Computational Physics - Fortran February 1997

Transcription

1 Fortran 90 Decision Structures IF commands 3 main possibilities IF (logical expression) IF (logical expression) THEN IF (logical expression) THEN IF (logical expression) THEN expression TRUE expression FALSE Fortran 90 Lecture 4 AS Fortran 90 Decision Structures (a) Logical expressions. : evaluate whether expression is true or false Decisions are made by testing the truth of logical expressions. e.g if x > 0 then do this Relational logical expressions: most common type Compare the values of arithmetic or character expressions. Relational operators: < <= == /= >= > FORTRAN 77 versions:.lt..le..eq..ne..ge..gt. e.g. b 2 < 4ac b*b < 4.*a*c I = J I == J temp 100 temp >= 100 (I + J)(I + K) L (I + J)*(I + K) /= L Answer = Yes Answer == "Yes" Fortran 90 Lecture 4 AS Decision Structures: Tips Evaluation of expression gives result either TRUE or FALSE. if INTEGER I == J integers held exactly in memory. if REAL/UBLE PRECISION A == B?? Real numbers are not held with complete accuracy. Never use == or /= to compare real expressions. Instead use: IF(ABS(A-B) < Tolerance) to test for 'equality'. Tolerance defined as small (Tolerance = 1.e-4) Recommended: Spaces to make expressions more readable. Same data type on each side of operator. Decision Structures, Logical Expressions (cont.) To combine logical expressions: Use.OR..AND..NOT. IF ((x < y).and. ( y < z)) THEN LOGICAL type variables; LOGICAL constants are.true..false. IF ( keep_going) THEN INDENT It is good programming practice to indent the body of an IF structure, the IF-block, by a few spaces to identify the block and improve readability of the code. Fortran 90 Lecture 4 AS Fortran 90 Lecture 4 AS Lecture 4 1

2 Decision Structures (cont.) (b) Control Statements Algorithm: if logical expression true then processing statement Logical Block IF structure IF (logical expression) THEN true IF-block false executable statements body Every IF (.) THEN must be balanced by (like parentheses) Fortran 90 Lecture 4 AS Decision Structures, Control Statements(cont.) Alternate processing when logical expression FALSE. Algorithm: if logical expression true then processing statement A else processing statement B statement IF (logical expression) THEN true false processing statement A IF-block true false processing statement B -block Fortran 90 Lecture 4 AS Decision Structures, Control Statements(cont.) For 3 or more branches IF ( ) THEN IF (logical expression) THEN at start of structure Indent. IF-block IF (logical expression) THEN any number of IF-block IFs not essential -block but must be last at end of structure The CASE construct The CASE statement (introduced in Fortran 90) provides an alternative method of selection between a number of branches. See the textbooks for details. LINE UP Fortran 90 Lecture 4 AS Nesting Structures The body of any structure, such as an IF-block, may contain another. IF (...) THEN 1 'IF' levels 1 : 0 IF (...) THEN 1 IF (...) THEN 2 IF (...) THEN 2 2 IF (...) THEN 3 : Fortran 90 Lecture 4 AS Lecture 4 2

3 Nesting Structures (cont.) Fortran 90 Looping Structures Always make sure the IFs and s balance correctly. A structure like IF IF is incomplete. Always use INDENTATION to identify blocks at successive nesting levels. Indent each block some consistent number of spaces more than the statements delimiting the block. The IF statement For when there are no IF or conditions and the action when the logical expression is true is a single statement. IF (logical expression) statement e.g. IF (X < 0) X = 0 Fortran 90 Lecture 4 AS Looping structures allow us to repeat blocks of code many times, usually with different data values. structure The only looping construct in Fortran. General form is loop control The, forming the loop body or -block, are executed repeatedly as indicated by the loop control. Fortran 90 Lecture 4 AS Looping Structures (endless) No loop control -block The statements in the -block will be executed repeatedly. This loop will never stop! Include a logical test and an EXIT statement to terminate it. EXIT transfers control to the statement following IF (logical expression) EXIT false -block true The EXIT test need not be the first statement in the loop. If required, may precede as well as follow it. Fortran 90 Lecture 4 AS Fortran 90 Lecture 4 AS Lecture 4 3

4 e.g. N = 7 IF (N <= 0) EXIT PRINT *, N What will happen here? If there were no output statement such a loop would go on for ever without it being obvious --- neither compiler nor run-time error checking can detect this error. BEWARE OF INFINITE LOOPS One of the variables in the logical expression must be modified in the body of the loop to make it terminate. Fortran 90 Lecture 4 AS Include N = N-1 in the loop and it will execute 7 times. N = 7 IF (N <= 0) EXIT PRINT *, N N = N-1 HINT: Include PRINT *, statements for critical variables at critical points while testing. Remove them when you're happy about that section of program. With decision structures you must test your code for correct flow and logic. If you have a problem add temporary PRINT *, statements. Fortran 90 Lecture 4 AS Endless loops are very useful when you need to read in a list of numbers and don't know in advance how many there will be. e.g. A set of non-negative numbers is followed by a negative one (e.g. 5, 4, 7, 20, 2, -5). Find the sum of the non-negative numbers. Initialize sum to zero. SUM = 0.0 Loop Read a number READ *, X If (negative) Exit IF (X < 0.) EXIT Add number to sum SUM = SUM + X Layout: INDENT the body of the loop to indicate the structure. Looping Structures (indexed) Algorithm: loop for index = values do processing statement To execute a processing statement a fixed number of times we could create an endless loop with a decreasing counter to exit the loop at zero as in the example previously used. N = 7 Initialize loop counter IF (N == 0) EXIT Test counter do 7 times N = N-1 Modify counter The may use the counter N e.g. to print a table of N**2 Warning: modifying N affects loop control. Fortran 90 Lecture 4 AS Fortran 90 Lecture 4 AS Lecture 4 4

5 Predetermined Loops Looping Structures (indexed, cont.) The statement also provides these facilities and specifies a -loop. i = initial_value, final [, increment] e.g. i = 7, 0, -1 i is the variable (loop counter) Parameters: initial_value : the initial value given to i. final_value : the final value, determines when to stop loop. increment : the value to be added to i each time round (default 1). OBLIGATORY: i is an INTEGER variable. the parameters are INTEGER variables, constants or expressions. Fortran 90 Lecture 4 AS Legally, the loop variable and parameters may be any type, but INTEGERs avoid rounding-off problems. Non-integer loop variables and parameters will be removed in a future Fortran standard. So don't use them! i = initial value, limit[, increment] Indent }-loop e.g. I = 2,10,2 executes loop for I = 2, 4, 6, 8, 10 I = 2,11,2 also executes loop for I = 2, 4, 6, 8, 10 because next time would be 12, > limit 11 I = 1,5 executes loop for I = 1, 2, 3, 4, 5 but I = 5,1,-1 executes loop for I = 5, 4, 3, 2, 1 Don't change loop index yourself within loop. Fortran 90 Lecture 4 AS Looping Structures (indexed, cont.) To use real numbers work as follows: e.g. to tabulate 2sinx x 2 e x from 0 to 3.5 in steps of 0.01 INTEGER :: I REAL :: X, Y I = 0, 350 X = REAL(I)/100.0 Y = 2.0*SIN(X) *X*X*EXP(X) PRINT *, Y While loops: These may be constructed using endless loops with the test and EXIT statement. Fortran 90 Lecture 4 AS Looping Structures (cont.) Nesting loops of both kinds may be nested as any block may contain another complete structure. I = 1,N J = 1,M inner loop outer loop loops may be included in IF-blocks and vice-versa. But a structure must be wholly contained within a block of another structure. Use EXIT to get out of a loop if you need to. Also see CYCLE statement in text books. Fortran 90 Lecture 4 AS Lecture 4 5