MATLAB SVD函数

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原文地址：MATLAB SVD 函数 作者：小周

>> a=[1 2 3 4;5 6 7 8;9 10 11 12;24 6 7.99999];
[u,s,v]=svds(a)

u =

  0.19309325290913 -0.39372991088164  0.80064042247500 -0.40824829032397
  0.47876392522628  0.03942520140203  0.32025628954945  0.81649658098368
  0.76443459754343  0.47258031368569 -0.16012784453451 -0.40824829049184
  0.38618628362685 -0.78745809913181 -0.48038515432194 -0.00000000008393

s =

27.55065585030689                 0                 0                 0
                 0  3.31077063809069                 0                 0
                 0                 0  0.00000263117785                 0
                 0                 0                 0   0.00000000000000

v =

  0.37164983947455  0.74958461105215  0.36514742344847 -0.40824829050286
  0.45181723566769  0.30961435841708 -0.18257455406715  0.81649658094722
  0.53198463186084 -0.13035589421799 -0.73029653281457 -0.40824829038587
  0.61215188788081 -0.57032376837933  0.54772334743922 -0.00000000005849

>> [u1,s1,v1]=svds(a,1,0)
Warning: (A-sigma*I) has small reciprocal condition estimate:0.000000
indicating that sigma is near an exact eigenvalue. The
algorithm may not converge unless you try a new value forsigma.

> In eigs at 556
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140
Warning: Matrix is singular to working precision.
> In eigs at 700
In svds at 140

u1 =

Empty matrix: 4-by-0

s1 =

[]

v1 =

Empty matrix: 4-by-0

>> u*s*v'

ans =

  1.00000000000000  2.00000000000000  3.00000000000000  4.00000000000000
  5.00000000000001  6.00000000000001  7.00000000000001  8.00000000000001
  9.00000000000001 10.00000000000001 11.00000000000001 12.00000000000001
  2.00000000000000  4.00000000000000  6.00000000000000  7.99999000000000