Introduction to Computer Sciences

References: [1] Fortran 95/2003 for Scientists and Engineers (3e) by Stephen J. Chapman. [2] Using Fortran 90 by Chester Forsythe.

Grading system: 1. Performance (quizzes): 30% 2. Midterm: 30% 3. Final: 40%

Office hours: (PH224) 1. Mon. 13:40~15:30 2. Wed. 10:10~12:00

An Intuitive Walk Through the World of Computers

What is a Computer Program?

A computer program consisters of a collection of instructions that put together In a specific order to make a computer accomplish some task.

e.g., PROGRAM sq_root REAL :: square_root square_root = SQRT(2.0) WRITE(*,*) square_root END PROGRAM

What a Computer Can’t do?

Computers have no built-in intelligence. They are not smart.

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

recognizes and executes.

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

The History of the Fortran Language

Fortran = Formula translation

Fortran 66 Fortran 77 Fortran 90 Fortran 95

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

Fortran 2003

(2004)

High-Level Languages

Fortran program Fortran compiler Machine language

Learn to Design First

Think before you act!It is essential to use your mind first and create designs for your programs.

Program Design:• Grasp the problem.• Break the problem down.• Shape the solution for each main idea.• Debug/Test the program.• Make each program unit clear and understandable.

The Structure of a Fortran Program

(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)

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

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)

Program Examples

Example (Temperature conversion)

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

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

Assignment Statements and Logical Calculations

Assignment statements: logical variable name = logical expression

Logical operators: • relational operators• combinational operators

Relational Operators

a1 op a2

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

operation 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) 7+3 < 2+11 .TRUE.

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 below)

operation meaning

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

Example

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.

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

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

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

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

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!)

Examples Using Block IF Constructs

Example 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

• while loops• iterative (or counting) loops

The While Loop

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

a code block

Control Constructs: Loops

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

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

Named Block IF Constructs

optional

optional

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

The Logical IF Statement

IF (logical_expr) Statement

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

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 )

Example 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!

The CYCLE and EXIT Statements

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

Named Loops

While loop:

optional

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

Counting loop:

optional

Nesting Loops and Block IF Construct

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:

Example 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

Character Assignments and Character Manipulations

Character Assignment

character variables name = character expression

Character operators:1. substring specifications2. concatenation

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

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.)

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’)