CGSVD Compact generalized SVD of a matrix pair in regularization problems.



sm = cgsvd(A,L)

[U,sm,X,V] = cgsvd(A,L) , sm = [sigma,mu]



Computes the generalized SVD of the matrix pair (A,L):

[ A ] = [ U 0 ]*[ diag(sigma) 0 ]*inv(X)

[ L ] [ 0 V ] [ 0 eye(n-p) ]

[ diag(mu) 0 ]

where

U is m-by-n , sigma is p-by-1

V is p-by-p , mu is p-by-1

X is n-by-n .



It is assumed that m >= n >= p, which is true in regularization problems.



Reference: C. F. Van Loan, Computing the CS and the generalized

singular value decomposition , Numer. Math. 46 (1985), 479-491.



Per Christian Hansen, IMM, 12/19/97.



Initialization. - CGSVD Compact generalized SVD of a matrix pair in regularization problems.

　

　sm = cgsvd(A,L)

　[U,sm,X,V] = cgsvd(A,L) ,　sm = [sigma,mu]

　

　Computes the generalized SVD of the matrix pair (A,L):

　　 [ A ] = [ U　0 ]*[ diag(sigma)　　　0　　]*inv(X)

　　 [ L ]　 [ 0　V ] [　　　0　　　 eye(n-p) ]

　　　　　　　　　　　[　diag(mu)　　　　0　　]

　where

　　 U　is　m-by-n ,　　sigma　is　p-by-1

　　 V　is　p-by-p ,　　mu　　 is　p-by-1

　　 X　is　n-by-n .

　

　It is assumed that m >= n >= p, which is true in regularization problems.



　Reference: C. F. Van Loan,　Computing the CS and the generalized

　singular value decomposition , Numer. Math. 46 (1985), 479-491.



　Per Christian Hansen, IMM, 12/19/97.



　Initialization.