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                                              AnIntroductionto Fortran 90
            This chapter aims at giving a short introduction to Fortran 90. As describing all features
            of the Fortran language would probably fill some hundred pages, we will concentrate
            onthebasicfeatures that will be needed to follow the rest of this textbook. Nevertheless,
            therearevariousFortrantutorialsoutintheinternetthatcouldbeusedascomplementary
            literature.
            2.1   AboutFortraningeneral
            2.1.1  Thehistory of Fortran
            Fortran is pretty old. Actually it is considered the first realized higher programming lan-
            guage. It goes back to a proposal by John W. Backus, an IBM programmer, in 1953. The
            termFortranisderivedfromTheIBMFormulaTranslationSystem. Beforethereleaseofthe
            first Fortran compiler in April 1957, people used to use assembly languages. The intro-
            duction of a higher programming language compiler reduced the number of code lines
            needed to write a program tremendously and therefore FORTRAN, the first release of
            the Fortran programming language, grew pretty fast in popularity. From 1957 on several
            versions followed the initial FORTRAN version, namely FORTRAN II and FORTRAN
            III in 1958 and FORTRAN IV in 1961. In 1966, the American Standards Association (now
            knownasthe ANSI) approved a standardized American Standard Fortran.Theprogram-
            minglanguagedefinedonthisstandardwascalledFORTRAN66. Approvinganupdated
            standardin1977,theANSIpavedthewayforanewFortranversionknownasFORTRAN
            77. This version became pretty popular in computational economics during the 80ies and
            beginning 90ies. More than 13 years later, the Fortran 90 standard was released by both
            ISO and ANSI in consecutive years. With FORTRAN 90, the fixed format standard was
            exchangedbyafreeformatstandard. Inaddition, manynewfeatures like modules, recur-
            sive procedures, derived data types and dynamic memory allocation made the language
            muchmoreflexible. From Fortran 90 on, there has only been one major revision which
            basically introduced object-oriented programming features into the Fortran language in
            2003. However, as object-oriented programming will not be needed and Fortran 90 is by
            far the more popular language, we will focus on the 1990 version in this book.
            4                                                      Chapter 2  –   AnIntroduction to Fortran 90
            2.1.2     WhytouseFortran
            Fortran is a general purpose, procedural, imperative, high-level programming language.
            Indetailthis meansthat(a)Fortranwasnotcreatedforaspecialpurposelikee.g. Matlab,
            MathematicaorGausswereforefficientlydealingwithmatricesorsolvingmathematical
            problems, (b) Fortran code that will be used severaltimescanbestoredinfunctionsand
            subroutines that can becalled from other program parts, (c) a Fortran program consists of
            statements that will be executed one after the other (i.e. a Fortran program starts with the
            first line and ends with the last), and (d) Fortran abstracts from the details of a computer,
            i.e. having the right compiler, Fortran code could be run on every computer independent
            of its hardware configuration and operating system.
            At this point our students usually ask "So, why to use Fortran? Why not a special pur-
            pose language or something more "fashionable" like Java?". Let us come up with some
            justifying points. First, special purpose languages might be relatively efficient in the spe-
            cific purpose they were created for, however, slow in other areas. Matlab, for example,
            is very good in working with matrices of regularorsparsenature.However,ifyouhave
            ever tried to run some do-loops in Matlab, you will know what we mean. Second, when
            it comes to the more "fashionable" languages like Java or C++, one has to always keep
            in mind that those languages are usually object-oriented and abundant. They are very
            goodforcreating software with Graphical User Interfaces, but not for running numerical
            maths code quickly and efficiently. As computational economics usually consists of at
            least 80% numerical methods, we need a programming language that is efficient in exe-
            cuting do-loops and if-statements, calling functions and subroutines and allows to per-
            manently store general code that is frequently used. Fortran is a language that matches
            all those features and not much more. The only real alternative we know would be C.
            ThereisnorealreasonwhynottouseCinsteadofFortran,it’sjustamatterofpreference.
            Last but not least, Fortran has been used a lot by engineers, numerical mathematicians
            and computational economists during the 80ies and 90ies where a lot of optimizers and
            interpolation techniques were written. Fortunately, Fortran 90 is backward compatible
            with FORTRAN77,i.e. all thecode that is out there can be easily included in our Fortran
            programs.
            All in all, it seems reasonable for us to have chosen a language that matches all the fea-
            tures we need but does not come with any unnecessary extras that just make execution
            less efficient.
            2.1.3     Thewayhigh-level programminglanguages work
            Low-level assembly languages that are basically used to program computers, micropro-
            cessors, etc. do not abstract from the computer’s instruction set architecture. Therefore,
            the syntax of assembly languages depends on the specific physical or virtual computer
            used. Inaddition, assemblylanguagesarequitecomplicatedandevenasmallprogramm
           2.1. About Fortran in general                                     5
           requires many lines of computer code.
           Inoppositetothat, high-levelprogramminglanguagesabstractfromthesystemarchitec-
           ture and are therefore portable between different systems. As in all other languages, one
           has to learn the vocabulary, grammar, and punctuation called syntax of that language.
           However,comparedtoreallanguages,thesyntaxofahigh-levellanguagecanbelearned
           within some hours. In addition, the semantics, i.e. the meaning or interpretation of the
           different symbols you use, usually follows principlesthat can be comprehendedby using
           purelogic.
           As high-level languages abstract from the computer’s instruction set architecture, one
           needsacompiler, sometimes also called interpreter, that interprets the statements given in
           the programandtranslatesthemintoacomputer’snativelanguage,i.e. binarycode. The
           wayhigh-level programming works can be seen from Figure 2.1. First, the programmer
                                 SourceCode               Programmer
                                   Compilation
                       Other Libraries     Object Code    Compiler
                                    Linkage
                                                          Operating
                               Executable (binary)        System/
                                                          Hardware
           Figure2.1: Thewayhigh-levelcompilers work
           hasto write his source code in the respective high-level language and hand it over to the
           compiler. The compiler now proceeds in two steps. In the compilation step he interprets
           the source code and creates a so called object code file which consists of binary code.
           Binary code files usually have the suffix .obj. During this step, the compiler usually
           performs a syntax validation scan. If there are any syntactical errors, it produces error
           messages and stops the compilation process. In order to create an executable file, which
           hasthesuffix.exeinMicrosoft®Windows,thecompilernowlinkstheobjectcodewithall
           other libraries that are needed to run the program, e.g. external numerical routines. The
           resulting executable can nowbesenttotheoperatingsystemwhichadvisesthehardware
           to do what exactly the programmer wants.
            6                                                      Chapter 2  –   AnIntroduction to Fortran 90
            2.1.4     Fortran Compilers for Windows® and Linux
            For beginners, we suggest to use the SilverFrost FTN95 compiler. You can download a
            free Personal Edition from http://www.silverfrost.com andinstallitonyoucom-
            puterbydouble-clickingonthedownloadedfile. Thesetupagentwillguideyouthrough
            the installation process. SilverFrost’s FTN95 compiler comes with a graphical user inter-
            face called Plato. You can open this program bydouble-clicking "Plato 3IDE"inthe"Start
            -> Programs -> Salford Software" menu. The user interface can be seen in Figure 2.2.
            Figure 2.2: The Plato user interface for the FTN95 compiler
            Belowthemainmenutherearetwolinesofshortcutsymbols,thefirstofwhichisnearly
            self-explanatory. The only thing that needs some explanation is the drop-down menu
            with the three possible execution modes for FTN95. The standard entry thereby is Check-
            Mate Win 32. CheckMate is a graphical debugger, the Debug mode is a simple console
            debuggingmode. UsingCheckMateorDebugandrunningintoanerror,thecompilerwill