SBDT03
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
SBDT03 reconstructs a bidiagonal matrix B from its 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( B - U * S * VT ) / ( n * norm(B) * EPS )
where VT = V' and EPS is the machine precision.
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( B - U * S * VT ) / ( n * norm(B) * EPS )
where VT = V' and EPS is the machine precision.
Arguments
| UPLO |
(input) CHARACTER*1
Specifies whether the matrix B is upper or lower bidiagonal.
= 'U': Upper bidiagonal = 'L': Lower bidiagonal |
| N |
(input) INTEGER
The order of the matrix B.
|
| KD |
(input) INTEGER
The bandwidth of the bidiagonal matrix B. If KD = 1, the
matrix B is bidiagonal, and if KD = 0, B is diagonal and E is not referenced. If KD is greater than 1, it is assumed to be 1, and if KD is less than 0, it is assumed to be 0. |
| D |
(input) REAL array, dimension (N)
The n diagonal elements of the bidiagonal matrix B.
|
| E |
(input) REAL 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'. |
| U |
(input) REAL array, dimension (LDU,N)
The n by n orthogonal matrix U in the reduction B = U'*A*P.
|
| LDU |
(input) INTEGER
The leading dimension of the array U. LDU >= max(1,N)
|
| S |
(input) REAL array, dimension (N)
The singular values from the SVD of B, sorted in decreasing
order. |
| VT |
(input) REAL array, dimension (LDVT,N)
The n by n orthogonal matrix V' in the reduction
B = U * S * V'. |
| LDVT |
(input) INTEGER
The leading dimension of the array VT.
|
| WORK |
(workspace) REAL array, dimension (2*N)
|
| RESID |
(output) REAL
The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS )
|