Fortran 95/2003 for Scientists and Engineers (3e) by

Stephen J. Chapman

Grading system: 1. Attendance & Performance: 30% 2. Midterm: 30% 3. Final: 40%

Office hours: (PH224) 1. Wed. 10:10~12:00 2. Fri. 09:10~10:00 11:10~12:00

Ch. 1 Introduction to Computers and

the Fortran Language Sec. 1.1 The Computer

Fig 1-1

Main Memory

Secondary Memory

C P U

(Central processing unit)

Input devices

Output devices

Sec 1.2 Data Representation in a Computer

bit : Each switch represents one binary digit.

ON 1

OFF 0

byte : a group of 8 bits

e.g.,

825 MB hard disk. ( 1MB = 106 byte)

Sec 1.2.1 The Binary Number System

The base 10 number system:

1 2 3 10 = 1 x 102 + 2 x 101 + 3 x 100 = 123

102 101 100

The base 2 number system:

1 0 1 2 = 1 x 22 + 0 x 21 + 1 x 20 = 5

1 1 1 2 = 1 x 22 + 1 x 21 + 1 x 20 = 7

22 21 20

3 bits can represent 8 possible values :

0 ~ 7 (or 0002 ~ 1112 )

In general, n bits 2n possible values.

e.g.,

8 bits ( = 1 byte) 28 = 256 (-128 ~ +127)

16 bits ( = 2 byte) 216 = 65,536 (-32,768 ~ +32,767)

Sec 1.2.3 Types of Data Stored in Memory• Character data : (western language, < 256, use 1 byte)

A ~ Z (26)

a ~ z (26)

0 ~ 9 (10)

Miscellaneous symbols: ( ) { } ! …

Special letters or symbols: à ë …

Sec 1.2.2 Octal (or base 8) and Hexadecimal (or base 16)

Representations of Binary Numbers (see Table 1-1)

Coding systems: (see App. A, 8-bit codes) • ASCII (American Standard Code for Information Interchange)• EBCDIC (Extended Binary Coded Decimal Interchange Code)*The unicode coding system uses 2 bytes for each character. (for any language)

• Integer data: (negative, zero, positive) For an n-bit integer, Smallest Integer value = - 2n-1

Largest Integer value = 2n-1 – 1

e.g., a 4-byte (= 32-bit) integer, the smallest = -2,147,483,648 ( = - 232-1) the largest = 2,147,483,647 ( = 232-1-1)

*Overflow condition: An integer > the largest or < the smallest.

• Real data: (or floating-point data) The base 10 system: 299,800,000 = 2.998 x 108 (scientific notation)

mantissa exponent

The base 2 system: e.g., a 4-byte real number = 24-bit mantissa + 8-bit exponent

value = mantissa x 2exponent

Precision: The number of significant digits that can be preserved in a number. e.g., 24-bit mantissa ± 223 (~ seven significant digits)

Range: The diff. between the largest and the smallest numbers. e.g., 8-bit exponent 2-128 ~ 2127 (range ~ 10-38 to 1038)

Sec 1.3 Computer Languages• Machine language: The actual language that a computer

recognizes and executes.

• High-level languages: Basic, C, Fortran, …

Sec 1.4 The History of the Fortran Language

Fortran = Formula translation

Fortran 66 Fortran 77 Fortran 90 Fortran 95

(1966) (1977) (1991) (1996)

Fortran 2003

(2004)

Ch. 2 Basic Element of Fortran

Sec. 2.1 Introduction

Write simple but practical Fortran programs !

Sec. 2.2 Fortran Character Set (case insensitive)

• A ~ Z (26)

• a ~ z (26)

• 0 ~ 9 (26)

• _ (underscore)

• + - * / ** (arithmatic symbols)

• ( ) . = , ‘ … (miscellaneous symbols)

Sec. 2.3 The Structure of a Fortran Statement

a Fortran program = a series of statements

• Executable statements: e.g., additions, subtractions, …• Non-executable statements: providing information.

Free-source form: Fortran statements may be entered anywhere on a line, up to 132 characters long.

e.g., 100 output = input1 + input2 ! Sum the inputs or 100 output = input1 & ! Sum the inputs + input2

(statement label, 1~99999, not a line number)

Sec. 2.4 The Structure of a Fortran Program

Fig 2-1 (A simple Fortran program)

PROGRAM my_first_program

! Purpose: …

! Declare the variables

INTEGER :: i, j, k !All variable are integers

! Get the variables WRITE (*,*) " Enter the numbers to multiply:" READ (*,*) i, j k = i * j ! Write out the result WRITE (*,*) 'Result = ', k STOP END PROGRAM

(DeclarationSection)

(ExecutionSection)

(Termination section)

Sec. 2.4.4 Program Style

Textbook : • Capitalizing Fortran keywords ( e.g., READ, WRITE)• Using lowercase for variables, parameters

Sec. 2.4.5 Compiling, Linking, and Executing the Fortran Program

Fig 2-2

Fortran program

Object file

Executable program

(Compile) (Link)

Sec. 2.5 Constants and Variables

Valid variable names: time distance z123456789 I_want_to_go_home(up to 31 chracters, and the 1st character in a name must always be alphabetic)

Invalid variable names: this_is _a_very_long_variable_name 3_days A$ ($ is an illegal character) my-help (“-” is an illegal character)

Five intrinsic types of Fortran constants and variables:1. INTEGER2. REAL3. COMPLEX4. LOGICAL5. CHARACTER

(numeric)

(logical, Ch. 3)(character)

Sec. 2.5.1 Integer Constant and Variables

Integer constants: (no decimal point) e.g., 0 -999 +17 1,000,000 (X) -100. (X)

Integer variables: 16-bit integers 32-bit integers(diff. kinds of integers, Ch. 11)

Sec. 2.5.2 Real Constants and Variables Real constants: (with a decimal point) e.g., 10. -999.9 1.0E-3 (= 1.0 x 10-3 or 0.001) 123.45E20 0.12E+1 1,000,000. (X) 111E3 (X) -12.0E1.5 (X)

Real variables: 32-bit real numbers 64-bit real numbers(diff. kinds of real numbers, Ch. 11)

Sec. 2.5.3 Character Constants and Variables Character constants: [enclosed in single (‘) or double (“) quotes)] e.g., ‘This is a test!’ “This is a test!” ‘ ‘ (a single blank) ‘{^}’ ‘3.141593’ (not a number) This is a test! (X) ‘This is a test!” (X)

A character variable contains a value of the character data type.

Sec. 2.5.4 Default and Explicit Variable Typing Default typing: Any variable names beginning with the letters I, J, K, L, M, or N are assumed to be of type INTEGER.

e.g., incr (integer data type) big (real data type)

(Conti.)

Explicit typing: The type of a variable is explicitly defined in the declaration section. e.g., PROGRAM example INTEGER :: day, month, year REAL :: second LOGICAL :: test1, test2 CHARACTER :: initial

(Executable statements)

*No default names for the character data type!

Sec. 2.5.5 Keeping Constants Consistent in a Program

Using the PARAMETER attribute : type, PARAMETER :: name=value

e.g., REAL, PARAMETER :: pi=3.14159 CHARACTER, PARAMETER :: error=‘unknown’

Sec. 2.6 Assignment Statements and Arithmetic Calculations

Assignment statement: variable_name = expression e.g., I = I + 1 ( I + 1 I )

Arithmetic operators:• binary operators: a + b (a + b, addition) a – b (a – b, subtraction) a * b (a x b, multiplication) a / b (a/b, division) a ** b (ab, exponentiation)• unary operators: + a - b

Rules:

1. No two operators may occur side by side. e.g., a*-b (X) a*(-b) a**-2 (X) a**(-2)

2. Implied multiplication is illegal. e.g., x (y + z) (X) x*(y + z)

3. Parentheses may be used to group terms whenever desired

e.g., 2**((8+2) / 5)

Sec. 2.6.1 Integer Arithmetic e.g., 3/4 = 0, 6/4 = 1 7/4 = 1, 9/4 = 2

Sec. 2.6.2 Real Arithmetic (or floating-point arithmetic) e.g., 3./4. = 0.75, 6./4. = 1.50 7./4. = 1.75, 9./4. = 2.25

Sec. 2.6.3 Hierarchy (or order) of Operators e.g., x = 0.5 * a * t **2

is equal to

x = 0.5 * a * (t **2) ? or x = (0.5 * a * t ) **2 ?

Order: 1. Parentheses, from inward to outward.2. Exponentials, from right to left.3. Multiplications and divisions, from left to right.4. Additions and subtractions, from left to right.

Example 2-1 a = 3. b = 2. c=5. d=4. e = 10. f = 2. g= 3.(1) output = a * b + c * d + e / f **g(2) output = a * (b + c) * d + (e / f) **g(3) output = a * (b + c) * (d + e) / f **g

Solu. : (1) output = 3. * 2. + 5. * 4. + 10. / 2. ** 3. = 6. + 20. + 1.25 = 27.25 (2) output = 3. * (2. + 5.) * 4. + (10. / 2.) ** 3. = 84. + 125. = 209. (3) output = 3. * (2. + 5.) * (4. + 10.) / 2. ** 3. = 3. * 7. * 14. / 8. = 294. / 8. = 36.75

Example 2-2 a = 3. b = 2. c=3. (1) output = a ** (b ** c)(2) output = (a ** b) ** c(3) output = a ** b ** c

Solu.: (1) output = 3. ** (2. ** 3.) = 3. ** 8. = 6561. (2) output = (3. ** 2.) ** 3. = 9. ** 3. = 729. (3) output = 3. ** 2. ** 3. = 3. ** 8. = 6561.

Sec. 2.6.4 Mixed-Mode Arithmetic In the case of an operation between a real number and an integer,the integer is converted by the computer into a real number. e.g., 3. / 2 = 1.5 1 + 1/4 = 1 1. + 1/4 = 1. 1 + 1./4 = 1.25

Automatic type conversion:

e.g., nres = 1.25 + 9/4 ave = (5 + 2) / 2 = 1.25 + 2 = 7/2 = 3.25 = 3. = 3

(a integer variable) (a real variable)

Logarithm

• Base 10: If 10x = N, then x = ? log N = x e.g., N = 100 log 100 = log (102) = 2

N = 3 log 3 = 0.47712…

• Base e (=2.71828…): (Natural logarithm)

If ex = N, then x = ? ln N = x e.g., N = e2 ln (e2) = 2

N = 3 ln 3 = 1.09861…

* If N < 0 ( log N ) or ( ln N ) is undefined !

Sec. 2.6.5 Mixed-Mode Arithmetic and Exponentiation

If both result and y are real, and n is an integer,

result = y ** n = y * y * y…*y (real arithmetic, not mixed-mode)

But if result, y and x are all real,

result = y ** x = ?

use yx = e x ln y ( e ∵ x ln y = e ln (yx) = yx )

e.g., (4.0) ** 1.5 = 8.

(8.0)**(1./3)=2.

(-2.0) ** 2 = 4. [ (-2.0) * (-2.0) = 4.]∵

(-2.0) ** 2.0 [X, ln (-2.0) is undefined!]∵

Sec. 2.7 Intrinsic Functions

• Intrinsic functions are the most common functions built directly into the Fortran language. ( see Table 2-4 and App. B)• External functions are supplied by the user. (see Ch. 7)

e.g., y = sin(3.141593) INT(2.9995) = 2 (truncates the real number) y = sin(x)

y = sin(pi*x) NINT(2.9995) = 3 (rounds the real number) y = sin(SQRT(x))

Generic functions: (can use more than one type of input data) e.g., If x is a real number, ABS(x) is real. If x is an integer, ABS(x) is integer.

Specific functions: (can use only one specific type of input data) e.g., IABS(i)

(integer only)

*See Appendix B for a complete list of all intrinsic functions.

Sec. 2.8 List-directed (or free-format) Input and Output Statements

• The list-directed input statement: READ (*,*) input_list

I/O unit format

• The list-directed output statement: WRITE (*,*) output_list I/O unit format

e.g., PROGRAM input_example INTEGER :: i, j REAL :: a CHARACTER (len=12) :: chars READ(*,*) i, j, a, chars WRITE(*,*) i, j, a, chars END PROGRAM

Input: 1, 2, 3., ‘This one.’ (or 1 2 3. ‘This one.’)

Output: 1 2 3.00000 This one.

(Try it out!)

Sec. 2.9 Initialization of Variables

E.g., PROGRAM init INTEGER :: i WRITE(*,*) I END PROGRAM

Output: i = ??? (uninitialized variable)

Run-time error! (depends on machines)

(Try it out!)

Three ways to initialize variables:

1. Assignment statements: e.g., PROGRAM init_1 INTEGER :: i i = 1 WRITE(*,*) i END PROGRAM

2. READ statements: e.g., PROGRAM init_2 INTEGER :: i READ(*,*) i WRITE(*,*) i END PROGRAM

3. Type declaration Statements: type :: var1 = value1, [var2 = value2, …]

e.g., REAL :: time = 0.0, distance = 5128. INTEGER :: loop = 10 LOGICAL :: done = .FALSE. CARACTER (len=12) :: string = ‘characters’

or

PROGRAM init_3 INTEGER :: i = 1 WRITE(*,*) i END PROGRAM

Sec. 2.10 The IMPLICIT NONE Statement

When the IMPLICIT NONE statement is included in a program, any variable that does not appear in an explicit type declaration statement is considered an error. e.g., PROGRAM test_1 REAL :: time time = 10.0 WRITE(*,*) ‘Time=‘, tmie END PROGRAM

Output:

Run-time error! (depends on machines)

+ IMPLICIT NONE,

PROGRAM test_1 IMPLICIT NONE REAL :: time time = 10.0 WRITE(*,*) ‘Time=‘, tmie END PROGRAM

Output:

Compile-time error! (depends on machines)

Sec. 2.10 Program Examples

Example 2-3 (Temperature conversion)

T (0F) = (9/5) T(0C) + 32

Fig. 2-6 PROGRAM temp IMPLICIT NONE REAL :: temp_c, temp_f WRITE(*,*) ’Enter T in degrees C:’ READ(*,*) temp_c temp_f = (9./5.) * temp_c + 32. WRITE(*,*) temp_c,’ degrees C =‘, temp_f, & ‘degrees F’ END PROGRAM

(Try it out!)

Example (extra)

Write a program for converting a 4 bits integer into a base 10 number, e.g.,

1 0 1 1 = 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20 = 11

The geometric mean for three real positive values is defined as xave= (x1x2x3

)1/3 .

Write a Fortran program to calculated xave. Use the IMPLICIT NONE statement

Test: x1=1.0, x2=2.0, x3=4.0,

xave= 2.0

Problem: (extra)

Ch. 3 Program Design and Branching Structures

Ch. 2: Sequential programs (simple and fixed order)

Here: Complex programs (using two control statements)

(1) branches

(2) loops

Sec. 3.1 Introduction to Top-down Design Techniques

Start

State the problem

Design thealgorithm

Convert algorithm into Fortran statements

Test the program

Finished !

Fig. 3-1 (a formal program design process)

Sec. 3.2 Use of Pseudocode and Flowcharts

(1) Pseudocode : a mixture of Fortran and English

(2) Flowcharts : graphical symbolsl

e.g.,

(1) The pseudocode for Example 2-3: Prompt user to enter temp. in degree Farenheit Read temp. in degree Farenheit temp_k in Kelvins (5./9.)*(temp_f-32.)+273.15 Write temp. in Kelvins

(2) The flowcharts for Example 2-3:

Start

Tell user toenter temp_f

Get temp_f

Calculate temp_k Write temp_k Stop

(an oval for start or stop)

(a parallelogram for I/O)

(a rectangle for computation)

Sec. 3.3 Logical Constants, Variables, and Operators

Sec. 3.3.1 Logical Constants and Variables Logical constants: e.g., .TRUE. .FALSE. TRUE (X) .FALSE (X)

A logical variable contains a value of the logical data type. e.g., LOGICAL :: var1 [var2, var3, …]

Sec. 3.3.2 Assignment Statements and Logical Calculations

Assignment statements: logical variable name = logical expression

Logical operators: • relational operators• combinational operators

Sec. 3.3.3 Relational Operators

a1 op a2

a1, a2: arithmetic expressions, variables, constants, or character strings.op: the relational logical operators. (see Table 3-1)

Table 3-1operation meaning

= = equal to / = not equal to > greater than > = greater than or equal to < less than < = less than or equal to

e.g., operation result 3 < 4 .TRUE. 3 < = 4 .TRUE. 3 = = 4 .FALSE. ‘A’ < ‘B’ .TRUE. (in ASCII, A 65, B 66, p.493) 7+3 < 2+11 .TRUE.

Sec. 3.3.4 Combinational Logic Operators

l1 .op. l2 and .NOT. l1 (.NOT. is a unary operator)

l1, l2: logical expressions, variables, or constants.op: the binary operators. (see Table 2-4)

Table 3-2operation meaning

.AND. logical AND .OR. logical OR .EQV. logical equivalence .NEQV. logical non-equivalence .NOT. logical NOT

The order of operations:

1. Arithmetic operators.

2. All relational operators, from left to right.

3. All .NOT. operators.

4. All .AND. operators, from left to right.

5. All .OR. operators, from left to right.

6. All .EQV. And .NEQV. operators, from left to right.

Example 3-1

L1 = .TRUE., L2 = .TRUE., L3 = .FALSE. (a) .NOT. L1 .FALSE.

(b) L1 .OR. L3 .TRUE.

(c) L1 .AND. L3 .FALSE.

(d) L2 .NEQV. L3 .TRUE.

(e) L1 .AND. L2 .OR. L3 .TRUE.

(f) L1 .OR. L2 .AND. L3 .TRUE.

(g) .NOT. (L1 .EQV. L2) .FALSE.

Sec. 3.3.6 The Significance of Logical Variables and Expressions

Most of the major branching and looping structures of Fortran are controlled by logical values.

Sec. 3.3.5 Logical Values in Input and Output Statements

See Ch. 5

Sec. 3.4 Control Constructs: Branches

• IF Statement

• SELECT CASE

Branches are Fortran statements that permit us to select and execute specific sections of code (called blocks) while skipping other sections of code.

Sec. 3.4.1 The Block IF Construct

This construct specifies that a block of code will be executed if and only if a certain logical expression is true.

IF (logical_expr) THEN Statement 1 Statement 2 . . .END IF

a block

Fig . 3-5 (Flowchart for a simple block IF construct)

logical_expr

Statement 1Statement 2 . .

.TRUE.

.FALSE.

(a diamond for choice)

Example:

ax2 + bx + c = 0,

x = -b ± ( b2 – 4ac )1/2

2a

If b2 – 4ac = 0

b2 – 4ac > 0

b2 – 4ac < 0

two distinct real roots

two complex roots

a single repeated root

Fig . 3-6 (Flowchart)

.TRUE.

.FALSE.

Problem: Tell the user if the eq. has complex roots.

b2 – 4ac < 0

WRITE ‘two complex roots’

Fortran: IF ( (b**2 – 4.*a*c) < 0. ) THEN WRITE(*,*) ‘Two complex roots!’ END IF

Sec. 3.4.2 The ELSE and ELSE IF Clauses

For many different options to consider,

IF + ELSE IF (one or more) + an ELSE

IF (logical_expr_1) THEN Statement 1 Statement 2 . .ELSE IF (logical_expr_2) THEN Statement 1 Statement 2 . .ELSE Statement 1 Statement 2 . .END IF

Block 1

Block 2

Block 3

Fig . 3-7 (flowchart)

.TRUE.

.FALSE.logical_expr_1

Block 1

logical_expr_2

Block 2

.TRUE.

.FALSE.

Block 3

Fig . 3-8 (flowchart)

.TRUE.

.FALSE.b2 - 4ac < 0

WRITE ‘two complex roots’

.TRUE.

.FALSE.

Example: Tell the user whether the eq. has two complex roots, two identical real roots, or two distinct real roots.

b2 - 4ac = 0

WRITE ‘two identical real roots’

WRITE ‘two distinct real roots’

Fortran: IF ( (b**2 – 4.*a*c) < 0. ) THEN WRITE(*,*) ‘two complex roots’ ELSE IF ( (b**2 – 4.*a*c) == 0. ) THEN WRITE(*,*) ‘two identical real roots’ ELSE WRITE(*,*) ‘two distinct real roots’ END IF

Write a complete Fortran program for a quadraticequation ax2 + bx + c = 0.

Input: a, b, c (e.g., 1., 5., 6. or 1., 4., 4. or 1., 2., 5.)

Output: ‘distinct real’ or ‘identical real’ or ‘complex roots’

(Try it out!)

PROGRAM abcIMPLICIT NONEREAL :: a, b, c

WRITE(*,*)'Enter the coeffs. a, b, and c:‘READ(*,*) a, b, c

IF ( (b**2-4.*a*c) < 0. ) THEN WRITE(*,*) 'two complex root‘ELSE IF ( (b**2-4.*a*c) == 0. ) THEN WRITE(*,*) 'two identical real roots‘ELSE WRITE(*,*) 'two distinct real roots‘END IF

END PROGRAM

Sec. 3.4.3 Examples Using Block IF Constructs

Example 3-2 The Quadratic Equation: (ax2 + bx + c =0) Write a program to solve for the roots of a quadratic equation, regardless of type.

Input: a, b, c

Output: rootsrealrepeated realcomplex

PROGRAM rootIMPLICIT NONEREAL :: a, b, c, d, re, im, x1, x2

WRITE(*,*)'Enter the coeffs. a, b, and c:‘READ(*,*) a, b, cd = b**2 – 4.*a*cIF ( d < 0. ) THEN WRITE(*,*) 'two complex root:‘ re = (-b)/(2.*a) im = sqrt(abs(d))/(2.*a) WRITE(*,*) ’x1=‘, re, ‘+ i’, im WRITE(*,*) ’x2=‘, re, ‘- i’, im ELSE IF ( d == 0. ) THEN WRITE(*,*) 'two identical real roots:‘ x1 = (-b) / (2.*a) WRITE(*,*) ’x1=x2=‘, x1

ELSE WRITE(*,*) 'two distinct real roots:‘ x1 = (-b + sqrt(d)) / (2.*a) x2 = (-b – sqrt(d)) / (2.*a) WRITE(*,*) ’x1=‘, x1 WRITE(*,*) ‘x2=‘, x2END IFEND PROGRAM

Test: (Try it out!)

x2 + 5x + 6 = 0, x1,2 = -2, -3

x2 + 4x + 4 = 0, x1,2 = -2

x2 + 2x + 5 = 0, x1,2 = -1 ± i 2

Example 3-3 Evaluation a Function of Two Variables:

f(x,y) =

x + y, x 0 ≧ and y 0≧x + y2, x 0 ≧ and y < 0x2 + y, x < 0 and y 0≧x2 + y2, x < 0 and y < 0

Input: x, y

Output: f

Fig . 3-11 (flowchart)

.TRUE.

.FALSE.x ≧ 0 &y 0≧

f = x + y

x 0 ≧ &y < 0

f = x2 + y

.TRUE.

.FALSE.

f = x2 + y2f = x + y2

x < 0 &y 0≧

.TRUE.

.FALSE.

WRITE f

Stop

Start

READ x, y

PROGRAM funxyIMPLICIT NONEREAL :: x, y, f

WRITE(*,*)'Enter x and y:‘READ(*,*) x, yIF ((x >= 0.) .AND. (y >= 0. )) THEN f = x + yELSE IF ((x >= 0.) .AND. (y < 0. )) THEN f = x + y**2ELSE IF ((x < 0.) .AND. (y >= 0. )) THEN f = x**2 + yELSE f = x**2 + y**2END IFWRITE(*,*) ‘f = ‘, fEND PROGRAM

Test: (Try it out!)

x y f

2. 3. 5. 2. -3. 11.-2. 3. 7.-2. -3. 13.

[name:] IF (logical_expr_1) THEN Statement 1 Statement 2 . .ELSE IF (logical_expr_2) THEN [name] Statement 1 Statement 2 . .ELSE [name] Statement 1 Statement 2 . .END IF [name]

Block 1

Block 2

Block 3

Sec. 3.4.4 Named Block IF Constructs

optional

optional

Sec. 3.4.5 Notes Concerning the Use of Logical IF Constructs

Nested IF Constructs:

outer: IF ( x > 0. ) THEN . . inner: IF ( y < 0. ) THEN . . END IF inner . .END IF outer

Example 3-4 Assigning Letter Grades:

95 < GRADE A86 < GRADE < 95 B76 < GRADE < 86 C66 < GRADE < 76 D 0 < GRADE < 66 F

Input: grade

Output: ‘The grade is A.’ or ‘The grade is B.’ or ‘The grade is C.’ or ‘The grade is D.’ or ‘The grade is F.’

Method (a): IF + ELSE IF

IF (grade > 95.) THEN WRITE(*,*) ‘The grade is A.’ELSE IF (grade > 86.) THEN WRITE(*,*) ‘The grade is B.’ELSE IF (grade > 76.) THEN WRITE(*,*) ‘The grade is C.’ELSE IF (grade > 66.) THEN WRITE(*,*) ‘The grade is D.’ELSE WRITE(*,*) ‘The grade is F.’END IF

Method (b): nested IF

if1: IF (grade > 95.) THEN WRITE(*,*) ‘The grade is A.’ELSE if2: IF (grade > 86.) THEN WRITE(*,*) ‘The grade is B.’ ELSE if3: IF (grade > 76.) THEN WRITE(*,*) ‘The grade is C.’ ELSE if4: IF (grade > 66.) THEN WRITE(*,*) ‘The grade is D.’ ELSE WRITE(*,*) ‘The grade is F.’ END IF if4 END IF if3 END IF if2END IF if1

Sec. 3.4.6 The Logical IF Statement

IF (logical_expr) Statement

e.g., IF ( (x >= 0.) .AND. (y >= 0.) ) f = x + y

[name:] SELECT CASE (case_expr)CASE (case_selector_1) [name] Statement 1 Statement 2 . . .CASE (case_selector_2) [name] Statement 1 Statement 2 . . .CASE DEFAULT [name] Statement 1 Statement 2 . . .END SELECT [name]

Block 1

Block 2

Block 3

Sec. 3.4.7 The Select CASE Construct

optional

optional

optional

case_expr: an integer, character, or logical expression.

The case_selector can take one of four forms:

1. case_value Execute block if case_value == case_expr2. low_value: Execute block if low_value <= case_expr3. : high_value: Execute block if case_expr <= high_value4. low value: high_value Execute block if low_value <= case_expr <= high_value

Fig . 3-13 (flowchart for a CASE construct)

In range

Not in range

case_sel_1

Block 1

case_sel_2

Block n

In range

NotIn range

Default BlockBlock 2

case_sel_n

In range

Not in range

e.g., (modified)

REAL :: temp_c. . .temp: SELECT CASE (temp_c)CASE (: -1.0) WRITE (*,*) ‘ It’s below freezing today!’CASE (0.0) WRITE (*,*) ‘ It’s exactly at the freezing point!’CASE (1.0:20.0) WRITE (*,*) ‘ It’s cool today!’CASE (21.0:33.0) WRITE (*,*) ‘ It’s warm today!’CASE (34.0:) WRITE (*,*) ‘ It’s hot today!’END SELECT temp

PROGRAM selectcIMPLICIT NONEINTEGER :: temp_cWRITE(*,*) “Enter today’s temp. in degree C:”READ(*,*) temp_ctemp: SELECT CASE (temp_c)CASE (: -1) WRITE (*,*) “It’s below freezing today!”CASE (0) WRITE (*,*) “It’s exactly at the freezing point!”CASE (1:20) WRITE (*,*) “It’s cool today!”CASE (21:33) WRITE (*,*) “It’s warm today!”CASE (34:) WRITE (*,*) “It’s hot today!”END SELECT tempEND PROGRAM

Problem: Determine whether an integer between 1 and 10 is even or odd. (Try it out!)

PROGRAM selectvINTEGER :: valueWRITE(*,*) 'Enter an inter between 1-10:'READ(*,*) valueSELECT CASE (value) CASE (1,3,5,7,9) WRITE(*,*) 'The value is odd.' CASE (2,4,6,8,10) WRITE(*,*) 'The value is even.' CASE (11:) WRITE(*,*) 'The value is too high' CASE DEFAULT WRITE(*,*) 'The value is negative or zero.'END SELECTEND PROGRAM

Ch. 4 Loops and Character Manipulation

• while loops• iterative (or counting) loops

Sec. 4.1.1 The While Loop

DO . . . IF (logical_expr) EXIT . . .END DO

a code block

Sec. 4.1 Control Constructs: Loops

Fig . 4-1 (Flowchart for a while loop)

.TRUE.

.FALSE.

logical_expr

Statement 1 . . .

Statement 1 . . .

Example 4-1 Statiscal Analysis:

Average: x_ave =

Σxii=1

N

N

Standard deviation:

S = N Σxi

2 – (i=1 i=1

N N

Σxi )2

N (N-1)

1/2

Input: x (i.e., xi , i = 1, 2, …, N) 0 ≧

Output: x_ave and S

Fig . 4-2 (Flowchart for Example 3-4)

.TRUE.

.FALSE.

x < 0

READ x

n = n + 1sum_x = sum_x + xsum_x2=sum_x2 + x2

Start

1

1

Calculate x_ave, s

Stop

WRITE x_ave, s, n

Initial values:n = 0sum_x = 0Sum_x2 = 0

Fig . 4-3 PROGRAM stats_1IMPLICIT NONEINTEGER :: n = 0REAL :: x, x_ave, s , sum_x = 0., sum_x2 = 0.

DO WRITE(*,*) ‘Enter the value x:’ READ (*,*) x IF ( x < 0. ) EXIT n = n + 1 sum_x = sum_x + x sum_x2 = sum_x2 + x**2END DOx_ave = sum_x / ns = sqrt (( n*sum_x2 – sum_x**2) / (n*(n-1)))WRITE(*,*) ‘n = ‘ , n, ‘ x_ave = ‘, x_ave, & ‘ s = ‘, sEND PROGRAM

Test:

Input: 3. 4. 5. -1.

Output: n = 3 x_ave = 4.00000 s = 1.00000

Sec. 4.1.2 The Do While Loop

DO WHILE (logical_expr) . . . . . . . . .END DO

Sec. 4.1.3 The Iterative or Counting Loop

DO index = istart, iend, incr Statement 1 . . . Statement nEND DO

e.g.,

(1) Do i = 1, 10 Statement 1 . . . Statement nEND DO

( incr = 1 by default)

(2) Do i = 1, 10, 2 Statement 1 . . . Statement nEND DO

( i = 1, 3, 5, 7, 9 )

Fig. 4-5 (Flowchart for a Do loop construct)

index*incr ≦iend * incr

index =istart

incr

Statement 1Statement 2 . . .

.TRUE..FALSE.

Example 4-2 The Factorial Function:

N ! = N × (N-1) × (N-2) … × 3 × 2 × 1, N > 0.0 ! = 1

e.g.,

4 ! = 4 × 3 × 2 × 1 = 24 5 ! = 5 × 4 × 3 × 2 × 1 = 120

Fortran Code: n_factorial = 1DO i = 1, n n_factorial = n_factorial * iEND DO

Problem: Write a complete Fortran program for the factorial function.

Input: n ( n > = 0 )

N ! = N × (N-1) × (N-2) … × 3 × 2 × 1, N > 0.

0 ! = 1

Output: n!

PROGRAM factorialIMPLICIT NONEINTEGER :: i, n, n_fact

WRITE(*,*) ’Enter an integer n ( > = 0 ):’READ(*,*) nn_fact = 1IF ( n > 0 ) THEN DO i = 1, n n_fact = n_fact * i END DOEND IF

WRITE(*,*) n, ‘! = ‘, n_factEND PROGRAM

Fig . 4-7

.TRUE. .FALSE.n < 2

READ n

sum_x = sum_x + xsum_x2 = sum_x2+x2

Start

1

1

Calculate x_ave, s

Stop

WRITE x_ave, s, n

Initial values:sum_x = 0sum_x2 = 0

Example 4-4 Statistical Analysis: (modified)

WRITE‘At least 2 values!’

i=1

i=i+1i n≦ ?

READ x

.FALSE. .TRUE.

Fig . 4-8PROGRAM stats_3IMPLICIT NONEINTEGER :: i, nREAL :: x, x_ave, s , sum_x = 0., sum_x2 = 0.

WRITE(*,*) ‘Enter the number of points n:’READ(*,*) nIF ( n < 2 ) THEN WRITE(*,*) ‘ At least 2 values!’ELSE DO i = 1, n WRITE(*,*) ‘Enter the value x:’ READ (*,*) x sum_x = sum_x + x sum_x2 = sum_x2 + x**2 END DO

x_ave = sum_x / ns = sqrt (( n*sum_x2 – sum_x**2) / (n*(n-1)))WRITE(*,*) ‘n = ‘ , n, ‘ x_ave = ‘, x_ave, & ‘ s = ‘, sEND IFEND PROGRAM

Test:

Input: 3 3. 4. 5.

Output: n = 3 x_ave = 4.00000 s = 1.00000

Sec. 4.1.4 The CYCLE and EXIT Statements

E.g., PROGRAM test_cycleINTEGER :: iDO i = 1, 5 IF ( i == 3 ) CYCLE WRITE(*,*) iEND DOWRITE(*,*) ‘End of loop!’END PROGRAM

Output: 1 2 4 5 End of loop!

PROGRAM test_exitINTEGER :: IDO i = 1, 5 IF ( i == 3 ) EXIT WRITE(*,*) iEND DOWRITE(*,*) ‘End of loop!’END PROGRAM

Output: 1 2 End of loop!

[name:] DO . . . IF (logical_expr) CYCLE [name] . . . IF (logical_expr) EXIT [name] . . . END DO [name]

Sec. 4.1.5 Named Loops

While loop:

optional

[name:] DO index = istart, iend, incr . . . IF (logical_expr) CYCLE [name] . . . END DO [name]

Counting loop:

optional

Sec. 4.1.6 Nesting Loops and Block IF Construct

e.g.,PROGRAM nested_loopsINTEGER :: i, j, productDO i = 1, 3 DO j = 1, 3 product = i * j WRITE(*,*) i, ‘*’, j, ‘=‘, product END DOEND DOEND PROGRAM

Output:

1 * 1 = 11 * 2 = 21 * 3 = 32 * 1 = 22 * 2 = 42 * 3 = 63 * 1 = 33 * 2 = 63 * 3 = 9

PROGRAM test_cycle_1INTEGER :: i, j, productDO i = 1, 3 DO j = 1, 3 IF ( j == 2 ) CYCLE product = i * j WRITE(*,*) i, ‘*’, j, ‘=‘, product END DOEND DOEND PROGRAM

Output: 1 * 1 = 11 * 3 = 32 * 1 = 22 * 3 = 63 * 1 = 33 * 3 = 9

PROGRAM test_cycle_2INTEGER :: i, j, productouter: DO i = 1, 3 inner: DO j = 1, 3 IF ( j == 2 ) CYCLE outer product = i * j WRITE(*,*) i, ‘*’, j, ‘=‘, product END DO innerEND DO outerEND PROGRAM

Output:1 * 1 = 12 * 1 = 23 * 1 = 3

Nesting loops within IF constructs and vice versa:

e.g.,outer: IF ( a < b ) THEN . . . inner: DO i = 1, 3 . . . ELSE . . . END DO innerEND IF outer

illegal!

outer: IF ( a < b ) THEN . . . inner: DO i = 1, 3 . . . END DO inner . . . ELSE . . . END IF outer

legal:

Sec. 4.2 Character Assignments and Character Manipulations

Sec. 4.2.1 Character Assignment

character variables name = character expression

Character operators:1. substring specifications2. concatenation

Sec. 4.2.2 Substring SpecificationsE.g., str1 = ‘123456’ str1(2:4) contains the string ‘234’.

Example 4-5 PROGRAM substring CHARACTER (len=8) :: a,b,c a = ‘ABCDEFGHIJ’ b = ‘12345678’ c = a(5:7) b(7:8) = a(2:6) WRITE(*,*) 'a=', a WRITE(*,*) 'b=', b WRITE(*,*) 'c=', c END PROGRAM

a = ? b = ? c = ? (Try it out!)

Solu: a = ‘ABCDEFGH’ ( len = 8)∵

∵ b(7:8) = a(2:6) = ‘BC’

b = ‘123456BC’

c = a(5:7) = ‘EFG’ = ‘EFG□□□□□‘ ( len = 8)∵

(Cont.)

Sec. 4.2.3 The Concatenation Operator

E.g., PROGRAM concate CHARACTER (len=10) :: a CHARACTER (len=8) :: b,c a = ‘ABCDEFGHIJ’ b = ‘12345678’ c = a(1:3) // b(4:5) // a(6:8) WRITE(*,*)’c=‘,c END PROGRAM

c = ? (Try it out: c =‘ABC45FGH’)

Sec. 4.2.4 Relational Operators with Character Data

E.g., ‘123’ = = ‘123’ (true)

‘123’ = = ‘1234’ (false)

‘A’ < ‘B’ (true, ASCII, A 65, B 66)∵

‘a’ < ‘A’ (false, a 97)∵

‘AAAAAB’ > ‘AAAAAA’ (true)

‘AB’ > ‘AAAA’ (true)

‘AAAAA’ > ‘AAAA’ (true)

Ch. 5 Basic I/O Concepts

Sec. 5.1 FORMATS and FORMETED WRITE STATEMENTS

READ (*,*) Not always convenient!

WRITE (*,*) Not always pretty!

e.g,. PROGRAM free_formatINTEGER :: i = 21REAL :: result = 3.141593WRITE(*,100) i, result100 FORMAT (‘□The□result□for□iteration□’, & I3, ‘□is□’, F7.3)END PROGRAM

Output: □The□result□for□iteration□□21□is□□□3.142

∵ I3 ∵ F7.3

The following three WRITE statements are equivalent:

• WRITE (*, 100) i, result 100 FORMAT (I6, F10.2)

• CHARACTER ( len=20 ) :: string string = ‘(I6, F10.2)’ WRITE(*,string) i, result

• WRITE(*, ‘(I6,F10.2)’) i, result

Output: □□□□21□□□□□□3.14

I6 F10.2

PROGRAM formatINTEGER :: i = 21REAL :: result = 3.141593CHARACTER ( len=20 ) :: string

WRITE (*, 100) i, result100 FORMAT (I6, F10.2)

string = '(I6, F10.2)'WRITE(*,string) i, result

WRITE(*, '(I6,F10.2)') i, result

END PROGRAM

Output: □□□□21□□□□□□3.14

Sec. 5.2 Output Devices

Line printers, laser printers, and terminals.

Sec. 5.3 Format Descriptors

Table 5-2 (Symbols used with format descriptors)

Symbol meaning

c column number d # of digits to the right of the decimal point m min. # of digit r repeat count w field width

Sec. 5.3.1 Integer Output – The I Descriptor

rIw or rIw.m

e.g., INTEGER :: index = -12, junk = 4, number = -12345 WRITE(*,200) index, index+12, junk, number WRITE(*,210) index, index+12, junk, number WRITE(*,220) index, index+12, junk, number 200 FORMAT ( 2I5, I6, I10) 210 FORMAT (2I5.0, I6, I10.8) 220 FORMAT (2I5.3, I6, I5)

Output: □□-12□□□□0□□□□□4□□□□-12345 □□-12□□□□□□□□□□4□-00012345 □-012□□000□□□□4*****

(Not in scale!)

I5 I5 I6 I10

PROGRAM iformatIMPLICIT NONEINTEGER :: index = -12, junk = 4, number = -12345

WRITE(*,200) index, index+12, junk, numberWRITE(*,210) index, index+12, junk, numberWRITE(*,220) index, index+12, junk, number200 FORMAT ( 2I5, I6, I10)210 FORMAT (2I5.0, I6, I10.8)220FORMAT (2I5.3, I6, I5)

END PROGRAM

Output: -12 0 4 -12345 -12 4 -00012345 -012 000 4*****

(Not in scale!)

Sec. 5.3.2 Real Output – The F Descriptor

rFw.d

e.g., REAL :: a = -12.3, b = .123, c = 123.456 WRITE(*,200) a, b, c WRITE(*,210) a, b, c 200 FORMAT (2F6.3, F8.3) 210 FORMAT (3F10.2)

Output: ******□0.123□123.456 □□□□-12.30□□□□□□0.12□□□□123.46

(Not in scale!)

F6.3 F6.3 F8.3

F10.2 F10.2F10.2

PROGRAM rformatIMPLICIT NONEREAL :: a = -12.3, b = .123, c = 123.456

WRITE(*,200) a, b, cWRITE(*,210) a, b, c200 FORMAT (2F6.3, F8.3)210 FORMAT (3F10.2)

END PROGRAM

Output: ****** 0.123 123.456 -12.30 0.12 123.46

(Not in scale!)

Sec. 5.3.3 Real Output – The E Descriptor

(Expomential notation)Scientific notation: 6.02 × 1023

Exponential notation: 0.602 × 1024(E Descriptor)

0.602 E+24

rFw.d ( w d + ≧ 7 )

e.g., REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10, d = -77.7E10WRITE (*,200) a, b, c, d200 FORMAT (2E14.4, E13.6, E11.6)

□□□□0.1235E+07□□□□0.1000E-02-0.777000E+12***********

E14.4 E11.6E13.6E14.4

Output:

( ‘E+**’ , ‘0.’, and ‘-’)∵

( 11 < 6 + 7)∵

PROGRAM routputIMPLICIT NONEREAL :: a = 1.2346E6, b = 0.001, c = -77.7E10, d = -77.7E10

WRITE (*, 200) a, b, c, d200 FORMAT (2E14.4, E13.6, E11.6)

END PROGRAM

Sec. 5.3.4 True Scientific Notation – The ES Descriptor

rESw.d ( w d + ≧ 7 )

e.g.,

REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10WRITE (*,200) a, b, c200 FORMAT (2ES14.4, ES12.6)

□□□□1.2346E+06□□□□1.0000E-03************

ES14.4 ES12.6 ES14.4

Output:

PROGRAM esformatIMPLICIT NONE

REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10WRITE (*, 200) a, b, c200 FORMAT (2ES14.4, ES12.6)

END PROGRAM

Sec. 5.3.5 Logical Output – The L Descriptor

rLw

e.g.,

LOGICAL :: output = .TRUE., debug = .FALSE.WRITE (*, 200) output, debug200 FORMAT (2L5)

□□□□T□□□□F

L5 L5

Output:

PROGRAM loutputIMPLICIT NONELOGICAL :: output = .TRUE., debug = .FALSE.

WRITE (*, 200) output, debug200 FORMAT (2L5)

END PROGRAM

Sec. 5.3.6 Character Output – The A Descriptor

rAw or rA

e.g.,

CHARACTER (len = 17) :: string = ‘This□is□a□string.’WRITE (*, 10) stringWRITE (*, 11) stringWRITE (*, 12) string10 FORMAT (A)11 FORMAT (A20)12 FORMAT (A6)

Output:

(i.e., the width is the same as the # of characters being displayed.)

17 characters

This□is□a□string.□□□This□is□a□string.This□i

PROGRAM aoutputIMPLICIT NONECHARACTER (len = 17) :: string = 'This is a string.‘

WRITE (*, 10) stringWRITE (*, 11) stringWRITE (*, 12) string10 FORMAT (A)11 FORMAT (A20)12 FORMAT (A6)

END PROGRAM

Sec. 5.3.7 Horizontal Position – The X and T Descriptors

X descriptor: nX

(the # of blanks to insert)

T descriptor:

Tc

(the column # to go to)

e.g,.

CHARACTER (len = 10) :: first_name = ‘James□’CHARACTER :: initial = ‘R’CHARACTER (len = 16) :: last_name = ‘Johnson□’CAHRACTER (len = 9) :: class = ‘COSC□2301’INTEGER :: grade = 92WRITE(*,100) first_name, initial, last_name, grade, class100 FORMAT (A10, 1X, A1, 1X, A10, 4X, I3, T51, A9)

Output:

James□□□□□□R□Johnson□□□□□□□□92 . . . COSC□2301

A10 A10 4X I3 A91X A1 1X

(51th column, T51)∵

orCHARACTER (len = 10) :: first_name = ‘James□’CHARACTER :: initial = ‘R’CHARACTER (len = 16) :: last_name = ‘Johnson□’CHARACTER (len = 9) :: class = ‘COSC□2301’INTEGER :: grade = 92WRITE(*,100) first_name, initial, last_name, class, grade100 FORMAT (A10, T13, A1, T15, A10, T51, A9, T29, I3)

Output:

James□□□□□□□R□Johnson□□□□□□□□92 . . . COSC□2301

A10 A10 I3 A9 A1

(13th column, T13)∵

(15th column, T15)∵ (29th column, T29)∵

(51th column, T51)∵

orCHARACTER (len = 10) :: first_name = ‘James□’CHARACTER :: initial = ‘R’CHARACTER (len = 16) :: last_name = ‘Johnson□’CAHRACTER (len = 9) :: class = ‘COSC□2301’INTEGER :: grade = 92WRITE(*,100) first_name, initial, last_name, class, grade100 FORMAT (A10, T13, A1, T15, A10, T17, A9, T29, I3)

Output:

James□□□□□□□R□JoCOSC□2301□□□□92

A10 A10 I3 A1

(13th column, T13)∵

(15th column, T15)∵

(29th column, T29)∵

(17th column, T17)∵

PROGRAM tformatCHARACTER (len = 10) :: first_name = 'James 'CHARACTER :: initial = 'R'CHARACTER (len = 16) :: last_name = 'Johnson 'CHARACTER (len = 9) :: class ='COSC 2301'INTEGER :: grade = 92

WRITE(*,100) first_name, initial, last_name, grade, classWRITE(*,110) first_name, initial, last_name, class, gradeWRITE(*,120) first_name, initial, last_name, class, grade100 FORMAT (A10, 1X, A1, 1X, A10, 4X, I3, T51, A9) 110 FORMAT (A10, T13, A1, T15, A10, T51, A9, T29, I3) 120 FORMAT (A10, T13, A1, T15, A10, T17, A9, T29, I3)

END PROGRAM

Sec. 5.3.8 Repeating Groups of Format Descriptors

E.g.,

320 FORMAT (1X, I6, I6, F10.2, F10.2, I6, F10.2, F10.2)321 FORMAT (1X, I6, 2(I6, 2F10.2))

320 FORMAT (1X, I6, F10.2, A, F10.2, A, I6, F10.2, A, F10.2, A)321 FORMAT (1X, 2(I6, 2(F10.2, A)))

Sec. 5.3.9 Changing Output Lines – The Slash ( / ) Descriptor e.g.,

WRITE (*, 100) index, time, depth, amplitude, phase100 FORMAT (T20, ‘Results for Test Number ‘, I3, ///, & 1X, ‘Time = ‘, F7.0/, & 1X, ‘Depth = ‘, F7.1, ‘ meters’, / , & 1X, ‘Amplitude = ‘, F8.2/, & 1X, ‘Phase = ‘, F7.1)

Output:

Results for Test Number . . .

Time = . . .Depth = . . . Amplitude = . . .Phase = . . .

(skip 2 lines)

Sec. 5.3.10 How Format Statements Are Used during WRITES

Example 4-1 Generating a Table of Information

Output:

Table of Square Roots, Squares, and Cubes

Number Square Root Square Cube====== ========== ====== ==== 1 1.000000 1 1 2 1.414214 4 8 . . . . . . . . . . . . 9 3.000000 81 729 10 3.162278 100 1000

PROGRAM tableIMPLICIT NONEINTEGER :: i, square, cubeREAL :: square_root

WRITE(*, 100)100 FORMAT(T4, ‘Table of Square Roots, Squares, and Cubes’/ )WRITE(*, 110)110 FORMAT(T4, ‘Number’, T13, ‘Square Root’, T29, ‘Square’, T39, ‘Cube’)WRITE(*, 120)120 FORMAT(T4, ‘======‘, T13, ‘===========‘, T29, & ‘======‘, T39, ‘====‘)DO i = 1, 10 square_root = SQRT(REAL(i)) square = i**2 cube = i**3 WRITE(*, 130) i, square_root, square, cube 130 FORMAT(T4, I4, T13, F10.6, T27, I6, T37, I6)END DOEND PROGRAM

Sec. 5.4 Formatted READ Statements

e.g., READ (*,100) increment100 FORMAT (6X, I6)

(skip the 1st six column)(col. 7~12: an integer)

Sec. 5.4.1 Integer Input – The I Descriptor

rIw

e.g.,READ(*, 100) a, b, c100 FORMAT(3I5)

Input:

□□□15□□15□□15□□

I5 I5 I5a = 15b = 15c = 15

PROGRAM iinputIMPLICIT NONEINTEGER :: a, b, c

READ(*, 100) a, b, c100 FORMAT(3I5)WRITE(*,*) 'a= ', aWRITE(*,*) 'b= ', bWRITE(*,*) 'c= ', c

END PROGRAM

Sec. 5.4.2 Real Input – The F Descriptor

rFw.d

e.g.,

READ (*, ‘(3F10.4)’ ) a, b, c

Input:

1.5□□□□□□□□0.15E+01□□□15.0E-01

F10.4 F10.4 F10.4

a = 1.5b = 1.5c = 1.5

PROGRAM rinputIMPLICIT NONEREAL :: a, b, c

READ (*, '(3F10.4)' ) a, b, cWRITE(*,*) 'a= ', aWRITE(*,*) 'b= ', bWRITE(*,*) 'c= ', c

END PROGRAM

If a number without a decimal point appears in the field, then a decimal point is assumed to be in the position specified by the d term of the format descriptor.

e.g.,READ (*, ‘(3F10.4)’ ) a, b, c

Input:

□□□□□□□□15□□□150□□□□□□15000□□□

F10.4 F10.4 F10.4

a = 0.0015b = 0.0150c = 1.5000

*The E and ES format descriptors are identical to the F descriptor.

Sec. 5.4.3 Logical Input – The L Descriptor

rLw

e.g.,READ (*, ‘(3L5)’ ) a, b, c

Input:

□□□□T□□□□F□□□□T

L5 L5 L5

a = Tb = Fc = T

(or T□□□□F□□□□T□□□□ )

PROGRAM linputIMPLICIT NONELOGICAL :: a, b, c

READ (*, '(3L5)' ) a, b, cWRITE(*,*) 'a= ', aWRITE(*,*) 'b= ', bWRITE(*,*) 'c= ', c

END PROGRAM

Sec. 5.4.4 Character Input – The A Descriptor

rA or rAw

e.g., CHARACTER (len=10) :: string_1, string_2CHARACTER (len=5) :: string_3CHARACTER (len=15) :: string_4, string_5READ (*, ‘(A)’ ) string_1READ (*, ‘(A10)’ ) string_2READ (*, ‘(A10)’ ) string_3READ (*, ‘(A10)’ ) string_4READ (*, ‘(A)’ ) string_5

Input:

ABCDEFGHIJKLMNOABCDEFGHIJKLMNOABCDEFGHIJKLMNOABCDEFGHIJKLMNOABCDEFGHIJKLMNO

String_1 = ‘ABCDEFGHIJ’String_2 = ‘ABCDEFGHIJ’String_3 = ‘FGHIJ’String_4 = ‘ABCDEFGHIJ □□□□□’String_5 = ‘ABCDEFGHIJKLMNO’

PROGRAM ainputIMPLICIT NONECHARACTER (len=10) :: string_1, string_2CHARACTER (len=5) :: string_3CHARACTER (len=15) :: string_4, string_5

READ (*, '(A)' ) string_1READ (*, '(A10)' ) string_2READ (*, '(A10)' ) string_3READ (*, '(A10)' ) string_4READ (*, '(A)' ) string_5WRITE(*,*)string_1WRITE(*,*)string_2WRITE(*,*)string_3WRITE(*,*)string_4WRITE(*,*)string_5

END PROGRAM

Sec. 5.4.5 Horizontal Positioning – The X and T Descriptor

e.g., CHARACTER (len=6) :: stringINTEGER :: iREAD (*, ‘(I6, T1, A6)’ ) i, string

Input: 123456

i = 123456string = ‘123456’

PROGRAM hpositionIMPLICIT NONECHARACTER (len=6) :: stringINTEGER :: i

READ (*, '(I6, T1, A6)' ) i, stringWRITE(*,'(I6)') iWRITE(*,'(A)') string

END PROGRAM

Sec. 5.4.6 Vertical Positioning – The Slash (/) Descriptor

e.g.,REAL :: a, b, c, dREAD (*, 300) a, b, c, d300 FORMAT (2F10.2, //, 2F10.2)

Input:

□□□□□□□1.0□□□□□□□2.0□□□□□□□3.0□□□□□□□4.0□□□□□□□5.0□□□□□□□6.0□□□□□□□7.0□□□□□□□8.0□□□□□□□9.0

a = 1.0b = 2.0c = 7.0d = 8.0

F10.2 F10.2 F10.2

PROGRAM vpositionIMPLICIT NONEREAL :: a, b, c, d

READ (*, 300) a, b, c, d300 FORMAT (2F10.2, //, 2F10.2)WRITE(*,*)'a= ',aWRITE(*,*)'b= ',bWRITE(*,*)'c= ',cWRITE(*,*)'d= ',d

END PROGRAM

Sec. 5.5 An Introduction to Files and File Processing

• i/o unit number:

e.g., READ (8, 100)

Typically, (vary from processor to processor)

READ (5,*) = READ (*,*)WRITE (6,*) = WRITE (*,*)

• I/O statement: (see Table 4-3)

OPEN, CLOSE, READ, WRITE, REWIND, and BACKSPACE.

Sec. 5.5.1 The OPEN Statement

OPEN ( open_list )

The five most important items from the list:

1. (the i/o unit number) UNIT = int_expr

2. (the file name of the file to be opened) FILE = char_expr

3. (the status of the file) STATUS = char_expr (‘OLD’, ‘NEW’, ‘REPLACE’, ‘SCRATCH’, or ‘UNKNOWN’)

4. (whether a file is to be opened for reading only, for writing only, or for both reading and writing) ACTION = char_expr (‘READ’, ‘WRITE’, or ‘READWRITE’)

5. (the status of the open operation) IOSTAT = int_var (If the OPEN statement is successful, a zero will be returned)

Example 1 (Opening a file for input)

INTEGER :: ierrorOPEN ( UNIT = 8, FILE = ‘INPUT.DAT’, & STATUS = ‘OLD’, ACTION = ‘READ’, & IOSTAT = ierror)

INTEGER :: ierrorOPEN ( UNIT = 25, FILE = ‘OUTPUT.DAT, & STATUS = ‘NEW’, ACTION = ‘WRITE’, & IOSTAT = ierror)

Example 2 (Opening a file for output)

Example 3 (Opening a scratch file)

OPEN ( UNIT = 12, STATUS = ‘SCRATCH’, & IOSTAT = ierror)

Sec. 5.5.2 The CLOSE Statement

CLOSE ( close_list )

e.g.,

CLOSE( UNIT = 8 )or

CLOSE( 8 )

Sec. 5.5.3 READS and WRITES to Disk Files

e.g.,OPEN ( UNIT = 8, FILE = ‘INPUT.DAT’, & STATUS = ‘OLD’, IOSTAT = ierror)READ (8,*) x, y, z

OPEN ( UNIT = 9, FILE = OUTPUT.DAT’, & STATUS = ‘REPLACE’, IOSTAT = ierror)READ (9,100) x, y, z100 FORMAT(‘ X= ‘, F10.2, ‘ Y = ‘, F10.2, ‘Z= ‘, F10.2)

Sec. 5.5.4 The IOSTAT = clause in the READ Statement

IOSTAT = int_var

e.g.,READ (8,*, IOSTAT = ierror)

If the READ statement is successful, ierror = 0.

If the READ statement is fail, ierror > 0 (format error) = -1 (end of file) = -2 (end of record)

Example 5-3 Reading Data from a File

1. State the problem. Write a program that can read in an unknown number of real values from a user-specified input data file and detect the end of the data file.

2. Define the input and output. input: (1) the filename of the data file (2) the data in that file output: the values in the data file

3. Describe the algorithm

4. Turn the algorithm into Fortran statements.

.TRUE.

.FALSE.

ierror1 = 0 ?

READ filename

Start1

nvals = nvals +1

Stop

WRITE nvals, value

Initial values:nvals = 0

Fig 5-9 (Flowchart)

WRITE ‘Error

opening file’

READ value

.FALSE.

.TRUE.

OPEN filename

1

2

ierror2 = 0 ?

ierror2 > 0 ?

WRITE ‘Error reading line’

WRITE ‘End of file’

.FALSE.

2

.TRUE.

PROGRAM readIMPLICIT NONECAHRACTER (len = 20) :: filenameINTEGER :: nvals = 0INTEGER :: ierror1, ierror2REAL :: value

WRITE(*,*) ‘Please enter input file name:’READ (*,*) filenameOPEN (UNIT = 3, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = ierror1)

openif: IF(ierror1 ==0) THEN readloop: DO READ(3,*), IOSTAT = ierror2) value IF (ierror2 /= 0) EXIT nvals = nvals + 1 WRITE(*, 1010) nvals, value 1010 FORMAT (‘Line ‘, I6, ‘:value=‘, F10.4) END DO readloop

readif: IF (ierror2 > 0) THEN WRITE(*, 1020) nvals + 1 1020 FORMAT (‘Error reading line’, I6) ELSE WRITE(*, 1030) nvals 1030 FORMAT (‘End of file. There are ‘, & I6, ‘ values in the file.’) END IF readifELSE openif WRITE(*, 1040) ierror1 1040 FORMAT (‘Error opening file: IOSTST=‘, I6)END IF openifCLOSE(3)END PROGRAM

Test the program:

(1) The valid input file READ1.TXT: (e.g., use Notepad)

-17.030.0011.012000.-0.012

Output: Please enter input file name:READ1.TXTLine 1: value = -17.0000Line 2: value = 30.0000 Line 3: value = 1.0000 Line 4: value = 12000.0000 Line 5: value = -0.0120 End of file. There are 5 values in the file.

(2) The invalid input file READ2.TXT:

-17.030.001ABCDEF12000.-0.012

Output:

Please enter input file name:READ2.TXTLine 1: value = -17.0000Line 2: value = 30.0000Error reading Line 3

(3) A file does not exist:

Output:Please enter input file name:JUNK.DATError opening file: IOSTAT = 128

(depends on machine)

Sec. 5.5.5 File Positioning

BACKSPACE ( UNIT = a unit # )

REWIND ( UNIT = a unit #)

and

Example 5-4 Using File-Positioning Commands:

(1) Write a program that accepts a series of nonnegative real values and stores them in a scratch file.

(2) Ask the user for a record number to display.

(2) Rewind the file, get that value, and display it.

PROGRAM scratchIMPLICIT NONEINTEGER, PARAMETER :: unit = 8REAL :: dataINTEGER :: icount = 0, irec, j

OPEN (UNIT = unit, STATUS = ‘SCRATCH’)WRITE(*, 100)100 FORMAT (1X, ‘Enter positive or zero input values.’, / , & 1X, ‘A negative value terminates input.’)DO WRITE(*, 110) icount + 1 110 FORMAT (1X, ‘Enter sample ‘, I4, ‘:’) READ (*,*) data IF ( data < 0. ) EXIT icount = icount + 1 WRITE(unit, 120) data 120 FORMAT (1X, ES16.6)END DO

WRITE(*, 130) icount130 FORMAT (1X, ‘Which record do you want to see ( 1 to’, I4, ‘)? ’)READ (*,*) irecIF ( ( irec >= 0) .AND. (irec <= icount) )THEN REWIND (UNIT = unit) DO j = 1, irec READ( unit, *) data END DO WRITE(*, 140) irec, data 140 FORMAT (1X, ‘ The value of record ‘, I4, ‘is’, ES14.5)ELSE WRITE(*, 150) irec 150 FORMAT (1X, ‘ Illegal record number entered: ‘, I8)END IFEND PROGRAM

Output:Enter positive or zero input values.A negative input value terminates input.Enter sample 1:234.Enter sample 2:12.34Enter sample 3:0.Enter sample 4:16.Enter sample 5:11.235Enter sample 6:2.Enter sample 7:-1.Which recore do you want to see ( 1 to 6)?5The value of record 5 is 1.12350E+01

Example 5-5 The linear fit problem:

Given a set of measurements (xi , yi), i = 1, . . . , N:

(x2, y2)

(x4, y4)

(x3 , y3)

(x1 , y1)

The best fit: y = mx + b

x

y

m = ?b = ?

The method of least squares:

m =

(Σxi yi ) - (Σxi ) y i=1

N

where

y = Σyii=1 i=1

N N

Σxi

N

b = y – m x

i=1

N

(Σxi2 ) - (Σxi ) x

N

i=1i=1

N

and x = N

PROGRAM least_squares_fitIMPLICIT NONEINTEGER, PARAMETER :: unit = 18CHARACTER (len = 24) :: filenameINTEGER :: ierror, n = 0REAL :: m, bREAL :: sum_x = 0., sum_x2 = 0., sum_xy = 0., sum_y = 0.REAL :: x, y, x_bar, y_bar

WRITE(*, 1000)1000 FORMAT (1X, ‘Enter the file name: ‘)READ (*, ‘(A)’) filenameOPEN (UNIT = unit, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = ierror)

errorcheck: IF (ierror > 0) THEN WRITE(*, 1020) filename 1020 FORMAT (1X, ‘ERROR: File ‘, A, ‘ does not exist! ’)ELSE

DO READ (unit, *, IOSTAT = ierror) x, y IF ( ierror /= 0 ) EXIT n = n + 1 sum_x = sum_x + x sum_y = sum_y + y sum_x2 = sum_x2 + x ** 2 sum_xy = sum_xy + x * y END DO x_bar = sum_x / n y_bar = sum_y / n m = (sum_xy – sum_x * y_bar) / (sum_x2-sum_x * x_bar) b = y_bar – m * x_bar WRITE(*, 1030) m, b, n 1030 FORMAT (1X, ‘ m = ‘, F12.3, / , & 1X, ‘ b = ‘, F12.3, / , & 1X, ‘ N = ‘, I12) CLOSE(18)END IF errorcheck END PROGRAM

Test the program:

(1) The input file INPUT.TXT:

1.1 1.12.2 2.23.3 3.34.4 4.45.5 5.56.6 6.67.7 7.7

Output:

m = 1.000 b = 0.000 N = 7

(2) The input file INPUT1.TXT:

1.1 1.012.2 2.303.3 3.054.4 4.245.5 5.756.6 6.487.7 7.84

Output:

m = 1.024 b = -0.12 N = 7

Ch. 6 Introduction to Arrays

Fig. 6-1

a(1)

a(2)

a(3)

a(4)

a(5)

. . .

. . .

array a

e.g.,DO i = 1, 100 a(i) = SQRT (a(i))END DO

Sec. 6.1 Declaring Arrays

• Type: real, integer, logical, or character

e.g.,

REAL, DIMENSION (16) :: voltage

voltage(1), voltage(2), . . . , voltage(16)

or

CHARACTER (len = 20), DIMENSION (50) :: last_name

last_name(1), . . . , last_name(50)

• Rank: The # of subscripts declared for a given array

e.g., REAL, DIMENSION (3, 6) :: sum

a rank-2 array

• Extent: The # of elements in a given dimension of an array

e.g., The extent of the 1st subscript of sum is 3.

The extent of the 2nd subscript of sum is 6.

• Size: the # of elements

• Shape: the combination of rank and extent in each dimension

e.g., The shape of sum = 3 6

e.g., The size of sum = 18

Array constructor:

e.g., INTEGER, DIMENDION (5) :: a = (/ 1, 2, 3, 4, 5 /)

Sec. 6.2 Using Array Elements in Fortran Statements

Sec. 6.2.1 Array Elements Are Just Ordinary Variables

e.g.,

INTEGER, DIMENDION (10) :: indexLOGICAL, DIMENSION (2) :: lvalREAL, DIMENSION (3) :: temp

Index(1) = 1Lval(2) = .TRUE.Temp(3) = REAL(index(1)) / 4.WRITE(*,*) ‘ index(1) = ‘, index(1)

Sec. 6.2.2 Initialization of Array Elements

e.g.,INTEGER, DIMENDION (10) :: jWRITE(*,*) ‘ j(1)=‘, j(1)

uninitialized array

?• Initialization arrays with assignment statements:

e.g.,REAL, DIMENDION (10) :: array1DO i = 1, 10 array1(i) = 0.0END DO

orREAL, DIMENDION (10) :: array1array1 = (/ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0. /)

• Initialization arrays in type declaration statements:

e.g.,

INTEGER, DIMENDION (5) :: array2 = (/ 1, 2, 3, 4, 5 /)

or

REAL, DIMENDION (100) :: array5 = 1.

or

INTEGER, DIMENDION (5) :: array2 = (/ ( i, i = 1, 5) /)

INTEGER, DIMENDION (25) :: array4 = (/ ((0, i = 1, 4), & 5*j, j = 1, 5) /)

0, 0, 0, 0, 5, 0, 0, 0, 0, 10, 0, 0, 0, 0, 15, . . .

or

array5(1) = 1., . . . , array5(100) = 1.

•Initialization arrays with Fortran READ statements:

Just like any other variables. (See Sec. 5.4: I/O of Array Elements)

Sec. 6.2.3 Changing the Subscript Range of an Array

e.g.,

REAL, DIMENSION(5) :: arr

arr(1), arr(2), arr(3), arr(4), arr(5)

but arr(0) = ?

e.g., c = Σ an = a0 + a1 + a2 + a3 + a4n=0

4

need a(0)!

Use

REAL, DIMENSION ( lower_bound : upper_bound ) :: arrar

e.g.,REAL, DIMENSION (-2:2) :: b

b(-2), b(-1), b(0), b(1), b(2)

orREAL, DIMENSION (5:9) :: c

c(5), c(6), c(7), c(8), c(9)

(5 elements)

(5 elements)

Example (Fig. 6-4)

i i2

-5 25-4 16… …+4 16+5 25

PROGRAM squares_2IMPLICIT NONEINTEGER :: IINTEGER, DIMENSION(-5:5) :: number, square

DO i = -5, 5 number(i) = I square(i) = number(i)**2 WRITE(*, 100) number(i), square(i) 100 FORMAT (1X, ‘Number = ‘, I6, ‘ Square= ‘, I6)END DOEND PROGRAM

Sec. 6.2.4 Out-of-bound Array Subscripts

e.g.,REAL, DIMENSION(5) :: a

a(1), a(2), a(3), a(4), a(5)

but if use a(6), out of bound!

Sec. 6.2.5 The Use of Named Constants with Array Declarations

e.g.,INTEGER, PARAMETER :: isize = 1000REAL, DIMENSION (isize) :: array1REAL, DIMENSION (isize) :: array2REAL, DIMENSION (2*isize) :: array3

PROGRAM extremesIMPLICIT NONEINTEGER, PARAMETER :: max_size = 10INTEGER, DIMENSION (max_size) :: inputINTEGER :: ilarge, ismall, j, nvals, tempWRITE(*,*) ' Enter number of values in data set:'READ(*,*) nvalssize: IF (nvals <= max_size) THEN in: DO j = 1, nvals WRITE(*, 100) ' Enter value ', j 100 FORMAT (' ', A, I3, ':' ) READ(*,*) input(j) END DO in temp = input(1) ilarge = 1 large: DO j = 2, nvals IF (input(j) > temp) THEN temp = input(j) ilarge = j END IF END DO large

Example 6-1 (Finding the largest and smallest values in a data set)

temp = input(1) ismall = 1 small: DO j = 2, nvals IF (input(j) < temp) THEN temp = input(j) ismall = j END IF END DO small WRITE(*, 110) 110 FORMAT(1X, 'The values are:') out: DO j = 1, nvals IF (j == ilarge) THEN WRITE(*, '(1X, I6, 2X, A)') input(j), 'LARGEST' ELSE IF (j == ismall) THEN WRITE(*, '(1X, I6, 2X, A)') input(j), 'SMALLEST' ELSE WRITE(*, '(1X, I6)') input(j) END IF END DO outELSE size WRITE(*, 120) nvals, max_size 120 FORMAT(1X, ' Too many input values: ', I6, '>', I6)END IF sizeEND PROGRAM

Test:

Enter number of values in data set:6Enter value 1:-6Enter value 2:5Enter value 3:-11Enter value 4:16Enter value 5:9Enter value 6:0

The values are: -6 5 -11 SMALLEST 16 LARGEST 9 0

Output

Sec. 6.3 Using Whole Arrays and Array Subsets in Fortran Statements

Sec. 6.3.1 Whole Array Operations

e.g.,

1.

2.

3.

4.

a(1)

a(4)

a(3)

a(2)

a

+

b(1)

b(2)

b(3)

b(4)

5.

6.

7.

8.

b

=

c

12.

10.

8.

6.

Fig. 6-9

PROGRAM add_arraysIMPLICIT NONEINTEGER :: IREAL, DIMENSION(4) :: a = (/ 1., 2., 3., 4. /)REAL, DIMENSION(4) :: b = (/ 5., 6., 7., 8. /)REAL, DIMENSION(4) :: c, d

DO i = 1,4 c(i) = a(i) + b(i)END DOd = a + bWRITE(*, 100) ‘c’, cWRITE(*, 100) ‘d’, d100 FORMAT (1X, A, ‘ =‘, 5(F6.1, 1X))END PROGRAM

If arrays a and b have the same shape,

Conformable!

e.g.,REAL, DIMENSION(1:4) :: a = (/ 1., 2., 3., 4. /)REAL, DIMENSION(5:8) :: b = (/ 5., 6., 7., 8. /)REAL, DIMENSION(101:104) :: cc = a + b

REAL, DIMENSION(4) :: a = (/ 1., 2., 3., 4. /)REAL :: b = 10REAL, DIMENSION(4) :: cc = a * b

or

c = (/ 10., 20., 30., 40. /)

(Not matrix multiplication)

Elemental intrinsic functions: (see App. B for a complete list)

ABS, SIN, COS, EXP, and LOG.

e.g.,REAL, DIMENSION(4) :: x = (/ 0., 3.14, 1., 2. /), yINTEGER :: iDO i = 1, 4 y(i) = SIN(x(i))END DO

or use y = SIN(x)

REAL, DIMENSION(4) :: a = (/ -1., 2., -3., 4. /), yy = ABS(a)

or

y = (/ 1., 2., 3., 4. /)

Sec. 6.3.2 Arrays Subsets

Array section: A subset of an array.

• Subscript triplet:

subscript_1 : subscript_2 : stride

e.g.,

INTEGER, DIMENSION(10) :: a = (/ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 /)

array(1:10:2) = [1, 3, 5, 7, 9]

Alternative forms: subscript_1 : subscript_2 subscript_1 : : subscript_2

stride = 1to the last subscriptto the 1st subscript

Example 6-2

INTEGER :: i = 3, j = 7REAL, DIMENSION(10) :: a = (/ 1., -2., 3., -4., 5, -6., 7., -8., & 9., -10. /)(a) a(:) = [1., -2., 3., -4., 5, -6., 7., -8., 9., -10.](b) a(i:j) = a(3:7:1) = [3., -4., 5., -6., 7.](c) a(i:j:i) = a(3:7:3) = [3., -6.](d) a(i:j:j) = a(3:7:7) = [3.](e) a(i:) = a(3:10:1) = [3., -4., 5., -6., 7., -8., 9., -10.](f) a(:j) = a(1:7:1) = [1., -2., 3., -4., 5., -6., 7.](g) a(::i) = a(1:10:3) = [1., -4., 7., -10.]

• Vector subscript:

INTEGER, DIMENSION(5) :: vec = (/ 1, 6, 4, 1, 9 /)REAL, DIMENSION(10) :: a = (/ 1., -2., -3., -4., 5, -6., 7., -8., & 9., -10. /)

a(vec) = [1., -6., -4., 1., 9.]

a(1) a(1) a(9)a(4)a(6)

e.g.,

*Vector subscript cannot be used on the left side of an assignment statement.

e.g., INTEGER, DIMENSION(3) :: vec = (/ 1, 2, 1 /)REAL, DIMENSION(3) :: a = (/ 10., 20., 30. /)REAL, DIMENSION(2) :: bb(vec) = a (Incorrect!)

Sec. 6.4 Input and Output

Sec. 6.4.1 Input and Output of Array Elements

e.g., WRITE(*, 100) a(1), a(2), a(3), a(4), a(5)100 FORMAT (1X, ‘a=‘, 5F10.2)

Just like any other variables.

Sec. 6.4.2 The Implied DO LOOP

e.g.,

WRITE(*, 100) (a(i), I = 1, 5)100 FORMAT (1X, ‘a=‘, 5F10.2)

Sec. 6.4.3 Input and Output of Whole Arrays and Array Sections

Fig. 6-11 (array I/O)

PROGRAM array_ioIMPLICIT NONEREAL, DIMENSION(5) :: a = (/ 1., 2., 3., 20., 10. /)INTEGER, DIMENSION(4) :: vec = (/ 4, 3, 4, 5 /)WRITE(*, 100) a100 FORMAT (2X, 5F8.3)WRITE(*, 100) a(2: :2)WRITE(*, 100) a(vec)END PROGRAM

(Output) 1.000 2.000 3.000 20.000 10.000 2.000 20.00020.000 3.000 20.000 10.000

Sec. 6.5 Examples

Example 6-3 Sorting Data

Ascending order (the lowest to the highest)

Descending order (the highest to the lowest)

or

e.g.,

(10, 3, 6, 4, 9)(sorting)

(3, 4, 6, 9, 10)

Fig. 6-12 (selection sort)

10

9

4

6

3

(swap)3

10

6

4

9

(swap)3

4

6

10

9

(no swap)

3

4

6

10

9

(swap)

3

4

6

10

9

Steps:

1. Get the input filename2. Open the input file3. Read the input data into an array4. Sort the data in ascending order5. Write the sorted data

Fig. 6-15PROGRAM sort1IMPLICIT NONEINTEGER, PARAMETER :: max_size = 10REAL, DIMENSION (max_size) :: aCHARACTER (len = 20) :: filenameINTEGER :: i, iptr, j, statusINTEGER :: nvals = 0REAL :: tempWRITE(*, 1000)1000 FORMAT (1X, ‘ Enter the file name’)READ(*, ‘(A20)’) filenameOPEN (UNIT = 9, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = status)fileopen: IF(status == 0) THEN DO READ (9, *, IOSTAT = status) temp IF (status /= 0) EXIT nvals = nvals + 1 a(nvals) = temp END DO

outer: DO i = 1, nvals – 1 iptr = i inner: DO j = i + 1, nvals minval: IF (a(j) < a(iptr)) THEN iptr = j END IF minval END DO inner ! swap a(iptr) with a(i) if i /= iptr swap: IF ( i /= iptr ) THEN temp = a(i) a(i) = a(iptr) a(iptr) = temp END IF swap END DO outer WRITE(*, ‘(A)’) ‘ The sorted data are:’ WRITE(*, 1040) ( a(i), i = 1, nvals) 1040 FORMAT (4X, F10.4)ELSE fileopenWRITE(*, 1050)status1050 FORMAT (1X, ‘File open failed: ’, I6)END IF fileopenEND PROGRAM

Test:

INPUT2.TXT

13.312.-3.00.4.06.64.-6.

output

Enter the file nameINPUT2.TXTThe sorted data are: -6.0000 -3.0000 0.0000 4.0000 4.0000 6.600012.000013.3000

(Sec. 6.6 Two-Dimensional Features of Arrays)

• 1-dim. array: rank-1 array or vector• 2-dim. array: rank-2 array or matrix

Fig. 6-17

a(1)

a(4)

a(2)

a(3)

row 1

row 3

row 2

row 4

a(irow)

(a) 1-dim array

b(1,1) b(1,2)

b(2,1) b(2,2)

b(1,3)

b(2,3)

row 1

row 2

col 1 col 2 col 3

b(irow, icol))

(b) 2-dim array

(Sec. 6.6.1 Declaring Rank-2 Arrays)

e.g.,REAL, DIMENSION(3,6) :: sumINTEGER, DIMENSION(0:100, 0:20) :: hist

(Sec. 6.6.2 Rank-2 Array Storage)

Fig. 6-19

a(1,1) a(1,2) a(1,3)

a(2,2)a(2,1) a(2,3)

a(irow, icol)

(Memory allocation)

a(1,1)

a(2,1)

a(1,2)

a(2,2)

a(1,3)

a(2,3)

column major order

(Sec. 6.6.3 Initializing Rank-2 Array)

1. Use assignment statements

e.g., 1

1

1

1

2

2

2

2

3

3

3

3

INTEGER, DIMENSION(4,3) :: istatDO i = 1, 4 DO j = 1, 3 istat(i, j) = j END DOEND DO

use

orDO j = 1, 3 istat(:, j) = jEND DO

cannot use

istat = (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /)

( Array constructors always produce rank-1 array!)∵

use

istat = RESHAPE ( (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /), (/4, 3/) )

(column major) (data to be reshaped)

(a new shape)

2. Use type declaration statements

INTEGER, DIMENSION(4, 3) :: istat (4,3) = & RESHAPE ( (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /), (/4, 3/) )

3. Use READ statements

INTEGER, DIMENSION(4,3) :: istatOPEN(7, FILE = ‘INITIAL.DAT’, STATUS = ‘OLD’, & ACTION = ‘READ’)READ (7, *) istat

(INITIAL.DAT: 1 1 1 1 2 2 2 2 3 3 3 3 )

or

READ (7, *) ((istat(i,j), j = 1, 3), i = 1, 4)

(INITIAL.DAT: 1 2 3 1 2 3 1 2 3 1 2 3 )

(i = 1) (i = 4)(i = 3)(i = 2)

(Sec. 6.6.4 Examples)

Examples 5-5

power =

20.0 40.3 42.0 20.419.8 40.1 41.5 26.920.1 40.0 41.3 38.420.0 39.5 41.1 42.020.0 39.9 39.8 12.219.9 40.0 41.0 6.0

use

REAL,DIMENSION(6,4) :: power…OPEN(9, FILE = ‘INPUT1’, STATUS = ‘OLD’, & ACTION = ‘READ’)READ (9, *) power

INPUT1: 20.0 19.8 20.1 20.0 20.0 19.9 40.3 40.1 40.0 39.5 39.9 40.0 42.0 41.5 41.3 41.1 39.8 41.0 20.4 26.9 38.4 42.0 12.2 6.0

OPEN(9, FILE = ‘INPUT2’, STATUS = ‘OLD’, & ACTION = ‘READ’)READ (9, *) ((power(i, j), j = 1, 4), i = 1, 6)

INPUT2:

or

20.0 40.3 42.0 20.419.8 40.1 41.5 26.920.1 40.0 41.3 38.420.0 39.5 41.1 42.020.0 39.9 39.8 12.219.9 40.0 41.0 6.0

(Sec. 6.6.5 Whole Array Operation and Array Subsets)

e.g.,

a =

1 2 3 4 5 6 7 8 9 1011 12 13 14 1516 17 18 19 2021 22 23 24 25

a(:, 1) =

1 6111621

a(1, :) = [ 1 2 3 4 5 ]

a(1:3, 1:5:2) =

1 3 5 6 8 1011 13 15

(Sec. 6.7 Multidimensional or Rank-n Array)

(up to 7)Fig. 5-22 ( A 2 × 2 × 2 array a)

a(1, 1, 1)

a(2, 1, 1)

a(1, 2, 1)

a(2, 2, 1)

a(1, 1, 2)

a(2, 1, 2)

a(1, 2, 2)

a(2, 2, 2)

(memory allocation)

…

…

(Sec. 6.8 Using Fortran Intrinsic Functions with Arrays)

(Sec. 6.8.1 Elemental Intrinsic Functions)

e.g.,

ABS, SIN, COS, TAN, EXP, LOG, LOG10, MOD, AND SQRT.

REAL, DIMENSION :: x = (/ 10., 3.14, 1., 2. /), yINTEGER :: iDO i = 1, 4 y(i) = sin(x(i))END DO

equiv.y = sin(x)

(Sec. 6.8.2 Inquiry Intrinsic Functions)

Table 6-1

LBOUND (ARRAY, DIM)SHAPE (SOURCE)SIZE(ARRAY, DIM)UBOUND (ARRAY, DIM)

(a particular dimension, e.g., 1 or 2)

Example 6-6 (Determining the Properties of an Array)

PROGRAM check_arrayREAL, DIMENSION(-5:5, 0:3) :: a = 0.WRITE(*, ‘(A, 7I6)’) ‘ The shape is: ‘, SHAPE(a)WRITE(*, ‘(A, I6)’) ‘ The size is: ‘, SIZE(a)WRITE(*, ‘(A, 7I6)’) ‘ The lower bounds are: ‘, LBOUND(a)WRITE(*, ‘(A, 7I6)’) ‘ The upper bounds are: ‘, UBOUND(a)END PROGRAM

Output:

11 5 (size(a, 1) = 11, size(a, 2) = 4)44-5 0 (LBOUND(a, 1) = -5, LBOUND(a, 2) = 0) 5 3 (UBOUND(a, 1) = 5, UBOUND(a, 2) = 3)

(Sec. 6.8.3 Transformational Intrinsic Functions)

Table 6-2

DOT_PRODUCT (VECTOR_A, VECTOR_B)MATMUL (MATRIX_A, MATRIX_B)RESHAPE (SOURCE, SHAPE)

Ch. 6 Introduction to Procedures

Sec. 7.1 Subroutines

The general form of a subroutine

SUBROUTINE subroutine_name (argument_list) . . . (Declaration section) . . . (Execution section) . . .RETURNEND SUBROUTINE [name]

The calling program uses a CALL statement to call a subroutine:

CALL subroutine_name (argument_list)

Fig. 7-1 (the hypotenuse of a right triangle)

SUBROUTINE calc_hypotenuse (side_1, side_2, hypotenuse)IMPLICIT NONEREAL, INTENT(IN) :: side_1, side_2REAL, INTENT(OUT) :: hypotenuseREAL :: temp

temp = side_1**2 + side_2**2hypotenuse = SQRT(temp)RETURNEND SUBROUTINE

Test : Write a test driven program.

Fig. 7-2

PROGRAM test_hypotenuseIMPLICIT NONEREAL :: s1, s2, hypot

WRITE(*,*) ‘Enter the length of side 1:’READ(*,*) s1WRITE(*,*) ‘Enter the length of side 2:’READ(*,*) s2

CALL calc_hypotenuse(s1, s2, hypot)WRITE(*, 1000) hypot1000 FORMAT (1X, ‘ The length of the hypotenuse is :’, F10.4)END PROGRAM

Fig. 7-3 PROGRAM sort1IMPLICIT NONEINTEGER, PARAMETER :: max_size = 10REAL, DIMENSION (max_size) :: aCHARACTER (len = 20) :: filenameINTEGER :: i, iptr, j, statusINTEGER :: nvals = 0REAL :: tempWRITE(*, 1000)1000 FORMAT (1X, ‘ Enter the file name’)READ(*, ‘(A20)’) filenameOPEN (UNIT = 9, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = status)fileopen: IF(status == 0) THEN DO READ (9, *, IOSTAT = status) temp IF (status /= 0) EXIT nvals = nvals + 1 a(nvals) = temp END DO

Sec. 7.1.1 Example Problem - Sorting

CALL sort(a, nvals)WRITE(*, ‘(A)’) ‘ The sorted data are:’ WRITE(*, 1040) ( a(i), i = 1, nvals) 1040 FORMAT (4X, F10.4)ELSE fileopenWRITE(*, 1050) status1050 FORMAT (1X, ‘File open failed: ’, I6)END IF fileopenEND PROGRAM

SUBROUTINE sort(arr, n)IMPLICIT NONEINTEGER, INTENT(IN) :: nREAL, DIMENSION(n), INTENT(INOUT) :: arrINTEGER :: i. iptr, jREAL :: tempouter: DO i = 1, n – 1 iptr = i inner: DO j = i + 1, n minval: IF (arr(j) < arr(iptr)) THEN iptr = j END IF minval END DO inner swap: IF ( i /= iptr ) THEN temp = arr(i) arr(i) = arr(iptr) arr(iptr) = temp END IF swap END DO outer END SUBROUTINE sort

Test:

INPUT2.TXT

13.312.-3.00.4.06.64.-6.

output

Enter the file nameINPUT2.TXTThe sorted data are: -6.0000 -3.0000 0.0000 4.0000 4.0000 6.600012.000013.3000

Sec. 7.1.2 The Intent Attribute

INTENT(IN), INTENT(OUT), INTENT(INOUT)

e.g.,

SUBROUTINE sub1(input, output)IMPLICIT NONEREAL, INTENT(IN) :: inputREAL, INTENT(OUT) :: output

output = 2. * inputinput = -1. ! This line is an errorEND SUBROUTINE

Sec. 7.1.3 Variable Passing in Fortran: The Pass-by-Reference Scheme

e.g.,

PROGRAM testREAL :: a, b(4)INTEGER :: next. . .CALL sub1(a, b, next). . .END PROGRAM test

SUBROUTINE sub1(x, y, i)REAL, INTENT(OUT) :: xREAL, INTENT(IN) :: y(4)INTEGER:: i. . .END SUBROUTINE sub1

Sec. 7.1.4 Passing Arrays to Subroutines

e.g.,

SUBROUTINE process (data1, data2, n, nvals)IMPLICIT NONEREAL, INTENT(IN), DIMENSION(n) :: data1REAL, INTENT(OUT), DIMENSION(n) :: data2

data2 = 3. * data1END SUBROUTINE process

Sec. 7.1.5 Passing Character Variables to Subroutines

e.g.,

PROGRAM test_sample_stringIMPLICIT NONECHARACTER (len=15) :: aCALL sample(a)END PROGRAM

SUBROUTINE sample (string)IMPLICIT NONECHARACTER (len=*), INTENT(IN) :: stringWRITE(*,’(1X, A, I3)’) ‘Length of variable = ‘, LEN(string)END SUBROUTINE

Sec. 7.1.6 Error Handling in Subroutines

Eg. 1, (Bad! If temp < 0, SQRT(temp) = ???)

SUBROUTINE process (a, b, result)IMPLICIT NONEREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultREAL :: temp

temp = a - bresult = SQRT(temp)END SUBROUTINE

Eg. 2, (Better! But still not good, STOP)∵

SUBROUTINE process (a, b, result)IMPLICIT NONEREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultREAL :: temp

temp = a – bIF ( temp >= 0.) THEN result = SQRT(temp)ELSE WRITE(*,*)’ Square root of negative value in sub. Process!’ STOPEND IFEND SUBROUTINE

Eg. 2, (Much better! error flag)∵

SUBROUTINE process (a, b, result, error)IMPLICIT NONEREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultINTEGER, INTENT(OUT) :: errorREAL :: temp

temp = a – bIF ( temp >= 0.) THEN result = SQRT(temp) error = 0ELSE result = 0 error = 1END IFEND SUBROUTINE

Example (Gauss-Jordan Elimination)

Linear eq.:

1 x1 + 1 x2 + 1 x3 = 1

2 x1 + 1 x2 + 1 x3 = 2

1 x1 + 3 x2 + 2 x3 = 4

(1)

(3)

(2)

or

1 1 1

2 1 1

1 3 2

x1

x2

x3

=

1

2

4

1 1 1

2 1 1

1 3 2

1

2

4

or

a1 x1 + 0 x2 + 0 x3 = b1

0 x1 + a2 x2 + 0 x3 = b2

0 x1 + 0 x2 + a3 x3 = b3

or

a1 0 0

0 a2 0

0 0 a3

x1

x2

x3

=

b1

b2

b3

.

.

.???

x1 = b1/a1,

x2 = b2/a2,

x3 = b3/a3.

Gauss-Jordan Elimination:

1 x1 + 1 x2 + 1 x3 = 1

2 x1 + 1 x2 + 1 x3 = 2

1 x1 + 3 x2 + 2 x3 = 4

(1)

(3)

(2)

1 1 1

0 -1 -1

0 2 1

1

0

3

(1) × -2 + (2) 0 x1 – x2 – x3 = 0 (4)

(1) × -1 + (3) 0 x1 + 2x2 + x3 = 3 (5)

(new row 2)

(new row 3)

∴ (1) (4) (5)

1 x1 ＋ 1 x2 ＋ 1 x3 = 1

0 x1 － 1 x2 － 1 x3 = 0

0 x1 ＋ 2 x2 ＋ 1 x3 = 3

(1)

(5)

(4)

1 0 0

0 -1 -1

0 0 1

1

0

3

(4) + (1) 1 x1 + 0 x2 + 0 x3 = 0 (6)

(4) × 2 + (5) 0 x1 + 0 x2 - 1 x3 = 3 (7)

(new row 2)

(new row 3)

∴ (6) (4) (7)

1 x1 ＋ 0 x2 ＋ 0 x3 = 1

0 x1 － 1 x2 － 1 x3 = 0

0 x1 ＋ 0 x2 － 1 x3 = 3

(6)

(7)

(4)

1 0 0

0 -1 0

0 0 -1

1

-3

3

(7) × -1 + (4) 0 x1 - 1 x2 + 0 x3 = 0 (8) (new row 2)

∴ (6) (7) (8)

x1 = -1,

-x2 = -3,

-x3 = 3.

x1 = -1, x2 = 3, x3 = -3.

Gauss-Jordan Elimination:

3 x1 – 6 x2 + 7 x3 = 3

9 x1 + 0 x2 – 5 x3 = 3

5 x1 – 8 x2 + 6 x3 = -4

(1)

(3)

(2)

9 0 -5

5 -8 6

3 -6 7

3

-4

3

9 x1 + 0 x2 – 5 x3 = 3

5 x1 – 8 x2 + 6 x3 = -4

3 x1 – 6 x2 + 7 x3 = 3

(1)

(3)

(2)

3

-51/9

2

(1) × (-5/9) + (2)

0 x1 – 8 x2 + (79/9) x3 = -51/9

(1) × (-3/9) + (3)

0 x1 – 6 x2 + (78/9) x3 = 2

(new row 2)

(new row 3)

9 x1 + 0 x2 – 5 x3 = 3

5 x1 – 8 x2 + 6 x3 = -4

3 x1 – 6 x2 + 7 x3 = 3

9 0 -5

0 -8 79/9

0 -6 78/9

3

-51/9

2row 2 × (-(-6) /(-8)) + row 3,

9 0 -5

0 -8 79/9

0 -6 78/9

9 0 -5

0 -8 79/9

0 0 75/36

3

-51/9

225/36

row 3 × (-(-5) /(75/36))+ row 1, 9 0 0

0 -8 79/9

0 0 75/36

18

-51/9

225/36

row 3 × (-(79/9) /(75/36))+ row 2,

9 0 0

0 -8 0

0 0 75/36

18

-32

225/36

x1 = 2,

x2 = 4,

x3 = 3.

9 0 0

0 -8 79/9

0 0 75/36

18

-51/9

225/36

Computer program:

Reorder the equations !

Maximum pivot technique

Avoids divided-by-zero errors.

Reduces round-off errors.

( Subroutine simul, [a] [x] = [b] )

SUBROUTINE simul (a, b, ndim, n, error)IMPLICIT NONEINTEGER, INTENT(IN) :: ndimREAL, INTENT(INOUT), DIMENSION(ndim,ndim) :: aREAL, INTENT(INOUT), DIMENSION(ndim) :: bINTEGER, INTENT(IN) :: nINTEGER, INTENT(OUT) :: errorREAL, PARAMETER :: epsilon = 1.0E-06REAL :: factor, tempINTEGER :: irow, ipeak, jrow, kcol

! Process n times to reorder the eqs.mainloop: DO irow = 1, n ! Find peak pivot for column irow in rows irow to n ipeak = irow

max_pivot: DO jrow = irow+1, n IF (ABS(a(jrow, irow)) > ABS(a(ipeak, irow))) THEN ipeak = jrow END IF END DO max_pivot ! Check for singular eqs.singular: IF ( ABS(a(ipeak, irow)) < epsilon)THEN error = 1 RETURN END IF singular! Otherwise, if ipeak /= irow, swap eqs irow and ipeak. swap_eqn : IF (ipeak /= irow) THEN DO kcol = 1, n temp = a(ipeak, kcol) a(ipeak, kcol) = a(irow, kcol) a(irow, kcol) = temp END DO

temp = b(ipeak) b(ipeak) = b(irow) b(irow) = temp END IF swap_eqn ! (Eq. irow) * [-a(jrow, irow)/a(irow, irow)] + (Eq. jrow) eliminate: DO jrow = 1, n IF (jrow /= irow) THEN factor = -a(jrow, irow) / a(irow, irow) DO kcol = 1, n a(jrow, kcol) = a(irow, kcol) * factor + a(jrow, kcol) END DO b(jrow) = b(irow) * factor + b(jrow) END IF END DO eliminateEND DO mainloop

divide: DO irow = 1, n b(irow) = b(irow) / a(irow, irow) a(irow, irow) = a(irow, irow) / a(irow, irow)END DO divideerror = 0END SUBROUTINE simul

(A test driven program)

PROGRAM test_simulIMPLICIT NONEINTEGER, PARAMETER :: max_size = 10INTEGER :: i, j, n, istat, errorREAL, DIMENSION(max_size, max_size) :: aREAL, DIMENSION (max_size) :: bCHARACTER(len=20) :: file_name

! Get the eqs.WRITE(*,1000)1000 FORMAT(‘Enter the filename containing the eqs:’)READ(*, ‘(A20)’) file_nameOPEN(UNIT=3, FILE=file_name, STATUS=‘OLD’, & ACTION=‘READ’, IOSTAT=istat)

file_open: IF (istat == 0) THEN READ(3, *) n size_ok: IF ( n <= max_size) THEN DO i = 1, n READ(3, *) (a(i, j), j = 1, n), b(i) END DO! Display coefficiants.WRITE(*, 1020)1020 FORMAT (/, 1X, ‘ Coeffs. Before call:’) DO i = 1, n WRITE(*, 1030) (a(i, j), j = 1, n), b(i) 1030 FORMAT (1X, 7F11.4) END DO! Solve eqs.CALL simul(a, b, max_size, n, error)

error_check: IF (error /= 0) THEN WRITE(*,1040) 1040 FORMAT (/1X, ‘Zero pivot encountered!’, & // 1X, ‘ No unique solu.’) ELSE error_check WRITE(*, 1050) 1050 FORMAT ( /, 1X, ‘ Coeffs. After call:’) DO i = 1, n WRITE(*, 1030) ( a(i, j), j = 1, n), b(i) END DO WRITE(*, 1060) 1060 FORMAT (/, 1X, ‘ The solus. are:’) DO i = 1, n WRITE(*, 1070) i, b(i) 1070 FORMAT (3X, ‘X(‘, I2, ‘)=‘, F16.6) END DO END IF error_checkEND IF size_ok

ELSE file_open WRITE(*, 1080) istat 1080 FORMAT(1X, ‘File open failed – status=‘, I6)END IF file_openEND PROGRAM

Test: LINPUT.TXT

31.0 1.0 1.0 1.02.0 1.0 1.0 2.01.0 3.0 2.0 4.0

x1 + x2 + x3 = 12 x1 + x2 + x3 = 2 x1 + 3x2 +2 x3 = 4

Output: x1 = 1 x2 = 3 x3 = -3

The SAVE Attribute and Statement

e.g.,

REAL, SAVE :: sums

SAVE :: var1, var2, …

or

or

SAVE (all local variables)

Any local variables declared with the SAVE attributewill be unchanged between calls to the procedure.

Example (Statiscal Analysis: Running Averages)

Average: x_ave =

Σ xii=1

N

N

Standard deviation:

S = N Σxi

2 – (i=1 i=1

N N

Σxi )2

N (N-1)

1/2

Input: x (i.e., xi , i = 1, 2, …, N) 0 ≧

Output: x_ave and S

e.g.,

xi N Σ xi Σxi2 xave S

3.0 1 3.0 9.0 3.00 0.02.0 2 5.0 13.0 2.50 0.707 3.0 3 8.0 22.0 2.67 0.5774.0 4 12.0 38.0 3.00 0.8162.8 5 14.8 45.84 2.96 0.713

SUBROUTINE running_average(x, x_ave, s, nvals, reset)! IF ‘reset’ is “.TRUE.”, clear running sums and exit.IMPLICIT NONEREAL, INTENT(IN) :: xREAL, INTENT(OUT) :: x_ave, sINTEGER, INTENT(OUT) :: nvalsLOGICAL, INTENT(IN) :: resetINTEGER, SAVE :: nREAL, SAVE :: sum_xREAL, SAVE :: sum_x2

calc_sums: IF (reset) THEN n=0; sum_x = 0. ; sum_x2 = 0. x_ave = 0. ; s = 0. ; nvals = 0ELSE n = n + 1

sum_x = sum_x + x sum_x2 = sum_x2 + x**2 x_ave = sum_x / n IF (n >= 2) then s = SQRT((n*sum_x2 – sum_x **2)/(n*(n-1))) ELSE s = 0. END IF nvals = nEND IF calc_sumsEND SUBROUTINE running_average

(Test driven program)

PROGRAM test_running_averageIMPLICIT NONEINTEGER :: istat, nvalsREAL :: x_ave, s, xCHARACTER(len=20) :: filename

! Clear the running sumsCALL running_average(0., x_ave, s, nvals, .TRUE.)WRITE(*,*)’ Enter the file name containing the data:’READ(*,’(A20)’) filenameOPEN(UNIT=21, FILE=filename, STATUS=‘OLD’, & ACTION=‘READ’, IOSTAT=istat)open ok: IF(istat == 0) THEN calc: DO READ(21, *, IOSTAT=istat) x IF (istat /= 0) EXIT

CALL running_average(x, x_ave, s, nvals, .FALSE.) WRITE(*,1020)’ Value = ‘, x, ‘ x_ave = ‘, x_ave, & ‘ Std_dev = ‘, s, ‘ N = ‘, nvals 1020 FORMAT(1X, 3(A, F10.4), A, I6) END DO calcELSE openok WRITE(*, 1030) istat 1030 FORMAT(1X, ‘File open failed-status = ‘, I6)END IF openokEND PROGRAM

Test: RUNNING.TXT

3.02.03.04.02.8

3.0 3.00 0.0 1 2.0 2.50 0.707 23.0 2.67 0.577 34.0 3.00 0.816 42.8 2.96 0.713 5

x x_ave S N

Output

Automatic Arrays

A local explicit-shape array with non-constant bounds.

e.g.,

SUBROUTINE sub1(x, y, n, m)IMPLICIT NONEINTEGER, INTENT(IN) :: n, mREAL, INTENT(IN), DIMENSION(n, m) :: xREAL, INTENT(OUT), DIMENSION(n, m) :: yREAL, DIMENSION(n, m) :: temp ! Auto. array

temp = 0.. . .END SUBROUTINE

( Auto. arrays are automatically destroyed when subroutine ends.)

Sec. 7.4 Sharing Data Using Modules

Programs Subroutines (or functions)

argument list

(exchange data)

Programs Subroutines (or functions)(share data)

module

Fig. 7-8 (a simple module)

MODULE testIMPLICIT NONESAVE INTEGER, PARAMETER :: num_vals = 5REAL, DIMENSION(num_vals) :: valuesEND MODULE test

(SAVE should always be included in any module that declares sharable data.)

To use the values in the module,

USE module_name

Fig. 7-9 (using a module to share data between a main program and a subroutine)PROGRAM test_moduleUSE testIMPLICIT NONEREAL, PARAMETER :: pi = 3.141592

values = pi * (/ 1., 2., 3., 4., 5. /)CALL sub1END PROGRAM

SUBROUTINE sub1USE testIMPLICIT NONEWRITE(*,*)valuesEND SUBROUTINE sub1

Output

3.14159 6.28318 9.42478 12.5664 15.7080

Sec. 7.3 Modules Procedures

e.g., MODULE my_subsIMPLICIT NONE. . . (declare shared data here)

CONTAINS SUBROUTINE sub1(a, b, c, x, error) IMPLICIT NONE REAL, DIMENSION(3), INTENT(IN) :: a REAL, INTENT(IN) :: b, c REAL, INTENT(OUT) :: x LOGICAL, INTENT(OUT) :: error . . . END SUBROUTINE sub1END MODULE my_subs

PROGRAM main_progUSE my_subsIMPLICIT NONE. . .CALL sub1(a, b, c, x, error). . .END PROGRAM

Sec. 7.3.1 Using Modules to Creat Explicit Interfaces

Why module procedure?

Explicit interface

(helps the compiler to catch errors)

Implicit interface: Assume that the programmer got the arguments right. (e.g., number, type, intent, …)

Fig. 7-12 (argument mismatch)MODULE my_subsIMPLICIT NONECONTAINS SUBROUTINE bad_argument(i) IMPLICIT NONE INTEGER, INTENT(IN) :: I WRITE(*,*) ‘ I=‘ ,i END SUBROUTINE END MODULE

PROGRAM bad_callUSE my_subsIMPLICIT NONEREAL :: x = 1.CALL bad_argument(x)END PROGRAM

The computer will catch the argument mismatch!

Assumed-shape Arrays

e.g., MODULE test_moduleCONTAINS SUBROUTINE process2(data1, data2) REAL, INTENT(IN), DIMENSION(:, :) :: data1 REAL, INTENT(IN), DIMENSION(:, :) :: data2 data2 = 3. * data1 END SUBROUTINE process2END MODULE test_module

( Assumed-shape arrays work only if a procedure has an explicit interface. However, the upper and lower bounds of each dimension cannot be determined.)

(The use of assumen-shape arrays)

MODULE test_moduleCONTAINS SUBROUTINE test_array(array) IMPLICIT NONE REAL, DIMENSION(:, :) :: array INTEGER :: i1, i2, j1, j2

i1 = LBOUND(array, 1) i2 = UBOUND(array, 1) j1 = LBOUND(array, 2) j2 = UBOUND(array, 2) WRITE(*, 100) i1, i2, j1, j2 100 FORMAT(1X, ‘ The bounds are: (‘, I2, ‘:’, I2,’,’, I2,’:’,I2,’)’) WRITE(*, 110) SHAPE(array) 110 FORMAT(1X, ‘ The shape is: ‘, 2I4) WRITE(*, 120) SIZE(array) 120 FORMAT(1X, ‘ The size is: ‘, I4) END SUBROUTINE test_arrayEND MODULE test_module

PROGRAM assumed_shapeUSE test_moduleIMPLICIT NONEREAL, DIMENSION(-5:5, -5:5) :: a = 0.REAL, DIMENSION(10, 2) :: b = 1.WRITE(*,*) ’ Calling test_array with array a:’CALL test_array(a)WRITE(*,*) ‘ Calling test_array with array b:’CALL test_array(b)END PROGRAM

Output:Calling test_array with array a:The bounds are: (1:11, 1:11)The shape is: 11 11The size is: 121Calling test_array with array b:The bounds are: (1:10, 1:2)The shape is: 10 2The size is: 20

Sec. 7.4 Fortran Functions

Intrinsic functions: e.g., SIN(x), LOG(x).

User-defined functions (or function subprograms)

The general form is

FUNCTION name ( argument_list) . . . (Declaration) . . . (Execution) . . . name = expression RETURNEND FUNCTION [name]

optional

Two equivalent forms:

INTEGER FUNCTION my_function(i, j)

FUNCTION my_function(i, j)INTEGER :: my_function

or

Fig. 7-13 (f(x) = ax2 + bx + c)

REAL FUNCTION quadf (x, a, b, c)IMPLICIT NONEREAL, INTENT (IN) :: x, a, b, c

quadf = a*x**2 + b*x + cEND FUNCTION

Fig. 7-14 (a test driven program)

PROGRAM test_quadfIMPLICIT NONEREAL :: quadfREAL :: a, b, c, x, temp

WRITE(*,*) ‘ Enter quadratic coeffs. a, b, and c:’READ(*,*) a, b, cWRITE(*,*) ‘ Enter x value:’READ(*,*) xTemp = quadf(x, a, b, c)WRITE(*,100) ‘ f(‘, x, ‘)=‘, temp100 FORMAT(A, F10.4, A, F12.4)END PROGRAM

Test: a = 1., b = 2., c=3.x = 2.

f (x) = 11.

If a function modifies the values in its argument list,

side effects. (Always declares all dummy arguments with the INTENT(IN) attribute.)

A function produces a single output value using its input arguments. If need more than one output value, should use a subroutine not a function.

Example 7-5 The Sinc Function

sinc(x) = sin(x)/x and sinc(0)=1.

See Fig. 7-15

Fig. 7-16 (sinc(x))

FUNCTION sinc(x)IMPLICIT NONEREAL, INTENT(IN) :: xREAL :: sincREAL, PARAMETER :: epsilon = 1.0E-30

IF(ABS(x) > epsilon) THEN sinc = sin(x) / xELSE sinc = 1.END IFEND FUNCTION sinc

Fig. 6-21 (a test driven program)

PROGRAM test_sincIMPLICIT NONEREAL :: xREAL :: sinc

WRITE(*,*) ‘ Enter x:’READ(*,*) xWRITE(*, 100) ‘ sinc(x) = ‘, sinc(x)100 FORMAT(1X, A, F8.5)END PROGRAM

Test: x sinc(x)

0. 1.000001.0E-29 1.000003.141593 0.000001.570796 0.63662

Sec. 7.5 Passing Procedures as Arguments to Other Procedures

e.g., PROGRAM testREAL, EXTERNAL :: fun_1, fun_2REAL :: x, y, output. . .CALL evaluate(fun_1, x, y, output)CALL evaluate(fun_2, x, y, output). . .END PROGRAMSUBROUTINES evaluate(fub, a, b, result)REAL, EXTERNAL :: funREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultResult = b*fun(a)END SUBROUTINE evaluate

(two user-defined funcs)

Sec. 7.5 .1 Passing User-Defined Functions as Arguments

Two equivalent forms:

REAL, EXTERNAL :: fun_1, fun_2

EXTERNAL fun_1, fun_2

or

EXAMPLE 7-6 (Passing Functions to Procedures in an Arguments List)

Σf(xi) i=1

N

Nave = , x1 = 0, xN = 1, N = 101

Δx =xN – x1

N - 1= 0.01

xi = x1 + (i -1) × Δx

Fig. 7-18

REAL FUNCTION ave_value (func, first_value, last_value, n)IMPLICIT NONEREAL, EXTERNAL :: funcREAL, INTENT(IN) :: first_value, last_valueINTEGER, INTENT(IN) :: nREAL :: delta, sumINTEGER :: I

Delta = (last_value – first_value) / (n-1)Sum = 0.DO I = 1, n sum = sum + func( first_value + (i-1) * delta)END DOAve_value = sum / nEND FUNCTION

Fig. 7-19 (Test driven program)

PROGRAM test_ave_valueIMPLICIT NONEREAL :: ave_valueREAL, EXTERNAL :: my_functionREAL :: aveAve = ave_value(my_function, 0., 1., 101)WRITE(*,1000) ‘ my-function’, ave1000 FORMAT (1X, ‘ The ave. value of ‘, A, & ‘ between 0. and 1. is ‘, F16.6, ‘.’)END PROGRAM

REAL FUNCTION my_function(x)IMPLICIT NONEREAL, INTENT(IN) :: xMy_function = 3. * xEND FUNCTION

Sec. 7.5 .2 Passing Subroutines as Arguments

Example 7-7 (Passing Subroutines to Procedures in an Argument List)

Fig 7-20

Subroutine subs_as_arguments(x, y, sub, result)IMPLICIT NONEEXTERNAL :: subREAL, INTENT(IN) :: x, yREAL, INTENT(OUT) :: result

CALL sub(x, y, result)END SUBROUTINE subs_as_arguments

Fig. 7-21 (Test driver program)

PROGRAM test_subs_as_argumentsIMPLICIT NONEEXTERNAL :: sum, prodREAL :: x, y, result

WRITE(*,*) ‘ Enter x:’READ(*,*) xWRITE(*,*) ‘ Enter y:’READ(*,*) y

CALL sub_as_arguments(x, y, prod, result)WRITE(*,*) ‘ The product is ‘, result

CALL sub_as_arguments(x, y, psum, result)WRITE(*,*) ‘ The sum is ‘, resultEND PROGRAM

SUBROUTINE prod(x, y, result)IMPLICIT NONEREAL, INTENT(IN) :: x, yREAL, INTENT(OUT) :: resultresult = x * yEND SUBTOUTINE prod

SUBROUTINE sum(x, y, result)IMPLICIT NONEREAL, INTENT(IN) :: x, yREAL, INTENT(OUT) :: resultresult = x + yEND SUBTOUTINE sum

Test: try x = 4 & y = 5

Ch. 8 Additional Data Types

Data types:Real data typeComplex data typeDerived data type

Sec. 8.1 Alternative KINDS of the REAL Data Type

REAL data type:

Single precision (32 bits, default): 6 ~ 7 significant digits, 10-38 ~ 1038 (range).

Double precision (64 bits): 15 ~ 16 significant digits, 10-308 ~ 10308 (range).

Sec. 8.1.1 Kinds of REAL Constants and Variables

Kind number:

e.g., REAL (KIND = 4) :: value_1REAL (KIND = 8), DIMENSION(20) :: arrayREAL (4) :: temp

A better approach:

INTEGER, PARAMETER :: single = 4INTEGER, PARAMETER :: double = 8REAL (KIND = single) :: value_1REAL (KIND = double), DIMENSION(20) :: arrayREAL (single) :: temp

Valid real constants:

34._4 34._double 3.0E0 3.0D0

(a single_precision const)

(a double_precision const)

(depends on machine)

Sec. 8.1.2 Determining the KIND of a Real Variable

Fig. 8-1

PROGRAM kindsIMPLICIT NONEWRITE(*, 100) KIND(0.0)WRITE(*, 101) KIND(0.0D0)100 FORMAT(‘The KIND for single precision is’, I2)101 FORMAT(‘The KIND for double precision is’, I2)END PROGRAM

Output:

The KIND for single precision is 1The KIND for double precision is 2

(depends on machine)

Sec. 8.1.3 Selecting Precision in a Process-Independent MannerUse

kind_number = SELECTED_REAL_KIND (p=precision, r=range)

e.g., kind_number = SELECTED_REAL_KIND (p = 6, r = 37)kind_number = SELECTED_REAL_KIND (p = 12)kind_number = SELECTED_REAL_KIND (r = 100)kind_number = SELECTED_REAL_KIND (13, 200)kind_number = SELECTED_REAL_KIND (13)kind_number = SELECTED_REAL_KIND (p = 17)

SELECTED_REAL_KIND(p, r)SELECTED_INT_KIND(r)KIND(x)PRECISION(x)RANGE(x)

Function

Table 8-1 ( KIND-related intrinsic functions)

Fig. 8-2 (Select desired kinds and get information about real values)

PROGRAM select_kindsIMPLICIT NONEINTEGER, PARAMETER :: sgl = SELECTED_REAL_KIND (p=6, r=37)INTEGER, PARAMETER :: dbl = SELECTED_REAL_KIND (p=13, r=200)REAL (kind = sgl) :: var1 = 0.REAL (kind = dbl) :: var2 = 0._dbl

WRITE(*, 100) ‘ Var1’, KIND(var1), PRECISION(var1), RANGE(var1)WRITE(*, 100) ‘ Var2’, KIND(var2), PRECISION(var2), RANGE(var2)100 FORMAT (1X, A, ‘: Kind = ‘, I2, ‘, Precision = ‘, I2, ‘, Range = ‘, I3)END PROGRAM

Output:

Var1: Kind = 1, Precision = 6, Range = 37Var2: Kind = 2, Precision = 15, Range = 307

Sec. 8.1.4 Mixed_Mode Arithmetic

e.g., 1/3 + 1/3 = 0.3333 … + 0.3333… = 0.6666 … (by hand)

By computer:

Expression Result

(1) 1.D0/3. + 1/3 3.333333333333333E-001(2) 1.D0/3. + 1./3. 6.666666333333333E-001(3) 1.D0/3. + 1./3.D0 6.666666666666666E-001

PROGRAM testREAL(2) :: aREAL(1) :: b

A = 1.0D-208B = 1.0E-37WRITE(*,*)’a = ‘, aWRITE(*,*)’b = ‘, bEND PROGRAM

Output:

a = 1.000000000000E-0208b = 1.000000E-37

Sec. 8.1.5 Double-Precision Intrinsic Functions

See Table B-1 (p. 501)

e.g., ABS, COS, SIN, EXP, LOG, . . .

COS(0.2) = 0.980067

COS(0.2d0) = 0.980066577841

Sec. 8.1.6 When to Use High-precision Real Values

Double-precision:

larger (twice) memory size and slower speed

reduces round-off error problems

Example 8-1 (Numerical Calculation of Derivatives)

d f(x)d x = limit

Δx 0

f(x+Δx)- f(x)Δx

In theory: The small Δx, the better the estimate of the derivative.

But, in practice: ???

e.g.,

f(x) = 1/x, df(x)/dx = -1/x2.

d f(x)

d x x = 0.15= - 44.44444444 . . .

Fig. 8-4 (The derivative of f(x) = 1/x at x = 0.15, single and double-precision)

PROGRAM diffIMPLICIT NONEINTEGER, PARAMETER :: single = SELECTED_REAL_KIND(p=6, r=37)INTEGER, PARAMETER :: double = SELECTED_REAL_KIND(p=13)INTEGER :: iREAL(KIND=double) :: ans, d_ans, d_error, d_fx, d_fxdx, d_dx, d_x = 0.15D0REAL(KIND=single) :: s_ans, s_error, s_fx, s_fxdx, s_dx, s_x = 0.15E0

WRITE(*,1)1 FORMAT(1X, ‘ DX TRUE ANS Sp ANS Dp ANS’, & ‘ Sp ERR DP ERR’)ans = -(1.D0/d_x**2)step_size: DO I = 1, 10 s_dx = 1.0 /10.0**i d_dx = 1.D0 / 10.D0 **I ! Calculate s-p ans. s_fxdx = 1. /(s_x + s_dx) s_fx = 1./(s_x) s_ans = (s_fxdx – s_fx) /s_dx

s_error = ((s_ans – ans)/ans)*100. ! Calculate d-p ans. d_fxdx = 1. /(d_x + d_dx) d_fx = 1./(d_x) d_ans = (d_fxdx – d_fx) /d_dx d_error = ((d_ans – ans)/ans)*100. WRITE(*, 100) d_dx, ans, s_ans, d_ans, s_error, d_error 100 FORMAT(1X, ES10.3, F12.7, F12.7, ES22.14, F9.3, F9.3) END DO step_sizeEND PROGRAM

Output: see Textbook (p. 370)!

Sec. 8.2 The Complex Data Type

c = a + i b = z θ,∠

a = z cosθ, b = z sin θ, θ= arctan (b/a).

e.g.,

c1 = a1 + i b1, c2 = a2 + i b2,

c1 ± c2 = (a1 ± a2) + i (b1± b2),

c1 × c2 = (a1a2 － b1b2) + i (a1b2 ± b1a2),

c1 (a1a2 ＋ b1b2) + i (b1a2 － a1b2)

c2 (a22

＋ b22 )

=

Sec. 8.2.1 Complex Constants and Variables

Complex constant:

(1., 0.) 1 + i 0

(0.7071, 0.7071) 0.7071 + i 0.7071

(0, － 1) － i

(1.01E6, 0.5E2) 1010000 + i 50

(1.12_dbl, 0.1_dbl) 1.12 + i 0.1

Complex variable:

COMPLEX (KIND = kind_num) :: var1, var2, . . .COMPLEX, DIMENSION (256) :: array

Sec. 8.2.2 Initializing Complex Variables

Eg. 1,COMPLEX, DIMENSION (256) :: array1array1 = (0., 0.)

Eg. 2,

Complex :: a1 = (3.141592, -3.141592)

Eg. 3,

COMPLEX :: a1READ(*, ‘(2F10.2)’) a1

COMPLEX :: a1READ(*, *) a1

or

INPUT: (no parentheses)e.g., 1.0 0.25

INPUT: (with parentheses)e.g., (1.0, 0.25)

Sec. 8.2.3 Using Complex Numbers with Relational Operators

Given c1 = a1 + i b1, c2 = a2 + i b2,

c1 == c2 (to see if equal)

c1 /= c2 (to see if not equal)

c1 c2 (cannot compare!)

<><=>=

|c1| |c2| (compare magnitude)

<><=>=

Sec. 8.2.4 Complex Intrinsic Functions

See App. B

1. Type conversion functions:

Given a and b,

COMPLX (a, b, kind) a + i b

Given c ( = a + i b),

REAL(c) a

AIMAG(c) b

2. Absolute function:

c = a + i b,

CABS(c) c = (a2 + b2)1/2

3. Math functions: (generic functions)

COS, SIN, EXP, ABS, . . .

e.g.,

PROGRAM compxlCOMPLEX :: a = (1.0, 0.25)write(*,*) cos(a)END PROGRAM

Output:(0.55727, -0.21256)

ax2 + bx + c = 0,

x = -b ± ( b2 – 4ac )1/2

2a

If b2 – 4ac = 0

b2 – 4ac > 0

b2 – 4ac < 0

two distinct real roots

two complex roots

a single repeated root

Example 8-3 The Quadratic Eq. (revisited)

PROGRAM roots_2IMPLICIT NONEREAL :: a, b, c, d, re, imCOMPLEX :: x1, x2

WRITE(*,*)'Enter the coeffs. a, b, and c:‘READ(*,*) a, b, cd = b**2 – 4.*a*cx1=(-b + SQRT(CMPLX(d,0.))) / (2. * a)x2=(-b – SQRT(CMPLX(d,0.))) / (2. * a)WRITE(*,*) ‘The roots are:‘WRITE(*,100) ’x1=‘, REAL(x1), ‘+ i’, AIMAG(x1)WRITE(*,100) ’x2=‘, REAL(x2), ‘+ i’, AIMAG(x2)100 FORMAT(A, F10.4, A, F10.4)END PROGRAM roots_2

Fig. 8-10

Test:

x2 + 5x + 6 = 0, x1,2 = -2, -3

x2 + 4x + 4 = 0, x1,2 = -2

x2 + 2x + 5 = 0, x1,2 = -1 ± i 2

Sec. 8.3 Derived Data Types

User-defined data types derived from intrinsic data types.

A convenient way to group together all the information about a particular item.

Derived data type: Array:

Components (names) Elements (numbers)

different types the same type

The form of a derived data type:

TYPE [::] type_name component definitions . . .END TYPR [type_name]

e.g.,

TYPE :: person CHARACTER(len=14) :: first_name CHARACTER :: middle_initial CHARACTER(len=14) :: last_name CHARACTER(len=14) :: phone INTEGER :: age CHARACTER :: sex CHARACTER(len=11) :: ssnEND TYPE person

(optional)

(optional)

Declare variables of the derived type person:

TYPE (person) :: john, janeTYPE(person), DIMENSION(100) :: people

(an array of 100 variables of type person)

Structure constructor:

e.g.,

e.g.,

john = person(‘John’, ‘R’, ‘Jones’, ‘323-6439’, 23, ‘M’, ‘123-45-6789’)jane = person(‘Jane’, ‘C’, ‘Bass’, ‘332-3060’, 17, ‘F’, ‘999-99-9999’)

A derived data type within another derived data type:

TYPE :: grade_info TYPE (person) :: student INTEGER :: num_quizzes REAL, DIMENSION(10) :: quiz_grades INTEGER :: num_exams REAL, DIMENSION(10) :: exam_grades INTEGER :: final_exam_grade REAL :: averageEND TYPETYPE(grade_info), DIMENSION(30) :: class

(an array class of 30 variables of type grade_info)

e.g.,

Sec. 8.3.1 Working with Derived Data Types

Component Selector:

e,g,.

john % age = 35

class(5) % final_exam_grade = 95

class(5) % student % age = 23

(variable of a derived data type)

(a component)

(5th student in the class)

(the age of the 5th student in the class)

Sec. 8.3.2 Input and Output of Derived Data Types

Fig. 8-11 (I/O of variables of derived data types)

PROGRAM test_ioIMPLICIT NONETYPE :: person CHARACTER (len = 14) :: first_name CHARACTER :: middle_initial CHARACTER (len = 14) :: last_name CHARACTER (len = 14) :: phone INTEGER :: age CHARACTER :: sex CHARACTER (len = 11) :: ssnEND TYPE personTYPE (person) :: johnjohn = person(‘John’, ‘R’, ‘Jones’, ‘323-6439’, 23, ‘M’, ‘123-45-6789’)WRITE(*,*) ‘ Free format:’, johnWRITE(*,1000) john1000 FORMAT(‘ Formatted I/O:’, /, 4(1X, A, /), 1X, I4, /, 1X, A, /, 1X, A)END PROGRAM

Sec. 8.3.3 Declaring Derived Data Types in Modules

Example 8-4 (Sorting derived data types by components)

Customer database:

John Q Public 123 Sesame Street Anywhere NY 10035James R Johnson Rt. 5 Box 207c West Monroe LA 71291. . .

Display the database in alphabetical order by last name, by city, or by zip code.

Fig. 8-12 (sort a customer database)

MODULE typesIMPLICIT NONETYPE :: personal_info CHARACTER(len=12) :: first CHARACTER(len=12) :: mi CHARACTER(len=12) :: last CHARACTER(len=26) :: street CHARACTER(len=12) :: city CHARACTER(len=2) :: state INTEGER :: zipEND TYPE personal_infoEND MODULE types

PROGRAM customer_databaseUSE typesIMPLICIT NONEINTEGER, PARAMETER :: max_size = 100LOGICAL, EXTERNAL :: lt_lastLOGICAL, EXTERNAL :: lt_cityLOGICAL, EXTERNAL :: lt_zipTYPE(personal_info), DIMENSION(max_size) :: customersLOGICAL :: exceed = .FALSE.CHARACTER (len=20) :: filenameINTEGER :: choice, i, nvals=0, statusTYPE(personal_info) :: temp

WRITE(*,*) ‘ Enter the file name:’READ(*,’(A20)’) filenameOPEN(UNIT=9, FILE=filename, STATUS=‘OLD’, IOSTAT=status) Fileopen: IF(status == 0) THEN

DO READ(9,1010, IOSTAT=status) temp 1010 FORMAT(A12,1X,A1,1X,A12,1X,A26,1X,A12,1X,A2,1X,I5) IF(status /= 0)EXIT nvals = nvals + 1 size: IF (nvals <= max_size) THEN customers(nvals) = temp ELSE exceed = .TRUE. END IF size END DO toobig: IF(exceed) THEN WRITE(*,1020) nvals, max_size 1020 FORMAT (‘ Max. array size exceeded:’, I6, ‘>’, I6)ELSEWRITE(*,1030)1030 FORMAT(1X, ‘Enter the way to sort database:’, /, 1X, & ‘ 1 - By last name’, /,1X, ‘ 2 - By city’, /, 1X, ‘ 3 - By zip code’)

READ(*,*) choice SELECT CASE (choice) CASE (1) CALL sort_database(customers, nvals, lt_last) CASE (2) CALL sort_database(customers, nvals, lt_city) CASE (3) CALL sort_database(customers, nvals, lt_zip) CASE DEFAULT WRITE(*,*)’ Invalid choice entered!’ END SELECT WRITE(*,’(A)’) ‘ The sorted database values are:’ WRITE(*, 1010)(customers(i), i=1, nvals) END IF toobigELSE fileopen WRITE(*,’(A, I6)’) ‘ File open error: IOSTAT=‘, statusEND IF fileopenEND PROGRAM

SUBROUTINE sort_database (array, n, lt_fun)USE typesIMPLICIT NONEINTEGER, INTENT(IN) :: nTYPE(personal_info), DIMENSION(n), INTENT(INOUT) :: arrayLOGICAL, EXTERNAL :: lt_funINTEGER :: i, iptr, jTYPE(personal_info) :: tempouter: DO I = 1, n-1 iptr = I inner: DO j = i+1, n minval: IF (lt_fun(array(j), array(iptr))) THEN iptr = j END IF minval END DO inner swap: IF( I /= iptr) THEN temp=array(i) array(i) = array(iptr) array(iptr) = temp END IF swapEND DO outerEND SUBROUTINE sort_database

LOGICAL FUNCTION lt_last(a,b)USE typesIMPLICIT NONETYPE(personal_info), INTENT(IN) :: a, blt_last = a%last < b%lastEND FUNCTION lt_last

LOGICAL FUNCTION lt_city(a,b)USE typesIMPLICIT NONETYPE(personal_info), INTENT(IN) :: a, blt_city = a%city < b%cityEND FUNCTION lt_city

LOGICAL FUNCTION lt_zip(a,b)USE typesIMPLICIT NONETYPE(personal_info), INTENT(IN) :: a, blt_zip = a%zip < b%zipEND FUNCTION lt_zip

Test:

DATABASE.TXT

John Q Public 123 Sesame Street Anywhere NY 10035James R Johnson Rt. 5 Box 207C West Monroe LA 71291Joseph P Ziskend P. O. Box 433 APO AP 96555Andrew D Jackson Jackson Square New Orleans LA 70003Jane X Doe 12 Lakeside Drive Glenview IL 60025Colin A Jeffries 11 Main Street Chicago IL 60003

Polar Coordinates: (extra)

c = a + i b = z θ,∠

z = (a2 + b2)1/2 , θ= arctan (b/a).a = z cosθ, b = z sin θ.

Given

p1 = z1 θ∠ 1, p2 = z2 θ∠ 2, θ1, θ2: in degrees.

p = p1 + p2 = z θ, z = ???, θ= ???.∠

Prob. Creat a derived data type called polar for z θ∠ ,

two components: magnitude z

angle θ

MODULE mathIMPLICIT NONEREAL, PARAMETER :: const = 57. 296 ! 1 rad=57.296 degreesTYPE :: polar REAL :: z ! magnitude REAL :: theta ! AngleEND TYPE polarEND MODULE math

PROGRAM test_polarUSE mathIMPLICIT NONETYPE(polar) :: p1, p2, pWRITE(*,*)’ Enter z1 and theta1 (in degrees):’READ(*,*) p1%z, p1%thetaWRITE(*,*)’ Enter z2 and theta2 (in degrees):’READ(*,*) p2%z, p2%thetaCALL add_polar(p1, p2, p)WRITE(*,*)’ z = ‘, p%z, ‘ theta = ‘, p%theta, ‘ degrees’END PROGRAM

SUBROUTINE add_polar(p1, p2, p)USE mathIMPLICIT NONETYPE(polar), INTENT(IN) :: p1, p2TYPE(polar), INTENT(OUT) :: pREAL :: a, ba = p1%z*cos(p1%theta/const) + p2%z*cos(p2%theta/const)b = p1%z*sin(p1%theta/const) + p2%z*sin(p2%theta/const)p%z = SQRT(a**2 + b**2)p%theta = ATAN2(b, a) * constRETURNEND SUBROUTINE

Test:

p1 = 3.0 30∠ 0, p2 = 4.0 60∠ 0,

Z = 6.766, θ= 47.190 .

Ch. 9 Advanced Features of Procedures and Modules

Sec. 9.1 Internal Procedures

Internal procedure

host program unit

Fig. 9-1 ( Sec(θ) )

PROGRAM test_secIMPLICIT NONEINTEGER, PARAMETER :: single = kind(0.0)REAL (KIND = single), PARAMETER :: pi = 3.141592REAL (KIND = single) :: thetaWRITE(*,*) ‘ Enetr angle in degrees:’READ(*,*) thetaWRITE(*, ‘(A, F10.4)’) ‘ The Secant is ‘, secant(theta)CONTAINS REAL FUNCTION secant(angle_in_degrees) REAL (KIND = single) :: angle_in_degrees secant = 1. /cos(angle_in_degrees * pi / 180.) END FUNCTION secantEND PROGRAM test_sec

Test: θ= 450, Sec(θ) = 1.4142

Sec. 9.2 Recursive Procedures

e.g., N! =

N(N-1)!, N 1≧

1, N = 0

Fig. 9-2RECURSIVE SUBROUTINE factorial (n, result)IMPLICIT NONEINTEGER, INTENT(IN) :: nINTEGER, INTENT(OUT) :: resultINTEGER :: tempIF ( n >= 1 ) THEN CALL factorial (n-1, temp) result = n * tempELSE result = 1END IFEND SUBROUTINE factorial

Fig. 9-3

RECURSIVE FUNCTION fact(n) RESULT(answer)IMPLICIT NONEINTEGER, INTENT(IN) :: nINTEGER :: answer

IF ( n >= 1 ) THEN answer = n * fact(n-1)ELSE answer = 1END IFEND FUNCTION fact

PROGRAM test_factorialIMPLICIT NONEINTEGER, EXTERNAL :: factINTEGER :: n, resultWRITE (*,*) ‘ Enter n ( >=0):’READ (*,*) nCALL factorial (n, result)WRITE(*,*) n, ‘! =‘, resultWRITE(*,*) n, ‘! =‘, fact(n)END PROGRAM

Test: 7 ! = 5040

Sec. 9.3 Keyword Arguments and Optional Arguments

Fig. 9-4 (The use of keyword arguments)

MODULE procsCONTAINS REAL FUNCTION calc (first, second, third) IMPLICIT NONE REAL, INTENT(IN) :: first, second, third calc = (first – second) / third END FUNCTION calcEND MODULE procs

(only with explicit interfaces)

PROGRAM test_keywordsUSE procsIMPLICIT NONEWRITE(*,*) calc (3., 1., 2.)WRITE(*,*) calc (first=3., second=1., third=2.)WRITE(*,*) calc (second=1., third=2., first=3. )WRITE(*,*) calc (3., third=2., second=1.)END PROGRAM test_keywords

Output:

1.00001.00001.00001.0000

Optional argument:

e.g., INTEGER, INTENT(IN), OPTIONAL :: upper_limit. . .IF ( PRESENT(upper_limit) ) THEN. . .ELSE. . .END IF

Example 9-1 (Finding the extreme values in a data set)

4 optional output arguments:

1. The max. value2. The location of the max. value3. The min. value4. The location of the min. value

Fig. 9-5MODULE procsCONTAINS SUBROUTINE extremes(a, n, maxval, pos_maxval, minval, pos_minval) IMPLICIT NONE INTEGER, INTENT(IN) :: n REAL, INTENT(IN), DIMENSION(n) :: a REAL, OPTIONAL :: maxval, minval INTEGER, OPTIONAL :: pos_maxval, pos_minval! local variables INTEGER :: i, pos_max, pos_min REAL :: real_max, real_min real_max = a(1) pos_max = 1 real_min = a(1) pos_min = 1! Find the extremes DO i = 2, n max: IF(a(I) > real_max) THEN real_max = a(i) pos_max = I END IF max

min: IF(a(i) < real_min) THEN real_min = a(I) pos_min = I END IF minEND DO!Report the resultsIF ( PRESENT(maxval)) THEN maxval = real_maxEND IFIF ( PRESENT(pos_maxval)) THEN pos_maxval = pos_maxEND IFIF ( PRESENT(minval)) THEN minval = real_minEND IFIF ( PRESENT(pos_minval)) THEN pos_minval = pos_minEND IFEND SUBROUTINEEND MODULE procs

PROGRAM test_extremesUSE procsIMPLICIT NONEINTEGER, PARAMETER :: max_size = 10REAL, DIMENSION(max_size) :: aREAL :: large, smallINTEGER :: large_pos, small_pos, nvals, IWRITE (*,*) “ Enter the number of values:”READ (*,*) nvalsDO i = 1, nvalsREAD (*,*) a(i)END DOCALL extremes(a, nvals, large, large_pos, small, small_pos)WRITE(*, *) ” All arguments in order:”, & large, large_pos, small, small_posCALL extremes(a, nvals, maxval=large, minval= small, & pos_maxval=large_pos, pos_minval=small_pos)WRITE(*, *) ” All arguments in arbitrary order:”, & large, large_pos, small, small_posCALL extremes(a, nvals, maxval=large, minval=small)WRITE(*, *) ” Large and small only:”, large, smallEND PROGRAM

Test:

Enter the number of values:71.34.-21.10.2-0.040.5.

Output:

All arguments in order: 34.0 2 -21.1 3All arguments in arbitrary order: 34.0 2 -21.1 3Large and Small only: 34.0 -21.1

Sec. 9.5 Extending Fortran with User-defined Operator and Assignments

Permit the programmer to define new operators or extend existing ones.

1. Interface operator block: INTERFACE OPERATOR (operator_symbol) MODULE PROCEDURE function_1 . . . END INTERFACE

2. Interface assignment block: INTERFACE ASSIGNMENT (=) MODULE PROCEDURE subroutine_1 . . . END INTERFACE

Example 9-3 (Vectors)

V1 = x1 i + y1 j + z1 k, V2 = x2 i + y2 j + z2 k ,^ ^ ^ ^^ ^

• Addition ( ＋ ) : V1 + V2 = (x1 + x2) i + (y1+ y2) j + (z1 + z2) k ^ ^ ^

• Subtraction ( － ) : V1 - V2 = (x1 - x2) i + (y1 - y2) j + (z1 - z2) k ^ ^ ^

• Dot product (.DOT.) : V1 ． V2 = (x1x2) + (y1y2) + (z1z2)

• Cross product (.CROSS.) :

^ ^ ^V1 × V2 = (y1z2 – y2z1) i + (z1x2 – z2x1) j + (x1y2 – x2y1) k

MODULE vectorsIMPLICIT NONETYPE vector REAL :: x REAL :: y REAL :: zEND TYPEINTERFACE OPERATOR (+) MODULE PROCEDURE vector_addEND INTERFACEINTERFACE OPERATOR (-) MODULE PROCEDURE vector_subtractEND INTERFACEINTERFACE OPERATOR (.DOT.) MODULE PROCEDURE vector_dotEND INTERFACEINTERFACE OPERATOR (.CROSS.) MODULE PROCEDURE vector_crossEND INTERFACE

CONTAINS FUNCTION vector_add(vec_1, vec_2) TYPE(vector) :: vector_add TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_add%x=vec_1%x+vec_2%x vector_add%y=vec_1%y+vec_2%y vector_add%z=vec_1%z+vec_2%z END FUNCTION vector_add

FUNCTION vector_subtract(vec_1, vec_2) TYPE(vector) :: vector_subtract TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_subtract%x=vec_1%x-vec_2%x vector_subtract%y=vec_1%y-vec_2%y vector_subtract%z=vec_1%z-vec_2%z END FUNCTION vector_subtract

FUNCTION vector_dot(vec_1, vec_2) REAL :: vector_dot TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_dot=vec_1%x*vec_2%x+vec_1%y*vec_2%y+vec_1%z*vec_2%z END FUNCTION vector_dot

FUNCTION vector_cross(vec_1, vec_2) TYPE (vector) :: vector_cross TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_cross%x=vec_1%y*vec_2%z-vec_1%z*vec_2%y vector_cross%y=vec_1%z*vec_2%x-vec_1%x*vec_2%z vector_cross%z=vec_1%x*vec_2%y-vec_1%y*vec_2%x END FUNCTION vector_cross END MODULE vectors

PROGRAM test_vectors USE vectors IMPLICIT NONE TYPE(vector) :: vec_1, vec_2

! Test addition vec_1 = vector(1., 2., 3.) vec_2 = vector(4., 5., 6.) WRITE(*, 1000) vec_1, vec_2, vec_1 + vec_2, vec_1 - vec_2, & vec_1 .DOT. vec_2, vec_1 .CROSS. vec_2 1000 FORMAT(' Test addition:', /, & 'vec_1 = ', 3F8.2,/, & 'vec_2 = ', 3F8.2,/, & 'vec_1 + vec_2 = ', 3F8.2,/, & 'vec_1 - vec_2 = ', 3F8.2,/, & 'vec_1 .DOT. vec_2 = ', F8.2, / , & 'vec_1 .CROSS. vec_2 = ', 3F8.2) END PROGRAM test_vectors

Output:

Test addition:vec_1 = 1.00 2.00 3.00vec_2 = 4.00 5.00 6.00vec_1 + vec_2 = 5.00 7.00 9.00vec_1 – vec_2 = -3.00 -3.00 -3.00vec_1 .DOT. vec_2 = 32.00vec_1 .CROSS. Vec_2 = -3.00 6.00 -3.00

Example: (extra)

z θ= z∠ 1 θ∠ 1 ± z2 θ∠ 2.

1. Define a new data type called POLAR that represents a complex number in polar form. Then write a module containing interface operator blocks to allow two polar numbers to be added and subtracted, i.e.,

2. Write a test driver program.

MODULE mathIMPLICIT NONEREAL, PARAMETER :: const = 57. 296 ! 1 rad=57.296 degreesTYPE :: polar REAL :: z ! magnitude REAL :: theta ! AngleEND TYPE polar

INTERFACE OPERATOR (+) MODULE PROCEDURE polar_addEND INTERFACE

INTERFACE OPERATOR (-) MODULE PROCEDURE polar_subtractEND INTERFACE

CONTAINS FUNCTION polar_add(p1, p2) TYPE(polar) :: polar_add TYPE(polar), INTENT(IN) :: p1, p2 REAL :: a, b a = p1%z*cos(p1%theta/const) + p2%z*cos(p2%theta/const) b = p1%z*sin(p1%theta/const) + p2%z*sin(p2%theta/const) polar_add%z = SQRT(a**2 + b**2) polar_add%theta = ATAN2(b, a) * const END FUNCTION polar_add

FUNCTION polar_subtract(p1, p2) TYPE(polar) :: polar_subtract TYPE(polar), INTENT(IN) :: p1, p2 REAL :: a, b a = p1%z*cos(p1%theta/const) - p2%z*cos(p2%theta/const) b = p1%z*sin(p1%theta/const) - p2%z*sin(p2%theta/const) polar_subtract%z = SQRT(a**2 + b**2) polar_subtract%theta = ATAN2(b, a) * const END FUNCTION polar_subtractEND MODULE math

PROGRAM test_polarUSE mathIMPLICIT NONETYPE(polar) :: p1, p2, pWRITE(*,*)' Enter z1 and theta1 (in degrees):'READ(*,*) p1%z, p1%thetaWRITE(*,*)' Enter z2 and theta2 (in degrees):'READ(*,*) p2%z, p2%thetaWRITE(*,*)' z1 + z2 = ', p1+p2WRITE(*,*)' z1 - z2 = ', p1-p2END PROGRAM

Test: Enter z1 and theta1 (in degrees):3.0 30.0Enter z2 and theta2 (in degrees):4.0 60.0

z1 + z2 = 6.76643 47.1791z1 – z2 = 2.05314 -73.0649