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
|
.TH rowcomp 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
rowcomp - row compression, range
.SH CALLING SEQUENCE
.nf
[W,rk]=rowcomp(A [,flag] [,tol])
.fi
.SH PARAMETERS
.TP 10
A
: real or complex matrix
.TP 10
flag
: character string
.TP 10
tol
:
real number
.TP
W
: square non-singular matrix (change of basis)
.TP
rk
: integer (rank of \fVA\fR)
.SH DESCRIPTION
Row compression of \fVA\fR. \fVAc = W*A\fR is a row compressed matrix: i.e.
\fVAc=[Af;0]\fR with \fVAf\fR full row rank.
.LP
\fVflag\fR and \fVtol\fR are optional parameters: \fVflag='qr'\fR
or \fV'svd'\fR (default \fV'svd'\fR).
.LP
\fVtol\fR is a tolerance parameter (of order \fVsqrt(%eps)\fR as default value).
.LP
The \fVrk\fR first columns of \fVW'\fR span the range of \fVA\fR.
.LP
The \fVrk\fR first (top) rows of \fVW\fR span the row range of \fVA\fR.
.SH Remark
A non zero vector \fVx\fR belongs to range(\fVA\fR) iff \fVW*x\fR is row
compressed in accordance with \fVAc\fR i.e the norm of its last components
is small w.r.t its first components.
.SH EXAMPLE
.nf
A=rand(5,2)*rand(2,4); // 4 col. vectors, 2 independent.
[X,dim]=rowcomp(A);Xp=X';
svd([Xp(:,1:dim),A]) //span(A) = span(Xp(:,1:dim)
x=A*rand(4,1); //x belongs to span(A)
y=X*x
norm(y(dim+1:$))/norm(y(1:dim)) // small
.fi
.SH SEE ALSO
colcomp, fullrf, fullrfk
.SH AUTHOR
F. D.
|
