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Fortran-90

1. Below are Fortran 90 DO structures with an EXIT The EXIT statement causes the process to exit the loop and can be very useful do i 1 100 if not sum lt 100 0 exit Highly desirable EXIT sum sum i of DO construct prevents end do infinite loops Safer than DO WHILE THINGS TO REMEMBER o Repetition structures with logic controls may easily become infinite Make sure the structure has a finite number of cycles EXAMPLE of INFINITE LOOP do while i gt 0 sum sum I Note gt will lead to 121 1 an infinite loop end do o Never change the loop index variable in a counter controlled DO loop Introduction of Fortran 90 for Numerical Programming 9 0 FUNCTION Program Unit o INTRINSIC Functions Compiler provided relatively safe to use careful with type of function and type of argument Use of a FUNCTION in a fortran statement returns the result of the FUNCTION to the statement Example Pythagoras Theorem HYPOTENUSE SQRT A 2 B 2 SQRT is an intrinsic function of type real in this application Arguments to the function must also be real Execution sequence B 2 A 2 SQRT Assignment e External Functions Programmer written to meet specific needs e g factorials Some care must be used Structure of an external function is similar to program unit Introduction of Fortran 90 for Numerical Programming type FUNCTION NAME dl d2 specification p
2. Initialize three variables Fortran 90 Character Set Fortran 90 adds eight new characters to the Fortran 77 standard character set These are listed in Table I Introduction of Fortran 90 for Numerical Programming Table I New Characters in Fortran 90 Symbol Name Function Exclamation Point Precedes a comment Double quotation Delimits a character constant Percent Separates derived type components amp Ampersand Designates a continuation line Semicolon Separates statements on a line lt Less than Symbolic relational operator for LT gt Greater than Symbolic relational operator for GT Allows all attributes of a variable to be n Double colon declared on a statement m Underscore Used for symbolic names The Fortran language is not case sensitive It is recommended to use small caps for source code and comments Fortran Line Continuation Fortran 90 limits the number of continuation lines to 39 However compiler options may extend this limit An ampersand amp is used at the end of initial line to indicate the following line is a continuation Example The following complete statement If exam grade gt 90 and lab grade gt 90 grade A may be written on two lines of source code with a continuation Introduction of Fortran 90 for Numerical Programming if exam grade 90 and amp lab grade gt 90 grade A Character strings which must be continued on the next line require
3. The simplest to use is unformatted I O and is called list directed Input FORTRAN source code allows for input data to be received interactively or by an input file Simplest for is the list directed output no format READ list or READ list READ RADIUS or READ RADIUS Output FORTRAN source code allows for output data to be transmitted interactively or by an input file Simplest for is the list directed output no format PRINT list or WRITE list PRINT AREA OF A CIRCLE IS CAREA WRITE AREA OF A CIRCLE IS CAREA o READY and WRITE Statements poem First is the unit number and the second is the format specifier or label number for the format specification Introduction of Fortran 90 for Numerical Programming 7 0 Intrinsic Functions Intrinsic functions are available to a program by referencing the function s name The function returns its results for the given argument and this result may be assigned to a variable Some Fortran 90 Intrinsic Functions ae E c Argument Value apse ABS x Abeolie value oF value of x Integer or Real Same as argument Sate eaten SIGN x y Ix Itimes sign of y x and y of same kind Same as x COS x Cosine of x in rads Real Real EXP x Exponential function Real Real INT x Integer part of x Real Integer LOG x Natural log of x Real Real LOGI10 x Common log of x Real Real MAXw
4. an executable statement Only one END statement per subroutine unit is allowed Syntax END A subroutine is referenced by the CALL Statement o CALL name actual argument list The actual argument list contains the actual arguments in the referencing program unit The number of actual arguments must be equal to the number of dummy arguments Each actual argument must agree with in type with the dummy argument Introduction of Fortran 90 for Numerical Programming o Corresponding pairs of actual and dummy arguments are associated with the same memory location o Declaring an dummy argument with INTENT IN protects it from being modified o Changing the values of dummy arguments within a sub program changes the values of the corresponding actual arguments that are variables INTENT option Attribute used ONLY in the declaration of dummy arguments in FUNCTIONS and SUBROUTINES INTENT IN As with a FUNCTION variables with attribute INTENT IN means the variables are used to transfer information to the FUNCTION or SUBROUTINE INTENT OUT A FUNCTION does not have any variables with this attribute since a FUNCTION does not return arguments A SUBROUTINE variable with attribute INTENT OUT indicates that these variables are used to transfer information from the SUBROUTINE back to the referencing program INTENT INOUT Implies dummy argument may be used for information transmission in both directions Introduction of For
5. most set Parentheses must balance that is they must occur in pairs Accumulating and Counting The assignment statement may be very useful in accumulating results summation and product or counting For example x x x Fap Pe i m m 1 n 1 m pseudocode Fortran 90 C sum 0 0 sum 0 0 fori m to n do doi m n for int i m i lt n 1 sum sum X sum sum x 1 sum x i end do end do Introduction of Fortran 90 for Numerical Programming Product Il x ecu x Eem k m m 1 n pseudocode Fortran 90 C prod 1 0 prod 1 0 for k m to n do do k m n for int i m i lt n I prod lt prod x prod prod x k sum x i end do end do forn m then product 1 0 Nested Polynomial Multiplication 2 3 P x a a x a x tax a x tax p x a x a x a Bruns F x a x a eus O Example p x 5 3x 1x 9x 2x 6x 5 x 3 1x 9x 2x 6x 2 5 x 8 x 1 9x 2x 6x 5 x 3 x 1 x 9 2x 6x 5 x 3 x 1 x 9 x 2 6x 5 x 3 x 1 x 9 x 2 x 6 Introduction of Fortran 90 for Numerical Programming pseudocode Fortran 90 C pa p a n p a n for i n 1 to 0 step 1 do do i n 1 0 1 for int n 1 i gt 0 1 p lt a xp p a x p p a i x p end do end do 6 0 List Directed Input and Output A program s ability to communicate with a user is critical Fortran supports I O functions in two forms formatted and unformatted
6. o Alternate Method for Array Declaration type array name extent 6699 real a 0 10 declares an array a with an extent of 11 units of type real storage Introduction of Fortran 90 for Numerical Programming Subscripted Variables Each individual element of an array is uniquely identified and accessed by means of a subscripted variable array variable name subscript identifier The subscript identifier is an integer value or variable o VALUE 1 o VALUE VALUE 1 VALUE 2 VALUE 3 VALUE 4 VALUE 5 I O and 1 D Arrays Initializing a 1 D array is efficiently performed with a DO LOOP Interactively initializing a 1 D array INTEGER PARAMETER LIMIT 50 REAL AXIS LIMIT DO I 1 LIMIT READ AXIS I END DO IMPLIED DO LOOP READ AXIS D I 1 LIMIT lt NICE Introduction of Fortran 90 for Numerical Programming program allocatable_array Introduce the concept of allocatable storage for a D array for storing a set of observables and calculating the average value of the observables real allocatable numbers real sum avg integer n sum 0 0 avg 0 0 write a advance no How many observables in the set read n allocate numbers n write a advance yes Enter the numerical values do i 1 n read numbers 1 sum sum numbers 1 end do avg sum n write Avg avg en
7. of data items of the same data type in a sequence Each data item in an array can be directly accessed from memory by specifying the position in the sequence Example REAL VALUE 5 READ VALUE 1 VALUEQ VALUE 5 VALUE 1 VALUE 2 VALUE 3 VALUE 4 1 D Array Declaration The name and the subscript range of each one dimensional array may be declared in two ways o DIMENSION array name l u DIMENSION array name l u or DIMENSION array name Introduction of Fortran 90 for Numerical Programming Fortran 90 enhances the classic array declaration with help of the double colon operator REAL DIMENSION 10 A The extent of the array must be an integer value or integer parameter REAL A DIMENSION A 100 and INTEGER LIMIT PARAMETER LIMIT 100 REAL A LIMIT These methods of declaring the array type and size require the number of elements to be know prior to run time o DIMENSION array name Fortran 90 allows the size or dimension of the array to be specified at run time as ALLOCATABLE DIMENSION array name This is a Fortran 90 declaration for an array The size is determined during run time These are called ALLOCATABLE arrays since the size is ALLOCATED at run time A program unit declares an allocatable array named NUMBERS as follows REAL ALLOCATABLE NUMBERS Once the array dimension is know during program execution the size is allocated as follows ALLOCATE NUMBERS N
8. of format descriptors Introduction of Fortran 90 for Numerical Programming Examples PRINT NUMBER TEMP PRINT TRI IS F8 27 NUMBER TEMP PRINT 20 NUMBER TEMP 20 FORMAT TRI I5 F8 2 WRITE NUMBER TEMP WRITE TRLIS F8 2 NUMBER TEMP WRITE 20 NUMBER TEMP 20 FORMAT TRIIS F8 2 Format Descriptors Format descriptors TR1 I5 and F8 2 specify the format in which values of variables in the output list are displayed Example For NUMBER 17 and TEMP 10 25 oa I I I I I I I I I I E I I S I I I I I I I I I I I mA l I i I H I I I I I H I N I l I I I tA I I I IDE NICE Introduction of Fortran 90 for Numerical Programming Summary of FORMAT Descriptors Li NEN Ee eme 1 E ML MN o Formatted READ is often needed for reading the formatted output of another code Introduction of Fortran 90 for Numerical Programming 12 Structured Data Types A collection of data values can be efficiently processed using structured data type such as arrays Arrays are very useful for processing a list of numerical character or logical variables and for numerical linear algebra 1 D Arrays A list of values stored in memory allow for fast and efficient data retrieval The list may be organized in memory using an ARRAY data type which groups a fixed number
9. reserved column 7 through 72 for Fortran statement is lifted as is the column 6 reservation for continuation characters Most Fortran 90 compilers identify the source code form from the extension of the file name Typically a 90 extension will always be for a free form source code File extensions such as for or f are likely reserved for fixed form source code Programmers are always encouraged to check with the Compiler User Manual for the proper extension However the following extensions are recommended since the author have used them successfully Introduction of Fortran 90 for Numerical Programming File Extension Naming Convention m f90 Free form Fortran 90 Source Code for Fixed form Source Code Comments Comments may appear anywhere after an exclamation point in free form source codes The exclamation point terminates a Fortran record and the compiler will proceed to the next line a pi r 2 Calculate the area of a circle Variable and Program Unit Names Fortran 90 allows a variable or program unit name length to be up to 31 characters in length and recognizes the underscore in symbolic names area of a circle pi circle radius 2 Multiple Statements on a Line Fortran 90 allows for multiple statements to appear on the same Fortran line A semicolon separates these statements This feature should be used with care since it may lead to unreadable coding a2 0 0 b 3 5 n 4
10. two amp One at the end of the first line and the other at the start of the continuation line Example write CSC 302 051 Introduction to Numerical Methods write CSC 302 051 Introduction to amp amp Numerical Methods 3 0 Data Types FORTRAN 77 included five intrinsic data types Fortran 90 supports these five and allows the programmer to derive a new data type from these intrinsic types Fortran 90 Data Types Intrinsic Derived O User Specified Numeric Non numeric o Integer O Boolean O Real Character O Complex Introduction of Fortran 90 for Numerical Programming Intrinsic Data Type Fortran requires identifiers to be declared a type This is performed in the declaration part of the program with type declarations REAL INTEGER COMPLEX CHARACTER and LOGICAL followed by the list of identifiers REAL AREA PI DIAMETER INTEGER NUMBER OF STUDENTS CHARACTER LEN 24 STUDENT NAME The LEN attribute to the type CHARACTER specifies the character string length The double colon is a Fortran 90 feature which allows for declaring multiple attributes to identifiers The attributes are on the left of the double colon and the identifiers are on the right It is imperative to declare all variables and avoid default type implicit declarations Use IMPLICIT NONE in the declaration part of the program to enforce type declaratio
11. x X Maximum of X x Integer or Real Same as argument MIN x X Minimum of X x Integer or Real Same as argument REAL x Converts x to real Integer Real SIN x Sine of x in rads Real Real Ee SQRT x Square root of x Real Ra TAN x Tangent of x rads Real random seed Provides Seed None Internal random number quasi random number Internal seed Real Introduction of Fortran 90 for Numerical Programming program get pi implicit none real pi pi 4 0 atan 1 0 Intrinsic Function atan arc tangent write PI pi end program get pi It is important to note that all trigonometric intrinsic functions such as sine and cosine use radians for angles not degrees 8 0 Structured Programming Fortran programs may be structured in sequential selective or repetition forms Each structure offer powerful tools for solving numerical problems Logical expressions and variables are essential to advanced methods of control and will be introduced in this section Sequential Programming Each FORTRAN statement is executed exactly one time in the order of appearance Simple to code and follow up however limited to relative simple programming needs Logical Operations Logical Data Type There are only two logical constants in FORTRAN and a variable typed LOGICAL may only have one of these two logical constants Note The periods are required Introduction of Fortran 90 f
12. Introduction of Fortran 90 for Numerical Programming A Brief Introduction to Fortran 90 for Numerical Programming by Pedro B Perez North Carolina State University June 1999 Introduction of Fortran 90 for Numerical Programming Abstract This brief review of the Fortran 90 language is intended to introduce some of the Fortran 90 features to programmers familiar with other scientific languages This work is by no means a complete introduction to the Fortran 90 language and will focus only features pertinent to numerical programming Examples and references are provided for the reader to commence a self paced training journey This work is based on lecture notes from CSC112 and CSC302 at NCSU and references to exercises are provided Introduction of Fortran 90 for Numerical Programming LO IDtodUCHOH 220r wd xmTIseERH LOC Ade Se age REA X Xx 2o Source Code Forms S e cate grs ies sten er o eec ORA e eos Nro dace grs qus 530 Data Types scd pu poneExe EE Fa oe PRS SQ E Eq EP VEE Eon AO OOGdC St ct re ra we Pace sia Se ae tette pur fi oats d iR pte jus 5 0 Math Operations 4zns iue AERE eee eee baa eoe RE qd 6 0 List Directed Input and Output at eases don ER Ee we Be Go TO DEEIDSIC FUNCIONS s scree end CERRAR ed EVE Vd abd 8 0 Structured Programming 2 ex eR OR POET ERR EEG 9 0 Function Sub Program Unit 0 0 0 0 0 e ee eee 10 0 Subroutine Sub Program Unit llle 11 0 Formatted I
13. al external cube root real x a o a cube root x o end program example real function cube root x implicit none calculates the cube root of a positive real number using logs real intent in x protect from changing dummy argument real log_x local variable to function log_x log x cube root exp log x 3 0 the result variable cube root end function cube root Introduction of Fortran 90 for Numerical Programming Example real function fact m implicit none Calculates the factorial of an integer integer j Use j as local variable integer intent in m real factorial j m factorial 1 0 Initialize here to reset value on each reference if j lt 0 then write Error integer j must be positive stop else if j 0 then fact 1 0 return else do while j gt 0 factorial factorial j j j 1 end do end if fact factorial return end function fact Introduction of Fortran 90 for Numerical Programming 10 0 Subroutine Program Unit A SUBROUTINE differs from a FUNCTION in how it is referenced and how the results if any are returned A FUNCTION is referenced simply by using its name followed by the arguments if any in parenthesis A SUBROUTINE is accessed by means of a CALL statement followed by the name of the subroutine and the arguments if any in parenthesis Unlike a FUNCTION a SUBROUTINE does not need to return anything to the re
14. art execution part RETURN END FUNCTION NAME type Declares the type of the result Name It is called the return variable and the function must assign the results of the calculation to this variable This is the only time a program unit name is used in an assignment statement dl d2 These are called dummy or formal arguments which represent the actual arguments variables when the function is referenced RETURN and END Statements O RETURN Functions may have at least one RETURN statement which instructs the sub program to pass the calculated result to the program unit O END Statement The END statement is the last statement in every FORTRAN program unit The END statement terminates execution and is an executable statement Only one END statement per function unit is allowed Introduction of Fortran 90 for Numerical Programming The external FUNCTION is referenced by the functions s NAME from the referencing program unit function name actual argument list o The actual argument list contains the actual arguments in the calling program unit o The number of actual arguments must be equal to the number of dummy or formal of the FUNCTION o Each actual argument must agree with the type of the dummy argument e Corresponding pairs of actual and dummy arguments are associated with the same memory location CAUTION o Changing the values of dummy arguments within a FUNCTION program unit changes the value
15. d program allocatable_array 10 Introduction of Fortran 90 for Numerical Programming program array demo implicit none real allocatable elements real sum average integer 1 j ii write Enter the array s starting and ending points read ij allocate elements i j write Enter the values for elements read elements ii ii ijj do ii i j 1 sum sum elements ii end do average sum abs i abs j 1 0 write write The following values have been entered for elements write do ii i j 1 write 10 ii elements ii end do write A f8 3 The average is average format tr2 Element 12 is f8 4 end Introduction of Fortran 90 for Numerical Programming Multidimensional Arrays Arrays are FORTRAN s version of structured data types Fortran 90 allows up to seven 7 dimensions which refered to as a rank seven array The shape of the array is determined from the rank and extent 2 D Array Declaration The name and the subscript range of each two dimensional array may be declared in two ways DIMENSION array name lj u lu Example REAL DIMENSION FLUX 1 2000 1 1000 REAL DIMENSION FLUX 2000 1000 The second and prefered way to declare an array is to subscript the variable when declaring the type REAL FLUX 1 2000 1 1000 REAL FLUX 2000 1000 o The range or dimension of the array must be an integer value o
16. der 33 0 41 0 1 2 11 0 12 3 98 0 Eso ao Desired Order for entering data at the keyboard BE 33 0 41 0 1 2 11 0 12 3 98 0 23 0 14 0 21 0 Method required Row wise Processing Desired Order for entering data at the keyboard 33 0 11 0 23 0 41 0 12 3 14 0 1 2 98 0 21 0 Method required Column wise processing Fortran default Introduction of Fortran 90 for Numerical Programming The programmer can select the processing order by controlling the use and order of subscripts The FORTRAN default convention is that 2 D arrays will be processed column wise COLUMN WISE PROCESSING The first subscript is varied first and the second subscript varies second ROW WISE PROCESSING The second subscript is varied first and the first subscript varies second Introduction of Fortran 90 for Numerical Programming I O and 2 D Arrays Initializing a 2 D array is efficiently performed with a DO LOOP Interactively initializing a 2 D array Desired array initialization order 33 0 41 0 1 2 11 0 12 3 98 0 CET REAL DEMO 3 3 User must enter ROW WISE PROCESSING 33 0 Nested Do Loops 41 0 1 2 DO F 1 3 11 0 DO J 1 3 12 3 READ AXIS IJ 98 0 END DO 23 0 END DO 14 0 to obtain 33 0 41 0 1 2 11 0 12 3 98 0 EosT Use Row Wise Processing Order Introduction of Fortran 90 for Numerical Programming ROW WISE PROCESSING The second subscript is varied first and the first subsc
17. ferencing program unit If the SUBROUTINE does return results it does so by means of one or more arguments Subroutine Program Unit Structure SUBROUTINE name dummy argument list O Declaration Part Oo Execution Part Oo END SUBROUTINE name name is a legal FORTRAN identifier The name should be distinct from all other names in the program and should be chosen to indicate the purpose of the subroutine Dummy argument list or Dummy arguments are used to associate values to and from the subroutine If there are no formal arguments the parentheses may be omitted Documentation should follow the SUBROUTINE as comment lines Specification This section includes non executable statements These provide information to be used during compilation of the program REAL INTEGER CHARACTER COMPLEX etc EXTERNAL INTENT IN Introduction of Fortran 90 for Numerical Programming Execution Statements Statements in FORTRAN are classified as executable or non executable Executable Statements Specify actions to be taken during program execution RETURN and END Statements o RETURN Subroutines have at least one RETURN statement which instructs the sub program to pass the calculated values to the main program unit Syntax RETURN Note Declared Obsolete in Fortran 90 END Statement The END statement is the last statement in every FORTRAN subroutine IT IS REQUIRED The END statement terminates execution and is
18. ide and then associates results with the variable Introduction of Fortran 90 for Numerical Programming Mixed mode Assignments A reminder that when variables of the same type are arithmetically combined the result preserves the type 9 0 4 0 2 2 25 Real 1 0 2 0 2 0 50 Real 9 422 Integer 1 220 Integer An integer quantity combined with a real quantity causes the integer to be converted to real and the result will be real Example of Exponent Trouble Avoid raising a base to a floating point value unless that is exactly what is needed and the base will always be greater than 0 2 0 3 2 0 2 0 2 0 8 0 2 0 302 e 01 29 3830 4 0 2 4 0 4 0 16 0 4 0 2 0 2 e _ UNDEFINED Priority Rules Expressions containing the arithmetic operations and are evaluated following the FORTRAN priority rules which are identical to c with the addition of exponentiation Introduction of Fortran 90 for Numerical Programming All exponentiations are done first consecutive exponentiations are performed from right to left All multiplications and divisions are performed next in the order in which they appear left to right Addition and subtraction are performed last in the order in which they Examples QT SOP 2S Tee OS 18 244 2 2 24 16 2 24 8 10 The standard order of evaluation can be overridden using parentheses Nested parentheses are evaluated from the inner
19. ise order READ AXIS LJ J 1 COLUMN I 1 ROW Oo Column wise order READ AXIS LJ I 1 ROW J 1 COLUMN NOTE The READ statement is only encountered once per loop and all the data for that loop can be on the same line Introduction of Fortran 90 for Numerical Programming Page 49 FILE 33 0 410 12 11 0 12 3 98 0 23 0 140 21 0 READ 10 ACJ J 1 3 1 1 3 ALJ 33 0 41 0 1 2 11 0 12 3 98 0 roo READ 10 ACJ 1 1 3 J 1 3 A LJ 330 11 0 23 0 41 0 123 14 0 12 980 Introduction of Fortran 90 for Numerical Programming Important to Remember The FORTRAN default convention is that 2 D arrays will be processed column wise ROW WISE PROCESSING The second subscript is varied first and the first subscript varies second COLUMN WISE PROCESSING The first subscript is varied first and the second subscript varies second Introduction of Fortran 90 for Numerical Programming Appendix A Fortran 90 Compiler Available at NCSU Numerical Algorithms Group s NAG Fortran 90 Compiler A third party Fortran 90 compiler was installed on the COS computing environment in early 1996 Since this is not a native compiler to the workstation the software most be added to the session eos gt add nagf90 Numerical Algorithms Group NAG NAGWare f90 Rel 2 1 Fortran 90 Compiler eos gt f90 filename for options Above will produce a file named a out which is an executable pr
20. ith the derived data type type periodic table elements 106 Array of the elements initialize one a array element for the element Uranium elements 92 element name Uranium elements 92 atomic mass 238 05 elements 92 atomic number 92 elements 92 fissile false Introduction of Fortran 90 for Numerical Programming Appendix C Fortran 90 Pause Routine SUBROUTINE F90 PAUSE subroutine to pause program requiring user to re initiate execution MPLICIT NONE CHARACTER PAUSE f WRITE A ADVANCE NO Press lt ENTER gt to continue gt READ A PAUSE END SUBROUTINE F90 PAUSE
21. n 4 0 Code Structure A Fortran code consists of program units of which one and only is called the PROGRAM unit Modular components include the Program Subroutines Functions and Modules Program units may consist of data and algorithms Each program unit is structured as follows HEADING Program unit name SPECIFICATION Variable Declarations EXECUTION Algorithm END End Statement Introduction of Fortran 90 for Numerical Programming Program Unit Composition Program Heading o The FORTRAN program heading has the form PROGRAM name name is a legal FORTRAN identifier This is the first statement in a Fortran program Specification The specification part of the program must appear next REAL INTEGER CHARACTER COMPLEX etc type declarations statements Execution Statements Statements in FORTRAN are classified as executable or non executable Non executable Statements provide information to be used during compilation of the program These do not cause any specific action to be performed during program execution REAL TYPE PROGRAM etc Executable Statements specify actions to be taken during program execution Executable statements are placed in the Execution Part of the program following the declaration part Introduction of Fortran 90 for Numerical Programming END and STOP Statements o END Statement The END statement is the last statement in every FORTRAN program The END statement terminate
22. ng For LOGICAL P Q NOT NOT P TRUE if P is FALSE FALSE if P is TRUE AND P AND Q Conjunction of P and Q TRUE only if both P and Q are TRUE OR P OR Q Disjunction of P and Q TRUE if P or Q or both are TRUE EQV P EQV Q Equivalence of P and Q TRUE if both P and Q are TRUE or FALSE NEQV P NEQV Q Non equivalence of P and Q TRUE if P or Q is TRUE and the other is FALSE Logical Truth Tables NOT P TRUE TRUE FALSE rasE o raNDO Poro Provo PNEQVQ F TRUE FALSE FALSE TRUE FALSE TRUE FALSE TRUE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE TRUE Introduction of Fortran 90 for Numerical Programming o Order of Combined Logical Operations and Relational Expressions 1 Relational Operators lt gt lt gt 2 NOT 3 AND 4 OR 2 EQV or NEQV Example N 4 N 2 1 gt 10 AND NOT N lt 3 TRUE Example program decay Calculate the decay of radioactive material and provide error checks for input implicit none logical error real n nO lambda t write Enter n O lambda and time read nO lambda t error lambda It 0 0 OR t 1t 0 0 if error eqv true then write Error detected in input stop end if n nO exp lambda t write Radioactive nuclide remaining n end program decay Selective Programming Structure This structu
23. nput and Output 328 sew eta oe e venero i pea 12 0 Structured Data Types Arrays 252i z tm Eb Rp eb Appendices A Fortran 90 Compiler at NCSU B Fortran 90 Derived Data Type C Fortran 90 Pause Routine Table of Contents Introduction of Fortran 90 for Numerical Programming 1 0 Introduction Fortran 90 is a standardized programming language which includes the entire Fortran 77 dialect The Fortran 90 highlights which are included in this monogram will be presented in the order the author believes will impact the beginning Fortran programmer The following topics are in included Source code form and Character set Code structure Input Output Data types Program Controls Relational Operators Arrays Intrinsic Functions Sub Programs and modules OO0o0000000 No attempt is made to be inclusive of all the Fortran 90 features under the above headings Only an introductory level explanation with an example are provide The reader is encouraged to read the reference literature for a complete explanation The Fortran 90 compiler used at NCSU as of the date of this document is the Numerical Algorithm Group Fortran 90 compiler One simply enters at eos prompt add nagf90 and then invoke the compiler by entering at the eos prompt f90 myprogram f90 2 0 Source Code Form Free form Source Code Source code lines in free form may now be 132 characters in length A programmer may use any column in the Fortran record for coding The
24. ogram Introduction of Fortran 90 for Numerical Programming Appendix B Derived Data Type This section is presented only because the introduction of derived data type was an important addition to the Fortran language Fortran 90 allows for user defined data types that are derived from intrinsic data types providing considerable flexibility in defining data structures The programmer defines a derived data type using the new Fortran 90 type statement in the declaration part of the program The general form is as follows TYPE derived name intrinsic type declaration symbolic name f Ses at Rte uu vp END TYPE derived name A variable is declared a derived data type by using the type statement as follows in the declaration part of the program unit TYPE derived name variable name The variable has been declared type derived name and is composed of a number of intrinsic data types It is important to notice the sequential order of the intrinsic data types and to use the symbol to separate these intrinsic components The following example demonstrate initializing variable variable name symbolic name constant Example declare a derived data type type periodic table character len 12 element name real atomic mass integer atomic number logical fissile end type periodic_table Introduction of Fortran 90 for Numerical Programming declare a variable to be declared w
25. or Numerical Programming Logical Variable Declaration Logical variables are declared in the specification part of the program unit i e main program or sub program just as other types LOGICAL name list eg LOGICAL LOVE CHECK SANITY Logical variables may specify actions to be taken during program execution Logical Expressions Simple Expressions e Logical Constants Logical Variables Relational Expressions o Compound Logical Expressions Combination of logical expressions using logical operators e Relational Operators expression 1 relational operator expression 2 Relational Operators symbol Meaning ae 1 Is less than ise 1 Is greater than Is equal to Is less than or equal to Is greater than or equal to Precis mnsre Ye Is not Ts notequalto to Introduction of Fortran 90 for Numerical Programming Examples xX 45 N 400 X lt 5 0 is TRUE N 999 is FALSE Logical expressions formed by comparing real variables with EQ are evaluated as FALSE even though the quantities are algebraically equal Example Real X Logical EQUALS Y X 1 0 X EQUALS Y EQ 1 0 results is usually FALSE o Compound Logical Expressions Compound logical expressions are formed by combining logical expressions using logical operators Logical Operators NOT AND OR EQV NEQV Introduction of Fortran 90 for Numerical Programmi
26. r integer parameter o Memory locations for the data type items are reserved according to the dimension of the array REAL DIMENSION A 100 100 Array A has reserved 10 000 floating point real words in memory o FORTRAN 77 does not allow for dynamic memory allocation for arrays but FORTRAN 90 does e Care is needed to only reserve the memory needed Introduction of Fortran 90 for Numerical Programming Subscripted Variables Each individual element of a 2 D array is uniquely identified and accessed by means of a subscripted variable variable name row subscript id column subscript id The subscript identifiers are integer values or variables VALUE 1 2 VALUE i j VALUE 1 J refers to array element and contents in the I row and J column Each element of the 2 D array can be accessed directly by using a two subscripted variable consisting of the array name and the desired element subscript INTEGER IMORN 2 3 IMORN 1 3 13 IMORN 2 3 23 Two Dimensional arrays suggests two natural orders for processing the data entries O Row wise Oo Column wise The Fortran default processing order is column wise which is different from c c which uses row wise processing Introduction of Fortran 90 for Numerical Programming Row wise processing 11 12 13 14 21 22 23 24 3l 32 33 34 pate oe u Column wise processing 11 12 13 14 21 22 23 24 3l 32 33 34 Example Desired array initialization or
27. red programming approach provides two or more paths of program execution The control scheme is by logical expressions Introduction of Fortran 90 for Numerical Programming IF construct or Block I F statement construct name IF logical expression THEN statement sequence END IF construct name Examples IF X gt 0 THEN CHECK X IF X 20 THEN Y X 2 Y X 2 Z SQRT X Z SQRT X END IF END IF CHECK X The Logical expression is evaluated first If it returns TRUE then the next two statements are executed If the logical expression returns FALSE then the nested expressions are bypassed The logical expression in an IF construct must be enclosed in parenthesis The structure on the right is given the name CHECK X to easily identify the purpose Logical IF Statement Simplified form of the IF construct and an old popular one for single statement sequences IF logical expression action statement Execution of the IF statement causes evaluation of the logical expression If the logical expression is TRUE the action statement is executed If FALSE the action statement is not executed Examples REAL LAMBDA IF LAMBDA 0 0 LAMBDA ABS LAMBDA IF THEN ELSE Constructs IF constructs also allow for an alternative statement sequence for execution when the logical expression is FALSE Introduction of Fortran 90 for Numerical Programming construct name IF logical expression THEN sta
28. ript varies second REAL AXIS 3 3 DO F1 3 DO 20 J 1 3 READ AXIS LJ END DO END DO When I 1 First Row When I 2 Second Row DO J 1 3 DO J 1 3 READ AXIS 1 J READ AXIS 2 J END DO END DO When I 3 Second Row DOJ 1 3 READ AXIS 3 J END DO Introduction of Fortran 90 for Numerical Programming Desired array initialization order 33 0 41 0 1 2 11 0 12 3 98 0 3o 140 REAL AXIS 3 3 User must enter 33 0 11 0 COLUMN WISE PROCESSING 23 0 41 0 DO J 1 3 12 3 DO I 1 3 14 0 READ AXIS IJ 1 2 END DO 98 0 END DO 21 0 COLUMN WISE PROCESSING The first subscript is varied first and the second subscript varies second REAL AXIS 3 3 DO J 1 3 DO I 1 3 READ AXIS LJ END DO END DO When J 1 Column 1 When J 2 Column 2 DO I 1 3 DO I 1 3 READ AXIS L1 READ AXIS L2 END DO END DO Introduction of Fortran 90 for Numerical Programming When J 3 Column 3 DO I 1 3 READ AXIS L3 END DO o It must be noticed that the READ statement is encountered nine 9 times in the nested do loop structure above o This means the data values must also be entered on nine separate lines o If the data is in a file the file structure for the column processing is for example 33 0 11 0 23 0 41 0 12 3 14 0 1 2 98 0 21 0 o The same limitation occurs with the WRITE statement I O Using Implied Do Loops AXIS ROW COLUMN o Row w
29. s execution and is an executable statement Only one END statement per program unit is allowed Syntax END or END program unit name where program unit is the Fortran program or subprogram and name is the name of the program unit end program example Oo STOP Statement Allows for the program execution to stop prior to terminating execution with the END statement Syntax STOP PAUSE Routine Allows for program execution to be interrupted and re started by referencing a routine supplied by the programmer Syntax CALL PAUSE This routine must be a user provided See the appendices Example A simple program in Fortran 90 and C C follows Introduction of Fortran 90 for Numerical Programming Fortran 90 program hello world implicit none write Hello World of Mine end program hello_world C include lt stdio h gt include lt iostream h gt main cout lt lt Hello World of Mine lt lt endl 5 0 Math Operations FORTRAN arithmetic operators are given by C C programmers should note that Fortran supports exponentiation Assignment Operator The assignment statement is used to assign values to variables variable expression The expression may be a constant variable or formula For example PI 3 1416 CAREA PI R 2 The assignment associates a memory location with the variable The assignment statement first evaluates the expression right hand s
30. s of the corresponding actual arguments that are variables The FUNCTION dummy arguments reference the memory storage address of the actual argument If the FUNCTION changes the dummy argument it will inadvertently change the actual argument in the referencing program unit which usually leads to errors How does the programmer protect the actual argument This is done by specifying the intent of each dummy argument Dummy Argument and its INTENT A dummy argument may be protected by specifying an INTENT IN for the dummy argument in the procedure Introduction of Fortran 90 for Numerical Programming Example real function cube root x implicit none calculates the cube root of a positive real number using logs real intent in x protect from changing dummy argument real log x local variable to function log x log x cube root exp log x 3 0 the result variable cube root end function cube root In this example o Local variable is not accessible outside of the FUNCTION CUBE ROOT o INTENT IN tells compiler X can not be changed by the procedure Oo Variable name CUBE ROOT is same as function name Special variable called the result variable o The type of the function program unit is declared BOTH in the referencing program unit and in the function Introduction of Fortran 90 for Numerical Programming Example program example implicit none uses function cube root re
31. tement sequence 1 ELSE statement sequence 2 END IF construct name IF ELSE IF Constructs The IF ELSE IF construct supports Multi Alternative selection structures IF logical expression 1 THEN statement sequence 1 ELSE IF logical expression 2 THEN statement sequence 2 ELSE statement sequence n END IF Example IF x lt 0 0 THEN funct x ELSE IF x lt 1 0 THEN funct x 2 ELSE funct 1 0 END IF Fortran Repetition Structures The third Fortran control structure is the Repetition Structure which is also called Loops Introduction of Fortran 90 for Numerical Programming Loop Control o Loops controlled by a counter DO Loops o Loops controlled by a logical expression DOWHILE Loops DO Loops o Loop is executed once for each value of a pre determined control variable range o The initial value the limit and the step size of the control variable are determined before repetition begins o These values may not be modified during loop execution DO Loop Structure DO index lower limit upper limit step size statement sequence END DO o The Loop structure automatically increments or decrements the loop index variable sum do do 1 10 1 1 sum sum 1 2 end do sum do do while 1 10 sum sum i i i1 1 end do Named Fortran 90 Do construct Note DO WHILE requires incrementing control index Introduction of Fortran 90 for Numerical Programming
32. tran 90 for Numerical Programming PROGRAM SUBROUTINE EXAMPLE IMPLICIT NONE INTEGER N20 REAL FACTORIAL WRITE Factorial Program enter an integer gt READ N CALL FACT N FACTORIAL Reference SUBROUTINE using CALL WRITE Factorial of N is FACTORIAL STOP END Pee E subroutine fact OEE SUBROUTINE FACT M F IMPLICIT NONE INTEGER J INTEGER INTENT IN M REAL INTENT OUT F J M F 1 0 Initialize here to reset value on each call FACTORIALS IF J LT 0 THEN STOP ELSE IF J EQ 0 THEN F 1 0 ELSE DO WHILE J GT 0 F F J J J 1 END DO END IF FACTORIALS END SUBROUTINE FACT Introduction of Fortran 90 for Numerical Programming 11 0 Formatted Input and Output Fortran formatted I O with the READ and WRITE statements allows for programmer specified formats and file access READ and WRITE Statements Oo x i x UNIT first The implies default I O unit number Typically the CRT monitor Format Specifier second The implies compiler default format for I O operations Formatted Output PRINT format specifier output list WRITE unit number format specifier output listing The format specifier specifies format for displaying expressions in the output list o An asterisk o A character constant or variable specifying format for the output list of format descriptors o The label number of a FORMAT statement FORMAT list

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