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---
:name: dlasd7
:md5sum: f4a96aafe698a9fe1dc5bee822c506d3
:category: :subroutine
:arguments:
- icompq:
:type: integer
:intent: input
- nl:
:type: integer
:intent: input
- nr:
:type: integer
:intent: input
- sqre:
:type: integer
:intent: input
- k:
:type: integer
:intent: output
- d:
:type: doublereal
:intent: input/output
:dims:
- n
- z:
:type: doublereal
:intent: output
:dims:
- m
- zw:
:type: doublereal
:intent: workspace
:dims:
- m
- vf:
:type: doublereal
:intent: input/output
:dims:
- m
- vfw:
:type: doublereal
:intent: workspace
:dims:
- m
- vl:
:type: doublereal
:intent: input/output
:dims:
- m
- vlw:
:type: doublereal
:intent: workspace
:dims:
- m
- alpha:
:type: doublereal
:intent: input
- beta:
:type: doublereal
:intent: input
- dsigma:
:type: doublereal
:intent: output
:dims:
- n
- idx:
:type: integer
:intent: workspace
:dims:
- n
- idxp:
:type: integer
:intent: workspace
:dims:
- n
- idxq:
:type: integer
:intent: input
:dims:
- n
- perm:
:type: integer
:intent: output
:dims:
- n
- givptr:
:type: integer
:intent: output
- givcol:
:type: integer
:intent: output
:dims:
- ldgcol
- "2"
- ldgcol:
:type: integer
:intent: input
- givnum:
:type: doublereal
:intent: output
:dims:
- ldgnum
- "2"
- ldgnum:
:type: integer
:intent: input
- c:
:type: doublereal
:intent: output
- s:
:type: doublereal
:intent: output
- info:
:type: integer
:intent: output
:substitutions:
ldgnum: n
ldgcol: n
:fortran_help: " SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, C, S, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLASD7 merges the two sets of singular values together into a single\n\
* sorted set. Then it tries to deflate the size of the problem. There\n\
* are two ways in which deflation can occur: when two or more singular\n\
* values are close together or if there is a tiny entry in the Z\n\
* vector. For each such occurrence the order of the related\n\
* secular equation problem is reduced by one.\n\
*\n\
* DLASD7 is called from DLASD6.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* ICOMPQ (input) INTEGER\n\
* Specifies whether singular vectors are to be computed\n\
* in compact form, as follows:\n\
* = 0: Compute singular values only.\n\
* = 1: Compute singular vectors of upper\n\
* bidiagonal matrix in compact form.\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\
* 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, this is\n\
* the order of the related secular equation. 1 <= K <=N.\n\
*\n\
* D (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension ( M )\n\
* On exit Z contains the updating row vector in the secular\n\
* equation.\n\
*\n\
* ZW (workspace) DOUBLE PRECISION array, dimension ( M )\n\
* Workspace for Z.\n\
*\n\
* VF (input/output) DOUBLE PRECISION array, dimension ( M )\n\
* On entry, VF(1:NL+1) contains the first components of all\n\
* right singular vectors of the upper block; and VF(NL+2:M)\n\
* contains the first components of all right singular vectors\n\
* of the lower block. On exit, VF contains the first components\n\
* of all right singular vectors of the bidiagonal matrix.\n\
*\n\
* VFW (workspace) DOUBLE PRECISION array, dimension ( M )\n\
* Workspace for VF.\n\
*\n\
* VL (input/output) DOUBLE PRECISION array, dimension ( M )\n\
* On entry, VL(1:NL+1) contains the last components of all\n\
* right singular vectors of the upper block; and VL(NL+2:M)\n\
* contains the last components of all right singular vectors\n\
* of the lower block. On exit, VL contains the last components\n\
* of all right singular vectors of the bidiagonal matrix.\n\
*\n\
* VLW (workspace) DOUBLE PRECISION array, dimension ( M )\n\
* Workspace for VL.\n\
*\n\
* ALPHA (input) DOUBLE PRECISION\n\
* Contains the diagonal element associated with the added row.\n\
*\n\
* BETA (input) DOUBLE PRECISION\n\
* Contains the off-diagonal element associated with the added\n\
* row.\n\
*\n\
* DSIGMA (output) DOUBLE PRECISION 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\
* 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\
* 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\
* IDXQ (input) 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 half 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\
* PERM (output) INTEGER array, dimension ( N )\n\
* The permutations (from deflation and sorting) to be applied\n\
* to each singular block. Not referenced if ICOMPQ = 0.\n\
*\n\
* GIVPTR (output) INTEGER\n\
* The number of Givens rotations which took place in this\n\
* subproblem. Not referenced if ICOMPQ = 0.\n\
*\n\
* GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 )\n\
* Each pair of numbers indicates a pair of columns to take place\n\
* in a Givens rotation. Not referenced if ICOMPQ = 0.\n\
*\n\
* LDGCOL (input) INTEGER\n\
* The leading dimension of GIVCOL, must be at least N.\n\
*\n\
* GIVNUM (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )\n\
* Each number indicates the C or S value to be used in the\n\
* corresponding Givens rotation. Not referenced if ICOMPQ = 0.\n\
*\n\
* LDGNUM (input) INTEGER\n\
* The leading dimension of GIVNUM, must be at least N.\n\
*\n\
* C (output) DOUBLE PRECISION\n\
* C contains garbage if SQRE =0 and the C-value of a Givens\n\
* rotation related to the right null space if SQRE = 1.\n\
*\n\
* S (output) DOUBLE PRECISION\n\
* S contains garbage if SQRE =0 and the S-value of a Givens\n\
* rotation related to the right null space if SQRE = 1.\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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