Introduction to Computer Sciences

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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

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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.

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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)

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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.

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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

(Declaration Section)

(Execution Section)

(Termination

section)

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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

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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)

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+ IMPLICIT NONE,

PROGRAM test_1 IMPLICIT NONE REAL :: time

time = 10.0

**WRITE(,) ‘Time=‘, tmie END PROGRAM**

Output:

Compile-time error! (depends on machines)

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Program Examples

Example (Temperature conversion)

T (

⁰

F) = (9/5) T(

⁰

C) + 32

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Example (extra)

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

1 0 1 1 = 1 x 2

³

+ 0 x 2

²

+ 1 x 2

¹

+ 1 x 2

⁰

= 11

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Assignment Statements and Logical Calculations

Assignment statements:

logical variable name = logical expression Logical operators:

• relational operators

• combinational operators

Relational Operators

a

₁

op a

₂

a

₁

, a

₂

: arithmetic expressions, variables, constants, or character strings.

op: the relational logical operators. (see Table below)

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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.

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Combinational Logic Operators

l

₁

.op. l

2

and .NOT. l

₁

(.NOT. is a unary operator) l

₁

, l

₂

: 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

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Example

L1 = .TRUE., L2 = .TRUE., L3 = .FALSE.

(a) .NOT. L

₁

.FALSE.

(b) L

₁

.OR. L

₃

.TRUE.

(c) L

₁

.AND. L

₃

.FALSE.

(d) L

₂

.NEQV. L

₃

.TRUE.

(e) L

₁

.AND. L

₂

.OR. L

₃

.TRUE.

(f) L

₁

.OR. L

₂

.AND. L

₃

.TRUE.

(g) .NOT. (L

₁

.EQV. L

₂

) .FALSE.

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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

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Example:

ax

²

+ bx + c = 0,

x = -b ± ( b

²

– 4ac )

^1/2

2a

If b

²

– 4ac = 0 b

²

– 4ac > 0

b

²

– 4ac < 0

two distinct real roots two complex roots

a single repeated root

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Fortran:

IF ( (b2 – 4.ac) < 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

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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

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Fortran:

IF ( (b2 – 4.ac) < 0. ) THEN**

**WRITE(,) ‘two complex roots’**

ELSE IF ( (b2 – 4.ac) == 0. ) THEN WRITE(,) ‘two identical real roots’**

ELSE

**WRITE(,) ‘two distinct real roots’**

END IF

Write a complete Fortran program for a quadratic equation ax

²

+ 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!)

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Examples Using Block IF Constructs

Example The Quadratic Equation: (ax

²

+ bx + c =0)

Write a program to solve for the roots of a quadratic equation, regardless of type.

Input: a, b, c

Output: roots

real

repeated real

complex

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• while loops

• iterative (or counting) loops

The While Loop

DO . . .

IF (logical_expr) EXIT . . .

END DO

a code block

Control Constructs: Loops

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Evaluation a Function of Two Variables:

f(x,y) =

x + y, x 0 ≧ and y 0 ≧ x + y

²

, x 0 ≧ and y < 0 x

²

+ y, x < 0 and y 0 ≧ x

²

+ y

²

, x < 0 and y < 0

Input: x, y

Output: f

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Test: (Try it out!) x y f 2. 3. 5.

2. -3. 11.

-2. 3. 7.

-2. -3. 13.

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[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

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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

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The Logical IF Statement

IF (logical_expr) Statement

e.g.,

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

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The Iterative or Counting Loop

DO index = istart, iend, incr Statement 1

. . .

Statement n END DO

e.g.,

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

Statement n END DO

( incr = 1 by default)

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

Statement n END DO

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

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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 = 1 DO i = 1, n

**n_factorial = n_factorial * i**

END DO

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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!

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The CYCLE and EXIT Statements

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[name:] DO . . .

IF (logical_expr) CYCLE [name]

. . .

IF (logical_expr) EXIT [name]

. . .

END DO [name]

Named Loops

While loop:

optional

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[name:] DO index = istart, iend, incr . . .

IF (logical_expr) CYCLE [name]

. . .

END DO [name]

Counting loop:

optional

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Nesting Loops and Block IF Construct

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Nesting loops within IF constructs and vice versa:

e.g.,

outer: IF ( a < b ) THEN . . .

inner: DO i = 1, 3 . . .

ELSE

. . .

END DO inner END IF outer

illegal!

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outer: IF ( a < b ) THEN . . .

inner: DO i = 1, 3 . . .

END DO inner . . .

ELSE

. . .

END IF outer

legal:

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Example Statiscal Analysis:

Average:

x_ave = Σ x

_i

i=1 N

N Standard deviation:

S =

N Σ x

_i²

– (

i=1 i=1

N ^N

Σ x

_i

)

²

N (N-1)

1/2

Input: x (i.e., x

_i

, i = 1, 2, …, N) 0 ≧

Output: x_ave and S

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Character Assignments and Character Manipulations

Character Assignment

character variables name = character expression Character operators:

1. substring specifications

2. concatenation

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Introduction to Computer Sciences

Introduction to Computer Sciences

References:

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

(Declaration Section)

(Execution Section)

(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 (

F) = (9/5) T(

C) + 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 2

square_root = SQRT(2.0) **WRITE(,) square_root END PROGRAM**

**WRITE (,) " Enter the numbers to multiply:"**

**READ (,) i, j k = i * j**

**WRITE (,) 'Result = ', k STOP**

**READ (,) input_list I/O unit format**

**WRITE (,) output_list**

**WRITE(,) ‘Time=‘, tmie END PROGRAM**

**WRITE(,) ‘Time=‘, tmie END PROGRAM**