Copyright (c) 1994 J. Adams, W. Brainerd, J. Martin, and B. Smith.
All rights reserved.
This file may not be copied without permission of the authors.

16 Complex Type and Constants

The complex type is used for data that are approximations to the mathematical complex numbers. A complex number consists of a real part and an imaginary part and is often represented as a + bi in mathematical terms, where a is the real part and b is the imaginary part.

Examples:

COMPLEX CUT, CTEMP, X(10)     ! Complex type declaration

COMPLEX (KIND=LONG) :: CTC    ! CTC has kind parameter LONG
REAL XX, Y
CTC = CMPLX (XX, Y, KIND = LONG)

COMPLEX (SELECTED_REAL_KIND (6,32)) NORTH
! NORTH is a complex variable or function
!   whose parts have at least 6 decimal digits of precision
!   and decimal range of 10-32 to 1032.

Examples of complex constants are:

(1.0,2.0)             A complex constant:
                          1.0 is the real part;
                          2.0 the imaginary part.
(4, -.4)              Integer values are converted to real.
(2, 3.E1)             One part is integer and the other is real.
(1.0_LONG, 2.0_LONG)  The complex constant has the kind LONG.

Related Topics:

Expressions
Implicit Typing
Real Type and Constants

Related Intrinsics:

CMPLX
EPSILON
KIND
MAXEXPONENT
MINEXPONENT
RADIX
SELECTED_REAL_KIND

To Read More About It:

ISO 1539 : 1991, Fortran Standard, 4.3.1.3, 5.1.1.4
Fortran 90 Handbook, 4.3.3, 5.1.4
Programmer's Guide to Fortran 90, 1.2.3,1.3.1

A COMPLEX type declaration statement is:

COMPLEX [ ( [ KIND = ] kind-parameter ) ] &
[ , attribute-list :: ] entity-list

A complex constant is:

( real-part , imaginary-part )

The real part is one of:

signed-integer-literal-constant
signed-real-literal-constant

The imaginary part is one of:

signed-integer-literal-constant
signed-real-literal-constant

Things To Know:

1. The arithmetic operators are +, -, /, *, **, unary +, unary -.
2. Only equal and not equal relational operators may be used for comparisons; the result is a default logical value.
3. There are at least two approximation methods for complex, one is default real, and one is default double precision. There are as many complex kinds as there are real kinds.
4. If both parts of a complex constant are integer, they are converted to real. If one part is integer, it is converted to the type and kind of the other part.
5. If both parts of a complex constant are real, but not with the same kind parameter, both take the kind parameter corresponding to the one with the higher precision.
6. The intrinsic function CMPLX (X, Y, KIND) converts complex, real, or integer arguments to complex type. If the first argument is complex, the second argument must not be present. The kind parameter also is optional.
7. Note that there is no default implicit typing for complex.