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---
:name: slasd2
:md5sum: e139bb4b0237d0c44116e11595e1c166
:category: :subroutine
:arguments:
- nl:
:type: integer
:intent: input
- nr:
:type: integer
:intent: input
- sqre:
:type: integer
:intent: input
- k:
:type: integer
:intent: output
- d:
:type: real
:intent: input/output
:dims:
- n
- z:
:type: real
:intent: output
:dims:
- n
- alpha:
:type: real
:intent: input
- beta:
:type: real
:intent: input
- u:
:type: real
:intent: input/output
:dims:
- ldu
- n
- ldu:
:type: integer
:intent: input
- vt:
:type: real
:intent: input/output
:dims:
- ldvt
- m
- ldvt:
:type: integer
:intent: input
- dsigma:
:type: real
:intent: output
:dims:
- n
- u2:
:type: real
:intent: output
:dims:
- ldu2
- n
- ldu2:
:type: integer
:intent: input
- vt2:
:type: real
:intent: output
:dims:
- ldvt2
- n
- ldvt2:
:type: integer
:intent: input
- idxp:
:type: integer
:intent: workspace
:dims:
- n
- idx:
:type: integer
:intent: workspace
:dims:
- n
- idxc:
:type: integer
:intent: output
:dims:
- n
- idxq:
:type: integer
:intent: input/output
:dims:
- n
- coltyp:
:type: integer
:intent: output
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions:
ldu2: n
ldvt2: m
:fortran_help: " SUBROUTINE SLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SLASD2 merges the two sets of singular values together into a single\n\
* sorted set. Then it tries to deflate the size of the problem.\n\
* There are two ways in which deflation can occur: when two or more\n\
* singular values are close together or if there is a tiny entry in the\n\
* Z vector. For each such occurrence the order of the related secular\n\
* equation problem is reduced by one.\n\
*\n\
* SLASD2 is called from SLASD1.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* NL (input) INTEGER\n\
* The row dimension of the upper block. NL >= 1.\n\
*\n\
* NR (input) INTEGER\n\
* The row dimension of the lower block. NR >= 1.\n\
*\n\
* SQRE (input) INTEGER\n\
* = 0: the lower block is an NR-by-NR square matrix.\n\
* = 1: the lower block is an NR-by-(NR+1) rectangular matrix.\n\
*\n\
* The bidiagonal matrix has N = NL + NR + 1 rows and\n\
* M = N + SQRE >= N columns.\n\
*\n\
* K (output) INTEGER\n\
* Contains the dimension of the non-deflated matrix,\n\
* This is the order of the related secular equation. 1 <= K <=N.\n\
*\n\
* D (input/output) REAL array, dimension (N)\n\
* On entry D contains the singular values of the two submatrices\n\
* to be combined. On exit D contains the trailing (N-K) updated\n\
* singular values (those which were deflated) sorted into\n\
* increasing order.\n\
*\n\
* Z (output) REAL array, dimension (N)\n\
* On exit Z contains the updating row vector in the secular\n\
* equation.\n\
*\n\
* ALPHA (input) REAL\n\
* Contains the diagonal element associated with the added row.\n\
*\n\
* BETA (input) REAL\n\
* Contains the off-diagonal element associated with the added\n\
* row.\n\
*\n\
* U (input/output) REAL array, dimension (LDU,N)\n\
* On entry U contains the left singular vectors of two\n\
* submatrices in the two square blocks with corners at (1,1),\n\
* (NL, NL), and (NL+2, NL+2), (N,N).\n\
* On exit U contains the trailing (N-K) updated left singular\n\
* vectors (those which were deflated) in its last N-K columns.\n\
*\n\
* LDU (input) INTEGER\n\
* The leading dimension of the array U. LDU >= N.\n\
*\n\
* VT (input/output) REAL array, dimension (LDVT,M)\n\
* On entry VT' contains the right singular vectors of two\n\
* submatrices in the two square blocks with corners at (1,1),\n\
* (NL+1, NL+1), and (NL+2, NL+2), (M,M).\n\
* On exit VT' contains the trailing (N-K) updated right singular\n\
* vectors (those which were deflated) in its last N-K columns.\n\
* In case SQRE =1, the last row of VT spans the right null\n\
* space.\n\
*\n\
* LDVT (input) INTEGER\n\
* The leading dimension of the array VT. LDVT >= M.\n\
*\n\
* DSIGMA (output) REAL array, dimension (N)\n\
* Contains a copy of the diagonal elements (K-1 singular values\n\
* and one zero) in the secular equation.\n\
*\n\
* U2 (output) REAL array, dimension (LDU2,N)\n\
* Contains a copy of the first K-1 left singular vectors which\n\
* will be used by SLASD3 in a matrix multiply (SGEMM) to solve\n\
* for the new left singular vectors. U2 is arranged into four\n\
* blocks. The first block contains a column with 1 at NL+1 and\n\
* zero everywhere else; the second block contains non-zero\n\
* entries only at and above NL; the third contains non-zero\n\
* entries only below NL+1; and the fourth is dense.\n\
*\n\
* LDU2 (input) INTEGER\n\
* The leading dimension of the array U2. LDU2 >= N.\n\
*\n\
* VT2 (output) REAL array, dimension (LDVT2,N)\n\
* VT2' contains a copy of the first K right singular vectors\n\
* which will be used by SLASD3 in a matrix multiply (SGEMM) to\n\
* solve for the new right singular vectors. VT2 is arranged into\n\
* three blocks. The first block contains a row that corresponds\n\
* to the special 0 diagonal element in SIGMA; the second block\n\
* contains non-zeros only at and before NL +1; the third block\n\
* contains non-zeros only at and after NL +2.\n\
*\n\
* LDVT2 (input) INTEGER\n\
* The leading dimension of the array VT2. LDVT2 >= M.\n\
*\n\
* IDXP (workspace) INTEGER array, dimension (N)\n\
* This will contain the permutation used to place deflated\n\
* values of D at the end of the array. On output IDXP(2:K)\n\
* points to the nondeflated D-values and IDXP(K+1:N)\n\
* points to the deflated singular values.\n\
*\n\
* IDX (workspace) INTEGER array, dimension (N)\n\
* This will contain the permutation used to sort the contents of\n\
* D into ascending order.\n\
*\n\
* IDXC (output) INTEGER array, dimension (N)\n\
* This will contain the permutation used to arrange the columns\n\
* of the deflated U matrix into three groups: the first group\n\
* contains non-zero entries only at and above NL, the second\n\
* contains non-zero entries only below NL+2, and the third is\n\
* dense.\n\
*\n\
* IDXQ (input/output) INTEGER array, dimension (N)\n\
* This contains the permutation which separately sorts the two\n\
* sub-problems in D into ascending order. Note that entries in\n\
* the first hlaf of this permutation must first be moved one\n\
* position backward; and entries in the second half\n\
* must first have NL+1 added to their values.\n\
*\n\
* COLTYP (workspace/output) INTEGER array, dimension (N)\n\
* As workspace, this will contain a label which will indicate\n\
* which of the following types a column in the U2 matrix or a\n\
* row in the VT2 matrix is:\n\
* 1 : non-zero in the upper half only\n\
* 2 : non-zero in the lower half only\n\
* 3 : dense\n\
* 4 : deflated\n\
*\n\
* On exit, it is an array of dimension 4, with COLTYP(I) being\n\
* the dimension of the I-th type columns.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Ming Gu and Huan Ren, Computer Science Division, University of\n\
* California at Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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