1DLASD3(1) LAPACK auxiliary routine (version 3.2) DLASD3(1)
2
6 DLASD3 - finds all the square roots of the roots of the secular equa‐
7 tion, as defined by the values in D and Z
8
10 SUBROUTINE DLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2,
11 LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO )
12 INTEGER INFO, K, LDQ, LDU, LDU2, LDVT, LDVT2, NL, NR, SQRE
14 INTEGER CTOT( * ), IDXC( * )
16 DOUBLE PRECISION D( * ), DSIGMA( * ), Q( LDQ, * ), U( LDU,
18 * ), U2( LDU2, * ), VT( LDVT, * ), VT2( LDVT2, * ),
19 Z( * )
20
22 DLASD3 finds all the square roots of the roots of the secular equation,
23 as defined by the values in D and Z. It makes the appropriate calls to
24 DLASD4 and then updates the singular vectors by matrix multiplication.
25 This code makes very mild assumptions about floating point arithmetic.
26 It will work on machines with a guard digit in add/subtract, or on
27 those binary machines without guard digits which subtract like the Cray
28 XMP, Cray YMP, Cray C 90, or Cray 2. It could conceivably fail on
29 hexadecimal or decimal machines without guard digits, but we know of
30 none.
31 DLASD3 is called from DLASD1.
32
34 NL (input) INTEGER
35 The row dimension of the upper block. NL >= 1.
36 NR (input) INTEGER
38 The row dimension of the lower block. NR >= 1.
39 SQRE (input) INTEGER
41 = 0: the lower block is an NR-by-NR square matrix.
42 = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The
43 bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N
44 columns.
45 K (input) INTEGER
47 The size of the secular equation, 1 =< K = < N.
48 D (output) DOUBLE PRECISION array, dimension(K)
50 On exit the square roots of the roots of the secular equation,
51 in ascending order.
52 Q (workspace) DOUBLE PRECISION array,
54 dimension at least (LDQ,K).
55 LDQ (input) INTEGER
57 The leading dimension of the array Q. LDQ >= K. DSIGMA (input)
58 DOUBLE PRECISION array, dimension(K) The first K elements of
59 this array contain the old roots of the deflated updating prob‐
60 lem. These are the poles of the secular equation.
61 U (output) DOUBLE PRECISION array, dimension (LDU, N)
63 The last N - K columns of this matrix contain the deflated left
64 singular vectors.
65 LDU (input) INTEGER
67 The leading dimension of the array U. LDU >= N.
68 U2 (input/output) DOUBLE PRECISION array, dimension (LDU2, N)
70 The first K columns of this matrix contain the non-deflated left
71 singular vectors for the split problem.
72 LDU2 (input) INTEGER
74 The leading dimension of the array U2. LDU2 >= N.
75 VT (output) DOUBLE PRECISION array, dimension (LDVT, M)
77 The last M - K columns of VT' contain the deflated right singu‐
78 lar vectors.
79 LDVT (input) INTEGER
81 The leading dimension of the array VT. LDVT >= N.
82 VT2 (input/output) DOUBLE PRECISION array, dimension (LDVT2, N)
84 The first K columns of VT2' contain the non-deflated right sin‐
85 gular vectors for the split problem.
86 LDVT2 (input) INTEGER
88 The leading dimension of the array VT2. LDVT2 >= N.
89 IDXC (input) INTEGER array, dimension ( N )
91 The permutation used to arrange the columns of U (and rows of
92 VT) into three groups: the first group contains non-zero
93 entries only at and above (or before) NL +1; the second contains
94 non-zero entries only at and below (or after) NL+2; and the
95 third is dense. The first column of U and the row of VT are
96 treated separately, however. The rows of the singular vectors
97 found by DLASD4 must be likewise permuted before the matrix mul‐
98 tiplies can take place.
99 CTOT (input) INTEGER array, dimension ( 4 )
101 A count of the total number of the various types of columns in U
102 (or rows in VT), as described in IDXC. The fourth column type is
103 any column which has been deflated.
104 Z (input) DOUBLE PRECISION array, dimension (K)
106 The first K elements of this array contain the components of the
107 deflation-adjusted updating row vector.
108 INFO (output) INTEGER
110 = 0: successful exit.
111 < 0: if INFO = -i, the i-th argument had an illegal value.
112 > 0: if INFO = 1, an singular value did not converge
113
115 Based on contributions by
116 Ming Gu and Huan Ren, Computer Science Division, University of
117 California at Berkeley, USA
118 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 DLASD3(1)