Fortran 90 overview

1

Fortran 90 Overview

J.E. Akin, Copyright 1998

This overview of Fortran 90 (F90) features is presented as a series of tables that illustrate the syntax
and abilities of F90. Frequently comparisons are made to similar features in the C++ and F77 languages
and to the Matlab environment.
These tables show that F90 has significant improvements over F77 and matches or exceeds newer
software capabilities found in C++ and Matlab for dynamic memory management, user defined data
structures, matrix operations, operator definition and overloading, intrinsics for vector and parallel pro-
cessors and the basic requirements for object-oriented programming.
They are intended to serve as a condensed quick reference guide for programming in F90 and for
understanding programs developed by others.

List of Tables

1 Comment syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Intrinsic data types of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Arithmetic operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4 Relational operators (arithmetic and logical) . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Precedence pecking order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Colon Operator Syntax and its Applications . . . . . . . . . . . . . . . . . . . . . . . . 5
7 Mathematical functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
8 Flow Control Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
9 Basic loop constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
10 IF Constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
11 Nested IF Constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
12 Logical IF-ELSE Constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
13 Logical IF-ELSE-IF Constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
14 Case Selection Constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
15 F90 Optional Logic Block Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
16 GO TO Break-out of Nested Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
17 Skip a Single Loop Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
18 Abort a Single Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
19 F90 DOs Named for Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
20 Looping While a Condition is True . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
21 Function definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
22 Arguments and return values of subprograms . . . . . . . . . . . . . . . . . . . . . . . 12
23 Defining and referring to global variables . . . . . . . . . . . . . . . . . . . . . . . . . 12
24 Bit Function Intrinsics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
25 The ACSII Character Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
26 F90 Character Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
27 How to type non-printing characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
28 Referencing Structure Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
29 Defining New Types of Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
30 Nested Data Structure Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
31 Declaring, initializing, and assigning components of user-defined datatypes . . . . . . . 14
32 F90 Derived Type Component Interpretation . . . . . . . . . . . . . . . . . . . . . . . 15
33 Definition of pointers and accessing their targets . . . . . . . . . . . . . . . . . . . . . . 15
34 Nullifing a Pointer to Break Association with Target . . . . . . . . . . . . . . . . . . . . 15
35 Special Array Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
36 Array Operations in Programming Constructs . . . . . . . . . . . . . . . . . . . . . . . 16
37 Equivalent Fortran90 and M ATLAB Intrinsic Functions . . . . . . . . . . . . . . . . . . 17
38 Truncating Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
39 F90 WHERE Constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
40 F90 Array Operators with Logic Mask Control . . . . . . . . . . . . . . . . . . . . . . 19
41 Array initialization constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
42 Array initialization constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3

LIST OF TABLES 3

43 Elementary matrix computational routines . . . . . . . . . . . . . . . . . . . . . . . . . 20
44 Dynamic allocation of arrays and pointers . . . . . . . . . . . . . . . . . . . . . . . . . 21
45 Automatic memory management of local scope arrays . . . . . . . . . . . . . . . . . . . 21
46 F90 Single Inheritance Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
47 F90 Selective Single Inheritance Form . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
48 F90 Single Inheritance Form, with Local Renaming . . . . . . . . . . . . . . . . . . . . 22
49 F90 Multiple Selective Inheritance with Renaming . . . . . . . . . . . . . . . . . . . . 22

4 LIST OF TABLES

Language Syntax Location
M ATLAB % comment (to end of line) anywhere
C /*comment*/ anywhere
F90 ! comment (to end of line) anywhere
F77 * comment (to end of line) column 1

Table 1: Comment syntax.

Storage M ATLAB a C++ F90 F77
byte char character:: character
integer int integer:: integer
single precision float real:: real
double precision double real*8:: double precision
b
complex complex:: complex
Boolean bool logical:: logical
argument parameter:: parameter
pointer * pointer::
structure struct type::
a M ATLAB 4 requires no variable type declaration; the only two distinct types in M ATLAB are strings and reals (which include

complex). Booleans are just 0s and 1s treated as reals. M ATLAB 5 allows the user to select more types.
b There is no specific data type for a complex variable in C++; they must be created by the programmer.

Table 2: Intrinsic data types of variables.

Description M ATLAB a C++ Fortranb
addition + + +
subtractionc - - -
multiplication * and .* * *
division / and ./ / /
exponentiation ˆ and .ˆ powd **
remainder %
increment ++
decrement --
parentheses (expres- () () ()
sion grouping)
a When doing arithmetic operations on matrices in M ATLAB , a period (‘.’) must be put before the operator if scalar arithmetic

is desired. Otherwise, M ATLAB assumes matrix operations; figure out the difference between ‘*’ and ‘.*’. Note that since matrix
and scalar addition coincide, no ‘.+’ operator exists (same holds for subtraction).
b Fortran 90 allows the user to change operators and to define new operator symbols.
c In all languages the minus sign is used for negation (i.e., changing sign).
¨¦¤¢
§ ¥ £ ¡
d In C++ the exponentiation is calculated by function pow .

Table 3: Arithmetic operators.

LIST OF TABLES 5

Description M ATLAB C++ F90 F77
Equal to == == == .EQ.
Not equal to ˜= != /= .NE.
Less than < < < .LT.
Less or equal <= <= <= .LE.
Greater than > > > .GT.
Greater or equal >= >= >= .GE.
Logical NOT ˜ ! .NOT. .NOT.
Logical AND & && .AND. .AND.
Logical inclusive OR ! || .OR. .OR.
Logical exclusive OR xor .XOR. .XOR.
Logical equivalent == == .EQV. .EQV.
Logical not equivalent ˜= != .NEQV. .NEQV.

Table 4: Relational operators (arithmetic and logical).

M ATLAB
C++ Operators F90 Operatorsa F77 Operators
Operators
() () [] -> . () ()
+ - ! ++ -- + ** **
- * & (type)
sizeof
* / * / % * / * /
+ -b + -b + -b + -b
< <= > >= << >> // //
== ˜= < <= > => == /= < <= > .EQ. .NE.
>= .LT. .LE.
.GT. .GE.
˜ == != .NOT. .NOT.
& && .AND. .AND.
| || .OR. .OR.
= | .EQV. .NEQV. .EQV. .NEQV.
?:
= += -= *= /=
%= &= ˆ= |=
<<= >>=
,
a User-deﬁned unary (binary) operators have the highest (lowest) precedence in F90.
b These are binary operators representing addition and subtraction. Unary operators + and - have higher precedence.

Table 5: Precedence pecking order.

B = Beginning, E = Ending, I = Increment

Syntax F90 M ATLAB Use F90 M ATLAB
Default B:E:I B:I:E Array subscript ranges yes yes
Character positions in a string yes yes

B B: B:
Loop control no yes
¡

E :E :E
Full range : : Array element generation no yes

Table 6: Colon Operator Syntax and its Applications.

6 LIST OF TABLES

Description M ATLAB C++ F90 F77
exponential exp(x) exp(x) exp(x) exp(x)
natural log log(x) log(x) log(x) log(x)
base 10 log log10(x) log10(x) log10(x) log10(x)
square root sqrt(x) sqrt(x) sqrt(x) sqrt(x)
raise to power ( ) ¡ ¢ x.ˆr pow(x,r) x**r x**r
absolute value abs(x) fabs(x) abs(x) abs(x)
smallest integer x £ ceil(x) ceil(x) ceiling(x)
largest integer x ¤ floor(x) floor(x) floor(x)
division remainder rem(x,y) fmod(x,y) mod(x,y) ¥ mod(x,y)
modulo modulo(x,y)a
complex conjugate conj(z) conjg(z) conjg(z)
imaginary part imag(z) imag(z) aimag(z)
drop fraction fix(x) aint(x) aint(x)
round number round(x) nint(x) nint(x)
cosine cos(x) cos(x) cos(x) cos(x)
sine sin(x) sin(x) sin(x) sin(x)
tangent tan(x) tan(x) tan(x) tan(x)
arc cosine acos(x) acos(x) acos(x) acos(x)
arc sine asin(x) asin(x) asin(x) asin(x)
arc tangent atan(x) atan(x) atan(x) atan(x)
arc tangentb atan2(x,y) atan2(x,y) atan2(x,y) atan2(x,y)
hyperbolic cosine cosh(x) cosh(x) cosh(x) cosh(x)
hyperbolic sine sinh(x) sinh(x) sinh(x) sinh(x)
hyperbolic tangent tanh(x) tanh(x) tanh(x) tanh(x)
hyperbolic arc cosine acosh(x)
hyperbolic arc sine asinh(x)
hyperbolic arctan atanh(x)
a Differ
©§¡
¨ ¦
for . ¡ ¥ £
b atan2(x,y) is used to calculate the arc tangent of in the range . The one-argument function atan(x)
¡ £
computes the arc tangent of in the range .
Table 7: Mathematical functions.

LIST OF TABLES 7

Description C++ F90 F77 M ATLAB
Conditionally execute statements if if if if
¡ ¢ end if end if end

Loop a speciﬁc number of times for k=1:n do k=1,n do # k=1,n for k=1:n
¡ ¢ end do # continue end

Loop an indeﬁnite number of times while do while — while
¡ ¢ end do — end

Terminate and exit loop break exit go to break

Skip a cycle of loop continue cycle go to —
Display message and abort error() stop stop error

Return to invoking function return return return return

Conditional array action — where — if

Conditional alternate statements else else else else
else if elseif elseif elseif

Conditional array alternatives — elsewhere — else
— — — elseif

Conditional case selections switch
¡ ¢ select case if if
end select end if end

Table 8: Flow Control Statements.

Loop M ATLAB C++ Fortran
Indexed loop for index=matrix for (init;test;inc)
do index=b,e,i
statements statements
end statements
¡ end do

Pre-test loop while test while (test)
do while (test)
statements statements
¡ statements
end end do

Post-test loop do
do
statements
¡ statements
while (test) if (test) exit
end do

Table 9: Basic loop constructs.

8 LIST OF TABLES

M ATLAB Fortran C++
if l expression IF (l expression) THEN if (l expression)

true group true group
end END IF true group;
¡
IF (l expression) true statement if (l expression)
true state-
ment;

Table 10: IF Constructs. The quantity l expression means a logical expression having a value that
is either TRUE of FALSE. The term true statement or true group means that the statement or group
of statements, respectively, are executed if the conditional in the if statement evaluates to TRUE.

M ATLAB Fortran C++
if l expression1 IF (l expression1) THEN if (l expression1)

true group A true group A
if l expression2 IF (l expression2) THEN true group A
true group B true group B if (l expression2)

end END IF
true group C true group C true group B
¡
end END IF
statement group D statement group D true group C
¡
statement group D

Table 11: Nested IF Constructs.

M ATLAB Fortran C++
if l expression IF (l expression) THEN if (l expression)

else ELSE true group A
¡
false group B false group B
end END IF else

false group B
¡

Table 12: Logical IF-ELSE Constructs.

M ATLAB Fortran C++
if l expression1 IF (l expression1) THEN if (l expression1)

elseif l expression2 ELSE IF (l expression2) THEN true group A
¡
true group B true group B
elseif l expression3 ELSE IF (l expression3) THEN else if (l expression2)

true group C true group C
else ELSE true group B
¡
default group D default group D
end END IF else if (l expression3)

true group C
¡
else
default group D
¡

Table 13: Logical IF-ELSE-IF Constructs.

LIST OF TABLES 9

F90 C++
SELECT CASE (expression) switch (expression)

CASE (value 1)
group 1 case value 1 :
CASE (value 2) group 1
group 2 break;
.
. case value 2 :
. group 2
CASE (value n) break;
group n .
CASE DEFAULT .
.
default group case value n :
END SELECT group n
break;
default:
default group
¡ break;

Table 14: Case Selection Constructs.

F90 Named IF F90Named SELECT
name: IF (logical 1) THEN name: SELECT CASE (expression)
true group A CASE (value 1)
ELSE IF (logical 2) THEN group 1
true group B CASE (value 2)
ELSE group 2
default group C CASE DEFAULT
ENDIF name default group
END SELECT name

Table 15: F90 Optional Logic Block Names.

Fortran C++
DO 1 ...
DO 2 ...
for (...)
for (...)

... ...
IF (disaster) THEN if (disaster)
GO TO 3 go to error
END IF ¡¡ ...
...
2 END DO
1 END DO error:
3 next statement

Table 16: GO TO Break-out of Nested Loops. This situation can be an exception to the general recom-
mendation to avoid GO TO statements.

10 LIST OF TABLES

F77 F90 C++
DO 1 I = 1,N DO I = 1,N for (i=1; in; i++)

... ...
IF (skip condi- IF (skip condi- if (skip condition)
tion) THEN tion) THEN continue; // to next
GO TO 1 CYCLE ! to next I else if
ELSE ELSE false group
false group false group end
END IF END IF ¡
1 continue END DO

Table 17: Skip a Single Loop Cycle.

F77 F90 C++
DO 1 I = 1,N DO I = 1,N for (i=1; in; i++)

IF (exit condi- IF (exit condi-
tion) THEN tion) THEN if (exit condition)
GO TO 2 EXIT ! this do break;// out of loop
ELSE ELSE else if
false group false group false group
END IF END IF end
¡
1 CONTINUE END DO
2 next statement next statement next statement

Table 18: Abort a Single Loop.

main: DO ! forever
test: DO k=1,k max
third: DO m=m max,m min,-1
IF (test condition) THEN
CYCLE test ! loop on k
END IF
END DO third ! loop on m
fourth: DO n=n min,n max,2
IF (main condition) THEN
EXIT main ! forever loop
END DO fourth ! on n
END DO test ! over k
END DO main
next statement

Table 19: F90 DOs Named for Control.

LIST OF TABLES 11

M ATLAB C++
initialize test initialize test
while l expression while (l expression)

true group
change test true group
end change test
¡

F77 F90
initialize test initialize test
# continue do while (l expression)
IF (l expression) THEN true group
true group change test
change test end do
go to #
END IF

Table 20: Looping While a Condition is True.

Function
M ATLABa C++ Fortran
Type
program statements main(argc,char **argv)
program main
[y1...yn]=f(a1,...,am) type y
[end of file] statements type a1,...,type am
y = f(a1,I,am); ¡ statements
y = f(a1,...,am)
call s(a1,...,am)
end program

subroutine void f subroutine s(a1,...,am)
(type a1,...,type am)
type a1,...,type am
statements
statements
¡ end

function function [r1...rn] type f (type a1,...,type am) function f(a1,...,am)
=f(a1,...,am) type f

statements ¡

statements type a1,...,type am
statements
end

a Every function or program in M ATLAB must be in separate files.

Table 21: Function definitions. In each case, the function being defined is named f and is called with m
arguments a1,...,am.

12 LIST OF TABLES

One-Input, One-Result Procedures
M ATLAB function out = name (in)
F90 function name (in) ! name = out
function name (in) result (out)
C++ name (in, out)

Multiple-Input, Multiple-Result Procedures
M ATLAB function [inout, out2] = name (in1, in2, inout)
F90 subroutine name (in1, in2, inout, out2)
C++ name(in1, in2, inout, out2)

Table 22: Arguments and return values of subprograms.

Global Variable Declaration
M ATLAB global list of variables
F77 common /set name/ list of variables
F90 module set name
save
type (type tag) :: list of variables
end module set name
C++ extern list of variables

Access to Global Variables
M ATLAB global list of variables
F77 common /set name/ list of variables
F90 use set name, only subset of variables
use set name2 list of variables
C++ extern list of variables

Table 23: Deﬁning and referring to global variables.

Action C++ F90
Bitwise AND iand
Bitwise exclusive OR ieor

Bitwise exclusive OR ¡ ior
Circular bit shift ishftc
Clear bit ibclr
Combination of bits mvbits
Extract bit ibits
Logical complement ¢ not
Number of bits in integer sizeof bit size
Set bit ibset
Shift bit left £ ishft
Shift bit right ¤ ishft
Test on or off btest
Transfer bits to integer transfer

Table 24: Bit Function Intrinsics.

LIST OF TABLES 13

0 NUL 1 SOH 2 STX 3 ETX 4 EOT 5 ENQ 6 ACK 7 BEL
8 BS 9 HT 10 NL 11 VT 12 NP 13 CR 14 SO 15 SI
16 DLE 17 DC1 18 DC2 19 DC3 20 DC4 21 NAK 22 SYN 23 ETB
24 CAN 25 EM 26 SUB 27 ESC 28 FS 29 GS 30 RS 31 US
32 SP 33 ! 34 35 # 36 $ 37 % 38 39 ’
40 ( 41 ) 42 * 43 + 44 , 45 - 46 . 47 /
48 0 49 1 50 2 51 3 52 4 53 5 54 6 55 7
56 8 57 9 58 : 59 ; 60 61 = 62 63 ?
64 @ 65 A 66 B 67 C 68 D 69 E 70 F 71 G
72 H 73 I 74 J 75 K 76 L 77 M 78 N 79 O
80 P 81 Q 82 R 83 S 84 T 85 U 86 V 87 W
88 X 89 Y 90 Z 91 [ 92 93 ] 94 ˆ 95 _
96 ‘ 97 a 98 b 99 c 100 d 101 e 102 f 103 g
104 h 105 i 106 j 107 k 108 l 109 m 110 n 111 o
112 p 113 q 114 r 115 s 116 t 117 u 118 v 119 w
120 x 121 y 122 z 123 { 124 | 125 } 126 ˜ 127 DEL
Table 25: The ACSII Character Set.

ACHAR (I) Character number I in ASCII collating set
ADJUSTL (STRING) Adjust left
ADJUSTR (STRING) Adjust right
CHAR (I)

Character I in processor collating set
IACHAR (C) Position of C in ASCII collating set
ICHAR (C) Position of C in processor collating set
INDEX (STRING, SUBSTRING)a Starting position of a substring
LEN (STRING) Length of a character entity
LEN TRIM (STRING) Length without trailing blanks
LGE (STRING A, STRING B) Lexically greater than or equal
LGT (STRING A, STRING B) Lexically greater than
LLE (STRING A, STRING B) Lexically less than or equal
LLT (STRING A, STRING B) Lexically less than
REPEAT (STRING, NCOPIES) Repeated concatenation
SCAN (STRING, SET)a Scan a string for a character in a set
TRIM (STRING) Remove trailing blank characters
VERIFY (STRING, SET)a Verify the set of characters in a string
STRING A//STRING B Concatenate two strings
a Optional arguments not shown.

Table 26: F90 Character Functions.

Action ASCII Character F90 Inputa C++ Input¡

Alert (Bell) 7 Ctrl-G a
¡

Backspace 8 Ctrl-H b
¡

Carriage Return 13 Ctrl-M r
End of Transmission 4 Ctrl-D Ctrl-D
¡

Form Feed 12 Ctrl-L f
¡

Horizontal Tab 9 Ctrl-I t
¡

New Line 10 Ctrl-J n
¡

Vertical Tab 11 Ctrl-K v
a “Ctrl-” denotes control action. That is, simultaneous pressing of the CONTROL key and the letter following.

Table 27: How to type non-printing characters.

14 LIST OF TABLES

C, C++ Variable.component.sub component
F90 Variable%component%sub component

Table 28: Referencing Structure Components.

C, C++ struct data tag

intrinsic type 1 component names;
¡ intrinsic type 2 component names;
;

F90 type data tag
intrinsic type 1 :: component names;
intrinsic type 2 :: component names;
end type data tag

Table 29: Defining New Types of Data Structure.

C, C++ struct data tag

intrinsic type 1 component names;
¡ struct tag 2 component names;
;

F90 type data tag
intrinsic type :: component names;
type (tag 2) :: component names;
end type data tag

Table 30: Nested Data Structure Definitions.

C, C++ struct data tag variable list; /* Definition */
¡
struct data tag variable = component values ; /* Initializa-
tion */
variable.component.sub component = value; /* Assignment */

F90 type (data tag) :: variable list ! Definition
variable = data tag (component values) ! Initialization
variable%component%sub component = value ! Assignment

Table 31: Declaring, initializing, and assigning components of user-defined datatypes.

LIST OF TABLES 15

INTEGER, PARAMETER :: j max = 6
TYPE meaning demo
INTEGER, PARAMETER :: k max = 9, word = 15
CHARACTER (LEN = word) :: name(k max)
END TYPE meaning demo
TYPE (meaning demo) derived(j max)
Construct Interpretation
derived All components of all derived’s elements
¤¢
£ ¡
derived(j) All components of element of derived
¦¥
£ ¡
derived(j)%name All k max components of name within element of derived
derived%name(k) Component k of the name array for all elements of derived
¦¥
£ ¡
derived(j)%name(k) Component k of the name array of element of derived

Table 32: F90 Derived Type Component Interpretation.

C++ F90
Declaration type tag *pointer name; type (type tag), pointer ::
pointer name
Target target name type (type tag), target :: target name
Examples char *cp, c; character, pointer :: cp
int *ip, i; integer, pointer :: ip
float *fp, f; real, pointer :: fp
cp = c; cp = c
§
ip = i; ip = i
§
fp = f; fp = f
§

Table 33: Deﬁnition of pointers and accessing their targets.

C, C++ pointer name = NULL
F90 nullify (list of pointer names)
F95 pointer name = NULL()

Table 34: Nulliﬁng a Pointer to Break Association with Target.

Purpose F90 M ATLAB
Form subscripts () ()
Separates subscripts elements , ,
Generates elements subscripts : :
Separate commands ; ;
Forms arrays (/ /) []
Continue to new line ...
Indicate comment ! %
Suppress printing default ;

Table 35: Special Array Characters.

16

Description Equation Fortran90 Operator Matlab Operator Original Sizes Result Size

¤
¤
§
§

£
£
£

¢

¢

¢
¥ ¦¤

¡
¡
¡
¨ ©§
¨ ©§

Scalar plus scalar

¤
¤
§

£
£
£

¢

¢

¥ ¦¤

¡
¡
¡

¢
¨
¨ ©§
¨

Element plus scalar and

¤

£
£
£

¢

¢

¥ ¦¤

¡
¡
¡

¢
¤
¨
¨
¨

Element plus element and

¤
¤
§
§

¢

¢

¢
¥ ¦¤

¡
¡
¡
¨ ©§
¨ ©§

Scalar times scalar

¤
¤
§

¢

¢

¥ ¤

¡
¡
¡

¢
¨
¨ ©§
¨

Element times scalar and

¤

¢

¢

¥ ¦¤

¡
¡
¡

¢
¤
¨
¨
¨

Element times element . and

¤
¤
§
§

¢

¢

¢
¥ ¦¤

¡
¡
¡
¨ ©§
¨ ©§

Scalar divide scalar

¤
¤
§

¢

¢

¥ ¦¤

¡
¡
¡

¢
¨
¨ ©§
¨

Scalar divide element and

¤

¢

¥ ¦¤

¡
¡
¡

¢
¤
¢
¨
¨
¨

Element divide element and

!
¤
§
§

¢

¢

¢
¥ ¦¤

¡
¡
¡
¨ ©§
¨ ©§

Scalar power scalar

!
¤
§

¢

¢

¥ ¦¤

¡
¡
¡

¢
¨
¨ ©§
¨

Element power scalar and

#
%$!
¤

¢

¢

¥ ¦¤

¡
¡
¡

¢
¨
¨
¨

Element power element . and

6
7
'
'

4
25

)(
10
32

¥ 8

¡
¡
¡

'
¨
¨

Matrix transpose

A
6
7

'
'

E

B
B

(

0
C
CD
F

¥ B

¡
¡
¡

9 @
9 '

¨
¨
¨ F
¨

Matrix times matrix and

A
6
7
6

'
'

B
B
B
§
§
§

D2
C

D2
C
¥ 7

¡
¡
¡

G'
¨
¨
¨ ©§

Vector dot vector 6 and
7

'
'

H
B
B
§
§
§

(
(

4
4
I

3
)
D H

¥ 8

¡
¡

¨
¨
¨
¨ ©§

and

Table 36: Array Operations in Programming Constructs. Lower case letters denote scalars or scalar elements of arrays. Matlab arrays are allowed a maximum of
two subscripts while Fortran allows seven. Upper case letters denote matrices or scalar elements of matrices.
LIST OF TABLES

LIST OF TABLES 17

Table 37: Equivalent Fortran90 and M ATLAB Intrinsic Functions.
The following KEY symbols are utilized to denote the TYPE of the in-
trinsic function, or subroutine, and its arguments: A-complex, integer,
or real; I-integer; L-logical; M-mask (logical); R-real; X-real; Y-real;
V-vector (rank 1 array); and Z-complex. Optional arguments are not
shown. Fortran90 and M ATLAB also have very similar array operations
and colon operators.

Type Fortran90 M ATLAB Brief Description
A ABS(A) abs(a) Absolute value of A.
R ACOS(X) acos(x) Arc cosine function of real X.
R AIMAG(Z) imag(z) Imaginary part of complex number.
R AINT(X) real(fix(x)) Truncate X to a real whole number.
L ALL(M) all(m) True if all mask elements, M, are true.
R ANINT(X) real(round(x)) Real whole number nearest to X.
L ANY(M) any(m) True if any mask element, M, is true.
R ASIN(X) asin(x) Arcsine function of real X.
R ATAN(X) atan(x) Arctangent function of real X.
R ATAN2(Y,X) atan2(y,x) Arctangent for complex number(X, Y).
I CEILING(X) ceil(x) Least integer = real X.
£
Z CMPLX(X,Y) (x+yi) Convert real(s) to complex type.
Z CONJG(Z) conj(z) Conjugate of complex number Z.
R COS(R Z) cos(r z) Cosine of real or complex argument.
R COSH(X) cosh(x) Hyperbolic cosine function of real X.
I COUNT(M) sum(m==1) Number of true mask, M, elements.
R,L DOT PRODUCT(X,Y) x’ y Dot product of vectors X and Y.
R
R,Z
EPSILON(X)
EXP(R Z)
eps
exp(r z)
Number, like X, ¢
. £¡
Exponential of real or complex number.
I FLOOR(X) floor Greatest integer X.
¡

R HUGE(X) realmax Largest number like X.
I INT(A) fix(a) Convert A to integer type.
R LOG(R Z) log(r z) Logarithm of real or complex number.
R LOG10(X) log10(x) Base 10 logarithm function of real X.
R MATMUL(X,Y)
x y Conformable matrix multiplication, X*Y.
I,V I=MAXLOC(X) [y,i]=max(x) Location(s) of maximum array element.
R Y=MAXVAL(X) y=max(x) Value of maximum array element.
I,V I=MINLOC(X) [y,i]=min(x) Location(s) of minimum array element.
R Y=MINVAL(X) y=min(x) Value of minimum array element.
I NINT(X) round(x) Integer nearest to real X.
A PRODUCT(A) prod(a) Product of array elements.
call
call
RANDOM NUMBER(X)
RANDOM SEED
x=rand
rand(’seed’)
Pseudo-random numbers in ©¢¨¦¥¤
.
Initialize random number generator.
§
R REAL (A) real(a) Convert A to real type.
R
I,V
RESHAPE(X, (/ I, I2 /))
SHAPE(X)
reshape(x, i, i2)
size(x)

Reshape array X into I I2 array.
Array (or scalar) shape vector.
R SIGN(X,Y) Absolute value of X times sign of Y.
R SIGN(0.5,X)-SIGN(0.5,-X) sign(x) Signum, normalized sign, –1, 0, or 1.
R,Z SIN(R Z) sin(r z) Sine of real or complex number.
R SINH(X) sinh(x) Hyperbolic sine function of real X.
I SIZE(X) length(x) Total number of elements in array X.
R,Z SQRT(R Z) sqrt(r z) Square root, of real or complex number.
R SUM(X) sum(x) Sum of array elements.
(continued)

18 LIST OF TABLES

Type Fortran90 M ATLAB Brief Description
R TAN(X) tan(x) Tangent function of real X.
R TANH(X) tanh(x) Hyperbolic tangent function of real X.
R TINY(X) realmin Smallest positive number like X.
R TRANSPOSE(X) x’ Matrix transpose of any type matrix.
R X=1 x=ones(length(x)) Set all elements to 1.
R X=0 x=zero(length(x)) Set all elements to 0.
For more detailed descriptions and example uses of these intrinsic functions see Adams, J.C., et al.,
Fortran 90 Handbook, McGraw-Hill, New York, 1992, ISBN 0–07–000406–4.

C++ – int – – floor ceil
F90 aint int anint nint floor ceiling
M ATLAB real (ﬁx) fix real (round) round floor ceil
Argument Value of Result
–2.000 –2.0 –2 –2.0 –2 –2 –2
–1.999 –1.0 –1 –2.0 –2 –2 –1
–1.500 –1.0 –1 –2.0 –2 –2 –1
–1.499 –1.0 –1 –1.0 –1 –2 –1
–1.000 –1.0 –1 –1.0 –1 –1 –1
–0.999 0.0 0 –1.0 –1 –1 0
–0.500 0.0 0 –1.0 –1 –1 0
–0.499 0.0 0 0.0 0 1 0
0.000 0.0 0 0.0 0 0 0
0.499 0.0 0 0.0 0 0 1
0.500 0.0 0 1.0 1 0 1
0.999 0.0 0 1.0 1 0 1
1.000 1.0 1 1.0 1 1 1
1.499 1.0 1 1.0 1 1 2
1.500 1.0 1 2.0 2 1 2
1.999 1.0 1 2.0 2 1 2
2.000 2.0 2 2.0 2 2 2

Table 38: Truncating Numbers.

WHERE (logical array expression)
true array assignments
ELSEWHERE
false array assignments
END WHERE

WHERE (logical array expression) true array assignment

Table 39: F90 WHERE Constructs.

LIST OF TABLES 19

Function Description Opt Example
all Find if all values are true, for a fixed di- d all(B = A, DIM = 1)
mension. (true, false, false)
any Find if any value is true, for a fixed di- d any (B § 2, DIM = 1)
mension. (false, true, true)
count Count number of true elements for a d count(A = B, DIM = 2)
fixed dimension. (1, 2)
maxloc Locate first element with maximum m maxloc(A, A
9)
value given by mask. (2, 3)
maxval Max element, for fixed dimension, given b maxval (B, DIM=1, B § 0)
by mask. (2, 4, 6)

££¥¥ ¡
merge Pick true array, A, or false array, B, ac- – merge(A, B, L)
cording to mask, L. © ¤£¢§
¨ ¦
minloc Locate first element with minimum value m minloc(A, A § 3)
given by mask. (2, 2)
minval Min element, for fixed dimension, given b minval(B, DIM = 2)
by mask. (1, 2)
pack Pack array, A, into a vector under control v pack(A, B
4)
of mask. (0, 7, 3)
product Product of all elements, for fixed dimen- b product(B) ; (720)
sion, controlled by mask. product(B, DIM = 1, T)
(2, 12, 30)
sum Sum all elements, for fixed dimension, b sum(B) ;(21)
controlled by mask. sum(B, DIM = 2, T)
(9, 12)

£¢§¡
© ¨ ¦ ¥
unpack Replace the true locations in array B con- – unpack(U, L, B)
trolled by mask L with elements from the
vector U.

§ ¨ § ¤ %§ © $$ #¡ § © £¢¥ ¡ § © ££¥ ¡
$ ! ¤£¢§ ¤£¢¦
¦ ¨
$
Table 40: F90 Array Operators with Logic Mask Control. and denote true and false, respectively.
Optional arguments: b -- DIM MASK, d -- DIM, m -- MASK, v -- VECTOR and DIM = 1 implies
for any rows, DIM = 2 for any columns, and DIM = 3 for any plane.

20 LIST OF TABLES

M ATLAB C++ F90
a
Pre-allocate A(100)=0 int A[100]; integer A(100)
linear array
Initialize to a for j=1:100 % slow for (j=0; j100; j++) A=12
constant value of A(j)=12 A[j]=12;
end
12 % better way
A=12*ones(1,100)
Pre-allocate A=ones(10,10) int A[10][10]; integer A(10,10)
two-dimensional
array
a C++ has a starting subscript of 0, but the argument in the allocation statement is the array’s size.

Table 41: Array initialization constructs.

Action M ATLAB C++ F90
a
Define A=zeros(2,3) int A[2][3]; integer,dimension(2,3)::A
size
Enter A=[1,7,-2; int A[2][3]=
¡¡ A(1,:)=(/1,7,-2/)
rows 3, 4, 6]; 1,7,2 , A(2,:)=(/3,4,6/)
3,4,6
¡;
a Optional in M ATLAB , but improves efficiency.

Table 42: Array initialization constructs.

M ATLAB C++ F90
Addition
¦¤¢
¥ £ ¡ C=A+B for (i=0; i10; i++)
for (j=0; j10; j++)
C=A+B
C[i][j]=A[i][j]+B[i][j];
¡
¡
Multiplication
§¢
¥ ¡ C=A*B for (i=0; i10; i++)
for (j=0; j10; j++)
C=matmul(A,B)
C[i][j] = 0;
for (k=0; k10; k++)
C[i][j] += A[i][k]*B[k][j];
¡ ¡
¡
Scalar
multiplication
©¢
¥¨ C=a*B for (i=0; i10; i++) C=a*B
for (j=0; j 10; j++)
C[i][j] = a*B[i][j];
¡
¡
Matrix
inverse
¥
¡ B=inv(A) a B=inv(A)a

a Neither C++ nor F90 have matrix inverse functions as part of their language definitions nor as part of standard collections

of mathematical functions (like those listed in Table 7). Instead, a special function, usually drawn from a library of numerical
functions, or a user defined operation, must be used.

Table 43: Elementary matrix computational routines.

LIST OF TABLES 21

C++ int* point, vector, matrix
...
point = new type tag
vector = new type tag [space 1]
¡
if (vector == 0) error process
matrix = new type tag [space 1 * space 2]
...
delete matrix
...
delete vector
delete point

F90 type tag, pointer, allocatable :: point
type tag, allocatable :: vector (:), matrix (:,:)
...
allocate (point)
allocate (vector (space 1), STAT = my int)
if (my int /= 0) error process
allocate (matrix (space 1, space 2))
...
deallocate (matrix)
if (associated (point, target name)) pointer action...
if (allocated (matrix)) matrix action...
...
deallocate (vector)
deallocate (point)

Table 44: Dynamic allocation of arrays and pointers.

SUBROUTINE AUTO ARRAYS (M,N, OTHER)
USE GLOBAL CONSTANTS ! FOR INTEGER K
IMPLICIT NONE
INTEGER, INTENT (IN) :: M,N
type tag, INTENT (OUT) :: OTHER (M,N) ! dummy array
! Automatic array allocations
type tag :: FROM USE (K)
type tag :: FROM ARG (M)
type tag :: FROM MIX (K,N)
...
! Automatic deallocation at end of scope
END SUBROUTINE AUTO ARRAYS

Table 45: Automatic memory management of local scope arrays.

module derived class name
use base class name
! new attribute declarations, if any
...
contains

! new member deﬁnitions
...
end module derived class name

Table 46: F90 Single Inheritance Form.

22 LIST OF TABLES

use base class name, only: list of entities
...
contains

...

Table 47: F90 Selective Single Inheritance Form.

use base class name, local name = £ base entity name
...
contains

...

Table 48: F90 Single Inheritance Form, with Local Renaming.

use base1 class name
use base2 class name
use base3 class name, only: list of entities
use base4 class name, local name = base entity name
£
...
contains

...

Table 49: F90 Multiple Selective Inheritance with Renaming.

Fortran 90 overview

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