| | | Scilab Reference Manual | |
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svd — singular value decomposition
s=svd(X) [U,S,V]=svd(X) [U,S,V]=svd(X,0) (obsolete) [U,S,V]=svd(X,"e") [U,S,V,rk]=svd(X [,tol])
| X | : a real or complex matrix |
| s | : real vector (singular values) |
| S | : real diagonal matrix (singular values) |
| U,V | : orthogonal or unitary square matrices (singular vectors). |
| tol | : real number |
[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'.
[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.
s = svd(X) by itself, returns a vector s containing the singular values.
[U,S,V,rk]=svd(X,tol) gives in addition rk, the numerical rank of X i.e. the number of singular values larger than tol.
The default value of tol is the same as in rank.
X=rand(4,2)*rand(2,4) svd(X) sqrt(spec(X*X'))
| << sva | sylv >> |