1.  Progress After Spring Break

• Updated up to 04/03/2003
• Material Covered
  • More on matrices:
    • matrix multiplication
      • standard version
      • row-oriented version
      • column-oriented version
      • loop representation vs. Fortran 90 constructs -- allowing operations on matrix parts
      • dot_product intrinsic function
      • matmul intrinsic function
    • tridiagonal matrices
      • standard 2D representation and its problems
      • 3-column representation
      • 3-vector representation
  • More on subprograms
    • internal vs. external subprograms
      • internal subprograms similar to blocks in Algol
      • saving local variables in internal subprograms
    • statement functions
    • array valued functions
    • recursive subprograms
    • subprograms as subprogram arguments
    • passing information to subprograms -- matrix arguments
      • call by address only
      • multi-dimensional matrices stored as single-dimensional vectors
      • need to define, pass and utilize the leading dimension(s) of multi-dimensional matrices
    • inefficiencies in subprograms -- leave them to the compiler
• Solving systems of n linear equations with n unknown values
  • solution of a system with an upper triangular matrix -- from the bottom up
  • solution of a system with a lower triangular matrix -- from the top down
  • problem formulated as a matrix problem -- Ax = b
  • possible operations on rows of matrix A
    • adding two rows
    • multiplying a row by a constant
    • exchanging two rows
  • elimination of the first column of A
  • elimination of the second column of A -- without making any changes to the first column
  • elimination of the remaining columns of A -- resulting in an upper triangular matrix U
  • operations on the right hand side b
  • what if the system is to be solved for multiple right hand sides?
  • storing values used to eliminate columns of A in the same locations
  • LU decomposition
  • pivoting to enable and stabilize the solution process
    • partial pivoting
    • full pivoting
    • row interchanges
    • storage of pivoting/row-exchange information
  • solving a system in four steps
    • LU decomposition with partial pivoting
    • application of row exchanges to the right hand side b
    • solution of the problem Lz = b -- forward elimination
    • solution of the problem Ux = z -- back substitution
• Operations on characters and character strings
  • Defining character variables
  • Defining character strings
  • Defining arrays of strings
  • Reading and printing strings
  • Extractions -- similarity between extracting substrings and operating on subarrays
  • Concatenations
  • Intrinsic functions:
    • length -- function len
    • substring inside of a string -- function index
    • comparisons -- function ichar
• Additional input/output possibilities
  • E - descriptor -- for floating point numbers in scientific notation
  • D - descriptor -- for double precision numbers
  • Complex numbers
  • T - descriptor -- for tabs
  • Formats as character strings
  • Reading a file
  • End-of-file
  • Formatted reads

Reading assignment: pages v-185