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Transcript of Fortan Beginner
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FORTRAN LESSON 1
Lesson Topics
Editing Fortran Assignment
Compiling Parameter
Running a Program Comments
Program Print *
Variables Read *
Declarations End
Types Operations
Implicit Quantifier Intrinsic Functions
View Demos Download Demos
# 1 # 1
Main Fortran Page
Introduction
Fortran is one of the oldest programming languages devised, but it is also still oneof 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 well-suited for mathematical programming; moreover, there aremillions of useful programs written in Fortran, created at considerable time and
expense, and understandably people are reluctant to trash these old programs andswitch to a new programming language.
The name Fortran originally referred to "Formula Translation", but it has longsince 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
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installed on UHUNIX and in the UH math lab. Even though this semester we havethus 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, aprogram is typed and saved with an editor(i.e., a word processor), and the program
is then turned into an executable file by a Fortrancompiler. To begin the process ofcreating 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 upFortran.
A most peculiar feature of Fortran 77 is its line structure, which is a carryover fromthe old days when programs were typed onpunch cards. A punch card had 80
columns, and so does a line of Fortran code. A "c" in column 1 indicates acomment (similar to REM in Basic). Columns 2-5 (usually left blank) are reservedfor 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 forsimplicity 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, makecertain 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 amath 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.
program circlearea
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real r, area, pi
parameter (pi = 3.14159)
c 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 column1, 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 seventhstatement 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 thecompiler recognizes it. After you have typed the above program, save the file asarea.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 thefiles in this directory by typingdirand 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 enterg77 name.f, where in place ofname you insert
the name of your source file. (If the source file resides in a directory different fromthat 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
enterg77 area.f.
If your program has mistakes (which usually happens on the first attempt atcompiling), 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 readinghundreds 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 thename 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
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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 (orname and return if you gave the file another name). After you run theprogram 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 andthe 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 beforechanges take effect.
If you do enough Fortran programming, sooner or later you will err and create andrun 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 aFortran 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 theprogram. 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 fromthe 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)
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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 aninteger 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) programmingpractice to declare the type ofevery variable, as otherwise mistakes are easily
made.
The implicitquantifier 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 doesnot 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 isparameter (name = constant expression)
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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 commentis similar to an REM statement in Basic. You can indicate a commentby 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 ", xprint *, 'The radius is', r, 'and the area is', area
Note that a comma follows "print *", and that commas (instead of semicolons as inBasic) 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 thesecond 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.
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End
The endstatement marks the end of the main Fortran program or of a subprogram.(It cannotbe 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 arecalled intrinsic functions. Below is a table of some of the functions mostcommonly 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
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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
Labels
View Demos Download Demos
# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10 # 1# 2# 3# 4# 5# 6# 7# 8# 9# 10
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" constructionsand 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.
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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 precedingtable. 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"
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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 endonly as the very last statement in theprogram, and use stop only to terminate the program before this last statement.
Violating these rules will fatally confuse the compiler - it regards an endstatement
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
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A character variable is analogous to a string variable in Basic. A charactervariable 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 eitherend 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 inBasic 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 noton 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 5 i = 1, 10
do j = 1, 10 | do 5 j = 1, 10
a(i,j) = i + j | a(i,j) = i + j
end do | 5 continue
end do |
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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
View Demos Download Demos
# 1# 2# 3# 4# 5# 6# 7# 8# 9 # 1# 2# 3# 4# 5# 6# 7# 8# 9
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 regardingworking 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 integerin Fortran is a whole number; it cannot contain commas or a decimalpoint. 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 bepreceded by a minus sign. Examples of numbers notconsidered 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.
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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, itinsists 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 compute11./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 toapply 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) orcos(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 thebeginning 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
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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 numberis to be multiplied by 10
n. 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 digitcan 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 realnumber. 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 numberin GNU Fortran can be represented by up to 17
digits before truncation occurs. Double precision numbers are written in scientificnotation 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. Forexample, if A is double precision and you want to assign A the value 3.2, you
should write
A = 3.2D0
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instead of just A = 3.2. (SeeBase 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 thecommand "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 isdouble 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" fromwithin the program, the number is notchanged 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 nofingers 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 as1/3 = .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 inbase 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 oferror. We give the computer the numbers in base 10, and the computer mustchange 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 singleprecision 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 errorappears 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 andreports its results.
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Even if the computer does no arithmetic at all, but just prints out the numbers, thebase 2 conversion error still appears. Here is a program illustrating the
phenomenon:
program demo
real xdouble 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 xbecause 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 ninedigits in which the results are printed. Thus the value of z prints exactly as it is
received. Using write andformatstatements (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, and10 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 Fortranis 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 followedby 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.
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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 ofthis 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 asexponents 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 multiplications1.2 * 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 realnumber 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, andthen taking the reciprocal of the result - so the number -5 is not involved in theactual 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 tocompute the value of 52/3. But Fortran will view 2 and 3 as integers and compute2/3 = 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 rootof 3 you would use the expression
3. ** (1./7.) .
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If N is an integer variable and you wish to compute the N-th root of the realvariable 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 preciselycontrol program output, in Fortran we can use write commands
withformatstatements. While these can get complicated, the most commonly usedoptions 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" refersto the label of theformatstatement for this write command. The x, y, and z are the
variables to be printed. Aformatstatement for thiswrite 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 befloating pointreal 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 aformat 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
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Strings (in quotes) may be placed in format statements, separated by commas. Hereare 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 numbersx 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
30 format (a,f8.5)same output as immediately above
write (*,40) x, y, z40 format (3d20.14)
3 double precision numbers x, y, zprinted, 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
do i = 1, 5
write (*,7) (m(i,j), j = 1, 6)
7 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.
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Here are other useful things to know about formatting:
1. If you do not specify a format, GNU Fortran will print real numbers usingabout 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. Aformat 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 justprint 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 variabledeclarations and before the endstatement.
6. Unless your format statement is very simple, the chances are that youroutput 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 thevalues, 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
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FORTRAN LESSON 4
Lesson Topics
Statement Functions
Do While Loops
Continuation Lines Sign Function
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# 1# 2# 3# 4# 5# 6 # 1# 2# 3# 4# 5# 6
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 typef(x,y,z,) =formula .
You may replace f with any name you like for your function, and x, y, z, withyour own variable names. Instead offormula 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 aprogram using a statement function, named "area", to compute areas of circles; theprogram computes in double precision the area of an annulus of inner radius a and
outer radius b:
program annulusdouble 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)
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10 format (a,f25.15)
end
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 variablesused 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 firstone.
Continuation Lines
Sometimes a Fortran statement will not all fit into columns 7-72. In such a caseyou 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, inFortran the test must be enclosed in parentheses, and the end of the loop is
identified with eitherend 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
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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 oftwo 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 thesame 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).
Calculus ComputerLab
Math 190
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FORTRAN LESSON 5
Lesson Topics
Arrays Factorials
Dimension Statement Arrays in Function Subprograms
Function Subprograms Return in Function Subprograms
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Main Fortran Page
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 adimension statement or atype 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
character student(30)*20
one-dimensional array studentof
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
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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 tobe 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 ofthe 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 cansometimes more efficiently do the same with single statements. For instance, the
above array weights can be input with only the statement
read *, weights .
This readstatement pauses the program to allow the user to enter all seven entriesof 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, youcan do so with the statement
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read *, (weights(i), i=1,5) .
Analogously, the single print statement
print *, weights
prints the seven entries ofweights 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 :
do i = 1, 5write (*,10) (A(i,j), j = 1,
6)
end do
10 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, andlists in parentheses the variables upon which the function depends. The
subprogram has its own type statements, declaring the type of the function itself, aswell 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 endstatement. In Fortran,
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function subprograms do not have to be declared as they do in Basic. The entirefunction subprogram appears in the source file after the final endstatement 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 Fortranupper 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 subprogramshould 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 endstatement for the main program. (The order in which the
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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 bedeclared 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
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Note that both the main program and the subprogram declare the type of thefunction "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 valueof 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
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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 - butusually 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 strangebehavior 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 thedefault 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 atthe 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 mainprogram. A subroutine must have a name, followed by a list of variables inparentheses. 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 statementhas also a list of variables, which are substituted for the subroutine variables. Thesubroutine 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 tonumber, 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 realnumbers, calls a subroutine named avg to average the numbers, and then prints the
average.
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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. (Althoughthe 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 substitutedback into the main program for x, y, z. (In this particular subroutine only cchanges, 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 listingthe 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 endstatement.
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 proceduresare 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,
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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 becomputed 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 andreturn 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 endstatement. 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
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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 integersfrom 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 loopand 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 forexample 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
y
z
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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 a
y b
z 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 coursewill have to change simultaneously along with a, b, and c. When the subroutineterminates 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 callstatement to
call demo(x,(y),z) .
When the variable y is enclosed in parentheses, Fortran treats (y) as a newexpression and assigns it a different memory location than that of y, but with the
save value as y. The last diagram changes to
x a
y(y) b
z 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.
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FORTRAN LESSON 7
Lesson Topics
Open Write (to Files)
Close Read
View Demos Download Demos
# 1# 2# 3 # 1# 2# 3
Main Fortran Page
Sometimes it is convenient in a Fortran program to usefiles for accessing orstoring data - especially when large amounts of data are involved. Too muchkeyboard 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 ofnumberyou insert a positive integer (but not 6) to be used to refer to thefile, and instead ofname you insert the name of the file. Here are examples
ofopen 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 laterreadand 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
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either side of the colon after the drive letter. If you do not specify a drive ordirectory 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 endorstop statement is executed. However, inprograms handling large amounts of data it can be prudent to close files before theend 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 commandwrite (7,*)
works like aprint * 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 numberin "write (7,5)" refers to the file number and the second to the label of the format
statement:
write (7,5) "The solutions are ", x1, " and ", x2
5 format (a,f16.10,a,f16.10)
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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 :
program divisors
c This program finds the divisors of an integer input by the user.
c 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 = 0end if
end do
write (1,5) (d(j), j = 1, k)
5 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 eachdivisor. It then begins a new count and repeats the procedure until all divisors arefound. 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 endstatement
will automatically close the file anyway.
Read (from Files)
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The readstatement is used to read data from a file. Generally data is read from afile in the standard way, line-by-line and from left to right. But you must remember
that each readstatement begins reading a new line, whether or not the
preceding readstatement used all the data in the preceding line.
Suppose for example that a file is numbered 7, and that the first two lines of thefile contain the data (separated by commas)
1.23 , 4.56 , 7.89
11, 13 , "Sally"
If the first two readstatements 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 situationx, 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 datais 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 readstatement to something like
read (7,*,end=10) .
This command instructs Fortran to read the next line in the file numbered 7, but tojump 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 readstatements, 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
read (7,5) n, x, y
5 format (i2,f5.2,f3.1) ,
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and in file number 7 place the corresponding line of data
7712345678 .
Fortran will read and separate the data, insert appropriate decimal points, andassign it to the variables. But as you can see the method is confusing and perhaps
not worth the effort.
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 statementsave 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 ,
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preserves the values ofall local variables in the subprogram. You cannot save alisted 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. Thecommonstatement can be used to shareadditional information.
The simplest form of the common statement is the blank common statement. Let ussuppose 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, andn, designated as triangles below:
x
y
n
These memory locations are then accessible by all subroutines of the programcontaining a similar common statement (but with possibly different variables). For
example, suppose a subroutine declares real variables u and v and an integervariable 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 u
y v
n 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 nmust match those of u, v, and m, respectively (and also dimensions must match in
the case of arrays.)
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It is possible for a third or even more subroutines to share the same three memorylocations. 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. Achange 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 thenamed
commonstatement 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" containthe 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 toshare 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 mainprogram 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 mainprogram and "demo2". It is not necessary that different units use the same variable
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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
Adatastatement is used to initialize (i.e., assign initial values to) variables before theprogram 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 listis a list of variables separated by commas, and each data is a list of valuesof 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
Thearithmetic ifstatement 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. Ifexpression is
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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 ifstatement
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
Thecomputed go tostatement 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 statementlabeled 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 userenters 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.