1. Review of lecture 3 Data type and declaration INTEGER E.g., a, b, c REAL E.g., x, y, z, w LOGICAL COMPLEX CHARACTER Examples: INTEGER::a=1,b=-5,c=5 REAL::x=2.0

2. Review of lecture 3 (cont.) Arithmetic expressions E.g., 5 + 2 *3 E.g., b**2 – 4*a*c It has a value by itself E.g. expression: 5 + 2*3 has a value of 11

3. Review of lecture 3 (cont.) Evaluating Complex Expressions Precedence Associativity (For expressions having operators with the same precedence). operatorsPrecedenceassociativity ()1Left to right **2Right to left *, /3Left to right +, -4Left to right

4. Review of lecture 3 (cont.) Mixed Mode Expressions If one operand of an arithmetic operator is INTEGER and the other is REAL the INTEGER value is converted to REAL the operation is performed the result is REAL 1 + 2.5  3.5 1/2.0  0.5 2.0/8  0.25 -3**2.0  -9.0 4.0**(1/2)  1.0 (since 1/2  0) 3/5 * 5.0  0.0 (since 3/5  0)

5. Review of lecture 3 (cont.) Statements Assignment statement: Variable = expression e.g., b = -5 (never the other way around, 5=b is not valid!) General statement: INTEGER a, b, c write (*,*) ‘Hello world!’

6. Selection in FORTRAN Lecture 4 By Nathan Friedman and Yi Lin Jan 16, 2007

7. Roots of a Quadratic (again) ! -------------------------------------------------- ! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 ! -------------------------------------------------- PROGRAM QuadraticEquation IMPLICIT NONE REAL :: a, b, c, d, root1, root2 ! read in the coefficients a, b and c WRITE(*,*) "A, B, C Please : " READ(*,*) a, b, c ! compute the square root of discriminant d d = SQRT(b*b - 4.0*a*c) ! solve the equation root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root ! display the results WRITE(*,*) "Roots are ", root1, " and ", root2 END PROGRAM QuadraticEquation

8. Run Time Error We assumed that the discriminant was positive What if it wasn’t? We would get an error when we run the program and attempt to compute the square root and the program would abort What should we do? Avoid trying to perform an illegal operation by branching around it -- use a selection control structure

9. Quadratics example d=b*b – 4.0*a*c D>=0.0 Calc root1, root2 Ouput “no real roots!”.TRUE..FALSE. end

10. IF-THEN-ELSE-END IF Used to select between two alternative sequences of statements. They keywords delineate the statement blocks. Syntax: IF (logical-expression) THEN first statement block, s_1 ELSE second statement block, s_2 END IF

11. IF-THEN-ELSE-END IF Semantics: Evaluate the logical expression. It can have value.TRUE. or value.FALSE. If the value is.TRUE., evaluate s_1, the first block of statements If the value is.FALSE., evlaluate s_2, the second block of statements After finishing either s_1 or s_2, execute the statement following the END IF

12. Roots of Quadratic – v.2 ! ---------------------------------------------------------------- ! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 ! ---------------------------------------------------------------- PROGRAM QuadraticEquation IMPLICIT NONE REAL :: a, b, c, d, root, root2 ! read in the coefficients a, b and c WRITE(*,*) "A, B, C Please : " READ(*,*) a, b, c !compute the square root of discriminant d d = b*b - 4.0*a*c IF (d >= 0.0) THEN ! is it solvable? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) "Roots are ", root1, " and ", root2 ELSE ! complex roots WRITE(*,*) "There is no real roots!" WRITE(*,*) "Discriminant = ", d END IF END PROGRAM QuadraticEquation

13. Logical Expressions Relational operators return result of.TRUE. or.FALSE, >=, ==, /= Relational operators are of lower precedence than all arithmetic operators 2 + 7 >= 3 * 3 .TRUE. There is no associativity a < b < c  illegal Note that == means “is equal to” but = means “assign the value on the right”

14. Data Type Logical Where do.TRUE. and.FALSE. come from? FORTRAN has a LOGICAL data type, just like it has INTEGER and REAL types We can declare variables to be of this type and assign values to them LOGICAL :: positive_x, condition condition =.TRUE. positive_x = x > 0

15. Is Number Even or Odd? IF (MOD(number, 2) == 0) THEN WRITE(*,*) number, " is even" ELSE WRITE(*,*) number, " is odd" END IF MOD(a, b): Intrinsic function, returning the remainder of a/b

16. Find Absolute Value REAL :: x, absolute_x x =..... IF (x >= 0.0) THEN absolute_x = x ELSE absolute_x = -x END IF WRITE(*,*) “The absolute value of “,& x, “ is “, absolute_x Note the use of & to indicate “continue on next line”

17. Which value is smaller? INTEGER :: a, b, min READ(*,*) a, b IF (a <= b) THEN min = a ELSE min = b END IF Write(*,*) “The smaller of “, a, & “ and “, b, “ is “, min

18. IF-THEN-END IF The IF-THEN-ELSE-END IF form allows us to choose between two alternatives There is another simpler selection mechanism that allows us to choose whether or not to perform a single block of actions We either perform the actions and go on, or skip them and go on

19. IF-THEN-END IF Syntax: IF (logical expression) THEN block of statements END IF Semantics: 1. Evaluate the logical expression 2. If it evaluates to.TRUE. execute the block of statements and then continue with the statement following the END IF 3. If the result is.FALSE. skip the block and continue with the statement following the END IF

20. Examples of IF-THEN-END IF absolute_x = x IF (x < 0.0) THEN absolute_x = -x END IF WRITE(*,*) "The absolute value of ", x, " is ", absolute_x ------------------------------------------------- INTEGER :: a, b, min READ(*,*) a, b min = a IF (a > b) THEN min = b END IF Write(*,*) "The smaller of ", a, " and ", b, " is ", min

21. Logical IF An even simpler form is sometimes useful Syntax: IF (logical expression) single- statement Semantics: equivalent to IF (logical expression) THEN single-statement END IF

22. Examples of Logical IF absolute_x = x IF (x < 0.0) absolute_x = -x WRITE(*,*) "The absolute value of ", x, & " is","absolute_x ------------------------------------------------- INTEGER :: a, b, min READ(*,*) a, b min = a IF (a > b) min = b Write(*,*) "The smaller of ", a, " and ", b, & " is ", min

23. IF-THEN-ELSE IF-END IF IF-THEN-ELSE-ENDIF can only handle processes which have two options. Sometimes we have more than 2 options for one process. For example, in the quadratic equation problem, there may be two equivalent roots. We want to detect this and complex roots at the same time. Solution: put another IF-THEN-ELSE-ENDIF in the ELSE block

24. IF-THEN-ELSE IF-END IF Syntax IF (logical-expression1) THEN first statement block, s_1 ELSE IF (logical-expression2) THEN second statement block, s_2 ELSE third statement block, s_3 END IF

25. IF-THEN-ELSE IF-END IF Semantics: Evaluate the logical expression 1. It can have value.TRUE. or value.FALSE. If the value is.TRUE., evaluate s_1, the first block of statements If the value is.FALSE., evaluate the logical expression 2. It can have value.TRUE. Or value.FALSE. If the value is.TRUE., evaluate s_2, the second block of statements If the value is.FALSE., evaluate s_3, the third block of statements After finishing either s_2 or s_3, execute the statement following ENDIF After finishing either s_1 or s_2 or s_3, execute the statement following the END IF

26. Roots of Quadratic v.3 ! --------------------------------------------------- ! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 ! Detect complex roots and repeated roots. ! --------------------------------------------------- PROGRAM QuadraticEquation IMPLICIT NONE REAL :: a, b, c, d, root1, root2 ! read in the coefficients a, b and c READ(*,*) a, b, c ! comute the discriminant d d = b*b - 4.0*a*c IF (d > 0.0) THEN ! distinct roots? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) 'Roots are ', root1, ' and ', root2 ELSE IF (d == 0.0) THEN ! repeated roots? WRITE(*,*) 'The repeated root is ', -b/(2.0*a) ELSE ! complex roots WRITE(*,*) 'There is no real roots!‘ WRITE(*,*) 'Discriminant = ', d END IF END PROGRAM QuadraticEquation

27. IF-THEN-ELSE IF-END IF You can put IF-THEN-ELSE IF-ENDIF within ELSE block repeatedly. IF (logical-expression1) THEN first statement block, s_1 ELSE IF (logical-expression2) THEN second statement block, s_2 ELSE IF-THEN-ELSE IF-ENDIF END IF There is a concise way to do this.

28. IF-ELSEIF-ELSE-ENDIF syntax IF (logical expression 1) THEN block 1 ELSEIF (logical expression 2) THEN block 2... ELSEIF (logical expression N-1) THEN block N-1 [ELSE block N] ENDIF

29. IF-ELSEIF-ELSE-ENDIF Semantics First evaluate the logical expression 1. It can have value.TRUE. or value.FALSE. If the value is.TRUE., evaluate the first block of statements. If the value is.FALSE., evaluate the logical expression 2. It can have value.TRUE. or value.FALSE. If the value is.TRUE., evaluate the second block of statements. Repeat this until all logical expressions have been evaluated. If none of them are.TRUE., evaluate block N within ELSE and ENDIF. After that, execute the statement following the ENDIF

30. Roots of Quadratic v.4 --------------------------------------------------- ! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 ! Detect complex roots and repeated roots. ! --------------------------------------------------- PROGRAM QuadraticEquation IMPLICIT NONE REAL :: a, b, c, d, root1,root2 ! read in the coefficients a, b and c READ(*,*) a, b, c ! compute the discriminant d d = b*b - 4.0*a*c IF (d > 0.0) THEN ! distinct roots? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) 'Roots are ', root1, ' and ', root2 ELSEIF (d == 0.0) THEN ! repeated roots? WRITE(*,*) 'The repeated root is ', -b/(2.0*a) ELSE ! complex roots WRITE(*,*) 'There is no real roots!‘ WRITE(*,*) 'Discriminant = ', d END IF END PROGRAM QuadraticEquation

31. Example in previous midterms PROGRAM X IMPLICIT NONE LOGICAL :: A,B,C INTEGER :: I,J,K I = 5/2+2.5 J= 13.0/3.0 + 0.66 K = 5 A = (I==J) B = (K > J) C = (K==I) WRITE (*,*) A, B, C END PROGRAM 1- T T T 2- T F T 3- T F F 4- F T F 5- None of the above

32. Complex Logical Expressions In addition to relational operators, more complex logical expressions can be formed using logical operators The Logical Operators listed in order of decreasing precedence are:.NOT..AND..OR..EQV.,.NEQV. The precedence of all logical operators is lower than all relational operators They all associate from left to right except.NOT. High Low

33. Logical operator:.AND. (&&) Examples (2>1).and. (3<4).TRUE. (2>1).and. (3>4).FALSE. (2<1).and. (3<4).FALSE. (2 4).FALSE..TRUE..FALSE..TRUE..FALSE..AND. exp2 exp1 &&.TRUE..FALSE.

34. Logical operator:.OR. (||) Examples (2>1).OR. (3<4).TRUE. (2>1).OR. (3>4).TRUE. (2<1).OR. (3<4).TRUE. (2 4).FALSE..TRUE..FALSE..TRUE..FALSE..TRUE..FALSE..OR. exp2 exp1 ||

35. Logical operator:.EQV. Examples (2>1).EQV. (3<4).TRUE. (2>1).EQV. (3>4).FALSE. (2<1).EQV. (3<4).FALSE. (2 4).TRUE..TRUE..FALSE..TRUE..FALSE..TRUE..EQV. exp2 exp1

36. Logical operator:.NEQV. Examples (2>1).NEQV. (3<4).FALSE. (2>1). NEQV. (3>4). TRUE. (2<1). NEQV. (3<4).TRUE. (2 4).FALSE..TRUE..FALSE..TRUE..FALSE..TRUE..FALSE..TRUE..FALSE..NEQV. exp2 exp1

37. Logical operator:.NOT. Examples.NOT. (2<1).TRUE..NOT. (2>1).FALSE..TRUE..FALSE..TRUE..NOT. exp

38. Examples Suppose we have the declaration: INTEGER :: age=34, old=92, young=16 What is the value of the following expressions? age /= old age >= young age == 62 age==56.and. old/=92 age==56.or. old/=92 age==56.or..not.(old/=92).not. (age==56.or. old/=92)

39. Another Example Suppose the integer variable, n has value 4. n**2 + 1 > 10.AND..NOT. n < 3  4**2 + 1 > 10.AND..NOT. 4 < 3  [4**2] + 1 > 10.AND..NOT. 4 < 3  16 + 1 > 10.AND..NOT. 4 < 3  [16 + 1] > 10.AND..NOT. 4 < 3  17 > 10.AND..NOT. 4 < 3  [17 > 10].AND..NOT. 4 < 3 .TRUE..AND..NOT. 4 < 3 .TRUE..AND..NOT. [4 < 3] .TRUE..AND..NOT..FALSE. .TRUE..AND. [.NOT..FALSE.] .TRUE..AND..TRUE. .TRUE.

40. Example in the final of Fall 2006 What is the output of the following Fortran program? PROGRAM exam IMPLICIT NONE LOGICAL :: X,Y INTEGER :: I=2, J=3 REAL :: A=5.0,B=9.0 X = (A/I) < (B/J) Y = (J/I) == (B/A) X = X.AND. Y Y = X.OR. Y WRITE (*,*) X, Y END PROGRAM exam a). TF b). TT c). FT d). F F e). The program does not compile