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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine dlasda | ( | integer | ICOMPQ, |
| integer | SMLSIZ, | ||
| integer | N, | ||
| integer | SQRE, | ||
| double precision, dimension( * ) | D, | ||
| double precision, dimension( * ) | E, | ||
| double precision, dimension( ldu, * ) | U, | ||
| integer | LDU, | ||
| double precision, dimension( ldu, * ) | VT, | ||
| integer, dimension( * ) | K, | ||
| double precision, dimension( ldu, * ) | DIFL, | ||
| double precision, dimension( ldu, * ) | DIFR, | ||
| double precision, dimension( ldu, * ) | Z, | ||
| double precision, dimension( ldu, * ) | POLES, | ||
| integer, dimension( * ) | GIVPTR, | ||
| integer, dimension( ldgcol, * ) | GIVCOL, | ||
| integer | LDGCOL, | ||
| integer, dimension( ldgcol, * ) | PERM, | ||
| double precision, dimension( ldu, * ) | GIVNUM, | ||
| double precision, dimension( * ) | C, | ||
| double precision, dimension( * ) | S, | ||
| double precision, dimension( * ) | WORK, | ||
| integer, dimension( * ) | IWORK, | ||
| integer | INFO | ||
| ) |
DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
Download DLASDA + dependencies [TGZ] [ZIP] [TXT]
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.
| [in] | ICOMPQ | ICOMPQ is 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. |
| [in] | SMLSIZ | SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree. |
| [in] | N | N is INTEGER
The row dimension of the upper bidiagonal matrix. This is
also the dimension of the main diagonal array D. |
| [in] | SQRE | SQRE is 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. |
| [in,out] | D | D is 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. |
| [in] | E | E is DOUBLE PRECISION array, dimension ( M-1 )
Contains the subdiagonal entries of the bidiagonal matrix.
On exit, E has been destroyed. |
| [out] | U | U is 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. |
| [in] | LDU | LDU is INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
GIVNUM, and Z. |
| [out] | VT | VT is 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. |
| [out] | K | K is 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. |
| [out] | DIFL | DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ),
where NLVL = floor(log_2 (N/SMLSIZ))). |
| [out] | DIFR | DIFR is 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. |
| [out] | Z | Z is 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. |
| [out] | POLES | POLES is 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. |
| [out] | GIVPTR | GIVPTR is 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. |
| [out] | GIVCOL | GIVCOL is 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. |
| [in] | LDGCOL | LDGCOL is INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM. |
| [out] | PERM | PERM is 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. |
| [out] | GIVNUM | GIVNUM is 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. |
| [out] | C | C is 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. |
| [out] | S | S is 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. |
| [out] | WORK | WORK is DOUBLE PRECISION array, dimension
(6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). |
| [out] | IWORK | IWORK is INTEGER array, dimension (7*N) |
| [out] | INFO | INFO is 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 |
1.9.4