AME 150 L

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AME 150 L

• Data Type and Structures

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Fortran Data Types

• Previously
• REAL, INTEGER, LOGICAL constants variables
• CHARACTER constants (not variables, yet)
• Last lecture
• Double Precision - REAL (Kind8)
• Are there Others?

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Single Precision

• Single precision (32-bit) floating-point numbers
  use 8 bits in the exponent and 23 bits in the
  fraction, which gives about 7 digit precision and
  allows storage of numbers whose magnitudes range
  from roughly 10-38 to about 1038.

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Double Precision

• Double precision (64-bit) floating-point numbers
  use 11 bits in the exponent and 52 bits in the
  fraction, which gives about 15 digit precision
  and allows storage of numbers whose magnitudes
  range from roughly 10-308 to about 10308.

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Fortran Double Precision

• REAL (Kind8) list of variable
• Machine dependent (not if use IEEE floating
  point)
• (Kind4) is normal
• Other Kinds
• INTEGER has Kind1, 2, and 4
• Logical has Kind1, 4

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More Double Precision

• Specifying Double Precision Constants
• lot of decimal digits or"d" in exponent 1.D0 (is
  double precision 1) or _"kind" 1.0_8
• Functions
• Selected_Real_Kind( p, r )
• Selected_Integer_Kind( r )
• Kind(x) - returns kind for x
• Precision(x) - returns precision for x
• Range(x) - returns decimal exponent range for x

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Complex Data Type

• Follows rules of Complex arithmetic
• z x i y, where i2 -1
• alternate form z x i y r (cos? i sin ? )
• where r (x2y2)1/2 and ? tan-1 (y/x)
• Syntax
• COMPLEX(Kind8 16),Dimension()
• Complex stores a pair of REAL numbers as real
  part and imaginary part of a complex number

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Complex (2)

• Complex Constants and variables
• Algebra z x i y
• Fortran z (1.0, 0.25) constant
• z CMPLX(Zr, Zi, Kind)
• where Zr,Zi are real and imaginary parts, and
  Kind is (optional) the "kind" of result (8 or 16)

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Complex (3)

• Complex data type follows all rules
• z1 z2 (z1r z2r) i (z1i z2i)
• z1z2 z1r z2r - z1i z2i i (z1r z2i z1i z2r
  )
• etc., and
• zn ? rn cos (n ? ) i sin (n ? ), etc.
• Note when complex numbers are input via READ
  statements, need (real, imag)

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Complex (3)

• Z CMPLX(x,y) ? x REAL(z) y AIMAG(z)
• CABS(Z) is same as SQRT(Zr2Zi2)
• Other functions do best they can
• SIN, COS, SQRT, LOG, etc.
• Use in Fortran
• COMPLEX z1, z2, z(4,5)
• z(1,j)z1z(2,k)-z2/z1 cos(z2)
• Can use relational operators or /, but not
  others (gt, gt, lt, lt)

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Overloading Operators

• Note that definition of , -, , /, , etc. are
  modified for complex numbers (this is called
  overloading)
• Other Overloads
• REAL A(3), B(3), C(3)
• C A B !Vector arithmetic
• B A C etc.

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Character Data Type

• Attribute of character is len (for length)
• Examples
• CHARACTER(len5)alpha, beta, gamma
• CHARACTER(5)delta
• CHARACTERepsilon
• alpha, beta, gamma, and delta are 5 characters
  long
• epsilon is 1 character long

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Character (2)

• Manipulating CHARACTER variables
• CHARACTER(8)c'abcdefghij',d
• CHARACTER(4)a'abcd',b'1234'
• d a // b !concatenation
• d a(14) // '.' // b(24)
• (xy) selects substring
• (5) means from character 5 to end of string
• (4) means from beginning to character 4
• Can use relational operators (gt, lt, etc) carefully

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Character (3)

• There are two character ?Integer functions
• ACHAR(I)or CHAR(I,kind) returns one character at
  position I in the ASCII collating sequence
• IACHAR(char) or ICHAR(char) returns an Integer
  code for the character " char "
• There are several Character String Utility
  Functions

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Character (4)

• Other Character Functions
• ADJUSTL(String) Left Justify
• ADJUSTR(String) Right Justify
• REPEAT(String, Ncopies) Concatenate Ncopies of
  String
• TRIM(String) Trim trailing blanks

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Derived Data Types

• Can create special data structures from Fortran's
  basic types integer, real, complex, logical,
  character
• TYPE name of derived type
• type declarations 1
• type declarations 2 . . .
• END TYPE name of derived type

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Definition of Derived Type

• TYPE person
• CHARACTER(Len14)first_name
• CHARACTER middle_initial
• CHARACTER(Len14)last_name
• CHARACTER(Len14)phone
• INTEGER age . . .
• END TYPE person

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Use of Derived Type

• TYPE (person)John, Jane
• TYPE (person),Dimension(100)people
• .. . .
• Johnperson('John','R','Jones',
• '323-1234',18,'M','123-45-6789')
• Janeperson('Jane','C','Bass',
• '765-4321',64,'F','987-65-4321')

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More Use of Derived Type

• Johnfirst_name "Milton"
• Johnage Johnage 1
• class(5)studentage 21
• Class(j) refers to every element assigned to
  class
• Any operation (and relational operators) can be
  custom defined