Fortran Lesson

FORTRAN LESSON Lesson Topics Editing Fortran

Assignment

Compiling

Parameter

Running a Program Comments Program

Print *

Variables

Read *

Declarations

End

Types

Operations

Implicit Quantifier

Intrinsic Functions

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Main Fortran Page

Introduction Fortran is one of the oldest programming languages devised, but it is also still one of the most popular, especially among engineers and applied scientists. It was developed in the 1950's at IBM. Part of the reason for Fortran's durability is that it is particularly wellsuited for mathematical programming; moreover, there are millions of useful programs written in Fortran, created at considerable time and expense, and understandably people are reluctant to trash these old programs and switch to a new programming language. The name Fortran originally referred to "Formula Translation", but it has long since taken on its own meaning. There are several versions of Fortran around, among them Fortran 77, Fortran 90, and Fortran 95. (The number denotes the year of introduction.) Fortran 77 is probably still the most used, and it is the version installed on UHUNIX and in the UH math lab. Even though this semester we have thus far studied Basic, at the same time we have studied Fortran, because commands and procedures are very similar in the two languages. Moving from QuickBasic to Fortran is more a matter of change of terminology than anything else.

Editing Fortran

Unlike in Basic, a Fortran program is not typed in a "Fortran window". Instead, a program is typed and saved with an editor (i.e., a word processor), and the program is then turned into an executable file by a Fortran compiler. To begin the process of creating a Fortran program in the math lab, you must open an editor. It is preferable to use a simple editor - such as Notepad or the DOS editor - because fancy word processors might add extraneous formatting notation that will hang up Fortran. A most peculiar feature of Fortran 77 is its line structure, which is a carryover from the old days when programs were typed on punch cards. A punch card had 80 columns, and so does a line of Fortran code. A "c" in column 1 indicates a comment (similar to REM in Basic). Columns 2-5 (usually left blank) are reserved for line numbers. Column 6 is used only to indicate a continuation of a line too long to fit on the card. Columns 7-72 contain the instructions of the program. Columns 73-80 were originally used for numbering the punch cards, but are rarely used nowadays - leave them blank and the compiler will ignore them. Fortran is case insensitive - that is, it does not distinguish between capital and small letters. Thus x and X refer to the same variable. Many programmers for simplicity use all small letters, but you may do as you like. Also, after column six Fortran does not recognize spaces (except for spaces inside quotations as in print statements). In general, spaces are mostly for the purpose of making code more readable by humans. When you type a Fortran program with an editor, make certain the editor indents more than six spaces; then if you begin every line with an indent you do not have to worry about counting six spaces at the beginnings of lines. Let us go through the steps of editing, compiling, and running a short program. First open Notepad under Windows, or type "edit" (and return) under a DOS prompt to open the DOS editor. (When you double-click the Fortran icon on a math lab computer, you get a DOS prompt.) Beginning each line with an indent (except for the fourth line, where the "c" must be placed in the first column), type the program exhibited below; the program computes the area of a circle of radius r, as input by the user. The resulting file that you save is called the source file for the program.

c

program circlearea real r, area, pi parameter (pi = 3.14159) This program computes the area of a circle. print *, "What is the radius?" read *, r area = pi * r ** 2 print *, "The area is", area print *, "Bye!" end

The first statement above gives the program name, the second declares that "r", "area", and "pi" will be single precision real quantities, and the third announces that pi has the value 3.14159. The fourth statement, beginning with "c" in column 1, is a comment describing what the program does; such comments are for the benefit of the programmer and are ignored by Fortran. The fifth statement prompts the user for the radius of the circle, and the sixth accepts this input. The seventh statement computes the area and the eighth informs the user of this area. Finally, the last two statements bid goodbye and terminate the program. The name for a source file in Fortran must end with the extension ".f" before the compiler recognizes it. After you have typed the above program, save the file as area.f. (If you type the file in Notepad, include the whole name in quotes when you save it, as otherwise the extension .txt will be added to the name.) The file will be saved to your h directory in the math lab. Under a DOS prompt you can view the files in this directory by typing dir and enter; under Windows you can double-click "My Computer" and then the icon for the h drive.

Compiling After you have created and saved a source file, you next must compile this file. Open a Fortran window and enter g77 name.f, where in place of name you insert the name of your source file. (If the source file resides in a directory different from that of the Fortran program, you will have to include also the directory path of the file.) To compile the file of our example above, in the math computer lab you just enter g77 area.f. If your program has mistakes (which usually happens on the first attempt at compiling), instead of a compiled file you will get Fortran error messages pointing out problems. Some of these messages can be hard to decipher, but after reading hundreds of them you will get better at it. If your program has no mistakes Fortran will simply return a DOS prompt - that is good news because it means Fortran has successfully created a compiled file. By default this new file is given the name a.exe. (You can give the compiled file a name of your own choosing by typing g77 area.f -o name.exe to compile the program but usually there is no reason not to accept the default name.) Your compiled file, also located in the h directory, is now executable - that means the program is ready to run.

Running a Program If your compiled file has the default name a.exe, you simply type a and return to run it (or name and return if you gave the file another name). After you run the program and see how it works, you can return to your editor and revise it as you wish. It is perhaps better to keep two windows open - both the Fortran window and the editing window - so that you can quickly switch from one to the other with a mouse-click. After revising a program, you must save and compile it again before changes take effect.

If you do enough Fortran programming, sooner or later you will err and create and run a program that never stops. In such a situation, type "Control-C" to interrupt the execution of the program. Now that we have discussed the basic nuts and bolts of creating and running a Fortran program, we discuss some terminology and commands. You will probably find that most of these remind you of similar things in Basic.

Program Every Fortran program must begin with a program line, giving the name of the program. Here are examples: program quadratic program mortgage program primes .

Variables, Declarations, Types After the program name come the declaration statements, stating the types of the variables used in the program. A variable name consists of characters chosen from the letters a-z and the digits 0-9; the first character of the name must be a letter. You are not allowed to use your program name as a variable, nor are you allowed to use words reserved for the Fortran language, such as "program", "real", "end", etc. The variable types in Fortran are 1) integer (in the range from about - 2 billion to + 2 billion) 2) real (single precision real variable) 3) double precision (double precision real variable) 4) character (string variable) 5) complex (complex variable) 6) logical (logical variable) As illustration, the declaration statements real r, area integer M, N double precision a, b declare that r and area are single precision real variables, that M and N are integers, and that a and b are double precision real variables.

If you do not declare the type of a variable, Fortran will by default make it an integer if it starts with one of the letters i through n, and will make it a single precision real variable otherwise. However, it is normal (and good) programming practice to declare the type of every variable, as otherwise mistakes are easily made. The implicit quantifier before a type declaration makes all variables starting with the listed letters of the specified type. For example, the declarations implicit integer (i-m) implicit real (r-t) make variables starting with i, j, k, l, m integers, and those starting with r, s, t real. However, the implicit quantifier is probably best avoided, as programmers with short memories will make mistakes. A declaration statement is nonexecutable - that is, it provides information but does not instruct Fortran to carry out any action. Declarations must appear before any executable statement (a statement that does tell Fortran to take some action).

Assignment The equals sign "=" assigns the variable on the left side the value of the number or expression on the right side (exactly as in Basic).

Parameter The parameter statement works like CONST in Basic - it specifies a value for a constant. The syntax is parameter (name = constant expression) where name is replaced by the name of the constant, and constant expression by an expression involving only constants. Thus parameter (pi = 3.14159) specifies a value for the constant pi, while the succeeding statement parameter (a = 2* pi, b = pi/2) fixes values of new constants a and b in terms of the old constant pi. Remember that once a constant is defined you are not allowed to change its value later. All parameter statements must appear before the first executable statement.

Comments

A comment is similar to an REM statement in Basic. You can indicate a comment by placing a "c" in column 1 and then the comment in columns 7-72. Alternatively, you can use an exclamation point "!" to indicate a comment; it may occur anywhere in the line (except columns 2-6). Everything on a line after an exclamation point becomes a comment.

Print * The command "print *" is analogous to PRINT in Basic; it instructs Fortran to print items to the screen. Examples are print *, x print *, "The solution is ", x print *, 'The radius is', r, 'and the area is', area Note that a comma follows "print *", and that commas (instead of semicolons as in Basic) appear between successive items to be printed. Observe also that either double or single quotes may enclose strings. The command "print *" on a line by itself (without a comma) serves as a line feed.

Read * The command "read *" is analogous to INPUT in Basic. Examples are read *, radius read *, A, B, C . In the first example the program pauses to allow the user to enter the radius. In the second example the user types the values of A, B, and C, separated by returns; alternatively, the user can type A, B, and C separated only by commas, and then one final return.

End The end statement marks the end of the main Fortran program or of a subprogram. (It cannot be used in the middle of the program, as in Basic.)

Operations of Arithmetic Here are the common arithmetical operations in Fortran: Addition

x+y

Subtraction

x-y

Multiplication

x*y

Division

x/y

Exponentiation x ** y Fortran performs exponentiations first, then multiplications and divisions, and lastly additions and subtractions. (When in doubt, use parentheses!) Be careful with division. If m and n are integers, then m/n is truncated to its integer part. Thus 3/4 is evaluated as 0, and 25/6 as 4. When working with constants rather than variables you can avoid this problem by using periods after integers. For example 3./4. is evaluated in the standard way as .75, as Fortran treats 3. and 4. as real variables rather than as integers.

Intrinsic Functions Many standard mathematical functions are built into Fortran - these are called intrinsic functions. Below is a table of some of the functions most commonly used in mathematical programming. All trig functions work in radians. (Note that arguments of functions must be enclosed in parentheses.) Function

Description

abs(x)

absolute value of x

acos(x)

arccosine of x

asin(x)

arcsine of x

atan(x)

arctangent of x

cos(x)

cosine of x

cosh(x)

hyperbolic cosine of x

dble(x)

converts x to double precision type

exp(x)

exponential function of x (base e)

log(x)

natural logarithm of x (base e)

mod(n,m) remainder when n is divided by m real(x)

converts x to real (single precision) type

sign(x,y)

changes the sign of x to that of y

sin(x)

sine of x

sinh(x)

hyperbolic sine of x

sqrt(x)

square root of x

tan(x)

tangent of x

tanh(x)

hyperbolic tangent of x

FORTRAN LESSON 2 Lesson Topics Logical Expressions

Go To

If ... Then ... Else

Character Variables

Stop

Do Loops

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Main Fortran Page We look at more of the commonly used features and commands of Fortran.

Logical Expressions A logical expression is a relation between variables or expressions that can have a value of TRUE or FALSE. Such expressions are used in "if … then" constructions and in loops, when testing whether to execute certain steps of a program. Relations and connectives appearing in logical expressions are listed in the following table; you will see how some of these are used in later examples. Relation/Connective Meaning .lt.

less than

.gt.

greater than

.le.

less than or equal to

.ge.

greater than or equal to

.eq.

equals

.ne.

not equal to

.and.

and

.or.

or

.not.

not

.xor.

"exclusive" or (i.e., only one is true)

.eqv.

equivalent (i.e., same truth values)

.neqv.

not equivalent

If ... Then ... Else Constructions "If … Then … Else" constructions in Fortran are pretty much like those in Basic, with but a few minor modifications. First, instead of using in the tests symbols like "=", "<", ">=", etc., as in Basic, you must use the abbreviations in the preceding table. Also, tests must be enclosed in parentheses, and "else if" may be two words. Here are several examples: 1) if (x .gt. 0) print *, "x is positive" 2)

if (x .ge. y .and. x .ge. z) go to 40

3)

if (x .ge. 0) then y = sqrt(x) print *, y, " squared = ", x end if

4)

if (x .ge. 0) then y = sqrt(x) print *, y, " squared = ", x else print *, "x has no square root" end if

5)

if (x .gt. 0) then print *, "x is positive" y = sqrt(x) else if (x .lt. 0) then print *, "x is negative" go to 60 else if (x .eq. 0) then

print *, "x is zero" y=0 end if Observe that, as in examples 1) and 2), the one-line "if" statement does not use "then". Moreover, "else" appears on a line by itself, while "else if" shares the line with the test condition and "then".

Stop A stop statement stops the execution of a program. For instance, the sequence of statements below terminates the program whenever n is less than zero: if (n .lt. 0) then print *, "Error - your age cannot be negative!" stop end if . Do not confuse stop and end. Use end only as the very last statement in the program, and use stop only to terminate the program before this last statement. Violating these rules will fatally confuse the compiler - it regards an end statement as the program's physical end.

Labels and Go To Labels and the "go to" statement work as in Basic, except that a label must be a number, and it must be typed in columns 2-5. Here is an example of a go to command directing the action to a labeled statement: if (x .lt. 0) go to 10 print *, "The square root of x is ", sqrt(x) stop 10 print *, "x is negative and has no square root"

Character Variables A character variable is analogous to a string variable in Basic. A character variable must be declared at the beginning of the program, and attached to it in the declaration must be a number following an asterisk "*"; this number indicates the maximum number of symbols in the string. For example, the declaration statement character name*20, ans*1 indicates that "name" is a character variable holding no more than 20 symbols, while "ans" is a character variable holding only one symbol. A string in Fortran may be enclosed in either double quotes, as in "hello", or in single quotes, as in 'goodbye'.

Do Loops "For … Next" loops in Basic become "Do Loops" in Fortran. Such a loop begins with a do statement, and ends with either end do, or a labeled continue statement. Here are two loops that add the squares of the integers from 1 to 10: sum = 0 | sum = 0 do i = 1, 10 | do 5 i = 1, 10 sum = sum + i ** 2 | sum = sum + i ** 2 end do | 5 continue print *, "The sum is", sum | print *, "The sum is", sum The end do and continue statements serve only to identify the end of the loop. The limits of the loop may be variables as well as numbers (e.g.: do i = m, n). As in Basic you may indicate a step size, which can be positive or negative. For example, the statement do i = 1, 9, 2 specifies that the loop variable i run over the odd numbers 1, 3, 5, 7, 9. Loops can be nested, and nested loops can end on the same continue statement (but not on the same end do statement). Here are two instances of nested loops assigning the entries of a 10 x 10 matrix: do i = 1, 10 do j = 1, 10 a(i,j) = i + j end do end do

| | | | |

5

do 5 i = 1, 10 do 5 j = 1, 10 a(i,j) = i + j continue

FORTRAN LESSON 3 Lesson Topics Integers

Exponentials

Real(x)

Rational Exponents

Single Precision

Roots

Double Precision

Write

Base 2 Conversion Errors

Format

Mixed Type Arithmetic

Format Code Letters

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Main Fortran Page In Fortran Lesson 1 we briefly looked at the types of variables in Fortran. To avoid mistakes in Fortran arithmetic you must pay close attention to rules regarding working with numbers of the various types. Whereas Basic is more lenient, allowing some flexibility in mixing variables and numbers of different types, Fortran is less forgiving and will make you pay for oversights. In this lesson we look more closely at some of the rules and conventions that must be observed.

Integers An integer in Fortran is a whole number; it cannot contain commas or a decimal point. Examples of numbers considered integers by Fortran are 12 , -1311 , 0 , +43 , 123456789 . For positive integers the plus sign is optional, but negative integers must be preceded by a minus sign. Examples of numbers not considered integers by Fortran are 22,547

,

3.

,

4.0

,

-43.57 .

Because of the decimal points, Fortran will regard 3. and 4.0 as real numbers. An integer N in GNU Fortran must lie within the range - 2,147,483,648 ≤ N ≤ 2,147,483,647 . One idiosyncrasy of Fortran is that when it performs arithmetic on integers, it insists on giving an answer that is likewise an integer. If the answer is not really an integer, Fortran makes it one by discarding the decimal point and all digits thereafter. For example, Fortran will assert that 11/8 = 1

,

15/4 = 3

,

-4/3 = -1

,

-50/6 = -8

,

2/3 = 0 .

If you want Fortran to give you the correct value of 11/8, you tell it to compute 11./8., so that it interprets the numbers as real numbers and produces the correct value 1.375. Integer arithmetic in Fortran can lead to other weird surprises - for instance, the distributive law of division is invalid, as demonstrated by the example

(2 + 3)/4 = 5/4 = 1

but

(2/4) + (3/4) = 0 + 0 = 0 .

Most of the built-in functions in Fortran apply to real numbers, and attempts to apply them to integers result in compiler error messages. The compiler will protest if you ask Fortran to compute sqrt(5), but it has no problem with sqrt(5.). Likewise, if you declare N to be an integer variable and ask Fortran to compute sqrt(N) or cos(N) or log(N), your program will not compile since these functions cannot act on integers. One way around this problem is to use the intermediate function real(x) , which converts x to a real number (if it is not already one). Then, for example, real(5) = 5.

,

sqrt(real(5)) = sqrt(5.) = 2.23606801 .

The compiler will have no objection if N is an integer variable and you ask Fortran to compute a composition like sqrt(real(N)) or cos(real(N)). If you declare that A is an integer and later make the assignment A = 3.45, Fortran will not complain but it will truncate 3.45 and assign A the value A = 3. Likewise, if you insert the statement A = sqrt (5.), Fortran will truncate sqrt (5.) = 2.23606801 and deduce that A = 2. But errors such as these are easily avoided if you are careful to make correct type declaration statements for all variables at the beginning of your program.

Single Precision Real Numbers A real number, or more precisely a single precision real number, is written with a decimal point by Fortran, even when it is a whole number. The sequence of statements real x integer y x=3 y=3 print *, "x = ", x, " but y = ", y, " - weird!" produces the output x = 3. but y = 3 - weird! GNU Fortran uses up to 9 digits, not counting the decimal point, to represent real numbers. It will report that sqrt (3.) = 1.73205078 , sqrt (1100.) = 33.1662483 , sqrt (2.25) = 1.5 . Fortran can use also scientific notation to represent real numbers. The sequence "En" attached to the end of a number, where n is an integer, means that the number is to be multiplied by 10n. Here are various ways of writing the number 12.345:

1.2345E1 , .12345E2 , .012345E3 , 12.345E0 , 12345E-3 . In working in single precision it is futile to assign more than 9 or 10 nonzero digits to represent a number, as Fortran will change all further digits to 0. (The 10th digit can affect how Fortran does the truncation.) The assignments x = 123456789876543. , x = 123456789800000. , x = 1234567898E5 produce the same result if x already has been declared a single precision real number. Note that commas are not used in representing numbers; as helpful as they might be to humans, computers find them unnecessary.

Double Precision Real Numbers A double precision real number in GNU Fortran can be represented by up to 17 digits before truncation occurs. Double precision numbers are written in scientific notation but with D usurping the role of E. Some various ways of writing the number 12.345 as a double precision real number are 1.2345D1 , .12345D2 , .012345D3 , 12.345D0 , 12345D-3 . When assigning a value to a double precision variable you should use this D-scientific notation, as otherwise the value will be read only in single precision. For example, if A is double precision and you want to assign A the value 3.2, you should write A = 3.2D0 instead of just A = 3.2. (See Base 2 Conversion Errors below for more explanation.) When a number is input from the keyboard in response to a "read *" command, the user need not worry about types or input format. Suppose for example that x is single or double precision, and the user is to enter a value for x in response to the command "read *, x". If the user enters simply "3" (integer format), GNU Fortran will change 3 to the proper format (to 3. if x is single precision and to 3D0 if x is double precision) before assigning it to x. Likewise, if x is double precision and the user enters 3.1 (single precision format), Fortran converts 3.1 to 3.1D0 before assigning it to x. (However, with an ordinary assignment statement "x = 3.1" from within the program, the number is not changed to double precision format before being assigned to x.) A number x can be converted to double precision by the function dble(x) .

Base 2 Conversion Errors

Whereas humans, having 10 fingers, do arithmetic in base 10, computers have no fingers but do arithmetic with on-off switches and therefore use base 2. As we know, some numbers have infinite decimal representations in base 10, such as 1/3 = .33333 … , 2/7 = .285714285714 … . There is no way to represent such numbers in base 10 with a finite number of digits without making a round-off error. Computers have the same problem working in base 2. In general, the only numbers representable with a finite number of digits in base 2 can be written in the form m/n, where m and n are integers and n is an integral power of 2. Examples are 6 (= 6/20) , 5/2 , 3/8 , 29/16 , 537/256 , -3/1024 . When we ask computers to do arithmetic for us, there is an inevitable source of error. We give the computer the numbers in base 10, and the computer must change them all over to base 2. For most numbers there is a round-off error, as the computer can work with only a finite number of digits at a time, and most numbers do not have a finite representation in base 2. If the computer is working in single precision Fortran, it works in about 9 digits (base 10), and so the round-off error will occur in about the 8th or 9th base 10 digit. In double precision this error appears much later, in about the 16th or 17th base 10 digit. If the arithmetic the computer performs is very complicated, these round-off errors can accumulate on top of each other until the total error in the end result is much larger. After the computer has done its job in base 2, it converts all numbers back to base 10 and reports its results. Even if the computer does no arithmetic at all, but just prints out the numbers, the base 2 conversion error still appears. Here is a program illustrating the phenomenon: program demo real x double precision y, z x = 1.1 y = 1.1 z = 1.1D0 print *, "x =", x, " , y =", y, " , z =", z end The somewhat surprising output when this program is run in GNU Fortran is x = 1.10000002 , y = 1.10000002 , z = 1.1 . The variable x is single precision, and base 2 conversion round-off error shows up in the 9th digit. Although y is double precision, it has the same round-off error as x because the value 1.1 is assigned to y only in single precision mode. (What happens is Fortran converts 1.1 to base 2 before changing it to double precision and assigning it to y.) Since

z is double precision, and it is assigned the value 1.1 in double precision mode, round-off error occurs much later, far beyond the nine digits in which the results are printed. Thus the value of z prints exactly as it is received. Using write and format statements (see below), it is possible to print z using 17 digits; if you do so, you will find that Fortran reports z = 1.1000000000000001, where the final erroneous 1 appears as the 17th digit. Base 2 round-off error occurs in the preceding example because 1.1 = 11/10, and 10 is not a power of 2. If you modify the program by replacing 1.1 with 1.125 = 9/8, there will be no round-off error because 8 = 23 is a power of 2 - so the values of x, y, and z will print exactly as assigned. (Try it!!)

Mixed Type Arithmetic In general, arithmetic in Fortran that mixes numbers of different types should be avoided, as the rules are quickly forgotten and mistakes are easily made. If Fortran is asked in some arithmetic operation to combine an integer number with a real one, usually it will wait until it is forced to combine the two and then convert the integer to real mode. Here are some calculations illustrating the process followed by Fortran, and showing why you should stay away from this nonsense: 5. * (3 / 4) = 5. * 0 = 5. * 0. = 0. (5. * 3) / 4 = (5. * 3.) / 4 = 15. / 4 = 15. / 4. = 3.75 5. + 3 / 4 = 5. + 0 = 5. + 0. = 5. 5 + 3. / 4 = 5 + 3. / 4. = 5 + .75 = 5. + .75 = 5.75 If x and y are declared as double precision variables, and you want to multiply x by a number, say 2.1 for example, to get y, you should write y = 2.1D0 * x . Writing just y = 2.1 * x will retain single precision when 2.1 is converted to base 2, thereby introducing a larger base 2 round-off error and defeating your efforts at double precision. Similar remarks apply to other arithmetic operations. Errors of this nature are easily made when working in double precision. The best way to avoid them is to follow religiously this general rule: Do not mix numbers of different types in Fortran arithmetic!!

Exponentials and Roots Already we point out an exception to the above rule - it is OK to use integers as exponents of real numbers. That is because, when serving as an exponent, an integer acts more as a "counter of multiplications" rather than as an active participant in the arithmetic. For instance, when Fortran does the calculation 1.25, it performs the multiplications 1.2 * 1.2 * 1.2 *1.2 * 1.2 ,

and the integer 5 never enters into the calculations! Thus, although it may appear so at first glance, the computation of 1.25 does not really mix an integer with a real number in any arithmetic operation. The same can be said of negative integers as exponents. The calculation of 1.2-5 involves multiplying five factors of 1.2, and then taking the reciprocal of the result - so the number -5 is not involved in the actual arithmetic. Rational exponents must be handled carefully. A common mistake of novice Fortran programmers is to write something like 5 ** (2/3) and expect Fortran to compute the value of 52/3. But Fortran will view 2 and 3 as integers and compute 2/3 = 0, and conclude that 5 ** (2/3) = 5 ** 0 = 1. The correct expression for computing 52/3 is 5. ** (2./3.) , wherein all numbers are viewed as real numbers. Roots of numbers are computed in the same manner. To compute the seventh root of 3 you would use the expression 3. ** (1./7.) . If N is an integer variable and you wish to compute the N-th root of the real variable x, do not write x ** (1/N), as Fortran will interpret 1/N as 0 when N > 1. Instead write x ** (1./real (N)), so that 1 and N are first converted to real variables.

Write and Format Statements Just as in Basic we use TAB and PRINT USING commands to more precisely control program output, in Fortran we can use write commands with format statements. While these can get complicated, the most commonly used options are pretty easy to use. A typical write statement is write (*,20) x, y, z . The "*" in the parentheses instructs Fortran to write to the screen, while "20" refers to the label of the format statement for this write command. The x, y, and z are the variables to be printed. A format statement for this write command might be 20

format (3f10.4) .

Inside the parentheses, the "3" indicates that 3 entities will be printed, the "f" denotes that these will be floating point real numbers (not exponential notation), the "10" stipulates that 10 places will be used for printing (counting the sign, decimal point, and the digits), and ".4" mandates 4 digits after the decimal point. Some printouts formatted this way are 12345.6789

,

-1234.5678

,

10002.3400 .

The letter "f" in this context is a format code letter; here are some of the more commonly used format code letters, with their implications: f

real number, floating point format

e single precision real number, exponential notation d double precision real number, exponential notation i

integer

a text string (character) x space /

vertical space (line feed)

t

tab indicator

Strings (in quotes) may be placed in format statements, separated by commas. Here are examples of write statements with corresponding format statements; at the right of each is a description of the corresponding output:

write (*,10) n, x, y 10 format (i4,4x,f10.4,2x,f10.4)

integer n printed using 4 places, then 4 spaces, then real numbers x and y printed with 2 spaces between, each using 10 places and 4 decimal places

write (*,20) area 20 format ("The area is ",f8.5)

string in quotes is printed, then the real number area is printed, using 8 places with 5 decimal places

write (*,30) "The area is ", area same output as immediately above 30 format (a,f8.5) write (*,40) x, y, z 40 format (3d20.14)

3 double precision numbers x, y, z printed, each reserving 20 spaces, with 14 decimal places

write (*,50) student, score 50 format (a20,4x,i3)

student, a text string up to 20 characters, is printed, then 4 spaces, then score, an integer using a maximum of 3 places

write (*,60) r, A 60 format (t10,f4.2,/,t10,f6.2)

tabs to column 10, prints real number r, goes to next line, tabs to column 10, prints real number A

You can use loops with format statements to print arrays; here are examples: do i = 1, 10 write (*,70) a(i) end do 70 format (f5.2)

an array a of real numbers, indexed from 1 to 10, is printed; each entry occupies 5 places with 2 decimal places, and is printed on a separate line

write (*,80) (a(i), i = 1, 10) 80 format (f5.2)

same output as immediately above

write (*,90) (a(i), i = 1, 10) 90 format (10f5.2)

same output as above, except that all entries are printed on the same line

7

do i = 1, 5 write (*,7) (m(i,j), j = 1, 6) format (6i3) end do

prints a 5 x 6 two-dimensional array m of integers, with each integer entry m(i,j) occupying 3 places. Each row of the matrix appears on its own line.

Here are other useful things to know about formatting: 1. If you do not specify a format, GNU Fortran will print real numbers using about 9 digits, even if you do calculations in double precision. If you want to print in double precision you must use write and format statements. When double precision is used the maximum number of digits possible is 17. A format specifier something like format (fm.n), where m is at least 20, is required to take full advantage of double precision. 2. If a value is too large to be printed in the specified format, Fortran will just print a string of asterisks (eg: ********** ). If you get such an output, you have to fix your format statement. 3. Real numbers are rounded off (not truncated) to fit the specified formatting. 4. If your formatting specifies more positions than the number requires, blanks are inserted to the left of the number. 5. Format statements may appear anywhere in a program after the variable declarations and before the end statement. 6. Unless your format statement is very simple, the chances are that your output won't look like you want on the first try - just fiddle with the formatting until you get it right. Following are examples of stored values, formatting specifications for printing the values, and resulting output. (The "^" symbol indicates a blank). Stored Value

Format Specifier Output

1.234567

f8.2

^^^^1.23

0.00001

f5.3

0.000

-12345

i5

*****

-12345

i6

-12345

12345

i6

^12345

0.00001234

e10.3

^0.123E-04

0.0001234

e12.4

^^0.1234E-03

1234567.89

e9.2

^0.12E+07

aloha

a8

^^^aloha

1.23456789123D0 d17.10

^0.1234567891E+01

FORTRAN LESSON 4 Lesson Topics Statement Functions

Do While Loops

Continuation Lines

Sign Function

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Main Fortran Page

Statement Functions A statement function in Fortran is like a single line function definition in Basic. These are useful in defining functions that can be expressed with a single formula. A statement function should appear before any executable statement in the program, but after any type declaration statements. The format is simple - just type f(x,y,z,…) = formula . You may replace f with any name you like for your function, and x, y, z, … with your own variable names. Instead of formula type the formula for your function. Examples :

area(r) = pi * r * r vol(r,h) = pi * r * r * h f(x,y,z) = sqrt(x / y) * cos(z) You should declare a type for the function in a declaration statement. Here is a program using a statement function, named "area", to compute areas of circles; the program computes in double precision the area of an annulus of inner radius a and outer radius b: program annulus double precision r, area, pi, a, b parameter (pi = 3.1415926535897932D0) area(r) = pi * r * r print *, "Enter the inner and outer radii of the annulus: " read *, a, b write (*,10) "The area of the annulus is ", area(b) - area(a) format (a,f25.15) end

10

In the type declaration statement just include the name of the function - do not include the parentheses or the function variables. Observe that variables plugged into the function need not be the same variables used in defining the function. It is possible to use a previous statement function in the definition of another. In the above program, for example, we have already defined the function area(r), so we could define further a second function "annarea", giving the area of the annulus as annarea(a,b) = area(b) - area(a)

.

But this second function definition must appear later in the program than the first one.

Continuation Lines Sometimes a Fortran statement will not all fit into columns 7-72. In such a case you may continue the statement onto the next line by placing a character in column 6 of that next line. Although any character is allowed, most programmers use "+", "&", or a digit (using 2 for the first continuation line, 3 for another if necessary, and so on). Example :

& &

det = a(1,1) * a(2,2) * a(3,3) + a(1,2) * a(2,3) * a(3,1) + a(2,1) * a(3,2) * a(1,3) - a(3,1) * a(2,2) * a(1,3) - a(2,1) * a(1,2) * a(3,3) - a(1,1) * a(3,2) * a(2,3)

Do While Loops A do while loop in Fortran is similar to the same loop in Basic. However, in Fortran the test must be enclosed in parentheses, and the end of the loop is identified with either end do or a labeled continue statement. As in "if … then" constructions, in loop tests one uses letter abbreviations for relations such as "≤", ">", "=", etc. Here are two loops adding the squares of the integers from 1 to 10; they differ only in the way the loops are terminated: N=1 | N=1 S=0 | S=0 do while (N .le. 10) | do 5 while (N .le. 10) S = S + N ** 2 | S = S + N ** 2 N=N+1 | N=N+1 end do | 5 continue

Sign Function The function sign in Fortran is called the sign transfer function. It is a function of two variables, and its definition involves two cases: CASE 1: If y ≥ 0 then sign(x,y) = abs(x) , CASE 2: If y < 0 then sign(x,y) = - abs(x) . The practical effect is that sign(x,y) has the same absolute value as x, but it has the same sign as y; thus the sign of y is transferred to x. (The case y = 0 is a little special - it gives sign(x,y) always a plus sign.) Examples : sign(2,3) = 2 , sign(2, -3) = - 2 , sign(-2,3) = 2 , sign(-2, -3) = - 2 . The variables x and y in sign(x,y) may be integers or real numbers, and either single or double precision. (And x and y may even be of different types.) If we substitute x = 1 in the sign transfer function, we get the sign of y; that is, CASE 1: If y ≥ 0 then sign(1,y) = 1 , CASE 2: If y < 0 then sign(1,y) = - 1 . Thus, sign(1,y) in Fortran is essentially the same as the function SGN(y) in Basic (except when y = 0, when the Fortran value is + 1 but the Basic value is 0).

FORTRAN LESSON 5 Lesson Topics Arrays

Factorials

Dimension Statement

Arrays in Function Subprograms

Function Subprograms Return in Function Subprograms View Demos

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Arrays There are only a few minor differences in the way Fortran and Basic treat arrays. Array declarations in Fortran go at the beginning of the program, before any executable statement. Arrays can be declared with either a dimension statement or a type declaration. The latter way is preferred, because it is best anyway to declare the type of the array. Here are examples of arrays introduced by type declarations: real a(10), b(5)

one-dimensional arrays a and b of real variables, indexed from 1 to 10 and from 1 to 5, respectively

integer n(3:8), m

one-dimensional array n of integers, indexed from 3 to 8, and an integer variable m

double precision c(4,5)

two-dimensional array c of double precision real numbers, the first index running from 1 to 4, and the second from 1 to 5

one-dimensional array student of character student(30)*20 strings, indexed from 1 to 30, each string up to 20 symbols long real num(0:5,1:10,-3:3)

three-dimensional array num of single precision real numbers, the first index running from 0 to 5, the second from

1 to 10, and the third from -3 to 3 In Fortran the default lower limit of the range of a subscript is 1, rather than 0 as in Basic. A colon separates the lower and upper limits whenever both are specified. Because arrays are declared at the beginning of the program, they must be given a fixed size - i.e., the limits must be constants rather than variables. (In this respect Fortran is less flexible than Basic, in that Basic allows the dimension of an array to be a variable whose value can be input by the user, thereby ensuring that exactly the right amount of storage space is reserved.) You don't have to use the full size of the array specified in the declaration statements; that is, you may reserve space for more entries in the array than you will need. If you use a dimension statement to declare an array, you should precede it with a type declaration. Here is one way to introduce a real array weights, indexed from 1 to 7: real weights dimension weights(7) But the same can be accomplished more briefly with the single statement real weights(7) . Although the upper and lower limits of an array cannot be variables, they can be constants declared in parameter statements. The sequence of statements integer max parameter (max = 100) character names(max)*30 real scores(max) instructs Fortran to set aside storage space for a list of at most 100 names, each a string of length no longer than 30 symbols, as well as a list of at most 100 scores, each a real number. As in Basic, in Fortran you may input and print arrays with do loops. But you can sometimes more efficiently do the same with single statements. For instance, the above array weights can be input with only the statement read *, weights . This read statement pauses the program to allow the user to enter all seven entries of the array. The user can either enter the seven weights one-by-one separated by returns, or alternatively, can enter all seven weights separated only by commas, and then a single

return. If you want to input say only the first five weights, you can do so with the statement read *, (weights(i), i=1,5) . Analogously, the single print statement print *, weights prints the seven entries of weights to the screen, while the statement print *, (weights(i), i=p,q) prints only the weights indexed from p to q. There are various formatting tricks useful in printing two-dimensional arrays. Here is one example demonstrating how to print a matrix A having 5 rows and 6 columns of real numbers, with each row of the matrix printed on its own line :

10

do i = 1, 5 write (*,10) (A(i,j), j = 1, 6) end do format (6f7.3)

More precise formatting can be accomplished with double loops and tab indicators.

Function Subprograms Function subprograms in Fortran define functions too complicated to describe in one line. Here is a function subprogram defining the factorial function, fact(n) = n! : function fact(n) integer fact, n, p p=1 do i = 1, n p=p*i end do fact = p end The first line of the function subprogram specifies the name of the function, and lists in parentheses the variables upon which the function depends. The subprogram has its own type statements, declaring the type of the function itself, as well as the types of the variables involved in computing the function. Somewhere in the subprogram there must be a line giving the value of the function. (Above it is the line "fact = p".) The subprogram concludes with an end statement. In Fortran, function subprograms do not

have to be declared as they do in Basic. The entire function subprogram appears in the source file after the final end statement of the main program. The above factorial subprogram, with variables of integer type, works only for nonnegative integers no larger than 12, as 13! = 6,227,020,800 exceeds the Fortran upper limit of 2,147,483,647 for integers. To handle larger integers, the types can be changed to real or double precision. In GNU Fortran, single precision real type handles factorials of integers as large as 34, and double precision as large as 170. The main program (or in fact any subprogram) utilizing a function subprogram should likewise specify the type of the function. Here is a simple main program using the above factorial function "fact": program demofactorial integer fact, n print *, "What is n?" read *, n print *, "The value of", n, " factorial is", fact(n) end Because n is declared an integer in the function subprogram defining fact(n), it must also be an integer in the main program when fact(n) is evaluated; if it is of a different type the compiler displays a type mismatch error message. A function subprogram may depend on several variables, and it may use an already defined statement function or a function defined by another function subprogram. Following is a function subprogram utilizing the above factorial function subprogram; it computes the Poisson probability function, defined as P(n,t) = tn e- t / n! , where n is a nonnegative integer and t any positive number: function poisson(n,t) real poisson, t integer n, fact poisson = (t ** n) * exp(-t) / fact(n) end Note that, as this subprogram references the function "fact", it must declare its type. Both this subprogram and the factorial subprogram will appear in the source file following the end statement for the main program. (The order in which the subprograms are typed makes no difference - just as long as they both follow the main program.)

Again, in referencing function subprograms one must respect types; for example, if the main program is to compute poisson(m,s) for some variables m and s, then, in order to conform to the type declarations in the function poisson, m must first be declared an integer and s of real type. Oversights will lead to compiler type-mismatch messages.

Arrays in Function Subprograms An array can be listed as a variable of a function defined by a function subprogram - but you just write the array name, with no parentheses after the name as in Basic. The type and dimension of the array must be specified in the function subprogram. Following is a program called "mean" that computes the mean, or average, of a list containing up to 100 numbers. The main program prompts for the list of numbers, and then references a function subprogram named "avg" that computes the average. program mean real numbers(100), avg integer m print *, "How many numbers are on your list?" print *, "(no more than 100, please)" read *, m do i =1, m print *, "Enter your next number:" read *, numbers(i) end do print *, "The average is", avg(m,numbers) end function avg(n,list) real avg, list(100), sum integer n sum = 0 do i = 1, n sum = sum + list(i) end do avg = sum/n end Note that both the main program and the subprogram declare the type of the function "avg". The main program calls the function subprogram with the arguments "m" and "numbers", and these are substituted into the function subprogram for the variables "n" and "list". The main program specifies the dimension of the array "numbers", while the subprogram specifies the dimension of the array "list". The subprogram does its calculations and returns the value of "avg" to the main program. For this procedure to

work, the types of the variables "m" and "n" must agree, as well as the types of "numbers" and "list".

Return (in Function Subprograms) A return statement in a function subprogram acts like a stop statement in the main program; the subprogram is terminated and Fortran returns to where it left off in the main program. Here is a function subprogram defined on integers n; the value of the function "demo" is 0 if n ≤ 0, and if n > 0 it is the sum of the squares of the integers from 1 to n: function demo(n) integer demo, n demo = 0 if (n .le. 0) return do i =1, n demo = demo + i * i end do end

FORTRAN LESSON 6 Lesson Topics Initializing Variables

Call Statement

Mod

Return in Subroutines

Subroutines

Variable Substitution

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Main Fortran Page

Initializing Variables Recall that in Basic the default value of a numeric variable is always zero - that is, if you introduce a numeric variable but do not specify its value, Basic automatically gives it the value zero. In GNU Fortran the situation is more confused. A real variable with no value specified will be given a value - but usually a very small value that is not precisely zero, and sometimes a value that is not even close to zero. An integer is given the default value

1. This strange behavior is hardly ever a problem, as usually when the variable is eventually used in the program it is given an appropriate value by some assignment statement. But trouble might arise if a forgetful programmer proceeds on the assumption that the default value is zero, or perhaps neglects to include an assignment statement. If you are worried about the problem, you can assign values to all your variables at the beginning of your program - a procedure called "initializing variables". The easiest way to do this is with ordinary assignment statements, such as "x = 0", or "y = 2.61", etc. (For programs with a large number of variables a more efficient method is to use DATA statements; we will discuss these later.)

Mod In Fortran the expression mod(n,m) gives the remainder when n is divided by m; it is meant to be applied mainly to integers. Examples are mod(8,3) = 2 , mod(27,4) = 3 , mod(11,2) = 1 , mod(20,5) = 0 .

Subroutines A subroutine in Fortran works like a subprogram in Basic, except that you do not declare a subroutine. Subroutines are typed in the source file after the main program. A subroutine must have a name, followed by a list of variables in parentheses. A variable may be of any type, including a character variable, and can be an array. A subroutine begins with variable declaration statements, just as the main program. The main program uses a call statement to call the subroutine. The call statement has also a list of variables, which are substituted for the subroutine variables. The subroutine executes, modifying some or all of its variables, which are then substituted back for the original call variables in the main program. The variables in the call statement must match the variables in the subroutine according to number, type, and dimension. (Oversights lead to type-mismatch error messages by the compiler.) Here is a simple program named average that prompts the user for two real numbers, calls a subroutine named avg to average the numbers, and then prints the average. program average real x, y, z print *, "What are the two numbers you want to average?" read *, x, y call avg(x,y,z) print *, "The average is", z end subroutine avg(a,b,c) real a, b, c c = (a + b)/2.

end When the subroutine is called it substitutes x for a, y for b, and z for c. (Although the user does not input z, GNU Fortran will have given it some default value.) After the subroutine does its calculations, the new values of a, b, c are substituted back into the main program for x, y, z. (In this particular subroutine only c changes, so x and y retain their original values.) After the subroutine completes its run, action is returned to the statement in the main program immediately following the call statement. Just remember that, except for the first statement naming the subroutine and listing the variables, a subroutine has the same general structure as a main program. It begins with type and dimension statements, has a main body carrying out the action, and concludes with an end statement. The advantage of using subroutines is that the main program can be kept relatively simple and easy to follow, while nitty-gritty calculations and complex procedures are shuffled off to various subroutines, each performing a specific task. A well-written subroutine can be saved in a subroutine "library", to be inserted into other main programs as the need arises. A subroutine can call another subroutine, and it can also access a function subprogram. A subroutine need not depend on any variables - in which case no parentheses follow the subroutine name. Here is a simple subroutine involving no variables: subroutine bluesky print *, "The sky is blue." end The call statement for this subroutine, call bluesky

,

likewise lists no variables. The following subroutine computes the product of a 2 x 2 matrix A with a 2 x 1 vector x, according to the formula

It accepts as variables a 2 x 2 array A and one-dimensional arrays x and y, each indexed from 1 to 2. The array y represents the product y = Ax.

subroutine prod(A,x,y) real A(2,2), x(2), y(2) y(1) = A(1,1) * x(1) + A(1,2) * x(2) y(2) = A(2,1) * x(1) + A(2,2) * x(2) end A call statement for this subroutine might be something like call prod(B,u,v)

,

where B and u are arrays known to the main program and the product v is to be computed by the subroutine. Of course the main program will have appropriately dimensioned these arrays. After the subroutine completes its task and returns control to the main program, the array v will represent the product Bu.

Return (in Subroutines) A return statement in a subroutine instructs Fortran to terminate the subroutine and return to the main program at the point where it departed. Thus it works like a stop statement in the main program, halting the program prematurely before the final end statement. A subroutine may have several returns, but only one end statement. Here is a subroutine, using a return statement, that decides whether a positive integer n is a prime number: subroutine check(n,result) integer n, i, root character result*9 if (n .eq. 1) then result = "not prime" return end if root = sqrt(real(n)) do i = 2, root if (mod(n,i) .eq. 0) then result = "not prime" return end if end do result = "prime" end The subroutine begins by checking whether n = 1, and if true it sets result = "not prime" and returns to the main program. If n > 1 the DO LOOP looks at integers from 2 up to the

square root of n, checking whether each is a divisor of n. If and when it finds such a divisor, it sets result = "not prime" and returns to the main program. But if no divisor of n is found, the subroutine completes the entire loop and sets result = "prime". After the subroutine ends, the main program need only look at the value of result to find out whether n is prime or not prime.

Variable Substitution in Subprograms We look in more detail at how variables are substituted for one another in the calling and execution of a subroutine or function subprogram. Let us suppose for example that a certain subroutine named "demo" depends on three variables, say a, b, and c, so that the first line of the subroutine is subroutine demo(a,b,c) . Let us assume also that the main program's call statement for this subroutine is call demo(x,y,z)

,

where x, y, and z are variables from the main program. The types and dimensions of x, y, and z will have been declared in the main program, and these must match the types and dimensions of a, b, and c, respectively, as declared in the subroutine. The values of x, y, and z will have been stored by Fortran in certain memory locations, designated in the diagram below as triangles: x→Δ y→Δ z →Δ When the subroutine "demo" is called, Fortran assigns the variable a the same memory location as x, b the same location as y, and c the same as z: x →Δ← a y →Δ← b z →Δ← c (This explains why the types and dimensions must match!) Now, as the subroutine "demo" runs, the variables a, b and c might change to new values. But since x, y, and z share memory locations with a, b, and c, the values of x, y, and z of course will have to change simultaneously along with a, b, and c. When the subroutine terminates and returns control to the main program, a, b, and c then are no longer active variables, but x, y, and z retain the final values of a, b, and c at the conclusion of the subroutine. There is a way to fool Fortran into not changing the value of a calling variable when the subroutine runs. In the above example, suppose we change the call statement to

call demo(x,(y),z)

.

When the variable y is enclosed in parentheses, Fortran treats (y) as a new expression and assigns it a different memory location than that of y, but with the same value as y. The last diagram changes to x →Δ← a y→Δ (y) → Δ ← b z →Δ← c Now, as b changes values during the execution of the subroutine, y is unaffected, so that at the conclusion of the subroutine y has its original value. The above analysis applies to function subprograms as well as to subroutines. Changes in the function variables during execution of a function subprogram induce corresponding changes in the variables used to call the function subprogram.

FORTRAN LESSON 7 Lesson Topics Open

Write (to Files)

Close

Read (from Files)

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Main Fortran Page Sometimes it is convenient in a Fortran program to use files for accessing or storing data especially when large amounts of data are involved. Too much keyboard input during the run of a program leads to mistakes and tedium, while too much screen output has similar consequences. Putting data into files - both for input and output - is a more leisurely and less error-prone approach.

Open

The open command is used to open files - that is, it makes files available so that Fortran can read or write to them. The simplest form of the command is open (unit = number, file = "name") . In place of number you insert a positive integer (but not 6) to be used to refer to the file, and instead of name you insert the name of the file. Here are examples of open commands: open (unit = 2, file = "scores") open (unit = 7, file = "a:scores.txt") open (unit = 5, file = "h:\\results\\primes") open (unit = 24, file = "c:\\fortran\\data\\divisors.dat") . Fortran uses the unit number to access the file with later read and write statements. Several files can be open at once, but each must have a different number. There is one thing to remember about numbering a file - you cannot use the number 6, as GNU Fortran reserves that number to refer to the screen. Note that quotes enclose the filename. Also, in specifying a directory path for a file, you must use double backslashes instead of single ones. Do not put a space on either side of the colon after the drive letter. If you do not specify a drive or directory path for a file, or if you specify the same drive upon which GNU Fortran is installed but without a path, GNU Fortran will by default assume the file is located on the same drive and in the same directory from where Fortran is running. If the named file does not already exist, Fortran will create it; if it does exist, Fortran will replace it. (So don't mistakenly give the file the same name as another important file!)

Close The close command is used to close one or more files - examples are close (5) , close (1, 3, 8) . The first of these commands closes the file numbered 5, while the second closes the three files numbered 1, 3, and 8. It is not necessary to close files; all files will automatically be closed when an end or stop statement is executed. However, in programs handling large amounts of data it can be prudent to close files before the end of the program in order to avoid possible memory problems and to increase efficiency.

Write (to Files) The write command is used to write data to a file. For example, the command write (7,*) works like a print * command, except that data is written to the file numbered 7 instead of to the screen. The two statements

print *, "The solutions to the equation are : ", x1, x2 write (7,*) "The solutions to the equation are : ", x1, x2 produce exactly the same output, except that the first writes to the screen and the second to file number 7. The command "write (7,*)" on a line by itself serves as a line feed, skipping a line in the file numbered 7 before the next writing to that file. You can also use write statements in conjunction with format statements to write to a file; this gives you better control of formatting. In the following, the first number in "write (7,5)" refers to the file number and the second to the label of the format statement:

5

write (7,5) "The solutions are ", x1, " and ", x2 format (a,f16.10,a,f16.10)

The "write (7,5)" command works exactly like the similar command "write (*,5)", except that in the former output is directed to file number 7, and in the latter to the screen. Each execution of a write command writes to a single line in a file. The next write command will write to a new line. Here is a program that finds and prints to a file the divisors of an integer n :

c c

5

program divisors This program finds the divisors of an integer input by the user. The divisors are printed to a file. integer n, k, d(10) open (unit = 1, file = "divisors") print *, "Enter a positive integer :" read *, n write (1,*) "Here are the divisors of ", n, " :" k=0 do i = 1, n if (mod(n,i) .eq. 0) then k=k+1 d(k) = i end if if (k .eq. 10) then write (1,5) (d(j), j = 1, 10) k=0 end if end do write (1,5) (d(j), j = 1, k) format (10i7) close (1)

print *, "The divisors are listed in the file 'divisors'. Bye." end Note that the program counts the divisors, storing them in an array d, until 10 are accumulated; then it prints these 10 on a single line, reserving 7 places for each divisor. It then begins a new count and repeats the procedure until all divisors are found. The last write statement prints whatever divisors are left over after the last full line of 10. The close statement, included here for demonstration only, is unnecessary, as the program is all but finished at that point and the end statement will automatically close the file anyway.

Read (from Files) The read statement is used to read data from a file. Generally data is read from a file in the standard way, line-by-line and from left to right. But you must remember that each read statement begins reading a new line, whether or not the preceding read statement used all the data in the preceding line. Suppose for example that a file is numbered 7, and that the first two lines of the file contain the data (separated by commas) 1.23 , 4.56 , 7.89 11, 13 , "Sally" If the first two read statements in the program are read (7,*) x, y, z read (7,*) m, n, first , then the program assigns x = 1.23, y = 4.56, z = 7.89, m = 11, n = 13, first = "Sally". The variables will have to be declared in the program to correspond with the data assigned them by the read statements. For instance, in the above situation x, y, and z will have been declared real variables, m and n integers, and "first" a character variable. Failure to match variable types with data types will most likely lead to error messages. It is possible that a program does not know beforehand the length of a file. If data is being read from a loop, there is a way to exit the loop when all data in the file has been read, thereby avoiding a program hang-up. One simply modifies the read statement to something like read (7,*,end=10) . This command instructs Fortran to read the next line in the file numbered 7, but to jump to the statement labelled 10 in the program in the event that the last line in that file has already been read.

You can also use format specifiers in read statements, but this can be somewhat tedious and we will not go into the details. As but one example, suppose you want to make the assignments n = 77

,

x = 123.45

,

y = 67.8 ,

where n is an integer and x and y are real variables. Then you may use the read and format statements

5

read (7,5) n, x, y format (i2,f5.2,f3.1)

,

and in file number 7 place the corresponding line of data 7712345678

.

Fortran will read and separate the data, insert appropriate decimal points, and assign it to the variables. But as you can see the method is confusing and perhaps not worth the effort.

MORE FORTRAN INFO Topics Intrinsic Functions (More) Data Save

Arithmetic If

Common (Blank)

Computed Go To

Common (Named) Main Fortran Page Following is further Fortran information not covered in the lessons.

More Intrinsic Functions This table lists additional functions intrinsic to Fortran, not already listed in Lesson 1. Function

Description

aint(x)

truncates the decimal part of x (without changing the type of x)

anint(x)

rounds x to the nearest integer (without changing the type of x)

int(x)

converts x to integer type, giving it the value of the integer closest to x but no larger than x in absolute value

log10(x)

common logarithm of x (base 10)

max(x1,x2,...,xn)

maximum of x1, x2, ..., xn

min(x1,x2,...,xn)

minimum of x1, x2, ..., xn

nint(x)

converts x to integer type, rounding x to the nearest integer

Save This command, used in a subprogram, preserves the values of local variables (i.e., variables used in the subprogram but not listed in the title statement) from one call of the subprogram to the next. For instance, the statement save m, z in a subroutine ensures that in calls after the first run the subroutine remembers the final values of m and z from the previous run. A save statement by itself, save

,

preserves the values of all local variables in the subprogram. You cannot save a listed variable of the subprogram - the compiler will give an error message. (EG: If a subroutine's first line is "subroutine area(r)", then you cannot save r.)

Common (Blank) Ordinarily the only information shared between the main program and subprograms are the values of variables appearing in variable lists. The common statement can be used to share additional information. The simplest form of the common statement is the blank common statement. Let us suppose for illustration that the main program has real variables x and y as well as an integer variable n which are to be shared with one or more subroutines. Then at the beginning of the main program, before any executable statements, you first declare the types of x, y, and n and next insert the "blank common" statement

common x, y, n . This instructs Fortran to preserve three "common" memory locations for x, y, and n, designated as triangles below: x→Δ y→Δ n→Δ These memory locations are then accessible by all subroutines of the program containing a similar common statement (but with possibly different variables). For example, suppose a subroutine declares real variables u and v and an integer variable m. If the subroutine contains also the common statement common u, v, m , then u, v, and m will share memory locations with x, y, and n, respectively : x →Δ← u y →Δ← v n →Δ← m When the values of u, v, and m change in the subroutine, then the values of x, y, and n in the main program change accordingly; and vice-versa - changes in x, y, or n in the main program produce changes in u, v, and m in the subroutine. Obviously, because of the sharing of memory locations, the types of x, y, and n must match those of u, v, and m, respectively (and also dimensions must match in the case of arrays.) It is possible for a third or even more subroutines to share the same three memory locations. If a third subroutine has real variables a and b and an integer variable k, as well as the statement common a, b, k , then x, u, a share one memory location, y, v, b another, and n, m, k a third. A change in one of these variables in the main program or a subroutine produces the same change in whatever variables share the same memory location. A common statement cannot list variables that are listed also in the title statement of the subprogram in which the common statement appears. (EG: If a subroutine's first line is "subroutine area(r)", then you cannot list r in the subroutine's common statement.)

Common (Named)

In programs with more than one subroutine it is sometimes desirable to share different sets of variables among different sets of program units. In such situations the named common statement is useful. The general form of this statement is common / name1 / list1 / name2 / list2 / name3 / list3 / … / nameN / listN . The "names" are names for the different sets of variables, and the "lists" contain the names of variables in these sets. Suppose, for example, that the main program uses variables A, B, C, D, E, F, G, while subroutine "demo1" uses variables A, B, C, D, and subroutine "demo2" uses variables C, D, E, F, G. If we want all program units using the same variable to share the value of that variable, then in the main program we insert the named common statement common / first / A, B / second / C, D / third / E, F G

,

in subroutine "demo 1" we insert common / first / A, B / second / C, D

,

and in "demo 2" we insert common / second / C, D / third / E, F, G

.

Then the variable set "first" consists of A and B, and is shared by the main program and demo1. Variable set "second" consists of C and D and is shared by all three units. Variable set "third" consists of E, F, and G and is shared by the main program and "demo2". It is not necessary that different units use the same variable names for shared data. For example, subroutine "demo2" could name its five variables V, W, X, Y, Z; then its common statement would change to common / second / V, W / third / X, Y, Z

,

and consequently V and C would share a memory location, as would W and D, X and E, Y and F, and Z and G.

Data A data statement is used to initialize (i.e., assign initial values to) variables before the program begins. All data statements must appear after parameter and type declarations; it is common practice to include them immediately following these statements. The general form of a data statement is data list1 / data1 / list2 / data2 / list3 / data 3 / ... / listN / dataN /

.

Each list is a list of variables separated by commas, and each data is a list of values of the variables in the preceding list. Following is a table of examples with the corresponding resulting assignments: data x, y, z / 2.1, 3.3, -4.4 /

x = 2.1, y = 3.3, z = - 4.4

data k, m, n, p / 3 * 0, 1 /

k = m = n = 0, p = 1

data first, last / "Jane", "Smith" /

first = "Jane", last = "Smith"

data A / 5.2 / B, C / 2.8, 3.9 /

A = 5.2, B = 2.8, C = 3.9

data x, y / 2*1. / m,n / 2*0 / pi / 3.14 / x = y = 1., m = n = 0, pi = 3.14 Note that in a data list the notation "n * x" means that the value x is to be assigned to n successive variables in the preceding variable list. Data statements were necessary in earlier versions of Fortran, when the compiler did not automatically initialize variables; in more modern versions of Fortran they can usually be omitted without repercussions.

Arithmetic If The arithmetic if statement has the form if (expression) k, m, n

,

where expression is some numeric expression that Fortran can evaluate, and k, m, n are integers representing labels of executable statements. If expression is negative, zero, or positive, then the program jumps to the statement labeled k, m, or n, respectively. As illustration, a program solving a quadratic equation ax2 + bx + c = 0 might have the arithmetic if statement if (b * b - 4 * a * c) 10, 20, 30 . Then if the discriminant b2 - 4ac is negative, the program jumps to the statement labeled 10, if it is zero the jump is to label 20, and if positive to label 30.

Computed Go To The computed go to statement has the form go to (n1 , n2 , ..., nm) integer expression

,

where n1, n2, ..., nm are integers representing labels of executable statements, and integer expression is some integer - valued expression that Fortran can evaluate. If the value of this expression is 1, the program jumps to the statement labeled n1, if the value is 2 the program jumps to the statement labeled n2, etc. For example, suppose a program contains the sequence print *, "Enter the number of the task you want to perform:" read *, n go to (10,12,14,16,18,20) n If the user enters 1, the program jumps to the statement labeled 10, if the user enters 2 it jumps to statement 12, if the user enters 3 it jumps to 14, etc. If the user errs and enters an integer different from 1, 2, 3, 4, 5, 6, Fortran defaults to the first statement listed, in this case statement 10.