Fortran 90 Two Commonly Used Statements

Transcription

1 Fortran 90 Two Commonly Used Statements 1. DO Loops (Compiled primarily from Hahn [1994]) Lab 6B BSYSE 512 Research and Teaching Methods The DO loop (or its equivalent) is one of the most powerful statements in any programming language. The DO loop is very frequently used in common scientific and engineering applications of Fortran programming Typical Forms of DO Loop One of the simplest forms of DO loop is or DO I = J, K block n DO n I = J, K block CONTINUE where I is an integer variable, J and K are integer expressions, and block stands for any number of statements. The block is executed repeatedly; the values of J and K determine how many repeats are made. On the first loop, I takes the value of J, and is then increased by 1 at the end of each loop (including the last). Looping stops once I has reached the value of K, and execution proceeds with the statement after END DO or CONTINUE with the label n. I will have the value K+1after completion of the loop (normal exit) An Example The square root x of any positive number a may be found using only the arithmetic operations of addition, subtraction and division, with Newton s method. This is an iterative procedure that refines an initial guess. The structure plan of the algorithm to find the square root, and the program with sample output for a = 2 is as follows. 1. Input a 2. Initialize x to 1 3. Repeat six times (say) Replace x by (x + a/x)/2 Print x 4. Stop PROGRAM Newton C Square rooting with the Newton method. IMPLICIT NONE REAL : : A INTEGER : : I REAL : : X! number to be square rooted! iteration counter! approximate square root of A 1

2 WRITE (*, 10, ADVANCE = NO ) Enter number to be square rooted: 10 FORMAT( a ) READ*, a PRINT*, a x = 1! initial guess DO I = 1, 6 x = (x + a / x) / 2 PRINT*, x ENDDO PRINT*, Fortran 90 s value:, SQRT ( a ) END If the number to be square rooted is 2 then the output obtained is Fortran 90 s value: The value of x converges to a limit, which is. Note that it is identical to the value returned by Fortran 90 s intrinsic SQRT function. Most computers and calculators use a similar method internally to compute square roots and other standard mathematical functions. Note: The non-advancing I/O in the WRITE statement allows the input on the same line as the prompt. To print an apostrophe (N) in a string, the apostrophe must be repeated (NN). Some pairs of keywords in Fortran 90, such as ENDDO, do not have to be separated. Recalling that in the last session, we introduced a few ways of assigning values to an array. With the DO loop function, array elements can be generated easily using the array subscript as the control variable. The following code assigns the first five even integers to the five elements of X (assumed correctly declared): DO I = 1, 5 X(I) = 2 * I The same effect can be achieved in a number of different ways with an array constructor: or X = (/ 2, 4, 6, 8, 10 /) X = (/ (I, I = 2, 10, 2) /) 2

3 2. The IF-THEN-ELSE Statement Like the DO loop, the IF-THEN-ELSE statement is frequently used in Fortran programming applications An Example As an example, suppose that the final course mark of students attending a university course is calculated as follows. Two examination papers are written at the end of the course. The final mark is either the average of the two papers, or the average of the two papers and the class record mark (all weighted equally), whichever is the higher. The following program computes and prints each student s mark, with the comment PASS or FAIL (50% being the pass mark). PROGRAM Final_Mark C Final mark for course based on class record and exams IMPLICIT NONE REAL : : CRM, REAL : : ExmAvg REAL : : Final REAL : : P1 REAL : : P2 INTEGER : : Stu! Class record mark! average of two exam papers! final mark! mark for first paper! mark for second paper! student counter OPEN (1, FILE = MARKS ) PRINT*, CRM Exam Avg Final Mark DO Stu = 1, 3 READ (1, * ) CRM, P1, P2 ExmAvg = (P1 + P2) / 2.0 IF (ExmAvg > CRM) THEN Final = ExmAvg ELSE Final = (P1 + P2 + CRM) / 3.0 IF (Final >= 50) THEN PRINT*, CRM, ExmAvg, Final, PASS ELSE PRINT*, CRM, ExmAvg, Final, FAIL END The students mark data are stored in an external file (MARKS) to make reading more efficient. For example, for a sample class of three students, the data could be: Therefore, the first student has a class record of 40 with exam marks of 60 and 43. Her final mark should be 51.5 (class record not used), whereas the second student s mark should be 49.3 (class record used). 3

4 2.2. The IF Construct In the previous example we see a situation where the computer must make decisions: whether or not to include the class record, and whether to pass or fail the student. The programmer cannot anticipate which of these possibilities will occur when writing the program, so it must be designed to allow for all of them. We need a conditional branch, which is another of the most powerful facilities in any programming language. A common form of the IF construct, as it is called in Fortran 90, is IF condition THEN block1 [ELSE blocke] where condition is a logical expression having a truth value of either true or false, and block1 and blocke are blocks of statements. If the condition is true, block1 is executed (and not blocke), otherwise blocke is executed (and not block1). The ELSE part is optional and may not be always needed. Execution continues in the normal sequential way with the next statement after. The word construct implies a construction with more than one statement (and hence more than one keyword). The condition may be formed from numeric expressions with relational operators, e.g., < (LT), <= (LE), == (EQ) and /= (NE), and from logical expressions with logical operators, such as.not.,.and. and.or The Logical IF Statement A shorter form of the IF construct is the IF statement: IF (condition) statement In this case only a single statement is executed if the condition is true. Nothing happens if it is false The Arithmetic IF Statement (based on Nyhoff and Leestma [1996]) The arithmetic IF statement has the form IF (expression) n 1, n 2, n 3 where the expression enclosed in parentheses is an arithmetic expression and n 1, n 2, n 3 are labels of executable statements, not necessarily distinct. When the statement is executed, the value of the expression is calculated, and execution continues with statement n 1 if this value is negative, with statement n 2 if this value is zero, and with statement n 3 if this value is positive. For instance, consider the following statement IF (y ** 0.3! 1.6) 10, 20, 30 If y has the value 14.0, statement 30 will be executed next. References Hahn, B.D., Fortran 90 for Scientist and Engineers, Butterworth-Heinemann, Woburn, MA, Nyhoff, L., and S. Leestma, FORTRAN 77 for Engineers and Scientists, 4 th ed., Prentice Hall, Upper Saddle River, NJ,

5 Lab 6 Assignment 1. Translate the following into Fortran statements. (2.5pts) (1) Add 1 to the value of I and store the result in I. (2) Cube I, add J to this, and store the result in I. (3) Set G equal to the larger of the two variable E and F (4) If D is greater than zero, set x equal to minus B (5) Set Q equal to the absolute value of Q 0 2. Translate the following formula into Fortran expression. (2.5 pts) (1) (2) (3) (4) (5) 3. Write a program which generates some random numbers R with (10 pts) CALL RANDOM_NUMBER (R) and counts how many of them are greater than 0.5, and how many are less than 0.5. Try increasing the number of random numbers generated. What do you expect? 4. Develop the first version of the pseudo code OR a flow chart for solving the class project problem. (10 pts) 5