-
Notifications
You must be signed in to change notification settings - Fork 0
/
ref.m
72 lines (65 loc) · 2.87 KB
/
ref.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
function [ref] = ref(A)
[r,c]=size(A); % r = # of row(s), c= # of column(s)
j=1; %starts with 1st column
previouslead=1;
% if # of columns equals to or less than # of rows for a given matrix
if c==r || r>c
for i = 1:c
% If given row and columnn is zero-number, swaping with the first non-zero row
if (A(i,j)==eps) && i<r && any(A(i:r,j),1)
nonzero=find(A(i:r,j),1,"first");
e = A(i,:); A(i,:)= A(i+nonzero-1,:); A(i+nonzero-1,:) = e;
end
% if first row and columnn is nonzero number
if any(A(i,:))
lead=find(A(i,:),1,"first");
A(i,:)= (1/A(i,lead))* A(i,:); %Leading value Divids with itslef to make it as 1
for k=i+1:r
A(k,:)=(-A(k,lead)* A(i,:)) + A(k,:); % Making zero for all rows below the leading value
end
end
j=j+1;
end
A=round(A,2); % Rounding to 2 decimal value
for i=1:c-1
if ~any(A(i,:)) % For a given row, if all columns is zero-number, swaping with the first non-zero row
x = A(i,:); A(i,:)= A(i+1,:); A(i+1,:) = x;
end
lead=find(A(i,:),1,"first");
if previouslead>lead % swaping, if leading one is not in a nonzero row appears to the left of the leading one in any lower row.
x = A(i,:); A(i,:)= A(i-1,:); A(i-1,:) = x ;
end
previouslead=lead;
end
end
% if # of column(s) is greater then # of row(s) for a given matrix
if r<c
for i = 1:r
% if first row and columnn is zero-number, swaping with the first non-zero row
if (A(i,j)==0) && i<r && any(A(i:r,j))
nonzero=find(A(i:r,j),1,"first");
e = A(i,:); A(i,:)= A(i+nonzero-1,:); A(i+nonzero-1,:) = e;
end
% if first row and columnn is nonzero number
if any(A(i,:))
lead=find(A(i,:),1,"first");
A(i,:)= (1/A(i,lead))* A(i,:); %Leading value Divids with itslef to make it as 1
for k=i+1:r
A(k,:)=(-A(k,lead)* A(i,:)) + A(k,:); % Making zero for all rows below the leading value
end
end
j=j+1 ;
end
A=round(A,2); % Rounding to 2 decimal value
for i=1:r-1
if ~any(A(i,:)) % For a given row, if all columns is zero-number, swaping with the first non-zero row
x = A(i,:); A(i,:)= A(i+1,:); A(i+1,:) = x;
end
lead=find(A(i,:),1,"first");
if previouslead>lead % swaping, if leading one is not in a nonzero row appears to the left of the leading one in any lower row
x = A(i,:); A(i,:)= A(i-1,:); A(i-1,:) = x;
end
previouslead=lead;
end
end
ref=A;