Tue Feb 18 19:04:08 GMT-0500 1992

TO: Paul Pendred
FR: Charles Severance
SU: Substitute Teaching

Thanks for sub-teaching for my LBS 290F Section.

The room is: C-104 Holmes

The Time is 1:50-2:40

I am moving my office hours and review session to Thursday evening...

Office Hours: Thursday 6-8 
Review session: Thursday 8-9

Don't try to deal with grading problems - have them come to my office hours.

They are working on two different programs - one with means and standard
deviations - it should be easy for you to find bugs in those.  The other
is a calculus program which does a newton-method for finding a polynomial
through certain x,y points - it is pretty tricky - you might find it hard 
to help the calculus students.



2/19/92 

OUTLINE

Two Dimensional arrays


Difference between a 2-D array and a 1-D array

  Syntax
    Declaration     REAL A(6,4)
    Usage           A(2,2) = 25.3
     - 2-D array references can be used anywhere a 1-D array 
       reference can be used.
      
     Left hand side:   A(2,2) = X + 1
     Right Hand side:  X = A(4,1) + A(1,3)
     I/O:              PRINT *,A(2,3)

    Statements like:   A = 0
             and       A(1) = 0
    are meaningless

  Pictorial representation - first dimension is row and second dimension is
  column.  - Draw a picture of a 1-D array and a 2-D array - point out some
  elements - emphasize that each of the cells is like a variable.

  Why do we use 2-D arrays?

    - Sometimes we want several one-dimensional arrays
    - Sometimes we want to represent some physical relationship using
      a 2-D array.

  Go over the example programs.


Write a program which will read up 10 sets of 3 numbers - print the numbers
out and along side each row, print the row total, and below each column 
print the column total.

Input:

1 2 4
2 2 5
6 1 2
8 8 2
1 8 2
8 2 6
7 3 4
1 9 3
2 3 5
7 4 0

Program:

      INTEGER DAT(10,3),ROWSUM(10),COLSUM(3)
      INTEGER ROW,COL
*
      DO 10 ROW=1,10
        READ *,DAT(ROW,1),DAT(ROW,2),DAT(ROW,3)
  10  CONTINUE
*
* Compute the row sums
*
      DO 30 ROW = 1,10
        ROWSUM(ROW) = 0
        DO 20 COL=1,3
          ROWSUM(ROW) = ROWSUM(ROW) + DAT(ROW,COL)
20      CONTINUE
30    CONTINUE
*
* Compute the column sums
*
      DO 50 COL=1,3
        COLSUM(COL) = 0
        DO 40 ROW=1,10
          COLSUM(COL) = COLSUM(COL) + DAT(ROW,COL)
   40   CONTINUE
   50 CONTINUE
*
      DO 70 ROW=1,10
        PRINT 5,DAT(ROW,1),DAT(ROW,2),DAT(ROW,3),ROWSUM(ROW)
70    CONTINUE
      PRINT 5,COLSUM(1),COLSUM(2),COLSUM(3)
5     FORMAT(1X,I5,1X,I5,1X,I5,1X,I5)
      END

Output:
     1     2     4     7
     2     2     5     9
     6     1     2     9
     8     8     2    18
     1     8     2    11
     8     2     6    16
     7     3     4    14
     1     9     3    13
     2     3     5    10
     7     4     0    11
    43    42    33

Write a program to simulate heat flow in a plate.  The plate is 100 cm by
100 cm.  The whole plate starts at 30 degrees celsius.  At position X=20,Y=10
there is a 100 degree celsius candle.  At position X=60, Y=40 there is
a 0-degree celsius ice cube.  We can simulate the heat flow in a single time
step by taking the average of all of the neighboring cells.  All of the edges
of the plate stay at 30 degrees. Find the heat at point X=50,Y=40 after 
30 time steps.   

No input

Program:

      REAL PLATE(100,100)
      INTEGER X,Y
      INTEGER TS
*
      DO 10 X=1,100
        DO 10 Y=1,100
          PLATE(X,Y) = 30.0
   10 CONTINUE
*
      PLATE(20,10) = 100.0
      PLATE(60,40) = 0.0
*
      DO 50 TS=1,30
        DO 40 X=2,98
          DO 30 Y=2,98
             IF ( X.EQ.20.AND.Y.EQ.10 ) THEN
                PLATE(X,Y) = 100.0
             ELSE IF ( X.EQ.60.AND.Y.EQ.40 ) THEN
                PLATE(X,Y) = 0.0
             ELSE
                PLATE(X,Y) = ( PLATE(X,Y) 
     !              + PLATE(X-1,Y-1) + PLATE(X-1,Y) + PLATE(X-1,Y+1)
     !              + PLATE(X,Y-1) + PLATE(X,Y) + PLATE(X,Y+1)
     !              + PLATE(X+1,Y-1) + PLATE(X+1,Y) + PLATE(X+1,Y+1) ) 
     !              /10.0
             ENDIF
30        CONTINUE
40      CONTINUE
50    CONTINUE
*
      PRINT *,'HEAT AT X=50, Y=40 AFTER 30 TIME STEPS ',PLATE(50,40)
      END

Output:

 HEAT AT X=50, Y=40 AFTER 30 TIME STEPS   2.974749756E+001 


Two Dimensional arrays

  Syntax
    Declaration     REAL A(6,4)
    Usage           
     Left hand side:   A(2,2) = X + 1
     Right Hand side:  X = A(4,1) + A(1,3)
     I/O:              PRINT *,A(2,3)

  Statements like:   A = 0
           and       A(1) = 0
  are meaningless (syntax errors)

  First dimension is row and second dimension is
  column.

  Why do we use 2-D arrays?

    - Sometimes we want several 
      one-dimensional arrays
    - Sometimes we want to represent 
      some physical relationship using
      a 2-D array.