Software Package for the Logistic Substitution Model

Nakicenovic, N.

IIASA Research ReportDecember 1979

Nakicenovic, N. (1979) Software Package for the Logistic Substitution Model. IIASA Research Report. IIASA,

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SOFTWARE PACKAGE FOR THE LOGISTIC SUBSTITUTION MODEL

N. Nakicenovic

RR-79- 1 2 December 1979

Work carried ou t under a grant from the Volkswagenwerk Foundation

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS Laxenburg, Austria

Resrarclr Rcporrs, which record research conducted at IIASA, are independently reviewed before publication. However, the views and opinions they express are not necessarily those of the Institute or the National Member Organizations that support i t or ol'the institution that sponsored the research.

Copyright O 1979 International Institute for Applied Systems Analysis

All riehtr reserved. No part of this publication may be reproduced or transmitted in ;Iny lorn1 or by any means, electronic or mechanical, including photocopy, recording. or any information storage or retrieval system, without permission in uriting irom the publisher.

SUMMARY

This report describes the computer program designed t o generate thc clynamics of market substitution of products and technologies. The report includes a simplified description of the substitution model but does not go into dctail about the nlodel. the results achieved by using it, or thc mc'tll- odology of the analysis: this manual should be iiscd in ionjilnction w ~ t ~ i the report o n energy substitution (Marchetti and Nakice~iovic. R R-79- 13 ).

Tlle computer program is interactive: it prompts :he user. and tllc user responds with parameters affecting the course of t.r,)granl execution. Input data (usually liistorical) are organized as time s;.ries. Model coef- ficients can be directly estimated by the program. o r tl1c.r. can be assumed beforehand. Model results can be projected for any spe\:if!ed time inttrval. An output file can be generated containing all inforr:ztion pertinent t o the results obtained. These results can be plotted c l r i . linear o r semilog scale.

PREFACE

One of the objectives of the Energy Systems Program of the International Institute for Applied Systems Analysis (IIASA) is t o improve the method- ology of medium- and long-range forecasting of the energy market and energy use.

This is commonly accomplished by using models that try t o capture and put into equations the numerous relationships and feedbacks char- acterizing the operation of an economic system o r parts of it. Such an approach encounters many difficulties, which are linked to the extreme complexity of the system and the fairly short-term variation of the param- eters and even of the equations used. Consequently, these model? lend themselves to short- and perhaps medium-range predictions, but usually fail to be useful for predictions over a period of about 50 years, the time horizon the Energy Systems Program has chosen for study.

Following the current scheme of attacking similar problems in the physical sciences, we have left aside all details and interactions and have attempted a macroscopic description of the system via the discovery of long-term invariants. Heuristically, this approach is certainly not new. In a broad sense, all science can in fact be seen as a systematic search for invariants.

This work is dedicated to the empirical testing and theoretical formu- lation of a certain invariant, namely, the logistic learning curve, as it applies t o the structural evolution of energy systems and systems related t o energy, such as coal mining, for example.

The great success of the model in organizing data of the past, and the insensitivity o f the structures obtained t o major political and economic perturbations seem to suggest that this invariant has great predictive power.

This Research Report represents only part of the work done in this area at the International Institute for Applied Systems Analysis, under a grant from the Volkswagenwerk Foundation, of the Federal Republic of Germany, for exploring the potential of logistic analysis in describing energy systems. The work is completely documented in an Administrative Report to the Foundation, The Dynamics o f Energy Systems and the Logistic Substitution Model, by C. Marchetti, N. Nakicenovic, V. Peterka, and F. Fleck (AR-78- 1 A,B,C; July 1978).

The present paper describes the computer program designed to gen- erate the dynamics of market substitution; it is a manual that includes a complete FORTRAN source code as an Appendix. Although a simplified description of the logistic substitution model is also given, the paper dis- cusses in detail neither the model nor the results or the methodology of the analysis. It should be used in conjunction with the descriptive part of the analysis (AR-78- 1 B) reproduced in The Dynamics o f Energy Systems and the Logistic Substitution Model, by C. Marchetti and N. Nakicenovic (RR-79-13).

As for the theoretical treatment in AR-78-lC, by V. Peterka, a new issue of Macrodynamics o f Technological Change: Market Penetration by New Technologies (RR-77-22) is available. F. Fleck's contributions on the regularity of market penetration are part of his forthcoming doctoral dissertation at the University of Karlsruhe.

1 INTRODUCTION

This report describes the computer program Pene.r that was designed to generate the dynamics of market substitution. After formulating the phe- nomenological model of market substitution, our primary goal was to analyze as many substitution examples as possible, in order to gain a better understanding of the substitution rule and also in the hope of learning something about the exceptions t o this rule. Each of these examples involves considerable data handling and considerable calculation effort, especially if the model is projected over long time intervals. Thus, it was obvious that the model in its initial form had to be implemented on a computer.

The program itself is designed in modules, each having a distinct function, so that it was possible to add new subroutines and modify or delete existing ones as the model evolved, or if necessary for some special applications. Thus the structure of the program is quite flexible, allowing the application of the program to any substitution process, even though it was designed primarily to handle energy substitution behavior.

The computer program was designed for interactive use; however, it can be also used in batch mode. It gives prompts t o the user, and the user responds to them with parameters affecting the course of program execu- tion. In batch mode, an input file called "Cards" controls the program execution.

Input (historical) data are organized as time series, one series per record, with a logical record number and name. They can then be used selectively in the program by identifying the desired record number and the program responds with the appropriate record name; this avoids pos-

sible confusion if an incorrect record number should accidentally be chosen. Model coefficients can be estimated directly by the program, read

from the coefficients input file, o r explicitly specified during the program execution. Finally, the market substitution simulation (projection) by the model can be conducted for any desired time interval whether it overlaps with the historical one (i.e., time period for which data are available) or not. At the end, an output file that contains the results and the input data can be generated, and all of this can be plotted on a Linear or semilog scale.

A simplified description of the model is given in the next section. This report does not go into the details of the model; these may be found in The Dynamics of Energy Systems and the Logistic S~i ts t i tu t ion Model (Marchetti and Nakicenovic, 1979). Next we will describe the Input and Output file structure, shown in Figure 3, and then we will deal directly with the computer program itself and its nine subroutines. Section 6 gives a colnplete description of all input information (see Figure 4) necessary for program execution, and, finally, Section 7 offers a simple tutorial example.

2 THE LOGISTIC SUBSTITUTION MODEL

Substitution of a new way of satisfying a given need for the old way has been the subject of a large number of studies. One general finding is that almost all binary substitution processes, expressed in fractional terms, follow characteristic S-shaped curves, which have been used for forecasting further competition between the two alternative technologies or products, and also for forecar-cing the final takeover by the new colnpetitor.

One of the most notable models of binary technological substi- tution was formulated by Fisher and Pry (1 970). This model uses the two- parameter logistic function to describe the substitiition process. The basic assumption postulated by Fisher and Pry is that once substitution of the new for the old has progressed as far as a few percent, it will proceed t o completion along a logistic substitution curve

j'1( 1 - f ' ) = exp(at + 0)

where t is the independent variable usually representin: some unit of time. a and 0 are constants, f is the fractional market share of the new competi- tor, and I - f that of the old one.

In dealing with more than two competing technologies. we have had to generalize the Fisher-Pry model since logistic substitution cannot bc preserved in all phases of the substitution process. Evcry given technology

undergoes three distinct substitution phases: growth, saturation, and decline. The growtl phase is similar to the Fisher-Pry binary logistic substitution, but it usually ends before full substitution is reached. I t is followed by the saturation phax , which is not logistic but which enconi- passes the slowing of growth and the beginning of decline. After the saturation phase of a technology, its market share declines logistically.

We assume that only one technology saturates the market at any given time, that declining technologies fade away steadily at logistic rates unin- fluenced by competition from new technologies, and that new technologies enter the market and grow at logistic rates. The current saturating tech-. nology is then left with the residual market share and is forced to follow a nonlogistic path that connects its period of growth t o its subsequent period of decline. After the current saturating technology has reached a logistic rate of decline, the next oldest technology enters its saturation phase, and the process is repeated until all but the most recent technology are in decline.

In effect, our model assumes that technologies that have already entered their period of market phaseout are not influenced by the intro- duction of new ones. The deadly competition exists between the saturating technology and all other technologies.

Let us assume that there are n competing technologies ordered chro- nologically in the sequence of their appearance in the market, technology 1 being the oldest and technology 11 the youngest. Over a certain historical interval we estimate the coefficients of the logistic functions for the tech- nologies in the logistic substitution phases. Historical periods we have investigated range from 130 to 20 years; the substitution process can be simulated, however, over any desired time interval, which need not overlap with the historical period. Let us call the beginning of this interval tB and the end l E .

After the coefficients have been estimated by the ordinary least squares (OLS) method i11 the subroutine Fit1in.f (see section 5 and Figure S), we have iz equations:

f i ( t ) = 1/[1 + exp(-a,t -p i ) ]

where i = 1 , . . . , n and where a,. and pi are the estimated coefficients. Now we identify the saturating technology, j, as the oldest technology still increasing its market share. The nrarket shares are then defined by

f , ( t ) = 1 / [ I + exp(-ait - Pi)] for i # j and

f,(t) = 1 - C f i ( t ) I # I

At this time technology j is in its saturation phase, and all other technolo- gies are either growing or declining logistically.

Now we need a criterion for the end of the saturation phase and the beginning of decline for technology j, at which point the function fi(t) will once again become logistic on its way down and the burdens of satu- ration will fall on technology j + 1. To establish this criterion we use the properties of the function

If j;.(t) were logistic, yi(t) would be linear in t. However, for G(t) in its saturation stage, the function yi(t) has negative curvature, passes through a maximum where technology j has its greatest market penetration, and then starts down. The curvature diminishes for a time, indicating that f i(t) is approaching the logistic form, but then, unless technology j is shifted into its period of decline, the curvature can begin to increase as newer technologies enter the marketplace. Phenomenological evidence from a number of substitutions suggests that the end of the saturation phase should be identified with the time at which the curvature of yi(t), relative to its slope, reaches its minimum value. We take this criterion as the final constraint in our generalization of the substitution model, and from it we determine the parameters for the jth technology in its logistic decline.

In mathematical form, the criterion for termination of the saturation phase for technology j is

y,!'(t)/y;(t) = minimum

(note that y" and y ' are both negative in the region of the minimum). When the minimum condition is satisfied, we call this time point ti+, , the time of the beginning of the saturation for technology j + 1 , and we determine coefficients a and p for the declining phase of technology j from the relationships

aj = yj'(ti+ ,)

Then the next oldest technology j + 1 enters its saturation phase, and the process is repeated until the last technology n enters its saturation phase, or the end of the time period tE is encountered.

These expressions determine the temporal relationships between the competing technologies. They have been formulated in algorithmic form,

so that the interpretation of the subroutine Penetr.f (see section 5) that estimates the fractional market shares is straightforward. We call this algo- rithm Penetration; it is illustrated in Figure 6. Only time t and the esti- mated coefficients ai and pi extracted from historical data in subroutine Fit1in.f have been treated as independent variables.

3 INPUT FILES

Punch

The Punch file contains the time series, their names and logical numbers. The Punch file is compatible with the Norman's Bank program (Norman 1977). The Bank program can create and maintain the time series on a random file. Thus it can be used in conjunction with the Pene program t o generate, modify, and store the Punch file. Table 1 reproduces the primary energy inputs for the world from different primary energy sources from 1860 to 1974 in the Punch file format with documentation. The original data are from Schilling and Hildebrandt (1 977) and Putnam ( 1953).

The Punch file can be also generated directly by a simple FORTRAN program. An example of such a program is given in Table 2, and input and output files in the Punch file format are shown in Table 3.

Coe f

The coefficients file can be generated by the program Pene if the param- eters are estimated or read directly by the program from the Coef file. This file is compatible with Norman's Auto program (Norman 1977), which offers wider options than the OLS estimates of the Pene program. Thus the coefficients can also be read by program Pene if they were generated either by Auto o r by Pene in some previous run. An Incards file is generated by the program Pene when the option for the estimation of the coefficients is used. This file can be renamed and used as Cards file. Table 4 gives an example of a Coef file generated from the data given in Table 1.

Cards

Storing the program execution instructions on this file permits the omis- sion of the interactive mode of program execution. An Incards file is generated during each program execution, which can then be renamed and used as Cards input file if a repetition o r batchlike execution of a given program run should be desired. An example of a Cards file is given in Table 5.

4 OUTPUT FILES

Output

The Output file is generated with the original data, the estimated coeffi- cients and their t-statistics, the correlation coefficients, the variance of the estimates, and the estimated values. An example of the Output file is given in Table 6.

Incoef

When the coefficients are estimated in the program, the Incoef file is generated; it can be renamed Coef and used later as an input file (see Table 4).

Incards

Each time the program is executed, an Incards file is generated; it can be renamed Cards and used later to control the program execution (see Table 5).

Plotter

The Plotter output can be sent either to the Plotter or to a file name (chosen by the user); the file can be displayed or plotted later. Figures 1 and 2 give an example of Plotter output using the Punch file in Table 1 and the Cards file in Table 5.

5 PROGRAM PENE.R

This program was designed to be executed on the PDP 1 1/70 with the Unix operating system. The source code is written in FORTRAN.IV, so that the program could be modified for implementation in another system. With the exception of the plot subroutines, most modifications could easily be made. Figure 3 shows the file structure of the program Pene.r, and the complete FORTRAN source code is given in the Appendix. The program Pene.r consists of a main program and nine subroutines:

Main. f

The Main program reads the input files, generates the output files, and controls the course of execution in accordance with the execution pa-

rameters provided by the user. This is illustrated by the flowchart in Figure 4.

This subroutine converts the absolute values of the time series competing for a market into fractional shares and puts them into a work matrix.

Fitlin. f

This subroutine generates OLS estimates of the coefficients for each fractional time series and the time series of the sum of all absolute values. The flow chart of this subroutine is given in Figure 5.

Penetr. f

This subroutine uses the estimated coefficients and the algorithm Pene- tration t o estimate the fractional market shares for the period specified by the user. The flowchart of algorithm Penetration is illustrated in Figure 6.

Testtot. f

This subroutine uses the estimated fractional market shares and the es- timated coefficients of the sum of all absolute values t o estimate the absolute market shares and puts them into the work matrix.

Tduttot. f

This subroutine transfers the time series of the absolute market shares (original data) t o the work matrix.

Func. f

This subroutine calculates the coefficients from two given values of fractional market shares.

This subroutine plots the content of the work matrix - either the original absolute and/or original fractional market shares or the estimated absolute and/or estimated fractional shares are plotted.

Plo tlin. f

This subroutine establishes scale, axes, and labels for all linear plots.

Plot log. f

This subroutine establishes scale, axes, and labels for all semilog plots.

6 INPUT LINES

In the interactive mode the program supplies as prompts mnemonic names for program execution parameters. The user then assigns parameter values under the mnemonic names right-adjusted (only names and titles are left- adjusted) and enters CR (carriage return) when he is finished. If he wishes t o use default values for parameters, only CR is necessary (for names, default values do not exist; however, if an input line starting with a name should be omitted, $$$, left-adjusted, must be given). This section explains the parameter values and their meanings. Error messages are supplied before the prompts of the next input line. If it is possible t o correct an error, the program will correct it or repeat the input line in question. Figure 4 gives the flowchart of the program execution in response t o the parameter lines (see above under Main.f).

A. Title

Yarke t Pene t ra t i on by Y. Yak i cennv i c IIAS4 Vers ion 2n.Rj.78

g i v e one-l ine t i t le w i th in th is field *abso lu te un i ts*

Under this prompt a title (up t o 50 characters long) characterizing the particular application of the model should be given within the specified field: To the right, under *absolute units*, the units of the data under analysis should be given (centered). Appropriate conversion of the units should be given if the scaling option for the data is used (see parameter exp in the next section).

B. Parameter Line

plt frc t o t iy no d 3 t st pr t Dar s c a exp

Mnemonic Default Value

pit 0 0 - 1

1 frc 0 0

tot

iy

no

dat

Par

sca

Integer

Integer

Explanation

To plot Plot but do not draw or label the axis No plot Semilog plot for fractional market

shares Linear plot for fractional market shares Linear plot for summed fractional

shares Semilog plot for absolute market shares Linear plot for absolute market shares Linear plot for summed absolute

shares Semilog plot for summed absolute

shares Initial year expressed as positive or

negative difference from 1900 Number of points (cannot be greater

than 300) Original time series as fractions and

absolute values Only fractions Only absolute values No original data Estimated market shares as fractions

and absolute values Only fractions Only absolute values No estimated market shares No output file Output file is generated; zeros are sup-

pressed Output file is generated; zeros are not

suppressed Do not sum absolute values Sum only the absolute values Time-scale of standard length

(4 cm/50 years) Where n is an integer, time-scale will

be 1 + n/2 times standard length Data will be unchanged Where n is an integer, data will be

multiplied by 10**(n)

The parameters iy and no should be used with care: iy specifies the beginning of the time period to be investigated as the difference between this point and the year 1900 - e.g., 1860 would be specified as iy = -40, and 1940 as iy = 40. no determines the end of the time period under in- vestigation. The parameter value is specified as the difference in years from the initial time point iy, excluding the year 1900 - e.g., investigation of the period 1860 to 2000 is specified by iy = -40 and no = 140. Further- more, no is rounded by the program by default to the nearest half century. For example, iy = -40 and no = 1 1 1 would imply the initial year 1860 and the final year 1971 ; however, the program will by default change no to 140 making 2000 the final year. If this option is not desired 9000, should be added t o the desired value of no; thus iy = -40 and no = 9 1 1 1 determine the interval of 1860 t o 1971.

C. Parameter Line

w r i t e n u m b e r s o f d e s i r e d s e r i e s f r o m p u n c h f i l e : nu: nu2 nu; nu4 n u 5 nu6 nu7

Logical numbers of time series to be used in the model are to be given under nu1 t o nu7 (a maximum of seven separate time series can be entered). The program will respond by giving the number and the names of the time series extracted from the Punch file.

D. Parameter Line

e n t e r $ $ $ f o r d e f a u l t , v a l u e s o t h e r w i s e : d e f a u l t i y d nod

iyd stands for the initial year of the time series to be used, expressed as positive or negative difference from 1900. If the default option is used, the initial year will be the first year occurring in the time series.

The value entered for nod determines the number of observations of the time series to be used. If the default option is used, all of the observa- tions in the time series will be used.

E. Parameter Line

e n t e r : fi t o r e a ? c o e f ; t o e s t i m a t e 2 t o a M ' c h a n g e

To read the model coefficients from the Coef file (see Coef and Incoef files above), zero should be entered; this leads directly to G. Parameter Line. To estimate coefficients (provided option dat = 3 in B. Parameter Line is not used), 1 should be entered. The third option, entering 2, also leads directly to G. Parameter Line, but in this case all coefficients are set to zero.

F. Parameter Line

y e a r y e a r na nu

If option 1 is used in E. Parameter Line, the user must give the time inter- val for which the coefficients are to be estimated by typing in the first and the last years of this interval. nu and na stand for the logical number and the name of the time series in question and are provided by the program. The time intervals for different series need not be the same.

G. Parameter Line

i f you 30 n o t change,/ar l? c o e f g i v e S S S under namc name e q n y e a r f r a c t i o n year f r a c t i o n

This option offers the possibility of adding scenarios about the behavior of new competitions that may not be available in the historical data base. It can also be used to change the estimated coefficients. The name of the competitor and its logical equation number (eqn) must be given, together with the two desired fractionaI market shares (fraction) and the corre- sponding year. $$$ is typed left-adjusted under name in order t o go t o the next parameter line.

The exponential growth rate of the sum of a11 absolute values can be changed four times throughout the estimation period by entering total under name and 8 under eqn. year in t h s case denotes the beginning year for the new growth rate, and the growth rates should be entered under fraction (in fractional terms). The values entered will be displayed.

H. Parameter Line

Because of the possible changes of the coefficients in G. Parameter Line, the user must establish a chronological order of competitors. n stands for the number of competitors defined by the user in the previous steps, and nal to na7 stand for the names of these competitors. Directly under these names and the numbers displayed above, which denote the current chrono- logical order, the new sequence numbers must be given by the user.

7 TUTORIAL EXAMPLE

The use of the program Penex is illustrated below by the example of pri- mary energy consumption of the world given in the Punch file (Table 1). The Punch file, containing the time series with consumption levels of dif- ferent primary energy sources in million tons of coal equivalent between the years 1860 and 1974, is read by the program. The model coefficients are estimated over the whole historical period, and the file Incoef will be generated automatically (Table 4). An alternative nuclear energy penetra- tion scenario is included specifying a 1 percent nuclear share in 1970 and a 6 percent share in 2000. In addition, total primary energy growth is changed twice from the long-term historical growth rate estimated over the period 1890 to 1950. The annual growth rate is changed to 6 percent in 1955 and to 3 percent in 1970. The model estimates are generated only for the historical period of 1860 to 1978. Two plots are generated in the plotter file (Figures 1 and 2). The first shows fractional market substitution on a linear axis plotted in the summed form, and the second shows the absolute consumption levels plotted on the logarithmic axis. Incards and Output files are also generated (Tables 5 and 6).

In the example below, the lines marked "u" in the left column show user input lines; other lines are program prompts.

M a r k e t ? e n e t r a t i o n by N . N a k i c e n o v i c I IASA V e r s i o n 20.03.78

g i v e one - l i ne t i t l e w i t h i n t h i s f i e l d * a b s o l u t e u n i t s * w o r l d - p r i m a r y ene rgy s u b s t i t u t i o n bi l l . t c e u

p:t f r c to t iy n o da t es t prt par s c a e x p u 2 - 5 0 9 1 1 a 1 1 - 3

0 2 0 - 5 0 1 1 6 0 O 1 0 1 - 3 w r i t e s e r i e s n u m b e r s o n p u n c h f i l e : nu1 n u 2 n u 3 n u 4 n u 5 nu6 n u 7

u 1 5 7 d 1 4 5 7 8 0 0

5 s e r i e s a re read f rom p u n c h f i l e to l o c a t i o n s : 3 u 5 1 2 0 7

w o o d pt o i l na t -gas c o a l - t o t n u c l e a r e n t e r $ 4 4 f o r d e f a u l t , v a l ! ~ e s o the rw ise : d e f a u l t i yd nod

u S $ $ -40 115

e n t e r : 0 t o r e a d c o e f 1 t o e s t i m a t e 2 t o a d d / c h a n g e

u 1 y e a r y e a r 1 wood p t

u lab3 1374 1860 1974 y e a r y e a r 2 o i l

u lad0 1974 lboO 1974 y e a r y e a r 3 n a t - g a s

u 1660 1974 lab0 1374 y e a r y e a r 4 c o a l - t o t

u lab0 1974 1800 1374 y e a r y e a r 5 n u c l e a r

u Id60 1974 la00 1574

i H R O R * * * 2 o o s e r v a t i o n s f o r t h i s eqn t h e r e f o r e no s t a t i s t i c s , b o t h o b s e r v a t i o n s e x p l a i n e d

y e a r y e a r d t o t a l u 1800 1953

ldO0 1950 i f you do n o t c h a n g e / a d d c o e f g i v e S $ $ u n d e r name name eqn y e a r f r a c t i o n y e a r f r a c t i o n

u n u c l e a r 5 1970 0.01 2030 0.56 n u c l e a r 5 14'10 0.010000 2000 0.060000 name eqn y e a r f r a c t i o n y e a r f r a c t i o n

u t o t a l a 1955 0.36 1970 0.03 t o t a l a y e a r g r o w t h y e a r g row th t o t a l a 1955 o.Oo0000 1970 S.030000 name eqn y e a r f r a c t i o n y e a r f r a c t i o n

u Z Y P w r i t e s e q u e n c e numoers f o r 5 e q u a t i o n s :

1 2 3 4 5 6 7 wooa p t o i l n a t - g a s c o a l - t o t n u c l e a r

u 1 3 4 2 5 1 3 4 2 5 0 0

new s e q u e n c e o f e q u a t i o n s i s : 1 2 3 4 5 6 7

wood p t c o a l - t o t o i l n a t - g a s n u c l e a r

REFERENCES

Putnam, P.C. (1953) Energy in the Future. New York: Van Nostrand. Fisher, J.C., and R.H. Pry (1970) A Simple Substitution Model of Technological

Change. Report 70-C-215. Schenectady, N.Y.: General Electric Company, Research and Development Center. See also Technological Forecasting and Social Change 3:75-88, 1971.

Norman, M. (1 977) Software Package for Economic Modeling. RR-77-2 1. Laxenburg, Austria: International Institute for Applied Systems Analysis.

Schilling, H.-D., and R. Hildebrandt ( 1 977) Primarenergie - Elektrische Energie. Essen, FRG: Verlag Gliickauf.

Marchetti, C., and N. Nakicenovic (1979) The Dynamics of Energy Systems and the Logistic Substitution Model. RR-79-13. Laxenburg, Austria: International Institute for Applied Systems Analysis.

Peterka, V. (1977) Macrodynamics of Technological Change: Market Penetration by New Technologies. RR-77-22. Laxenburg. Austria: International Institute for Applied Systems Analysis.

Marchetti, C., N. Nakicenovic, V. Peterka, and F. Fleck (1978) The Dynamics of Energy Systems and the Logistic Substitution Model. AR-78-1 A,B,C. Laxenburg, Austria: International Institute for Applied Systems Analysis. Report prepared for Stiftung Volkswagenwerk.

TABLES AND FIGURES

TABLE 1 Punch file. World primary energy 1974.

1 wood p t 91 -40 1 1 317.000 317.000 317.000 jld.000 3ld.000 318.000 324.000 323.000 322.000 317.500 317.000 316.000 ~ 5 U . 0 0 0 307.000 304 .OOO L90.000 293.000 292.000 281 .OOO 276.000 275.500 201.000 259.000 257.050 235 .OOO 227.000 226.000 203.500 202.000 196.000 170.000 173.000 104.000 149.500 147,000 144.000 2 coal 115 -40 1 1 13Z.000 140.000 139.000 192.000 199.500 204.000 L07.000 273.000 273.000 390 .JOO 361 .500 362.000 4'99.505 4d7.000 509.000 751 .JOO 716.500 734.000 900.000 1b10 .a00 1057.000

1152.000 1215.000 1195.000 118d.000 1165.000 1177.000

952.500 997.000 1092.000 1417.300 1*03.500 150u.000 1405.000 1319.000 1431.000 1060.000 1733.000 1815.000 2200.000 2128.300 2306.000 2200.500 2220.600 2276.100

3 lig-coal 115 -40 1 1 2.000 2.000 2 .ooo 4.000 4.000 r.500 7.500 7 .500 7.000 9.500 10.300 10.000

14.000 15.000 15.000 24.500 25.500 25.000 35.500 36.500 jo.000 44.305 45 .000 47.500 j7.500 62.500 02.000 50.500 58.000 6j.000

102.J00 104.050 103.000 jo.200 107 .000 127.500

1Ud.000 19U.000 204.500 24d.JOO 240.000 244.000 200.400 272.200 273.d00 4 011 113 - j8 1 1

1 .3CO 1 .000 3.000 1 .do0 1 .500 1 .OOO 3.JOO 4.030 5.000 6.330 d.000 9.000

10.000 10.000 20.505 ji.500 34.300 3d.000 51.300 00.500 02.000 56.530 57.500 121 .000

152.300 221.000 232.005 207.000 290.000 314.300 ?bl.JJO 390.000 454.000 oj0.300 705.000 743.500

llj7.300 1222.300 1321.300 ~ J 7 5 . 0 0 0 2210.000 2414.300 jj90.930

inputs, by source,

0 0 0 0 0 0 0 0 , , , ,"------> I : o ~ - : o ~ u L i ~ L ~ - O Z U l O W * O N - G * U L . , N - - - 4 U # W h - - 0 O U - L k , - o n a a r r n a o , m - O G - G z . & G N - - - 4 a W - W w O w O O C N - w O W N O C W - -

UI

6 1 o J 3 o r o L ~ ~ S - ~ O ~ ~ - ~ ~ ~ O W ~ ~ ~ W I O ~ O C O - ~ W ~ - ~ - ~ * U I O ~ ~ ( P C ~ O V I O - ~ N + W ~ . * ) c " O ~ % = v O , . r C O O - , O w . . c . . . . . . . . . . . . . . . o . . . . . . . . . . y . . . . . . . . . . . . U C O O m u n ~ " , - + , - ~ O Y C O * 0 ~ 0 u 0 " 0 0 0 0 0 0 0 0 0 0 0 0 m C o G o G O o 0 G 0 ~ ' L o C O 0 O O G o ~ o o "

O r " C 0 1 - l r I I D r e P 5 0 1 ~ 0 0 0 0 0 0 G 0 0 C 0 0 0 0 0 k - 0 C ~ G O G O O O O O 1 0 O O G O O O O O O G O 8 + m v o 1 o ~ m l o t - r m m , - " 0 3 7 m O 0 0

0 0 0 0 0 0 0 G 0 0 0 0 0 0 0 0 0 0 , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 m U v " a m

L 1 B S P Y 0 O m 0 E o 1 0 C U 1 O ~ P O ~ a m r o o w ~ d - - - 2 - - " 0 - -

0 u r n 0 Y n

C L . a L U O N N O - 4 U # W N N - U I W N - - O I J L W C W U - 4 W N ~ ~ C ~ ~ C O U ~ O ~ - C V I L v I U I O m w N - O G V I N - C - O - 4 W - 4 U # N - - O G , - ~ C ~ ~ U B V O = C C u O N - ~ S - O - ~ ~ - ~ O O W N - G W N - W ~ ~ O - ~ ~ ~ V N ~ O - ~ ~ O ~ W O ~ ~ \ C ~ - ~ C ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 Y V 0 6 0 . L u I . . . . . . . . . . VI 0 u 8, ,- " a v o C O I D O , - Y " 1

- 2 0 ' . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - 4 0 0 0 0 G 0 0 G G - G O O 0 0 0 0 0 0 0 0

w 3 m 0 0 c W Y N O O C G O O O O O O O O O O O O ~ O O C O O O O G G O G G O O G O O O O O O O #

v Y 7 l a B O c O O O O O C 0 O O O O o O O O O O G t O O O O O G O O O O 0 0 0 0 0 0 0 0 0 0 0 0 -

A " C 0 0

u v a n V I

* - a 0 . 0

O * " O - m . o l

r , - 0 * a 1 7

m a I

0 m m

0 1 " - m - 0 1 0 0 1 r r " 0 3 0 . - B D 0 0

1 m r o x - 8 m

0 O I I D C . 1 T m a ., , - o r - *

1 r r 1 r , P B r o z ~ o o l m n 1 r - 0 0 0 0 X O I Y

,- Y X ? 8 1 - 0 0 v r l o - x a a v r - r o ~ a m = r

n B , - " o n " L!, m L I - 9 0 0 O U ~ O v - J l r u u > a r - r , - 1 0 n V I c . . a P v J " O % - P m a W - 3

" O a k - C D - - 1 , - k - y l k - c 2 Y - r . 0 k - " -3 ~n a a = , - a c 0 n y l m r a m z J " 0 - . B I , r - 5 - - 0 . C -D U 1 . I D - o - o c - - m a " w - 0 m

I D " " - 1 . O

O - ~ D ~ Y 1 - . . " Y W b. 0.1. Ut &. e, *,

W N - - a - 4 a U I \ L . o 1 5 w - O N a m m 0 . a C W . . . . . . . . . O G O O O O O O G 0 0 0 0 0 0 0 0 G 0 0 0 0 0 0 0 0 0

TABLE 2 Simple FORTRAN program.

rea l *8 t, for d imension f (300 ,7) , t (7 ) , fo r (9 ) format( i2 ) format (gad ) f o r m a t ( i 4 , x , a 8 , 4 i 4 / ( a f 1 0 . 3 ) ) f o r m a t ( S x , 3 h $ $ $ / / S x , 3 h $ $ $ / )

read (5 ,105 ) n read (5 ,106 ) ( f o r ( j ) , j = l , g ) do 3 j = l , n read ( 5 , 1 0 6 ) t ( j ) do 1 i = 1 , 3 0 0 read ( 5 , f o r , e n d = 2 ) i y i , ( f ( i , j ) , j = l , n ) no=i-1 i f (i.gt.1) go to 1 i y = i y i con t inue n i= iy -1900 ip l= l ib l= l do 9 j = l , n wr i te ( 8 , 1 0 7 ) j , t ( j ) , n o , n i , i p l , i b l , ( f ( i , j ) , i = l , n o ) cont inue wr i te ( 6 , 1 0 8 ) s top end

TABLE 3 Input and Output files for the simple FORTRAN program.

5 ci4,5crlo.2)) total 011 nat-gas coal nuclear 190J 412b.00 1301 4225.70 1902 4527.60 1903 4674.24 1304 jlod.dO lYo5 5529.06 lYoo 5650.34 1907 5392.76 l ~ b o 5637.dd l'ib9 b292.64 1970 6728.92 1971 b971.90 1972 7287.56 1973 7b21 .j4 1974 7091.34

I N P U T

O U T P U T

1 total 15 60 1 1 41Zb.000 4225.7b0 4527.600 4874.240 516d.300 5229.680 56Y7.060 0292.040 072d.920 6971.d00 7287.5d0 7621.540

2 311 15 00 1 1 1321.500 1402.000 1517.000 1652.000 17d4.500 1921.500 iUl4.500 Zbll.300 2854.500 3029.000 3179.705 3U26.bOO

3 n a t - p a s 15 60 1 1 013.dOO 005.000 729.500 793.000 364.500 925.000

1162.500 1295.000 1417.500 1513.300 15d3.700 1619.900

5 ouclear 15 00 1 1 3.350 1.7t0 2.653 4.2'40 6.300 3.060

iO.do3 24.uU0 30.320 42.600 57.280 76.240

TABLE 4

wood p t o i l n a t - g a s c o a l - t o t n u c l e a r t o t a l $40

Incoef and Coef files.

TABLE 5 Incards and Cards files.

w o r l d - p r i m a r y e n e r g y s u b s t i t u t i o n b i l l . t c e 0 2 0 - 5 0 9 1 1 8 0 0 1 9 1 -3 1 4 5 7 8 0 0

b r s 0 0 1 1500 1974 1600 1974 lb00 1974 loo3 1974 ld0O 1974 loo0 1 ~ 5 0 n u c l e a r 5 1370 0.313000 2000 0.060500 t o t a l d 1955 0.000000 1970 0.030000

0 0 0.000000 5 0.900000

TABLE 6 Output file.

d.RR2 3 . o a ~

a . a @ r 8 . R R 2 a .CQ1 a . t a 2 I . 0 W 0.E02 3 .~702 0.aRa a . r n ~ 3 a .za3 .I.aas d.0R1 3.AB3 a . 2 0 5 ?.BBb 'a.aea Q.Jd9 H.HRS I.PYI7 a . ZOO a . ads w . a t 1 a . a t i . 4 . B l 2 * . a t 4 4 . P l h 3.d17 ? , ? I 9 1 . 1 1 9 1 . 3 1 9 4.a21 1.122 'a.d.?3 d . i l 2 3 d.J23 1.a23 2.227 ?..129 a . 8 1 9 a . 3 3 2 4 . P l I " . d ? O

a . 3 3 1 9 . 2 3 1 m.837 r . a s q d . 8 4 1

'CE

TABLE 6 Corztirzued.

TABLE 6 Continued. VLAP r n f ~ l doon -1 r OIL r M A T - C A ~ ? C O A L - T O T ? Y U C L E A ~ r 1918 1 . v 3.18 0.V3b 1.58 a.217 2 . ~ 1 0 . ~ 3 9 8 . 0 6 a.aa8 1913 l .b2 3.43 a.asc 1.b2 1,213 2.50 e.328 a.88 0.010 1974 1 . b ~ 3 . ~ 0 a.442 1.6s *.ZIE 2.15 u.332 a . 0 ~ a.812

E Q N I 'CGD 0 1 I S : I . -J.?uO.lr 74,541 4e.2 n.990 VIR . d , a ~ i (-q4.a451 [ s3.51n1

i,3:1 3 d r l - C A I Ill r ?, i3ug . l . -96,SlM Re.2 . 3 , Q l Q VIP m -3.025 ( 58.6381 t-bB.bq81

TABLE 6 Continued. OIL

e.35 9 . 3 1 a.3a a . a * . 4 l a .42 a .uu 8.46 u.41 0 . 6 9 a.se d.52 8 - 5 4

COAL-TOT P MUCLLAI P

TABLE 6 Continued. OIL

1-51 1.56 1.57 1.58 1.59 l.bd 1.91 l.b? l.h2 1.62 1.63 l , b 2 I .b2 I.b2 1.61 I .b7 1 - 7 2 I. 78 1.10 1.w 1.97 z.a3 2.99 2 . 1 5 2.21 2.28 1.14 2.YB r.07 2.53 2.52 2.50 z.*q z.*r 2.45 2.43 ?.'I >,>a

WORLO - PRIMARY ENERGY SUBSTITUTION

1.0

3.0

0 .6

0.4

0 .2

9 .0 1050 1900 1950 2000

FIGURE 1 Example of Plotter output using Punch and Cards files.

WORLD - PRIMARY ENERGY SU8STITUTION

BILL- TCE

10

FIGURE 2 Example of Plotter output using Punch and Cards files.

PUNCH FILE COEF FILE CARDS FI LE

INPUT FILES ----- ----- ----- ---------

P R O G R A M P E N E . R

I DEV 77 (2' 1 I DEV I I D E V I

-------- -- I OUTPUT F l L E S T fi PROMPTS

I DEV (?) 1

FIGURE 3 File structure of the program Pene.r. 1. Cards file contains control parameters. In interactive use, DEV 5 (device 5) should be the terminal input, and prompts file should also be sent there; DEV 6 (device 6) should be the output to the terminal. Incards file has the same information and structure as Cards file.

2. These files are optional and will be read or generated in accordance with the control parameters. Incoef file has the same structure as Coef file.

b 8. PARAMETER LlNE

ENTER CONTROL VALUES

€.PARAMETER LlNE C.PARAMETER LlNE

SPECIFY WHETHER TO READ OR ESTI. NUMBERS OF TIME- MATE MODEL CO- SERIES TO BE READ EFFlClENTS P

FROM PUNCH FlLE

+ D.PARAMETER LINE- SPECIFY POINTS TO BE USED FROM TIME- SERIES

F.PARAMETER LINE I

SPECIFY INTERVALS FOR COEFFICIENTS

+ READ COEFFICIENTS FROM COEF FlLE

ADD SCENARIOS ABOUT NEW COMPETITORS AND/ OR CHANGE HISTORICAL

SPECIFY CHRONOLO- GICAL SEQUENCE OF

CALL PL0TLIN.F CALL PL0TF.F CALL PL0TLIN.F

V.DAT=l

L I : =EST=O.V.EST-Z LZ: =DAT=O.V DAT=Z

I

CALL PLOTL0G.F CALL PLOTF F +

CALL PLOTLIN F CALL PLOTL0G.F GENERATE CALL PLOTF F 1 OUTPUT FILE CALL PLOTLIN F - I I - I -

FIGURE 4 Flowchart of the main program: Pene.r.

FITLIN (fi(t), iyd, nod, ai, pi)

t, : = iyd + 1900

v( t ) : = log [ f i ( t ) / ( l .- f i ( t ) ) l w

a.* Js t la: =

t

,,&

RETURN < FIGURE 5 Flowchart of the estimation subroutine fit1in.f. var is the variance of y(t); t /a and t/p are t-statistics with t2 - t , - 2 degrees of freedom under the hypotheses a = O a n d P = O .

t,: = 1901 + iyo + no

t : = 1900 + iyo

+ f i ( t ) = 1/(1 + exp(-ai t -Pi))

v ( t ) = log [ f j ( t ) / ( l - f j ( t ) ) l

ai = y' ( t )

i f ~ ' ( t ) < 0 -4

FIGURE 6 Flowchart of the market substitution subprogram: Penetr.f (algorithm Penetration).

Appendix

FORTRAN Source Code

i t t a ~ . ~ ~ I L ~ ~ , F L A ~ , ~ ~ A ~ ~ , ~ ~ A F , ~ J A ~ , ~ s , I s ~ ~ A L , Y A T D T ~ ~ ~ T , T I T L ~ , ~ ~ ~ , F ~ ~ J I , T ~ G F ~ C ~ L T , ~ ~ T , F ~ C , T J T , ~ A T , L S T , F I T , F A ~ , S C I , E X P L O G I L A L ~ 3 ; l C

' i ; < q I r l ' i r : ( 7 ) , T * ( 7 ) , T J T L F ( 2 r ? ) , T Y P E [ ? , l P ) D n T r ~ ~ , I S 5 , ! L , T P ? l I D O l S C b ~ E L . / l H S , 3 ~ S ~ f ~ U H 1 1 1 1 1 2 . l : ) A T L I ; T ' T , Y r ~ B . , ~ * ~ r : / 8 L j ~ u ~ ~ ~ ,::.,e,/ I I A T L T V ~ E ( ~ , ~ I . , T V P F . ( ~ , ~ ) , T Y P ~ ~ ~ , u ~ / u n ~ ~ ~ c , u ~ ~ I O ~ , u h ( F ) / r b T S A: '57L, ! !T i . ,U : I , T S / U ~ ~ H S O , U. (LUTE,OH U h I , U H l S / CAT; F ~ ; v E , S V ~ F , ~ L U / U H F / ( ~ , ~ H - F ) , U P / U L T L P [ . , , Y F L Y ( I ) / ~ ~ ~ ~ T A R T I ' . G I 1 . E 3 P / C L T : F ? F ( I ] ,FO: I Z ) , F t l i ( 3 ) , f n W ( d ) , F @ R [ 5 ) , F O R ( ~ ) I F O R ( ~ ) , F O R t 8 )

h / + , G 1 7 , 7 ' , . , T 1 ~ . l ' r ' I F 1 i ' i ' ? ~ , ~ , A 4 ~ f ' , b X f ~ U * , ' ( I ~ ' , ~ ) ' /

C E L L 5;TTTL ( 6 , PIIT'] IT'] C A L L S : T r I I ( 4 , ' 9 , ;'".I C A L L s i l T I L ( 3 , . t r l i F ' ) C A L L S f TF ] L ( 2 , ' l ' ; 'nC,:S' l C A L I S !TF IL [~ ; I r C 3 i F ' )

r D 2 q A T ( 1 4 , I I , L ~ , U I u / ( 9 F l t t 3 ) J F ? ; " L T ( l : , k , ' E Q b n ' a t . S E w l i S ' , I 2 , .: I R . G ? . I P ' ) FOC. *&T ! A + , 1 3 , ' Y F L ~ L P O ~ T ~ ~ Y E A R G R O W T H . ) f O-'"AT ( 1 r , I?,' S E E I E S ARE C F A D F P O Y Pup.CH F I L L

b T C L ~ ~ Q T I ? : ! ~ : . / ~ ( ~ U , U X ) / ~ A ~ ) F f ; " L T ( ' d ; I r E ! . . J * ~ E K S OF C E ~ I R E D S E R I E S F R O M P U V C H FILE:.

& / ' ' ! I ] VJ: h1.,3 1.24 t.!J5 NLlb 1 4 ~ 7 ' ) F O R V L T [ / B x ; 9 n Q r ; f T D E t : E l f i A T l o ~ RY h, ~ A K I c E Y O V I C ' /

b l b X , . I I L S A V f P 5 1 ' 1 ~ ~ 2 6 . @ 3 , ? h * / ) F C a ' l l T ( l o , l x , b h , 1 3 / ~ 9 A 8 1 ) F O Q N j r T ( / ' P L T F R C TOT J Y ND D A T E S T P Q T P A R SCA E X P ' ) F D c M L T ( l l 1 U ) r n a r a r ( l x , ~ 2 , ' E O L T I C ~ S A P L ~ E n n F R O M COEF FILE

6 T ? L , ' ~ ~ I ~ ~ S : ' / ~ [ ~ U , U X ) / B I P ) F D s Y t . T ( ' d P I l f SF9 l lF : JCE 1.,J'lBERS F O P .

& , I ! , ' E c L I A ? J O ! ~ S : ' / ~ [ I U , U X ) / ~ A A ) F o r * n T ( 7 ( l ? , u X ) I FO;; , .~AT ( ' ' d ~ i S ~ L I ' J F : r~ OF ~ ~ ' , , r r ~ p r ; s IS:

a ' / 7 ( 1 ~ , i , x l / 7 A 5 ) F r ? f i r ~ l ( . I F YOU 7.L ' !PT C H A N T . E / A ~ D COEF G I V E $ 5 5 L lNDEF N A M E ' ) I O R * ~ L T ( ' b A 1 3 E ' , r i X , ' E l J f . Y F A ? F H P C T I G N Y E A R FRACTION*^ F o v V i r ( f i b , ~ 3 , 2 ( ~ 5 , r ~ . b ) ) F O L Y ~ T ( 5 ~ , ' E F e P Q E Q ' d ' , I 2 , ' S A M E T I T L E b S E O N * , I ? ~ ' : ' , A 8 1 F ~ F - L T ( 5 X , 'EFCCiK * * a E E l . ' , 1 2 , ' .G?.7') FGFf'AT ( .Ep4TES: 2 1 3 E E A D c O t F ' /

a 7x;l 7 : E S T I h r T L 0 / 8 7 x I ' 2 r n A D D / C H A I . G E . ]

F n a . i b T ( T 1 ) F C ~ " ~ ~ ( ~ 6 , 2 1 U 1 ~ ~ 1 4 . ~ , / ~ 1 b ~ ~ ~ ~ 1 ~ . 0 ) ) FOE:IAT ( ' Y E A K Y E b P ' , I 1 , l L , A R ) F f l R Y b ? ( T 4 , ; S ) F O F Y A T ( . ~ Y T E F $ s $ F D c D E F ~ u L T , V A L U E S O T H E R Y J S E : ' /

R ' D E F ~ I , ( T I Y C : ~ ( l n ' )

Main.f continued

1 2 4 F @ P Y L T ( L F , ? I u ) 12s r o n q A T ( * s s s * / / * * s c * / ) 126 F O d u l & l ( ' r r , l V f C I N E - L I ' J E T I T L F W I T H I h T H I S F I E L D '

b , ' e ~ b s 7 ; L I l E U p . I T S * * ) 1 ? 7 F r P Y L T ( 7 A R I 4 1 4 ) J 2 F F C ? ~ ~ T ( / / J ? I , ' C ~ E F F ~ C I F . N ~ S F H O E F I L E C O E F * / ) 1 2 3 T @ P ~ ~ T ( / ~ X , * L J I I * , I ~ , ' ' , ~ b , * I S : Y = ' , F 7 . 3 , ' * T * ' -

R , 4 # , A h , 1 5 / ! . F Q L ' ~ L T ( / / ~ ~ X , ' C ~ L F F I C I ~ I I T S C b T J M b T E t I k F I T L I I 4 . F . J F O i ' L T ( / S k , ' E f f ? r , - r r e hf l .GT.3PF * T R Y b G 4 I N e P / ( ; F O P ~ L ~ [ / ~ X ; ~ . ~ F ; I ~ - ' e r t LEOHL P 4 F b r E T E F S P E C I F I C A T ' N S

R , * * T ~ V A ~ ~ I I . * . / / ) F P R V h 1 ( / ~ x l a E B i ~ O C e e e * , I u , * . G T . ' , I ~ , ' * T R Y 4 G A * ' / / ) F f l R r r r ( / 5 k I a ~ a r o + r e * r : n r a . t a . ~ Nn OBSEPVATIDNS i A D . 1 F @ K ? . r T ( / ' E t . T E k D ~ T L S C A L I N ~ ; M L J L T I P L J C A T I O ~ F A C l O k , * ,

8 ' EIPO~,I~:T A ; . - L : K ~ T S IF c H ~ r r G t n : * / ~ ' F A C T C J ~ F k P * A R S O L ~ J T F U I d I l S * * )

F t P ~ l ( F b . O , ~ ~ , l X , U A 4 1 F O B E b T ( / 5 X I ' E ? F ~ l ~ : * r r S E F ~ t s ' , I 2 , * : N O L . G T . 1 5 V * T R V A G A I N * ' / / ) F(IPtI / .T( ' t + , ~ * g t R S At,i\ T I T L E S L)F S E R I E S O N P O N L h F I L E : ' ) F O ~ p L T ( l z ( I d , ~ r l ) F 5 P ' r L T ( I Z A P )

Main.f continued

r n r . ~ ~ . ~ I F ( ~ r G 1 : ) * + I T € ( 6 , 1 3 2 ) I F [ L C F I C I G C 7 3 5 6 S C A L ~ ~ = S C L L E X + F L ~ A T ( S C ~ ) 1 P r 2 r P n a PAW;: X l ' i r i C l ,

I F ( E X p , ~ T , 9 7 9 ) Gi' TCf 6 6 n S I T F ( h , 1 3 5 ) QFA3 ( 5 , 1 3 b l 1( ' l L ,EXI : , (TYPL ( 1 , J ) , . l = l ,(I)

1 ;:. I F [X ' " I~ IL .LE.~ . ) G O TO h 7 x r d L = u W j ~ / l : . I = 1 + 1 I F [X'IJL.C.T. 1.) G S 1:) 6 8 E x P = t r ~ + : * s l T ? ( 2 , 1 3 6 ) x Y ~ L , € x P , ( ~ v P i ( l , J ) , J = i , 4 ) D O 7: . ~ = l , u I F ( T I P F ( 1 , J ) . I J E . ~ L ~ I ) LT,GTCI.THLJE. 3 5 6 9 : : I ,* I c (LCI~TC) rr(J!:TYFF ( 1 , J ) TVI 'C[ I . . I I .bL3 v k I T r ( h , 13;) K Y u L , F X P , ( c ( J ) , JZI , U J IC ( I ' E l , F ; . . ) G r ; Ti) 57

C F E A " ~ Y F I ~ * L L DATA F a g 1 ? PUNCH f I L E

I F ( ~ ? A T . L T . J ? ? ' ) G O 1 5 7 5 M C 1 n m i d R I T E ( h , l 3 R ) D C 7 3 1 8 1 , 7 2 f iEA3 ( ( 1 , 1 3 2 ) ~ ! ! ~ , D L A ~ ~ ~ ~ , ~ ) , ~ ~ ~ I , I Y ~ , I P ~ , ~ R ~ ~ ( O ~ J ~ ~ ~ Y O ~ ) h1.t I F LA^('+,*) .F;.ISS) t . r 6 - l L ~ ~ . I C = K , E ~ . ~ ; . ~ ~ . O L A ! ~ ( I ~ , K ) . E G . I S S I F [ L O G I C ) * R I T E ( 6 , 1 3 9 ) ( J , J s l , N ) I F ( L D ~ l f l dfi1T.E ( 6 , 1 4 0 1 ( E L A B ( Y , J ) , J s ~ , N ) I F ( P L A ~ ( ' : , K ) . E ~ . I S S ] G C TO 7 4 I t r K + l I F (K. r .T , l? l 'I=+'+!

1 3 I F ( K . t T . l a ) K:l 7 11 R E A I L ? 4

Main.f continued

L L L L S ~ T ~ I L ( U ~ t i l i c b J * ; 7 5 WUITC ( h , l X '

P.EP! [ 5 , 1 : . ~ : I ( L ) , L = l , 7 ) *.CITE ( 6 , ' ( l ' L J ~ [ l l ~ , I l = i , 7 ~ * , P I T F ( 2 ( - ; 8 ~ u ( 1 2 1 , 1 2 = 1 , 7 1 1'; 1 I . ! . I F [ ~ , ~ ~ q ( I l .GT.?) ~ , '~ l : ; ' l b+ l DC I J : l , 1 5 T r ( l , J l = r . J: ' J = J + l P F L C ( a , I I : l ) ~ ~ ~ I , ~ ~ L I , ~ @ ~ ~ T Y ~ ~ ~ P I ~ ~ B ~ , ~ D ( ~ I I ~ ~ I ~ ~ I ~ @ ~ ~ IF (1P1..: .T.IFl) c = l T i . ( b r l ; ' l ) P'Ul I F ( ' T l . G ? . l S ^ ) * " I T E ( b , 1 3 7 ) 'd'il I F ( :?1. : ,7 .15;+) LC T ' ? 5 8 I F ( , , A 1 ,E;, l S 5 ) .:;? T C ' 2 < t .: DD 4 1 = 1 I F ( - , \ l f l ( I ) .E-~:.oll K = l I F (h,FZ," LCJ 1:' 5 D l 6 5 J 1 = 1 , 1 5 ' F ( J , J l j = ' ! ( l , J l l 1 ( r ) G Tr 6 5

: : ( l , J t ) z : . t Z: C?' T I \ ; l F

' : O ~ ~ ( J ) = ' 2 . ~ 1 ( J > : h L l

h C i ( J ) r r : 3 l I Y ( J ) = I v I G2 1 , 3

5 DC! 7 1 . I I C L , I S Z 7 1 L t l , J l ) = ? .

J - J - 1 ;3 T i 7

2 h 9 I T E ( 6 , 1 ; 3 ) ' lri, ( L , L : ~ , ~ ) I r 1 ~ L D ~ I ) , I = l , N G ) 1 v r ~ = 3 r ~ ~ "I?=< D'? 'b I = l , h t I X : ~ ~ S P + I V ( T ) * ( ~ Y ( I ) + I ~ ~ - ~ ) / I P D I v r = ~ ' l : i i ( I v D , I ~ ( 1 1 1 I :33=b'A~a( I : ' ,S l I X ) b r ~ : ~ + ( r i : j " - 1 9 0 : ~ - I Y I ) * I P D - I 6 ? + 2 "UITE ( 6 , 1 2 3 ) % E A C ( 5 , 1 2 4 ) ' A l ~ l Y l , ~ O l w ~ I T c ( ~ , 1 2 4 ) ' J A l , l V 1 , ' ~ Q l I F ( , . A l . C 2 , I S S ) I Y l = I Y ? I F ( I Y ~ . L T . I Y ~ ) I Y ~ = I Y P I F (tub1 ,L;,ISSl t~O lc f iOC) I F ( I V I . ; T . I V ~ + N O ~ ) l r i = I v n + r d o n I F ( ~ v l + ~ j n l . G T . I V ~ ) + ~ ~ D D ) r i n ~ = 4 3 n + 1 v n - 1 ~ 1 *R ITE ( b , 1 2 U ) E L , I V l , ~ @ l I v I = I v l 1vF:IYn I F ( I V ~ , L T , I Y D ) IYO=IYD I F ( I r n - ~ v n . ~ T . ? ) ~ ~ n ~ = t i n ~ + I r i l - I r O I F ( I vp - lY ; ,LT . i3 ) 1V@:IV? I I = 1 - l v n + I r ~ tiT)i)=HOt

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C ~ > c I I M L " . T A T I ~ ' . FGO14 ~ L J ' I C H F I L E

I F ( t x L t 1 . E [ i . ? ) G7 1 2 1 2 I F ( ' . A 1 . F G . I S S l $ 5 T I ! 1 7 It=.-

3i. 1: J Z ~ ,ri3 1 C I F ( , P ? ( J ) , E : . : ' n l ) r = J

I F ( 6 . F 3 . Z ) t 2 T!; R

T Y P E ( 1 , ? ) = T Y P E ( 2 1 2 ) T y P C ( 1 , 3 ) = T v ? E ( 2 , 3 ) T Y D L ( 1 , U ) = T Y ~ E ( 2 , u ) I' ( L T S T C . ~ : , ) . (F~:.EO.I .OR.FHC.EW))

& C A L L P ! n ~ ~ ~ ~ . ( l ~ ~ n t x , % ~ A ~ , x ~ I ~ , v ~ ~ x , Y M I ~ J , S C ~ L E % ~ ~ I T L E D T V P E ) IF ~ E S T . E : . ~ ) Cn r n 1 9

C w E n c : ! 3 E r F I C I E 1 4 T S F Q D M c O E F F I L E

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I F ( l r b ~ . ~ T . 3 . A t , ~ D . ~ i 5 L : . E o . , l G L I TO 4 2 IF [ r y T . c : . ~ ) G ? 1:' 4 1 I F (F1T.E'l.Z) 6 5 'q 4 2 JF ( ' I T , G T , ~ , O ~ . , F I T , L T . ! ~ ) WRITE ( 6 , 1 3 2 ) I F (FTT,;T,?,JK,FlT,LT.2) b? TO b 4 I F (P?T.Ej . l .JR.V7T,EO.2) * R I T E ( 8 , 1 2 6 1 1 1 =I 12=-' J:.'

1 3 J = J + l ~ E A J f 3 , i Z c ) J A ~ , ' . I I ~ ! T . ~ ~ C , l i ( L ) , ~ s l , N I : ) I F ( ! r & l , E 7 , I S S ] 6 0 T? 1 4 I F (P~T,';, l ,OL."ET.L3.2) * Q I T F ( 8 , 1 2 9 ) YU'lC,NAl, ( w ( L 1 , L = l , H C 1 W K I T C ( b , 1 ~ 9 ) r i ~ l ' l T . , I . r A l , [ 4 ( L ) , ~ = l , w C ) m = J DD 1 5 1=1,!4-

1 5 I F ( - i b l , E ~ . ! ~ ~ D ( l l ) K = I I F ( < . * J E . P ) 1 2 = T 2 + 1 I F ( n , r : E , p ) C.9 T r ! I h

I l ' l l + l K 3 ' 4 3 + 1 1 +4 = < I F ( , .41 .E?. .d~ '2T) K:? I F (b.1, 1.B) G ' ! 7 , ] h

I 1 = 1 1 - 1 NATZ' ;A l

16 ~ A F ( K ) s v A ~ I)?) 1 7 ~ z l , " C

1 7 COEF ( ~ , L ) = , . ( L ) I F (k,FC,B) K " G O Ti; 1 3

1 4 L F z 1 ; 3 + 1 i : J F * I l * I ? h E I T F ( 0 , 1 9 9 ) IJF, ( : 1 , 1 1 = 1 , 7 ) 1 ( ~ ~ b F ( I 2 ) r I 2 = 1 . 7 1 rr1AT

G O Ti? U ? 4 1 I F (PPT.ES. l .9k.PPT.ER.2) J U I T E ( R , I S B J

I F t l v i . L T . 1 2 ) I v ? = I 2 I F ( I V ? . L T , I V l l * I ? I T E ( b , 1 3 3 ) I V l t I V 2 I F ( I v ? . L T . I V ~ ) G? T f l b 2 N R I T k ( b , I ? ? ) 1 V 1 ~ 1 V 2 * R I T E ( ? , 1 2 ? ) I v l , I Y ? IYAF (I):'JL[)(I) CALL F I T L I ' J ( I , ~ V I , I V Z )

4 3 J R I T E ( l r 1 2 J ) Y A F ( T ~ , I ~ ~ , [ C n t F ( I , . l l , J = l , ? ) 7 2 t4RITE ( 5 , 1 2 1 ) h,!iATOT

READ ( 5 , 1 2 ? ) I Y 1 , I Y Z I l * l v ~ ~ + I v ~ l + ( I 3 3 - : ) /1:3r1 I F ( I v I . L T . I I ) I l l s 1 1 I F [ I v ? . ~ T . l i l I f ? = I i

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1 ? = 1 9 - , . + 1 VCl+ [~ l ! l - l+~ i . ,a - ,? ) / ]h, . l

I F ( !v l . ;T . I? ) I V l c T ? I F : 1 ~ ? . G T . 1 ? 1 I v % = l z I F ( I v ~ . , - T . I V l ) C ~ J I T F ( b 1 1 3 3 1 I Y I I I Y ~ 1: [ l ~ > . ~ T , l v I ) Lt l 7 ' ' 7 ? * a i 7 i [ n , 1 2 2 ) I V l , f Y ? . J R I T ' ( ? , I 2 2 1 I Y l . I Y 2 t . A I [ A ) = f l L T ! l T C4LL f T T c : ' r ! : \ , I V ! , J Y 2 ] J V I T L ( 1 , 1 ? : 1 11aF(F,1 ,5 ,2 , f C n t F ( f l , I ) , 1 * 1 1 2 J r I q I T T ( 1 , 1 2 5 ) t1C: 1,; L i z 4')

4 2 A a l T C ( 6 , 1 1 3 ) 3 ? ~ 2 l T i ( 6 , l l U )

k E k ? ( 5 , 11'3) ' ~ A ~ ~ ' ! ~ ! " L ~ ~ Y ~ , ~ ~ I I Y ~ , P ~ .:TT: ( 7 , 1 1 5 ) ' 4 A l , ~ l " ' L ~ I Y 1 , + ' 1 , T Y Z , P 2 I F ( r n l . E : ~ . I s S ) 7,C T r j 2 5 J l = - I r C . , , I . ~ C , E ~ ; . Q ~ ~ ) J \ - 3 7 0 I F [ :ll,.?C.E;:.QqV) " I ' 1f :Sa

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SF Tl l 29 7 7 1 F !I> ,UE.~.IJIIC) G ? T n 2 9 2 3 r R I T r ( 6 , 1 1 5 ) ~ . ~ 1 , ~ ~ ~ ~ ~ ~ C , l v i , ~ l , I v 2 , P 2

~ l = A ~ ~ ~ ; f ~ 1 / ~ 1 . - p 1 1 : P 2 = A ~ t 7 G f ~ ? / ( l . - P 2 1 ) Y I l - l f l Y I 2 - I Y 2 C A L L ~ ' J ' ~ C ! P ~ , ~ ~ , ~ I ~ , Y I % , ~ O ~ . F ( K , ~ ) , C U E ~ ( ~ ~ ~ ) ) r v ~ F ( b ) = t i 4 1 l Y ? = l q : ! ~ + I ~ r l t@ T l i 5 5

5 4 * r? ITF_ ( h l 1 3 2 ) " A 1 ; I I J ~ C , v s ~ ~ ~ r b , 1 1 5 ) , I A ~ , ~ : ~ I ~ ! c , I V ~ , P ~ , I Y ~ , F ~ Y I l = l v l r 1 2 = 1 ~ 2 C O E F ( 9 , 2 ) = C O E F ( 6 , l ) * Y I l + t n L F ( ~ , 2 ) CqEF ( 9 , 1 ) =111 C O r F ( q , ? ) = C @ C r ( s , Z ) - C O E F ( P t 1 J t Y I 1 C n E f [ l r , 2 ) = C 7 C F ( 3 , i ) * Y I ? + t [ ) E l [ 9 , 2 ) C C l E F ( l ~ , l ) = p 2 C ~ E F ( ~ ~ , ? ) = C . I ~ T ( 1 7 , 2 ) - C n F F [ l l ' , I ) * V I ? I F t v l l . E 2 . O . ) Y I l = Y E A 4 ( 1 ) I F [YI?.ES.~.) Y I 2 = Y E A R ( 2 ) Y E A ~ ( ~ ) = v ! ~ Y E A J ( 2 ) = Y I 2 I F [PQT.E7,1.UP.p?T,EG.2)

h id;ITE ( 9 , 1 ? 9 ) : I J ~ ~ C , N A ~ , C O F ~ ( ~ , ~ ) ~ C O E ~ ( ~ ~ ~ ~ ~ B ~ ~ ~ ~ ~ K = 1 ?

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6 R I T t I ( 6 , l l q ) l < k t ( L , L ~ ~ I ~ > , ( ~ ~ A F ( I ? ) , J ? R ~ , ' ) RE&: ( i , 1 1 1 ) ( ! * , f ~ > , L : l , ? l U Q I T C ( 6 1 1 1 1 ) ( l . ' ( L l , L = l , ? ) , 4 P I T L (?,ill) ( 1 1 ( L ) , L = 1 ~ 7 1 pn ?? I-1,7 O D 2 2 .1=1,7 IC ( I d [ I ) . E O . J ) ! J [ ! ~ ( J ) = I * U l T t ( 6 , ) 1 2 ) (L,L:l , 7 ) , !dAF ( : I d6 ( . I ) ) , J = I , ' J F ) IF ( F ~ C . + I E . ~ . C J I . . P P T . ~ U . ~ I Ln Tr, h ~ ' D[t 51 1 S ! , P 4 ? ?

V I I..!. " 3 h l J = l , : l i l F ( l l l l r (-11 ? ) S F (11,lf ( \ I ) , l ) + V ~ l Y I 1 s t ( * J , l F ( J ) , I ) I F (LS~;~C.A:~:~.~:AT.LT.~.AN~.~JUO.~T.J) CALL P L ~ T F I F (ESr.ES.31 b1-1 T n 5 9 I F ( E S T . L T , ~ ) CALL PEHETE I F ( L ~ T , I C . A ~ ~ ~ . C S T . L T . ? ) C 4LL PLOTE I ' ~ L ! E x = ~ 33 4 4 1 = 1 , 7 T I T L E ( 2 , I ) = I J A F ( ~ J ! J F ( 1 ) ) I F (EST.ES.S) T I T L L ! ? , I l ' ~ d A 9 ( 1 ) I F ( L % T C . A ~ O . ~ ~ ~ L . E ~ . ~ ) CALL P L ~ T L ~ ~ G [ ~ ~ ~ ~ E X , X ~ ~ ~ X , ~ ~ ~ Y ~ Y Y A ~ , Y ~ I ~ , S C ~ L E X I T I T L E , T Y P E ) I F ( L ~ G I C . A ~ G O . ( F ~ C . E 3 . 1 . O R . F c : C C E 1 . 2 ) ) C A L L PL;ITLII<(I r n c x , Y ' I A X , x r c I h , vh \nx , Y Y I ~ , S C P L E X , T I T L E , T Y P E ) 1 i J D t x r y

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2 SS'SS*l) ( ' I , I 1 I F (SS,EO.:?.) G O T f i 1 a'? 5 J + l , U Q

5 F ( J , I ) = ? ( J , I ) / S S I I Y ~ I v ~ * ~ ~ J ~ + ( I B S * I - ~ ) ~ I P ~ IF par.^^.?) G ~ Y T S ij

FOQYLT ( l ) c F O U ( 7 ) F C R W A T ( J ) - F O R ( 3 ) I F ( j s . Z T . 9 7 9 7 1 4 . 9 9 ) F O U * A T ( ~ ) = F O " ( ~ ) I F (S j .GT.979990 '3 .91 F ~ ? M A T ( Z ) = F O Q ( ~ ) I F ( S S . E ' J . ~ , . A . ! ~ J . P Y T . E I . 1 ) ~ u R ~ L T ( ~ ) I I F o ~ ( b ) I F ( X S . F , ! , a , . Ab:3.PPT . F ? . 1 1 S ~ C R L FO"'1nT ( 1 7 ) o F D R ( 9 ) U O 4 J . 1 , ' J ! , J l . = 2 * 1 * 1 J~.?. . l *? FOl'*:? ( J l l r F r . r R ( 3 ) FCIJwAT (J2) :F l Ic ( A ) x Y = J 9 9 q 9 , 9 9 9 0 0 l r 5 5 = 1 , 2 d X = g x . 1 7 J .

1 i? I F ( ~ J ( J , I! . G T . ~ x ) FORMAT ( . 1 1 ) = F 0 7 ( 3 - J J ) IF ( P R T . E O . ~ ) G O T L ~ v I F ( U ( J . 1 ) .E17.0.1 FJQ*cAT(J l ) ;FCla (6) I F ( r ( ~ , I ) . E 3 . 0 . ) F O R ~ ~ A T ( J ~ ) E F O Q ( S ) I F ( F ( . ~ , l ) . E i i . > . ) F ( J , I ) s a L

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I ) I I Y , S 5 1 ( I J ( J , I ) , F ( J f I ) ~ J x l ~ P . i D ) B C 5 4 . I : ! , i n

I F ( . : ( J , ~ ) . € : : . I ! L ) 1 ~ ( J , 1 ) = 1 . I F C E C . I , I I .E4 . ! 3L ) F ( J I I I S P . I c ( F ( J . 1 1 . G T . . q 9 3 9 1 F ( J , T ) : , 9 9 9 Q IF (FPC.EO.1 . O i i . F 2 C . E 2 . 2 ) LO To U

~ ~ ( J , l l = F [ J , I ) / ( l . - F ( J r 1 1 ) I F ( ~ ( J , I ) . L T . I ' . : \ " ~ ) F ( J I l l = S , I F ~ F ~ J , I ) . L T . c . ~ ~ I . A ~ . ~ ~ . J F ~ ~ . . ~ J E , - ~ ) F ( J , I ) = ~ . I F ( F ( J , I I , E C . ~ . ) Gn l o u F ( J , l ) . A L O t ( f ( J , I ) )

J C f l L . T I h ~ ~ F I CD!$T]h( lF

s u b i ( u ) = e . P.'! 0 . J . j # Y P ~

h S c l F ' ( h ) = S : I + ( 9 ) +SUb ' ( J ) nc 7 J = I , : ,P

7 FF ( J ) c s L I ' ~ ( J ~ / S I J : ~ ( Y ) I F (PQT.E,J . 1 . i ]E .PHT. t :L i .2 )

b W R I T E ( A , l p l ) I t r t t , I 7 5 , S 1 1 * c ( 0 ) , ( S ! l : . 1 ( J ) , F F ( J ) , J s l r N n ) R E T l J Z ' . t t i - ,

S ? ~ D & ' ! J ~ : T ~ ' ! ; T I T L T I ( J , I V I , I v ? ) t r l ' 1 4 ~ , r , ~ ! ~ ~ T ~ ~ F ( ~ , ~ ~ ~ ) , I ~ I . A R ( ~ , I C ~ , K D ~ I Y O , ~ J ~ L ,

8 J t , 1 [ ~ ( 7 ) , f d & i ' , ( 7 ) , t ~ ' J ( 7 ) 1 1 V ( 7 ) A / ~ ~ A C / ~ ( ~ , ~ ' J ) , F L A ~ ( ~ I I ~ ) , P I F , I Y F I ~ J ~ F ,

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!. P L T , F F C , I F Q I , T p T , ? A T , E S T , Y H A X , V k ! I f *

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1 ? 5 F n f ' l b ~ 1 5 r , ' S R & ; l i : .+t i! C J z S E I ( V 4 T I O : J S F r 1 1 T Y I S t Q t < ' / a 5 r , ~ r , , ~ 2 c r r i ~ c .:' ~ T L ; I S ; ] L ~ , f in111 ~ I P S ~ Q V A T I O ; S E ; P L A J K E D * )

1 ~ l i l F S r ) ' . , t ~ f / S x , . E l !I*, 1 2 , , A 8 , ' I S : Y = ' , F 7 . 3 , * T + , F 8 . 3 , (I ' F a * ? r ' , F o . 3 , ' V A Q = ' , F h . 3 )

I .lli F 3 2 ! L T ( ? * ~ , ' ( ' , ' ~ . J , ' J ( . , ~ 1 . 3 , ' ) ' 1

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V I I - C S F ~ ( J , I ) * i * t O e F ( J , ? ) c = y - v . < j E : & F + c S E 2 = S r ? + F * E c 3 . r T I ! . L J E V 4 9 = S F ? / ( k ' , - 2 . 1

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11' s ' j 3 ' ( : , I l = . ' . lr1ATCb:1:l~3+ [ l ; l 1 ~ + I r 1 r ~ - % ) IPL! I F , ! i l : ] q l : + I v F * [ ' : 3 F + I I ; f i - > ) / 1 P 1 I F [ I v ~ . G T , ? , i h T C ~ ' 1 ) I O A T ~ + J I I : I Y F v r ) L d : * l . ~ + 3 , 7 YVAX:-1.E-3' OC. \ I . \ , U 3 F X = I ~ Y ~ + T Y F + ( I + ; R ~ - z ) 1 1 0 ~ 1 x = x ,:a I F ( X . G E . Y E A t t ( 1 ) ) h.4 I F (X .GE.YEAU(2) ) 1 - 1 8 I F ( X . t E . V E A R ( 3 ) ) K = l l l c ( x . i ; F . v i n i ? ( ~ l I f i r 1 2 x=COEF ( K , 1 ) * g + C O E F (',2) J F (K.67.63.) k s h d . IF (L .LT . - c , ~ I r=-oa. X:EXp ( x ) L I ~ 4 J2= l , :JF J=';UF ( , u F - J 2 + 1 ) IF (F(J,I).ED.3..Dr.FRC."E.G) G O 747 8 ~ ~ J ~ I ~ = l , - ( l , ~ ( I . + E X ~ ~ ~ ~ J , I ) ~ ~ )

5 I F ( F ~ J , l ) . L T . . l . ~ 1 1 ) F ( . l , I l = J . I F (FgC. ' IE.2) G D TO 1 5 x x r 7 I . I F (:.=,.12,;7,7) xX:F (L.II.JF [,IF - J .? ) , I) F ( J , I l . ' ( J , I ] - X X I F ( 6 ( . I , I ) .LT . ! ! .31) F ( J r I l = a .

1 5 J 1 ' 1 I F ( I . , ; E . I D A T E l i n - I Y F + 1 ) J I :2 S S ~ ( F C ( J ) + F ( J , I ) * I ) / 2 . 5 ~ J ' A ( . 1 , J 1 ) ~ ~ l l 1 1 [ J , J 1 ) + S S S I J ~ ! ( ~ , J I ) = S J + : L ~ , J ~ ) + S S

4 F F [ J ) = F ( J , I ) * X I F (PQT.E>.P) G O TO 5 FOifYAT ( I ) =FOG ( 7 ) FgRYAT ( ? ) r F D Q ( 3 ) I F ( x . 6 7 . 9 9 9 9 9 9 . 9 9 ) FORMAT ( 2 ) w F D R ( 2 ) I F ( x . ~ T . 9 9 9 9 9 ~ 9 . 9 ) F D R M A T L ? I r F g R ( l ) I F ( X , E ~ , ? , , A N ~ . P P T . E ~ . ~ 1 F D ~ * A T ( 2 ) : $ 3 R ( b ) I F (X.E?.i3,.A'J1 . P ~ T . E ' d . I ) X r d L

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l!D l b , I C l , ' J l = ? * J + l J 2 - 2 . I + ? 1 O . > " i T ( . l i ) : F " , ~ ( 3 1

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v q r x l ; - l . t - 3 Y ? 1 - . 1 = . 1 . r + < , I * ? 1 1:) ;.?? 5 . ' . x = . - . iJ3 1 1 1 E :, ' ' s .

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n L d A V 5 P L i t ? V r ? , S C A L F X = ~ ~ t r ~ : I ~ T I I ' L ~ ~ A T ~ I I ~ I F A C T O W F O R T H E L E N G T H O F T H t

X-AXIS, L F I J K T H I; 5 . m S C A L E X P L O T T E H U I 4 I T . S P E R J S E R U N I T S v - n r I S I S 4 1 , J A V S 5 P L f l T T t C U t 4 I T S H I G H

T I T i . F f i , 7 ) = L I T E ~ A I T I T L ~ UF T H E P L B T T I 7 ~ [ ( 2 , 7 ) = L I T E C A l . T I T L F . * H E + " 1 1 4 0 E X r R T f P ; . ( ! , l T ) r L T T E L A L T V P F U P l I T S rl'J T h E V - A X 1 5 T f P I ( 2 , 1 ' ) : c 1 T E k A ~ t R!lT I 4 P S '13 FIII.CTI'IL?

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-. I F ( t - i ~ , ~ C . l i . . a ~ l , . T + t , . C ; t . l . > G f 1 7 a ?

U l C l ) ' i T 1 8 ~ l l r I F [v.~\,.r,; , l ..A i :~.vl.! ' ! ,LT, l a , ) T I : '

a,? I F ( v ~ ' 1 . E , , 4 d i ( ~ q 4 i x ] ; G C T I u u C 4 U = V ~ 1 ' : / 1 3 . * * 1 1 I F (,:. '<,?T.l.) t 4 * ' t ? i 6 - . 1 * 9 q 9 9 9 q v r r + d ~ : r , n r T ( I ~ I X ( ~ ~ ~ ) ) * ~ Z . . I I c . t r ;v : 'b . ( l / v8 . !1 ' 1 I F ( t . ~ K m C L . l P . . C P . i . t H k i . G i , Y * I ~ ~ l ) Y Y I N I S P I .

u 3 C @ V T I ' . d ' t YL.5. ~ V : [ Y ~ ' b ~ l - V " I ~ ~ l ] / ( l ' , , ) T l r l ? . V S = Y L / ( v ~ ~ A x ~ - Y ~ I ' . ~ ) XSS;. i ? . S C A L i x K A X : l i ! k ( i Y A X l ! ~ ~ N : I F I x ( K ~ ~ I ' w ~ ) ' ' I = ( 9 A r - - ' I h i ) / 1 ; ' STFDV=-? . *TV+V ' : J . 1 YST4:Vv1' l -TV .? , 7 5 X ~ ' ~ I * . ~ = X ~ ~ T 1 1 - 9 , . / s ~ A L E ~

CALL S C 4 L F ( l . , I . , !.,'.) C ~ L C F P t 3 T ( l r 1.,-13, '

C A L L S C A L f- ( 1 ., l., ' . r 7 . ) t 4 ~ L F D 1 n T ( l , u . , 2 . )

C I F I : u ? E Y c . l i l ' i ~ V G a l p THE A x L S

ELI U I : 1 ,0 5 T E P Y ~ S T i P V * 2 . * l V I F ( I . C I J . ~ . ~ ~ . I . F I > . ~ ) l;Q T O 5 CAI.L FD( O T ( - 2 , i I ! l ' J 1 , S T F P Y ) C A L L F P L I I T ( - 1 , i 4 ' 4 i 1 , S T E F Y ]

5 S T F P Y L r $ T E p Y - L l . ~ * ? 5 * T V C L L L F T . I ~ A ~ ~ % ~ ' ~ I ~ ~ , ~ ~ € P Y V I . ~ ? I . ~ ~ ~ B . ) d R I T E ( 7 , 1 0 ) S T E P V C A L L tlF[ a;(1) T I T l ' l . l B * Y h q b X l CALL F t l j A S ( ~ 3 ' 1 . l T I T 1 , . 1 7 1 . 1 5 1 P , ) J R I T k ( 7 , 1 5 1 [ T V P L [ l t l ) 1 l s 1 t l ~ 1 )

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t I F I \ ~ F A - ~ v ; ~ v i T Y ~ p E IF@= T t . t l l E i T P L O T

S U ? ~ ~ ~ I ~ T ' I ~ C S T A ~ ~ L I S I I ~ L S s c n ~ t , A X I S AN!: L A B E L S F O Q L O G E ( ~ 1 . 0 ~ ) Y - n u 1 5 4'11) L I . $ F A ' X - A X I S F O P G b I D P'I'1 L A . ~ ~ c S i ) F Y - 4 x 1 5 S U t l H O I J T I N t YL0GA.k I S CALLED T l l t P F ' . 1 5 ~ S S l l l l F l ' TI; i l E - 1 P L O T T K P O q l T s I h X D I R t i T I O f d AN11 - 3 P ( . l T T E i ' , j . r I T a T I . y n I l t C T T O t . ! A W A Y F R ( I ~ 1 THE P L O T T I p J G O C l I G I N (XU! : , I '1 , ; ) = > " q r ; r T n l a C;i T M F P ~ P E R " r t l E I CALLTI? v l !T1~: IJ~)LI:- S t 4 ~ f . ' ILL dF. S F 1 n!.lr' r x F S "JILL R C DHAuH ~ t . 1 0 L A B C L C D I r n r _ x < r S C ~ L E ~ 1 1 ' ) A X E S Gg:n ILL D E Z E T I ' . W t r > 7 P E t v * I L L P E UCTU1I iF I ) TO THE ROTTO11 OF TYE P A P E R " FlJH

T , ~ F _ ~ I E Z T P L O T h l ~ ~ t l " P J C H T I ~ Y-AXIS L A B L L E O A Y D T I T L E n I ' J C E i s l TLIF 5A' IL AS * l iE l4 I N ~ I E X W ( + RUT NO L A B E L S O K T I T L E Y:.:AX r "4X IY IJ 'q VALLJL nh Y - A l l 5 X ' I I ' . = ' I I ' I I ~ I I J ~ ' V 4 L I I r 0.1 Y - A X I S AND Y - A X I S I N T E R C E P T Y' lA, : b c 4 x 1 ~ J r l V A L t I t fl'! v - A X I S (FOR P L O T T I N G X 10'4.) V f ' I r = : I ! ! I11:J' ' VLl. ' lL l lh V - A X I S (FOR P L O T T I ' J G Z Y.31) SC4L:x : T r l t ~ ~ ~ J L T I ~ L I C A T I ! I ' J FACT'IR F O ? THE LEI~GTII OF T H t

X - A X I S , LEI IGTH IS ~ . * S C A L F . X ~ ' L O T T E R i r h r I T s PER IJSCH U'J ITS V-LX I~ T S A L J ~ Y S 5 P L n T T E U U Y I T S ~ I G Y

T V J ; ( I , ! ' ) : L ? T C P A I T Y P F flF ( J f l l T S 0'4 THE " L E F T " Y - A X I S T I P i ( ; i , l r ) : ( .TTF-;hL 'VPF 0 ; U:,ITS 914 T n S " R I G H T " CL3S114T.

V - A X I J T I T , F ( ] , 7 ) r i . l T t t 4 ~ T I T L ~ LIF T 3 E PLOT T l T ~ ' ( 2 . 7 ) = I J T E P A L T I T L E U ~ K N I N ~ E X W :

KEAL.5 T I T L F I ;T!~E 1 s I n . I TITLI(%.~) , T V P T 1 2 , 1 7 1 , I ~ A T E ( L , I F C l q q i T f l + i )

F U H r i T ( F U , ~ )

F O R H L T ( I O ) FO2'4AT ( T K , * 1 0 ' > F o P q n r ! 9 ~ , 1 1 ) FQh':,LT ( ' * r * I I A S L VERST[) t ! * , ? ( A 2 , ' . * ) , * 2 , . 9 Y :., N A K J t F N O V I t ' ) F ~ ? Y L T f I + i , 3 ( 1 P X P I 1 J . 7 ) ) F O H 4 A T ( ' ', l . ! ( A O ) ) F O R ' I A T ( * ' , 7 ( ~ f l , ' . ) I F O R ' l i T ( * ' , 7A.j)

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C A L L P T L A G ( I 1 B E = a r t l . J O E L = A ~ Q L ( ? E l C A L L F r . 4 ~ 2 [ r ~ ? : j ~ ~ , ~ r I , . I ? , . 1 5 1 a . 1 Ik!FITt (7,RL'l I 1 C A L L pFL L G ( 1 1 1 T T ~ s a ~ o , , [ ~ 1 ! n r ~ t i . ) C A L L F t L l 4 F ( X _ ( ' I ' J t T I T l , . I ? , . I ~ , : ' . ) v.li:TF ( 7 , 1 ? ? ] ( T Y D i (l~Ilr!' lr!r)

C A L I I 8 F L . 4 r - [ 1 )

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C A L L F c H A W ( X N I I 1 1 1 Y ~ T ~ l L , . l ? 1 , 1 5 ~ r . ) P - t J I l ~ r v ~ l l ~ l l / ( 1 . * Y l ' I ' ~ l ) k D l T c [7,57) F t 4 1 1 C A L L D C L A G ( 1 ) 0 0 1 7 I a l r o , ? Y V L = F I , 1 & T f 1 ) / 1 ! ! . Y L A : A , ( I K ( V ~ , L / ( I . - f V A 1 1 C A L I F r . i I C I x ~ 8 1 + . 1 1 r V L P r . 1 2 , . 1 5 , Y . , ) d P I T f ( 7 , $ ; , 1 Y V *

C A L L P F L A G : 1 ) 1 7 C D ' I ' I ' L I T

C A L L P - C H L ~ ( X ~ I I I . ~ I , ~ ~ ' A ~ ~ I I . 1 2 t . 1 5 1 t ' e ) F ~ ~ ~ x c v t ~ ~ k l / ( l . * V I ~ A x l ) I . ~ ~ T E [7,5r3] F M A X CALL P F L l t ( 1 ) h Y O = X H I Y 1 * 1 5 L ~ . T I T l r A l O G [ Y ' q A X l * 5 . ) C A L L r r L t A D ( X j h ! ' u , T ? T l ~ . 1 2 , .15,@.) d V I T E ( 7 , 1 0 ? ) ( T I P C ( 2 1 1 ) 1 l ' l t l R l C A L L P F L A C ( 1 )

b C 0 ' 4 T I I I I IE

C A L L r p ~ - ~ ~ ( i , r l i : 11 , V ' q ~ r , i ~ )

P1otlog.f continued

RELATED IlASA PLlBLlCATlONS

Software Package for Economic Modelling, by M. Norman.

Food and Energy Choices for India: A Model for Energy Planning with Endogenous Demand, by K.S Parikh and T.N. Srinivasan.

The Bratsk-llimsk Territorial Production Complex: A Field Study Report, H. Knop and A. Straszak, eds.

A Review of Energy Models No. 4 - July 1978. J.-M. Beaujean and J.-P. Charpentier, eds.

MEDEE 2: A Model for Long-Term Energy Demand Evaluation, by B. Lapillonne.

Methods of Systems Analysis for Long-Term Energy Development, Yu.D. Kononov, ed.

Medium-Term Aspects of a Coal Revival: Two Case Studies. Report of the IlASA Coal Task Force, W. Sassin, F. Hoffmann, and M. Sadnicki, eds,

Climate and Solar Energy Conversion: Proceedings of a I IASA Workshop, December 8-1 0, 1976, J. Williams, G. Kromer, and J. Weingart, eds.