code/" SRT! Job
Onto ~ost No.
Code!
Onto
:nnp
21500
21
4000
22
2100
23
11
18
1 SET PUMP
7000
2
2
4
2
24
11
14
'1 ER ECT STR STI
3000
1
2
2
3
25
4000
4
2
6
1
5000
2200
1
2
3
4
2
18
22
~
14
17
' INSTAl.! ·ROOFING
{;OMPLETE PIPING
+ SIDING
17
21
2 INSTALL LIGHTS
1
22
23
23
25
1 WIRE PUMP
1 TEST PUMP
1500
1200
3
2
3
1
4
1
21
25
2 PAINT
5000
1
2
7
3
6
1
21
25
1 INSTALL POWER DROP
1200
3
2
700
1
23
1
4
1
25
26
2 GOVT INSPEC
21
22
o RESTRAIN
,
OU
26
2
2
+ PANELS
~
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_0
6
27
28
1
29
30
31
32
7
33
1
34
"
,
,
.
,
"
,
r:
1
5
.
9
13
38
40
46
51
56
"1
66
~l
175
[1.<1
nI
N
(J
....
o
o
NAP REPORT NU. 1
OMNIMETRICS CKITICAL PATH/COSTING/PLUTTING
CPH SCHEDULc
SAI"IPLE SCHEUULE FOR aOOSTER PUMP STATIm.,;
4
5
6
3
2
1
8
1
10
11
14
9
12
17
16
15
13
20
~
~
~
21
22
23
19
?4
25
26
27
28
34
29
31
32
30
33
~
*
*
*
~
.::
'"
*
TOTAL
CODE
1
2
3
4
5
6
7
STAR T Et\D TIME EARL Y
NODE NODE EST. START
ACTIVITY
UESCRIPT lUN
SUBMIT PRE-FA~ ~ET SLDG S
SUBi-l IT CONC II,A TLS+IHX DES
1-108 IL IZE
SUBMIT PLBG MATLS
SUBMIT ELECT MATLS
SUBMIT PAINT CERT+SAMPLES
SUJ{VEY
GRAUE SITE
RESTRAIN
CUT+STU~-UP PIPE MAIN
GOVT OK
TRENCH FOOTINGS
GOVT OK
GOVT OK
GLJVT OK
GUVT UK
PRUCURE
PRUCURE+DELIVER
10 FORrHPLACE
PROCURE+DELIVER
PROCURE+UtLIVER
PKOCURE+DELIVER
CURe
ScT PUi·W
ERECT STR STL
COMPLETE PIPING
INSTALL ROOFING+SIDING
INSTALL LIGHTS+PANELS
RESTRAIN
WIRE Pur:IP
PAII~T
INSTALL POWER OKUP
TEST PUt-'.P
(iQVT IN SPEC
ESTI~ATED DURATIO~
RESOURCE DESCRIPTION
ADMINISTRATIUN (AU)
ERECTORS (E:R)
ELECTRICIANS (EL)
PLlJr·lt3ERS (PU
CARPt:NTERS (CA)
LABORERS (LA)
PAINTERS (PA)
1
ES,LF
SOfATH/CUS T I,'lG/P LUTT h~G SYSTt:i·,
01
:;; I"',AKKS CR IT I CAL PATH
~
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2
6
4
4
5
0
*
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*
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ij
14
20
STATIU~
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1
1
1
9
4
5
2
~
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r'
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lATt:
START
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4
0
0
.5
0
1
4
2
LATE
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FRt:F.
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TOTAL
FLUAT
0
0
0
1
4,
4.
6
6
0
TOTAL THIS CURR
AVAIL JOts TOTAL
eST.
CUST
>-0
i!
.0
2
2
2000
~
1:
CUhPLt:TcU
4 CUi;PLl:TEU
14 GOVT OK
5
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.9
4
4
8
4
8
0
0
0
CW-iPLI:TEU
,,/
COi-,PLETt:U
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-3
?
2
1
2
2
2
3
2
2
'2 '
2
1
3
2
1
2
'0
10
11
10
8
18
8
18
0
0
21000
2
2
2
-2
2
!)
2
l~
l~
20 CUj·l PLE TE D
2S ERECT STK STL
14
0
3
18
21
18
21
0
0
3000
2
2
2'
11
2
2
21
2.1
25 COi'jPLI:TEU
27 INSTALL ROO~ING+SIOING
14
17
3
21
24
21
24
0
0
5000
2
2
2
2
2
24
24
27
28
I~STALL
17
21
2
24
26
24'
26
0
0
2200
2
2
2
2
0
2
26
28 cm-, PLE TE 0
31 PAINT
21
25
2
26
28
26
2
2
0
28
0
0
~ooo
2
~
2
31 COi',PLETEIJ
33 GOVT,INSPEC
25
26
2
28
30
28
30
0
0
700
2
2
2
2
2
.* 26
28
'*
ACT! VI TY
lit:SCRIPTIul~
0
0
~OOST~R
2~
COi-IPLETED
LIGHTS+PANELS
1
ANU RESOURCES RECUIREO ANALYSIS
4 SUcl~IT PRE-FAa ~ET BLDG S
5 SU~~IT CONC hATLS+~IX DES
6 j.,u:jILIZE
0
SCHEUULE FOR
SA~PLE
PAGE
j
'
0
0
I
I,
o
o
o
.
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....
i!
f'
/'
.
I
~eQUIR~MENT
~~PURT
OMNlhETRICS
C~ITICAL
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SA~PLE
*
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MARKS CRITICAL PATH
JOa
T ll'it:
I~O.
*
:>::
ACTIVITY
IJESCRIPTIUN
18
18
24 SET PUl'lP
25 ERECT STK STL
19
24
21
21
25 COi1PLETED
27 INSTALL ROOFING+SIDING
24
27
PAGE:
SYST~M
START I:::ND T IHE EARLY
NODE r\ODE EST. START
EARLY
FINISH
LATE
START
LATE
FINISH
FREE
FLOAT
TOTAL
FLUAT
18
18
19
21
20
18
21
21
0
0
2
11
11
18
14
1
3
0
EST.
C05T
7000
3000
CQ.·,PLETEO
CUi'j PLET t: 0
14
2
SCHEDULE FOR aUOSTER PUMP STATION
FUR RcSuURCt CODE 02
PROJ
0
0
0
17
3
21
24
21
24
0
0
5000
TOTAL THIS CURR
AVAIL JU~ TOTAL
4
4
3
2
5
4
2
3
4
4
3·
0
4
4
4
4
0
2
...........
{j....
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tx:I
I
N
-
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*
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03
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*
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SYSTth
PAGt:
SAl"; PL t: SCht:UUL E FUP. BUUS Tt: K PUi-IP STA T·I Ol'i
ANu RESUURCt:S REQUIRED ANALYSIS
S or ART EN UTIl'I E EARLY
I~OUE I\IUOE: I:ST.
START
I:ARLY
FINISH
.. LATE
START
LATE
FINISH
FREE
FLOAT
TOTAL
FLOAT
EST.
CU!)T
TOTAL THIS CUKH
AVAIL Jeb TUTAL
24
2B Ii\STALL LIGHTS+PAI\lI:LS
17
21
2
24
26
24
26
0
0
2200
2
2
2
26
26
26
2ti
2';
CUI·,PLi: TI:U
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0
23
25
1
1
26
26
27
27
26
27
27
28
0
0
1~00
1
1
1200
2
2
2
2
22
21
2
2
4
27
29
2
2
0
27
27
32 Cl,..·.PLE THJ
30 TI: Sr' PUi·Oj-)
0
2~
1
27
28
27
28
0
0
1200
2
2
2
23
1
1
.2tt
2d
30 CUr·.PLt::TI:U
33 GUVT II~SPt:C
2
1
0
25
26
2·
28
30
28
30
0
0
100
2
1
1
~2
~"I
3
CUI·.PL~TEU
2
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o
o
0
0
REQUIREMENT REPORT
OMN~METRICS CKITICAL PATH/COSTING/PLOTTING SYST~M
FOR RESOURCE COOE 04
SAr-iPLE SCHEUULE FOR BOOSTER PUI>iP STATI{JI'l
*
AND RESOURCES REOUIRED ANALYSIS
MARKS CRITICAL PATH
. PROJ
TINE
*
*
JOB
NO.
ACTIVITY
DESCRIPTION
3
11 CUT+STUB-UP PIPE MAIN
6
11
START, END TII'-iE EARLY
NODE NODE EST. START
0
PAGI:
EARLY
F IN I SH
'I;ATE
START
LATE
FINISH
FREE
FLOAT
TOTAL
FLOAT
7
10
3
4
3
7
3
3
6
EST.
CUST
3000
CONPLETED
18
24 SE T PUI-i P
11
18
1
18
19
20
21
0
2
7000
19
19
24 COi-'IPLETEU
26 COMPLETE PIPING
18
22
5
19
24
21
26
2
2
4000
24
26
27
30 TEST PUNP
23
25
1
-27
28
27
28
0
0
1200
28
2a
30 CONPLETEO
33 GOVT INSPEC
25
26
2
28
30
28
30
0
0
700
COMPLETED
4
TOTAL THIS ClJRR
AVAIL JOB TOTAL
2
2
2
2
2
0
2
2
2
2
2
2
0
2
2
2
0
2
1
1
2
1
0
2
1
1
2
"
~
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I
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atJ
REQUIRE~ENT
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~
MARKS CRITICAL PATH
PROJ
TUiE
JOB
NO.
ACTIVITY
UESCRIPTION
2
2
8 SURVEY
7 GRADE SITE
3
8
4
4
7 CQr'IPLETED
9 TRENCH FOUTINGS
5
9
9
9
12
OM~IMETRICS
SAMPLE
A~D
CKITICAL
PATH/COSTING/PLOTTI~G
FOR BOOSTER PUMP
SCHE~ULE
P~Gt:
STATIO~
RESOURCES REQUIRED ANALYSIS
START END TIi'll: EARLY
NODE NODE EST. START
2
2
3
1
4
2
2
2
EARLY
FINISH
LATE
S'TART
LATE
FII~ISH
3
6
7
4
7
.9
FREE
FLOAT
TOTAL
FLOAT
0
0
5
4
':ST.
COST
1000
4000
COMPLETED
TOTAL THIS CUl~l~
AVAIL JUu TuTAl
2
2
1
1
:; 1
2
2
1
1
1
1
0
2
1
(l
2
3
3
2
3_
CJ
2
4
7
1
4
5
9
10
4
5
1000
CUfviPLET~U
7·
8
9
3
18 FORH+PLACI:
12
18 CANNOT BE RUN - TOtAL REWU: ·2MENT GREATER THAN AVAILI3ILITY
18
SYST~K
COr-1PLETED
10
13
0
1
6!>OO
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?
1
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~
~
o
o
o
,
o
o
REQUIREMENT REPORT
OMNIMETRICS
FOR RESOURCE CODE 06
SAI'IPL~/"
*
AND RESOURCES REQUIRED ANALYSIS
HARKS CRITICAL PATH
PROJ
TIME
JOB
NO.
2 ;.
2
,;
3
"D
*
~
*
ACTIVITY
DESCRIPTIUN
C~ITICAL
SCHEDULE FOR
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PAG~
PUt-!P STATION
EARLY
FINISH
7 GRADE SITE
4
2
2
2
4
7 CANNOT BE RUN - TOTAL REQUIREMENT GR~ATER THAN-AVAILIBILITY
11 CUT+STUB-UP PIPE MAIN
o
·l.ATE
START
LATE
FINISH
FREE
FLOAT
TOTAL
FLOAT
7
9
0
5
4000
2
3
3_
eST.
CUST
TOTAL THIS CURR
AVAIL JOb TUTAL
3
7
3
3
6
7
10
3
4
3000
2
1
4
4
7
1
4
5
9
10
4
5
1000
2
2
'3
2
1
3
2
2
1
2
1
0
2
4
4
7
9
5
9
CUi'iPLt:TED
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SOLUTION OF A PROBLEM IN HEAT TRANSFER
J. C. Caslin, H. E. Fettis
and
J. W. Goresh
In studying the effect of varying wall conditions on heat conduction in a
fully developed turbulent gas flow in a long tube, it is necessary to solve
the partial different~l. ei.uation
a
{ (1-x')
ax
ae
=" x'l
x
I\.
ae
(1)
trB"
The equation must be solved subject to the conditions
ae
+ ke = 0 )
"lfj{
o
and e at
X=
X= 0
(2)
1 be finite. Here A. is a physical parameter depending on the
physical properties of the gas,
e,
a non-dimensional temperature difference,
k, a parameter depending on the conductivities of the gas and wall insulation,
and rand
i§
are non-dimensional radial and axial distances and
In addition, the distribution of temperature at
e(0, x)
=
i§=
X=
(1_r 2 )1/7
•
0 is given as:
f(x)
(3)
The complete solution of equation (1) is approximated as a sum of the
series
9
n
=1
a.
."1.
A e -, r..1iI!
n
\fI n (x))
(4)
n= 1
where the constants A are chosen such that
. I'{~ Fn ~n (x: J-f(x>f ' x
q
o
dx
(5)
o
is a minimum. The 1/1 n
a~e
eigenfunctions of the ordinary differential
equation
-k-
t
(I_x" )
d1/l n
)
~
'1-
i\
0.
x" 1/1
n
rhese and the corresponding eigenvalues
(6)
= 0
n
~a.n
are found by the Ritz method
in terms of the 'eigen functions of the equation
:x j
(I-x")
}+
::
[3 x
5
(7)
y= 0
which may be solved in terms of hypergeometric functions.
The program consists of a simple input-output routine for introducing
the physical parameters. In order to find the eigen values and eigenfunctions
for equation 7, it is necessary to solve a transcendental equation involving
gamma functions.
tt
o
This is accomplished by a root-finding subroutine using
False Position" together with a subroutine for generating the gamma
functions. These functions depend only on the parameter k. The eigenfunctions
thus determined are then used as coordinate functions in a Ritz type analysis
to obtain approximations to the eigenvalues and eigenfunctions of equation (6).
This portion requires a subroutine which evaluates integrals involving products
of hypergeometric series and a matrix eigenvalue-eigenvector routine based
on the Jacobi diagonalization method. Finally, the initial temperature distribution is expressed in terms of the eigenfunctions of equation (61,;i* lftaking use
of the orthogonality relations for these functions (according to equations (3)
and
(4»)." 'W'ith the
now be determined.
An known, the temperature at any value of rand
i§
may
o
0 :,\'
",
oP CRACOVIANS
SOME APPLICATIONS
by
Marco Tulio Rincon Bo
Geodetic Engineer
Proffessor of La Universidad del Zulia
Maracaibo - Venezuela
o
COMMON WESTERN REGION WINTER MEETING
December 6 - 7 - 8 1965
Los Angeles
o
0
CQlifornia
o
CONTENT
PREFACE
1•
GENERAL DEFINITtONS
1
2.
BASIC OPERATIONS IN CRACOVIAN ALGEBRA
3
3.
GENERAL SOLUTION OF LINEAR EQUATIONS SYSTEMS
8
3~1.
Description of method
8
3.2. THE PROGRAM
14
3.2.1. General
14
Organ~zation
3.2.2. Flow chart
17
3.2.3. Program l-isting and solution of a numerical
example
4.
SOLUTION OF NORMAL EQUATIONS SYSTEMS
4.1
Deescription of method
20
o
4.1.1. Obtainment of unknowns
24
4.1.2. Obtainment of mean square errors of unknowns
30
4.2.
THE PROGRAM
4.2.1. General organization
34
4.2.2. Flow chart
3S
4.2.3. Program listinf and solution of a numerical
example.
40
o
o
I
PREFACE.
Arrival of calculat ing machines originated a reVolution in numerical
calculus and nowadays, electronic computers represent
the
highest
exponent of this marvelous revolutionoThe old classical logarithmic treatment of problems, often
long and tedious transformations only to make possible
the use
with
of
logarithms, has been substi tuted by new calculating methods which still
are in a continuous transformation and evolutio-oD, based on new concepts
derived from existence of calculating machineso"Cracovian methods" constitute a good example of trese new ooncepts
o
At first they were created because of the needs of new
methods
0
to
compute with calculating machines but very soon, they showed a gre'at
analitical power which caused the origin-of "CracOYian Algebra"
m~ans
of which it has been
~ossible
to
atta~ka
by
lot of problems with
many advantages over classical methods.Some typical applications of Cracovian Algebra are:
\
Direct solution of problems in
spheri~al: poligono~etry
common in Astronomy. The new method is shorter
and
very
simpler
than classical method of decomposition into spherical trianglesoSolution of linear equations systems by means of a typical cr-i
covian operation' which makes possible
to
solve practically
systems with any number of unknownso-
o
New treatment of Errors Theory and Least Squares
Adjustmentwi~
very general procedures to solve symmetrical systemso-
II
In all these applications, cracovian calculus offers 'the following
0
advantages:
l~ws
and
c) Calculating procedures very easy to memorize, lightening
in
a) A great analitical power verified by discovering of
relations in Physics and Mathematics Sciencesob) Brightness and briefness of cracovian expressionso-
this way mental effort of calculatorod) Economy of calculations and good propagation of
because
eTIro~
of compact manner of cracovian calculating schemes which. in
a fluid way and using only additions of products, make
PQs~bre
to shorten the intermediate notesoIn spite of the mencionated advantages, cracovian methods
are
practically unknowno The capital reason for this is that the biblio=
graphy is written in polish, because their inventor, Oro
Banachiewicz, Director of the Astronomical
Obs~rVatory
,~
Tadeusz
in
Cracow
Poland, and his follower, like Kochsmanski, Sierpinski ani
HausbTandt~
are all polisho
However, in Venezuela and thanks to the interest of
polish~fo
Ing? Bernardo Wahl, two articles written in Spanish have been
pOOlishw~
"Calculo de Cracovianos" (Cracovian calculus) and "La Aplicacion del
Algebra Cracoviana en el Cilculo de Compensaci6n" (Application
Cracovian Algebra in Least Squares Adjustment)
0
These two
of
articles,
published by the Engineering School of La Universidad del Zulia
j
constitute the basis of this worko-
o
,wtt'C!!!ttlfttrY!I:!efmreerrr-::
'7
III
Two programs developed to solve 'linear equations systems by means
of cracovian calculus, are described in this worko The first
one
is
applicable to general linear systems; the second one is a mo'difieation
,'1..:, 0(
.,. ,.r . .
~.I
'.
.•
•
! .
•
Ii '\I
I
of a program developed by the author in .his special work to
obtain
the title of Engineer and is applicable only to' normal equations systemS
derived from least squares adjustments
0
The last section
second program is devoted to calculate the mean s4uare
of
error
unknowns although northameridan geodetist do not consider
this calculationo However, if it is
poss~ble
thisof
important
to use an electronic
computer, it is advisable to calculate these errors which offer a very
good criterion of measurement precissiono Moreover, cratovian methods
make possible this calculation with minnimum programming e:fforto
o
All .these programs have been made with aids of an IBM 1620 with
1.622 Card Read-Punch which works in the "Institutode Calculo Aplic,!
do" in Engineering SchooloIn addition to the descriptions of the programs
j
there
are two
sections about general definitions and 'basic operations in cracovian
algebra in order to popularize these methods which, by the explained
reasons, are practically unknowno- As it is explained in those sections,
"cracovians" are rectangular arrays of numbers which obey to certain
operations rules and whose name is derived from Cracow, natal
of Dro Banachiewiczo There is a great similitude between
city
matrix
algebra and cracovian algebra; nevertheless, there is a remarkable
difference between them derived from the different way to
4C)
accompl~h
muitiplication: with matrices, this operation is rows by columns
17D
II
IV
while with cracovians it is columns by columnso This fact, apparently
o
with no importance, is the reason f.or all advantages of cracovian
algebra in calculations practice as it can be noticed in the appUcations>
described in the present work which are only a very little example of
the innumerable cracovian applicationsoTo finish these short lines, the author wishes to thank very
much the organizers of this meeting the opportunity to participate in
such an active way and to express his hopes of having contributed to
the divulgation of these calculation
methodso-
Marco To Rinc6n 80
-November,
o
19650
o
17(
0
1
1 • .,. '. GENERAL DEFINIjIONS
1• 1•
(1)
"Cracovians" are rectangular arrays, of
numbers
subj ecti to the
rules of operations ,giveri below.'They will be represented by means of the symbols
. ..
,"'
.!,=
•
•
•
•
•
•
•
•
0
•
•
0
•
•
~
•
. . . . . . . . . . . . . .0. .
•
...
b 2n ' •••
The numbers a rs are called "elements of the crac.o.v,ian". The fiIst
subscript indicates the column . ,and the s.econd subscript ind:ica1es
the row in which the element stands.,~
,
In-:::agreement with the "Cracovian Cal,culus
N~rms
In
Computati9ns" dated the 30 - 6 - 1 ~S9 and prepared
Geodetic
~
,
the "Polish
~
.
Committee of Norms", the symbolical repr,esentatio~s of cracoVians
are
a)'Por";printing, black letters
b) In writing by hand or
,
. 1.2.
'"
0
",".
.~
t9~iwtit~r,
A cracovian "()f m columns and Ii rows
is
underlined lettets
said to be
of
order
tIm
(1) This section and section 2 have been taken. with some modifications, from the article of Proff.s$ors B. Wahl 'and Ernesto Ho
Battiste1la "Calculo, de Cracoviartos" published in N: 2 'of the
"Revista de laFacultad de Ingenier~a"''''' Universidad del Zulia Maracatbo - Venezri~la-
-
1 •
172---
1 .3.
A "square cracovian" has equal number of columns and rows. It is
said to be
~'diagonal"
when d rs -0
r;, s
o
o • •
o
d 22
•••
0
o • • • • • •
0
• • •
II
•
II
II
II
o
The cracovian 1: , or "unit cracovian" is a special case of diagonal cracovian in which d rr - 1
o
...
1
1:•
•
•
•
0
•
0
•
•
The elements all' a22'
•
•
•
•
o
II
...
o
1.4.
•
o
••• ', ann are call~d "diagonal" elements".
The straight line which contains aii'these elements
is called
"principal diagonal" and is a g~ometrical resemblance that helps
to unde;stand many operat i~ns ,. of
1.S.
c1;'a~ovian
algebra
,,~.&,)
" h
==
0
==
0
(10-5)
o
o
As cracovian
h is
diff~re~t fro~
zero, then
(11-1)
unknow~s
The cracovian of
is easily obtained fron this craco -
vian equation by using the definition of cracovian
multipli~Dnt
In order to make clear this procedure, it is advisable
equation
(11-1)
supposing
1
g
2' t 21
x3 r\g31
x·
1.
r,'·1
X
1·
.,v
o
." .f.'
.' 1
n -
t~
devekp
3
0
0
1
0
g32
1
=
0
( 11-2)
i'2
that is
Xl + g21 • x 2 +' g31 • x3 +
x2 + g32
0
ii -
x3 + l~
X
9
3 + i 3
0
- 0
-
(11-3)
0
Obviously, the'unknowns are· obtained from back solution of this
system.By making the substitutions
L1 -
a n+ 1,1
·
(11-4)
o
-
11
=
l12--
and supposing ag~in
n - 3,the following equality is obtained
t,
4[)
"
,~
8
21
8
31
8
22
8
32 -
8
33
==
'.
8
23
g21 g31
h21
1
832
h22
1
0
0
The elements of cracovians ,& and
h
( 12-1)
are obtained :in the following
way:
a) The first row of'
column of.&
h
is obtained by multiplying the first
by each coltimn of
h
,
so
(12-2)
It can be noticed that the first row of
the first column of
h,
is equal
h
is'obtained,:the first row of.,&
can be obtained by mul tiplying the first column of
I
As
h 11 ==
row of
A
8
11
o
~
b) Once the first row of
each column of
to
h
by
.&, so
' the fi rst row of
divided by
.&
is equal to the first
all
o
== 12 ==
Ir3
c) Using now the second column
of
•
.&
,
the expressions
0
821- h21
+ hll
g21 - h31
+
-
&22
h32 ~
&23
(13-1)
make possible to obtain the second row of
.&
d) The second row of
second column of
a
is
o~tarrlid
h
by mUltiplying
by each column of
the
that is
.& ,
(13-2)
e) The last element of
h
is obtained from
c!
( 13-3)
and the last element of
A
from
( 13-4)
• a 43
It is remarkable that each element of cracovians
.&
and
h
is
alw,ys obtained from solving .an equation with an unknown, Moreover,
as all operations are additions of
pro~ucts,
~:.
I
they can be acoomplished
1\
with a calculating machine making no notes of
intermediate re -
sults.In brief, the typical cracovian operation of decomposition into
o
two canonical cracovians, makes possible to obtain the solution
of practically any system of linear equations in a very simple
way.-
3.2.
o
THE PROGRAM.
3.2.1. General organization
Q-
According to the explanations of preceding section, it is very
easy to develop general expressions to obtain the elements
& and
cracovians
first row of
h
r1
a
(14-1)
lr
& from
and the first row of
g
r1
a
a
r1
/h
r
11.
s r
- a
rs
-
(g
r1
starting from
0
h
s1
r == 2
+ g
r2
•h
and s
starting from
r1
• h ..
s == 2
•1
+ g
and
r2
()
.t
n, n+1
"
are obtained from
h
s2
+ ... " + g
== r, r+1,
and the second and other rows of
(g
.. ..
2t 3 t
==
The second and other rows of
h
the
is obtained from
h
a
h. By considering substitutions (11-4)
of
•h
s2
"0"
r , r- 1
,
n
,S-
1
.. h
S ,
r-1
)
(14-3)
& from
+. .... +
g
r
.. h
s, S -1
)l/h
J
ss
(14-4)
r == 8+1,8+2,0"0
== 14 ==
I f,E)"
, n+1
o
These expressions allow ihe obtainment of the elements of ~ and
~
h
in alternated way: first and element of
of
&.
later an elemEnt
,
and so on.-
"-.
In order to save core storage, the program has been developed in
such a way that the elements of
~
A and
are obtained
by-
accomplishing a convenient trasformation on cracovian
~
this trasformation has been accomplished, cracovian
contains ~
.!.
a) over the principal diagonal, the elements different
zero of cracovian
value i$ always 1
Once
0
from
A , except the diagonal elements whose
0
b) in and under the principal diagonal, the elements different
from zero of the transpose of
That is, supposing
o
a
n
a
=
h
•
3 , c~icovian
is transformed into
.!.
31
g21 g31
a22 a 32
h22 g32
a
h32 h33
21
23
a 33
In order to achieve this transformation, expressions (14-2)
.
(14-3)
I
and (14-4) have been changed into
=
r
a
~.
rs
0
2, 3,
Q
+ a
_. a - (a
a
+ a
<> a
+
'r8
r1 1s
r2
2s
0
0
0
( 15=2)
n+1
,
r, r-1
0
a
r-1,8
)
( 15-3)
starting from
r
=
2
and
8
= r,
r+ 1,
0
Q
<>
,
n
o
= 15 =
/ 1'?-.
----===-===";;CJiC4IW&ium==:a:
.....
I
1/
I
o
, j;
starting from
8
=
2
and r • 8+1,8+2, _,ItO, n+l
( 16-1)
By means of this procedure it is only necessary to keep craco vian
A. As explained in page 11, obtainment of unknowns
inmediate once the cracovian
is
A has been ,obtainedo-
The flow chart and program listing may
h~lp
the reader to
make
clear the whole procedure of decomposition and to study all the
possibilities of the programo-
o
o
=
16
=
I? 7
3 •. 2.2 FLOW CHART OF PROGRAM'
l
(General Solution of Linear Equations Systems)
m•
NUMBER OF UNKNOWNS
i ......
SYMMETRICAL
1
COEF FIC IE; NT S
NONSYMMETRtCAl..
COEFFICIENTS
o
.j +- 1
j +-1
J+- J + 1
Oij
+-
Oji
j+- j + 1
i +- i ..fa
<
<
<
<
1
.i+-i+l
o
=
==
Ma.......m
17
it;
WiUWAiUilUlli=====k:& h,4
,\Lana; "
, ..'!f.I4fA4 ,Hf.A .. Mf44T?TA&fMI£¥4RW ",..
o
i +-J + 1
ajl+-- ail 1011
J :: 2~ 3'.0" ...... ml
S4-- 0
J+--2
k+--l
ia+-J-l
+-- j
k'+- k + 1
i+-i + 1
OJ
s..--o
t
k4-~- 1
Qij .-COij
+ S}/Ojj
<
0ji4- Oji
+
S "'--_.IIC
o
=
18
=
{fC{
......-----t" Xi +- - Oml,i -
+-- m
J
~--,,'+-i-l
+-- m
s..
0
=
s~s
S
+
. 0"J I X·J
J..-J-l
;. 19 -
3.2.3. Program listing and
C
C
C
solution.~f
a numerical example
DECOMPOSITION OF A CRACOVIAN INTO TWO CANONICAL CRACOVIANS
AND SOLUTION OF GENERAL LINEAR EQUATIONS SYSTEMS
C
1
.
0
DIMENSION ~(21,26), X(26)
READ 100 ,M !
PRINT 101,M
M1=~1+1
.)
IF(SENSE S~ITCH2)2,4
2 DO 3 l=l,M
DO 3 J=I,Hl
READ 102, A(J,I)
3 A ( I , J ) =A ( J, I )
GO TO 6
4 DO 5 l=l,H
DO 5 J=l,Ml
5 READ 102,A(J,I)
6 IF(SENSE-SWITCH 1)7,15
7 PRINT 103
IF(M.... 6)8,8,12
8 DO 9 l=l,M
9 TYPE 104, I
TYPE 105··
DO 11 l=l,M
DO 10 J=1,M1
10 TYPE 102,A(J,I)
11 CONTROL 102
GO TO 15
12 DO 14 l=l,M
DO 13 J=1,~11
13 PRINT 102,A(J,I)
14 CONTROL 102
C
C
C
DECOMPOSITION OF CRACOVIAN A
15 DO 16 J=2,Ml
16 A ( J, 1 ) =A. (J , 1 ) / A (1 , 1 )
0020 J=2,M
IA=J-l
DO .18 I =J ,M
SaO.
DO ,17 K=::l I A
17 S=S-A(J,K~*A(K,I)
18 A(J,I)=A(J,I)+S
Jl=J+l
00 20 I=Jl,Ml
S=O.
DO 19 K=l IA
1
19 S=S-A (K, J~*A CI , K)
.
20 A(I,J)=(A(I,J)+S)/A(J,J)
= 20
=
{cr I
C
C
C
CALCULATION OF UNKNOWNS
I-H,
21 JaM,
.'_ SaO.
22 IF(J-I)23 t 24,23
23 S=S+A(J,I}*X(J)
. Ja:J-l
GO TO 22
24 X(I)=(-A(Ml,I)-S)
I F ( 1-1 ) 25 , 26, 25
25 1=1-1
GO TO 21
26 I F (SENSE
SWI TCH 1 )27,44
27 PRINT 106
.
I F .( M-6 ) 28 , 28 , 36
28 ONE-l.·,·
DO 31 l=l,M
TYPE 102,ONE
11=1+1
J==ll,M1
29 TYPE 102. A(J,I)
-00 29
o
CONTROL 102 " .
IF( I-M)30,32,30
DO 31 K= 1 , 1
30
31 TYPE107·
32 PRINT 108
DO 35 l=l,M
DO 3 3 J ==1 , M ,
33. TYPE 102,A(I,J)
IF(I-M)3Q.,44,34
34 CONTROL 102
DO 35 K=1, I
35 TYPE 107
36 ZERO=O.
DO 39 l=l,H·
PRINT 102,ONE
11=1+1
DO
37 J=ll,Hl
37 PRINT 102,A(J,I)
CONTROL 102 . I F( I ....M) 38,,40,38
38 00 39 K=l" I -,
0'
39 PRINT 102,ZERO
o
=
21
=
,12=====W4I.4liMh&JMAtUMi"",,· •.,.,. ""'
MailZA.t::,,.!,!'":·
40 PRINT 108
. DO 43 l-l,M
.00 41 J-I,M
41 PRINT 102,A(1 J)
IF ( I-M) 42,44, 42
42 CONTROL 102 .
DO 43 K-l, I
.43 PRINT 102,ZERO
44 PRINT 109
DO 45 l-l,M
45 PRINT 110,I,X(I)
PAUSE
GO TO 1
100· FORMAT (14)
101 FORMAT(/ll0HUNKNOWNS - 13)
102 FORMAT(El'.4) .
,
103 FORMAT(//25HCOEFFICIENTS OF EQUATIONSII)
104 FORMAT(4X2HX{,12,3H ) )
105 FORMAT (3X7HC •... TERMI I)
106 FORMAT(//11HCRACOVIAN GIl)
107 FOR~1A T( 11 X)
108 FORMAT(//11HCRACOVIAN HII)
109 FORMAT(/II0X8HUNKNOWNS/I)
110 FORMAT(2HX(,13,2H)-E".4)
END
=
22
=
11 '3
o
o
6
UNKNOWNS =
COEFFICIENTS OF EQUATIONS
xc
X( 1 )
2 )
x( 3 )
X( 4 )
~6518E 03 -.2392E 03
-.1196E
.9460E
-.9390E
.7420E
03
02
02
02
~5800E 02
.8867E
-.1922E
-.2260E
-.5150E
.3720E
.9460E 02 .1880E 03
04 -.9610E 03 -.2260E 03
04 .2439E 05 .4740E 03
03 .2370E 03 .4810E 05
03 -.2410E 04 -.2370E 04
03 .5920E 03 -.4030E 04
x( 5 )
.1480E
-.5150E
-.4820E
-.2370E
.7860E
-.1284E
03
03
04
04
05
05
X( 6 )
.5800E
.1860E
.5920E
-.2015E
-.6420E
.1585E
02
03
03
04
04
06
c.
TERM
-.4315E
-.1885E
-.8270E
-.1200E
-.5250E
-.3350E
03
03
02
03
02
02
CRACOVIAN G
.1000E 01 -.3669E 00 .1451E 00 .2884E 00 .2270E 00 .8898E-01 -.6620£ 00
.1000E 01 -.1069E 00 -.2170E-01 -.5529E-01 .2228E-01 -.3033E-01
.1000E 01 .1678E-01 -.2045E 00 .2588E-01 -.3198E~02
.1000E 01 -.4816E-01 -.4170E-Ot -.3935E-02
.1000E 01 -.8276E-01 -.4539E-03 .
• 1000E 01 ~.1880E-04
CRACOVIAN H
.6518E 03 -.1196E 03 .9460£ 02 -.9390E 02
.8823E 04 -.1887E 04 -.2604E 03
.2417E 05 ~2227E 03
.4811E 05
'.7420£
-.4877E
-.2472E
-.2360E
.7793E
02 .5800E 02
03 .3932E 03
04 .6256E 03
04 -.4048E 04
05 -.1289E 05
.1572E 06
UNKNOWNS
X(
X(
X(
X(
X(
X(
1)= .6715E 00
2)= .3079E-01
3)= .3225E-02
4)= .3957E-02
5)= .4554E-03
6)= • 1880E-04
'0
= 23 =
._£Milia
t ..io.'.i . LQU.. '
·.j~,il'
"
I
-.I
I
4.
SOLUTION OF NORMAL EQUATIONS SYSTEMS
4.1.'
Description of method
o -
o
Q
4.1.1. Obtainment of unknw.Dso
App~ication
of least sguares adjustment leads to linear
equations systems of symmetrical coefficients called "normal
equations systems·'. Although in this case it is also possible
to use the method of decomposition into two canonical cracovians explained in section 3, it is advisable to use
a spe-
cial method which provides the possibility to obtain the mean
square errors of unknowns in a very simple
waYo~This
special
method consists in decomposition of cracovian of coefficients
into two equal canonical cracovians and it is called "the cra
covian root method"o-
o
The system of error equations
v. =
0000 + g.oX
1
1
m + l 1.
(24-1)
i
=
1,2,0000 , n
may be written very conveniently in cracovia.n notation as
v
= x • 'ta
+
l
(24-2)
l
0
=
24
=
,.
"Iij
I ,~
,
,j
I,:'
in Which
b
•••
1
b2
:x.
=
•••
;~=
• • • •• • • • •••• ••
b
·...
n
Jntroducing the diagonal cracovian
o
=
• •• 0
(25-2)
• •••• • • • •••
o
()
in which the p. are the weight coefficients of observations,
1
it is obvious that cracovian expression
'':"'.
~
• [ (!;
0
I!J
0
.!J + t'
0
(Z5-- 3)
(.! • l!.)' = 0
represents the normal equations system deTived from system
-( 24-1).- Making the substitutio'ris
-a
L =
..
t
0
(!!
0
:e,)
(Z5-4 )
o
=
Z5 '=
£&&&&2?1klikU=: ;:;,,",# ,a: "A. ,uaat '11", ;,;"
_ I ..
g4AQG,.,#AMJ, ,. . !n:
i
I
expression (25 -3) becomes
x
•
o
A
=
L
+
0
(26-1),
Developing this last equation, the following system is
. ....,.
~
All· xl
+
A21 • xl
+
•
•
•
•
•
•
0
•
A
m~ 1 xl
•
AZ1 • x2
AZ2 • x 2
0
+
•
•
•
•
•
•
•
+
.0.
+
+
eo.
+
•
•
•
0
0
•
...
+
A
,m, 2.x2
0
0
Am , lox m + Ll =
Am , 2 0x m + L2 =
•
•
•
•
0
0
e
0
0
A
oX
m,m m
+
0
0
0
0
0
0
(26-2)
0
Lm =
+
0
0
where, in agreement with classical Gauss notation
All
=
[paa] ; A:21-- 'FpabJ
A:
22
o
'Arn, 1 = Ji>ag]; L 1=[ P a lJ
.00
= [pbbJ and so
rn'=m +1 and Li= Am' , i; then the normal equations system
Let
,
(~6
-2) may be enlarged and transformed into
A
Zl
A
m, ,
. •xl',+
A
2
+ •••
+
A21' . • x"l + A 22' ' .x2
+0 • 0
+ A m, 1.:
oX + Am' , 2
'
~
All
~
.x,+
•••••
A ,.,.
m ,
0' • • •
x,
0
+'A
•••
•x
0 •• 0
mt , 2 x 2
0
0
•
0 0 000
0
0
•••.
000
0
0
0
0
000
0
=
0,
=
0
0
(26-3)
= [pvv]
+00.
=
~
m' , 1
26
=
o
o
The la~t added equation,. equivalent to the known relation
[pal]' xl + [pbl] x2 +
•• , t
[pgl] ~ + .[ pi!] = [pvv]
will provide the very important control of [pvvJ as explained
later.- Introducing the cracovians
A
A
·A
A
, 11
21
22
21
x' =
x
m
A
•••
A
m, 1
,
m,2
m,m
m,2
m, 1
A
m' , 1
0
A
m' 1
A
At= • • • • • • • • • • • • • • • • • • • • •
A
A
A
• •• A
1
0
•••
0
C =
00.
0
m',m
f:pvv J
A
A ••• A
m' ,m m' ,m'
m' ,2
system ( 26 -3 ) may be wri tte-n as
x' • A'
{27~
.£
=
1}
CracovianA' may, be decomposed into tW{) e{fual canonical
cracovian's such that
A'
= B
B
=
B2
(27-2)
As cracovian At is symmetric, according to '2.11, page 6
o
=
27
=
tll!
#£4m.u.::aW::tI")#.#,,.,1. $ "
________
. ... ' ' ' ' ". . . . . "., .
-"----------------.w~~~-~--~~-------------~"'-""'''~
B
21
B
11
B
22
0
B
=
•
o • •
•
•
•
0
•
•
•
0
0
0
0
•
•
.0.
•
•
•
•
•
•
•
•
•
...
...
B
m, 1
B
B
m,2
B
0
•
•
0
0
mt ,'I
mt ,2
•
•
•
•
•
•
B
0
B
mt ,m
m,m
B
mt ,m'
0
The elements of cracovian B are obtained by applying the
definition of cracovian multiplication by means of the
following relations
Bl1
=
R,;
Brr
=
VArr
·r
=
B
=
rs
-
2»,,3,.
11
r1 •
Arl / All
2
2
Br2
(B rl +
o ...
...
=
r
000
+
2,3,
..
0
0
,
(28-1 )
m'
o
B2
)
r , r-1
, m'
(28-2)
00.
starting from
s = 2 and
r
=
s + 1,
OF- "-
0
(B • B)
(!o' • 'tB) • B
=
2~
000
,
m'
(lS-7J)
Introducing (27 -2) into (27-1)
x'
s +
- c
=
C
o
28 =
I
I
I
I
I ,I
!,
Multiplyng both sides by ~B-l
o
.. \
According to 2.7, page
this ex,Tession may be written
S,
as
• 1:8). ('rB -1 • ':i ~).
(.!. '
(!.;' • ?;'B) • ~
= C •n -1
£.. 't'~-1,
=
that is
= . .£.
x' .?fB
')fB-
1
(29-1)
,/ then
C' •
-1
o
Bl1
• •• y 1 ,m'
o
o
• •• y 2 ,m'.
...
[pvv]
•
o
=
o
•
o
•
•
•
•
•
•
•
o
•
•
•
•
•
•
•
...
-1
Bm' , m'
.
o
=
29
=
"':.;UdlUUZ":',.$".WM.44., . ,.. ,%';.1.#
II
I
I
Developing (29 -1 ) , the following system· is obtained
0
B11 • xl +
B21 • x 2 + • • • + Bm, 1 0x m +
B22 • x 2 + .0. + Bm,2· Xm +
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
0
•
•
Bm' , 1=
B
=
m" 2
0
0
•
0 •
Obviously, unknowns are obtained £rom
•
•
•
•
b~ck
•
•
•
•
•
solution of this
system and the last relation gives the sOhtrol
82
=
(pvv]
m!· ,m~
It is remarkable that cracovian of normal equations coefficients is equal to the square of
~Tacovian
o
of error equations
coefficients which is different from zero o Thus, it is always
possible to obtain the cracovian root in case of geodetic prQ
blems.4.1.2. Obtainment of mean square errors of unknowns,,Mean square error of unit weight observation may be obtained
from
m
=
V[PVV] /
(n
-
m)
(30-1)
/y'n
-
m'
(30- 2)
0
or
m
=
B
m'
0
,Tn'
.
o
=
30
=
I,'
I:
I
1"1
o
Weight coefficients are then used to obtain
m~an
square
errors of unknowns from
=
mo
VQii I
(31-1)
If F is a linear function of QnkJ:lowns such that
o
0
. 't"'.,
F
o
The normal equations
= x
+
0
f.x
m m
(31-2)
;: ..
f
(31-3)
sr~"tem" i . c"as'e:"of
uniform weight
opservations may be writt"en:f as
(31-4)
x
Multiplying
bo~h
sides by (!?) -1
+ (t
0
a)
2 _1
0
(~)
o
= 0
(31~S)
(31-6)
o
=
31
=
/
===I4.LM"S"MmeJklMltUu(.· ," \ @¥Ph?, ,.PMg
.,WM ",- ..~~
'I
I
".
o
Introducing this value of x in (31 - 3)
F
= {-
F
=
..
Application of law of errors propagation leads to
m2
F
= m02
o {
= m02
o
= m02
· {fi·
f.era
- (a- 2) -1
-
0
(fr -L (.!,2-1
)
0
o
] }2
?:a J~ f}
- -
(.!,2)-1]. f }
This expression may be written as
o
(32-1)
To obtain the mean square error of xi it is only necessary
to stablish F = x. , that is
1
0
0
f.=
1•
•
0
1
in i-th row
0
o
=
32
=
Expression (32- 1) becomes
o
m
x
=
m
=
m0
0
~-1)
JCf.
-1
f.
. -1
i
~
11
This means that weight ~o-efficient of i-th unknown_is equal
to the element of the inverse of cracovian of coefficients
'which stands in the i-th row and column, that is to say that
diagonal elements of the inverse of cracovian of coefficients
are the weight coefficients of unknownso-
0
1
,,~
Calculation of thtse elements is made in a very simple way by
,
calculating first the inverse of the cracovian root of A
because
=
(53=1)
and obtainment of the inverse of a canonical cracovian is
inmediate .. Let
Q=
B- 1 ; then, the ernements
orr =
lIB
Drs =
o
of
0 are obtained from
rr
if
r s
rs =
startin from r =1 and
D
o
=
33
s
=
r
+
1, r
+
2,
000,
m
=
====.iTAa.,,::.:::
~;,HiWiA#.@~.¥.
¥"P;'P. - - "
4.2.
Tb.e program
4.2.1
General organization
o
In order to save core storage, the program has been developed
in such a way that it is only necessary to keep coefficients
0\£
normal equations in and over principal diagonal by means
of an unidimensional arrayoThe correspondence in nomenclature is
in which
In
t
=
r + (s -
1) (m + 1 - s/2)
the first part of program, the CRi are transformed into
o
the elements of cracovian root and the unknowns are obtainedo
In the second part, the CR i are again transformed into the
elements of the inverse of cracovian rci'ot and the mean square
errors of unknowns are calculatedo'\
Flow chart and program listing may help the reader to
understand better these short
=
34
explan~tionso
=
o
I.•
4.2'.'2
>
FLOW CHART OF PROGRAM
II
(Solution of Normal Equations Systems)
o
m = NUMBER
nobs =
"
OF
..
UNKNOWNS
OBSERVATIONS
CONOITIONATEO
OBSERVATIONS
INDEPENDENT
OBSERVATIONS
o
ml+-m'+ 1
m2+- 2.ml
nx... (m+l)(m+2)
nx = NUMBER
OF COEFFICIENTS OF NORMAl.
EQUATIONS OVER PRINCIPAL DIAGONAL
!
CR1+-V CR1'
CRi 4-- CRi/CRl
o
i=
2.3,: ..... ml
_a=-Wi.tUnk a:U$MM4A 7A .. ,,%4&,9&&.¥;::O,
i..--i+l
k~k+
J ..
1
o
2
i2 +- (l-l){ m2 -.e) /2
i<1 +-- i +i2
ka '--J+i2
i
CRk.-CRk - CRkl· CR k2
,,2, ........ i 1
J
'II
.e=
k+- i +(J ... l}(m2-J) /2
k3+-k
il +- i-I
<
kl4- i .. (1-1 )(m2-f)/2
CRk+-CRk -(CR kl)2
.e=
o
',2, ......... il
J4--J+l
CR k1--
VC'Rk
<
=
36
=
o
o
i.~---m
J4
..-__----1.-
k+-ml til
kl4-- i
+ il
m
i 1 +- (i -1)(m2-i)/2
A4
0
i.-i-l
k+-J+il
mo+- CRnx/Rn
A+- A+ CR k • X j
m0;:
MEAN SQUARE fR
OF UNIT WEIGHT oeSER
J+-J-l
o
=
37
=
2-O?
;===£M&@ ':,,"421 1m .M#¢R.
,"
,**4-.,1----'·
o
i+--i+l
i 1 .... (i -
1)(m2-i)!2
k +-- i + il
o
J<4-J .. l
k+-k .. 1
i2+-J -1
ka4-Jt (J-l)(m2·-J),I;
A4-0 .
kl+J +(t.. l )(m2-~)/2
ka-.e+ it
A.- A-CR k1 .CR k2
~ ;'j,
i +I............ i ~
=
38
=
o
I".J
8
0)
..-----ooot~M m6CR nx/JnobS-m'
~,
~~
1
k +--ml
H
i.
1
i•
~
.
~
H
A~
1
0
mX4--mo.~
H
i
J~
..
PRINT
~
A4
0
"A + (CR
..
Xi
2
t
mx, CR k
e)
i+- i +1
,
ml+--ml-l
4~
.e +--.e+ 1
k4- k+ ml
J'-J+l
'H
J ::m
<
<
i::m
=
=
.. ,
CR,,+-- A
PRINT
mo
H
.e+-~+ 1
..
,
i :: m
0
<
=
=
39
=
2/0
AWA_===IUkUW;:::m",a",,:t,,1I tui..,,;,. ,
",
.#!ifdLffw.;;;;
,--1.'; .,.14
~
I
'I
4.2.3. Program listing and solution of a numerical example
CRACOVIAN ALGORITHM FOR SOLVING NORMAL EQUATIONS
6-11-65 * PDQ FORTRAN
C
C
C
o
DIMENSION CR(496)t X(30)
IF(SENSE SWITCH 2j2,3
2 READ 100,H
PRINT 112
TYPE 100,~1
GO TO 4
3 READ 100,M,NOBS
PRINT 103,M,NOBS
4 M1=M+l
1
~12=2*Ml
5
6
7
8
C
C
C
9
NX=(M+2)*(M+l)/2
DO 5 l=l,NX
READ 101,CR(1)
IF(SENSE SWITCH 1)6,10
PRINT 106
1F (~1-6 ) 7 t 7 , 9
DO 8 1=1 ,~1
TYPE 107, I
TYPE 108
EXECUTE PROCEDURE 300
CRACOVIAN ROOT
Q
10 CR(l)=SQRT{CR(l»
DO 11 1=2,Ml
11 CR(I)=CR(I)/CR(l)
J=2
12 I =J
K=I+(J-1)*(M2-J)/2
K3=K
11=1-1
DO 13 L= 1 11
K1=1+(L-1'*(M2-L)/2
13 CR{K)=CR(K)-CR(K1)**2
CR(K)=SQRT(CR(K»
IF(J-M1)14,17,14
lL~
15
16
17
18
1=1+1
K=K+l
DO 15 L=~, 11
12=(L-l)*(M2-L)/2
Kl=I+12
K2=J+12
CR(K)=CR{K)-CR(Kl)*CR(K2)
CR(K)=CR(K)/CR{K3)
I F ( I -M 1 ) 14, 16, 14
J=J+l
GO TO 12
IF(SENSE SWITCH 1)18,19
PRINT 109
EXECUTE PROCEDURE 300
::; 40
o
=
?-/(
o
C
C
C
C
C
C
CALCULATION' OF UNKNOWNS
19 I=M
20 J=M
11=( 1-1 )*(M2-1 )/2
A=O.
21 IF(J-I )22,23,22
22 K=J+11 '
A=A+CR(K)*X(J)
J=J-l
GO TO 21
23 K=M1+11
K1==1+ll
X(I)=(-CR(K)-A)/CR(K1)
.
IF(I-1)24,25,24
24 1=1-1
GO TO 20
25 IF(SENSE SWITCH 2)26,28
26 PRINT 112
CONTROL 102
T=M
ECERO=CR(NX)/SQRT(T)
DO 27 1=1 ,M
27 PRINT 102,I,X(I)
GO TO 39
28
29
30
31
32
33
34
INVERSE
OF'CRACOVIAN ROOT
..
1=1
J= I
,
11=(1-1)*(M2-1)/2
K= 1+11
CR(K)=l./CR(K)
IF(I-M)30,33,30
J=J+l
K=K+l
12=J-l
K3=J+(J-1)*(M2-J)/2
A=O.
DO 31 L= I 12
Kl=J+(L-l~*(M2-L)/2
K2=L+ll
A=A-CR(K1)*CR(K2)
CR(K)=A/CR(K3)
IF(J-M)30,32,30
1=1+1
GO TO 29
IF(SENSE SWITCH 1)34,35
PRINT 110
Ml=M
EXECUTE PROCEDURE 300
o
==
41
==
._4UU:ni¢[(H4. ,,, ,"", ,4#
..
& &..... .4$¥ibffii¥4(1~''.r~
C
C
C
CALCULATI~N ~F
WEIGHT
C~EFFICIENTS
35 Lal
'. DO 3,7 l=l,M
OF
UNK~OWNS
o
AaO.
D~ 36 J==I,M
A-A+CR(L)**2
36 L=L+1
CR (L)=A
37 L=L+1
, 'T==NOBS-H
ECERO==CR(NX)/SQRT(T)
PRINT 112
TYPE 105
Hl-M+l
K=Ml
DO 38 l-l,M
EHX==ECERO*SQRT (CR,(K»
PRINT 102,I,X(I),EHX,CR(K)
Ml=Ml-1
38 K=K+~11
39 PRINT "',ECERO
PAUSE
GO TO 1
BEGIN PROCEDURE 300
IF(M-6)40,40,47
40 L=1
DO 45 1==1 ,H1
D~41 J=I,Ml
T YP E 101 , CR ( L)
41 l=L+1
"
I F ( I -M 1 ) 42 , 46, 42
42 CONTROL 102
IF(M-Ml)44,43,44
43 l=L+1
"
44 D~ 45 K== 1 , I
45 TYPE 113 ,.
,46 RETURN 300
47 l=l
D~ 50 I a1,M1
DO 48 J==I,M1
PRINT 101 ,CR(l)
48 L=L+l " , , ',
IF(M-Ml)50,49,50
49 L=L+l
"
50 CONTROL 102
END PROCEDURE 300
II:
42 •
o
II
I:
0)
100
101
102
103
105
106
107
108
109
110
111
112
11 3
FORMAT(214)
FORMAT(El'.4)
-'
FORMAT(2HX(,13 2H)==E1'.4,2Et,5. 4 )
FORMAT(119HUNK~OWNS==14/13HOBSERVATIONS==1411}
FORMAT(5X10HMEAN ERROR 5Xl0HQ COEFF. II)
FORMAT(/32HCOEFFICIENTS OF NORMAL EQUATIONSII)
FORMAT (4X2HX(., I 2, 3H »
FORMAT (3X7HC.- TERMII)
FORMAT(/14HCRACOVIAN ROOTII)
FORMAT(/25HINVERSE OF CRACOVIAN ROOTII)
FORMAT(/19HMEAN SQUARE ERROR ==El,.4/1)
FORMAT(1110X8HUNKNOWNS)
FORMAT ( 1-1 X)
END
I
Q
o
= 43 =
.:====AtUmu":Jt6tt; n,.
"1"
T
....
".;;,.".# ..•.
.UNKNOWNS-
4
OB~ERVATIONSa
8'
o
COEFFICIENTS OF NORMAL EQUATIONS
x(.
x(
1)
2)
4)
X(
3)
X(
C. TERM
\
.1200E 02 - •. 2000E 01 - .. 4000E 01.0000E-SO - •. 2000E-01
~6000E 01
.0006E-50 -.2000E 01 .S600E 00
.2000E 02 -.7000E 01 .2020E 01
.1700E 02 -.2560E 01
.2176E 01
CRACOVIAN ROOT
.3464E 01 -.S773E 00 -.1154E 01 .0000E-50 -.5773E-02
.2380E,01 ~.2800E 00 -.8401E 00 .2338EOO
'.4311E 01 -.1678E 01 .• 4821E 00
.3671E 01 -.4233E 00
.1307E 01
INVERSE OF CRACOVIAN ROOT
.2886E 00
~7001E-01
.4200E 00
UNKNOWNS
.8186E-01
.2728E-01
.2319E 00
.S344E-01
.1086E 00
.1060E 00
- .2723E 00
MEAN ERROR
...
.
.'Or
.• 2044E
... 2842E
.,1667E
.1780E
X( 1)= -:.3154E-01
X( 2)= - ... 6540E-01
X( , 3)= - ... 6694E-01
X( 4)= .1153E 00
Q COEFF.
00
00
00
00
,
.9779E-01
.1890E 00
•. 6503E-01
.7419E-01
..
MEAN SQUARE ERROR ..
• 6537E 00
o
=
44
=
2/~
o
MRI PLarTER SUBROUTINES
by
David A. Bingham
Dean W. lawrence
o
o
&&2&&==4.=,$.l"r;~.,,,g,.,m"'r"''''''
$$ ._-- t.
$.#.-.;.':
o
MRI PLOTTER SUBROillINES
I NrR ODUcr I ON
This set of plotter subroutines is provided in the hope of eliminating much of the redundant effort that has apparently been expended in past
uses of the IBM 1620's on-line plotter.
The set is built around modified versions of the IBM-provided PLOT
and CHAR routines. The MRI versions of PLOT and CHAR offer the following
features:
Both can be used as LOCAL subroutines.
Changing directions of lettering the CHAR routine takes less
than 1/5 second.
The PLOT routine can be reinitialized without having executed a
CALL PLOT(7) statement.
The PLOT routine can move the pen to any location without
dropping the pen when the move is terminated.
o
New graphs can be automatically started above) below) and to
the left of the present graph (as well as to the right).
Up to nine unique characters can be used to plot points instead
of the standard + character.
The write-up on PLOT and CHAR is essentially that found in IBM publication No. C26-5841 with appropriate changes.
SUBROUTINE PLOT
The following definitions apply to the terms used in the description
of this subroutine. All X and Y values are to be expressed in inches.
1.
XMIN : : ; minimum X value to be plotted.
2.
XMAX
~
3.
XL
the required phYSical length of the plot in the X dire cti on.
=
maximum X value to be plotted.
217
0
o
4. XD = X increment to be indicated on plot outline
XMIN)/INC, where INC equals the number of increments desired.
= (XMAX
-
5 • YMIN 2. minimum Y value to be plotted.
6.
YMAX":' maximum Y value to be plotted.
7. YL = the required physical length of the plot in Y direction.
8. YD = Y increment to be indicated on plot outline
YMIN)/INC, where INC equals the number of increments desired.
= (YMAX
-
9. IC = control integer which must have one of the following
values: 1, 101, 201, 0, 9, 89, 90, 99, 7, 70, -7, -70. See "Use of Control Integer" under the specific Programming Procedure in question.
Choice of variable names for the above information is left to the
discretion of the programmer, except for the restrictions that the control
integer must be a fixed-point variable or constant and the rest be floatingpoint variables (with or without subscripts), constants or expressions.
Array names must not be used.
o
The first time the subroutine is entered, scaling factors are calculated and a plotting outline or grid is drawn governed by the control integer
IC. During subsequent entries into the subroutine, the X and Y coordinates
of a pOint are scaled and the point is plotted governed by the control integer. After all points have been plotted, the subroutine is reinitialized
for a new plot. In brief, the subroutine has three sections:
1.
Framing and scaling
2.
Point-to-point plotting
3.
Reinitialization
Each of these subroutine sections has a set of control integers (IC) to
govern the functions of the subroutine.
Framing and Scaling Section
In this section, two scaling constants are calculated and a plot
outline or grid is drawn governed by the control integer IC. The subroutine
calculates these scaling constants as follows:
o
218
",«IIMAI -. ;, i,e Lt...
.4.
4.,
&Fe'
XL
ex = X scaling constant = XMAX-XMIN
cy
=Y
scaling constant
o
= Y.MAX:~N
These scaling constants are then used to scale all X and Y values in the
point-to-point plot section.
After the frame is drawn the pen is placed in the up status.
Use of Control Integer
(Ie)
One of the following three control integers must be used in this
section:
Ie
=
1
Ie = 101
Ie = 201
o
When Ie = 1 is used, scale constants are calculated and a plotting
area outline is drawn (Fig. 1). When Ie = 101 is used, scale constants are
calculated and a grid over the plotting area is drawn (Fig. 2). When Ie = 201
is used, scale constants are calculated, but neither a plotting area outline
nor grid is drawn. (For efficient programming, set XD equal to XMAX-XMIN and
YD equal to YMAX-YMIN, when Ie = 201 is used.) The latter control integer is
used when a reference frame is already available or when one is not required.
219
o
o
7
XMIN, Y MAX
YL
YO
T
~--------XL----------~
X MAX, Y MIN
X MIN, Y MIN
c
Fig. 1 - IC
7
=1
X MIN, Y MAX
YO
YL
X MAX, Y MIN
X MIN, Y MIN
o
Fig. 2 - IC
= 101
220
A"W:;:«;; ,MS.•1I15hZ T,,,.lS4###
--~, "
·.,twx.- _.' ; .
1/
o
Point-Point Plot Section
CALL PWT (IC, ICHAR, X, Y)
This section of the subroutine first scales a given point (X,' y) to
a set of coordinates (X plot, Y plot) as follows:
X plot = (X-XMIN)
*cx
Y plot = (Y-YMIN) *CY
'Where CX and (J'f are the scaling constants calculated in the framing and scaling section of the subroutine.
Use of Control Integer (IC)
One of the following two control integers must be used in this
section:
NOTE: The pen always moves to the point to be plotted in the
status in which it was left (up or down) from the previous call.
o
IC = 0
IC = 9
IC = o. When IC = 0 is used, the point (X, Y) is scaled, the pen moves to
the resultant coordinate (X plot, Y plot) one of 9 characters is drawn through
the point. The pen remains down af'ter the character is drawn.
IC = 9. When IC = 9 is used, the point (X, Y) is scaled, the pen moves to
the resultant coordinate (X plot, Y plot) one of' 9 characters is drawn through
the point. The pen is placed in the up status after the character is drawn.
o
221
I..
O
~ll
I,
Use of Character Control Integer (ICRAR)
One of the following nine character control integers must be used:
POINT
REPRESENTATION
VALUE Of
ICHAR
1
+
2
e
a
m
't
~
5
•
0
S
x
7
.
S
,
9
Fig. 3
Pen Movement Section
CALL PLOr (IC, X, Y)
This section of the subroutine scales a given point (X,
(X plot, Y plot) as in the point-to-point section.
Y) to
Use of the Control Integer (IC)
IC must assume one of the following three values,:
o
IC = 89. When IC = 89 is used, the point (X, Y) is scaled and the pen moves
to the resultant coordinates (X plot, Y plot). The pen is commanded up when
the point is reached.
222
i==='UZklki";Z,MMiA,k.A'
.MM,."" .... qgn;mnm# .... .¥4.~.;.$$¥iif¥'I4- .... -
.. !.,.1
Ie = 90. When Ie = 90 is used, the point (X, Y) is scaled, and the pen moves
to the resultant coordinate (X plot, Y plot). The pen is corruna.nded down when
the point to be plotted is reached.
Ie = 99. When IC = 99 is used, the pen is commanded up.
takes place.
o
No other action
NOTE: If the pen up or dawn status is altered manually or by some
routine other than PLOT (for example, the annotation routine) Ie = 99 should
be executed prior to the resumption of point-to-point plotting. The reason
for this lies in the fact that PLOT is deSigned to keep track of pen up or
down status so that the pen does not have to be commanded to assume its present status. (One hundred ms are required for each pen up or down command.)
By executing an Ie = 99 call, as just described, pen up status is established
physically and within the program.
Reinitialization Section
CALL PLar (Ie)
After all points have been plotted within a frame, PLOT can be
called to automatically move the pen to a new position pripr to starting a
new frame. The following table shows the possible options available:
Value of IC
7
70
- 7
-70
calls.
o
Position to Which Pen
Will Be Moved
(XMAX + 3. 0", YMIN)
(XMIN, YMAX + 3.")
(XMIN - (XL + 3."), YMIN)
(XMIN) YMIN - (YL + 3."»
NOTE: PLOT does not have to be reini tialized with one of these
An alternative would be
CALL PLOT (89, X deSired, Y desired)
..)
CALL . PLOT (1,
These two statements would start a new frame at the point (X deSired, Y
desired).
223
o
o
PLOT PROGRAMMING PROCEDURE
Prior to calling the PLOT subroutine, the programmer m~ determine
and place in storage the XMIN, XMAX, XL, XD, YMIN, YMAX, YL, YD, IC, and ICHAR
information as previously defined.
Access to the PLOT Subroutine
The PIDT subroutine is accessed by the following statement:
CALL PLOT (IC, LlST)
where IC must be equal to 1, 101, 201, 0, 9, 89, 90, 99, 7, 70, -7, or -70.
LIST depends upon the value of the control integer (IC) as follows:
If IC = 1, 101, or 201, LIST must contain XMIN, XMAX, XL, XD, YMIN,
YMAX, YL, and YD as previously defined.
If IC
=
° or 9, integer),
LIST must contain IeHAB (the character control
X, and Y where X and Yare the coordinates of the point to be plotted.
o
If IC
= 89
If IC
= 7, 70, -7, -70,
or 90, LIST must contain X and Y where X and Yare the
coordinates of the point to be plotted.
or 99, LIST must not be used.
The actual names of the variables are unimportant as long as IC is
fixed-point variable or constant and LIST is made of floating-point variables, constant~ or expressions, except that array names must not be used.
a
Because of the makeup of the subroutine, the first time it is
entered the following statement must be used:
CALL PLOT (IC, XMIN, XMAX, XL, XD, YMIN, YMAX, YL, YD) .
where IC must equal 1, 101, or 201.
After the initial statement has been executed, the subroutine can
be entered at any time by one of the following three statements:
CALL PLOT (IC, ICHAB,
X, Y)
CALL ProT (Ie, x, Y)
CALL PLOT (IC)
o
224
wa., ;ax:.::aA, ;. J£U:'.144
.4", __,'~
I
i
o
III
III
V
III
III
III
/
III
'"
III
'"
I!J
III
III
1lI'/
a//
I!J~V
a~
IC
ICHAR
/
/
=3
C7
/
v
/
/
V
IC
V
V
/
V
V
.V
[::7
/V
V
V
V"
101
!CHAR
= If
o
Fig. 4 - Plotter Options
o
225
i
,~
I,
o
SUBROUTINE CHAR
This relocatable subroutine is titled CHAR. As a. subroutine, it
allows a FORTRAN II or FORTRAN II-D program to plot letters, numbers and all
FORTRAN special characters from information supplied by Format statements •
./
Program Description
The CHAR subroutine uses the typewriter I/O subroutine from the
When the CHAR subroutine is
called, it modifies the typewriter I/O routine to perfor.m the lettering function and restores it when the function is campleteo The position of the pen,
at the time CHAR is called, is at the lower left-hand corner of the character
to be drawn. Because the infor.mation to be plotted is obtained from For.mat
statements furnished by the programmer, actual variable values can be plotted
at object time.
FORTRAN II or FORTRAN II-D Programming System.
Each character that is plotted is represented in the subroutine by
a string of digits. These digits, when transmitted to the plotter, cause the
proper pen and paper motion required to dra.w the desired character. The same
string of digits is used for all character sizes and for horizontal or vertical displacement of the character. Horizontal or vertical pla.cement of characters with respect to the X axis is accomplished internally by the subroutine.
The conversion fram horizontal placement to vertical placement or fram vertical to horizontal, requires less th~~ 1/5 second.
When all of the specified characters are drawn, the pen is returned
to the starting position with the pen in the up status.
\
\
\
o
226
__
~_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _AAi_____
m:,11I'lI!iii.l!ll!!lliJiXii\lllla;!IIII/I!;::;""":!'-.•
'I'!l'.,!!III!'
, ::.U.ii!!llllU12ft1!.Itm"".!II"I¥"",.III!!II!_!!II!I
..
.1IIWi_P~
-!!!III!4!111MmM.,4!!!!11!1,JM2I1,
.--..
..,.-"..
-,-~-
..
...... .. ""-
,...... "
,
.•.. ..- - . - - - - - - - - - - - - - - - .
"",.•,.,
~.,,
·1
i1
:
1
o
ABCOEfGHIJKLMNOPGRSTUVWXYZ
.1 Inch Lettering
ABCDEFGHIJkLMNOPQRSTUVWXYZ
0123Lf-56789
-}
.2 Inch Lettering
o
Fig. 5 - Character Set
Programndng Procedures
Because of the design of the annotation subroutine, it must be accessed by the following two FORTRAN statements in the order shown.
CAIL CHAR (N, SIZE, lIN, VAAl'
V~--VARN)
The arguments in the call statement are defined as follows:
N
=A
fixed-point variable or constant e~ual in value to the number of
variables and/or constants (VAR) whose obj ect time values are to
be plotted as specified in the Format statement that follows the
Call statement.
Example!
If one variable (VAR l ) is to be plotted, N
227
1.
.0
C·'~
'I
SIZE = A floatinS-point variable or constarit equal in value to the size
(expressed 111 inche,s) of the characters to be plotted.
Example:
It characters are to be drawn two-tenths of an inch high,
SIZE
mY
= A fixed-po111t
variable or constant. I t mv = 0, characters are
drawn parallel to the X-axis, otherwise the characters are
drawn para.llel to the Y-axis.
v~ =
.
= 002.
Floating-point or fixed-point variables or constants whose values
are drawn at object time. The Format specifications to which
these variables are. drawn must be specified in the Format statement following the Call statement.
The Format statement used with the Call statement supplies 1ntonoation to the subroutine as to what 1s to' be drawn and under what Format specification. It 1s also used to calculate the correct return address trom. the
subroutine. It is, therefore, mandatory that a Format statement follow the
Call statement. The items in the Format statement are detined as follows:
o
S = A Format specification. The Format spec 1ticat10n( s) may not be
separated by a slash oD'T = The digit that governs which point character is to be used
(see character control integer in PLOT arguments). It
IPOINT is ze~, the actual. points will not be plotted.
XINCH
= The
value ot one physical inch in terms ot X-axis measure
XMAX-XMIN
"
XINCH =
XL
in terms ot the PLOT subroutine
arguments.
YINCH = The value
ot one physical inch on the
Y-axis.
GRAPH uses the second order Lagrangian polynom1al over X(K), X(K+l),
(When K+2 = J, the polynomial is also used to draw the curve between X(K+l) and X(J).) ihecurve is "
composed ot short line segments less than 0.1 inch long. The actual length ot
these segments 1s a variable that depends on the physical distance tram (X(K),
F.X(K» to (X(K+l), FX(K+l».
"
and X(K+2) to draw the curve between X(K) and X(K+l).
The tollowing assumptions are made tor GRAPH: (1) '!he points are
stored in either ascending or descending values ot X. (2) No two successive
values ot X are equal.
GRAPH uses about
14,374 positions ot core.
The tollowing "illustrations show the two types ot plots ava1labJ.e
when GRAPH is used.
23~
-
--""-------~-~"""--""----
-------"."-"_ .. -
"""--~~-.---"
..- " - -
o
()
o
Fig. 7
232
'I
II
o
SUBROUTINE IABEL (SIZE, XMAX,· XMm, XL,XD, YMm, ·YMAX, YL, YD)
SUBROUTINE IABELX (Same Arguments)
SUBROUTmE !ABLE (Same Arguments)
SUBROUTINE IABLEX (Same Arguments)
The purpose of these four subroutines is to place labels along the
X and Y axes drawn by the initializing call of the PLOT subroutine, i.e.,
(1)
where
IC
CALL PLOT (IC, XMIN, XMAX, XL, XD, YMIN, YMAX, YL, YD)
=1
or 101.
The arguments are the same for all four subroutines.
SpecificaJ.ly,
SIZE = The value of the character size expressed in inches (e.g., SIZE =
02 means all characters will be .2 of an inch in height)
XMm
XMAX
XL
YMm
YMAX
= Must
o
be exactly the same as used in (1)
YL
~} = The
same as used in (1) or integer multip1es* of' that value
All four subroutines will place numerical values adjacent to the "ticl! marks
on each axis. In addition LABLE and LABLEX read two cards; the first is used
as an X-axis heading and the second as the Y-axis heading. (Column 40 is assum~d to be the midpoint of the axis.)
'!he following chart shows the exact
distinctions of the four routines.
* If XD is the value used when PLOT is initialized, and 3.*XD is used as this
argument, then every third II tic" mark on the X axis will be labeled with
a value.
233
~
Name
Range of
Values
IABEL
-999 to 9999
IABELX
Any
Format of
Representation
14
MAX*
~
10
~
MAX < 10,000 ; 15
.1
~
MAX < 10 ; F5.2
10,000 ; ES.l
Axis
Headings
Core
Required
No
1402
No
2550
MAX < .1 ; ES.l
IABLE
Same
as
IABEL
Yes
2314
IABLEX
Same
as
IABEIX
Yes
3472
o
*
MAX = is the maximum of IXMAXI and IXMINI (or of IYMAXI and IYMINI ); e.g.,
if XMIN = -10 and XMAX is 0 then MAX = 10 and 15 format is used.
234
ES_MAMa:; Ii", " .. $II ..it.,,!,
-0
TIM£
CALL PLOT (1,0.,10., 5.,1.,0.,9.99, 5.,1.11)
CALL LABLEX (.1,0.,10., 5.,1.,0.,9.99, 5.,3.33)
9.99
8.88
7.77
6.66
5.55
t.....
.....
14-
't .......
2.22
o.oo~'--~--~~
o
__ __________ ____ __ ________
~
~
2
6
~
~
8
10
-rIME
CALL PLOT (1,0.,10.,5.,1.,0.,9.99, 5.,1.11)
CALL LABLEX (.1,0.,10., 5.,2.,0.,9.99, 5.,1.11);
Fig. 8
235
o
SUBROUTINE QUADRG (N, X, Y, A, B, C)
The subroutine QUADRG computes A, B, and C in the second-order. regression for.mula:
Y=A+BX+C~
X
= The
single-subscripted
Y
= The
single-subscripted array of dependent variable values
N
= The
number of (X, Y) values
arr~
of independent variable values
QUADRG requires about 2300 core positions and the single subscript
library subroutine.
This routine will be particularly useful. in plotter applicatioIl$.•
The regression curve can be plotted by the following sequence of statements:
:xJ'
= J*
DX
= (X(N)
Xl
= X(l)
- X(l))/XJ
CALL PLOT (99)
CALL PLOT
(90,
DO 10 I
= 1,
= Xl
+ DX
Xl
10 CALL PLOT
Xl, A+B*Xl.+C*Xl*Xl.)
J
(90, Xl, A+B*Xl*C*Xl*Xl)
* Where J
is sane suitable number that depends on the degree of curvature and
the physical distance between X(l) and X(N) or the plot.
236
SUBROUTINE LINREG eN, x, Y, A, B)
LINREG is a subroutine that computes the y-intercept, A, and slope,
B, of the linear regression line fitted to the points (X(I), Y(I)), I = 1,2 ... ,
N.
(That is, the linear least squares fit to a set of data points.)
X, the independent variable, and Y, must be Single-subscripted in
the calling program.
The running time of the subroutine is dependent on N, the number of
data points. Roughly, it computes about one second for every 15 data points.
This subroutine will be particularly useful in plotter applications.
The regression line can be plotted by the following sequence of statements:
CALL PLDr (99)
CALL PWI' (90, X(l), A + B*X(l))
CALL PLDr (90, X(N), A + B*X(N))
LINREG requires 1056 core positions and the single subscript library
subroutine.
237
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