dbdt04()

subroutine dbdt04	(	character	UPLO,
		integer	N,
		double precision, dimension( * )	D,
		double precision, dimension( * )	E,
		double precision, dimension( * )	S,
		integer	NS,
		double precision, dimension( ldu, * )	U,
		integer	LDU,
		double precision, dimension( ldvt, * )	VT,
		integer	LDVT,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DBDT04

Purpose:

 DBDT04 reconstructs a bidiagonal matrix B from its (partial) SVD:
    S = U' * B * V
 where U and V are orthogonal matrices and S is diagonal.

 The test ratio to test the singular value decomposition is
    RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )
 where VT = V' and EPS is the machine precision.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix B is upper or lower bidiagonal. = 'U': Upper bidiagonal = 'L': Lower bidiagonal
[in]	N	N is INTEGER The order of the matrix B.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the bidiagonal matrix B.
[in]	E	E is DOUBLE PRECISION array, dimension (N-1) The (n-1) superdiagonal elements of the bidiagonal matrix B if UPLO = 'U', or the (n-1) subdiagonal elements of B if UPLO = 'L'.
[in]	S	S is DOUBLE PRECISION array, dimension (NS) The singular values from the (partial) SVD of B, sorted in decreasing order.
[in]	NS	NS is INTEGER The number of singular values/vectors from the (partial) SVD of B.
[in]	U	U is DOUBLE PRECISION array, dimension (LDU,NS) The n by ns orthogonal matrix U in S = U' * B * V.
[in]	LDU	LDU is INTEGER The leading dimension of the array U. LDU >= max(1,N)
[in]	VT	VT is DOUBLE PRECISION array, dimension (LDVT,N) The n by ns orthogonal matrix V in S = U' * B * V.
[in]	LDVT	LDVT is INTEGER The leading dimension of the array VT.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (2*N)
[out]	RESID	RESID is DOUBLE PRECISION The test ratio: norm(S - U' * B * V) / ( n * norm(B) * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.