A=rand(5,6)
A =
0.9501 0.7621 0.6154 0.4057 0.0579 0.2028
0.2311 0.4565 0.7919 0.9355 0.3529 0.1987
0.6068 0.0185 0.9218 0.9169 0.8132 0.6038
0.4860 0.8214 0.7382 0.4103 0.0099 0.2722
0.8913 0.4447 0.1763 0.8936 0.1389 0.1988
B=[1 -2 4;1 6 7;1 0 5]
B =
1 -2 4
1 6 7
1 0 5
svd(A)
ans =
2.9659
1.0658
0.6916
0.4881
0.1202
svd(B)
ans =
10.4705
4.8340
0.0395
cond(B)
ans =
264.9773
help cond
COND Condition number with respect to inversion.
COND(X) returns the 2-norm condition number (the ratio of the
largest singular value of X to the smallest). Large condition
numbers indicate a nearly singular matrix.
COND(X,P) returns the condition number of X in P-norm:
NORM(X,P) * NORM(INV(X),P).
where P = 1, 2, inf, or 'fro.'
See also CONDEST, CONDEIG, NORM, NORMEST.
cond(B,1)
ans =
392
cond(B,inf)
ans =
546
cond(B,'fro')
ans =
291.8673
help svd
SVD Singular value decomposition.
[U,S,V] = SVD(X) produces a diagonal matrix S, of the same
dimension as X and with nonnegative diagonal elements in
decreasing order, and unitary matrices U and V so that
X = U*S*V'.
S = SVD(X) returns a vector containing the singular values.
[U,S,V] = SVD(X,0) produces the "economy size"
decomposition. If X is m-by-n with m > n, then only the
first n columns of U are computed and S is n-by-n.
See also SVDS, GSVD.
[U,S,V]=svd(B)
U =
0.2682 -0.7491 0.6057
0.8586 0.4710 0.2024
0.4369 -0.4658 -0.7695
S =
10.4705 0 0
0 4.8340 0
0 0 0.0395
V =
0.1493 -0.1539 0.9767
0.4408 0.8946 0.0735
0.8851 -0.4195 -0.2014
B - U*S*V'
ans =
1.0e-014 *
0.0111 0 0.0888
0.0444 0.2665 0.6217
0 0.1438 0.2665
[U,S,V]=svd(A)
U =
0.4414 -0.5206 0.0193 -0.4329 0.5885
0.4386 0.2312 -0.3558 0.6878 0.3932
0.5313 0.6945 0.0714 -0.4628 -0.1269
0.3975 -0.3864 -0.5271 -0.0284 -0.6435
0.4154 -0.2095 0.7682 0.3530 -0.2624
S =
2.9659 0 0 0 0 0
0 1.0658 0 0 0 0
0 0 0.6916 0 0 0
0 0 0 0.4881 0 0
0 0 0 0 0.1202 0
V =
0.4743 -0.3699 0.5898 -0.4761 0.2198 -0.1239
0.3566 -0.6464 -0.3437 0.2235 -0.1631 0.5102
0.4975 0.1696 -0.6619 -0.2194 0.2939 -0.3888
0.5431 0.2778 0.3046 0.7113 -0.0690 -0.1561
0.2272 0.5473 0.0508 -0.2252 0.2231 0.7388
0.2321 0.1997 -0.0209 -0.3443 -0.8855 -0.0554
B
B =
1 -2 4
1 6 7
1 0 5
B(2:3,[1,3])
ans =
1 7
1 5
pi:-0.1:2
ans =
Columns 1 through 7
3.1416 3.0416 2.9416 2.8416 2.7416 2.6416 2.5416
Columns 8 through 12
2.4416 2.3416 2.2416 2.1416 2.0416
pi:0.1:4
ans =
Columns 1 through 7
3.1416 3.2416 3.3416 3.4416 3.5416 3.6416 3.7416
Columns 8 through 9
3.8416 3.9416
help colon
: Colon.
J:K is the same as [J, J+1, ..., K].
J:K is empty if J > K.
J:D:K is the same as [J, J+D, ..., J+m*D] where m = fix((K-J)/D).
J:D:K is empty if D > 0 and J > K or if D < 0 and J < K.
COLON(J,K) is the same as J:K and COLON(J,D,K) is the same as J:D:K.
The colon notation can be used to pick out selected rows, columns
and elements of vectors, matrices, and arrays. A(:) is all the
elements of A, regarded as a single column. On the left side of an
assignment statement, A(:) fills A, preserving its shape from before.
A(:,J) is the J-th column of A. A(J:K) is [A(J),A(J+1),...,A(K)].
A(:,J:K) is [A(:,J),A(:,J+1),...,A(:,K)] and so on.
The colon notation can be used with a cell array to produce a comma-
separated list. C{:} is the same as C{1},C{2},...,C{end}. The comma
separated list syntax is valid inside () for function calls, [] for
concatenation and function return arguments, and inside {} to produce
a cell array. Expressions such as S(:).name produce the comma separated
list S(1).name,S(2).name,...,S(end).name for the structure S.
For the use of the colon in the FOR statement, See FOR.
For the use of the colon in a comma separated list, See VARARGIN.
inv(A)
??? Error using ==> inv
Matrix must be square.
inv(B)
ans =
15.0000 5.0000 -19.0000
1.0000 0.5000 -1.5000
-3.0000 -1.0000 4.0000
ans*B
ans =
1 0 0
0 1 0
0 0 1
c=1:4
c =
1 2 3 4
d=4:-1:1
d =
4 3 2 1
c.*d
ans =
4 6 6 4
ls ../mfiles
../mfiles not found.
ls ../../mfiles
. .. afosr capon narcfun pbf_wav
ls ../../mfiles/narcfun
. CHECK.M DEMO_LAG.M Mod2.m PBF_EVAL.M SITE_DIS.M
.. CREATEFN.M EQSP_CEN.M NEW_LAG.M PLOT_APD.M WAVIAN.M
ADJ_PHD.M DEMO_BL.M LAGRANGE.M NEW_POLY.M POLY_PBF.M round_off.m
BUTLER.M DEMO_BRC.M LAG_INT.M OLS_CENT.M RESIDUAL.M
round_off
??? Undefined function or variable 'round_off'.
type round_off
??? Error using ==> type
round_off.m: File not found.
path
MATLABPATH
C:\mfiles\pbf_wav
C:\mfiles\capon
C:\mfiles\afosr
C:\mfiles
C:\MATLABR11\toolbox\matlab\general
C:\MATLABR11\toolbox\matlab\ops
C:\MATLABR11\toolbox\matlab\lang
C:\MATLABR11\toolbox\matlab\elmat
C:\MATLABR11\toolbox\matlab\elfun
C:\MATLABR11\toolbox\matlab\specfun
C:\MATLABR11\toolbox\matlab\matfun
C:\MATLABR11\toolbox\matlab\datafun
C:\MATLABR11\toolbox\matlab\polyfun
C:\MATLABR11\toolbox\matlab\funfun
C:\MATLABR11\toolbox\matlab\sparfun
C:\MATLABR11\toolbox\matlab\graph2d
C:\MATLABR11\toolbox\matlab\graph3d
C:\MATLABR11\toolbox\matlab\specgraph
C:\MATLABR11\toolbox\matlab\graphics
C:\MATLABR11\toolbox\matlab\uitools
C:\MATLABR11\toolbox\matlab\strfun
C:\MATLABR11\toolbox\matlab\iofun
C:\MATLABR11\toolbox\matlab\timefun
C:\MATLABR11\toolbox\matlab\datatypes
C:\MATLABR11\toolbox\matlab\winfun
C:\MATLABR11\toolbox\matlab\demos
C:\MATLABR11\toolbox\wavelet\wavelet
C:\MATLABR11\toolbox\wavelet\wavedemo
C:\MATLABR11\work
C:\MATLABR11\toolbox\local
fplot('sin(3*x)',[-pi,pi])
quit