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template<typename T>
void lasd2(integer *nl, integer *nr, integer *sqre, integer *k, T *d, T *z, T *alpha, T *beta, T *u, integer *ldu, T *vt, integer *ldvt, T *dsigma, T *u2, integer *ldu2, T *vt2, integer *ldvt2, integer *idxp, integer *idx, integer *idxc, integer *idxq, integer *coltyp, integer *info)# LASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
Purpose:
LASD2 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more singular values are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one. SLASD2 is called from SLASD1.
- Parameters:
NL – [in]
NL is INTEGER
The row dimension of the upper block. NL >= 1.
NR – [in]
NR is INTEGER
The row dimension of the lower block. NR >= 1.
SQRE – [in]
SQRE is INTEGER
= 0: the lower block is an NR-by-NR square matrix.
= 1: the lower block is an NR-by-(NR+1) rectangular matrix.
The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.
K – [out]
K is INTEGER
Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N.
D – [inout]
D is REAL array, dimension (N)
On entry D contains the singular values of the two submatrices to be combined. On exit D contains the trailing (N-K) updated singular values (those which were deflated) sorted into increasing order.
Z – [out]
Z is REAL array, dimension (N)
On exit Z contains the updating row vector in the secular equation.
ALPHA – [in]
ALPHA is REAL
Contains the diagonal element associated with the added row.
BETA – [in]
BETA is REAL
Contains the off-diagonal element associated with the added row.
U – [inout]
U is REAL array, dimension (LDU,N)
On entry U contains the left singular vectors of two submatrices in the two square blocks with corners at (1,1), (NL, NL), and (NL+2, NL+2), (N,N).
On exit U contains the trailing (N-K) updated left singular vectors (those which were deflated) in its last N-K columns.LDU – [in]
LDU is INTEGER
The leading dimension of the array U. LDU >= N.
VT – [inout]
VT is REAL array, dimension (LDVT,M)
On entry VT**T contains the right singular vectors of two submatrices in the two square blocks with corners at (1,1), (NL+1, NL+1), and (NL+2, NL+2), (M,M).
On exit VT**T contains the trailing (N-K) updated right singular vectors (those which were deflated) in its last N-K columns. In case SQRE =1, the last row of VT spans the right null space.LDVT – [in]
LDVT is INTEGER
The leading dimension of the array VT. LDVT >= M.
DSIGMA – [out]
DSIGMA is REAL array, dimension (N)
Contains a copy of the diagonal elements (K-1 singular values and one zero) in the secular equation.
U2 – [out]
U2 is REAL array, dimension (LDU2,N)
Contains a copy of the first K-1 left singular vectors which will be used by SLASD3 in a matrix multiply (SGEMM) to solve for the new left singular vectors. U2 is arranged into four blocks. The first block contains a column with 1 at NL+1 and zero everywhere else; the second block contains non-zero entries only at and above NL; the third contains non-zero entries only below NL+1; and the fourth is dense.
LDU2 – [in]
LDU2 is INTEGER
The leading dimension of the array U2. LDU2 >= N.
VT2 – [out]
VT2 is REAL array, dimension (LDVT2,N)
VT2**T contains a copy of the first K right singular vectors which will be used by SLASD3 in a matrix multiply (SGEMM) to solve for the new right singular vectors. VT2 is arranged into three blocks. The first block contains a row that corresponds to the special 0 diagonal element in SIGMA; the second block contains non-zeros only at and before NL +1; the third block contains non-zeros only at and after NL +2.
LDVT2 – [in]
LDVT2 is INTEGER
The leading dimension of the array VT2. LDVT2 >= M.
IDXP – [out]
IDXP is INTEGER array, dimension (N)
This will contain the permutation used to place deflated values of D at the end of the array. On output IDXP(2:K) points to the nondeflated D-values and IDXP(K+1:N) points to the deflated singular values.
IDX – [out]
IDX is INTEGER array, dimension (N)
This will contain the permutation used to sort the contents of D into ascending order.
IDXC – [out]
IDXC is INTEGER array, dimension (N)
This will contain the permutation used to arrange the columns of the deflated U matrix into three groups: the first group contains non-zero entries only at and above NL, the second contains non-zero entries only below NL+2, and the third is dense.
IDXQ – [inout]
IDXQ is INTEGER array, dimension (N)
This contains the permutation which separately sorts the two sub-problems in D into ascending order. Note that entries in the first hlaf of this permutation must first be moved one position backward; and entries in the second half must first have NL+1 added to their values.
COLTYP – [out]
COLTYP is INTEGER array, dimension (N)
As workspace, this will contain a label which will indicate which of the following types a column in the U2 matrix or a row in the VT2 matrix is:
1 : non-zero in the upper half only
2 : non-zero in the lower half only
3 : dense
4 : deflated
On exit, it is an array of dimension 4, with COLTYP(I) being the dimension of the I-th type columns.INFO – [out]
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.