Fortran 95/2003 for Scientists and Engineers (3e) by Stephen J. Chapman
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Transcript of Fortran 95/2003 for Scientists and Engineers (3e) by Stephen J. Chapman
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Fortran 95/2003 for Scientists and Engineers (3e) by
Stephen J. Chapman
Grading system: 1. Attendance & Performance: 30% 2. Midterm: 30% 3. Final: 40%
Office hours: (PH224)
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Ch. 1 Introduction to Computers and
the Fortran Language Sec. 1.1 The Computer
Fig 1-1
Main Memory
Secondary Memory
C P U
(Central processing unit)
Input devices
Output devices
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Sec 1.2 Data Representation in a Computer
bit : Each switch represents one binary digit.
ON 1
OFF 0
byte : a group of 8 bits
e.g.,
825 MB hard disk. ( 1MB = 106 byte)
Sec 1.2.1 The Binary Number System
The base 10 number system:
1 2 3 10 = 1 x 102 + 2 x 101 + 3 x 100 = 123
102 101 100
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The base 2 number system:
1 0 1 2 = 1 x 22 + 0 x 21 + 1 x 20 = 5
1 1 1 2 = 1 x 22 + 1 x 21 + 1 x 20 = 7
22 21 20
3 bits can represent 8 possible values :
0 ~ 7 (or 0002 ~ 1112 )
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In general, n bits 2n possible values.
e.g.,
8 bits ( = 1 byte) 28 = 256 (-128 ~ +127)
16 bits ( = 2 byte) 216 = 65,536 (-32,768 ~ +32,767)
Sec 1.2.3 Types of Data Stored in Memory• Character data : (western language, < 256, use 1 byte)
A ~ Z (26)
a ~ z (26)
0 ~ 9 (10)
Miscellaneous symbols: ( ) { } ! …
Special letters or symbols: à ë …
Sec 1.2.2 Octal (or base 8) and Hexadecimal (or base 16)
Representations of Binary Numbers (see Table 1-1)
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Coding systems: (see App. A, 8-bit codes) • ASCII (American Standard Code for Information Interchange)• EBCDIC (Extended Binary Coded Decimal Interchange Code)*The unicode coding system uses 2 bytes for each character. (for any language)
• Integer data: (negative, zero, positive) For an n-bit integer, Smallest Integer value = - 2n-1
Largest Integer value = 2n-1 – 1
e.g., a 4-byte (= 32-bit) integer, the smallest = -2,147,483,648 ( = - 232-1) the largest = 2,147,483,647 ( = 232-1-1)
*Overflow condition: An integer > the largest or < the smallest.
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• Real data: (or floating-point data) The base 10 system: 299,800,000 = 2.998 x 108 (scientific notation)
mantissa exponent
The base 2 system: e.g., a 4-byte real number = 24-bit mantissa + 8-bit exponent
value = mantissa x 2exponent
Precision: The number of significant digits that can be preserved in a number. e.g., 24-bit mantissa ± 223 (~ seven significant digits)
Range: The diff. between the largest and the smallest numbers. e.g., 8-bit exponent 2-128 ~ 2127 (range ~ 10-38 to 1038)
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Sec 1.3 Computer Languages• Machine language: The actual language that a computer
recognizes and executes.
• High-level languages: Basic, C, Fortran, …
Sec 1.4 The History of the Fortran Language
Fortran = Formula translation
Fortran 66 Fortran 77 Fortran 90 Fortran 95
(1966) (1977) (1991) (1996)
Fortran 2003
(2004)
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Ch. 2 Basic Element of Fortran
Sec. 2.1 Introduction
Write simple but practical Fortran programs !
Sec. 2.2 Fortran Character Set (case insensitive)
• A ~ Z (26)
• a ~ z (26)
• 0 ~ 9 (26)
• _ (underscore)
• + - * / ** (arithmatic symbols)
• ( ) . = , ‘ … (miscellaneous symbols)
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Sec. 2.3 The Structure of a Fortran Statement
a Fortran program = a series of statements
• Executable statements: e.g., additions, subtractions, …• Non-executable statements: providing information.
Free-source form: Fortran statements may be entered anywhere on a line, up to 132 characters long.
e.g., 100 output = input1 + input2 ! Sum the inputs or 100 output = input1 & ! Sum the inputs + input2
(statement label, 1~99999, not a line number)
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Sec. 2.4 The Structure of a Fortran Program
Fig 2-1 (A simple Fortran program)
PROGRAM my_first_program
! Purpose: …
! Declare the variables
INTEGER :: i, j, k !All variable are integers
! Get the variables WRITE (*,*) " Enter the numbers to multiply:" READ (*,*) i, j k = i * j ! Write out the result WRITE (*,*) 'Result = ', k STOP END PROGRAM
(DeclarationSection)
(ExecutionSection)
(Termination section)
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Sec. 2.4.4 Program Style
Textbook : • Capitalizing Fortran keywords ( e.g., READ, WRITE)• Using lowercase for variables, parameters
Sec. 2.4.5 Compiling, Linking, and Executing the Fortran Program
Fig 2-2
Fortran program
Object file
Executable program
(Compile) (Link)
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Sec. 2.5 Constants and Variables
Valid variable names: time distance z123456789 I_want_to_go_home(up to 31 chracters, and the 1st character in a name must always be alphabetic)
Invalid variable names: this_is _a_very_long_variable_name 3_days A$ ($ is an illegal character) my-help (“-” is an illegal character)
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Five intrinsic types of Fortran constants and variables:1. INTEGER2. REAL3. COMPLEX4. LOGICAL5. CHARACTER
(numeric)
(logical, Ch. 3)(character)
Sec. 2.5.1 Integer Constant and Variables
Integer constants: (no decimal point) e.g., 0 -999 +17 1,000,000 (X) -100. (X)
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Integer variables: 16-bit integers 32-bit integers(diff. kinds of integers, Ch. 11)
Sec. 2.5.2 Real Constants and Variables Real constants: (with a decimal point) e.g., 10. -999.9 1.0E-3 (= 1.0 x 10-3 or 0.001) 123.45E20 0.12E+1 1,000,000. (X) 111E3 (X) -12.0E1.5 (X)
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Real variables: 32-bit real numbers 64-bit real numbers(diff. kinds of real numbers, Ch. 11)
Sec. 2.5.3 Character Constants and Variables Character constants: [enclosed in single (‘) or double (“) quotes)] e.g., ‘This is a test!’ “This is a test!” ‘ ‘ (a single blank) ‘{^}’ ‘3.141593’ (not a number) This is a test! (X) ‘This is a test!” (X)
A character variable contains a value of the character data type.
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Sec. 2.5.4 Default and Explicit Variable Typing Default typing: Any variable names beginning with the letters I, J, K, L, M, or N are assumed to be of type INTEGER.
e.g., incr (integer data type) big (real data type)
(Conti.)
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Explicit typing: The type of a variable is explicitly defined in the declaration section. e.g., PROGRAM example INTEGER :: day, month, year REAL :: second LOGICAL :: test1, test2 CHARACTER :: initial
(Executable statements)
*No default names for the character data type!
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Sec. 2.5.5 Keeping Constants Consistent in a Program
Using the PARAMETER attribute : type, PARAMETER :: name=value
e.g., REAL, PARAMETER :: pi=3.14159 CHARACTER, PARAMETER :: error=‘unknown’
Sec. 2.6 Assignment Statements and Arithmetic Calculations
Assignment statement: variable_name = expression e.g., I = I + 1 ( I + 1 I )
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Arithmetic operators:• binary operators: a + b (a + b, addition) a – b (a – b, subtraction) a * b (a x b, multiplication) a / b (a/b, division) a ** b (ab, exponentiation)• unary operators: + a - b
Rules:
1. No two operators may occur side by side. e.g., a*-b (X) a*(-b) a**-2 (X) a**(-2)
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2. Implied multiplication is illegal. e.g., x (y + z) (X) x*(y + z)
3. Parentheses may be used to group terms whenever desired
e.g., 2**((8+2) / 5)
Sec. 2.6.1 Integer Arithmetic e.g., 3/4 = 0, 6/4 = 1 7/4 = 1, 9/4 = 2
Sec. 2.6.2 Real Arithmetic (or floating-point arithmetic) e.g., 3./4. = 0.75, 6./4. = 1.50 7./4. = 1.75, 9./4. = 2.25
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Sec. 2.6.3 Hierarchy (or order) of Operators e.g., x = 0.5 * a * t **2
is equal to
x = 0.5 * a * (t **2) ? or x = (0.5 * a * t ) **2 ?
Order: 1. Parentheses, from inward to outward.2. Exponentials, from right to left.3. Multiplications and divisions, from left to right.4. Additions and subtractions, from left to right.
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Example 2-1 a = 3. b = 2. c=5. d=4. e = 10. f = 2. g= 3.(1) output = a * b + c * d + e / f **g(2) output = a * (b + c) * d + (e / f) **g(3) output = a * (b + c) * (d + e) / f **g
Solu. : (1) output = 3. * 2. + 5. * 4. + 10. / 2. ** 3. = 6. + 20. + 1.25 = 27.25 (2) output = 3. * (2. + 5.) * 4. + (10. / 2.) ** 3. = 84. + 125. = 209. (3) output = 3. * (2. + 5.) * (4. + 10.) / 2. ** 3. = 3. * 7. * 14. / 8. = 294. / 8. = 36.75
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Example 2-2 a = 3. b = 2. c=3. (1) output = a ** (b ** c)(2) output = (a ** b) ** c(3) output = a ** b ** c
Solu.: (1) output = 3. ** (2. ** 3.) = 3. ** 8. = 6561. (2) output = (3. ** 2.) ** 3. = 9. ** 3. = 729. (3) output = 3. ** 2. ** 3. = 3. ** 8. = 6561.
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Sec. 2.6.4 Mixed-Mode Arithmetic In the case of an operation between a real number and an integer,the integer is converted by the computer into a real number. e.g., 3. / 2 = 1.5 1 + 1/4 = 1 1. + 1/4 = 1. 1 + 1./4 = 1.25
Automatic type conversion:
e.g., nres = 1.25 + 9/4 ave = (5 + 2) / 2 = 1.25 + 2 = 7/2 = 3.25 = 3. = 3
(a integer variable) (a real variable)
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Logarithm
• Base 10: If 10x = N, then x = ? log N = x e.g., N = 100 log 100 = log (102) = 2
N = 3 log 3 = 0.47712…
• Base e (=2.71828…): (Natural logarithm)
If ex = N, then x = ? ln N = x e.g., N = e2 ln (e2) = 2
N = 3 ln 3 = 1.09861…
* If N < 0 ( log N ) or ( ln N ) is undefined !
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Sec. 2.6.5 Mixed-Mode Arithmetic and Exponentiation
If both result and y are real, and n is an integer,
result = y ** n = y * y * y…*y (real arithmetic, not mixed-mode)
But if result, y and x are all real,
result = y ** x = ?
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use yx = e x ln y ( e ∵ x ln y = e ln (yx) = yx )
e.g., (4.0) ** 1.5 = 8.
(8.0)**(1./3)=2.
(-2.0) ** 2 = 4. [ (-2.0) * (-2.0) = 4.]∵
(-2.0) ** 2.0 [X, ln (-2.0) is undefined!]∵
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Sec. 2.7 Intrinsic Functions
• Intrinsic functions are the most common functions built directly into the Fortran language. ( see Table 2-4 and App. B)• External functions are supplied by the user. (see Ch. 7)
e.g., y = sin(3.141593) INT(2.9995) = 2 (truncates the real number) y = sin(x)
y = sin(pi*x) NINT(2.9995) = 3 (rounds the real number) y = sin(SQRT(x))
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Generic functions: (can use more than one type of input data) e.g., If x is a real number, ABS(x) is real. If x is an integer, ABS(x) is integer.
Specific functions: (can use only one specific type of input data) e.g., IABS(i)
(integer only)
*See Appendix B for a complete list of all intrinsic functions.
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Sec. 2.8 List-directed (or free-format) Input and Output Statements
• The list-directed input statement: READ (*,*) input_list
I/O unit format
• The list-directed output statement: WRITE (*,*) output_list I/O unit format
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e.g., PROGRAM input_example INTEGER :: i, j REAL :: a CHARACTER (len=12) :: chars READ(*,*) i, j, a, chars WRITE(*,*) i, j, a, chars END PROGRAM
Input: 1, 2, 3., ‘This one.’ (or 1 2 3. ‘This one.’)
Output: 1 2 3.00000 This one.
(Try it out!)
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Sec. 2.9 Initialization of Variables
E.g., PROGRAM init INTEGER :: i WRITE(*,*) I END PROGRAM
Output: i = ??? (uninitialized variable)
Run-time error! (depends on machines)
(Try it out!)
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Three ways to initialize variables:
1. Assignment statements: e.g., PROGRAM init_1 INTEGER :: i i = 1 WRITE(*,*) i END PROGRAM
2. READ statements: e.g., PROGRAM init_2 INTEGER :: i READ(*,*) i WRITE(*,*) i END PROGRAM
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3. Type declaration Statements: type :: var1 = value1, [var2 = value2, …]
e.g., REAL :: time = 0.0, distance = 5128. INTEGER :: loop = 10 LOGICAL :: done = .FALSE. CARACTER (len=12) :: string = ‘characters’
or
PROGRAM init_3 INTEGER :: i = 1 WRITE(*,*) i END PROGRAM
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Sec. 2.10 The IMPLICIT NONE Statement
When the IMPLICIT NONE statement is included in a program, any variable that does not appear in an explicit type declaration statement is considered an error. e.g., PROGRAM test_1 REAL :: time time = 10.0 WRITE(*,*) ‘Time=‘, tmie END PROGRAM
Output:
Run-time error! (depends on machines)
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+ IMPLICIT NONE,
PROGRAM test_1 IMPLICIT NONE REAL :: time time = 10.0 WRITE(*,*) ‘Time=‘, tmie END PROGRAM
Output:
Compile-time error! (depends on machines)
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Sec. 2.10 Program Examples
Example 2-3 (Temperature conversion)
T (0F) = (9/5) T(0C) + 32
Fig. 2-6 PROGRAM temp IMPLICIT NONE REAL :: temp_c, temp_f WRITE(*,*) ’Enter T in degrees C:’ READ(*,*) temp_c temp_f = (9./5.) * temp_c + 32. WRITE(*,*) temp_c,’ degrees C =‘, temp_f, & ‘degrees F’ END PROGRAM
(Try it out!)
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Example (extra)
Write a program for converting a 4 bits integer into a base 10 number, e.g.,
1 0 1 1 = 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20 = 11
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Ch. 3 Program Design and Branching Structures
Ch. 2: Sequential programs (simple and fixed order)
Here: Complex programs (using two control statements)
(1) branches
(2) loops
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Sec. 3.1 Introduction to Top-down Design Techniques
Start
State the problem
Design thealgorithm
Convert algorithm into Fortran statements
Test the program
Finished !
Fig. 3-1 (a formal program design process)
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Sec. 3.2 Use of Pseudocode and Flowcharts
(1) Pseudocode : a mixture of Fortran and English
(2) Flowcharts : graphical symbolsl
e.g.,
(1) The pseudocode for Example 2-3: Prompt user to enter temp. in degree Farenheit Read temp. in degree Farenheit temp_k in Kelvins (5./9.)*(temp_f-32.)+273.15 Write temp. in Kelvins
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(2) The flowcharts for Example 2-3:
Start
Tell user toenter temp_f
Get temp_f
Calculate temp_k Write temp_k Stop
(an oval for start or stop)
(a parallelogram for I/O)
(a rectangle for computation)
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Sec. 3.3 Logical Constants, Variables, and Operators
Sec. 3.3.1 Logical Constants and Variables Logical constants: e.g., .TRUE. .FALSE. TRUE (X) .FALSE (X)
A logical variable contains a value of the logical data type. e.g., LOGICAL :: var1 [var2, var3, …]
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Sec. 3.3.2 Assignment Statements and Logical Calculations
Assignment statements: logical variable name = logical expression
Logical operators: • relational operators• combinational operators
Sec. 3.3.3 Relational Operators
a1 op a2
a1, a2: arithmetic expressions, variables, constants, or character strings.op: the relational logical operators. (see Table 3-1)
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Table 3-1operation meaning
= = equal to / = not equal to > greater than > = greater than or equal to < less than < = less than or equal to
e.g., operation result 3 < 4 .TRUE. 3 < = 4 .TRUE. 3 = = 4 .FALSE. ‘A’ < ‘B’ .TRUE. (in ASCII, A 65, B 66, p.493) 7+3 < 2+11 .TRUE.
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Sec. 3.3.4 Combinational Logic Operators
l1 .op. l2 and .NOT. l1 (.NOT. is a unary operator)
l1, l2: logical expressions, variables, or constants.op: the binary operators. (see Table 2-4)
Table 3-2operation meaning
.AND. logical AND .OR. logical OR .EQV. logical equivalence .NEQV. logical non-equivalence .NOT. logical NOT
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The order of operations:
1. Arithmetic operators.
2. All relational operators, from left to right.
3. All .NOT. operators.
4. All .AND. operators, from left to right.
5. All .OR. operators, from left to right.
6. All .EQV. And .NEQV. operators, from left to right.
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Example 3-1
L1 = .TRUE., L2 = .TRUE., L3 = .FALSE. (a) .NOT. L1 .FALSE.
(b) L1 .OR. L3 .TRUE.
(c) L1 .AND. L3 .FALSE.
(d) L2 .NEQV. L3 .TRUE.
(e) L1 .AND. L2 .OR. L3 .TRUE.
(f) L1 .OR. L2 .AND. L3 .TRUE.
(g) .NOT. (L1 .EQV. L2) .FALSE.
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Sec. 3.3.6 The Significance of Logical Variables and Expressions
Most of the major branching and looping structures of Fortran are controlled by logical values.
Sec. 3.3.5 Logical Values in Input and Output Statements
See Ch. 5
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Sec. 3.4 Control Constructs: Branches
• IF Statement
• SELECT CASE
Branches are Fortran statements that permit us to select and execute specific sections of code (called blocks) while skipping other sections of code.
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Sec. 3.4.1 The Block IF Construct
This construct specifies that a block of code will be executed if and only if a certain logical expression is true.
IF (logical_expr) THEN Statement 1 Statement 2 . . .END IF
a block
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Fig . 3-5 (Flowchart for a simple block IF construct)
logical_expr
Statement 1Statement 2 . .
.TRUE.
.FALSE.
(a diamond for choice)
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Example:
ax2 + bx + c = 0,
x = -b ± ( b2 – 4ac )1/2
2a
If b2 – 4ac = 0
b2 – 4ac > 0
b2 – 4ac < 0
two distinct real roots
two complex roots
a single repeated root
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Fig . 3-6 (Flowchart)
.TRUE.
.FALSE.
Problem: Tell the user if the eq. has complex roots.
b2 – 4ac < 0
WRITE ‘two complex roots’
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Fortran: IF ( (b**2 – 4.*a*c) < 0. ) THEN WRITE(*,*) ‘Two complex roots!’ END IF
Sec. 3.4.2 The ELSE and ELSE IF Clauses
For many different options to consider,
IF + ELSE IF (one or more) + an ELSE
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IF (logical_expr_1) THEN Statement 1 Statement 2 . .ELSE IF (logical_expr_2) THEN Statement 1 Statement 2 . .ELSE Statement 1 Statement 2 . .END IF
Block 1
Block 2
Block 3
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Fig . 3-7 (flowchart)
.TRUE.
.FALSE.logical_expr_1
Block 1
logical_expr_2
Block 2
.TRUE.
.FALSE.
Block 3
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Fig . 3-8 (flowchart)
.TRUE.
.FALSE.b2 - 4ac < 0
WRITE ‘two complex roots’
.TRUE.
.FALSE.
Example: Tell the user whether the eq. has two complex roots, two identical real roots, or two distinct real roots.
b2 - 4ac = 0
WRITE ‘two identical real roots’
WRITE ‘two distinct real roots’
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Fortran: IF ( (b**2 – 4.*a*c) < 0. ) THEN WRITE(*,*) ‘two complex roots’ ELSE IF ( (b**2 – 4.*a*c) == 0. ) THEN WRITE(*,*) ‘two identical real roots’ ELSE WRITE(*,*) ‘two distinct real roots’ END IF
Write a complete Fortran program for a quadraticequation ax2 + bx + c = 0.
Input: a, b, c (e.g., 1., 5., 6. or 1., 4., 4. or 1., 2., 5.)
Output: ‘distinct real’ or ‘identical real’ or ‘complex roots’
(Try it out!)
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PROGRAM abcIMPLICIT NONEREAL :: a, b, c
WRITE(*,*)'Enter the coeffs. a, b, and c:‘READ(*,*) a, b, c
IF ( (b**2-4.*a*c) < 0. ) THEN WRITE(*,*) 'two complex root‘ELSE IF ( (b**2-4.*a*c) == 0. ) THEN WRITE(*,*) 'two identical real roots‘ELSE WRITE(*,*) 'two distinct real roots‘END IF
END PROGRAM
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Sec. 3.4.3 Examples Using Block IF Constructs
Example 3-2 The Quadratic Equation: (ax2 + bx + c =0) Write a program to solve for the roots of a quadratic equation, regardless of type.
Input: a, b, c
Output: rootsrealrepeated realcomplex
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PROGRAM rootIMPLICIT NONEREAL :: a, b, c, d, re, im, x1, x2
WRITE(*,*)'Enter the coeffs. a, b, and c:‘READ(*,*) a, b, cd = b**2 – 4.*a*cIF ( d < 0. ) THEN WRITE(*,*) 'two complex root:‘ re = (-b)/(2.*a) im = sqrt(abs(d))/(2.*a) WRITE(*,*) ’x1=‘, re, ‘+ i’, im WRITE(*,*) ’x2=‘, re, ‘- i’, im ELSE IF ( d == 0. ) THEN WRITE(*,*) 'two identical real roots:‘ x1 = (-b) / (2.*a) WRITE(*,*) ’x1=x2=‘, x1
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ELSE WRITE(*,*) 'two distinct real roots:‘ x1 = (-b + sqrt(d)) / (2.*a) x2 = (-b – sqrt(d)) / (2.*a) WRITE(*,*) ’x1=‘, x1 WRITE(*,*) ‘x2=‘, x2END IFEND PROGRAM
Test: (Try it out!)
x2 + 5x + 6 = 0, x1,2 = -2, -3
x2 + 4x + 4 = 0, x1,2 = -2
x2 + 2x + 5 = 0, x1,2 = -1 ± i 2
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Example 3-3 Evaluation a Function of Two Variables:
f(x,y) =
x + y, x 0 ≧ and y 0≧x + y2, x 0 ≧ and y < 0x2 + y, x < 0 and y 0≧x2 + y2, x < 0 and y < 0
Input: x, y
Output: f
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Fig . 3-11 (flowchart)
.TRUE.
.FALSE.x ≧ 0 &y 0≧
f = x + y
x 0 ≧ &y < 0
f = x2 + y
.TRUE.
.FALSE.
f = x2 + y2f = x + y2
x < 0 &y 0≧
.TRUE.
.FALSE.
WRITE f
Stop
Start
READ x, y
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PROGRAM funxyIMPLICIT NONEREAL :: x, y, f
WRITE(*,*)'Enter x and y:‘READ(*,*) x, yIF ((x >= 0.) .AND. (y >= 0. )) THEN f = x + yELSE IF ((x >= 0.) .AND. (y < 0. )) THEN f = x + y**2ELSE IF ((x < 0.) .AND. (y >= 0. )) THEN f = x**2 + yELSE f = x**2 + y**2END IFWRITE(*,*) ‘f = ‘, fEND PROGRAM
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Test: (Try it out!)
x y f
2. 3. 5. 2. -3. 11.-2. 3. 7.-2. -3. 13.
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[name:] IF (logical_expr_1) THEN Statement 1 Statement 2 . .ELSE IF (logical_expr_2) THEN [name] Statement 1 Statement 2 . .ELSE [name] Statement 1 Statement 2 . .END IF [name]
Block 1
Block 2
Block 3
Sec. 3.4.4 Named Block IF Constructs
optional
optional
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Sec. 3.4.5 Notes Concerning the Use of Logical IF Constructs
Nested IF Constructs:
outer: IF ( x > 0. ) THEN . . inner: IF ( y < 0. ) THEN . . END IF inner . .END IF outer
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Example 3-4 Assigning Letter Grades:
95 < GRADE A86 < GRADE < 95 B76 < GRADE < 86 C66 < GRADE < 76 D 0 < GRADE < 66 F
Input: grade
Output: ‘The grade is A.’ or ‘The grade is B.’ or ‘The grade is C.’ or ‘The grade is D.’ or ‘The grade is F.’
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Method (a): IF + ELSE IF
IF (grade > 95.) THEN WRITE(*,*) ‘The grade is A.’ELSE IF (grade > 86.) THEN WRITE(*,*) ‘The grade is B.’ELSE IF (grade > 76.) THEN WRITE(*,*) ‘The grade is C.’ELSE IF (grade > 66.) THEN WRITE(*,*) ‘The grade is D.’ELSE WRITE(*,*) ‘The grade is F.’END IF
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Method (b): nested IF
if1: IF (grade > 95.) THEN WRITE(*,*) ‘The grade is A.’ELSE if2: IF (grade > 86.) THEN WRITE(*,*) ‘The grade is B.’ ELSE if3: IF (grade > 76.) THEN WRITE(*,*) ‘The grade is C.’ ELSE if4: IF (grade > 66.) THEN WRITE(*,*) ‘The grade is D.’ ELSE WRITE(*,*) ‘The grade is F.’ END IF if4 END IF if3 END IF if2END IF if1
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Sec. 3.4.6 The Logical IF Statement
IF (logical_expr) Statement
e.g., IF ( (x >= 0.) .AND. (y >= 0.) ) f = x + y
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[name:] SELECT CASE (case_expr)CASE (case_selector_1) [name] Statement 1 Statement 2 . . .CASE (case_selector_2) [name] Statement 1 Statement 2 . . .CASE DEFAULT [name] Statement 1 Statement 2 . . .END SELECT [name]
Block 1
Block 2
Block 3
Sec. 3.4.7 The Select CASE Construct
optional
optional
optional
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case_expr: an integer, character, or logical expression.
The case_selector can take one of four forms:
1. case_value Execute block if case_value == case_expr2. low_value: Execute block if low_value <= case_expr3. : high_value: Execute block if case_expr <= high_value4. low value: high_value Execute block if low_value <= case_expr <= high_value
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Fig . 3-13 (flowchart for a CASE construct)
In range
Not in range
case_sel_1
Block 1
case_sel_2
Block n
In range
NotIn range
Default BlockBlock 2
case_sel_n
In range
Not in range
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e.g., (not REAL)
INTEGER :: temp_c. . .temp: SELECT CASE (temp_c)CASE (: -1) WRITE (*,*) ‘ It’s below freezing today!’CASE (0) WRITE (*,*) ‘ It’s exactly at the freezing point!’CASE (1:20) WRITE (*,*) ‘ It’s cool today!’CASE (21:33) WRITE (*,*) ‘ It’s warm today!’CASE (34:) WRITE (*,*) ‘ It’s hot today!’END SELECT temp
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PROGRAM selectcIMPLICIT NONEINTEGER :: temp_cWRITE(*,*) “Enter today’s temp. in degree C:”READ(*,*) temp_ctemp: SELECT CASE (temp_c)CASE (: -1) WRITE (*,*) “It’s below freezing today!”CASE (0) WRITE (*,*) “It’s exactly at the freezing point!”CASE (1:20) WRITE (*,*) “It’s cool today!”CASE (21:33) WRITE (*,*) “It’s warm today!”CASE (34:) WRITE (*,*) “It’s hot today!”END SELECT tempEND PROGRAM
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Problem: Determine whether an integer between 1 and 10 is even or odd. (Try it out!)
PROGRAM selectvINTEGER :: valueWRITE(*,*) 'Enter an inter between 1-10:'READ(*,*) valueSELECT CASE (value) CASE (1,3,5,7,9) WRITE(*,*) 'The value is odd.' CASE (2,4,6,8,10) WRITE(*,*) 'The value is even.' CASE (11:) WRITE(*,*) 'The value is too high' CASE DEFAULT WRITE(*,*) 'The value is negative or zero.'END SELECTEND PROGRAM
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Ch. 4 Loops and Character Manipulation
• while loops• iterative (or counting) loops
Sec. 4.1.1 The While Loop
DO . . . IF (logical_expr) EXIT . . .END DO
a code block
Sec. 4.1 Control Constructs: Loops
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Fig . 4-1 (Flowchart for a while loop)
.TRUE.
.FALSE.
logical_expr
Statement 1 . . .
Statement 1 . . .
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Example 4-1 Statiscal Analysis:
Average: x_ave =
Σxii=1
N
N
Standard deviation:
S = N Σxi
2 – (i=1 i=1
N N
Σxi )2
N (N-1)
1/2
Input: x (i.e., xi , i = 1, 2, …, N) 0 ≧
Output: x_ave and S
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Fig . 4-2 (Flowchart for Example 3-4)
.TRUE.
.FALSE.
x < 0
READ x
n = n + 1sum_x = sum_x + xsum_x2=sum_x2 + x2
Start
1
1
Calculate x_ave, s
Stop
WRITE x_ave, s, n
Initial values:n = 0sum_x = 0Sum_x2 = 0
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Fig . 4-3 PROGRAM stats_1IMPLICIT NONEINTEGER :: n = 0REAL :: x, x_ave, s , sum_x = 0., sum_x2 = 0.
DO WRITE(*,*) ‘Enter the value x:’ READ (*,*) x IF ( x < 0. ) EXIT n = n + 1 sum_x = sum_x + x sum_x2 = sum_x2 + x**2END DOx_ave = sum_x / ns = sqrt (( n*sum_x2 – sum_x**2) / (n*(n-1)))WRITE(*,*) ‘n = ‘ , n, ‘ x_ave = ‘, x_ave, & ‘ s = ‘, sEND PROGRAM
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Test:
Input: 3. 4. 5. -1.
Output: n = 3 x_ave = 4.00000 s = 1.00000
Sec. 4.1.2 The Do While Loop
DO WHILE (logical_expr) . . . . . . . . .END DO
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Sec. 4.1.3 The Iterative or Counting Loop
DO index = istart, iend, incr Statement 1 . . . Statement nEND DO
e.g.,
(1) Do i = 1, 10 Statement 1 . . . Statement nEND DO
( incr = 1 by default)
(2) Do i = 1, 10, 2 Statement 1 . . . Statement nEND DO
( i = 1, 3, 5, 7, 9 )
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Fig. 4-5 (Flowchart for a Do loop construct)
index*incr ≦iend * incr
index =istart
incr
Statement 1Statement 2 . . .
.TRUE..FALSE.
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Example 4-2 The Factorial Function:
N ! = N × (N-1) × (N-2) … × 3 × 2 × 1, N > 0.0 ! = 1
e.g.,
4 ! = 4 × 3 × 2 × 1 = 24 5 ! = 5 × 4 × 3 × 2 × 1 = 120
Fortran Code: n_factorial = 1DO i = 1, n n_factorial = n_factorial * iEND DO
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Problem: Write a complete Fortran program for the factorial function.
Input: n ( n > = 0 )
N ! = N × (N-1) × (N-2) … × 3 × 2 × 1, N > 0.
0 ! = 1
Output: n!
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PROGRAM factorialIMPLICIT NONEINTEGER :: i, n, n_fact
WRITE(*,*) ’Enter an integer n ( > = 0 ):’READ(*,*) nn_fact = 1IF ( n > 0 ) THEN DO i = 1, n n_fact = n_fact * i END DOEND IF
WRITE(*,*) n, ‘! = ‘, n_factEND PROGRAM
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Fig . 4-7
.TRUE. .FALSE.n < 2
READ n
sum_x = sum_x + xsum_x2 = sum_x2+x2
Start
1
1
Calculate x_ave, s
Stop
WRITE x_ave, s, n
Initial values:sum_x = 0sum_x2 = 0
Example 4-4 Statistical Analysis: (modified)
WRITE‘At least 2 values!’
i=1
i=i+1i n≦ ?
READ x
.FALSE. .TRUE.
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Fig . 4-8PROGRAM stats_3IMPLICIT NONEINTEGER :: i, nREAL :: x, x_ave, s , sum_x = 0., sum_x2 = 0.
WRITE(*,*) ‘Enter the number of points n:’READ(*,*) nIF ( n < 2 ) THEN WRITE(*,*) ‘ At least 2 values!’ELSE DO i = 1, n WRITE(*,*) ‘Enter the value x:’ READ (*,*) x sum_x = sum_x + x sum_x2 = sum_x2 + x**2 END DO
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x_ave = sum_x / ns = sqrt (( n*sum_x2 – sum_x**2) / (n*(n-1)))WRITE(*,*) ‘n = ‘ , n, ‘ x_ave = ‘, x_ave, & ‘ s = ‘, sEND IFEND PROGRAM
Test:
Input: 3 3. 4. 5.
Output: n = 3 x_ave = 4.00000 s = 1.00000
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Sec. 4.1.4 The CYCLE and EXIT Statements
E.g., PROGRAM test_cycleINTEGER :: iDO i = 1, 5 IF ( i == 3 ) CYCLE WRITE(*,*) iEND DOWRITE(*,*) ‘End of loop!’END PROGRAM
Output: 1 2 4 5 End of loop!
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PROGRAM test_exitINTEGER :: IDO i = 1, 5 IF ( i == 3 ) EXIT WRITE(*,*) iEND DOWRITE(*,*) ‘End of loop!’END PROGRAM
Output: 1 2 End of loop!
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[name:] DO . . . IF (logical_expr) CYCLE [name] . . . IF (logical_expr) EXIT [name] . . . END DO [name]
Sec. 4.1.5 Named Loops
While loop:
optional
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[name:] DO index = istart, iend, incr . . . IF (logical_expr) CYCLE [name] . . . END DO [name]
Counting loop:
optional
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Sec. 4.1.6 Nesting Loops and Block IF Construct
e.g.,PROGRAM nested_loopsINTEGER :: i, j, productDO i = 1, 3 DO j = 1, 3 product = i * j WRITE(*,*) i, ‘*’, j, ‘=‘, product END DOEND DOEND PROGRAM
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Output:
1 * 1 = 11 * 2 = 21 * 3 = 32 * 1 = 22 * 2 = 42 * 3 = 63 * 1 = 33 * 2 = 63 * 3 = 9
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PROGRAM test_cycle_1INTEGER :: i, j, productDO i = 1, 3 DO j = 1, 3 IF ( j == 2 ) CYCLE product = i * j WRITE(*,*) i, ‘*’, j, ‘=‘, product END DOEND DOEND PROGRAM
Output: 1 * 1 = 11 * 3 = 32 * 1 = 22 * 3 = 63 * 1 = 33 * 3 = 9
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PROGRAM test_cycle_2INTEGER :: i, j, productouter: DO i = 1, 3 inner: DO j = 1, 3 IF ( j == 2 ) CYCLE outer product = i * j WRITE(*,*) i, ‘*’, j, ‘=‘, product END DO innerEND DO outerEND PROGRAM
Output:1 * 1 = 12 * 1 = 23 * 1 = 3
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Nesting loops within IF constructs and vice versa:
e.g.,outer: IF ( a < b ) THEN . . . inner: DO i = 1, 3 . . . ELSE . . . END DO innerEND IF outer
illegal!
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outer: IF ( a < b ) THEN . . . inner: DO i = 1, 3 . . . END DO inner . . . ELSE . . . END IF outer
legal:
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Sec. 4.2 Character Assignments and Character Manipulations
Sec. 4.2.1 Character Assignment
character variables name = character expression
Character operators:1. substring specifications2. concatenation
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Sec. 4.2.2 Substring SpecificationsE.g., str1 = ‘123456’ str1(2:4) contains the string ‘234’.
Example 4-5 PROGRAM substring CHARACTER (len=8) :: a,b,c a = ‘ABCDEFGHIJ’ b = ‘12345678’ c = a(5:7) b(7:8) = a(2:6) WRITE(*,*) 'a=', a WRITE(*,*) 'b=', b WRITE(*,*) 'c=', c END PROGRAM
a = ? b = ? c = ? (Try it out!)
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Solu: a = ‘ABCDEFGH’ ( len = 8)∵
∵ b(7:8) = a(2:6) = ‘BC’
b = ‘123456BC’
c = a(5:7) = ‘EFG’ = ‘EFG□□□□□‘ ( len = 8)∵
(Cont.)
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Sec. 4.2.3 The Concatenation Operator
E.g., PROGRAM concate CHARACTER (len=10) :: a CHARACTER (len=8) :: b,c a = ‘ABCDEFGHIJ’ b = ‘12345678’ c = a(1:3) // b(4:5) // a(6:8) WRITE(*,*)’c=‘,c END PROGRAM
c = ? (Try it out: c =‘ABC45FGH’)
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Sec. 4.2.4 Relational Operators with Character Data
E.g., ‘123’ = = ‘123’ (true)
‘123’ = = ‘1234’ (false)
‘A’ < ‘B’ (true, ASCII, A 65, B 66)∵
‘a’ < ‘A’ (false, a 97)∵
‘AAAAAB’ > ‘AAAAAA’ (true)
‘AB’ > ‘AAAA’ (true)
‘AAAAA’ > ‘AAAA’ (true)
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Ch. 5 Basic I/O Concepts
Sec. 5.1 FORMATS and FORMETED WRITE STATEMENTS
READ (*,*) Not always convenient!
WRITE (*,*) Not always pretty!
e.g,. PROGRAM free_formatINTEGER :: i = 21REAL :: result = 3.141593WRITE(*,100) i, result100 FORMAT (‘□The□result□for□iteration□’, & I3, ‘□is□’, F7.3)END PROGRAM
Output: □The□result□for□iteration□□21□is□□□3.142
∵ I3 ∵ F7.3
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The following three WRITE statements are equivalent:
• WRITE (*, 100) i, result 100 FORMAT (I6, F10.2)
• CHARACTER ( len=20 ) :: string string = ‘(I6, F10.2)’ WRITE(*,string) i, result
• WRITE(*, ‘(I6,F10.2)’) i, result
Output: □□□□21□□□□□□3.14
I6 F10.2
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PROGRAM formatINTEGER :: i = 21REAL :: result = 3.141593CHARACTER ( len=20 ) :: string
WRITE (*, 100) i, result100 FORMAT (I6, F10.2)
string = '(I6, F10.2)'WRITE(*,string) i, result
WRITE(*, '(I6,F10.2)') i, result
END PROGRAM
Output: □□□□21□□□□□□3.14
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Sec. 5.2 Output Devices
Line printers, laser printers, and terminals.
Sec. 5.3 Format Descriptors
Table 5-2 (Symbols used with format descriptors)
Symbol meaning
c column number d # of digits to the right of the decimal point m min. # of digit r repeat count w field width
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Sec. 5.3.1 Integer Output – The I Descriptor
rIw or rIw.m
e.g., INTEGER :: index = -12, junk = 4, number = -12345 WRITE(*,200) index, index+12, junk, number WRITE(*,210) index, index+12, junk, number WRITE(*,220) index, index+12, junk, number 200 FORMAT ( 2I5, I6, I10) 210 FORMAT (2I5.0, I6, I10.8) 220 FORMAT (2I5.3, I6, I5)
Output: □□-12□□□□0□□□□□4□□□□-12345 □□-12□□□□□□□□□□4□-00012345 □-012□□000□□□□4*****
(Not in scale!)
I5 I5 I6 I10
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PROGRAM iformatIMPLICIT NONEINTEGER :: index = -12, junk = 4, number = -12345
WRITE(*,200) index, index+12, junk, numberWRITE(*,210) index, index+12, junk, numberWRITE(*,220) index, index+12, junk, number200 FORMAT ( 2I5, I6, I10)210 FORMAT (2I5.0, I6, I10.8)220FORMAT (2I5.3, I6, I5)
END PROGRAM
Output: -12 0 4 -12345 -12 4 -00012345 -012 000 4*****
(Not in scale!)
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Sec. 5.3.2 Real Output – The F Descriptor
rFw.d
e.g., REAL :: a = -12.3, b = .123, c = 123.456 WRITE(*,200) a, b, c WRITE(*,210) a, b, c 200 FORMAT (2F6.3, F8.3) 210 FORMAT (3F10.2)
Output: ******□0.123□123.456 □□□□-12.30□□□□□□0.12□□□□123.46
(Not in scale!)
F6.3 F6.3 F8.3
F10.2 F10.2F10.2
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PROGRAM rformatIMPLICIT NONEREAL :: a = -12.3, b = .123, c = 123.456
WRITE(*,200) a, b, cWRITE(*,210) a, b, c200 FORMAT (2F6.3, F8.3)210 FORMAT (3F10.2)
END PROGRAM
Output: ****** 0.123 123.456 -12.30 0.12 123.46
(Not in scale!)
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Sec. 5.3.3 Real Output – The E Descriptor
(Expomential notation)Scientific notation: 6.02 × 1023
Exponential notation: 0.602 × 1024(E Descriptor)
0.602 E+24
rFw.d ( w d + ≧ 7 )
e.g., REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10, d = -77.7E10WRITE (*,200) a, b, c, d200 FORMAT (2E14.4, E13.6, E11.6)
□□□□0.1235E+07□□□□0.1000E-02-0.777000E+12***********
E14.4 E11.6E13.6E14.4
Output:
( ‘E+**’ , ‘0.’, and ‘-’)∵
( 11 < 6 + 7)∵
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PROGRAM routputIMPLICIT NONEREAL :: a = 1.2346E6, b = 0.001, c = -77.7E10, d = -77.7E10
WRITE (*, 200) a, b, c, d200 FORMAT (2E14.4, E13.6, E11.6)
END PROGRAM
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Sec. 5.3.4 True Scientific Notation – The ES Descriptor
rESw.d ( w d + ≧ 7 )
e.g.,
REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10WRITE (*,200) a, b, c200 FORMAT (2ES14.4, ES12.6)
□□□□1.2346E+06□□□□1.0000E-03************
ES14.4 ES12.6 ES14.4
Output:
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PROGRAM esformatIMPLICIT NONE
REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10WRITE (*, 200) a, b, c200 FORMAT (2ES14.4, ES12.6)
END PROGRAM
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Sec. 5.3.5 Logical Output – The L Descriptor
rLw
e.g.,
LOGICAL :: output = .TRUE., debug = .FALSE.WRITE (*, 200) output, debug200 FORMAT (2L5)
□□□□T□□□□F
L5 L5
Output:
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PROGRAM loutputIMPLICIT NONELOGICAL :: output = .TRUE., debug = .FALSE.
WRITE (*, 200) output, debug200 FORMAT (2L5)
END PROGRAM
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Sec. 5.3.6 Character Output – The A Descriptor
rAw or rA
e.g.,
CHARACTER (len = 17) :: string = ‘This□is□a□string.’WRITE (*, 10) stringWRITE (*, 11) stringWRITE (*, 12) string10 FORMAT (A)11 FORMAT (A20)12 FORMAT (A6)
Output:
(i.e., the width is the same as the # of characters being displayed.)
17 characters
This□is□a□string.□□□This□is□a□string.This□i
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PROGRAM aoutputIMPLICIT NONECHARACTER (len = 17) :: string = 'This is a string.‘
WRITE (*, 10) stringWRITE (*, 11) stringWRITE (*, 12) string10 FORMAT (A)11 FORMAT (A20)12 FORMAT (A6)
END PROGRAM
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Sec. 5.3.7 Horizontal Position – The X and T Descriptors
X descriptor: nX
(the # of blanks to insert)
T descriptor:
Tc
(the column # to go to)
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e.g,.
CHARACTER (len = 10) :: first_name = ‘James□’CHARACTER :: initial = ‘R’CHARACTER (len = 16) :: last_name = ‘Johnson□’CAHRACTER (len = 9) :: class = ‘COSC□2301’INTEGER :: grade = 92WRITE(*,100) first_name, initial, last_name, grade, class100 FORMAT (A10, 1X, A1, 1X, A10, 4X, I3, T51, A9)
Output:
James□□□□□□R□Johnson□□□□□□□□92 . . . COSC□2301
A10 A10 4X I3 A91X A1 1X
(51th column, T51)∵
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orCHARACTER (len = 10) :: first_name = ‘James□’CHARACTER :: initial = ‘R’CHARACTER (len = 16) :: last_name = ‘Johnson□’CHARACTER (len = 9) :: class = ‘COSC□2301’INTEGER :: grade = 92WRITE(*,100) first_name, initial, last_name, class, grade100 FORMAT (A10, T13, A1, T15, A10, T51, A9, T29, I3)
Output:
James□□□□□□□R□Johnson□□□□□□□□92 . . . COSC□2301
A10 A10 I3 A9 A1
(13th column, T13)∵
(15th column, T15)∵ (29th column, T29)∵
(51th column, T51)∵
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orCHARACTER (len = 10) :: first_name = ‘James□’CHARACTER :: initial = ‘R’CHARACTER (len = 16) :: last_name = ‘Johnson□’CAHRACTER (len = 9) :: class = ‘COSC□2301’INTEGER :: grade = 92WRITE(*,100) first_name, initial, last_name, class, grade100 FORMAT (A10, T13, A1, T15, A10, T17, A9, T29, I3)
Output:
James□□□□□□□R□JoCOSC□2301□□□□92
A10 A10 I3 A1
(13th column, T13)∵
(15th column, T15)∵
(29th column, T29)∵
(17th column, T17)∵
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PROGRAM tformatCHARACTER (len = 10) :: first_name = 'James 'CHARACTER :: initial = 'R'CHARACTER (len = 16) :: last_name = 'Johnson 'CHARACTER (len = 9) :: class ='COSC 2301'INTEGER :: grade = 92
WRITE(*,100) first_name, initial, last_name, grade, classWRITE(*,110) first_name, initial, last_name, class, gradeWRITE(*,120) first_name, initial, last_name, class, grade100 FORMAT (A10, 1X, A1, 1X, A10, 4X, I3, T51, A9) 110 FORMAT (A10, T13, A1, T15, A10, T51, A9, T29, I3) 120 FORMAT (A10, T13, A1, T15, A10, T17, A9, T29, I3)
END PROGRAM
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Sec. 5.3.8 Repeating Groups of Format Descriptors
E.g.,
320 FORMAT (1X, I6, I6, F10.2, F10.2, I6, F10.2, F10.2)321 FORMAT (1X, I6, 2(I6, 2F10.2))
320 FORMAT (1X, I6, F10.2, A, F10.2, A, I6, F10.2, A, F10.2, A)321 FORMAT (1X, 2(I6, 2(F10.2, A)))
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Sec. 5.3.9 Changing Output Lines – The Slash ( / ) Descriptor e.g.,
WRITE (*, 100) index, time, depth, amplitude, phase100 FORMAT (T20, ‘Results for Test Number ‘, I3, ///, & 1X, ‘Time = ‘, F7.0/, & 1X, ‘Depth = ‘, F7.1, ‘ meters’, / , & 1X, ‘Amplitude = ‘, F8.2/, & 1X, ‘Phase = ‘, F7.1)
Output:
Results for Test Number . . .
Time = . . .Depth = . . . Amplitude = . . .Phase = . . .
(skip 2 lines)
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Sec. 5.3.10 How Format Statements Are Used during WRITES
Example 4-1 Generating a Table of Information
Output:
Table of Square Roots, Squares, and Cubes
Number Square Root Square Cube====== ========== ====== ==== 1 1.000000 1 1 2 1.414214 4 8 . . . . . . . . . . . . 9 3.000000 81 729 10 3.162278 100 1000
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PROGRAM tableIMPLICIT NONEINTEGER :: i, square, cubeREAL :: square_root
WRITE(*, 100)100 FORMAT(T4, ‘Table of Square Roots, Squares, and Cubes’/ )WRITE(*, 110)110 FORMAT(T4, ‘Number’, T13, ‘Square Root’, T29, ‘Square’, T39, ‘Cube’)WRITE(*, 120)120 FORMAT(T4, ‘======‘, T13, ‘===========‘, T29, & ‘======‘, T39, ‘====‘)DO i = 1, 10 square_root = SQRT(REAL(i)) square = i**2 cube = i**3 WRITE(*, 130) i, square_root, square, cube 130 FORMAT(T4, I4, T13, F10.6, T27, I6, T37, I6)END DOEND PROGRAM
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Sec. 5.4 Formatted READ Statements
e.g., READ (*,100) increment100 FORMAT (6X, I6)
(skip the 1st six column)(col. 7~12: an integer)
Sec. 5.4.1 Integer Input – The I Descriptor
rIw
e.g.,READ(*, 100) a, b, c100 FORMAT(3I5)
Input:
□□□15□□15□□15□□
I5 I5 I5a = 15b = 15c = 15
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PROGRAM iinputIMPLICIT NONEINTEGER :: a, b, c
READ(*, 100) a, b, c100 FORMAT(3I5)WRITE(*,*) 'a= ', aWRITE(*,*) 'b= ', bWRITE(*,*) 'c= ', c
END PROGRAM
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Sec. 5.4.2 Real Input – The F Descriptor
rFw.d
e.g.,
READ (*, ‘(3F10.4)’ ) a, b, c
Input:
1.5□□□□□□□□0.15E+01□□□15.0E-01
F10.4 F10.4 F10.4
a = 1.5b = 1.5c = 1.5
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PROGRAM rinputIMPLICIT NONEREAL :: a, b, c
READ (*, '(3F10.4)' ) a, b, cWRITE(*,*) 'a= ', aWRITE(*,*) 'b= ', bWRITE(*,*) 'c= ', c
END PROGRAM
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If a number without a decimal point appears in the field, then a decimal point is assumed to be in the position specified by the d term of the format descriptor.
e.g.,READ (*, ‘(3F10.4)’ ) a, b, c
Input:
□□□□□□□□15□□□150□□□□□□15000□□□
F10.4 F10.4 F10.4
a = 0.0015b = 0.0150c = 1.5000
*The E and ES format descriptors are identical to the F descriptor.
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Sec. 5.4.3 Logical Input – The L Descriptor
rLw
e.g.,READ (*, ‘(3L5)’ ) a, b, c
Input:
□□□□T□□□□F□□□□T
L5 L5 L5
a = Tb = Fc = T
(or T□□□□F□□□□T□□□□ )
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PROGRAM linputIMPLICIT NONELOGICAL :: a, b, c
READ (*, '(3L5)' ) a, b, cWRITE(*,*) 'a= ', aWRITE(*,*) 'b= ', bWRITE(*,*) 'c= ', c
END PROGRAM
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Sec. 5.4.4 Character Input – The A Descriptor
rA or rAw
e.g., CHARACTER (len=10) :: string_1, string_2CHARACTER (len=5) :: string_3CHARACTER (len=15) :: string_4, string_5READ (*, ‘(A)’ ) string_1READ (*, ‘(A10)’ ) string_2READ (*, ‘(A10)’ ) string_3READ (*, ‘(A10)’ ) string_4READ (*, ‘(A)’ ) string_5
Input:
ABCDEFGHIJKLMNOABCDEFGHIJKLMNOABCDEFGHIJKLMNOABCDEFGHIJKLMNOABCDEFGHIJKLMNO
String_1 = ‘ABCDEFGHIJ’String_2 = ‘ABCDEFGHIJ’String_3 = ‘FGHIJ’String_4 = ‘ABCDEFGHIJ □□□□□’String_5 = ‘ABCDEFGHIJKLMNO’
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PROGRAM ainputIMPLICIT NONECHARACTER (len=10) :: string_1, string_2CHARACTER (len=5) :: string_3CHARACTER (len=15) :: string_4, string_5
READ (*, '(A)' ) string_1READ (*, '(A10)' ) string_2READ (*, '(A10)' ) string_3READ (*, '(A10)' ) string_4READ (*, '(A)' ) string_5WRITE(*,*)string_1WRITE(*,*)string_2WRITE(*,*)string_3WRITE(*,*)string_4WRITE(*,*)string_5
END PROGRAM
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Sec. 5.4.5 Horizontal Positioning – The X and T Descriptor
e.g., CHARACTER (len=6) :: stringINTEGER :: iREAD (*, ‘(I6, T1, A6)’ ) i, string
Input: 123456
i = 123456string = ‘123456’
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PROGRAM hpositionIMPLICIT NONECHARACTER (len=6) :: stringINTEGER :: i
READ (*, '(I6, T1, A6)' ) i, stringWRITE(*,'(I6)') iWRITE(*,'(A)') string
END PROGRAM
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Sec. 5.4.6 Vertical Positioning – The Slash (/) Descriptor
e.g.,REAL :: a, b, c, dREAD (*, 300) a, b, c, d300 FORMAT (2F10.2, //, 2F10.2)
Input:
□□□□□□□1.0□□□□□□□2.0□□□□□□□3.0□□□□□□□4.0□□□□□□□5.0□□□□□□□6.0□□□□□□□7.0□□□□□□□8.0□□□□□□□9.0
a = 1.0b = 2.0c = 7.0d = 8.0
F10.2 F10.2 F10.2
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PROGRAM vpositionIMPLICIT NONEREAL :: a, b, c, d
READ (*, 300) a, b, c, d300 FORMAT (2F10.2, //, 2F10.2)WRITE(*,*)'a= ',aWRITE(*,*)'b= ',bWRITE(*,*)'c= ',cWRITE(*,*)'d= ',d
END PROGRAM
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Sec. 5.5 An Introduction to Files and File Processing
• i/o unit number:
e.g., READ (8, 100)
Typically, (vary from processor to processor)
READ (5,*) = READ (*,*)WRITE (6,*) = WRITE (*,*)
• I/O statement: (see Table 4-3)
OPEN, CLOSE, READ, WRITE, REWIND, and BACKSPACE.
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Sec. 5.5.1 The OPEN Statement
OPEN ( open_list )
The five most important items from the list:
1. (the i/o unit number) UNIT = int_expr
2. (the file name of the file to be opened) FILE = char_expr
3. (the status of the file) STATUS = char_expr (‘OLD’, ‘NEW’, ‘REPLACE’, ‘SCRATCH’, or ‘UNKNOWN’)
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4. (whether a file is to be opened for reading only, for writing only, or for both reading and writing) ACTION = char_expr (‘READ’, ‘WRITE’, or ‘READWRITE’)
5. (the status of the open operation) IOSTAT = int_var (If the OPEN statement is successful, a zero will be returned)
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Example 1 (Opening a file for input)
INTEGER :: ierrorOPEN ( UNIT = 8, FILE = ‘INPUT.DAT’, & STATUS = ‘OLD’, ACTION = ‘READ’, & IOSTAT = ierror)
INTEGER :: ierrorOPEN ( UNIT = 25, FILE = ‘OUTPUT.DAT, & STATUS = ‘NEW’, ACTION = ‘WRITE’, & IOSTAT = ierror)
Example 2 (Opening a file for output)
Example 3 (Opening a scratch file)
OPEN ( UNIT = 12, STATUS = ‘SCRATCH’, & IOSTAT = ierror)
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Sec. 5.5.2 The CLOSE Statement
CLOSE ( close_list )
e.g.,
CLOSE( UNIT = 8 )or
CLOSE( 8 )
Sec. 5.5.3 READS and WRITES to Disk Files
e.g.,OPEN ( UNIT = 8, FILE = ‘INPUT.DAT’, & STATUS = ‘OLD’, IOSTAT = ierror)READ (8,*) x, y, z
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OPEN ( UNIT = 9, FILE = OUTPUT.DAT’, & STATUS = ‘REPLACE’, IOSTAT = ierror)WRITE (9,100) x, y, z100 FORMAT(‘ X= ‘, F10.2, ‘ Y = ‘, F10.2, ‘Z= ‘, F10.2)
Sec. 5.5.4 The IOSTAT = clause in the READ Statement
IOSTAT = int_var
e.g.,READ (8,*, IOSTAT = ierror)
If the READ statement is successful, ierror = 0.
If the READ statement is fail, ierror > 0 (format error) = -1 (end of file) = -2 (end of record)
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Example 5-3 Reading Data from a File
1. State the problem. Write a program that can read in an unknown number of real values from a user-specified input data file and detect the end of the data file.
2. Define the input and output. input: (1) the filename of the data file (2) the data in that file output: the values in the data file
3. Describe the algorithm
4. Turn the algorithm into Fortran statements.
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.TRUE.
.FALSE.
ierror1 = 0 ?
READ filename
Start1
nvals = nvals +1
Stop
WRITE nvals, value
Initial values:nvals = 0
Fig 5-9 (Flowchart)
WRITE ‘Error
opening file’
READ value
.FALSE.
.TRUE.
OPEN filename
1
2
ierror2 = 0 ?
ierror2 > 0 ?
WRITE ‘Error reading line’
WRITE ‘End of file’
.FALSE.
2
.TRUE.
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PROGRAM readIMPLICIT NONECAHRACTER (len = 20) :: filenameINTEGER :: nvals = 0INTEGER :: ierror1, ierror2REAL :: value
WRITE(*,*) ‘Please enter input file name:’READ (*,*) filenameOPEN (UNIT = 3, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = ierror1)
openif: IF(ierror1 ==0) THEN readloop: DO READ(3,*), IOSTAT = ierror2) value IF (ierror2 /= 0) EXIT nvals = nvals + 1 WRITE(*, 1010) nvals, value 1010 FORMAT (‘Line ‘, I6, ‘:value=‘, F10.4) END DO readloop
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readif: IF (ierror2 > 0) THEN WRITE(*, 1020) nvals + 1 1020 FORMAT (‘Error reading line’, I6) ELSE WRITE(*, 1030) nvals 1030 FORMAT (‘End of file. There are ‘, & I6, ‘ values in the file.’) END IF readifELSE openif WRITE(*, 1040) ierror1 1040 FORMAT (‘Error opening file: IOSTST=‘, I6)END IF openifCLOSE(3)END PROGRAM
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Test the program:
(1) The valid input file READ1.TXT: (e.g., use Notepad)
-17.030.0011.012000.-0.012
Output: Please enter input file name:READ1.TXTLine 1: value = -17.0000Line 2: value = 30.0000 Line 3: value = 1.0000 Line 4: value = 12000.0000 Line 5: value = -0.0120 End of file. There are 5 values in the file.
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(2) The invalid input file READ2.TXT:
-17.030.001ABCDEF12000.-0.012
Output:
Please enter input file name:READ2.TXTLine 1: value = -17.0000Line 2: value = 30.0000Error reading Line 3
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(3) A file does not exist:
Output:Please enter input file name:JUNK.DATError opening file: IOSTAT = 128
(depends on machine)
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Sec. 5.5.5 File Positioning
BACKSPACE ( UNIT = a unit # )
REWIND ( UNIT = a unit #)
and
Example 5-4 Using File-Positioning Commands:
(1) Write a program that accepts a series of nonnegative real values and stores them in a scratch file.
(2) Ask the user for a record number to display.
(2) Rewind the file, get that value, and display it.
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PROGRAM scratchIMPLICIT NONEINTEGER, PARAMETER :: unit = 8REAL :: dataINTEGER :: icount = 0, irec, j
OPEN (UNIT = unit, STATUS = ‘SCRATCH’)WRITE(*, 100)100 FORMAT (1X, ‘Enter positive or zero input values.’, / , & 1X, ‘A negative value terminates input.’)DO WRITE(*, 110) icount + 1 110 FORMAT (1X, ‘Enter sample ‘, I4, ‘:’) READ (*,*) data IF ( data < 0. ) EXIT icount = icount + 1 WRITE(unit, 120) data 120 FORMAT (1X, ES16.6)END DO
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WRITE(*, 130) icount130 FORMAT (1X, ‘Which record do you want to see ( 1 to’, I4, ‘)? ’)READ (*,*) irecIF ( ( irec >= 0) .AND. (irec <= icount) )THEN REWIND (UNIT = unit) DO j = 1, irec READ( unit, *) data END DO WRITE(*, 140) irec, data 140 FORMAT (1X, ‘ The value of record ‘, I4, ‘is’, ES14.5)ELSE WRITE(*, 150) irec 150 FORMAT (1X, ‘ Illegal record number entered: ‘, I8)END IFEND PROGRAM
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Output:Enter positive or zero input values.A negative input value terminates input.Enter sample 1:234.Enter sample 2:12.34Enter sample 3:0.Enter sample 4:16.Enter sample 5:11.235Enter sample 6:2.Enter sample 7:-1.Which recore do you want to see ( 1 to 6)?5The value of record 5 is 1.12350E+01
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Example 5-5 The linear fit problem:
Given a set of measurements (xi , yi), i = 1, . . . , N:
(x2, y2)
(x4, y4)
(x3 , y3)
(x1 , y1)
The best fit: y = mx + b
x
y
m = ?b = ?
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The method of least squares:
m =
(Σxi yi ) - (Σxi ) y i=1
N
where
y = Σyii=1 i=1
N N
Σxi
N
b = y – m x
i=1
N
(Σxi2 ) - (Σxi ) x
N
i=1i=1
N
and x = N
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PROGRAM least_squares_fitIMPLICIT NONEINTEGER, PARAMETER :: unit = 18CHARACTER (len = 24) :: filenameINTEGER :: ierror, n = 0REAL :: m, bREAL :: sum_x = 0., sum_x2 = 0., sum_xy = 0., sum_y = 0.REAL :: x, y, x_bar, y_bar
WRITE(*, 1000)1000 FORMAT (1X, ‘Enter the file name: ‘)READ (*, ‘(A)’) filenameOPEN (UNIT = unit, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = ierror)
errorcheck: IF (ierror > 0) THEN WRITE(*, 1020) filename 1020 FORMAT (1X, ‘ERROR: File ‘, A, ‘ does not exist! ’)ELSE
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DO READ (unit, *, IOSTAT = ierror) x, y IF ( ierror /= 0 ) EXIT n = n + 1 sum_x = sum_x + x sum_y = sum_y + y sum_x2 = sum_x2 + x ** 2 sum_xy = sum_xy + x * y END DO x_bar = sum_x / n y_bar = sum_y / n m = (sum_xy – sum_x * y_bar) / (sum_x2-sum_x * x_bar) b = y_bar – m * x_bar WRITE(*, 1030) m, b, n 1030 FORMAT (1X, ‘ m = ‘, F12.3, / , & 1X, ‘ b = ‘, F12.3, / , & 1X, ‘ N = ‘, I12) CLOSE(18)END IF errorcheck END PROGRAM
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Test the program:
(1) The input file INPUT.TXT:
1.1 1.12.2 2.23.3 3.34.4 4.45.5 5.56.6 6.67.7 7.7
Output:
m = 1.000 b = 0.000 N = 7
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(2) The input file INPUT1.TXT:
1.1 1.012.2 2.303.3 3.054.4 4.245.5 5.756.6 6.487.7 7.84
Output:
m = 1.024 b = -0.12 N = 7
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Ch. 6 Introduction to Arrays
Fig. 6-1
a(1)
a(2)
a(3)
a(4)
a(5)
. . .
. . .
array a
e.g.,DO i = 1, 100 a(i) = SQRT (a(i))END DO
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Sec. 6.1 Declaring Arrays
• Type: real, integer, logical, or character
e.g.,
REAL, DIMENSION (16) :: voltage
voltage(1), voltage(2), . . . , voltage(16)
or
CHARACTER (len = 20), DIMENSION (50) :: last_name
last_name(1), . . . , last_name(50)
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• Rank: The # of subscripts declared for a given array
e.g., REAL, DIMENSION (3, 6) :: sum
a rank-2 array
• Extent: The # of elements in a given dimension of an array
e.g., The extent of the 1st subscript of sum is 3.
The extent of the 2nd subscript of sum is 6.
• Size: the # of elements
• Shape: the combination of rank and extent in each dimension
e.g., The shape of sum = 3 6
e.g., The size of sum = 18
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Array constructor:
e.g., INTEGER, DIMENDION (5) :: a = (/ 1, 2, 3, 4, 5 /)
Sec. 6.2 Using Array Elements in Fortran Statements
Sec. 6.2.1 Array Elements Are Just Ordinary Variables
e.g.,
INTEGER, DIMENDION (10) :: indexLOGICAL, DIMENSION (2) :: lvalREAL, DIMENSION (3) :: temp
Index(1) = 1Lval(2) = .TRUE.Temp(3) = REAL(index(1)) / 4.WRITE(*,*) ‘ index(1) = ‘, index(1)
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Sec. 6.2.2 Initialization of Array Elements
e.g.,INTEGER, DIMENDION (10) :: jWRITE(*,*) ‘ j(1)=‘, j(1)
uninitialized array
?• Initialization arrays with assignment statements:
e.g.,REAL, DIMENDION (10) :: array1DO i = 1, 10 array1(i) = 0.0END DO
orREAL, DIMENDION (10) :: array1array1 = (/ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0. /)
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• Initialization arrays in type declaration statements:
e.g.,
INTEGER, DIMENDION (5) :: array2 = (/ 1, 2, 3, 4, 5 /)
or
REAL, DIMENDION (100) :: array5 = 1.
or
INTEGER, DIMENDION (5) :: array2 = (/ ( i, i = 1, 5) /)
INTEGER, DIMENDION (25) :: array4 = (/ ((0, i = 1, 4), & 5*j, j = 1, 5) /)
0, 0, 0, 0, 5, 0, 0, 0, 0, 10, 0, 0, 0, 0, 15, . . .
or
array5(1) = 1., . . . , array5(100) = 1.
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•Initialization arrays with Fortran READ statements:
Just like any other variables. (See Sec. 5.4: I/O of Array Elements)
Sec. 6.2.3 Changing the Subscript Range of an Array
e.g.,
REAL, DIMENSION(5) :: arr
arr(1), arr(2), arr(3), arr(4), arr(5)
but arr(0) = ?
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e.g., c = Σ an = a0 + a1 + a2 + a3 + a4n=0
4
need a(0)!
Use
REAL, DIMENSION ( lower_bound : upper_bound ) :: arrar
e.g.,REAL, DIMENSION (-2:2) :: b
b(-2), b(-1), b(0), b(1), b(2)
orREAL, DIMENSION (5:9) :: c
c(5), c(6), c(7), c(8), c(9)
(5 elements)
(5 elements)
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Example (Fig. 6-4)
i i2
-5 25-4 16… …+4 16+5 25
PROGRAM squares_2IMPLICIT NONEINTEGER :: IINTEGER, DIMENSION(-5:5) :: number, square
DO i = -5, 5 number(i) = I square(i) = number(i)**2 WRITE(*, 100) number(i), square(i) 100 FORMAT (1X, ‘Number = ‘, I6, ‘ Square= ‘, I6)END DOEND PROGRAM
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Sec. 6.2.4 Out-of-bound Array Subscripts
e.g.,REAL, DIMENSION(5) :: a
a(1), a(2), a(3), a(4), a(5)
but if use a(6), out of bound!
Sec. 6.2.5 The Use of Named Constants with Array Declarations
e.g.,INTEGER, PARAMETER :: isize = 1000REAL, DIMENSION (isize) :: array1REAL, DIMENSION (isize) :: array2REAL, DIMENSION (2*isize) :: array3
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PROGRAM extremesIMPLICIT NONEINTEGER, PARAMETER :: max_size = 10INTEGER, DIMENSION (max_size) :: inputINTEGER :: ilarge, ismall, j, nvals, tempWRITE(*,*) ' Enter number of values in data set:'READ(*,*) nvalssize: IF (nvals <= max_size) THEN in: DO j = 1, nvals WRITE(*, 100) ' Enter value ', j 100 FORMAT (' ', A, I3, ':' ) READ(*,*) input(j) END DO in temp = input(1) ilarge = 1 large: DO j = 2, nvals IF (input(j) > temp) THEN temp = input(j) ilarge = j END IF END DO large
Example 6-1 (Finding the largest and smallest values in a data set)
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temp = input(1) ismall = 1 small: DO j = 2, nvals IF (input(j) < temp) THEN temp = input(j) ismall = j END IF END DO small WRITE(*, 110) 110 FORMAT(1X, 'The values are:') out: DO j = 1, nvals IF (j == ilarge) THEN WRITE(*, '(1X, I6, 2X, A)') input(j), 'LARGEST' ELSE IF (j == ismall) THEN WRITE(*, '(1X, I6, 2X, A)') input(j), 'SMALLEST' ELSE WRITE(*, '(1X, I6)') input(j) END IF END DO outELSE size WRITE(*, 120) nvals, max_size 120 FORMAT(1X, ' Too many input values: ', I6, '>', I6)END IF sizeEND PROGRAM
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Test:
Enter number of values in data set:6Enter value 1:-6Enter value 2:5Enter value 3:-11Enter value 4:16Enter value 5:9Enter value 6:0
The values are: -6 5 -11 SMALLEST 16 LARGEST 9 0
Output
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Sec. 6.3 Using Whole Arrays and Array Subsets in Fortran Statements
Sec. 6.3.1 Whole Array Operations
e.g.,
1.
2.
3.
4.
a(1)
a(4)
a(3)
a(2)
a
+
b(1)
b(2)
b(3)
b(4)
5.
6.
7.
8.
b
=
c
12.
10.
8.
6.
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Fig. 6-9
PROGRAM add_arraysIMPLICIT NONEINTEGER :: IREAL, DIMENSION(4) :: a = (/ 1., 2., 3., 4. /)REAL, DIMENSION(4) :: b = (/ 5., 6., 7., 8. /)REAL, DIMENSION(4) :: c, d
DO i = 1,4 c(i) = a(i) + b(i)END DOd = a + bWRITE(*, 100) ‘c’, cWRITE(*, 100) ‘d’, d100 FORMAT (1X, A, ‘ =‘, 5(F6.1, 1X))END PROGRAM
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If arrays a and b have the same shape,
Conformable!
e.g.,REAL, DIMENSION(1:4) :: a = (/ 1., 2., 3., 4. /)REAL, DIMENSION(5:8) :: b = (/ 5., 6., 7., 8. /)REAL, DIMENSION(101:104) :: cc = a + b
REAL, DIMENSION(4) :: a = (/ 1., 2., 3., 4. /)REAL :: b = 10REAL, DIMENSION(4) :: cc = a * b
or
c = (/ 10., 20., 30., 40. /)
(Not matrix multiplication)
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Elemental intrinsic functions: (see App. B for a complete list)
ABS, SIN, COS, EXP, and LOG.
e.g.,REAL, DIMENSION(4) :: x = (/ 0., 3.14, 1., 2. /), yINTEGER :: iDO i = 1, 4 y(i) = SIN(x(i))END DO
or use y = SIN(x)
REAL, DIMENSION(4) :: a = (/ -1., 2., -3., 4. /), yy = ABS(a)
or
y = (/ 1., 2., 3., 4. /)
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Sec. 6.3.2 Arrays Subsets
Array section: A subset of an array.
• Subscript triplet:
subscript_1 : subscript_2 : stride
e.g.,
INTEGER, DIMENSION(10) :: a = (/ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 /)
array(1:10:2) = [1, 3, 5, 7, 9]
Alternative forms: subscript_1 : subscript_2 subscript_1 : : subscript_2
stride = 1to the last subscriptto the 1st subscript
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Example 6-2
INTEGER :: i = 3, j = 7REAL, DIMENSION(10) :: a = (/ 1., -2., 3., -4., 5, -6., 7., -8., & 9., -10. /)(a) a(:) = [1., -2., 3., -4., 5, -6., 7., -8., 9., -10.](b) a(i:j) = a(3:7:1) = [3., -4., 5., -6., 7.](c) a(i:j:i) = a(3:7:3) = [3., -6.](d) a(i:j:j) = a(3:7:7) = [3.](e) a(i:) = a(3:10:1) = [3., -4., 5., -6., 7., -8., 9., -10.](f) a(:j) = a(1:7:1) = [1., -2., 3., -4., 5., -6., 7.](g) a(::i) = a(1:10:3) = [1., -4., 7., -10.]
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• Vector subscript:
INTEGER, DIMENSION(5) :: vec = (/ 1, 6, 4, 1, 9 /)REAL, DIMENSION(10) :: a = (/ 1., -2., -3., -4., 5, -6., 7., -8., & 9., -10. /)
a(vec) = [1., -6., -4., 1., 9.]
a(1) a(1) a(9)a(4)a(6)
e.g.,
*Vector subscript cannot be used on the left side of an assignment statement.
e.g., INTEGER, DIMENSION(3) :: vec = (/ 1, 2, 1 /)REAL, DIMENSION(3) :: a = (/ 10., 20., 30. /)REAL, DIMENSION(2) :: bb(vec) = a (Incorrect!)
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Sec. 6.4 Input and Output
Sec. 6.4.1 Input and Output of Array Elements
e.g., WRITE(*, 100) a(1), a(2), a(3), a(4), a(5)100 FORMAT (1X, ‘a=‘, 5F10.2)
Just like any other variables.
Sec. 6.4.2 The Implied DO LOOP
e.g.,
WRITE(*, 100) (a(i), I = 1, 5)100 FORMAT (1X, ‘a=‘, 5F10.2)
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Sec. 6.4.3 Input and Output of Whole Arrays and Array Sections
Fig. 6-11 (array I/O)
PROGRAM array_ioIMPLICIT NONEREAL, DIMENSION(5) :: a = (/ 1., 2., 3., 20., 10. /)INTEGER, DIMENSION(4) :: vec = (/ 4, 3, 4, 5 /)WRITE(*, 100) a100 FORMAT (2X, 5F8.3)WRITE(*, 100) a(2: :2)WRITE(*, 100) a(vec)END PROGRAM
(Output) 1.000 2.000 3.000 20.000 10.000 2.000 20.00020.000 3.000 20.000 10.000
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Sec. 6.5 Examples
Example 6-3 Sorting Data
Ascending order (the lowest to the highest)
Descending order (the highest to the lowest)
or
e.g.,
(10, 3, 6, 4, 9)(sorting)
(3, 4, 6, 9, 10)
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Fig. 6-12 (selection sort)
10
9
4
6
3
(swap)3
10
6
4
9
(swap)3
4
6
10
9
(no swap)
3
4
6
10
9
(swap)
3
4
6
10
9
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Steps:
1. Get the input filename2. Open the input file3. Read the input data into an array4. Sort the data in ascending order5. Write the sorted data
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Fig. 6-15PROGRAM sort1IMPLICIT NONEINTEGER, PARAMETER :: max_size = 10REAL, DIMENSION (max_size) :: aCHARACTER (len = 20) :: filenameINTEGER :: i, iptr, j, statusINTEGER :: nvals = 0REAL :: tempWRITE(*, 1000)1000 FORMAT (1X, ‘ Enter the file name’)READ(*, ‘(A20)’) filenameOPEN (UNIT = 9, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = status)fileopen: IF(status == 0) THEN DO READ (9, *, IOSTAT = status) temp IF (status /= 0) EXIT nvals = nvals + 1 a(nvals) = temp END DO
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outer: DO i = 1, nvals – 1 iptr = i inner: DO j = i + 1, nvals minval: IF (a(j) < a(iptr)) THEN iptr = j END IF minval END DO inner ! swap a(iptr) with a(i) if i /= iptr swap: IF ( i /= iptr ) THEN temp = a(i) a(i) = a(iptr) a(iptr) = temp END IF swap END DO outer WRITE(*, ‘(A)’) ‘ The sorted data are:’ WRITE(*, 1040) ( a(i), i = 1, nvals) 1040 FORMAT (4X, F10.4)ELSE fileopenWRITE(*, 1050)status1050 FORMAT (1X, ‘File open failed: ’, I6)END IF fileopenEND PROGRAM
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Test:
INPUT2.TXT
13.312.-3.00.4.06.64.-6.
output
Enter the file nameINPUT2.TXTThe sorted data are: -6.0000 -3.0000 0.0000 4.0000 4.0000 6.600012.000013.3000
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(Sec. 6.6 Two-Dimensional Features of Arrays)
• 1-dim. array: rank-1 array or vector• 2-dim. array: rank-2 array or matrix
Fig. 6-17
a(1)
a(4)
a(2)
a(3)
row 1
row 3
row 2
row 4
a(irow)
(a) 1-dim array
b(1,1) b(1,2)
b(2,1) b(2,2)
b(1,3)
b(2,3)
row 1
row 2
col 1 col 2 col 3
b(irow, icol))
(b) 2-dim array
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(Sec. 6.6.1 Declaring Rank-2 Arrays)
e.g.,REAL, DIMENSION(3,6) :: sumINTEGER, DIMENSION(0:100, 0:20) :: hist
(Sec. 6.6.2 Rank-2 Array Storage)
Fig. 6-19
a(1,1) a(1,2) a(1,3)
a(2,2)a(2,1) a(2,3)
a(irow, icol)
(Memory allocation)
a(1,1)
a(2,1)
a(1,2)
a(2,2)
a(1,3)
a(2,3)
column major order
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(Sec. 6.6.3 Initializing Rank-2 Array)
1. Use assignment statements
e.g., 1
1
1
1
2
2
2
2
3
3
3
3
INTEGER, DIMENSION(4,3) :: istatDO i = 1, 4 DO j = 1, 3 istat(i, j) = j END DOEND DO
use
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orDO j = 1, 3 istat(:, j) = jEND DO
cannot use
istat = (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /)
( Array constructors always produce rank-1 array!)∵
use
istat = RESHAPE ( (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /), (/4, 3/) )
(column major) (data to be reshaped)
(a new shape)
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2. Use type declaration statements
INTEGER, DIMENSION(4, 3) :: istat (4,3) = & RESHAPE ( (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /), (/4, 3/) )
3. Use READ statements
INTEGER, DIMENSION(4,3) :: istatOPEN(7, FILE = ‘INITIAL.DAT’, STATUS = ‘OLD’, & ACTION = ‘READ’)READ (7, *) istat
(INITIAL.DAT: 1 1 1 1 2 2 2 2 3 3 3 3 )
or
READ (7, *) ((istat(i,j), j = 1, 3), i = 1, 4)
(INITIAL.DAT: 1 2 3 1 2 3 1 2 3 1 2 3 )
(i = 1) (i = 4)(i = 3)(i = 2)
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(Sec. 6.6.4 Examples)
Examples 5-5
power =
20.0 40.3 42.0 20.419.8 40.1 41.5 26.920.1 40.0 41.3 38.420.0 39.5 41.1 42.020.0 39.9 39.8 12.219.9 40.0 41.0 6.0
use
REAL,DIMENSION(6,4) :: power…OPEN(9, FILE = ‘INPUT1’, STATUS = ‘OLD’, & ACTION = ‘READ’)READ (9, *) power
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INPUT1: 20.0 19.8 20.1 20.0 20.0 19.9 40.3 40.1 40.0 39.5 39.9 40.0 42.0 41.5 41.3 41.1 39.8 41.0 20.4 26.9 38.4 42.0 12.2 6.0
OPEN(9, FILE = ‘INPUT2’, STATUS = ‘OLD’, & ACTION = ‘READ’)READ (9, *) ((power(i, j), j = 1, 4), i = 1, 6)
INPUT2:
or
20.0 40.3 42.0 20.419.8 40.1 41.5 26.920.1 40.0 41.3 38.420.0 39.5 41.1 42.020.0 39.9 39.8 12.219.9 40.0 41.0 6.0
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(Sec. 6.6.5 Whole Array Operation and Array Subsets)
e.g.,
a =
1 2 3 4 5 6 7 8 9 1011 12 13 14 1516 17 18 19 2021 22 23 24 25
a(:, 1) =
1 6111621
a(1, :) = [ 1 2 3 4 5 ]
a(1:3, 1:5:2) =
1 3 5 6 8 1011 13 15
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(Sec. 6.7 Multidimensional or Rank-n Array)
(up to 7)Fig. 5-22 ( A 2 × 2 × 2 array a)
a(1, 1, 1)
a(2, 1, 1)
a(1, 2, 1)
a(2, 2, 1)
a(1, 1, 2)
a(2, 1, 2)
a(1, 2, 2)
a(2, 2, 2)
(memory allocation)
…
…
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(Sec. 6.8 Using Fortran Intrinsic Functions with Arrays)
(Sec. 6.8.1 Elemental Intrinsic Functions)
e.g.,
ABS, SIN, COS, TAN, EXP, LOG, LOG10, MOD, AND SQRT.
REAL, DIMENSION :: x = (/ 10., 3.14, 1., 2. /), yINTEGER :: iDO i = 1, 4 y(i) = sin(x(i))END DO
equiv.y = sin(x)
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(Sec. 6.8.2 Inquiry Intrinsic Functions)
Table 6-1
LBOUND (ARRAY, DIM)SHAPE (SOURCE)SIZE(ARRAY, DIM)UBOUND (ARRAY, DIM)
(a particular dimension, e.g., 1 or 2)
Example 6-6 (Determining the Properties of an Array)
PROGRAM check_arrayREAL, DIMENSION(-5:5, 0:3) :: a = 0.WRITE(*, ‘(A, 7I6)’) ‘ The shape is: ‘, SHAPE(a)WRITE(*, ‘(A, I6)’) ‘ The size is: ‘, SIZE(a)WRITE(*, ‘(A, 7I6)’) ‘ The lower bounds are: ‘, LBOUND(a)WRITE(*, ‘(A, 7I6)’) ‘ The upper bounds are: ‘, UBOUND(a)END PROGRAM
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Output:
11 5 (size(a, 1) = 11, size(a, 2) = 4)44-5 0 (LBOUND(a, 1) = -5, LBOUND(a, 2) = 0) 5 3 (UBOUND(a, 1) = 5, UBOUND(a, 2) = 3)
(Sec. 6.8.3 Transformational Intrinsic Functions)
Table 6-2
DOT_PRODUCT (VECTOR_A, VECTOR_B)MATMUL (MATRIX_A, MATRIX_B)RESHAPE (SOURCE, SHAPE)
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Ch. 7 Introduction to Procedures
Sec. 7.1 Subroutines
The general form of a subroutine
SUBROUTINE subroutine_name (argument_list) . . . (Declaration section) . . . (Execution section) . . .RETURNEND SUBROUTINE [name]
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The calling program uses a CALL statement to call a subroutine:
CALL subroutine_name (argument_list)
Fig. 7-1 (the hypotenuse of a right triangle)
SUBROUTINE calc_hypotenuse (side_1, side_2, hypotenuse)IMPLICIT NONEREAL, INTENT(IN) :: side_1, side_2REAL, INTENT(OUT) :: hypotenuseREAL :: temp
temp = side_1**2 + side_2**2hypotenuse = SQRT(temp)RETURNEND SUBROUTINE
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Test : Write a test driven program.
Fig. 7-2
PROGRAM test_hypotenuseIMPLICIT NONEREAL :: s1, s2, hypot
WRITE(*,*) ‘Enter the length of side 1:’READ(*,*) s1WRITE(*,*) ‘Enter the length of side 2:’READ(*,*) s2
CALL calc_hypotenuse(s1, s2, hypot)WRITE(*, 1000) hypot1000 FORMAT (1X, ‘ The length of the hypotenuse is :’, F10.4)END PROGRAM
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Fig. 7-3 PROGRAM sort1IMPLICIT NONEINTEGER, PARAMETER :: max_size = 10REAL, DIMENSION (max_size) :: aCHARACTER (len = 20) :: filenameINTEGER :: i, iptr, j, statusINTEGER :: nvals = 0REAL :: tempWRITE(*, 1000)1000 FORMAT (1X, ‘ Enter the file name’)READ(*, ‘(A20)’) filenameOPEN (UNIT = 9, FILE = filename, STATUS = ‘OLD’, & ACTION = ‘READ’, IOSTAT = status)fileopen: IF(status == 0) THEN DO READ (9, *, IOSTAT = status) temp IF (status /= 0) EXIT nvals = nvals + 1 a(nvals) = temp END DO
Sec. 7.1.1 Example Problem - Sorting
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CALL sort(a, nvals)WRITE(*, ‘(A)’) ‘ The sorted data are:’ WRITE(*, 1040) ( a(i), i = 1, nvals) 1040 FORMAT (4X, F10.4)ELSE fileopenWRITE(*, 1050) status1050 FORMAT (1X, ‘File open failed: ’, I6)END IF fileopenEND PROGRAM
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SUBROUTINE sort(arr, n)IMPLICIT NONEINTEGER, INTENT(IN) :: nREAL, DIMENSION(n), INTENT(INOUT) :: arrINTEGER :: i. iptr, jREAL :: tempouter: DO i = 1, n – 1 iptr = i inner: DO j = i + 1, n minval: IF (arr(j) < arr(iptr)) THEN iptr = j END IF minval END DO inner swap: IF ( i /= iptr ) THEN temp = arr(i) arr(i) = arr(iptr) arr(iptr) = temp END IF swap END DO outer RETURN END SUBROUTINE sort
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Test:
INPUT2.TXT
13.312.-3.00.4.06.64.-6.
output
Enter the file nameINPUT2.TXTThe sorted data are: -6.0000 -3.0000 0.0000 4.0000 4.0000 6.600012.000013.3000
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Sec. 7.1.2 The Intent Attribute
INTENT(IN), INTENT(OUT), INTENT(INOUT)
e.g.,
SUBROUTINE sub1(input, output)IMPLICIT NONEREAL, INTENT(IN) :: inputREAL, INTENT(OUT) :: output
output = 2. * inputinput = -1. ! This line is an errorEND SUBROUTINE
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Sec. 7.1.3 Variable Passing in Fortran: The Pass-by-Reference Scheme
e.g.,
PROGRAM testREAL :: a, b(4)INTEGER :: next. . .CALL sub1(a, b, next). . .END PROGRAM test
SUBROUTINE sub1(x, y, i)REAL, INTENT(OUT) :: xREAL, INTENT(IN) :: y(4)INTEGER, INTENT(IN) :: i. . .END SUBROUTINE sub1
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Sec. 7.1.4 Passing Arrays to Subroutines
e.g.,
SUBROUTINE process (data1, data2, n, nvals)IMPLICIT NONEINTEGER, INTENT(IN) :: n, nvalsREAL, INTENT(IN), DIMENSION(n) :: data1REAL, INTENT(OUT), DIMENSION(n) :: data2
data2 = 3. * data1END SUBROUTINE process
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Sec. 7.1.5 Passing Character Variables to Subroutines
e.g.,
PROGRAM test_sample_stringIMPLICIT NONECHARACTER (len=15) :: aCALL sample(a)END PROGRAM
SUBROUTINE sample (string)IMPLICIT NONECHARACTER (len=*), INTENT(IN) :: stringWRITE(*,’(1X, A, I3)’) ‘Length of variable = ‘, LEN(string)END SUBROUTINE
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Sec. 7.1.6 Error Handling in Subroutines
Eg. 1, (Bad! If temp < 0, SQRT(temp) = ???)
SUBROUTINE process (a, b, result)IMPLICIT NONEREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultREAL :: temp
temp = a - bresult = SQRT(temp)END SUBROUTINE
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Eg. 2, (Better! But still not good, STOP)∵
SUBROUTINE process (a, b, result)IMPLICIT NONEREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultREAL :: temp
temp = a – bIF ( temp >= 0.) THEN result = SQRT(temp)ELSE WRITE(*,*)’ Square root of negative value in sub. Process!’ STOPEND IFEND SUBROUTINE
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Eg. 2, (Much better! error flag)∵
SUBROUTINE process (a, b, result, error)IMPLICIT NONEREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultINTEGER, INTENT(OUT) :: errorREAL :: temp
temp = a – bIF ( temp >= 0.) THEN result = SQRT(temp) error = 0ELSE result = 0 error = 1END IFEND SUBROUTINE
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Example (Gauss-Jordan Elimination)
Linear eq.:
1 x1 + 1 x2 + 1 x3 = 1
2 x1 + 1 x2 + 1 x3 = 2
1 x1 + 3 x2 + 2 x3 = 4
(1)
(3)
(2)
or
1 1 1
2 1 1
1 3 2
x1
x2
x3
=
1
2
4
1 1 1
2 1 1
1 3 2
1
2
4
or
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a1 x1 + 0 x2 + 0 x3 = b1
0 x1 + a2 x2 + 0 x3 = b2
0 x1 + 0 x2 + a3 x3 = b3
or
a1 0 0
0 a2 0
0 0 a3
x1
x2
x3
=
b1
b2
b3
.
.
.???
x1 = b1/a1,
x2 = b2/a2,
x3 = b3/a3.
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Gauss-Jordan Elimination:
1 x1 + 1 x2 + 1 x3 = 1
2 x1 + 1 x2 + 1 x3 = 2
1 x1 + 3 x2 + 2 x3 = 4
(1)
(3)
(2)
1 1 1
0 -1 -1
0 2 1
1
0
3
(1) × -2 + (2) 0 x1 – x2 – x3 = 0 (4)
(1) × -1 + (3) 0 x1 + 2x2 + x3 = 3 (5)
(new row 2)
(new row 3)
∴ (1) (4) (5)
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1 x1 + 1 x2 + 1 x3 = 1
0 x1 - 1 x2 - 1 x3 = 0
0 x1 + 2 x2 + 1 x3 = 3
(1)
(5)
(4)
1 0 0
0 -1 -1
0 0 -1
1
0
3
(4) + (1) 1 x1 + 0 x2 + 0 x3 = 1 (6)
(4) × 2 + (5) 0 x1 + 0 x2 - 1 x3 = 3 (7)
(new row 1)
(new row 3)
∴ (6) (4) (7)
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1 x1 + 0 x2 + 0 x3 = 1
0 x1 - 1 x2 - 1 x3 = 0
0 x1 + 0 x2 - 1 x3 = 3
(6)
(7)
(4)
1 0 0
0 -1 0
0 0 -1
1
-3
3
(7) × -1 + (4) 0 x1 - 1 x2 + 0 x3 = -3 (8) (new row 2)
∴ (6) (7) (8)
x1 = -1,
-x2 = -3,
-x3 = 3.
x1 = -1, x2 = 3, x3 = -3.
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Gauss-Jordan Elimination:
3 x1 – 6 x2 + 7 x3 = 3
9 x1 + 0 x2 – 5 x3 = 3
5 x1 – 8 x2 + 6 x3 = -4
(1)
(3)
(2)
9 0 -5
5 -8 6
3 -6 7
3
-4
3
9 x1 + 0 x2 – 5 x3 = 3
5 x1 – 8 x2 + 6 x3 = -4
3 x1 – 6 x2 + 7 x3 = 3
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(1)
(3)
(2)
3
-51/9
2
(1) × (-5/9) + (2)
0 x1 – 8 x2 + (79/9) x3 = -51/9
(1) × (-3/9) + (3)
0 x1 – 6 x2 + (78/9) x3 = 2
(new row 2)
(new row 3)
9 x1 + 0 x2 – 5 x3 = 3
5 x1 – 8 x2 + 6 x3 = -4
3 x1 – 6 x2 + 7 x3 = 3
9 0 -5
0 -8 79/9
0 -6 78/9
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3
-51/9
2row 2 × (-(-6) /(-8)) + row 3,
9 0 -5
0 -8 79/9
0 -6 78/9
9 0 -5
0 -8 79/9
0 0 75/36
3
-51/9
225/36
row 3 × (-(-5) /(75/36))+ row 1, 9 0 0
0 -8 79/9
0 0 75/36
18
-51/9
225/36
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row 3 × (-(79/9) /(75/36))+ row 2,
9 0 0
0 -8 0
0 0 75/36
18
-32
225/36
x1 = 2,
x2 = 4,
x3 = 3.
9 0 0
0 -8 79/9
0 0 75/36
18
-51/9
225/36
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Computer program:
Reorder the equations !
Maximum pivot technique
Avoids divided-by-zero errors.
Reduces round-off errors.
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( Subroutine simul, [a] [x] = [b] )
SUBROUTINE simul (a, b, ndim, n, error)IMPLICIT NONEINTEGER, INTENT(IN) :: ndimREAL, INTENT(INOUT), DIMENSION(ndim,ndim) :: aREAL, INTENT(INOUT), DIMENSION(ndim) :: bINTEGER, INTENT(IN) :: nINTEGER, INTENT(OUT) :: errorREAL, PARAMETER :: epsilon = 1.0E-06REAL :: factor, tempINTEGER :: irow, ipeak, jrow, kcol
! Process n times to reorder the eqs.mainloop: DO irow = 1, n ! Find peak pivot for column irow in rows irow to n ipeak = irow
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max_pivot: DO jrow = irow+1, n IF (ABS(a(jrow, irow)) > ABS(a(ipeak, irow))) THEN ipeak = jrow END IF END DO max_pivot ! Check for singular eqs.singular: IF ( ABS(a(ipeak, irow)) < epsilon)THEN error = 1 RETURN END IF singular! Otherwise, if ipeak /= irow, swap eqs irow and ipeak. swap_eqn : IF (ipeak /= irow) THEN DO kcol = 1, n temp = a(ipeak, kcol) a(ipeak, kcol) = a(irow, kcol) a(irow, kcol) = temp END DO
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temp = b(ipeak) b(ipeak) = b(irow) b(irow) = temp END IF swap_eqn ! (Eq. irow) * [-a(jrow, irow)/a(irow, irow)] + (Eq. jrow) eliminate: DO jrow = 1, n IF (jrow /= irow) THEN factor = -a(jrow, irow) / a(irow, irow) DO kcol = 1, n a(jrow, kcol) = a(irow, kcol) * factor + a(jrow, kcol) END DO b(jrow) = b(irow) * factor + b(jrow) END IF END DO eliminateEND DO mainloop
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divide: DO irow = 1, n b(irow) = b(irow) / a(irow, irow) a(irow, irow) = a(irow, irow) / a(irow, irow)END DO divideerror = 0END SUBROUTINE simul
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(A test driven program)
PROGRAM test_simulIMPLICIT NONEINTEGER, PARAMETER :: max_size = 10INTEGER :: i, j, n, istat, errorREAL, DIMENSION(max_size, max_size) :: aREAL, DIMENSION (max_size) :: bCHARACTER(len=20) :: file_name
! Get the eqs.WRITE(*,1000)1000 FORMAT(‘Enter the filename containing the eqs:’)READ(*, ‘(A20)’) file_nameOPEN(UNIT=3, FILE=file_name, STATUS=‘OLD’, & ACTION=‘READ’, IOSTAT=istat)
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file_open: IF (istat == 0) THEN READ(3, *) n size_ok: IF ( n <= max_size) THEN DO i = 1, n READ(3, *) (a(i, j), j = 1, n), b(i) END DO! Display coefficiants.WRITE(*, 1020)1020 FORMAT (/, 1X, ‘ Coeffs. Before call:’) DO i = 1, n WRITE(*, 1030) (a(i, j), j = 1, n), b(i) 1030 FORMAT (1X, 7F11.4) END DO! Solve eqs.CALL simul(a, b, max_size, n, error)
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error_check: IF (error /= 0) THEN WRITE(*,1040) 1040 FORMAT (/1X, ‘Zero pivot encountered!’, & // 1X, ‘ No unique solu.’) ELSE error_check WRITE(*, 1050) 1050 FORMAT ( /, 1X, ‘ Coeffs. After call:’) DO i = 1, n WRITE(*, 1030) ( a(i, j), j = 1, n), b(i) END DO WRITE(*, 1060) 1060 FORMAT (/, 1X, ‘ The solus. are:’) DO i = 1, n WRITE(*, 1070) i, b(i) 1070 FORMAT (3X, ‘X(‘, I2, ‘)=‘, F16.6) END DO END IF error_checkEND IF size_ok
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ELSE file_open WRITE(*, 1080) istat 1080 FORMAT(1X, ‘File open failed – status=‘, I6)END IF file_openEND PROGRAM
Test: LINPUT.TXT
31.0 1.0 1.0 1.02.0 1.0 1.0 2.01.0 3.0 2.0 4.0
x1 + x2 + x3 = 12 x1 + x2 + x3 = 2 x1 + 3x2 +2 x3 = 4
Output: x1 = 1 x2 = 3 x3 = -3
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The SAVE Attribute and Statement
e.g.,
REAL, SAVE :: sums
SAVE :: var1, var2, …
or
or
SAVE (all local variables)
Any local variables declared with the SAVE attributewill be unchanged between calls to the procedure.
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Example (Statiscal Analysis: Running Averages)
Average: x_ave =
Σ xii=1
N
N
Standard deviation:
S = N Σxi
2 – (i=1 i=1
N N
Σxi )2
N (N-1)
1/2
Input: x (i.e., xi , i = 1, 2, …, N) 0 ≧
Output: x_ave and S
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e.g.,
xi N Σ xi Σxi2 xave S
3.0 1 3.0 9.0 3.00 0.02.0 2 5.0 13.0 2.50 0.707 3.0 3 8.0 22.0 2.67 0.5774.0 4 12.0 38.0 3.00 0.8162.8 5 14.8 45.84 2.96 0.713
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SUBROUTINE running_average(x, x_ave, s, nvals, reset)! IF ‘reset’ is “.TRUE.”, clear running sums and exit.IMPLICIT NONEREAL, INTENT(IN) :: xREAL, INTENT(OUT) :: x_ave, sINTEGER, INTENT(OUT) :: nvalsLOGICAL, INTENT(IN) :: resetINTEGER, SAVE :: nREAL, SAVE :: sum_xREAL, SAVE :: sum_x2
calc_sums: IF (reset) THEN n=0; sum_x = 0. ; sum_x2 = 0. x_ave = 0. ; s = 0. ; nvals = 0ELSE n = n + 1
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sum_x = sum_x + x sum_x2 = sum_x2 + x**2 x_ave = sum_x / n IF (n >= 2) then s = SQRT((n*sum_x2 – sum_x **2)/(n*(n-1))) ELSE s = 0. END IF nvals = nEND IF calc_sumsEND SUBROUTINE running_average
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(Test driven program)
PROGRAM test_running_averageIMPLICIT NONEINTEGER :: istat, nvalsREAL :: x_ave, s, xCHARACTER(len=20) :: filename
! Clear the running sumsCALL running_average(0., x_ave, s, nvals, .TRUE.)WRITE(*,*)’ Enter the file name containing the data:’READ(*,’(A20)’) filenameOPEN(UNIT=21, FILE=filename, STATUS=‘OLD’, & ACTION=‘READ’, IOSTAT=istat)open ok: IF(istat == 0) THEN calc: DO READ(21, *, IOSTAT=istat) x IF (istat /= 0) EXIT
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CALL running_average(x, x_ave, s, nvals, .FALSE.) WRITE(*,1020)’ Value = ‘, x, ‘ x_ave = ‘, x_ave, & ‘ Std_dev = ‘, s, ‘ N = ‘, nvals 1020 FORMAT(1X, 3(A, F10.4), A, I6) END DO calcELSE openok WRITE(*, 1030) istat 1030 FORMAT(1X, ‘File open failed-status = ‘, I6)END IF openokEND PROGRAM
Test: RUNNING.TXT
3.02.03.04.02.8
3.0 3.00 0.0 1 2.0 2.50 0.707 23.0 2.67 0.577 34.0 3.00 0.816 42.8 2.96 0.713 5
x x_ave S N
Output
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Automatic Arrays
A local explicit-shape array with non-constant bounds.
e.g.,
SUBROUTINE sub1(x, y, n, m)IMPLICIT NONEINTEGER, INTENT(IN) :: n, mREAL, INTENT(IN), DIMENSION(n, m) :: xREAL, INTENT(OUT), DIMENSION(n, m) :: yREAL, DIMENSION(n, m) :: temp ! Auto. array
temp = 0.. . .END SUBROUTINE
( Auto. arrays are automatically destroyed when subroutine ends.)
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Sec. 7.4 Sharing Data Using Modules
Programs Subroutines (or functions)
argument list
(exchange data)
Programs Subroutines (or functions)(share data)
module
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Fig. 7-8 (a simple module)
MODULE testIMPLICIT NONESAVE INTEGER, PARAMETER :: num_vals = 5REAL, DIMENSION(num_vals) :: valuesEND MODULE test
(SAVE should always be included in any module that declares sharable data.)
To use the values in the module,
USE module_name
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Fig. 7-9 (using a module to share data between a main program and a subroutine)PROGRAM test_moduleUSE testIMPLICIT NONEREAL, PARAMETER :: pi = 3.141592
values = pi * (/ 1., 2., 3., 4., 5. /)CALL sub1END PROGRAM
SUBROUTINE sub1USE testIMPLICIT NONEWRITE(*,*)valuesEND SUBROUTINE sub1
Output
3.14159 6.28318 9.42478 12.5664 15.7080
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Sec. 7.3 Modules Procedures
e.g., MODULE my_subsIMPLICIT NONE. . . (declare shared data here)
CONTAINS SUBROUTINE sub1(a, b, c, x, error) IMPLICIT NONE REAL, DIMENSION(3), INTENT(IN) :: a REAL, INTENT(IN) :: b, c REAL, INTENT(OUT) :: x LOGICAL, INTENT(OUT) :: error . . . END SUBROUTINE sub1END MODULE my_subs
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PROGRAM main_progUSE my_subsIMPLICIT NONE. . .CALL sub1(a, b, c, x, error). . .END PROGRAM
Sec. 7.3.1 Using Modules to Creat Explicit Interfaces
Why module procedure?
Explicit interface
(helps the compiler to catch errors)
Implicit interface: Assume that the programmer got the arguments right. (e.g., number, type, intent, …)
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Fig. 7-12 (argument mismatch)MODULE my_subsIMPLICIT NONECONTAINS SUBROUTINE bad_argument(i) IMPLICIT NONE INTEGER, INTENT(IN) :: I WRITE(*,*) ‘ I=‘ ,i END SUBROUTINE END MODULE
PROGRAM bad_callUSE my_subsIMPLICIT NONEREAL :: x = 1.CALL bad_argument(x)END PROGRAM
The computer will catch the argument mismatch!
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Assumed-shape Arrays
e.g., MODULE test_moduleCONTAINS SUBROUTINE process2(data1, data2) REAL, INTENT(IN), DIMENSION(:, :) :: data1 REAL, INTENT(IN), DIMENSION(:, :) :: data2 data2 = 3. * data1 END SUBROUTINE process2END MODULE test_module
( Assumed-shape arrays work only if a procedure has an explicit interface. However, the upper and lower bounds of each dimension cannot be determined.)
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(The use of assumen-shape arrays)
MODULE test_moduleCONTAINS SUBROUTINE test_array(array) IMPLICIT NONE REAL, DIMENSION(:, :) :: array INTEGER :: i1, i2, j1, j2
i1 = LBOUND(array, 1) i2 = UBOUND(array, 1) j1 = LBOUND(array, 2) j2 = UBOUND(array, 2) WRITE(*, 100) i1, i2, j1, j2 100 FORMAT(1X, ‘ The bounds are: (‘, I2, ‘:’, I2,’,’, I2,’:’,I2,’)’) WRITE(*, 110) SHAPE(array) 110 FORMAT(1X, ‘ The shape is: ‘, 2I4) WRITE(*, 120) SIZE(array) 120 FORMAT(1X, ‘ The size is: ‘, I4) END SUBROUTINE test_arrayEND MODULE test_module
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PROGRAM assumed_shapeUSE test_moduleIMPLICIT NONEREAL, DIMENSION(-5:5, -5:5) :: a = 0.REAL, DIMENSION(10, 2) :: b = 1.WRITE(*,*) ’ Calling test_array with array a:’CALL test_array(a)WRITE(*,*) ‘ Calling test_array with array b:’CALL test_array(b)END PROGRAM
Output:Calling test_array with array a:The bounds are: (1:11, 1:11)The shape is: 11 11The size is: 121Calling test_array with array b:The bounds are: (1:10, 1:2)The shape is: 10 2The size is: 20
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Sec. 7.4 Fortran Functions
Intrinsic functions: e.g., SIN(x), LOG(x).
User-defined functions (or function subprograms)
The general form is
FUNCTION name ( argument_list) . . . (Declaration) . . . (Execution) . . . name = expression RETURNEND FUNCTION [name]
optional
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Two equivalent forms:
INTEGER FUNCTION my_function(i, j)
FUNCTION my_function(i, j)INTEGER :: my_function
or
Fig. 7-13 (f(x) = ax2 + bx + c)
REAL FUNCTION quadf (x, a, b, c)IMPLICIT NONEREAL, INTENT (IN) :: x, a, b, c
quadf = a*x**2 + b*x + cEND FUNCTION
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Fig. 7-14 (a test driven program)
PROGRAM test_quadfIMPLICIT NONEREAL :: quadfREAL :: a, b, c, x, temp
WRITE(*,*) ‘ Enter quadratic coeffs. a, b, and c:’READ(*,*) a, b, cWRITE(*,*) ‘ Enter x value:’READ(*,*) xTemp = quadf(x, a, b, c)WRITE(*,100) ‘ f(‘, x, ‘)=‘, temp100 FORMAT(A, F10.4, A, F12.4)END PROGRAM
Test: a = 1., b = 2., c=3.x = 2.
f (x) = 11.
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If a function modifies the values in its argument list,
side effects. (Always declares all dummy arguments with the INTENT(IN) attribute.)
A function produces a single output value using its input arguments. If need more than one output value, should use a subroutine not a function.
Example 7-5 The Sinc Function
sinc(x) = sin(x)/x and sinc(0)=1.
See Fig. 7-15
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Fig. 7-16 (sinc(x))
FUNCTION sinc(x)IMPLICIT NONEREAL, INTENT(IN) :: xREAL :: sincREAL, PARAMETER :: epsilon = 1.0E-30
IF(ABS(x) > epsilon) THEN sinc = sin(x) / xELSE sinc = 1.END IFEND FUNCTION sinc
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Fig. 7-17 (a test driven program)
PROGRAM test_sincIMPLICIT NONEREAL :: xREAL :: sinc
WRITE(*,*) ‘ Enter x:’READ(*,*) xWRITE(*, 100) ‘ sinc(x) = ‘, sinc(x)100 FORMAT(1X, A, F8.5)END PROGRAM
Test: x sinc(x)
0. 1.000001.0E-29 1.000003.141593 0.000001.570796 0.63662
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Sec. 7.5 Passing Procedures as Arguments to Other Procedures
e.g., PROGRAM testREAL, EXTERNAL :: fun_1, fun_2REAL :: x, y, output. . .CALL evaluate(fun_1, x, y, output)CALL evaluate(fun_2, x, y, output). . .END PROGRAMSUBROUTINES evaluate(fub, a, b, result)REAL, EXTERNAL :: funREAL, INTENT(IN) :: a, bREAL, INTENT(OUT) :: resultResult = b*fun(a)END SUBROUTINE evaluate
(two user-defined funcs)
Sec. 7.5 .1 Passing User-Defined Functions as Arguments
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Two equivalent forms:
REAL, EXTERNAL :: fun_1, fun_2
EXTERNAL fun_1, fun_2
or
EXAMPLE 7-6 (Passing Functions to Procedures in an Arguments List)
Σf(xi) i=1
N
Nave = , x1 = 0, xN = 1, N = 101
Δx =xN – x1
N - 1= 0.01
xi = x1 + (i -1) × Δx
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Fig. 7-18
REAL FUNCTION ave_value (func, first_value, last_value, n)IMPLICIT NONEREAL, EXTERNAL :: funcREAL, INTENT(IN) :: first_value, last_valueINTEGER, INTENT(IN) :: nREAL :: delta, sumINTEGER :: I
Delta = (last_value – first_value) / (n-1)Sum = 0.DO I = 1, n sum = sum + func( first_value + (i-1) * delta)END DOAve_value = sum / nEND FUNCTION
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Fig. 7-19 (Test driven program)
PROGRAM test_ave_valueIMPLICIT NONEREAL :: ave_valueREAL, EXTERNAL :: my_functionREAL :: aveAve = ave_value(my_function, 0., 1., 101)WRITE(*,1000) ‘ my-function’, ave1000 FORMAT (1X, ‘ The ave. value of ‘, A, & ‘ between 0. and 1. is ‘, F16.6, ‘.’)END PROGRAM
REAL FUNCTION my_function(x)IMPLICIT NONEREAL, INTENT(IN) :: xMy_function = 3. * xEND FUNCTION
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Sec. 7.5 .2 Passing Subroutines as Arguments
Example 7-7 (Passing Subroutines to Procedures in an Argument List)
Fig 7-20
Subroutine subs_as_arguments(x, y, sub, result)IMPLICIT NONEEXTERNAL :: subREAL, INTENT(IN) :: x, yREAL, INTENT(OUT) :: result
CALL sub(x, y, result)END SUBROUTINE subs_as_arguments
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Fig. 7-21 (Test driver program)
PROGRAM test_subs_as_argumentsIMPLICIT NONEEXTERNAL :: sum, prodREAL :: x, y, result
WRITE(*,*) ‘ Enter x:’READ(*,*) xWRITE(*,*) ‘ Enter y:’READ(*,*) y
CALL sub_as_arguments(x, y, prod, result)WRITE(*,*) ‘ The product is ‘, result
CALL sub_as_arguments(x, y, psum, result)WRITE(*,*) ‘ The sum is ‘, resultEND PROGRAM
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SUBROUTINE prod(x, y, result)IMPLICIT NONEREAL, INTENT(IN) :: x, yREAL, INTENT(OUT) :: resultresult = x * yEND SUBTOUTINE prod
SUBROUTINE sum(x, y, result)IMPLICIT NONEREAL, INTENT(IN) :: x, yREAL, INTENT(OUT) :: resultresult = x + yEND SUBTOUTINE sum
Test: try x = 4 & y = 5
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Ch. 8 Additional Data Types
Data types:Real data typeComplex data typeDerived data type
Sec. 8.1 Alternative KINDS of the REAL Data Type
REAL data type:
Single precision (32 bits, default): 6 ~ 7 significant digits, 10-38 ~ 1038 (range).
Double precision (64 bits): 15 ~ 16 significant digits, 10-308 ~ 10308 (range).
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Sec. 8.1.1 Kinds of REAL Constants and Variables
Kind number:
e.g., REAL (KIND = 4) :: value_1REAL (KIND = 8), DIMENSION(20) :: arrayREAL (4) :: temp
A better approach:
INTEGER, PARAMETER :: single = 4INTEGER, PARAMETER :: double = 8REAL (KIND = single) :: value_1REAL (KIND = double), DIMENSION(20) :: arrayREAL (single) :: temp
Valid real constants:
34._4 34._double 3.0E0 3.0D0
(a single_precision const)
(a double_precision const)
(depends on machine)
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Sec. 8.1.2 Determining the KIND of a Real Variable
Fig. 8-1
PROGRAM kindsIMPLICIT NONEWRITE(*, 100) KIND(0.0)WRITE(*, 101) KIND(0.0D0)100 FORMAT(‘The KIND for single precision is’, I2)101 FORMAT(‘The KIND for double precision is’, I2)END PROGRAM
Output:
The KIND for single precision is 1The KIND for double precision is 2
(depends on machine)
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Sec. 8.1.3 Selecting Precision in a Process-Independent MannerUse
kind_number = SELECTED_REAL_KIND (p=precision, r=range)
e.g., kind_number = SELECTED_REAL_KIND (p = 6, r = 37)kind_number = SELECTED_REAL_KIND (p = 12)kind_number = SELECTED_REAL_KIND (r = 100)kind_number = SELECTED_REAL_KIND (13, 200)kind_number = SELECTED_REAL_KIND (13)kind_number = SELECTED_REAL_KIND (p = 17)
SELECTED_REAL_KIND(p, r)SELECTED_INT_KIND(r)KIND(x)PRECISION(x)RANGE(x)
Function
Table 8-1 ( KIND-related intrinsic functions)
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Fig. 8-2 (Select desired kinds and get information about real values)
PROGRAM select_kindsIMPLICIT NONEINTEGER, PARAMETER :: sgl = SELECTED_REAL_KIND (p=6, r=37)INTEGER, PARAMETER :: dbl = SELECTED_REAL_KIND (p=13, r=200)REAL (kind = sgl) :: var1 = 0.REAL (kind = dbl) :: var2 = 0._dbl
WRITE(*, 100) ‘ Var1’, KIND(var1), PRECISION(var1), RANGE(var1)WRITE(*, 100) ‘ Var2’, KIND(var2), PRECISION(var2), RANGE(var2)100 FORMAT (1X, A, ‘: Kind = ‘, I2, ‘, Precision = ‘, I2, ‘, Range = ‘, I3)END PROGRAM
Output:
Var1: Kind = 1, Precision = 6, Range = 37Var2: Kind = 2, Precision = 15, Range = 307
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Sec. 8.1.4 Mixed_Mode Arithmetic
e.g., 1/3 + 1/3 = 0.3333 … + 0.3333… = 0.6666 … (by hand)
By computer:
Expression Result
(1) 1.D0/3. + 1/3 3.333333333333333E-001(2) 1.D0/3. + 1./3. 6.666666333333333E-001(3) 1.D0/3. + 1./3.D0 6.666666666666666E-001
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PROGRAM testREAL(2) :: aREAL(1) :: b
A = 1.0D-208B = 1.0E-37WRITE(*,*)’a = ‘, aWRITE(*,*)’b = ‘, bEND PROGRAM
Output:
a = 1.000000000000E-0208b = 1.000000E-37
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Sec. 8.1.5 Double-Precision Intrinsic Functions
See Table B-1 (p. 501)
e.g., ABS, COS, SIN, EXP, LOG, . . .
COS(0.2) = 0.980067
COS(0.2d0) = 0.980066577841
Sec. 8.1.6 When to Use High-precision Real Values
Double-precision:
larger (twice) memory size and slower speed
reduces round-off error problems
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Example 8-1 (Numerical Calculation of Derivatives)
d f(x)d x = limit
Δx 0
f(x+Δx)- f(x)Δx
In theory: The small Δx, the better the estimate of the derivative.
But, in practice: ???
e.g.,
f(x) = 1/x, df(x)/dx = -1/x2.
d f(x)
d x x = 0.15= - 44.44444444 . . .
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Fig. 8-4 (The derivative of f(x) = 1/x at x = 0.15, single and double-precision)
PROGRAM diffIMPLICIT NONEINTEGER, PARAMETER :: single = SELECTED_REAL_KIND(p=6, r=37)INTEGER, PARAMETER :: double = SELECTED_REAL_KIND(p=13)INTEGER :: iREAL(KIND=double) :: ans, d_ans, d_error, d_fx, d_fxdx, d_dx, d_x = 0.15D0REAL(KIND=single) :: s_ans, s_error, s_fx, s_fxdx, s_dx, s_x = 0.15E0
WRITE(*,1)1 FORMAT(1X, ‘ DX TRUE ANS Sp ANS Dp ANS’, & ‘ Sp ERR DP ERR’)ans = -(1.D0/d_x**2)step_size: DO I = 1, 10 s_dx = 1.0 /10.0**i d_dx = 1.D0 / 10.D0 **I ! Calculate s-p ans. s_fxdx = 1. /(s_x + s_dx) s_fx = 1./(s_x) s_ans = (s_fxdx – s_fx) /s_dx
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s_error = ((s_ans – ans)/ans)*100. ! Calculate d-p ans. d_fxdx = 1. /(d_x + d_dx) d_fx = 1./(d_x) d_ans = (d_fxdx – d_fx) /d_dx d_error = ((d_ans – ans)/ans)*100. WRITE(*, 100) d_dx, ans, s_ans, d_ans, s_error, d_error 100 FORMAT(1X, ES10.3, F12.7, F12.7, ES22.14, F9.3, F9.3) END DO step_sizeEND PROGRAM
Output: see Textbook (p. 370)!
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Sec. 8.2 The Complex Data Type
c = a + i b = z θ,∠
a = z cosθ, b = z sin θ, θ= arctan (b/a).
e.g.,
c1 = a1 + i b1, c2 = a2 + i b2,
c1 ± c2 = (a1 ± a2) + i (b1± b2),
c1 × c2 = (a1a2 - b1b2) + i (a1b2 ± b1a2),
c1 (a1a2 + b1b2) + i (b1a2 - a1b2)
c2 (a22
+ b22 )
=
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Sec. 8.2.1 Complex Constants and Variables
Complex constant:
(1., 0.) 1 + i 0
(0.7071, 0.7071) 0.7071 + i 0.7071
(0, - 1) - i
(1.01E6, 0.5E2) 1010000 + i 50
(1.12_dbl, 0.1_dbl) 1.12 + i 0.1
Complex variable:
COMPLEX (KIND = kind_num) :: var1, var2, . . .COMPLEX, DIMENSION (256) :: array
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Sec. 8.2.2 Initializing Complex Variables
Eg. 1,COMPLEX, DIMENSION (256) :: array1array1 = (0., 0.)
Eg. 2,
Complex :: a1 = (3.141592, -3.141592)
Eg. 3,
COMPLEX :: a1READ(*, ‘(2F10.2)’) a1
COMPLEX :: a1READ(*, *) a1
or
INPUT: (no parentheses)e.g., 1.0 0.25
INPUT: (with parentheses)e.g., (1.0, 0.25)
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Sec. 8.2.3 Using Complex Numbers with Relational Operators
Given c1 = a1 + i b1, c2 = a2 + i b2,
c1 == c2 (to see if equal)
c1 /= c2 (to see if not equal)
c1 c2 (cannot compare!)
<><=>=
|c1| |c2| (compare magnitude)
<><=>=
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Sec. 8.2.4 Complex Intrinsic Functions
See App. B
1. Type conversion functions:
Given a and b,
COMPLX (a, b, kind) a + i b
Given c ( = a + i b),
REAL(c) a
AIMAG(c) b
2. Absolute function:
c = a + i b,
CABS(c) c = (a2 + b2)1/2
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3. Math functions: (generic functions)
COS, SIN, EXP, ABS, . . .
e.g.,
PROGRAM compxlCOMPLEX :: a = (1.0, 0.25)write(*,*) cos(a)END PROGRAM
Output:(0.55727, -0.21256)
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ax2 + bx + c = 0,
x = -b ± ( b2 – 4ac )1/2
2a
If b2 – 4ac = 0
b2 – 4ac > 0
b2 – 4ac < 0
two distinct real roots
two complex roots
a single repeated root
Example 8-3 The Quadratic Eq. (revisited)
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PROGRAM roots_2IMPLICIT NONEREAL :: a, b, c, d, re, imCOMPLEX :: x1, x2
WRITE(*,*)'Enter the coeffs. a, b, and c:‘READ(*,*) a, b, cd = b**2 – 4.*a*cx1=(-b + SQRT(CMPLX(d,0.))) / (2. * a)x2=(-b – SQRT(CMPLX(d,0.))) / (2. * a)WRITE(*,*) ‘The roots are:‘WRITE(*,100) ’x1=‘, REAL(x1), ‘+ i’, AIMAG(x1)WRITE(*,100) ’x2=‘, REAL(x2), ‘+ i’, AIMAG(x2)100 FORMAT(A, F10.4, A, F10.4)END PROGRAM roots_2
Fig. 8-10
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Test:
x2 + 5x + 6 = 0, x1,2 = -2, -3
x2 + 4x + 4 = 0, x1,2 = -2
x2 + 2x + 5 = 0, x1,2 = -1 ± i 2
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Sec. 8.3 Derived Data Types
User-defined data types derived from intrinsic data types.
A convenient way to group together all the information about a particular item.
Derived data type: Array:
Components (names) Elements (numbers)
different types the same type
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The form of a derived data type:
TYPE [::] type_name component definitions . . .END TYPR [type_name]
e.g.,
TYPE :: person CHARACTER(len=14) :: first_name CHARACTER :: middle_initial CHARACTER(len=14) :: last_name CHARACTER(len=14) :: phone INTEGER :: age CHARACTER :: sex CHARACTER(len=11) :: ssnEND TYPE person
(optional)
(optional)
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Declare variables of the derived type person:
TYPE (person) :: john, janeTYPE(person), DIMENSION(100) :: people
(an array of 100 variables of type person)
Structure constructor:
e.g.,
e.g.,
john = person(‘John’, ‘R’, ‘Jones’, ‘323-6439’, 23, ‘M’, ‘123-45-6789’)jane = person(‘Jane’, ‘C’, ‘Bass’, ‘332-3060’, 17, ‘F’, ‘999-99-9999’)
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A derived data type within another derived data type:
TYPE :: grade_info TYPE (person) :: student INTEGER :: num_quizzes REAL, DIMENSION(10) :: quiz_grades INTEGER :: num_exams REAL, DIMENSION(10) :: exam_grades INTEGER :: final_exam_grade REAL :: averageEND TYPETYPE(grade_info), DIMENSION(30) :: class
(an array class of 30 variables of type grade_info)
e.g.,
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Sec. 8.3.1 Working with Derived Data Types
Component Selector:
e,g,.
john % age = 35
class(5) % final_exam_grade = 95
class(5) % student % age = 23
(variable of a derived data type)
(a component)
(5th student in the class)
(the age of the 5th student in the class)
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Sec. 8.3.2 Input and Output of Derived Data Types
Fig. 8-11 (I/O of variables of derived data types)
PROGRAM test_ioIMPLICIT NONETYPE :: person CHARACTER (len = 14) :: first_name CHARACTER :: middle_initial CHARACTER (len = 14) :: last_name CHARACTER (len = 14) :: phone INTEGER :: age CHARACTER :: sex CHARACTER (len = 11) :: ssnEND TYPE personTYPE (person) :: johnjohn = person(‘John’, ‘R’, ‘Jones’, ‘323-6439’, 23, ‘M’, ‘123-45-6789’)WRITE(*,*) ‘ Free format:’, johnWRITE(*,1000) john1000 FORMAT(‘ Formatted I/O:’, /, 4(1X, A, /), 1X, I4, /, 1X, A, /, 1X, A)END PROGRAM
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Sec. 8.3.3 Declaring Derived Data Types in Modules
Example 8-4 (Sorting derived data types by components)
Customer database:
John Q Public 123 Sesame Street Anywhere NY 10035James R Johnson Rt. 5 Box 207c West Monroe LA 71291. . .
Display the database in alphabetical order by last name, by city, or by zip code.
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Fig. 8-12 (sort a customer database)
MODULE typesIMPLICIT NONETYPE :: personal_info CHARACTER(len=12) :: first CHARACTER(len=12) :: mi CHARACTER(len=12) :: last CHARACTER(len=26) :: street CHARACTER(len=12) :: city CHARACTER(len=2) :: state INTEGER :: zipEND TYPE personal_infoEND MODULE types
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PROGRAM customer_databaseUSE typesIMPLICIT NONEINTEGER, PARAMETER :: max_size = 100LOGICAL, EXTERNAL :: lt_lastLOGICAL, EXTERNAL :: lt_cityLOGICAL, EXTERNAL :: lt_zipTYPE(personal_info), DIMENSION(max_size) :: customersLOGICAL :: exceed = .FALSE.CHARACTER (len=20) :: filenameINTEGER :: choice, i, nvals=0, statusTYPE(personal_info) :: temp
WRITE(*,*) ‘ Enter the file name:’READ(*,’(A20)’) filenameOPEN(UNIT=9, FILE=filename, STATUS=‘OLD’, IOSTAT=status) Fileopen: IF(status == 0) THEN
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DO READ(9,1010, IOSTAT=status) temp 1010 FORMAT(A12,1X,A1,1X,A12,1X,A26,1X,A12,1X,A2,1X,I5) IF(status /= 0)EXIT nvals = nvals + 1 size: IF (nvals <= max_size) THEN customers(nvals) = temp ELSE exceed = .TRUE. END IF size END DO toobig: IF(exceed) THEN WRITE(*,1020) nvals, max_size 1020 FORMAT (‘ Max. array size exceeded:’, I6, ‘>’, I6)ELSEWRITE(*,1030)1030 FORMAT(1X, ‘Enter the way to sort database:’, /, 1X, & ‘ 1 - By last name’, /,1X, ‘ 2 - By city’, /, 1X, ‘ 3 - By zip code’)
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READ(*,*) choice SELECT CASE (choice) CASE (1) CALL sort_database(customers, nvals, lt_last) CASE (2) CALL sort_database(customers, nvals, lt_city) CASE (3) CALL sort_database(customers, nvals, lt_zip) CASE DEFAULT WRITE(*,*)’ Invalid choice entered!’ END SELECT WRITE(*,’(A)’) ‘ The sorted database values are:’ WRITE(*, 1010)(customers(i), i=1, nvals) END IF toobigELSE fileopen WRITE(*,’(A, I6)’) ‘ File open error: IOSTAT=‘, statusEND IF fileopenEND PROGRAM
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SUBROUTINE sort_database (array, n, lt_fun)USE typesIMPLICIT NONEINTEGER, INTENT(IN) :: nTYPE(personal_info), DIMENSION(n), INTENT(INOUT) :: arrayLOGICAL, EXTERNAL :: lt_funINTEGER :: i, iptr, jTYPE(personal_info) :: tempouter: DO I = 1, n-1 iptr = I inner: DO j = i+1, n minval: IF (lt_fun(array(j), array(iptr))) THEN iptr = j END IF minval END DO inner swap: IF( I /= iptr) THEN temp=array(i) array(i) = array(iptr) array(iptr) = temp END IF swapEND DO outerEND SUBROUTINE sort_database
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LOGICAL FUNCTION lt_last(a,b)USE typesIMPLICIT NONETYPE(personal_info), INTENT(IN) :: a, blt_last = a%last < b%lastEND FUNCTION lt_last
LOGICAL FUNCTION lt_city(a,b)USE typesIMPLICIT NONETYPE(personal_info), INTENT(IN) :: a, blt_city = a%city < b%cityEND FUNCTION lt_city
LOGICAL FUNCTION lt_zip(a,b)USE typesIMPLICIT NONETYPE(personal_info), INTENT(IN) :: a, blt_zip = a%zip < b%zipEND FUNCTION lt_zip
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Test:
DATABASE.TXT
John Q Public 123 Sesame Street Anywhere NY 10035James R Johnson Rt. 5 Box 207C West Monroe LA 71291Joseph P Ziskend P. O. Box 433 APO AP 96555Andrew D Jackson Jackson Square New Orleans LA 70003Jane X Doe 12 Lakeside Drive Glenview IL 60025Colin A Jeffries 11 Main Street Chicago IL 60003
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Polar Coordinates: (extra)
c = a + i b = z θ,∠
z = (a2 + b2)1/2 , θ= arctan (b/a).a = z cosθ, b = z sin θ.
Given
p1 = z1 θ∠ 1, p2 = z2 θ∠ 2, θ1, θ2: in degrees.
p = p1 + p2 = z θ, z = ???, θ= ???.∠
Prob. Creat a derived data type called polar for z θ∠ ,
two components: magnitude z
angle θ
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MODULE mathIMPLICIT NONEREAL, PARAMETER :: const = 57. 296 ! 1 rad=57.296 degreesTYPE :: polar REAL :: z ! magnitude REAL :: theta ! AngleEND TYPE polarEND MODULE math
PROGRAM test_polarUSE mathIMPLICIT NONETYPE(polar) :: p1, p2, pWRITE(*,*)’ Enter z1 and theta1 (in degrees):’READ(*,*) p1%z, p1%thetaWRITE(*,*)’ Enter z2 and theta2 (in degrees):’READ(*,*) p2%z, p2%thetaCALL add_polar(p1, p2, p)WRITE(*,*)’ z = ‘, p%z, ‘ theta = ‘, p%theta, ‘ degrees’END PROGRAM
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SUBROUTINE add_polar(p1, p2, p)USE mathIMPLICIT NONETYPE(polar), INTENT(IN) :: p1, p2TYPE(polar), INTENT(OUT) :: pREAL :: a, ba = p1%z*cos(p1%theta/const) + p2%z*cos(p2%theta/const)b = p1%z*sin(p1%theta/const) + p2%z*sin(p2%theta/const)p%z = SQRT(a**2 + b**2)p%theta = ATAN2(b, a) * constRETURNEND SUBROUTINE
Test:
p1 = 3.0 30∠ 0, p2 = 4.0 60∠ 0,
Z = 6.766, θ= 47.190 .
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Ch. 9 Advanced Features of Procedures and Modules
Sec. 9.1 Internal Procedures
Internal procedure
host program unit
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Fig. 9-1 ( Sec(θ) )
PROGRAM test_secIMPLICIT NONEINTEGER, PARAMETER :: single = kind(0.0)REAL (KIND = single), PARAMETER :: pi = 3.141592REAL (KIND = single) :: thetaWRITE(*,*) ‘ Enetr angle in degrees:’READ(*,*) thetaWRITE(*, ‘(A, F10.4)’) ‘ The Secant is ‘, secant(theta)CONTAINS REAL FUNCTION secant(angle_in_degrees) REAL (KIND = single) :: angle_in_degrees secant = 1. /cos(angle_in_degrees * pi / 180.) END FUNCTION secantEND PROGRAM test_sec
Test: θ= 450, Sec(θ) = 1.4142
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Sec. 9.2 Recursive Procedures
e.g., N! =
N(N-1)!, N 1≧
1, N = 0
Fig. 9-2RECURSIVE SUBROUTINE factorial (n, result)IMPLICIT NONEINTEGER, INTENT(IN) :: nINTEGER, INTENT(OUT) :: resultINTEGER :: tempIF ( n >= 1 ) THEN CALL factorial (n-1, temp) result = n * tempELSE result = 1END IFEND SUBROUTINE factorial
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Fig. 9-3
RECURSIVE FUNCTION fact(n) RESULT(answer)IMPLICIT NONEINTEGER, INTENT(IN) :: nINTEGER :: answer
IF ( n >= 1 ) THEN answer = n * fact(n-1)ELSE answer = 1END IFEND FUNCTION fact
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PROGRAM test_factorialIMPLICIT NONEINTEGER, EXTERNAL :: factINTEGER :: n, resultWRITE (*,*) ‘ Enter n ( >=0):’READ (*,*) nCALL factorial (n, result)WRITE(*,*) n, ‘! =‘, resultWRITE(*,*) n, ‘! =‘, fact(n)END PROGRAM
Test: 7 ! = 5040
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Sec. 9.3 Keyword Arguments and Optional Arguments
Fig. 9-4 (The use of keyword arguments)
MODULE procsCONTAINS REAL FUNCTION calc (first, second, third) IMPLICIT NONE REAL, INTENT(IN) :: first, second, third calc = (first – second) / third END FUNCTION calcEND MODULE procs
(only with explicit interfaces)
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PROGRAM test_keywordsUSE procsIMPLICIT NONEWRITE(*,*) calc (3., 1., 2.)WRITE(*,*) calc (first=3., second=1., third=2.)WRITE(*,*) calc (second=1., third=2., first=3. )WRITE(*,*) calc (3., third=2., second=1.)END PROGRAM test_keywords
Output:
1.00001.00001.00001.0000
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Optional argument:
e.g., INTEGER, INTENT(IN), OPTIONAL :: upper_limit. . .IF ( PRESENT(upper_limit) ) THEN. . .ELSE. . .END IF
Example 9-1 (Finding the extreme values in a data set)
4 optional output arguments:
1. The max. value2. The location of the max. value3. The min. value4. The location of the min. value
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Fig. 9-5MODULE procsCONTAINS SUBROUTINE extremes(a, n, maxval, pos_maxval, minval, pos_minval) IMPLICIT NONE INTEGER, INTENT(IN) :: n REAL, INTENT(IN), DIMENSION(n) :: a REAL, OPTIONAL :: maxval, minval INTEGER, OPTIONAL :: pos_maxval, pos_minval! local variables INTEGER :: i, pos_max, pos_min REAL :: real_max, real_min real_max = a(1) pos_max = 1 real_min = a(1) pos_min = 1! Find the extremes DO i = 2, n max: IF(a(I) > real_max) THEN real_max = a(i) pos_max = I END IF max
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min: IF(a(i) < real_min) THEN real_min = a(I) pos_min = I END IF minEND DO!Report the resultsIF ( PRESENT(maxval)) THEN maxval = real_maxEND IFIF ( PRESENT(pos_maxval)) THEN pos_maxval = pos_maxEND IFIF ( PRESENT(minval)) THEN minval = real_minEND IFIF ( PRESENT(pos_minval)) THEN pos_minval = pos_minEND IFEND SUBROUTINEEND MODULE procs
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PROGRAM test_extremesUSE procsIMPLICIT NONEINTEGER, PARAMETER :: max_size = 10REAL, DIMENSION(max_size) :: aREAL :: large, smallINTEGER :: large_pos, small_pos, nvals, IWRITE (*,*) “ Enter the number of values:”READ (*,*) nvalsDO i = 1, nvalsREAD (*,*) a(i)END DOCALL extremes(a, nvals, large, large_pos, small, small_pos)WRITE(*, *) ” All arguments in order:”, & large, large_pos, small, small_posCALL extremes(a, nvals, maxval=large, minval= small, & pos_maxval=large_pos, pos_minval=small_pos)WRITE(*, *) ” All arguments in arbitrary order:”, & large, large_pos, small, small_posCALL extremes(a, nvals, maxval=large, minval=small)WRITE(*, *) ” Large and small only:”, large, smallEND PROGRAM
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Test:
Enter the number of values:71.34.-21.10.2-0.040.5.
Output:
All arguments in order: 34.0 2 -21.1 3All arguments in arbitrary order: 34.0 2 -21.1 3Large and Small only: 34.0 -21.1
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Sec. 9.5 Extending Fortran with User-defined Operator and Assignments
Permit the programmer to define new operators or extend existing ones.
1. Interface operator block: INTERFACE OPERATOR (operator_symbol) MODULE PROCEDURE function_1 . . . END INTERFACE
2. Interface assignment block: INTERFACE ASSIGNMENT (=) MODULE PROCEDURE subroutine_1 . . . END INTERFACE
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Example 9-3 (Vectors)
V1 = x1 i + y1 j + z1 k, V2 = x2 i + y2 j + z2 k ,^ ^ ^ ^^ ^
• Addition ( + ) : V1 + V2 = (x1 + x2) i + (y1+ y2) j + (z1 + z2) k ^ ^ ^
• Subtraction ( - ) : V1 - V2 = (x1 - x2) i + (y1 - y2) j + (z1 - z2) k ^ ^ ^
• Dot product (.DOT.) : V1 . V2 = (x1x2) + (y1y2) + (z1z2)
• Cross product (.CROSS.) :
^ ^ ^V1 × V2 = (y1z2 – y2z1) i + (z1x2 – z2x1) j + (x1y2 – x2y1) k
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MODULE vectorsIMPLICIT NONETYPE vector REAL :: x REAL :: y REAL :: zEND TYPEINTERFACE OPERATOR (+) MODULE PROCEDURE vector_addEND INTERFACEINTERFACE OPERATOR (-) MODULE PROCEDURE vector_subtractEND INTERFACEINTERFACE OPERATOR (.DOT.) MODULE PROCEDURE vector_dotEND INTERFACEINTERFACE OPERATOR (.CROSS.) MODULE PROCEDURE vector_crossEND INTERFACE
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CONTAINS FUNCTION vector_add(vec_1, vec_2) TYPE(vector) :: vector_add TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_add%x=vec_1%x+vec_2%x vector_add%y=vec_1%y+vec_2%y vector_add%z=vec_1%z+vec_2%z END FUNCTION vector_add
FUNCTION vector_subtract(vec_1, vec_2) TYPE(vector) :: vector_subtract TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_subtract%x=vec_1%x-vec_2%x vector_subtract%y=vec_1%y-vec_2%y vector_subtract%z=vec_1%z-vec_2%z END FUNCTION vector_subtract
FUNCTION vector_dot(vec_1, vec_2) REAL :: vector_dot TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_dot=vec_1%x*vec_2%x+vec_1%y*vec_2%y+vec_1%z*vec_2%z END FUNCTION vector_dot
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FUNCTION vector_cross(vec_1, vec_2) TYPE (vector) :: vector_cross TYPE(vector), INTENT(IN) :: vec_1, vec_2 vector_cross%x=vec_1%y*vec_2%z-vec_1%z*vec_2%y vector_cross%y=vec_1%z*vec_2%x-vec_1%x*vec_2%z vector_cross%z=vec_1%x*vec_2%y-vec_1%y*vec_2%x END FUNCTION vector_cross END MODULE vectors
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PROGRAM test_vectors USE vectors IMPLICIT NONE TYPE(vector) :: vec_1, vec_2
! Test addition vec_1 = vector(1., 2., 3.) vec_2 = vector(4., 5., 6.) WRITE(*, 1000) vec_1, vec_2, vec_1 + vec_2, vec_1 - vec_2, & vec_1 .DOT. vec_2, vec_1 .CROSS. vec_2 1000 FORMAT(' Test addition:', /, & 'vec_1 = ', 3F8.2,/, & 'vec_2 = ', 3F8.2,/, & 'vec_1 + vec_2 = ', 3F8.2,/, & 'vec_1 - vec_2 = ', 3F8.2,/, & 'vec_1 .DOT. vec_2 = ', F8.2, / , & 'vec_1 .CROSS. vec_2 = ', 3F8.2) END PROGRAM test_vectors
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Output:
Test addition:vec_1 = 1.00 2.00 3.00vec_2 = 4.00 5.00 6.00vec_1 + vec_2 = 5.00 7.00 9.00vec_1 – vec_2 = -3.00 -3.00 -3.00vec_1 .DOT. vec_2 = 32.00vec_1 .CROSS. Vec_2 = -3.00 6.00 -3.00
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Example: (extra)
z θ= z∠ 1 θ∠ 1 ± z2 θ∠ 2.
1. Define a new data type called POLAR that represents a complex number in polar form. Then write a module containing interface operator blocks to allow two polar numbers to be added and subtracted, i.e.,
2. Write a test driver program.
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MODULE mathIMPLICIT NONEREAL, PARAMETER :: const = 57. 296 ! 1 rad=57.296 degreesTYPE :: polar REAL :: z ! magnitude REAL :: theta ! AngleEND TYPE polar
INTERFACE OPERATOR (+) MODULE PROCEDURE polar_addEND INTERFACE
INTERFACE OPERATOR (-) MODULE PROCEDURE polar_subtractEND INTERFACE
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CONTAINS FUNCTION polar_add(p1, p2) TYPE(polar) :: polar_add TYPE(polar), INTENT(IN) :: p1, p2 REAL :: a, b a = p1%z*cos(p1%theta/const) + p2%z*cos(p2%theta/const) b = p1%z*sin(p1%theta/const) + p2%z*sin(p2%theta/const) polar_add%z = SQRT(a**2 + b**2) polar_add%theta = ATAN2(b, a) * const END FUNCTION polar_add
FUNCTION polar_subtract(p1, p2) TYPE(polar) :: polar_subtract TYPE(polar), INTENT(IN) :: p1, p2 REAL :: a, b a = p1%z*cos(p1%theta/const) - p2%z*cos(p2%theta/const) b = p1%z*sin(p1%theta/const) - p2%z*sin(p2%theta/const) polar_subtract%z = SQRT(a**2 + b**2) polar_subtract%theta = ATAN2(b, a) * const END FUNCTION polar_subtractEND MODULE math
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PROGRAM test_polarUSE mathIMPLICIT NONETYPE(polar) :: p1, p2, pWRITE(*,*)' Enter z1 and theta1 (in degrees):'READ(*,*) p1%z, p1%thetaWRITE(*,*)' Enter z2 and theta2 (in degrees):'READ(*,*) p2%z, p2%thetaWRITE(*,*)' z1 + z2 = ', p1+p2WRITE(*,*)' z1 - z2 = ', p1-p2END PROGRAM
Test: Enter z1 and theta1 (in degrees):3.0 30.0Enter z2 and theta2 (in degrees):4.0 60.0
z1 + z2 = 6.76643 47.1791z1 – z2 = 2.05314 -73.0649