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qr(G) Scilab Function qr(G)
NAME
qr - QR decomposition
CALLING SEQUENCE
[Q,R]=qr(X)
[Q,R,E]=qr(X)
[Q,R,rk,E]=qr(X [,tol])
PARAMETERS
X : real or complex matrix
tol : nonnegative real number
Q : square orthogonal or unitary matrix
R : matrix with same dimensions as X
E : permutation matrix
rk : integer (QR-rank of X*E)
DESCRIPTION
[Q,R] = qr(X) produces an upper triangular matrix R of the same dimension
as X and a unitary matrix Q so that X = Q*R.
[Q,R,E] = qr(X) produces a (column) permutation matrix E, an upper triangu-
lar R with decreasing diagonal elements and a unitary Q so that X*E = Q*R.
[Q,R,rk,E] = qr(X ,tol) returns rk = rank estimate of X i.e. rk is the
number of diagonal elements in R which are larger than tol.
[Q,R,rk,E] = qr(X) returns rk = rank estimate of X i.e. rk is the number
of diagonal elements in R which are larger than R(1,1)*%eps*max(size(R).
EXAMPLE
A=rand(5,2)*rand(2,5);
[Q,R,rk,E] = qr(A,1.d-10);
norm(Q'*A-R)
svd([A,Q(:,1:rk)]) //span(A) =span(Q(:,1:rk))
SEE ALSO
rank, svd, rowcomp, colcomp
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