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---
:name: slalsa
:md5sum: 3817ef103afe5374c5f2833dfd84f267
:category: :subroutine
:arguments:
- icompq:
:type: integer
:intent: input
- smlsiz:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- b:
:type: real
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- bx:
:type: real
:intent: output
:dims:
- ldbx
- nrhs
- ldbx:
:type: integer
:intent: input
- u:
:type: real
:intent: input
:dims:
- ldu
- smlsiz
- ldu:
:type: integer
:intent: input
- vt:
:type: real
:intent: input
:dims:
- ldu
- smlsiz+1
- k:
:type: integer
:intent: input
:dims:
- n
- difl:
:type: real
:intent: input
:dims:
- ldu
- nlvl
- difr:
:type: real
:intent: input
:dims:
- ldu
- 2 * nlvl
- z:
:type: real
:intent: input
:dims:
- ldu
- nlvl
- poles:
:type: real
:intent: input
:dims:
- ldu
- 2 * nlvl
- givptr:
:type: integer
:intent: input
:dims:
- n
- givcol:
:type: integer
:intent: input
:dims:
- ldgcol
- 2 * nlvl
- ldgcol:
:type: integer
:intent: input
- perm:
:type: integer
:intent: input
:dims:
- ldgcol
- nlvl
- givnum:
:type: real
:intent: input
:dims:
- ldu
- 2 * nlvl
- c:
:type: real
:intent: input
:dims:
- n
- s:
:type: real
:intent: input
:dims:
- n
- work:
:type: real
:intent: workspace
:dims:
- n
- iwork:
:type: integer
:intent: workspace
:dims:
- 3 * n
- info:
:type: integer
:intent: output
:substitutions:
ldbx: n
nlvl: (int)(1.0/log(2.0)*log((double)n/(smlsiz+1))) + 1
:fortran_help: " SUBROUTINE SLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SLALSA is an itermediate step in solving the least squares problem\n\
* by computing the SVD of the coefficient matrix in compact form (The\n\
* singular vectors are computed as products of simple orthorgonal\n\
* matrices.).\n\
*\n\
* If ICOMPQ = 0, SLALSA applies the inverse of the left singular vector\n\
* matrix of an upper bidiagonal matrix to the right hand side; and if\n\
* ICOMPQ = 1, SLALSA applies the right singular vector matrix to the\n\
* right hand side. The singular vector matrices were generated in\n\
* compact form by SLALSA.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
*\n\
* ICOMPQ (input) INTEGER\n\
* Specifies whether the left or the right singular vector\n\
* matrix is involved.\n\
* = 0: Left singular vector matrix\n\
* = 1: Right singular vector matrix\n\
*\n\
* SMLSIZ (input) INTEGER\n\
* The maximum size of the subproblems at the bottom of the\n\
* computation tree.\n\
*\n\
* N (input) INTEGER\n\
* The row and column dimensions of the upper bidiagonal matrix.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of columns of B and BX. NRHS must be at least 1.\n\
*\n\
* B (input/output) REAL array, dimension ( LDB, NRHS )\n\
* On input, B contains the right hand sides of the least\n\
* squares problem in rows 1 through M.\n\
* On output, B contains the solution X in rows 1 through N.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of B in the calling subprogram.\n\
* LDB must be at least max(1,MAX( M, N ) ).\n\
*\n\
* BX (output) REAL array, dimension ( LDBX, NRHS )\n\
* On exit, the result of applying the left or right singular\n\
* vector matrix to B.\n\
*\n\
* LDBX (input) INTEGER\n\
* The leading dimension of BX.\n\
*\n\
* U (input) REAL array, dimension ( LDU, SMLSIZ ).\n\
* On entry, U contains the left singular vector matrices of all\n\
* subproblems at the bottom level.\n\
*\n\
* LDU (input) INTEGER, LDU = > N.\n\
* The leading dimension of arrays U, VT, DIFL, DIFR,\n\
* POLES, GIVNUM, and Z.\n\
*\n\
* VT (input) REAL array, dimension ( LDU, SMLSIZ+1 ).\n\
* On entry, VT' contains the right singular vector matrices of\n\
* all subproblems at the bottom level.\n\
*\n\
* K (input) INTEGER array, dimension ( N ).\n\
*\n\
* DIFL (input) REAL array, dimension ( LDU, NLVL ).\n\
* where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.\n\
*\n\
* DIFR (input) REAL array, dimension ( LDU, 2 * NLVL ).\n\
* On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record\n\
* distances between singular values on the I-th level and\n\
* singular values on the (I -1)-th level, and DIFR(*, 2 * I)\n\
* record the normalizing factors of the right singular vectors\n\
* matrices of subproblems on I-th level.\n\
*\n\
* Z (input) REAL array, dimension ( LDU, NLVL ).\n\
* On entry, Z(1, I) contains the components of the deflation-\n\
* adjusted updating row vector for subproblems on the I-th\n\
* level.\n\
*\n\
* POLES (input) REAL array, dimension ( LDU, 2 * NLVL ).\n\
* On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old\n\
* singular values involved in the secular equations on the I-th\n\
* level.\n\
*\n\
* GIVPTR (input) INTEGER array, dimension ( N ).\n\
* On entry, GIVPTR( I ) records the number of Givens\n\
* rotations performed on the I-th problem on the computation\n\
* tree.\n\
*\n\
* GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).\n\
* On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the\n\
* locations of Givens rotations performed on the I-th level on\n\
* the computation tree.\n\
*\n\
* LDGCOL (input) INTEGER, LDGCOL = > N.\n\
* The leading dimension of arrays GIVCOL and PERM.\n\
*\n\
* PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).\n\
* On entry, PERM(*, I) records permutations done on the I-th\n\
* level of the computation tree.\n\
*\n\
* GIVNUM (input) REAL array, dimension ( LDU, 2 * NLVL ).\n\
* On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-\n\
* values of Givens rotations performed on the I-th level on the\n\
* computation tree.\n\
*\n\
* C (input) REAL array, dimension ( N ).\n\
* On entry, if the I-th subproblem is not square,\n\
* C( I ) contains the C-value of a Givens rotation related to\n\
* the right null space of the I-th subproblem.\n\
*\n\
* S (input) REAL array, dimension ( N ).\n\
* On entry, if the I-th subproblem is not square,\n\
* S( I ) contains the S-value of a Givens rotation related to\n\
* the right null space of the I-th subproblem.\n\
*\n\
* WORK (workspace) REAL array.\n\
* The dimension must be at least N.\n\
*\n\
* IWORK (workspace) INTEGER array.\n\
* The dimension must be at least 3 * N\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 Ren-Cang Li, Computer Science Division, University of\n\
* California at Berkeley, USA\n\
* Osni Marques, LBNL/NERSC, USA\n\
*\n\
* =====================================================================\n\
*\n"
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