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template<typename T>
void lasda(integer *icompq, integer *smlsiz, integer *n, integer *sqre, T *d, T *e, T *u, integer *ldu, T *vt, integer *k, T *difl, T *difr, T *z, T *poles, integer *givptr, integer *givcol, integer *ldgcol, integer *perm, T *givnum, T *c, T *s, T *work, integer *iwork, integer *info)# LASDA computes the singular value decomposition (SVD) of a
real upper bidiagonal matrix with diagonal d and off-diagonal e.
Used by sbdsdc.Purpose:
Using a divide and conquer approach, LASDA 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, SLASD0, computes the singular values and the singular vectors in explicit form.
- Parameters:
ICOMPQ – [in]
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.
SMLSIZ – [in]
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the computation tree.
N – [in]
N is INTEGER
The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D.
SQRE – [in]
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.
D – [inout]
D is REAL 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 – [in]
E is REAL array, dimension (M-1)
Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.
U – [out]
U is REAL 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 – [in]
LDU is INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.
VT – [out]
VT is REAL 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 – [out]
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.DIFL – [out]
DIFL is REAL array, dimension (LDU, NLVL),
where NLVL = floor(log_2 (N/SMLSIZ))).
DIFR – [out]
DIFR is REAL 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 SLASD8 for details.
Z – [out]
Z is REAL 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 – [out]
POLES is REAL 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 – [out]
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.
GIVCOL – [out]
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.
LDGCOL – [in]
LDGCOL is INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM.
PERM – [out]
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.GIVNUM – [out]
GIVNUM is REAL 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 – [out]
C is REAL 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 – [out]
S is REAL 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 – [out] WORK is REAL array, dimension (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
IWORK – [out] IWORK is INTEGER array, dimension (7*N).
INFO – [out]
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