Fortran has good facilities for handling arrays. They can have up to seven dimensions. The program STATS reads a set of real numbers from a data file and puts them into a one-dimensional array. It then computes their mean and standard deviation. Given an array of values x1, x2, x3, ... xN, the mean standard deviation are given by:
To simplify this program, it will be assumed that the first number in the file is an integer which tells the program how many real data points follow.
PROGRAM STATS CHARACTER FNAME*50 REAL X(1000) WRITE(UNIT=*, FMT=*) 'Enter data file name:' READ(UNIT=*, FMT='(A)') FNAME OPEN(UNIT=1, FILE=FNAME, STATUS='OLD') *Read number of data points NPTS READ(UNIT=1, FMT=*) NPTS WRITE(UNIT=*, FMT=*) NPTS, ' data points' IF(NPTS .GT. 1000) STOP 'Too many data points' READ(UNIT=1, FMT=*) (X(I), I = 1,NPTS) CALL MEANSD(X, NPTS, AVG, SD) WRITE(UNIT=*, FMT=*) 'Mean =', AVG, ' Std Deviation =', SD END SUBROUTINE MEANSD(X, NPTS, AVG, SD) INTEGER NPTS REAL X(NPTS), AVG, SD SUM = 0.0 SUMSQ = 0.0 DO 15, I = 1,NPTS SUM = SUM + X(I) SUMSQ = SUMSQ + X(I)**2 15 CONTINUE AVG = SUM / NPTS SD = SQRT(SUMSQ - NPTS * AVG)/(NPTS-1) ENDThis program has several new statement forms.
CHARACTER statement declares that the variable FNAME is
to hold a
string of 50 characters: this should be long enough for the file-names
used by most operating systems.
REAL statement declares an array X with 1000 elements
numbered from X(1) to X(1000).
READ statement uses a format item A which is needed to
in a character string: A originally stood for ``alpha-numeric".
OPEN statement then assigns I/O unit number one (any small
integer could have been used) to the file. This unit number is
needed in subsequent input/output statements. The item STATUS='OLD'
is used to specify that the file already exists.
IF statement is a special form which can replace an IF-block
where it would only contain one statement: its effect is to stop the
program running if the array would not be large enough.
READ statement which follows it has a special form known
as an implied-DO-loop: this reads all the numbers from the file in
to successive elements of the array X in one operation.
CALL statement corresponds to the SUBROUTINE statement
in the same way that a function reference corresponded to a
FUNCTION statement. The difference is that the arguments X
NPTS transfer information into the subroutine, whereas AVG and
SD return information from it. The direction of transfer is
determined only by the way the dummy arguments are used within
the subroutine. An argument can be used to pass information in
either direction, or both.
INTEGER statement is, as before, not really essential but it is
good practice to indicate clearly the data type of every procedure
REAL statement declares that X is an array but uses a
option available only to dummy arguments: it uses another
argument, NPTS, to specify its size and makes it an adjustable
array. Normally in Fortran array bounds must be specified by
constants, but the rules are relaxed for arrays passed into
procedures because the actual storage space is already allocated in
the calling program unit; the REAL statement here merely specifies
how many of the 1000 elements already allocated are actually to be
used within the subroutine.
The rest of the subroutine uses a loop to accumulate the sum of the elements in SUM, and the sum of their squares in SUMSQ. It then computes the mean and standard deviation using the usual formulae, and returns these values to the main program, where they are printed out.