Contents

• A quick tour of Fortran 95
  • Program Form
  • Free vs. Fixed Formats
  • Declaration of Variables
    • Memory Organization. Variables
    • Integers.
    • Characters.
    • Reals.
    • Double Precision.
    • Complex
    • Logical.
    • General Form of Declarations
    • Implicit declarations
  • Assignment
  • Intrinsic Numerical Operations
  • Literal Constants
  • Relational Operators
  • Intrinsic Logical Operations
  • Intrinsic Character Operations
    • Substrings
    • Concatenation
  • Operator Precedence
  • Intrinsic Functions
  • Controlling the flow of the program
    • Conditional execution
    • Examples
    • Repetitive action
  • Application to DO loops: Fahrenheit to Celsius
  • Problems
  • Input and Output
    • Standard (keyboard/console)
    • File I/O
    • Application
  • Arrays
    • Application
  
  
• The Building Blocks of a Fortran Application
  • Program Units
  • External Procedures
  • External Functions
  • Actual arguments, formal (dummy) arguments and local variables
    • Implicit Interfaces
  • Subroutines
  • Comments
  • Modules
  • Scope of Variables
  • Lifetime of Variables
  • Global Storage
    • Circle Example
    • Taylor Approximation of the Exponential
  • F77 Global Storage. Storage Association.
  • BLOCK DATA statements
  • Include files
  • More on Storage Association
  
  
• More on Flow Control
  • Named IF and DO Blocks
  • The IF Statement
  • More on DO Loops
    • Conditional EXIT
    • Conditional CYCLE
    • Exit and Cycle with named loops
    • Initial Test (DO...WHILE) Loop
  • SELECT CASE
  • Exceptional Situations
    • STOP
    • RETURN
    • GO TO
  
  
• Computer Representation of Numbers and Computer Arithmetic
  • Binary numbers
  • Memory
    • Characters in Memory
    • The Memory Model
  • Reprentation of Signed Integers
    • Integers in Memory
    • Note.
  • Floating-Point Numbers
  • The IEEE standard
    • Floating Point Types
    • Detailed IEEE representation
    • Number range
    • Precision
  • The Set of FP Numbers
  • Rounding - up or down
  • Chopping
  • Rounding to nearest.
  • Arithmetic Operations
  • IEEE Arithmetic
  • The Guard Digit
  • Special Arithmetic Operations
    • Signed zeros
    • Operations with
    • Operations with NaN
    • Comparisons
  • Arithmetic Exceptions
    • Division by 0
    • Overflow
    • Underflow
    • Inexact
    • Summary
  • Flags and Exception Trapping
  • Systems Aspects, from D. Goldberg, p. 193
    • Instruction Sets
    • Ambiguity
    • Programming Language Features
    • Optimizers
    • Exception Handling
  • Long Summations
  • Tipical pitfalls with floating point programs
    • Binary versus decimal
    • Floating point comparisons
    • Funny conversions
    • Memory versus register operands
    • Cancellation (``Loss-of Significance'') Errors
    • Insignificant Digits
    • Order of Operations Matters
  • Integer Multiplication
  • Homework
  
  
• Applications Part I.
  • The Fibonacci Sequence
  • Summation Formulas
  
  
• Intrinsic Functions
  • Generic vs. Specific Functions
  • Numerical Type Conversions
  • Numerical Intrinsic Functions
  • Mathematical Intrinsic Functions
  • Examples
  • Mixing Types
    • Mixed-Type Expressions
    • Mixed-Type Assignement
    • Integer Division
  
  
• Input and Output.
  • List-Directed Input and Output
  • Formats
    • Editor Descriptors
    • Example: READ Integer Data
    • Example: READ Character Data
  • File I/O
    • Records and Files
    • OPEN
    • READ
    • READ example
    • WRITE
    • FORMAT
  • File Positioning
  • Writing to a string
  
  
• Arrays
  • Declaring Arrays
  • Memory Storage
  • Array Attributes
  • Subscripting
  • Conformance
  • Array Expressions
  • Array Sections
  • RESHAPE intrinsic function
  • Array Constructors
  • Allocatable Arrays
  • Masked Assignment
  • Vector-valued Subscripts
  • Homework
  • Vector and Matrix Multiplication Intrinsics
  • Maximum and Minimum Intrinsics
  • Array Reduction Intrinsics
  • Array Arguments
    • Explicit Shape Arrays
    • Assumed Shape Arrays
    • Automatic Arrays
    • F77's Assumed-Size Arrays
  • Array-Valued Functions
  
  
• More on Procedures
  • Recall F90 Program Units
  • Side Effects
  • Argument Intent
  • Pure Functions
  • Internal Procedures
  • Modules Hosting Procedures
  • Scope
  • Scope example
  • Procedure Interfaces
    • More on Implicit Interfaces
    • Explicit Interfaces
    • Explicit Interfaces for Internal Procedures
    • Explicit Interfaces for External Procedures
  • Required Interfaces
  • Keyword Arguments
  • Optional Arguments
  • Recursive Functions
  • Recursive Subroutines
  
  
• Parametrised Intrinsic Types
  • Rationale
  • Parametrised Integers
  • Parametrized Reals
  • Kind Functions
  • Mixed KIND Expressions
  • Parametrised Logical Vaiables
  • Parametrised Character
  • Kinds and Procedures
  
  
• Derived Types
  • Defininig Derived Types
  • Arrays and Derived Types
  • Derived Types and Procedures
  
  
• Pointers and Targets
  • Pointers and Targets
  • Pointer Declaration
  • Target Declaration
  • Pointer Assignment
  • Association with Arrays
    • Example: Array swapping
  • Status of a Pointer
  • Dynamic Targets
  • Pointers to Arrays vs Allocatable Arrays
  • Pointers and Procedures
  • Pointer Valued Functions
  • Pointers and Derived Types
  • Example: Linked Lists
  • Arrays of Pointers
  • Example: Sorting Vectors
  
  
• Elements of object-oriented programming
  • Public and Private Entities
  • Derived Type Constructors
  • Generic Procedures
  
  
• Linear Systems of Algebraic Equations
  • Least Squares Fitting
  • The problem
  • Row Operations
  • The triangular form
  • Solving the upper triangular system
  • General algorithms
  • Computing the determinant
  • Pivoting
  • Triangular form with pivoting
  • Operation count
  • Singularity
  • Multiple systems with the same matrix
  • Computing the inverse of a matrix
  • Coding the LU decomposition
  • Coding the forward-backward substitution
  • LAPACK and BLAS.
  • Homework
    • LU decomposition
    • Back-substitution
  • Tests
  
  
• Linear Least Squares
  • Least Squares Data Fitting
  • The general problem formulation
  • The Calculus Approach
  • Orthogonality
  • Augmented system
  • Matlab
  • Algorithm for polynomial least squares fitting
  • Note
  
  
• Nonlinear Equations
  • The Newton Method for Nonlinear Equations
    • Order of convergence
  • The Secant Method
  • The Modified Newton Method
  • Fixed point iterations
  • The Newton Method for Systems
  • The Modified Newton Method for Systems
  
  
• Polynomial Interpolation
  • Example
  • Direct algorithm for polynomial interpolation
  • Nested polynomial evaluation
  • Lagrange form of the interpolation polynomial
  • Newton form of the interpolation polynomial
  • Reconstructing functions
  • Chebyshev points
  
  
• Numerical Integration
  • The Numerical Integration Problem
  • The Trapezoidal Method
  • The Simpson Method
  • Example.
  • Homework
  • Test Problem.
  
  
• Piecewise Polynomial Interpolation. Splines.
  • The Piecewise Interpolation Problem
  • Piecewise linear interpolation
  • Spline interpolation
    • Interpolation and Continuity.
    • Same slope condition.
    • Same curvature condition.
  • Example
  • Homework
    • Input.
    • Output.
    • Test
    • Note
    • Submit
    • Test Driver
  
  
• Taylor Polynomials
  • The Taylor Polynomial
  • Taylor Remainder
  • Important functions
  • Applications
  • Polynomial Evaluation
  • Sample Program
  • homework
    • Taylor polynomials
    • The project
  
  
• About this document ...