1CLALSA(1) LAPACK routine (version 3.1) CLALSA(1)
2
6 CLALSA - an itermediate step in solving the least squares problem by
7 computing the SVD of the coefficient matrix in compact form (The singu‐
8 lar vectors are computed as products of simple orthorgonal matrices.)
9
11 SUBROUTINE CLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU,
12 VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
13 PERM, GIVNUM, C, S, RWORK, IWORK, INFO )
14 INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, SML‐
16 SIZ
17 INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), K( *
19 ), PERM( LDGCOL, * )
20 REAL C( * ), DIFL( LDU, * ), DIFR( LDU, * ), GIVNUM( LDU,
22 * ), POLES( LDU, * ), RWORK( * ), S( * ), U( LDU, *
23 ), VT( LDU, * ), Z( LDU, * )
24 COMPLEX B( LDB, * ), BX( LDBX, * )
26
28 CLALSA is an itermediate step in solving the least squares problem by
29 computing the SVD of the coefficient matrix in compact form (The singu‐
30 lar vectors are computed as products of simple orthorgonal matrices.).
31 If ICOMPQ = 0, CLALSA applies the inverse of the left singular vector
33 matrix of an upper bidiagonal matrix to the right hand side; and if
34 ICOMPQ = 1, CLALSA applies the right singular vector matrix to the
35 right hand side. The singular vector matrices were generated in compact
36 form by CLALSA.
37
40 ICOMPQ (input) INTEGER Specifies whether the left or the right singular
41 vector matrix is involved. = 0: Left singular vector matrix
42 = 1: Right singular vector matrix
43 SMLSIZ (input) INTEGER The maximum size of the subproblems at the bot‐
45 tom of the computation tree.
46 N (input) INTEGER
48 The row and column dimensions of the upper bidiagonal matrix.
49 NRHS (input) INTEGER
51 The number of columns of B and BX. NRHS must be at least 1.
52 B (input/output) COMPLEX array, dimension ( LDB, NRHS )
54 On input, B contains the right hand sides of the least squares
55 problem in rows 1 through M. On output, B contains the solution
56 X in rows 1 through N.
57 LDB (input) INTEGER
59 The leading dimension of B in the calling subprogram. LDB must
60 be at least max(1,MAX( M, N ) ).
61 BX (output) COMPLEX array, dimension ( LDBX, NRHS )
63 On exit, the result of applying the left or right singular vec‐
64 tor matrix to B.
65 LDBX (input) INTEGER
67 The leading dimension of BX.
68 U (input) REAL array, dimension ( LDU, SMLSIZ ).
70 On entry, U contains the left singular vector matrices of all
71 subproblems at the bottom level.
72 LDU (input) INTEGER, LDU = > N.
74 The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
75 GIVNUM, and Z.
76 VT (input) REAL array, dimension ( LDU, SMLSIZ+1 ).
78 On entry, VT' contains the right singular vector matrices of all
79 subproblems at the bottom level.
80 K (input) INTEGER array, dimension ( N ).
82 DIFL (input) REAL array, dimension ( LDU, NLVL ).
84 where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
85 DIFR (input) REAL array, dimension ( LDU, 2 * NLVL ).
87 On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record distances
88 between singular values on the I-th level and singular values on
89 the (I -1)-th level, and DIFR(*, 2 * I) record the normalizing
90 factors of the right singular vectors matrices of subproblems on
91 I-th level.
92 Z (input) REAL array, dimension ( LDU, NLVL ).
94 On entry, Z(1, I) contains the components of the deflation-
95 adjusted updating row vector for subproblems on the I-th level.
96 POLES (input) REAL array, dimension ( LDU, 2 * NLVL ).
98 On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
99 singular values involved in the secular equations on the I-th
100 level.
101 GIVPTR (input) INTEGER array, dimension ( N ). On entry,
103 GIVPTR( I ) records the number of Givens rotations performed on
104 the I-th problem on the computation tree.
105 GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
107 On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
108 locations of Givens rotations performed on the I-th level on the
109 computation tree.
110 LDGCOL (input) INTEGER, LDGCOL = > N. The leading dimension of
112 arrays GIVCOL and PERM.
113 PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).
115 On entry, PERM(*, I) records permutations done on the I-th level
116 of the computation tree.
117 GIVNUM (input) REAL array, dimension ( LDU, 2 * NLVL ). On
119 entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- values
120 of Givens rotations performed on the I-th level on the computa‐
121 tion tree.
122 C (input) REAL array, dimension ( N ).
124 On entry, if the I-th subproblem is not square, C( I ) contains
125 the C-value of a Givens rotation related to the right null space
126 of the I-th subproblem.
127 S (input) REAL array, dimension ( N ).
129 On entry, if the I-th subproblem is not square, S( I ) contains
130 the S-value of a Givens rotation related to the right null space
131 of the I-th subproblem.
132 RWORK (workspace) REAL array, dimension at least
134 max ( N, (SMLSZ+1)*NRHS*3 ).
135 IWORK (workspace) INTEGER array.
137 The dimension must be at least 3 * N
138 INFO (output) INTEGER
140 = 0: successful exit.
141 < 0: if INFO = -i, the i-th argument had an illegal value.
142
144 Based on contributions by
145 Ming Gu and Ren-Cang Li, Computer Science Division, University of
146 California at Berkeley, USA
147 Osni Marques, LBNL/NERSC, USA
148 LAPACK routine (version 3.1) November 2006 CLALSA(1)