1DLALSA(1) LAPACK routine (version 3.2) DLALSA(1)
2
6 DLALSA - is 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 DLALSA( 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, WORK, 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 DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ), DIFL(
22 LDU, * ), DIFR( LDU, * ), GIVNUM( LDU, * ), POLES(
23 LDU, * ), S( * ), U( LDU, * ), VT( LDU, * ), WORK( *
24 ), Z( LDU, * )
25
27 DLALSA is an itermediate step in solving the least squares problem by
28 computing the SVD of the coefficient matrix in compact form (The singu‐
29 lar vectors are computed as products of simple orthorgonal matrices.).
30 If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector
31 matrix of an upper bidiagonal matrix to the right hand side; and if
32 ICOMPQ = 1, DLALSA applies the right singular vector matrix to the
33 right hand side. The singular vector matrices were generated in compact
34 form by DLALSA.
35
37 ICOMPQ (input) INTEGER Specifies whether the left or the right singular
38 vector matrix is involved. = 0: Left singular vector matrix
39 = 1: Right singular vector matrix SMLSIZ (input) INTEGER The maximum
40 size of the subproblems at the bottom of the computation tree.
41 N (input) INTEGER
43 The row and column dimensions of the upper bidiagonal matrix.
44 NRHS (input) INTEGER
46 The number of columns of B and BX. NRHS must be at least 1.
47 B (input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS )
49 On input, B contains the right hand sides of the least squares
50 problem in rows 1 through M. On output, B contains the solution
51 X in rows 1 through N.
52 LDB (input) INTEGER
54 The leading dimension of B in the calling subprogram. LDB must
55 be at least max(1,MAX( M, N ) ).
56 BX (output) DOUBLE PRECISION array, dimension ( LDBX, NRHS )
58 On exit, the result of applying the left or right singular vec‐
59 tor matrix to B.
60 LDBX (input) INTEGER
62 The leading dimension of BX.
63 U (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
65 On entry, U contains the left singular vector matrices of all
66 subproblems at the bottom level.
67 LDU (input) INTEGER, LDU = > N.
69 The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
70 GIVNUM, and Z.
71 VT (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
73 On entry, VT' contains the right singular vector matrices of all
74 subproblems at the bottom level.
75 K (input) INTEGER array, dimension ( N ).
77 DIFL (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
79 where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
80 DIFR (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
82 On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record distances
83 between singular values on the I-th level and singular values on
84 the (I -1)-th level, and DIFR(*, 2 * I) record the normalizing
85 factors of the right singular vectors matrices of subproblems on
86 I-th level.
87 Z (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
89 On entry, Z(1, I) contains the components of the deflation-
90 adjusted updating row vector for subproblems on the I-th level.
91 POLES (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
93 On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
94 singular values involved in the secular equations on the I-th
95 level. GIVPTR (input) INTEGER array, dimension ( N ). On
96 entry, GIVPTR( I ) records the number of Givens rotations per‐
97 formed on the I-th problem on the computation tree. GIVCOL
98 (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ). On
99 entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the loca‐
100 tions of Givens rotations performed on the I-th level on the
101 computation tree. LDGCOL (input) INTEGER, LDGCOL = > N. The
102 leading dimension of arrays GIVCOL and PERM.
103 PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).
105 On entry, PERM(*, I) records permutations done on the I-th level
106 of the computation tree. GIVNUM (input) DOUBLE PRECISION array,
107 dimension ( LDU, 2 * NLVL ). On entry, GIVNUM(*, 2 *I -1 : 2 *
108 I) records the C- and S- values of Givens rotations performed on
109 the I-th level on the computation tree.
110 C (input) DOUBLE PRECISION array, dimension ( N ).
112 On entry, if the I-th subproblem is not square, C( I ) contains
113 the C-value of a Givens rotation related to the right null space
114 of the I-th subproblem.
115 S (input) DOUBLE PRECISION array, dimension ( N ).
117 On entry, if the I-th subproblem is not square, S( I ) contains
118 the S-value of a Givens rotation related to the right null space
119 of the I-th subproblem.
120 WORK (workspace) DOUBLE PRECISION array.
122 The dimension must be at least N.
123 IWORK (workspace) INTEGER array.
125 The dimension must be at least 3 * N
126 INFO (output) INTEGER
128 = 0: successful exit.
129 < 0: if INFO = -i, the i-th argument had an illegal value.
130
132 Based on contributions by
133 Ming Gu and Ren-Cang Li, Computer Science Division, University of
134 California at Berkeley, USA
135 Osni Marques, LBNL/NERSC, USA
136 LAPACK routine (version 3.2) November 2008 DLALSA(1)