1. 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

2. 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.

3. 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)

4. 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.

5. 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)

6. 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

7. 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)

8. + IMPLICIT NONE, PROGRAM test_1 IMPLICIT NONE REAL :: time time = 10.0 WRITE(*,*) ‘Time=‘, tmie END PROGRAM Output: Compile-time error! (depends on machines)

9. Program Examples Example (Temperature conversion) T ( 0 F) = (9/5) T( 0 C) + 32

10. 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

11. 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)

12. 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.

13. 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

14. 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.

15. 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

16. Example: ax 2 + bx + c = 0, x = -b ± ( b 2 – 4ac ) 1/2 2a Ifb 2 – 4ac = 0 b 2 – 4ac > 0 b 2 – 4ac < 0 two distinct real roots two complex roots a single repeated root

17. 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

18. 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

19. 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 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!)

20. 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

21. while loops iterative (or counting) loops The While Loop DO... IF (logical_expr) EXIT... END DO a code block Control Constructs: Loops

22. 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

23. Test: (Try it out!) x y f 2. 3. 5. 2. -3. 11. -2. 3. 7. -2. -3. 13.

24. [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

25. 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

26. The Logical IF Statement IF (logical_expr) Statement e.g., IF ( (x >= 0.).AND. (y >= 0.) ) f = x + y

27. 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 )

28. 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

29. 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!

30. The CYCLE and EXIT Statements

31. [name:] DO... IF (logical_expr) CYCLE [name]... IF (logical_expr) EXIT [name]... END DO [name] Named Loops While loop: optional

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

33. Nesting Loops and Block IF Construct

34. 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!

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

36. Example Statiscal Analysis: Average: x_ave = ΣxiΣxi i=1 N N Standard deviation: S = N Σ x i 2 – ( 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

37. Character Assignments and Character Manipulations Character Assignment character variables name = character expression Character operators: 1.substring specifications 2.concatenation

38. Substring Specifications E.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!)

39. Solu: a = ‘ABCDEFGH’ ( ∵ len = 8) ∵ b(7:8) = a(2:6) = ‘BC’ b = ‘123456BC’ c = a(5:7) = ‘EFG’ = ‘EFG □□□□□ ‘ ( ∵ len = 8) (Cont.)

40. 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’)