Fortran Tutorial

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Fortran 90 Tutorial

Dr. C.-K. Shene

Associate Professor

Department of Computer Science

Michigan Technological University

You are visitor since July 1, 1998. Last update: August 20, 1998.

Select the topics you wish to review:

Introduction and Basic Fortran

Selective Execution (IF-THEN-ELSE and SELECT CASE)

Repetitive Execution (DO Loops)

Functions and Modules

Subroutines

One-Dimensional Arrays

Multi-Dimensional Arrays

Formated Input and Output

Please send comments and suggestions to [email protected]

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Introduction and Basic Fortran

Select the topics you wish to review:

Introduction Program Structure Comments Continuation Lines Basic Fortran Alphabets Constants Identifiers

Variables and Their Types Variable Declarations

Assigning a Constant a Name - PARAMETER attribute Initializing Variables

Arithmetic Operators

Simple Mode Arithmetic Expressions Mixed Mode Arithmetic Expressions The Assignment Statement

Intrinsic Functions

List-Directed Input: The READ Statement List-Directed Output: The WRITE Statement

Programming Examples:

Three Programming Traps Computing Means

Quadratic Equation Solver

The Length of a Parabola Segment Projectile motion (intrinsic functions) Character Operator and Substrings (Optional)

Download my course overheads

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Program structure

Program Structure

Your program should have the following form:

PROGRAM program-name IMPLICIT NONE

[specification part] [execution part] [subprogram part]

END PROGRAM program-name

Here are some addition notes:

● Contents in [ ] are optional.

● Keyword IMPLICIT NONE must present.

● A program starts with the keyword PROGRAM, ❍ followed by a program name,

❍ followed by the IMPLICIT NONE statement, ❍ followed my some specification statements, ❍ followed by the execution part,

❍ followed by a set of internal subprograms,

❍ followed by the keywords END PROGRAM and the program name.

● For improving readability, your program should add comment lines.

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Fortran identifiers

Fortran Identifiers

A Fortran identifier must satisfy the following rules:

● It has no more than 31 characters ● The first character must be a letter,

● The remaining characters, if any, may be letters, digits, or underscores,

● Fortran identifiers are case insensitive. That is, Smith, smith, sMiTh, SMiTH, smitH are all identical identifiers. ● Correct Examples:

❍ MTU, MI, John, Count ❍ I, X

❍ I1025, a1b2C3, X9900g ❍ R2_D2, R2D2_, A__ ● Incorrect Examples:

❍ M.T.U.: only letters, digits, and underscores can be used ❍ R2-D2: same as above

❍ 6feet: the first character must be a letter ❍ _System: same as above

● Use meaningful names

❍ Good names: Total, Rate, length

❍ Not so good names: ThisIsALongFORTRANname, X321, A_B_012cm, OPQ

● Fortran has many keywords such as INTEGER, REAL, PARAMETER, PROGRAM, END, IF, THEN,

ELSE, DO, just name a few; however, Fortran does not have any reserved words. More precisely, a programmer can use these keywords as identifiers. Therefore, END, PROGRAM, DO are perfectly legal Fortran identifiers. However, this is definitely not a good practice.

Except for strings, Fortran 90 is not case sensitive. Therefore, identifier Name is identical to name, nAmE, NAme, NamE and namE. Similarly, PROGRAM is identical to program, PROgram, and progRAM. In this course, all keywords such as PROGRAM, READ, WRITE and END are in upper case and other identifiers use mixed cases.

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Fortran comments

Fortran Comments

Comments should be used liberally to improve readability. The following are the rules for making comments:

● All characters following an exclamation mark, !, except in a character string, are commentary, and are ignored by the

compiler.

PROGRAM TestComment1 ...

READ(*,*) Year ! read in the value of Year ...

Year = Year + 1 ! add 1 to Year ...

END PROGRAM TestComment1

● An entire line may be a comment

! This is a comment line !

! This is a comment line in the middle of a program ...

● A blank line is also interpreted as a comment line.

READ(*,*) Count

! The above blank line is a comment line WRITE(*,*) Count + 2

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Fortran alphabets

Fortran Alphabets

Fortran only uses the following characters:

● Letters: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z ● Digits: 0 1 2 3 4 5 6 7 8 9 ● Special Characters: space ' " ( ) * + - / : = _ ! & $ ; < > % ? , . http://www.cs.mtu.edu/~shene/COURSES/cs201/NOTES/chap02/alphabet.html8/5/2006 8:02:12 PM

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Fortran continuation lines

Fortran Continuation Lines

In Fortran, a statement must start on a new line. If a statement is too long to fit on a line, it can be continued with the following methods:

● If a line is ended with an ampersand, &, it will be continued on the next line. ● Continuation is normally to the first character of the next non-comment line.

A = 174.5 * Year & + Count / 100

The above is equivalent to the following

A = 174.5 * Year + Count / 100

Note that &is notpart of the statement. A = 174.5 * Year &

! this is a comment line + Count / 100

The above is equivalent to the following, since the commentis ignored by the compiler: A = 174.5 * Year + Count / 100

● If the first non-blank character of the continuation line is &, continuation is to the first character after the &:

A = 174.5 + ThisIsALong& &VariableName * 123.45

is equivalent to

A = 174.5 + ThisIsALongVariableName * 123.45

In this case, there should be no spaces between the last character and the &on the first line. For example, A = 174.5 + ThisIsALong &

&VariableName * 123.45

is equivalent to

A = 174.5 + ThisIsALong VariableName * 123.45

Note that there are spaces between ThisIsALongand VariableName. In this way, a token (name and number) can be split over two lines. However, this is not recommended

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Fortran Constants

Constants or more formally literal constants are the tokens used to denote the value of a particular type. Fortran has five types of constants: integer, real, complex, logical, and character string.

● Integer Constants: a string of digits with an optional sign: ❍ Correct Examples: 0, -345, 768, +12345

❍ Incorrect Examples:

■ 1,234 : comma is not allowed ■ 12.0: no decimal point

■ --4 and ++3: too many optional signs

■ 5- and 7+: the optional sign must precede the string of digits

● Real Constants: There are two representations, decimal representation and exponential representation.

❍ Decimal Representation: A decimal point must be presented, but no commas are allowed. A real constant

can have an optional sign.

■ Correct Examples: 23.45, .123, 123., -0.12, -.12 ■ Incorrect Examples:

■ 12,345.95: no comma is allowed

■ 75: real constant must have a decimal point ■ 123.5-: the optional sign must precede the number ■ $12.34: cannot use dollar sign $

❍ Exponential Representation: It consists of an integer or a real number in decimal representation (the

mantissa or fractional part), followed by the letter E or e, followed by an integer (the exponent).

■ Correct Examples

■ 12.3456E2 or 12.3456e2: this is equal to 1234.56 ■ -3.14E1 or -3.14e1: this is equal to -31.4

■ -1.2E-3 or -1.2e-3: this is equal to -0.0012 ■ 12E3 or 12e3: this is equal to 12000.0 ■ 0E0 or 0e0: this is equal to 0.0

■ Incorrect Examples

■ 12.34E1.2: the exponential part must be an integer constant ■ 12.34-5: there is no exponential sign E or e

● Complex: Will not be covered in this course ● Logical: See Chapter 3

● Character String: Character constants must be enclosed between double quotes or apostrophes (single quotes).

The content of a string consists of all characters, spaces included, between the single or quote quotes, while the length of the string is the number of characters of its content. The content of a string can be zero and in this case it is an empty string

❍ Correct Examples:

■ 'John' and "John": content = John and length = 4 ■ ' ' and " ": content = a single space and length = 1

■ 'John Dow #2' and "John Dow #2": content = John Dow #2 and length = 11 ■ '' and "": content = nothing and length = 0 (empty string)

■ 'you and me: the closing apostrophe is missing ■ Hello, world': the opening apostrophe is missing

■ 'Hi" and "Hi': the opening and closing quotes do not match.

If single quote is used in a string, then double quotes should be used to enclose the string:

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Fortran Constants

"Lori's apple"

This string has content Lori's apple and length 12. Alternatively, you can write the single quote twice as follows: 'Lori''s apple'

The compiler will treat a pair of single quotes in the content of a string as one. Thus, the content of the above string is still Lori's apple.

❍ Correct Examples:

■ 'What''s this?': content = What's this? and length = 11 ■ '''''': content = '' and length = 2

■ 'Tech's seminar': the single quote between h and s should be written twice.

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Fortran Variables and Their Types

A Fortran variable can be considered as a box that is capable of holding a single value of certain type. Thus, a variable has a name, the variable name and a type. The way of choosing a name for a variable must fulfill the rules of composing a Fortran identifier. The type of a variable can be one of the following:

● INTEGER: the variable is capable of holding an integer ● REAL: the variable is capable of holding a real number

● COMPLEX: the variable is capable of holding a complex number

● LOGICAL: the variable is capable of holding a logical value (i.e., true or false) ● CHARACTER: the variable is capable of holding a character string of certain length

Click here to learn the forms of these values. Click here to learn more about declaring variables.

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Fortran Variable Declarations

Declaring the type of a Fortran variable is done with type statements. It has the following form:

type-specifier :: list

where the type-specifier is one of the following and list is a list of variable names separated with commas:

● INTEGER : the variables in list can hold integers ● REAL: the variables in list can hold real numbers

● COMPLEX: the variables in list can hold complex numbers

● LOGICAL: the variables in list can hold logical values (i.e., true or false) ● CHARACTER: the variables in list can hold character strings

Types INTEGER and REAL are easy. The following are examples:

● Variables ZIP, Mean and Total are of type INTEGER:

INTEGER :: ZIP, Mean, Total

● Variables Average, error, sum and ZAP are of type REAL:

REAL :: Average, error, sum, ZAP

Type CHARACTER is more involved. Since a string has a length attribute, a length value must be attached to character variable declarations. There are two ways to do this:

● Use CHARACTER(LEN=i) to declare character variables of length i. For examples,

❍ Name and Street are character variables that can hold a string of no more than 15 characters:

CHARACTER(LEN=15) :: Name, Street

❍ FirstName, LastName and OtherName are character variables that can hold a string of no more than 20

characters:

CHARACTER(LEN=20) :: FirstName, LastName, OtehrName

● Use CHARACTER(i) to declare character variables of length i. That is, there is no LEN= in the parenthesis. For

examples,

❍ Name and Street are character variables that can hold a string of no more than 15 characters:

CHARACTER(15) :: Name, Street

❍ FirstName, LastName and OtherName are character variables that can hold a string of no more than 20

characters:

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Fortran Variable Declarations

CHARACTER(20) :: FirstName, LastName, OtehrName

● If a variable can only hold a single character, the length part can be removed. The following three declarations are all

equivalent:

CHARACTER(LEN=1) :: letter, digit CHARACTER(1) :: letter, digit CHARACTER :: letter, digit

Here, variables letterand digitcan only hold no more than one character.

● If you want to declare character variables of different length with a single statement, you can attach a length

specification, *i, to the right of a variable. In this case, the corresponding variable will have the indicated length and all other variables are not affected.

CHARACTER(LEN=10) :: City, Nation*20, BOX, bug*1

Here, variables Cityand BOXcan hold a string of no more than 10 characters, Nationcan hold a string of no more than 20 characters, and bugcan hold only one character.

● There is one more way of specifying the length of a character variable. If the length value is replaced with a asterisk

*, it means the lengths of the declared variables are determined elsewhere. In general, this type of declarations is used in subprogram arguments or in PARAMETER and is refereed to as assumed length specifier.

CHARACTER(LEN=*) :: Title, Position

Here, the actual lengths of variables Titleand Positionare unknown and will be determined elsewhere.

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The PARAMETER Attribute

In many places, one just wants to assign a name to a particular value. For example, keep typing 3.1415926 is tedious. In this case, one could assign a name, say PI, to 3.1415926 so that one could use PI rather than 3.1415926. To assign a name to a value, one should do the following:

● Add PARAMETER in front of the double colon (::) and use a comma to separate the type name (i.e., REAL) and

the word PARAMETER

● Following each name, one should add an equal sign (=) followed by an expression. The value of this expression is

then assigned the indicated name.

● After assigning a name to a value, one can use the name, rather than its value throughout the program. The compiler

would convert that name to its corresponding value.

● It is important to note that the name assigned to a value is simply an alias of the value. Therefore, that name is not a

variable.

● After assigning a name to a value, that name can be used in a program, even in subsequent type statements.

Examples:

● In the example blow, Limit is a name for the integer value 30, while Max_Count is a name for the integer value

100:

INTEGER, PARAMETER :: Limit = 30, Max_Count = 100

● In the example below, E is a name for the real value 2.71828, while PI is a name for the real value 3.141592:

REAL, PARAMETER :: E = 2.71828, PI = 3.141592

● In the example below, Total and Count are names for 10 and 5, respectively. The name, Sum, is defined to be the

product of the values of Total and Count and hence Sum is the name for the value 50(=10*5). INTEGER, PARAMETER :: Total = 10, Count = 5, Sum = Total*Count

● In the example below, Name is a name for the string 'John' and State is a name for the string "Utah"

CHARACTER(LEN=4), PARAMETER :: Name = 'John', State = "Utah"

It is importantto know when assigning a name to a string:

❍ If the string is longer, truncation to the right will happen. In the following case, since the length of the string

"Smith" is 5 while the length of Name is 4, the string is truncated to the right and the content of Name is "Smit"

CHARACTER(LEN=4), PARAMETER :: Name = 'Smith'

❍ If the string is shorter, spaces will be added to the right. Since the string "LA" is of length 2 while the name

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The PARAMETER Attribute

City is of length 4, two spaces will be padded to the right and the content of City becomes "LA " CHARACTER(LEN=4), PARAMETER :: City = "LA"

● This is where the assumed length specifier comes in. That is, Fortran allows the length of character name to be

determined by the length of s string. In the example below, names Name and City are declared to have assumed length. Since the lengths of 'John' and "LA" are 4 and 2, the length of the names Name and City are 4 and 2, respectively.

CHARACTER(LEN=*), PARAMETER :: Name = 'John', City = "LA"

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Variables Initialization

A variable can be considered as a box that can hold a single value. However, initially the content of a variable (or a box) is empty. Therefore, before one can use a variable, it must receive a value. Do not assume the compiler or computer will put some value, say 0, into a variable. There are at least three ways to put a value into a variable:

● initializing it when the program is run ● using an assignment statement

● reading a value from keyboard or other device with a READ statement.

The way of initializing a variable is very similar to the use of PARAMETER attribute. More precisely, do the following to initial a variable with the value of an expression:

● add an equal sign (=) to the right of a variable name

● to the right of the equal sign, write an expression. It is important to note that all names in the expression must

constants or names of constants.

Initializing a variable is only done exactly once when the computer loads your program into memory for execution. That is, all initializations are done before the program starts its execution. Using un-initialized variables may cause unexpected result.

Examples:

● The following example initializes variables Offset to 0.1, Length to 10.0, and tolerance to 1.E-7.

REAL :: Offset = 0.1, Length = 10.0, tolerance = 1.E-7

● The following example initializes variables State1 to "MI", State2 to "MN", and State3 to "MD".

CHARACTER(LEN=2) :: State1 = "MI", State2 = "MN", State3 = "MD"

● The following example first defines three named integer constants with PARAMETER and uses these values to

initialize two integer variables. Thus, variables Pay and Received are initialized to have values 4350 (=10*435) and 8 (3+5), respectively.

INTEGER, PARAMETER :: Quantity = 10, Amount = 435, Period = 3 INTEGER :: Pay = Quantity*Amount, Received = Period+5

● The following example contains a mistake. While the compiler is processing the initialization value for variable

Received, the value of Period is unknown, although it will be defined on the next line. INTEGER, PARAMETER :: Quantity = 10, Amount = 435

INTEGER :: Pay = Quantity*Amount, Received = Period+5 INTEGER, PARAMETER :: Period = 3

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Arithmetic Operators

Fortran has four types of operators: arithmetic, relational, logical, and character. The following is a table of these

operators, including their priority and associativity.

Type Operator Associativity

Arithmetic ** right to left * / left to right + - left to right Relational < <= > >= == / = none Logical

.NOT. right to left .AND. left to right

.OR. left to right .EQV. .NEQV. left to right

Some Useful Notes:

● In the table, the operator on the top-most row (**) has the highest priority (i.e., it will be evaluated first) while the

operators on the bottom-most row (i.e., .EQV. and .NEQV.) have the lowest priority. The operators on the same row have the same priority. In this case, the order of evaluation is based on their associativity law.

● In addition to addition +, subtraction -, multiplication * and division /, Fortran has an exponential operator **. Thus,

raising X to the Y-th power is written as X**Y. For example, the square of 5 is 5**2, and the square root of 5 is 5**0.5. The exponential operator has the highest priority.

● Operators + and - can also be used as unary operators, meaning that they only need one operand. For example, -A

and +X. The former means change the sign of A, while the latter is equivalent to X.

● Unary operators + and - have the same priority as their binary counterparts (i.e., addition + and subtraction -). As a

result, since ** is higher than the negative sign -, -3**2 is equivalent to -(3**2), which is -9.

● For arithmetic operators, the exponential operator ** is evaluated from right to left. Thus, A**B**C is equal to A**

(B**C) rather than (A**B)**C

Click here for single mode arithmetic expressions Click here for mixed mode arithmetic expressions

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Single Mode Arithmetic Expressions

An arithmetic expression is an expression using additions +, subtractions -, multiplications *, divisions /, and exponentials **. A single mode arithmetic expression is an expression all of whose operands are of the same type (i.e. INTEGER, REAL or COMPLEX). However, only INTEGER and REAL will be covered in this note. Therefore, those values or variables in a single mode arithmetic expression are all integers or real numbers.

In single mode arithmetic expressions, the result of an operation is identical to that of the operands. The following is a table showing this fact. The empty entries will be discussed in mixed mode arithmetic expressions.

Operator INTEGER REAL INTEGER INTEGER mixed mode

REAL mixed mode REAL

Simple Examples:

● 1 + 3 is 4 ● 1.23 - 0.45 is 0.78 ● 3 * 8 is 24 ● 6.5/1.25 is 5.2

● 8.4/4.2 is 2.0 rather than 2, since the result must be of REAL type. ● -5**2 is -25

● 12/4 is 3

● 13/4 is 3 rather than 3.25. Since 13/4 is a single mode arithmetic expression and since all of its operands are of

INTEGER type, the result must also be of INTEGER type. The computer will truncate the mathematical result (3.25) making it an integer. Therefore, the result is 3.

● 3/5 is 0 rather than 0.6.

Rules for Evaluating Expressions

The following are rules of evaluating a more complicated single mode arithmetic expression:

● Expressions are always evaluated from left to right

● If an operator is encountered in the process of evaluation, its priority is compared with that of the next one: ❍ if the next one is lower, evaluate the current operator with its operands

3 * 5 - 4

In the above expression, in the left to right scan, operator *is encountered first. Since the the operator -is lower, 3 * 5is evaluated first transforming the given expression to 15 - 4. Hence, the result is 11.

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Single Mode Arithmetic Expressions

❍ if the next one is equal to the current, the associativity rules are used to determine which one should be

evaluated. For example, if both the current and the next operators are *, then 3 * 8 * 6 will be evaluated as (3 * 8) * 6. On the other hand, if the operator is **, A ** B ** C will be evaluated as A ** (B ** C).

❍ if the next one is higher than the current, the scan should continue with the next operator. For example,

consider the following expression: 4 + 5 * 7 ** 3

if the current operator is +, since the next operator *has higher priority, the scan continues to *. Once the scan arrives at *, since the next operator **is higher, 7 ** 3is evaluated first, transforming the given expression to

4 + 5 * 343

Then, the new expression is scan again. The next operator to be evaluated is *, followed by +. Thus, the original expression is evaluated as 4 + (5 * (7 ** 3)).

More Complicated Examples:

In the following examples, brackets are used to indicated the order of evaluation.

● The result is 4 rather than 4.444444 since the operands are all integers.

2 * 4 * 5 / 3 ** 2 --> [2 * 4] * 5 / 3 ** 2 --> 8 * 5 / 3 ** 2 --> [8 * 5] / 3 ** 2 --> 40 / 3 ** 2 --> 40 / [3 ** 2] --> 40 / 9 --> 4

● As in mathematics, subexpressions in parenthesis must be evaluated first.

100 + (1 + 250 / 100) ** 3 --> 100 + (1 + [250 / 100]) ** 3 --> 100 + (1 + 2) ** 3 --> 100 + ([1 + 2]) ** 3 --> 100 + 3 ** 3 --> 100 + [3 ** 3] --> 100 + 27 --> 127

● In the following example, x**0.25 is equivalent to computing the fourth root of x. In general, taking the k-th root of

x is equivalent to x**(1.0/k) in Fortran, where k is a real number.

1.0 + 2.0 * 3.0 / ( 6.0*6.0 + 5.0*44.0) ** 0.25

--> 1.0 + [2.0 * 3.0] / (6.0*6.0 + 5.0*44.0) ** 0.25

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Single Mode Arithmetic Expressions --> 1.0 + 6.0 / (6.0*6.0 + 5.0*55.0) ** 0.25 --> 1.0 + 6.0 / ([6.0*6.0] + 5.0*44.0) ** 0.25 --> 1.0 + 6.0 / (36.0 + 5.0*44.0) ** 0.25 --> 1.0 + 6.0 / (36.0 + [5.0*44.0]) ** 0.25 --> 1.0 + 6.0 / (36.0 + 220.0) ** 0.25 --> 1.0 + 6.0 / ([36.0 + 220.0]) ** 0.25 --> 1.0 + 6.0 / 256.0 ** 0.25 --> 1.0 + 6.0 / [256.0 ** 0.25] --> 1.0 + 6.0 / 4.0 --> 1.0 + [6.0 / 4.0] --> 1.0 + 1.5 --> 2.5

Click here to continue with mixed mode arithmetic expressions.

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Mixed Mode Arithmetic Expressions

If operands in an expression contains both INTEGER and REAL constants or variables, this is a mixed mode arithmetic expression.

In mixed mode arithmetic expressions, INTEGER operands are always converted to REAL before carrying out any computations. As a result, the result of a mixed mode expression is of REAL type. The following is a table showing this fact.

Operator INTEGER REAL INTEGER INTEGER REAL

REAL REAL REAL

The rules for evaluating mixed mode arithmetic expressions are simple:

● Use the rules for evaluating single mode arithmetic expressions for scanning. ● After locating an operator for evaluation, do the following:

❍ if the operands of this operator are of the same type, compute the result of this operator.

❍ otherwise, one of the operand is an integer while the other is a real number. In this case, convert the integer to

a real (i.e., adding .0 at the end of the integer operand) and compute the result. Note that since both operands are real numbers, the result is a real number.

● There is an exception, though. In a**n, where a is a real and n is a positive integer, the result is computed by

multiplying n copies of a. For example, 3.5**3 is computed as 3.5*3.5*3.5

Simple Examples:

● 1 + 2.5 is 2.5 ● 1/2.0 is 0.5 ● 2.0/8 is 0.25 ● -3**2.0 is -9.0

● 4.0**(1/2) is first converted to 4.0**0 since 1/2 is a single mode expression whose result is 0. Then, 4.0**0 is 1.0

An Important Note:

In expression a**b where a is REAL, the result is undefined if the value of a is negative. For example, -4.0**2 is defined with -16.0 as its result, while (-4.0)**2 is undefined.

More Complicated Examples:

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Mixed Mode Arithmetic Expressions

In the following, brackets will be used to indicated the order of evaluation and braces will be used to indicated an integer-to-real conversion.

● Note that 6.0 ** 2 is not converted to 6.0 ** 2.0. Instead, it is computed as 6.0 * 6.0.

5 * (11.0 - 5) ** 2 / 4 + 9 --> 5 * (11.0 - {5}) ** 2 / 4 + 9 --> 5 * (11.0 - 5.0) ** 2 / 4 + 9 --> 5 * ([11.0 - 5.0]) ** 2 / 4 + 9 --> 5 * 6.0 ** 2 / 4 + 9 --> 5 * [6.0 ** 2] / 4 + 9 --> 5 * 36.0 / 4 + 9 --> {5} * 36.0 / 4 + 9 --> 5.0 * 36.0 / 4 + 9 --> [5.0 * 36.0] / 4 + 9 --> 180.0 / 4 + 9 --> 180.0 / {4} + 9 --> 180.0 / 4.0 + 9 --> [180.0 / 4.0] + 9 --> 45.0 + 9 --> 45.0 + {9} --> 45.0 + 9.0 --> 54.0

● In the following, 25.0 ** 1 is not converted, and 1 / 3 is zero.

25.0 ** 1 / 2 * 3.5 ** (1 / 3) --> [25.0 ** 1] / 2 * 3.5 ** (1 / 3) --> 25.0 / 2 * 3.5 ** (1 / 3) --> 25.0 / {2} * 3.5 ** (1 / 3) --> 25.0 / 2.0 * 3.5 ** (1 / 3) --> 12.5 * 3.5 ** (1 / 3) --> 12.5 * 3.5 ** ([1 / 3]) --> 12.5 * 3.5 ** 0 --> 12.5 * [3.5 ** 0] --> 12.5 * 1.0 --> 12.5

Click here to continue with single mode arithmetic expressions.

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The Assignment Statement

The assignment statement has the following form:

variable = expression

Its purpose is saving the result of the expression to the right of the assignment operator to the variable on the left. Here are some rules:

● The expression is evaluated first with the rules discussed in the single mode or the mixed mode expressions pages. ● If the type of the expression is identical to that of the variable, the result is saved in the variable.

● Otherwise, the result is converted to the type of the variable and saved there.

❍ If the type of the variable is INTEGER while the type of the result is REAL, the fractional part, including

the decimal point, is removed making it an integer result.

❍ If the type of the variable is REAL while the type of the result is INTEGER, then a decimal point is

appended to the integer making it a real number.

● Once the variable receives a new value, the original one disappears and is no more available.

● CHARACTER assignment follows the rules stated in the discussion of the PARAMETER attribute.

Examples:

● The program segment below declares three INTEGER variables. The first assignment statement saves an integer

value to variable Unit. The second saves a real number 100.99 into variable Amount. However, since Amount is an INTEGER variable, the real value 100.99 is converted to an integer, 100, and saved into Amount. Thus, after the second assignment completes, variable Amount holds 100. The third assignment computes the single mode expression, yielding a result 500 = 5*100. Thus, variable Total receives 500.

INTEGER :: Total, Amount, Unit

Unit = 5

Amount = 100.99

Total = Unit * Amount

● In the following, PI is a PARAMETER and is an alias of 3.1415926. The first assignment statement puts integer

value 5 into integer variable Radius. The expression in the second assignment is first evaluated, yielding a result 78.539815, which is then saved into REAL variable Area.

REAL, PARAMETER :: PI = 3.1415926 REAL :: Area INTEGER :: Radius Radius = 5 Area = (Radius ** 2) * PI http://www.cs.mtu.edu/~shene/COURSES/cs201/NOTES/chap02/assign.html (1 of 3)8/5/2006 8:03:06 PM

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● In the following, Counter is an INTEGER variable initialized to zero.

The meaning of the first assignment is computing the sum of the value in Counter and 1, and saves it back to Counter. Since Counter's current value is zero, Counter + 1 is 1+0 = 1 and hence 1 is saved into Counter. Therefore, the new value of Counter becomes 1 and its original value 0 disappears.

The second assignment statement computes the sum of Counter's current value and 3, and saves the result back to Counter. Thus, the new value of Counter is 1+3=4.

INTEGER :: Counter = 0

Counter = Counter + 1 Counter = Counter + 3

● The following swaps the values in A and B, with the help of C. That is, after completing the following three

assignment statements, A and B have 5 and 3, respectively.

Initially, A and B are initialized to 3 and 5, respectively, while C is uninitialized. The first assignment statement puts A's value into C, making A=3, B=5 and C=3.

The second assignment statements puts B's value into A. This destroys A's original value 3. After this, A = 5, B = 5 and C = 3.

The third assignment statement puts C's value into B. This makes A=5, B=3 and C=3. Therefore, the values in A and B are exchanged.

INTEGER :: A = 3, B = 5, C

C = A A = B B = C

The following is another possible solution; but, it uses one more variable. INTEGER :: A = 3, B = 5, C, D C = A D = B A = D B = C

An Important Note:

A name declared with the PARAMETER attribute is an alias of a value and is not a variable.

Therefore, it cannot be used on the left-hand side of =, although it can be used on the right-hand side. The following is wrong!

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INTEGER, PARAMETER :: InchToCM = 2.54, factor = 123.45 INTEGER :: X = 15

InchToCM = factor * X

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Fortran Intrinsic Functions

Fortran provides many commonly used functions, called intrinsic functions. To use a Fortran function, one needs to

understand the following items:

● the name and meaning of the function such as ABS() and SQRT() ● the number of arguments

● the range of the argument ● the types of the arguments

● the type of the return value or the function value

For example, function SQRT() accepts a REAL argument whose value must be non-negative and computes and returns the square root of the argument. Therefore, SQRT(25.0) returns the square root of 25.0 and SQRT(-1.0) would cause an error since the argument is negative.

● Mathematical functions:

Function Meaning Arg. Type Return Type ABS(x) absolute value of x INTEGER INTEGER

REAL REAL

SQRT(x) square root of x REAL REAL

SIN(x) sine of x radian REAL REAL

COS(x) cosine of x radian REAL REAL TAN(x) tangent of x radian REAL REAL

ASIN(x) arc sine of x REAL REAL

ACOS

(x) arc cosine of x REAL REAL

ATAN

(x) arc tangent of x REAL REAL

EXP(x) exp(x) REAL REAL

LOG(x) natural logarithm of

x REAL REAL

Note that all trigonometric functions use radian rather than degree for measuring angles. For function ATAN(x), x must be in (-PI/2, PI/2). For ASIN(x) and ACOS(x), x must be in [-1,1].

● Conversion functions:

Function Meaning Arg. Type Return

Type

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Fortran Intrinsic Functions

INT(x) integer part x REAL INTEGER

NINT(x) nearest integer to x REAL INTEGER

FLOOR(x) greatest integer less than or equal to

x REAL INTEGER

FRACTION

(x) the fractional part of x REAL REAL

REAL(x) convert x to REAL INTEGER REAL

● Other functions:

Function Meaning Arg. Type Return

Type MAX(x1, x2, ..., xn) maximum of x1, x2, ... xn INTEGER INTEGER REAL REAL

MIN(x1, x2, ..., xn) minimum of x1, x2, ... xn INTEGER INTEGER

REAL REAL

MOD(x,y) remainder x - INT(x/y) *y

INTEGER INTEGER

REAL REAL

Functions in an Expression:

● Functions have higher priority than any arithmetic operators.

● All arguments of a function can be expressions. These expressions are evaluated first and passed to the function for

computing the function value.

● The returned function value is treated as a value in the expression.

An Example:

The example below has three initialized variables A, B and C. The result is computed and saved into uninitialized variable R.

REAL :: A = 1.0, B = -5.0, C = 6.0 REAL :: R

R = (-B + SQRT(B*B - 4.0*A*C))/(2.0*A)

The following uses brackets to indicated the order of evaluation: (-B + SQRT(B*B - 4.0*A*C))/(2.0*A)

--> ([-B] + SQRT(B*B - 4.0*A*C))/(2.0*A)

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Fortran Intrinsic Functions --> (5.0 + SQRT(B*B - 4.0*A*C))/(2.0*A) --> (5.0 + SQRT([B*B] - 4.0*A*C))/(2.0*A) --> (5.0 + SQRT(25.0 - 4.0*A*C))/(2.0*A) --> (5.0 + SQRT(25.0 - [4.0*A]*C))/(2.0*A) --> (5.0 + SQRT(25.0 - 4.0*C))/(2.0*A) --> (5.0 + SQRT(25.0 - [4.0*C))/(2.0*A) --> (5.0 + SQRT(25.0 - 24.0))/(2.0*A) --> (5.0 SQRT([25.0 - 24.0]))/(2.0*A) --> (5.0 + SQRT(1.0))/(2.0*A) --> (5.0 + 1.0)/(2.0*A) --> ([5.0 + 1.0])/(2.0*A) --> 6.0/(2.0*A) --> 6.0/([2.0*A]) --> 6.0/2.0 --> 3.0 Therefore, R receives 3.0. http://www.cs.mtu.edu/~shene/COURSES/cs201/NOTES/chap02/funct.html (3 of 3)8/5/2006 8:03:18 PM

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Listed-Directed Input: The READ Statement

List-directed input is carried out with the Fortran READ statements. The READ statement can read input values into a set of variables from the keyboard.

The READ statement has the following forms:

READ(*,*) var1, var2, ..., varn READ(*,*)

The first form starts with READ(*,*), followed by a list of variable names, separated by commas. The computer will read values from the keyboard successively and puts the value into the variables. The second form only has READ(*,*), which has a special meaning.

● The following example reads in four values into variables Factor, N, Multiple and tolerance in this order.

INTEGER :: Factor, N

REAL :: Multiple, tolerance

READ(*,*) Factor, N, Multiple, tolerance

● The following example reads in a string into Title, followed by three real numbers into Height, Length and Area.

CHARACTER(LEN=10) :: Title

REAL :: Height, Length, Area

READ(*,*) Title, Height, Length, Area

Preparing Input Data:

Preparing input data is simple. Here are the rules:

● If a READ statement needs some input values, start a new line that contains the input. Make sure the type of the

input value and the type of the corresponding variable are the same. The input data values must be separated by space or commas.

For the following READ

CHARACTER(LEN=5) :: Name

REAL :: height, length INTEGER :: count, MaxLength

READ(*,*) Name, height, count, length, MaxLength

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The input data may look like the following:

"Smith" 100.0 25 123.579 10000

Note that all input data are on the same line and separated with spaces. After reading in this line, the contents of the variables are Name "Smith" height 100.0 count 25 length 123.579 MaxLength 100000

● Input values can be on several lines. As long as the number of input values and the number of variables in the

corresponding READ agree, the computer will search for the input values. Thus, the following input should produce the same result. Note that even blank lines are allowed in input.

"Smith" 100.0

25

123.579 10000

● The execution of a READ always starts searching for input values with a new input line.

INTEGER :: I, J, K, L, M, N

READ(*,*) I, J READ(*,*) K, L, M READ(*,*) N

If the above READstatements are used to read the following input lines, 100 200

300 400 500 600

then I, J, K, L, Mand Nwill receive 100, 200, 300, 400, 500 and 600, respectively.

● Consequently, if the number of input values is larger than the number of variables in a READ statement, the extra

values will be ignored. Consider the following: INTEGER :: I, J, K, L, M, N

READ(*,*) I, J, K READ(*,*) L, M, N

If the input lines are

100 200 300 400

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500 600 700 800 900

Variables I, Jand Kreceive 100, 200 and 300, respectively. Since the second READstarts with a new line, L, Mand Nreceive 500, 600 and 700, respectively. 400 on the first input line is lost. The next READwill start reading with the third line, picking up 900. Hence, 800 is lost.

● A limited type conversion is possible in a READ statement. If the input value is an integer and the corresponding

variable is of REAL type, the input integer will be convert to a real number.

But, if the input value is a real number and the corresponding variable is of INTEGER type, an error will occur. The length of the input string and the length of the corresponding CHARACTER variable do not have to be equal. If they are not equal, truncation or padding with spaces will occur as discussed in the PARAMETER attribute page.

● Finally, a READ without a list of variables simply skips a line of input. Consider the following:

INTEGER :: P, Q, R, S

READ(*,*) P, Q READ(*,*)

READ(*,*) R, S

If the input lines are 100 200 300 400 500 600 700 800 900

The first READreads 100 and 200 into Pand Qand 300 is lost. The second READstarts with a new input line, which is the second one. It does not read in anything. The third READstarts with the third line and reads 700 and 800 into Rand S. As a result, the three input values (i.e., 400, 500 and 600) are all lost. The third value on the third line, 900, is also lost.

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Listed-Directed Output: The WRITE Statement

Listed-directed output is carried with the Fortran WRITE statement. The WRITE statement can display the results of a set of expressions and character strings. In general, WRITE displays the output on the screen.

The WRITE statement has the following forms:

WRITE(*,*) exp1, exp2, ..., expn WRITE(*,*)

The first form starts with WRITE(*,*), followed by a list of arithmetic expressions or character strings, separated by commas. The computer will evaluate the arithmetic expressions and displays the results. Note that if a variable does not contain a value, its displayed result is unpredictable. The second form only has WRITE(*,*), which has a special meaning.

● The following example displays the values of four variables on screen:

INTEGER :: Factor, N

REAL :: Multiple, tolerance

WRITE(*,*) Factor, N, Multiple, tolerance

● The following example displays the string content of Title, followed by the result of (Height + Length) * Area.

CHARACTER(LEN=10) :: Title

REAL :: Height, Length, Area

WRITE(*,*) Title, (Height + Length) * Area

There are some useful rules:

● Each WRITE starts with a new line.

● Consequently, the second form in which the WRITE does not have a list of expressions just displays a blank line.

INTEGER :: Target

REAL :: Angle, Distance

CHARACTER(LEN=*), PARAMETER :: Time = "The time to hit target " & IS = " is " & UNIT = " sec."

Target = 10 Angle = 20.0 Distance = 1350.0

WRITE(*,*) 'Angle = ', Angle WRITE(*,*) 'Distance = ', Distance WRITE(*,*)

WRITE(*,*) Time, Target, IS, Angle * Distance, UNIT

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Listed-Directed Output: The WRITE Statement

This example may produce the following result: Angle = 20.0

Distance = 1350.0

The time to hit target 10 is 27000sec.

The blank line is generated by the third WRITE.

The above example uses assumed length specifier (i.e., LEN=*) and continuation lines (i.e., symbol &).

● If there are too many results that cannot be fit into a single line, the computer will display remaining results on the

second, the third line and so on.

Output Format:

There is nothing to worry about the output format. The computer will use the best way to display the results. In other words, integers and real numbers will be displayed as integers and real numbers. But, only the content of a string will be displayed. The computer will also guarantee that all significant digits will be shown so that one does not have to worry how many positions should be used for displaying a number. The consequence is that displaying a good-looking table is a challenge. This will be discussed in FORMAT statement.

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Programming Example: Three Programming Traps

Problem Statement

The purpose of this program is to show you three common programming traps:

● A**B**C is not equal to (A**B)**C.

● Dividing an integer with another integer always yields an integer result.

● In PARAMETER, assignment statement and READ, strings may be truncated if the length of the variable at the

receiving end is not long enough.

Solution

! ---! This program illustrates the following points:

! (1) The exponential trap:

! That is, A**B**C is equal to A**(B**C) rather ! than (A**B)**C.

! (2) The integer division trap:

! That is, 4/6 is ZERO in Fortran rather than ! a real number 0.666666

! Function REAL() is used to illustrate the ! differences.

! (3) The string truncation trap:

! What if the length assigned to a CHARACTER ! is shorter than the length of the string you ! expect the identifier to have? The third part ! shows you the effect.

!

---PROGRAM Fortran_Traps IMPLICIT NONE

INTEGER, PARAMETER :: A = 2, B = 2, H = 3 INTEGER, PARAMETER :: O = 4, P = 6

CHARACTER(LEN=5), PARAMETER :: M = 'Smith', N = 'TEXAS' CHARACTER(LEN=4), PARAMETER :: X = 'Smith'

CHARACTER(LEN=6), PARAMETER :: Y = 'TEXAS'

! The exponential trap

WRITE(*,*) "First, the exponential trap:"

WRITE(*,*) A, ' ** ', B, ' ** ', H, ' = ', A**B**H

WRITE(*,*) '( ', A, ' ** ', B, ' ) **', H, ' = ', (A**B)**H

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WRITE(*,*) A, ' ** ( ', B, ' ** ', H, ' ) = ', A**(B**H) WRITE(*,*)

! The integer division trap. Intrinsic function REAL() converts ! an integer to a real number

WRITE(*,*) "Second, the integer division trap:" WRITE(*,*)

WRITE(*,*) O, ' / ', P, ' = ', O/P

WRITE(*,*) 'REAL( ', O, ' ) / ', P, ' = ', REAL(O)/P WRITE(*,*) O, ' / REAL( ', P, ' ) = ', O/REAL(P) WRITE(*,*)

! The string truncation trap

WRITE(*,*) "Third, the string truncation trap:" WRITE(*,*) 'IS ', M, ' STILL IN ', N, '?'

WRITE(*,*) 'IS ', X, ' STILL IN ', Y, '?'

END PROGRAM Fortran_Traps

Click here to download this program.

Program Output

First, the exponential trap: 2 ** 2 ** 3 = 256

( 2 ** 2 ) **3 = 64 2 ** ( 2 ** 3 ) = 256

Second, the integer division trap:

4 / 6 = 0

REAL( 4 ) / 6 = 0.666666687 4 / REAL( 6 ) = 0.666666687

Third, the string truncation trap: IS Smith STILL IN TEXAS?

IS Smit STILL IN TEXAS ?

Discussion

● All names in this program are aliases of constants.

● Consider the first group. Variables A, B and H are aliases of 2, 2 and 3. The first WRITE computes A**B**H,

which is equivalent to A**(B**H), and the result is 2**(2**3)=256. The second WRITE computes (A**B)**C and the result is (2**2)**3=64. The third WRITE computes A**(B**H) and the result is 2**(2**3)=256. Thus, it is

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clear that A**B**H equal to A**(B**H).

● The second group illustrates the problem unique to integer division. Two integer aliases are involved, namely O and

P with values 4 and 6, respectively. The first WRITE displays O/P and the result is 4/6=0 since it is an integer division. The second WRITE converts O to real with intrinsic function REAL(). Thus, in computing REAL(O)/P, the expression is REAL(4)/6, which becomes 4.0/6 and then 4.0/6.0. Thus, the result is 0.6666667. The third WRITE should give the same result.

● Go back to the top of this program. Alias M and N should have no problem since the length of the names and the

length of the strings agree. Since the length of X is 4 and is shorter than the length of string 'Smith', X only receives the left-most 4 characters. Now take a look at Y. Since the length of Y is longer than the length of string 'TEXAS', spaces will be appended to the end to fill up to 6 characters. Thus, Y actually becomes 'TEXAS '. The output should look like the following:

IS Smith STILL IN TEXAS? IS Smit STILL IN TEXAS ?

On the second line, it is easily seen that the original Smithbecomes Smitand the original TEXASbecomes TEXAS_, where _indicates a space.

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Programming Example: Computing Means

Problem Statement

Given three real numbers, its arithmetic mean (average), geometric mean and harmonic mean are defined as follows:

Write a program to compute and display the means of three REAL variables initialized with positive real values.

Solution

! ---! Computes arithmetic, geometric and harmonic means !

---PROGRAM ComputeMeans IMPLICIT NONE

REAL :: X = 1.0, Y = 2.0, Z = 3.0 REAL :: ArithMean, GeoMean, HarmMean

WRITE(*,*) 'Data items: ', X, Y, Z WRITE(*,*)

ArithMean = (X + Y + Z)/3.0

GeoMean = (X * Y * Z)**(1.0/3.0)

HarmMean = 3.0/(1.0/X + 1.0/Y + 1.0/Z)

WRITE(*,*) 'Arithmetic mean = ', ArithMean WRITE(*,*) 'Geometric mean = ', GeoMean WRITE(*,*) 'Harmonic Mean = ', HarmMean

END PROGRAM ComputeMeans

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Programming Example: Computing Means

Program Output

Data items: 1., 2., 3. Arithmetic mean = 2. Geometric mean = 1.81712067 Harmonic Mean = 1.63636363

Discussion

● Variables X, Y and Z are initialized in the first REAL statement, while the second declares three variables,

ArithMean, GeoMean and HarmMean, for holding the result.

● The first WRITE statement displays the values of X, Y and Z. The second WRITE generates a blank line. ● In the second assignment statement that computes the geometric mean, the exponent part is 1.0/3.0 instead of 1/3,

since the latter is zero. 1.0/3 and 1.0/3 also work fine. But, you should not use 0.3, since it is not equal to 1/3. The parenthesis surrounding X * Y * Z cannot be removed; otherwise, the expression X * Y * Z **(1.0/3.0) means X * Y * (Z **(1.0/3.0)) since ** has a priority higher than that of *.

● The parenthesis in the third assignment cannot be removed either. Why?

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Programming Example: Quadratic Equation Solver

Problem Statement

Given a quadratic equation as follows:

if b*b-4*a*c is non-negative, the roots of the equation can be computed with the following formulae:

Write a program to read in the coefficients a, b and c, and compute and display the roots. You can assume that b*b - 4*a*c is always non-negative.

Solution

! ---! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 !

---PROGRAM QuadraticEquation IMPLICIT NONE

REAL :: a, b, c REAL :: d

REAL :: root1, root2

! read in the coefficients a, b and c

WRITE(*,*) 'A, B, C Please : ' READ(*,*) a, b, c

! compute the square root of discriminant d

d = SQRT(b*b - 4.0*a*c)

! solve the equation

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Programming Example: Quadratic Equation Solver

root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root

! display the results

WRITE(*,*)

WRITE(*,*) 'Roots are ', root1, ' and ', root2

END PROGRAM QuadraticEquation

Program Output

A, B, C Please : 1.0 -5.0 3.0

Roots are 4.30277538 and 0.697224379

The input to the above problem consists of three real numbers, 1.0, -5.0 and 3.0, and the computed roots are 4.30277538 and 0.697224379.

Discussion

● The WRITE displays a message like this

A, B, C Please :

After displaying this message, the computer executes READ. Since there is no input value, it will wait until the user types in three real values and hits the Returnkey. Then, these values are stored in a, band c.

● The first assignment statement computes the square root of the discriminant (i.e., b*b - 4.0*a*c) and stores it into

variable d.

● The roots are computed with the second and third assignments. Note that the parenthesis surrounding 2.0*a cannot

be removed; otherwise, it is equivalent to ((-b + d)/2.0)*a, which is wrong.

● The last two WRITE statements display the roots.

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Programming Example: The Length of a Parabola Segment

Problem Statement

Given base b and height h, the length of a special segment on a parabola can be computed as follows:

Write a program to read in the values of base and height, and use the above formula to compute the length of the parabola segment. Note that both base and height values must be positive.

Solution

! ---! Calculate the length of a parabola given height and

base. *

!

---PROGRAM ParabolaLength IMPLICIT NONE

REAL :: Height, Base, Length REAL :: temp, t

WRITE(*,*) 'Height of a parabola : ' READ(*,*) Height

WRITE(*,*) 'Base of a parabola : ' READ(*,*) Base

! ... temp and t are two temporary variables

t = 2.0 * Height

temp = SQRT(t**2 + Base**2)

Length = temp + Base**2/t*LOG((t + temp)/Base)

WRITE(*,*)

WRITE(*,*) 'Height = ', Height WRITE(*,*) 'Base = ', Base WRITE(*,*) 'Length = ', Length

END PROGRAM ParabolaLength

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Programming Example: The Length of a Parabola Segment

Program Output

Height of a parabola : 100.0 Base of a parabola : 78.5 Height = 100. Base = 78.5 Length = 266.149445

The input values for Height and Base are 100.0 and 78.5, respectively. The computed length is 266.149445.

Discussion

● The values of base and height will be stored in REAL variables Base and Height, respectively. Length will be used

to store the parabola segment length.

● Since the content in the square root is used twice, it would be more convenient to save the result in a variable. This

value will be stored in temp. Since 2h also appears a few times, variable t is used to store this value. After reading in Height and Base, 2.0 * Height is computed and stored in t with the first assignment. Then, the second assignment computes the content in the square root and stores the result into temp.

● The third assignment compute the segment length and stores the result into Length. Note that intrinsic function LOG

() is used.

● The four WRITE statements display the input and the results.

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Programming Example: Projectile Motion

Problem Statement

This program computes the position (x and y coordinates) and the velocity (magnitude and direction) of a projectile, given t, the time since launch, u, the launch velocity, a, the initial angle of launch (in degree), and g=9.8, the acceleration due to gravity.

The horizontal and vertical displacements are given by the following formulae:

The horizontal and vertical components of the velocity vector are computed as

and the magnitude of the velocity vector is

Finally, the angle between the ground and the velocity vector is determined by the formula below:

Write a program to read in the launch angle a, the time since launch t, and the launch velocity u, and compute the position, the velocity and the angle with the ground.

Solution

! ---! Given t, the time since launch, u, the launch velocity, a, the

! initial angle of launch (in degree), and g, the acceleration due to ! gravity, this program computes the position (x and y coordinates) ! and the velocity (magnitude and direction) of a projectile.

!

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PROGRAM Projectile IMPLICIT NONE

REAL, PARAMETER :: g = 9.8 ! acceleration due to gravity REAL, PARAMETER :: PI = 3.1415926 ! you knew this. didn't you

REAL :: Angle ! launch angle in degree REAL :: Time ! time to flight

REAL :: Theta ! direction at time in degree REAL :: U ! launch velocity

REAL :: V ! resultant velocity REAL :: Vx ! horizontal velocity REAL :: Vy ! vertical velocity

REAL :: X ! horizontal displacement REAL :: Y ! vertical displacement

READ(*,*) Angle, Time, U

Angle = Angle * PI / 180.0 ! convert to radian X = U * COS(Angle) * Time

Y = U * SIN(Angle) * Time - g*Time*Time / 2.0 Vx = U * COS(Angle)

Vy = U * SIN(Angle) - g * Time V = SQRT(Vx*Vx + Vy*Vy)

Theta = ATAN(Vy/Vx) * 180.0 / PI

WRITE(*,*) 'Horizontal displacement : ', X WRITE(*,*) 'Vertical displacement : ', Y WRITE(*,*) 'Resultant velocity : ', V WRITE(*,*) 'Direction (in degree) : ', Theta

END PROGRAM Projectile

Program Output

If the input to the program consists of the following three real values: 45.0 6.0 60.0

The program will generate the following output:

Horizontal displacement : 254.558472 Vertical displacement : 78.158432 Resultant velocity : 45.4763107 Direction (in degree) : -21.1030636

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Discussion

● The program uses Angle for the angle a, Time for t, and U for u. The READ statement reads the input. ● The first assignment statement converts the angle in degree to radian. This is necessary since all intrinsic

trigonometric functions use radian rather than degree.

● Variables X and Y, which are computed in the second and third assignments, hold the displacements. ● The next two assignments compute the components of the velocity vector.

● The velocity itself is computed in the sixth assignment.

● Finally, the angle with ground, Theta, is computed with the last assignment. Note that ithe result is converted back

to degree, since ATAN(x) returns the arc tangent value of x in radian.

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CHARACTER Operator and Substrings

Concatenation Operator //

Fortran has only one character operator, the concatenation operator //. The concatenation operator cannot be used with arithmetic operators. Given two strings, s1 and s2 of lengths m and n, respectively, the concatenation of s1 and s2, written as s1 // s2, contains all characters in string s1, followed by all characters in string s2. Therefore, the length of s1 // s2 is m +n.

Consider the following statements:

CHARACTER(LEN=4) :: John = "John", Sam = "Sam" CHARACTER(LEN=6) :: Lori = "Lori", Reagan = "Reagan" CHARACTER(LEN=10) :: Ans1, Ans2, Ans3, Ans4

Ans1 = John // Lori Ans2 = Sam // Reagon Ans3 = Reagon // Sam Ans4 = Lori // Sam

● Variable Ans1 contains a string "JohnLori**", where * denotes a space. These two spaces come from variable

Lori since its content is "Lori**".

● Variable Ans2 contains a string "Sam Reagan". The space in the string comes from variable Sam since its content

is "Sam*", where, as above, * denotes a space.

● Variable Ans3 contains a string "ReaganSam*". ● Variable Ans4 contains a string "Lori**Sam*".

Substrings

A consecutive part of a string is called a substring. One can append the extent specifier at the end of a CHARACTER variable to indicate a substring. An extent specifier has a form of

( integer-exp1 : integer-exp2 )

It starts with a (, followed by an integer expression, followed by a colon :, followed by another integer expression, followed by ). The first integer indicates the first position of the substring, while the second integer indicates the last position of the substring. Therefore, (3:5) means the substring consists of the third, fourth and fifth characters. If the content of variable String is "abcdefghijk", then String(3:5) is a string "cde".

If the first integer expression is missing, the value is assumed to be 1. If the second integer expression is missing, the value is assumed to be the last character of the string. Continue with the example in previous paragraph. String(:4) is string "abcd". String(2+5:) is string "ghijk".

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As a good programming practice, the value of the first integer expression should be greater than or equal to 1, and the value of the second integer expression should be less than of equal to the length of the string.

A string variable with an extent specifier can be used on the left-hand side of an assignment. Its meaning is assigning the string content on the right-hand side into the substring part of the string variable. Let the content of a string variable LeftHand of length 10 be "1234567890". The following are a few examples:

● LeftHand(3:5) = "abc": the new content of LeftHand is "12abc67890". ● LeftHand(1:6) = "uvwxyz": the new content of LeftHand is "uvwxyz7890". ● LeftHand(:6) = "uvzxyz": the result is identical to the previous example. ● LeftHand(4:) = "lmnopqr": the new content of LeftHand is "123lmnopqr".

● LeftHand(3:8) = "abc": the new content of LeftHand is "12abc***90", where * denotes a space. Note that since

LeftHand(3:8) consists of 6 character positions and "abc" has only three characters, the remaining will be filled with spaces.

● LeftHand(4:7) = "lmnopq": the new content of LeftHand is "123lmno890". It is due to truncation.

Example

! ---! This program uses DATE_AND_TIME() to retrieve the system date ! and the system time. Then, it converts the date and time ! information to a readable format. This program demonstrates ! the use of concatenation operator // and substring

!

---PROGRAM DateTime IMPLICIT NONE

CHARACTER(LEN = 8) :: DateINFO ! ccyymmdd CHARACTER(LEN = 4) :: Year, Month*2, Day*2

CHARACTER(LEN = 10) :: TimeINFO, PrettyTime*12 ! hhmmss.sss CHARACTER(LEN = 2) :: Hour, Minute, Second*6

CALL DATE_AND_TIME(DateINFO, TimeINFO)

! decompose DateINFO into year, month and day.

! DateINFO has a form of ccyymmdd, where cc = century, yy = year ! mm = month and dd = day

Year = DateINFO(1:4) Month = DateINFO(5:6) Day = DateINFO(7:8)

WRITE(*,*) 'Date information -> ', DateINFO WRITE(*,*) ' Year -> ', Year WRITE(*,*) ' Month -> ', Month WRITE(*,*) ' Day -> ', Day

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! decompose TimeINFO into hour, minute and second.

! TimeINFO has a form of hhmmss.sss, where h = hour, m = minute ! and s = second

Hour = TimeINFO(1:2) Minute = TimeINFO(3:4) Second = TimeINFO(5:10)

PrettyTime = Hour // ':' // Minute // ':' // Second

WRITE(*,*)

WRITE(*,*) 'Time Information -> ', TimeINFO WRITE(*,*) ' Hour -> ', Hour WRITE(*,*) ' Minite -> ', Minute WRITE(*,*) ' Second -> ', Second WRITE(*,*) ' Pretty Time -> ', PrettyTime

! the substring operator can be used on the left-hand side.

PrettyTime = ' ' PrettyTime( :2) = Hour PrettyTime(3:3) = ':' PrettyTime(4:5) = Minute PrettyTime(6:6) = ':' PrettyTime(7: ) = Second WRITE(*,*)

WRITE(*,*) ' Pretty Time -> ', PrettyTime

END PROGRAM DateTime

Program Output

Date information -> 19970811 Year -> 1997 Month -> 08 Day -> 11 Time Information -> 010717.620 Hour -> 01 Minite -> 07 Second -> 17.620 Pretty Time -> 01:07:17.620 Pretty Time -> 01:07:17.620 http://www.cs.mtu.edu/~shene/COURSES/cs201/NOTES/chap02/char-opr.html (3 of 4)8/5/2006 8:03:46 PM

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Discussion

● Subroutine DATE_AND_TIME() returns the date of time and day information into two character arguments. The

first one, DateINFO, must have a length of at least 8. The returned value is in the form of ccyymmdd, where cc gives the century, yy the year, mm the month, and dd the day. If today is August 11, 1997, the call to this subroutine returns a string of eight characters "19970811"

● The second argument, TimeINFO, will receive a string of 12 characters with a form of hhmmss.sss, where hh gives

the hour value, mm the minute value, and ss.sss the second value. Thus, if the time this subroutine is called is 1 after 7 minutes and 17.620 seconds, the returned value is "010717.620"