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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
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’)