DLASDA
June 2010
Purpose
Using a divide and conquer approach, DLASDA computes the singular
value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
B with diagonal D and offdiagonal E, where M = N + SQRE. The
algorithm computes the singular values in the SVD B = U * S * VT.
The orthogonal matrices U and VT are optionally computed in
compact form.
A related subroutine, DLASD0, computes the singular values and
the singular vectors in explicit form.
value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
B with diagonal D and offdiagonal E, where M = N + SQRE. The
algorithm computes the singular values in the SVD B = U * S * VT.
The orthogonal matrices U and VT are optionally computed in
compact form.
A related subroutine, DLASD0, computes the singular values and
the singular vectors in explicit form.
Arguments
| ICOMPQ |
(input) INTEGER
Specifies whether singular vectors are to be computed
in compact form, as follows = 0: Compute singular values only. = 1: Compute singular vectors of upper bidiagonal matrix in compact form. |
| SMLSIZ |
(input) INTEGER
The maximum size of the subproblems at the bottom of the
computation tree. |
| N |
(input) INTEGER
The row dimension of the upper bidiagonal matrix. This is
also the dimension of the main diagonal array D. |
| SQRE |
(input) INTEGER
Specifies the column dimension of the bidiagonal matrix.
= 0: The bidiagonal matrix has column dimension M = N; = 1: The bidiagonal matrix has column dimension M = N + 1. |
| D |
(input/output) DOUBLE PRECISION array, dimension ( N )
On entry D contains the main diagonal of the bidiagonal
matrix. On exit D, if INFO = 0, contains its singular values. |
| E |
(input) DOUBLE PRECISION array, dimension ( M-1 )
Contains the subdiagonal entries of the bidiagonal matrix.
On exit, E has been destroyed. |
| U |
(output) DOUBLE PRECISION array,
dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left singular vector matrices of all subproblems at the bottom level. |
| LDU |
(input) INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
GIVNUM, and Z. |
| VT |
(output) DOUBLE PRECISION array,
dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right singular vector matrices of all subproblems at the bottom level. |
| K |
(output) INTEGER array,
dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th secular equation on the computation tree. |
| DIFL |
(output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),
where NLVL = floor(log_2 (N/SMLSIZ))).
|
| DIFR |
(output) DOUBLE PRECISION array,
dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
dimension ( N ) if ICOMPQ = 0. If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) record distances between singular values on the I-th level and singular values on the (I -1)-th level, and DIFR(1:N, 2 * I ) contains the normalizing factors for the right singular vector matrix. See DLASD8 for details. |
| Z |
(output) DOUBLE PRECISION array,
dimension ( LDU, NLVL ) if ICOMPQ = 1 and
dimension ( N ) if ICOMPQ = 0. The first K elements of Z(1, I) contain the components of the deflation-adjusted updating row vector for subproblems on the I-th level. |
| POLES |
(output) DOUBLE PRECISION array,
dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and POLES(1, 2*I) contain the new and old singular values involved in the secular equations on the I-th level. |
| GIVPTR |
(output) INTEGER array,
dimension ( N ) if ICOMPQ = 1, and not referenced if
ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records the number of Givens rotations performed on the I-th problem on the computation tree. |
| GIVCOL |
(output) INTEGER array,
dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations of Givens rotations performed on the I-th level on the computation tree. |
| LDGCOL |
(input) INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM.
|
| PERM |
(output) INTEGER array,
dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records permutations done on the I-th level of the computation tree. |
| GIVNUM |
(output) DOUBLE PRECISION array,
dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not
referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- values of Givens rotations performed on the I-th level on the computation tree. |
| C |
(output) DOUBLE PRECISION array,
dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
If ICOMPQ = 1 and the I-th subproblem is not square, on exit, C( I ) contains the C-value of a Givens rotation related to the right null space of the I-th subproblem. |
| S |
(output) DOUBLE PRECISION array, dimension ( N ) if
ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
and the I-th subproblem is not square, on exit, S( I ) contains the S-value of a Givens rotation related to the right null space of the I-th subproblem. |
| WORK |
(workspace) DOUBLE PRECISION array, dimension
(6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
|
| IWORK |
(workspace) INTEGER array.
Dimension must be at least (7 * N).
|
| INFO |
(output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge |
Further Details
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA