1DLALSA(1) LAPACK routine (version 3.1) DLALSA(1)
2
6 DLALSA - 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
32 matrix of an upper bidiagonal matrix to the right hand side; and if
33 ICOMPQ = 1, DLALSA applies the right singular vector matrix to the
34 right hand side. The singular vector matrices were generated in compact
35 form by DLALSA.
36
39 ICOMPQ (input) INTEGER Specifies whether the left or the right singular
40 vector matrix is involved. = 0: Left singular vector matrix
41 = 1: Right singular vector matrix
42 SMLSIZ (input) INTEGER The maximum size of the subproblems at the bot‐
44 tom of the computation tree.
45 N (input) INTEGER
47 The row and column dimensions of the upper bidiagonal matrix.
48 NRHS (input) INTEGER
50 The number of columns of B and BX. NRHS must be at least 1.
51 B (input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS )
53 On input, B contains the right hand sides of the least squares
54 problem in rows 1 through M. On output, B contains the solution
55 X in rows 1 through N.
56 LDB (input) INTEGER
58 The leading dimension of B in the calling subprogram. LDB must
59 be at least max(1,MAX( M, N ) ).
60 BX (output) DOUBLE PRECISION array, dimension ( LDBX, NRHS )
62 On exit, the result of applying the left or right singular vec‐
63 tor matrix to B.
64 LDBX (input) INTEGER
66 The leading dimension of BX.
67 U (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
69 On entry, U contains the left singular vector matrices of all
70 subproblems at the bottom level.
71 LDU (input) INTEGER, LDU = > N.
73 The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
74 GIVNUM, and Z.
75 VT (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
77 On entry, VT' contains the right singular vector matrices of all
78 subproblems at the bottom level.
79 K (input) INTEGER array, dimension ( N ).
81 DIFL (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
83 where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
84 DIFR (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
86 On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record distances
87 between singular values on the I-th level and singular values on
88 the (I -1)-th level, and DIFR(*, 2 * I) record the normalizing
89 factors of the right singular vectors matrices of subproblems on
90 I-th level.
91 Z (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ).
93 On entry, Z(1, I) contains the components of the deflation-
94 adjusted updating row vector for subproblems on the I-th level.
95 POLES (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
97 On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
98 singular values involved in the secular equations on the I-th
99 level.
100 GIVPTR (input) INTEGER array, dimension ( N ). On entry,
102 GIVPTR( I ) records the number of Givens rotations performed on
103 the I-th problem on the computation tree.
104 GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
106 On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
107 locations of Givens rotations performed on the I-th level on the
108 computation tree.
109 LDGCOL (input) INTEGER, LDGCOL = > N. The leading dimension of
111 arrays GIVCOL and PERM.
112 PERM (input) INTEGER array, dimension ( LDGCOL, NLVL ).
114 On entry, PERM(*, I) records permutations done on the I-th level
115 of the computation tree.
116 GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL
118 ). On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-
119 values of Givens rotations performed on the I-th level on the
120 computation tree.
121 C (input) DOUBLE PRECISION array, dimension ( N ).
123 On entry, if the I-th subproblem is not square, C( I ) contains
124 the C-value of a Givens rotation related to the right null space
125 of the I-th subproblem.
126 S (input) DOUBLE PRECISION array, dimension ( N ).
128 On entry, if the I-th subproblem is not square, S( I ) contains
129 the S-value of a Givens rotation related to the right null space
130 of the I-th subproblem.
131 WORK (workspace) DOUBLE PRECISION array.
133 The dimension must be at least N.
134 IWORK (workspace) INTEGER array.
136 The dimension must be at least 3 * N
137 INFO (output) INTEGER
139 = 0: successful exit.
140 < 0: if INFO = -i, the i-th argument had an illegal value.
141
143 Based on contributions by
144 Ming Gu and Ren-Cang Li, Computer Science Division, University of
145 California at Berkeley, USA
146 Osni Marques, LBNL/NERSC, USA
147 LAPACK routine (version 3.1) November 2006 DLALSA(1)