Chapter 3. Control Structures and Program Design ► Two broad categories of control statement:  Branches  Loops ► These will make the program more complex. To avoid programming errors, a formal program design procedure is needed, which is based on the technique known as top-down design.

► 3.1 Top-down design techniques program to be solved design an algorithm (step-by-step procedure) for finding solution substak pseudocode Fortan statement unit test each program final progam pseudocode Fortan statement Fortan statement Fortan statement Fortan statement unit test each program

► 3.2 Pseudocode and Flowcharts  Stands forms to describe the algorithm  Pseudocode: hybrid mixture of English & Fortran  Flowchart: graphical description

► 3.3 Control Constructs: Branches  Block IF construct  Logical IF statement if (logical expression) then statement block end if logical expression statement block.false..true. if (logical expression) statement

 ELSE and ELSE IF clauses if (logical expression 1) then statement block 1 else if (logical expression 2) then statement block 2 else statement block n end if logical expression 1 statement block 1.false..true. logical expression 2.false..true. statement block 2

 Example using Block if: Solve ax 2 +bx+c=0 for x given a, b, and c.  Design the algorithm: ► Read the input data a, b, and c ► Calculate the roots ► Write out the roots

 Flowchart start read a, b, c echo a, b, c b**2-4.*a*c < 0b**2-4.*a*c = 0 write 'The equation has complex roots.' write 'The equation has two identical read roots.' write 'The equation has two distinct real roots.' calculate real_part, imag_part calcaulate x1calcaulate x1, x2 write real + i imag read – i imag write x1write x1, x2 stop.false..true.

progam roots ! Purpose: ! This program solves for the roots of a quadratic equation of the form ! a*x**2 + b*x + c = 0. It calculates the answers regardless of the type of ! roots that the equation possesses. implicit none ! Declare the variables used in this program real :: a ! Coefficient of x**2 term of equation real :: b ! Coefficient of x term of equation real :: c ! Constant term of equation real :: discriminant ! Discriminant of the equation real :: imag_part ! Imaginary part of equation (for complex roots) real :: real_part ! Real part of equation (for complex roots) real :: x1 ! First solution of equation (for real roots) real :: x2 ! First solution of equation (for real roots) ! Prompt the user for the coefficients of the equation write(*,*) 'This program solves for the roots of a quadratic ' write(*,*) 'equation of the form a*x**2 + b*x + c = 0. ' write(*,*) 'Enter the coefficients a, b, and c: ' read(*,*) a, b, c ! Echo back coefficients write(*,*) 'The coefficients a, b, and c are: ', a, b, c ! Calculate discriminant discriminant = b** *a*c >Continued on next page...

...< ! Solve for the roots, depending upon the value of the discriminant if (discriminant > 0.0) then x1 = (-b + sqrt(discriminant)) / (2.0*a) x2 = (-b - sqrt(discriminant)) / (2.0*a) write(*,*) 'This equation has two real roots:' write(*,*) 'x1 = ', x1 write(*,*) 'x2 = ', x2 else if (discriminant == 0.0) then x1 = (-b) / (2.0*a) write(*,*) 'This equation has two identical real roots:' write(*,*) 'x1 = x2 = ', x1 else ! there are complex roots, so... real_part = (-b) / (2.0*a) imag_part = sqrt(abs(discriminant)) / (2.0*a) write(*,*) 'This equation has complex roots:' write(*,*) 'x1 = ', real_part, ' +i ', imag_part write(*,*) 'x2 = ', real_part, ' -i ', imag_part end if end program

 "Name" Block IF Constructs [name:] if (logical expression 1) then statement block 1 else if (logical expression 2) then [name] statement block 2 else [name] statement block n end if [name]

 "Nested" Block IF Constructs  A better program is: if (test 1) then statement block if (test 2) then statement block if (test 3) then statement block end if outer: if (test 1) then statement block middle: if (test 2) then statement block inner: if (test 3) then statement block end if inner end if middle end if outer

 Example Using Block IF and Nested Block IF ► Block IF if (x > 95) then write(*,*) 'Grade is A' else if (x > 86) then write(*,*) 'Grade is B' else if (x > 76) then write(*,*) 'Grade is C' else if (x > 66) then write(*,*) 'Grade is D' else write(*,*) 'Grade is E' end if 95 < x A 86 < x ≤ 95 B 76 < x ≤ 86 C 66 < x ≤ 76 D 0 < x ≤ 66 0 < x ≤ 66E

► Nested Block IF aif: if (x > 95) then write(*,*) 'Grade is A' else aif bif: if (x > 86) then write(*,*) 'Grade is B' else bif cif: if (x > 76) then write(*,*) 'Grade is C' else cif dif: if (x > 66) then write(*,*) 'Grade is F' else dif write(*,*) 'Grade is F' end if dif end if cif end if bif end if aif

 CASE construct [name:] select case (integer case_expression) case (case_selector_1) [name] statement block case (case_selector_2) [name] statement block... case default [name] statement block end select [name]

► 3.4 Control Constructs: Loops ► while loops ► iterative loops (counting loops)  WHILE Loop do statement block if (logical_expression) exit statement block end do logical expression statement block.false..true. statement block do while (logical_expression) statement block end do logical expression statement block.false..true.

 Examle: Recall in a set of numbers and calculate the mean and standard deviation of the data x<0 n=n+1 sum_x=sum_x+x sum_x2=sum_x2+x.false..true. read x x_bar = sum_x/n std_dev = sqrt((n*sum_x2-sum_x**2) / (n*(n-1))

progam stats_2 ! Purpose: ! To calculate mean and standard deviation of input data set ! containing an arbitrary number of input values. ! implicit none integer :: n = 0 ! The number of input samples real :: std_dev ! The standard deviation of the input samples real :: sum_x = 0 ! The sum of the input values real :: sum_x2 = 0 ! The sum of the squares of the input values real :: x = 0 ! An input data value real :: x_bar ! The average of the input samples ! While loop to read input values do ! Read in next value write(*,*) 'Enter number:' read(*,*) x write(*,*) 'The number is ', x ! Test of loop exit if (x < 0) exit ! Otherwise, accumulate sums n = n + 1 sum_x = sum_x + x sum_x2 = sum_x2 + x**2 end do >Continued on next page...

...< ! Check to see if we have enough input data if (n < 2) then write(*,*) 'At least 2 values must be entered!' else x_bar = sum_x / real(n) std_dev = sqrt((real(n)*sum_x2-sum_x**2)/(real(n)*real(n-1)) write(*,*) 'The mean of this data set is:', x_bar write(*,*) 'The standard deviation is: ', std_dev write(*,*) 'The number of data points is:', n end if end program

 Iterative Loop (Counting loop) do index = istart, iend[, incr] statement block end do index*incr ≤ iend*incr statements.false..true. index = index+incr index=istart 1.istart, iend, incr can be contatns, variables or expression of integer. 2.If incr is not specified, incr=1.

progam stats_3 ! Purpose: ! To calculate mean and standard deviation of input data set, ! where each input value can be positive, negative or zero. ! implicit none integer :: i ! Loop index integer :: n = 0 ! The number of input samples real :: std_dev ! The standard deviation of the input samples real :: sum_x = 0 ! The sum of the input values real :: sum_x2 = 0 ! The sum of the squares of the input values real :: x = 0 ! An input data value real :: x_bar ! The average of the input samples ! Get the number of data to input write(*,*) 'Enter number of points: ' read(*,*) n ! Check to see if we have enough input data if (n < 2) then write(*,*) 'At least 2 values must be entered.' else ! Loop to read input values do i = 1, n write(*,*) 'Enter number: ' read(*,*) x write(*,*) 'The number is ', x sum_x = sum_x + x sum_x2 = sum_x2 + x**2 >Continued on next page...

...< ! Calculate statistics x_bar = sum_x / real(n) std_dev = sqrt((real(n)*sum_x2-sum_x**2)/(real(n)*real(n-1)) write(*,*) 'The mean of this data set is:', x_bar write(*,*) 'The standard deviation is: ', std_dev write(*,*) 'The number of data points is:', n end program

► Examples do i = 1, end do do i = 1, 10, 2... end do do i = 1, 10, end do do i = 3, -3, end do i = 1, 2, 3,..., 10 i = 1, 3, 5, 7, 9 Initially, 1*(-1) > 10*(-1) so exits i = 3, 1, -1, -3

 Notes: do i = 1, 4... i = 2 end do do i = 1, 5... if (i >= 3) exit... end do do i = 1, end do goto 100 will produce infinite loops branch out of a do loop is ok but, branch into the loop is illegal

► CYCLE statement ► EXIT statement ► Nesting loops (loop within loop) do i = 1, 5 if (i == 3) cycle write(*,*) i end do do i = 1, 5 if (i == 3) exit write(*,*) i end do do i = 1, 3 do j = 1, 4 write(*,*) i, j end do the output will be 1, 2, 4, 5 the output will be 1,