channelflow.org

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
<code matlab>
% 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

</code>
channelflow.org

User Tools

Site Tools

Page Tools
