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% This diary demonstrates strategies for entering large matrices
% with lots of zero elements, in preparationfor lab 2.
% (The *real* way to do this is with 'sparse' matrices --but
% we'll get to that later). 
 
c = sqrt(2)
c =
    1.4142
 
% Suppose we ant to enter a 5 x 5 matrix (25 elements). 
% You can type in the matrix literally, as we've done before
 
A = [c 1 0 0 0 ; 0 1 -2 1 0 ; 1 0 c 0 0 ; 3 0 0 0 7 ; 0 1 0 -c 0]
 
A =
    1.4142    1.0000         0         0         0
         0    1.0000   -2.0000    1.0000         0
    1.0000         0    1.4142         0         0
    3.0000         0         0         0    7.0000
         0    1.0000         0   -1.4142         0
 
% But that's tedious and error prone, and it doesn't scale well 
% really big matrices.
 
% Here's a better way: Allocate a 5 x 5 matrix of zeros and then
% assign the nonzero elements
 
A = zeros(5,5)
 
A =
 
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
 
A(1,1) =  c
 
A =
 
    1.4142         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
 
A(1,1) =  c
 
A =
 
    1.4142    1.0000         0         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
 
A(2,2) =  1
 
A =
 
    1.4142    1.0000         0         0         0
         0    1.0000         0         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
 
A(2,3) =  -2 
 
A =
 
    1.4142    1.0000         0         0         0
         0    1.0000   -2.0000         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
 
% etc. That's still a lot of typing.
 
% Here's an even better way: assign all nonzero elems in a row at once
A = zeros(5,5);
 
A(1, [1 2] ) = [c 1]
 
A =
    1.4142    1.0000         0         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
 
A(2, [2 3 4] ) = [1 -2 1]
 
A =
    1.4142    1.0000         0         0         0
         0    1.0000   -2.0000    1.0000         0
         0         0         0         0         0
         0         0         0         0         0
         0         0         0         0         0
 
A(3, [1 3] ) = [1 c]
 
A =
    1.4142    1.0000         0         0         0
         0    1.0000   -2.0000    1.0000         0
    1.0000         0    1.4142         0         0
         0         0         0         0         0
         0         0         0         0         0
 
A(4, [1 5] ) = [3 7]
 
A =
    1.4142    1.0000         0         0         0
         0    1.0000   -2.0000    1.0000         0
    1.0000         0    1.4142         0         0
    3.0000         0         0         0    7.0000
         0         0         0         0         0
 
A(5, [2 4] ) = [1 -c]
A =
 
    1.4142    1.0000         0         0         0
         0    1.0000   -2.0000    1.0000         0
    1.0000         0    1.4142         0         0
    3.0000         0         0         0    7.0000
         0    1.0000         0   -1.4142         0
 
% Now solve Af = b, for the given b. 
b  = [ 0 5 4 -1 2]'
 
b =
     0
     5
     4
    -1
     2
 
f = A\b
 
f =
  -12.0711
   17.0711
   11.3640
   10.6569
    5.0305
 
A*f - b
 
ans =
 
   1.0e-14 *
 
         0
    0.1776
   -0.5329
         0
         0
 
% Awesome!
 
% An even, even better way to do this: SCRIPTS
% A script is a list of commands in a file that
% Matlab will execute sequentially
 
% I will write a file name 'solveAfb.m' that does the row 
% assignments as performed above
 
clear all
 
solveAfb
 
f =
  -12.0711
   17.0711
   11.3640
   10.6569
    5.0305
 
clear all
 
% Note that the script has created new variables A,b,c, and f.
who
 
Your variables are:
 
A  b  c  f  
 
A
 
A =
    1.4142    1.0000         0         0         0
         0    1.0000   -2.0000    1.0000         0
    1.0000         0    1.4142         0         0
    3.0000         0         0         0    7.0000
         0    1.0000         0   -1.4142         0