In Chapter 5 we learned how to assign values to variables, but we could assign only one value per variable. A variable which can take only one value is referred to as an unsubscripted or scalar variable. So far, we have worked only with scalar variables. Often there is a need to assign more than one value per variable, i.e., to connect a group or "array" of values with one variable name. A variable which can take an array of values is referred to as a subscripted variable. Arrays can be of one dimension (a vector), two dimensions (a matrix), or multidimensional (a multidimensional matrix, limited to a maximum of seven dimensions). In Chapter 3 we learned how to use declaration state ments to specify variable types (integer, real, complex, and so on). In this chapter we learn how to use the DIMENSION statement to specify the name and size of subscripted variables. The size of a subscripted variable refers to the number of values it can store for later reference. When the program includes many subscripted variaables and corresponding DIMENSION statements, the PARAMETER statement may be used to list a common variable size as a program parameter (see Section 8.2). Input/output of subscripted variables is accomplished
with the implied DO list, which combines the features of
a DO loop and a READ/WRITE. When program units include subscripted variables, array specification is accomplished with DIMENSION statements (Section 8.1), their
input/output with implied DO lists (Section 8.4), and their
manipulation with one or more single or nested DO loops
(Section 7.1) 8.1 ARRAY SPECIFICATION
The specification block is a block of nonexecutable state ments which is placed immediately after the PROGRAM statement and before all executable statements in a program unit (see Table 1.1). The specification block contains the usual declaration statements (INTEGER, REAL, COMPLEX, DOUBLE PRECISION, LOGICAL, and CHARACTER) and all other specification statements, including IMPLICIT (Section 11.6), PARAMETER and DIMENSION. INTEGER and REAL arrays may be declared implicitly or explicitly (see Chapter 3). As before, DOUBLE PRECISION, LOGICAL, and CHARACTER arrays may only be declared explicitly. Specification of Integer or Real Arrays that Are Declared Implicitly The DIMENSION statement is used to specify arrays of integer or real type that are declared implicitly. The DIMENSION statement defines:
The following examples illustrate the DIMENSION statement: DIMENSION ITEM(10),A(3,5) DIMENSION VELOCITY(10,20,5) In the first example, ITEM(10) defines
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ In the same example, A(3,5) defines
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
A program unit may have as many DIMENSION statements as is necessary to properly specify all subscripted variables. However, several arrays may be listed in one DIMENSION statement. Thus, within one program unit, subcripted variables may be specified either (1) in one long DIMENSION statement, using column 6 for continuation, or (2) in several short DIMENSION statements, avoiding the use of column 6. The decision of whether to have one long or several short DIMENSION statements is one of individual preference. Specification of Integer or Real Arrays that are Declared Explicitly The specification of arrays of integer or real type that are declared explicitly is accomplished in either of the following ways:
The first case is illustrated below. INTEGER TEST REAL LENGTH DIMENSION TEST(10),LENGTH(10,3) In these statements, TEST and LENGTH are explicitly declared as integer and real variables, respectively, and they are specified as one and twodimensional arrays, respectively, by the DIMENSION statement. The second case is the following: INTEGER TEST(10) REAL LENGTH(10,3) In these statements, TEST and LENGTH are explicitly declared as integer and real variables, and specified in the declaration statement as one and twodimensional arrays, respectively. Both of these cases are equivalent. Note that a subscripted variable may be specified only once in a program unit. Therefore, the following set of statements will cause an error during compilation, because the size of the array TEST has been defined twice. INTEGER TEST(10) REAL LENGTH DIMENSION TEST(10),LENGTH(10,3) Arrays of Logical and Character Type The specification of arrays of logical or character type is accomplished with the LOGICAL or CHARACTER state ments, respectively, as illustrated by the following examples: LOGICAL SWITCH(10) CHARACTER*15 NAME(12),SSNO(12)*11 In these examples:
Lower and Upper Bounds of Arrays Arrays have lower and upper bounds. The lower bound of a onedimensional array is the subscript number of its first (base) element; the upper bound is the subscript of its last element. The array bounds are specified in the DIMENSION or declaration (INTEGER or REAL) statements. For example, in DIMENSION A(1:10) the lower bound is 1 and the upper bound is 10. This array can hold up to 10 elements or values, subscripted from 1 to 10. As another example, in DIMENSION A(0:20) the lower bound is 0 and the upper bound is 20. This array can hold up to 21 elements, subcripted from 0 to 20. If the lower bound is equal to 1, it can be omitted. For instance, inDIMENSION A(30) the lower bound is 1 and the upper bound is 30. This array can hold up to 30 elements, subscripted from 1 to 30. As another example, in DIMENSION A(10:10),B(5:25) the lower bound of array A is 10, and the upper bound is +10. This array can hold up to 21 values, subcripted from 10 to +10, including 0. Likewise, array B can hold up to 31 values, subscripted from 5 to +25, including 0. Another example is: DIMENSION C(0:10,0:5) Array C is a twodimensional array. It can hold 11 rows, subscripted from 0 to 10, and 6 columns, subscripted from 0 to 5, for a total of 11 × 6 = 66 values. 8.2 PARAMETER STATEMENT
The PARAMETER statement is a nonexecutable statement placed within the specification block, i.e., on top of the program unit (see Table 1.1). It is an important statement because it is used to permanently associate a variable name (to be taken as a program parameter) with a constant or with a constant arising from the execution of a constant expression. The PARAMETER statement takes the form: PARAMETER (p1=c1, p2=c2, p3=c3,...) where p1, p2, and p3 are parameters, and c1, c2, and c3 are constants or constant expressions. The parentheses en closing the parameter list are required in standard Fortran; however, they may be optional in some extensions. An example of a PARAMETER statement is: PARAMETER (PI=3.1416) Adhere to the following guidelines:
CHARACTER*(NC) ALPHA the character variable ALPHA has a maximum length of NC characters. The value of NC should be defined in the specification block, prior to the appearance of this statement (see next Section).
8.3 SEQUENCE OF STATEMENTS IN SPECIFICATION BLOCK
The required sequence of statements in the specification block is that which assures that all variable types are declared and all parameters are defined prior to their usage within the block. If this does not occur, errors will result during compilation or execution. For example: LOGICAL FLAG PARAMETER (FLAG=.TRUE.) PARAMETER (NC=10) CHARACTER*(NC) ALPHA10 PARAMETER (ALPHA10='ABCDEFGHIJ') PARAMETER (EX=2.71828,PI=3.1416) PARAMETER (PIO2=PI/2) As shown above:
Alternatively, the specification block shown above can be written as follows: LOGICAL FLAG CHARACTER*(*) ALPHA10 PARAMETER (FLAG=.TRUE.) PARAMETER (ALPHA10='ABCDEFGHIJ') PARAMETER (EX=2.71828,PI=3.1416) PARAMETER (PIO2=PI/2) In this example, the asterisk * has been used as a free length specifier in place of the parameter NC in the CHARACTER statement. This eliminates the need for prior definition of the parameter NC. Sizing DIMENSION Statements with Parameters The PARAMETER statement can be used to conveniently size one or more DIMENSION statements. This is particularly useful when many arrays have the same size, as shown in the set of statements that follow: PARAMETER (NR=10,NC=20,NL=5) DIMENSION A(NR),B(NR),C(NR),D(NR) DIMENSION XX(NR,NC),YY(NR,NC) DIMENSION ZZ(NR,NC,NL) In this example, a change in parameter will cause an automatic and corresponding adjustment in one or more DIMENSION statements. The defining PARAMETER statement must precede the DIMENSION statement that references the parameter. 8.4 INPUT/OUTPUT OF ARRAYS
Often, arrays are read from an input file or written to an output file. This input/output is usually performed with an implied DO list. An implied DO list is a combination of a DO loop and a READ or WRITE in one statement. Using implied DO lists, array input/output can be accomplished by either
Rules governing the interaction between: (1) implied DO lists, (2) combined implied DO list and explicit DO loop, and (3) formatted and unformatted input/output are discussed below. Implied DO Lists in READ/WRITE Statements The following examples illustrate the usage of the implied DO list. Example 1 READ(5,10) (A(J),J=1,10) WRITE(6,20) (B(J),C(J),J=1,20) READ(5,30) ((D(J,K),E(J,K),J=1,10),K=1,5) WRITE(6,40)(((F(J,K,L),J=1,8),K=1,5),L=1,3) The J in A(J),J=1,10 is the control variable of the DO loop (see Section 7.1). Likewise, the K and L are control variables of nested DO loops. Note the required syntax of implied DO lists:
In this example, the first statement reads 10 values of onedimensional array A. The second statement writes 20 pairs of values of onedimensional arrays B and C. The third statement reads 10 × 5 = 50 pairs of values of two dimensional arrays D and E. The fourth statement writes 8 × 5 × 3 = 120 values of threedimensional array F. The format statements have not been included. Example 2 WRITE(6,100) (B(J),C(J),J=2,20,2) READ(5,200) ((D(J,1),E(J,1),J=1,10) WRITE(6,300) ((F(J,K,1),J=1,8),K=1,5) The first statement writes 10 even values of one dimensional arrays B and C. The second statement reads 10 pairs of values of twodimensional arrays D and E (a total of 20 values) and assigns them to the first column of the respective arrays. The third statement writes 8 × 5 = 40 values of threedimensional array F and assigns them to the first layer (the third dimension) of the array. Again, the format statements have not been included. Example 3 DIMENSION A(8) READ(5,400) (A(J),J=1,5) 400 FORMAT(5F10.2) The array A has 8 elements; the first 5 elements are being read, five to a record, following format 400. Example 4 In the special case when all the elements of the array are being read (or written in the case of output), the implied DO list of Example 3 can be simplified as follows: DIMENSION A(8) READ(5,500) A 500 FORMAT(8F10.2) Example 5 DIMENSION B(10,20) READ(5,600) ((B(J,K),J=1,10),K=1,20) 600 FORMAT(10F8.2) In this example, the twodimensional array B contains 10 × 20 = 200 elements, all of which are being read. Input/output of twodimensional arrays can be accom plished in either: (1) column order, or (2) row order. In Example 5, matrix B is being read in column order, i.e., first, column K = 1 is read, with J varying from 1 to 10; then, column K = 2 is read, with J varying from 1 to 10; and so on, until the last column (K = 20) is read. Example 6
DIMENSION B(10,20) READ(5,600) ((B(J,K),K=1,20),J=1,10) 600 FORMAT(10F8.2) This is the same as Example 5, but with matrix B being read in row order, i.e., first, row J= 1 is read, with K vary ing from 1 to 20; then, row J= 2 is read, with K varying from 1 to 20; and so on, until the last row (J= 10) is read. Example 7 DIMENSION B(10,20) READ(5,600) B 600 FORMAT(10F8.2) This example should be compared with Examples 5 and 6 above. The implied DO list has been shortened to contain only the name of the array (B). In this case, the processor expects to read the entire array (10 rows by 20 columns, i.e., 200 values), and the data must be arranged by the programmer and read in column order. Combined Implied DO Lists with Explicit DO Loops Implied DO lists of arrays of two or more dimensions can be written by combining an implied DO list with one or more explicit DO loops. For instance, compare the implied DO list READ(5,100) ((D(J,K),E(J,K),J=1,5),K=1,15) 100 FORMAT(10F8.2)
with the combined implied DO list and explicit DO loop: DO K= 1,15 READ(5,100) (D(J,K),E(J,K),J=1,5) END DO 100 FORMAT(10F8.2) The two forms accomplish the same task of reading 15 records, each containing 5 pairs (10 values). As another example, compare the implied DO list WRITE(6,200)(((F(J,K,L),J=1,8),K=1,5),L=1,3) with the combined implied DO list and explicit DO loop: DO L= 1,3 WRITE(6,200) ((F(J,K,L),J=1,8),K=1,5) END DO or, alternatively, with the combined implied DO list and two explicit DO loops: DO L= 1,3 DO K= 1,5 WRITE(6,200) (F(J,K,L),J=1,8) END DO END DO The three forms may accomplish the task, depending on the nature of the listtoformat interaction (see following section). 8.5 LISTTOFORMAT INTERACTION
The implied DO lists interact with formatted or unformatted input/output. There are four areas of interaction:
Interaction of Implied DO Lists with FORMAT Statements The interaction of implied DO lists with FORMAT statements follows rules similar to those applicable to input/output of variable lists (Section 6.3). The implied DO list retains control, and it executes the transfer of a number of data items equal to the number of subscripted variables on the list, multiplied by the number of values to read or write per variable. For example, READ(5,100) (A(J),B(J),J=1,10) will read two variables (A and B), 10 values per variable, for a total of 20 values transferred. WRITE(6,200) ((C(J,1),D(J,1),J=1,15) will write two variables (C and D), 15 values per variable, for a total of 30 values transferred. READ(5,300) ((F(J,K,1),J=1,5),K=1,8) will read one variable (F), in 5 rows, 8 columns, and 1 layer, for a total of 40 values transferred. In each of the above examples, the implied DO list interacts with its format as one READ/WRITE statement. Therefore, the format is referenced only once to transfer the entire DO list. Note the following:
Example 1 READ(5,100) (A(J),J=1,10) 100 FORMAT(10F8.2) The implied DO list has 10 values of array A, and it is connected to format 100, whose field descriptor specifies 10 real fields of 8 characters each. The number of values in the implied DO list (10) exactly matches the number of fields specified in the format (10). Ten real values of array A will be read under the specified format. Example 2 READ(5,200) (B(J),J=1,5) 200 FORMAT(8F10.2) The implied DO list has 5 values of array B, and it is connected to format 200, whose field descriptor specifies 8 real fields of 10 characters each. The field descriptor list is longer than the implied DO list. Therefore, 5 real values of array B will be read under the specified format. The remaining unused three fields (8  5 = 3) will be ignored. Example 3 READ(5,300) (C(J),J=1,20) 300 FORMAT(10F8.2) The implied DO list has 20 values of array C, and it is connected to format 300, whose field descriptor specifies 10 real fields of 8 characters each. The field descriptor is shorter than the implied DO list; therefore, the format is interpreted as typical. Twenty real values of array C will be read under the specified format, ten in each of two data records. Example 4 WRITE(6,400) (D(K),E(K),K=1,120) 400 FORMAT(1X,12F10.0) The implied DO list has two variables (arrays D and E), and 120 values per variable, for a total of 240 paired values. It is connected to format 400, whose field descrip tor specifies 12 real fields of 10 characters each. The field descriptor list is shorter than the implied DO list; there fore, the format is interpreted as typical. Onehundred andtwenty pairs of real values of arrays D and E will be written under the specified format, six pairs per record, for a total of twenty records. Example 5 WRITE(6,500)((F(J,K,1),J=1,8),K=1,4) 500 FORMAT(1X,8E15.6) The implied DO list has one threedimensional variable F, with 8 rows, 4 columns, and only 1 layer, for a total of 32 values. It is connected to format 500, whose field descriptor specifies 8 real E fields of 15 characters each. The field descriptor is shorter than the implied DO list; therefore, the format is interpreted as typical. Thirtytwo values of real threedimensional array F will be written under the specified format, eight values per record, for a total of four records. The first record contains all J values for K= 1; the second all J values for K= 2; and so on. Example 6 WRITE(6,500)((F(J,K,1),J=1,4),K=1,8) 500 FORMAT(1X,8E15.6) This example is similar to Example 5. The field descriptor list is shorter than the implied DO list; therefore, the format is interpreted as typical. Thirtytwo values of real threedimensional array F will be written, 8 values per record, for a total of 4 records. However, unlike Example 5, the first record contains all J values for K= 1, followed by all J values for K= 2; the second record contains all J values for K= 3, followed by all J values for K= 4; and so on. Example 7 WRITE(6,510)((F(J,K,1),J=1,4),K=1,8) 510 FORMAT(1X,E15.6) This example is similar to Examples 5 and 6, except that the format specification contains only one field descriptor (E15.6). The field descriptor list is shorter than the implied DO list; therefore, the format is interpreted as typical. Thirtytwo values of real threedimensional array F will be written, one per record, for a total of thirtytwo records. The first record contains the value for J= 1 and K= 1; the second for J= 2 and K= 1; the third for J= 3 and K=1; and so on. Interaction of Implied DO Lists with Unformatted READ and WRITE The interaction of implied DO lists with unformatted READ and WRITE follows rules similar to those applicable to input/output of variable lists (Section 6.3). Control remains with the implied DO list, which executes the transfer of a number of data items equal to the number of subscripted variables on the list, multiplied by the number of values to read or write per variable. For example, READ(5,*) (A(J),B(J),J=1,15) will read two variables (A and B), 15 values per variable, for a total of 15 pairs = 30 values transferred, in free format (see Section 2.5 for unformatted input/output rules). The processor will read as many records as needed to accomplish the transfer of 30 values. At least one record will be read. In this case, it is likely that several records will be read. Likewise, the following example WRITE(6,*) ((C(J,K),J=1,4),K=1,8) will write a twodimensional matrix (C), of 4 rows by 8 columns, for a total of 32 values transferred, in free format. The processor will write as many records as needed to accomplish the transfer of 32 values. Assuming that the processor writes five values per record under free format, this example will write seven records, the first six with five values each, and the last one with the two remaining values. Writing arrays in free format may change the character of the array (visually confuse rows and columns) and, therefore, is not recommended. Arrays, particularly two and threedimensional arrays, should always be written following a format. Interaction of Combined Implied DO Lists and Explicit DO Loops with FORMAT Statements The interaction of combined implied DO lists and explicit DO loops with FORMAT statements follows rules similar to those applicable to that of implied DO lists with FORMAT statements. Control remains with the implied DO list, which executes the transfer of a number of data items equal to the number of subscripted variables on the list, multiplied by the number of values to read or write per variable. There is, however, one important difference. Unlike the implied DO list, which interacts with the FORMAT as one statement, the combined implied DO list and explicit DO loops interact with the FORMAT as two or more state ments. This is because the FORMAT is referenced as many times as required by the explicit DO loops. Example 1 DO K= 1,4 READ(5,100) (A(J,K),J=1,8) END DO 100 FORMAT(8F10.2) The combined implied DO list and explicit DO loop has one twodimensional variable (A), of 8 rows by 4 columns, for a total of 8 × 4 = 32 values. The implied DO list is connected to format 100, whose field descriptor specifies 8 real fields of 10 characters each. Notice that the number of values in the implied DO list (8) matches exactly the number of fields specified in the format (8). Eight real values of array A will be read with the implied DO loop under the specified format. The format will be referenced four times by the explicit DO loop, transfer ring 4 data records, 8 values per record, for a total of 4 X 8 = 32 values. The first record contains all eight J values for K= 1; the second all eight J values for K= 2; and so on. Example 2 DO K= 1,4 READ(5,200) (A(J,K),J=1,6) END DO 200 FORMAT(8F10.2) This is similar to Example 1, but the twodimensional variable A has 6 rows by 4 columns, for a total of 6 × 4 = 24 values. The implied DO list is connected to format 200, whose field descriptor specifies 8 real fields of 10 characters each. The number of values specified in the format (8) is longer than the number of values in the implied DO list (6), which takes precedence. Six real values of array A will be read in the first record under the specified format; the remaining two fields will be ignored. The format will be referenced four times by the explicit DO loop, transferring 4 data records, 6 values per record, for a total of 4 × 6 = 24 values. The first record contains all six J values for K= 1; the second all six J values for K= 2; and so on. Example 3 DO K= 1,4 READ(5,300) (A(J,K),J=1,8) END DO 300 FORMAT(4F10.2) This is similar to Example 1, but uses a slightly different format. The implied DO list is connected to format 300, whose field descriptor specifies 4 real fields of 10 characters each. The number of values specified in the format (4) is shorter than the number of values in the implied DO list (8); therefore, the format is interpreted as typical. Four real values of array A will be read with the implied DO loop in the first record, and the remaining four in the second record. The format will be referenced four times by the explicit DO loop, transferring 8 data records, 4 values per record, for a total of 8 × 4 = 32 values. The first and second records contains all eight J values for K= 1; the third and fourth all eight J values for K= 2; and so on. Example 4 DO L= 1,2 DO K= 1,4 WRITE(6,400) (B(J,K,L),J=1,6) END DO END DO 400 FORMAT(1X,8F10.3) The combined implied DO list and two nested explicit DO loops have one threedimensional variable (B), of 6 rows, 4 columns, and 2 layers, for a total of 6 × 4 × 2 = 48 values. The implied DO list is connected to format 400, whose field descriptor specifies 8 real fields of 10 characters each. The number of values specified in the format (8) is longer than the number of values in the implied DO list (6), which takes precedence. Six real values of array B will be written in the first record under the specified format; the remaining two fields will be ignored. The format will be referenced 2 × 4 = 8 times by the nested DO loops, transferring 8 data records, 6 values per data record, for a total of 8 × 6 = 48 values. The first record contains all six J values for K =1 and L = 1; the second all six J values for K= 2 and L= 1; and so on. Example 5 DO L= 1,2 WRITE(6,500) ((B(J,K,L),J=1,6),K=1,4) END DO 500 FORMAT(1X,8F10.3) This is similar to Example 4, but uses only one explicit DO loop instead of two. The implied DO list is connected to format 500, whose field descriptor specifies 8 real fields of 10 characters each. The number of values specified in the format (8) is shorter than the number of values in the implied DO list (6 × 4 = 24); therefore, the format is interpreted as typical. The implied DO list will write twentyfour real values of array B, eight values per record, making a total of three records. The format will be referenced twice by the explicit DO loop, each time transferring 3 data records and 8 values per record, for a total of 2 × 3 × 8 = 48 values. The first record contains all six J values for K = 1 and L = 1, and the first two J values for K = 2 and L = 1; the second record contains the remaining four values for K = 2 and L = 1, and the first four values for K = 3 and L = 1, and so on. This type of listtoformat interaction will change the character of the array (visually confuse rows, columns, and layers), and therefore, is not recommended. A better way of writing array B is shown in the following example. Example 6 DO L= 1,2 WRITE(6,600) ((B(J,K,L),J=1,6),K=1,4) END DO 600 FORMAT(1X,6F10.3) This differs from Example 5 in that it uses a slightly different format. The implied DO list is connected to format 600, whose field descriptor specifies 6 real fields of 10 characters each. The number of values specified in the format (6) is shorter than the number of values in the implied DO list (6 x 4 = 24); therefore, the format is interpreted as typical. The implied DO list will write twentyfour real values of array B, six values per record, for a total of four records. The format will be referenced twice by the explicit DO loop, each time transferring 4 data records and 6 values per record, making a total of 2 × 4 × 6 = 48 values. The first record contains all six J values for K= 1 and L= 1; the second contains all six J values for K= 2 and L= 1; and so on. Unlike Example 5, this type of listtoformat interaction does not alter the visual character of the array. Interaction of Combined Implied DO Lists and Explicit DO Loops with Unformatted READ and WRITE The interaction of combined implied DO lists and explicit DO loops with unformatted READ and WRITE follows rules similar to those applicable to implied DO lists. As before, control remains with the implied DO list, which executes the transfer of a number of data items equal to the number of subscripted variables on the list, multiplied by the number of values to read or write per variable. However, unlike the implied DO list, which interacts with the free format as one statement, the combined implied DO list and explicit DO loops interact with the free format as two or more statements. Example 1 DO K= 1,4 READ(5,*) (A(J,K),J=1,8) END DO The combined implied DO list and explicit DO loop has one twodimensional variable, of 8 rows by 4 columns, for a total of 8 × 4 = 32 values. Eight real values of array A will be read by the implied DO loop in free format. The free format will be referenced 4 times by the explicit DO loop, transferring a total of 8 × 4 = 32 values. At least 4 records will be read. As many as 32 records could be read (in case that there is only one value per record). Example 2 DO 20 L= 1,2 DO 20 K= 1,4 WRITE(6,*) (B(J,K,L),J= 1,6) END DO END DO The combined implied DO list and two nested explicit DO loops have one threedimensional variable (B), of 6 rows, 4 columns, and 2 layers, for a total of 6 × 4 × 2 = 48 values. Six real values of array B will be written by the implied DO loop in free format. The free format will be referenced 2 × 4 = 8 times by the nested DO loops, transferring at least 8 records, with up to 6 values per record, for a total of 8 × 6 = 48 values. Each record is written into at least one line. Remember that writing arrays in free format is not recommended because it may alter their appearance in an unpredictable manner.
8.6 IMPLIED DO LISTS IN DATA STATEMENTS
Often it is necessary to use DATA statements to provide initial values of one or more arrays. For this purpose, the implied DO list is included in a DATA statement, as illustrated by the following examples: Example 1 DIMENSION A(10) DATA (A(J),J= 1,5) /1.,4.,3.,10.,25./ This example considers an array A of 10 elements. The first 5 elements of the array are initialized in a DATA statement using an implied DO list. Example 2 DIMENSION A(5) DATA (A(J),J= 1,5) /1.,4.,3.,10.,25./ The array A has 5 elements. The entire array is initialized in a DATA statement using an implied DO list. Example 3 DIMENSION A(5) DATA A /1.,4.,3.,10.,25./ This is similar to Example 2. Since the entire array is being initialized, the reference to the implied DO list in the DATA statement may be omitted. Example 4 DIMENSION B(4,6) DATA *((B(J,K),K=1,3),J=1,2) /3.,4.,7.,2.,9.,0.5/ The twodimensional array B has 4 rows by 6 columns, for a total of 4 × 6 = 24 values. Six (2 × 3 = 6) values of the array are being initialized. Note that the array is being initialized in row order, i.e., first, all K values of row J= 1, second, all K values of row J= 2. The matrix B is stored as follows:
Example 5 DIMENSION B(2,3) DATA *((B(J,K),K=1,3),J=1,2)/3.,4.,7.,2.,9.,0.5/ This is similar to Example 4, with the difference that the entire array is being initialized. As with Example 4, the array is being initialized in row order, i.e., first, all K values of row J= 1, second, all K values of row J= 2. Example 6 DIMENSION B(2,3) DATA *(B(J,K),J=1,2),K=1,3)/3.,4.,7.,2.,9.,0.5/ This is similar to Example 5, with the difference that the array is being initialized in column order, i.e., first, all J values of column K= 1; second, all J values of column K= 2; third, all J values of column K= 3. The matrix B is stored as follows:
Example 7 DIMENSION B(2,3) DATA B /3.,4.,7.,2.,9.,0.5/ This is the same as Example 6. The array has 6 values (2 × 3), and the DATA statement lists 6 values, i.e., the entire array is being initialized. In this case, the reference to the implied DO list in the DATA statement may be omitted. If a DATA statement contains an array, and the implied DO list is missing, the array is assumed to be in column order, and is stored as such. Example 8 DIMENSION C(5,12) DATA C /60*1./ The entire array C, consisting of 5 × 12 = 60 values, has been initialized with an implied DO list in a DATA statement. A repeat counter 60, placed within the delimiting slashes and preceding the asterisk, is used to express that all elements are being initialized with the value 1. As with Example 7, the reference to the implied DO list has been omitted. Example 9 DIMENSION C(5,12) DATA C /28*1.,32*0./ This is similar to Example 8. The array C consists of 5 × 12= 60 values. The entire array is being initialized with an implied DO list. The reference to the implied DO list has been omitted. A repeat counter is used to express that the first 28 elements are being initialized with the value 1., and the remaining 32 with the value 0. The array C is stored in column order as shown below.
8.7 SORTING OF ARRAYS THE BUBBLE SORT
When working with arrays, you may need to sort the entries to arrange them in a specific order. For instance, consider the following onedimensional array A: 12. 45. 23. 87. 51. 20. 11. To arrange it in ascending order, i.e., to produce 11. 12. 20. 23. 45. 51. 87. a sorting procedure must be implemented. The bubble sort is a commonly used sorting procedure. In a bubble sort, the values of two variables (addresses) A(J) and A(J+1) are to be interchanged. First, a temporary variable TEMP is created by assigning the value of A(J) to TEMP. Second, the value of A(J+1) is assigned to A(J). Third, the value of TEMP, i.e., the value of A(J), is assigned to A(J+1). This procedure effectively switches the values of A(J) and A(J+1). The following program implements a bubble sort for the previous example. Example Program: Bubble Sort
In this example program, each execution of the outer loop positions the largest value to the right of the array. Complete execution of the program sorts the array in ascending order. 8.8 EXAMPLE PROGRAM
Matrix Multiplication This program reads an array A of 2 rows by 3 columns, and an array B of 3 rows by 2 columns, and multiplies the arrays to obtain C, of 2 rows by 2 columns. [Note that in order to multiply A × B, the number of columns of A (three rows) has to be equal to the number of rows of B (three columns)]. Array C has the same number of rows as A (two rows) and the same number of columns as B (two columns). Note the features of this program:
Example Program: Matrix Multiplication
The input arrays are: A= 1. 2. 3. B= 7. 1. 4. 5. 6. 8. 2. 9. 3. The output array is: C= 50. 14. 122. 32. For instance, the first row and column of the output
array C is: 8.9 SUMMARY
This chapter describes subscripted variables, which can take an array of values.
PROBLEMS
1. Solve Problem 4.5 (water utility billing) using formatted input/output, subscripted variables, and two indexed DO loops, one to calculate the values and another to print them. 2. Solve Problem 4.10 (electric utility billing) using formatted input/output, subscripted variables, and two indexed DO loops, one to cal culate the values and another to print them. 3. Solve Problem 6.3 (natural log table) using subscripted variables. Use a twodimensional array, nested DO loops, and combined explicit DO loops and implied DO lists. 4. Solve Problem 6.7 (table of hyperbolic sines) using using subscripted variables. Use a twodimensional array, nested DO loops, and combined explicit DO loops and implied DO lists. 5. Solve Problem 6.11 (radiantodegree conversion table) using subscripted variables. Use two indexed DO loops, one to calculate the values and another to print them. 6. Solve Problem 7.12 (annuity table) using a onedimensional array for the annuity factor A/P. 7. Solve Problem 7.12 (annuity table) using a twodimensional array for the annuity factor A/P. Calculate and print the array in two separate DO loops. 8. Solve Problem 7.19 using subscripted variables. Include the calculation of the median, the value which divides the distribution into two equal parts (half of the values are lower than the median). 9. Write a program to read a twodimensional array of M rows by N columns, and to search for and report the entry having the minimum absolute value. Test your program with the following array: 11. 34. 67. 12. 23. 76. 12. 10.5 43. 78. 112. 13. 12. 56.5 120. 56. 23. 78. 90. 111. 90.1 10. Write a program to read a twodimensional array of M rows by N columns, to sum all rows and all columns, and to report the row or column with the minimum sum. As an example, the output should read: ROW 3 HAS THE MINIMUM SUM, EQUAL TO 34.5. Test your program with the input array of Problem 8.9. 11. Write a program to read from an input file a twodimensional array of M rows by N columns, to sort all rows in descending order, and print the sorted array to an output file. Test your program with the input array of Problem 8.9. 12. Write a program to read from an input file a twodimensional array of M rows by N columns, to sort all columns in ascending order, and print the sorted array to an output file. Test your program with the input array of Problem 8.9. 13. Write a program to read a square matrix of size N, and to calculate and report the average of the entries in the outside rows and columns, and the average of the inside entries. Test your program with the following matrix: 10. 12. 13. 12. 15. 18. 11. 23. 21. 17. 13. 10. 12. 21. 10. 16. 12. 14. 12. 13. 14. 16. 12. 20. 10. 12. 14. 21. 22. 21. 15. 12. 13. 23. 21. 20. 14. Write a program to read a square matrix A of size N (for N even), and to partition the matrix into four square submatrices each of size N/2. If N is not even, print an appropriate message and stop execution. Calculate and report a square matrix B, of size 2, with each entry being the average of all entries in each of the four square submatrices. Test your program with the input array of Problem 8.13. 10. 12. 13. 12. 15. 18. 11. 23. 21. 17. 13. 10. 12. 21. 10. 16. 12. 14. 12. 13. 14. 16. 12. 20. 10. 12. 14. 21. 22. 21. 15. 12. 13. 23. 21. 20. 15. Solve Problem 7.17 (numeral design) using subscripted variables. 16. Write a program to print the following numeric pattern:1012345678
Use subscripted variables, and a combined implied DO list and explicit DO loop. 17. Write a program to calculate the parameters a, b, and c of the nonlinear equation z= ax^{b}y^{c}, given three data arrays x, y, and z, of n elements each. Taking u= log x, v= log y, and w= log z, use the following regression equations (Σ is the summation from 1 to n): b= (AC  BE)/(A^{2}  DE) c= (B  bD)/A a= log^{1} [(Σw  b Σu  c Σv)/n] in which: A= n Σuv  Σu Σv B= n Σwu  Σw Σu C= n Σwv  Σw Σv D= n Σ(u^{2}) (Σu)^{2} E= n Σ(v^{2}) (Σv)^{2} Test your program with the following data:
18. Eight persons take a TRUE or FALSE test containing ten questions. Write a program to calculate the number of correct answers for each person. Test your program with the following data: KEY T T F F T F T F F F JONES T T T F F F T F T F LONG F F F F F T T F T F MARTIN F F F F T T F F T T PETERS F F F F T F T F T F DALEY F F F F T F T F T F PEREZ T T T F F F T F F T FONG F F F F T T F T F T JACKSON T T F F F T T T F T Your output should read, for example: JONES NO. OF CORRECT ANSWERS: 7

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FORTRAN FOR SCIENTISTS AND ENGINEERS VICTOR M. PONCE • ONLINE EDITION •  
Copyright © 2014 • Victor M. Ponce • All rights reserved. 