LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine dlasd2 | ( | integer | NL, |
integer | NR, | ||
integer | SQRE, | ||
integer | K, | ||
double precision, dimension( * ) | D, | ||
double precision, dimension( * ) | Z, | ||
double precision | ALPHA, | ||
double precision | BETA, | ||
double precision, dimension( ldu, * ) | U, | ||
integer | LDU, | ||
double precision, dimension( ldvt, * ) | VT, | ||
integer | LDVT, | ||
double precision, dimension( * ) | DSIGMA, | ||
double precision, dimension( ldu2, * ) | U2, | ||
integer | LDU2, | ||
double precision, dimension( ldvt2, * ) | VT2, | ||
integer | LDVT2, | ||
integer, dimension( * ) | IDXP, | ||
integer, dimension( * ) | IDX, | ||
integer, dimension( * ) | IDXC, | ||
integer, dimension( * ) | IDXQ, | ||
integer, dimension( * ) | COLTYP, | ||
integer | INFO | ||
) |
DLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
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DLASD2 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. DLASD2 is called from DLASD1.
[in] | NL | NL is INTEGER The row dimension of the upper block. NL >= 1. |
[in] | NR | NR is INTEGER The row dimension of the lower block. NR >= 1. |
[in] | SQRE | 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. |
[out] | K | K is INTEGER Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 <= K <=N. |
[in,out] | D | D is DOUBLE PRECISION 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. |
[out] | Z | Z is DOUBLE PRECISION array, dimension(N) On exit Z contains the updating row vector in the secular equation. |
[in] | ALPHA | ALPHA is DOUBLE PRECISION Contains the diagonal element associated with the added row. |
[in] | BETA | BETA is DOUBLE PRECISION Contains the off-diagonal element associated with the added row. |
[in,out] | U | U is DOUBLE PRECISION 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. |
[in] | LDU | LDU is INTEGER The leading dimension of the array U. LDU >= N. |
[in,out] | VT | VT is DOUBLE PRECISION 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. |
[in] | LDVT | LDVT is INTEGER The leading dimension of the array VT. LDVT >= M. |
[out] | DSIGMA | DSIGMA is DOUBLE PRECISION array, dimension (N) Contains a copy of the diagonal elements (K-1 singular values and one zero) in the secular equation. |
[out] | U2 | U2 is DOUBLE PRECISION array, dimension(LDU2,N) Contains a copy of the first K-1 left singular vectors which will be used by DLASD3 in a matrix multiply (DGEMM) 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. |
[in] | LDU2 | LDU2 is INTEGER The leading dimension of the array U2. LDU2 >= N. |
[out] | VT2 | VT2 is DOUBLE PRECISION array, dimension(LDVT2,N) VT2**T contains a copy of the first K right singular vectors which will be used by DLASD3 in a matrix multiply (DGEMM) 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. |
[in] | LDVT2 | LDVT2 is INTEGER The leading dimension of the array VT2. LDVT2 >= M. |
[out] | IDXP | 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. |
[out] | IDX | IDX is INTEGER array dimension(N) This will contain the permutation used to sort the contents of D into ascending order. |
[out] | IDXC | 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. |
[in,out] | IDXQ | 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. |
[out] | COLTYP | 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. |
[out] | INFO | INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. |
Definition at line 271 of file dlasd2.f.