1SBDSDC(1) LAPACK routine (version 3.1) SBDSDC(1)
2
6 SBDSDC - the singular value decomposition (SVD) of a real N-by-N (upper
7 or lower) bidiagonal matrix B
8
10 SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK,
11 IWORK, INFO )
12 CHARACTER COMPQ, UPLO
14 INTEGER INFO, LDU, LDVT, N
16 INTEGER IQ( * ), IWORK( * )
18 REAL D( * ), E( * ), Q( * ), U( LDU, * ), VT( LDVT, * ),
20 WORK( * )
21
23 SBDSDC computes the singular value decomposition (SVD) of a real N-by-N
24 (upper or lower) bidiagonal matrix B: B = U * S * VT, using a divide
25 and conquer method, where S is a diagonal matrix with non-negative
26 diagonal elements (the singular values of B), and U and VT are orthogo‐
27 nal matrices of left and right singular vectors, respectively. SBDSDC
28 can be used to compute all singular values, and optionally, singular
29 vectors or singular vectors in compact form.
30 This code makes very mild assumptions about floating point arithmetic.
32 It will work on machines with a guard digit in add/subtract, or on
33 those binary machines without guard digits which subtract like the Cray
34 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
35 hexadecimal or decimal machines without guard digits, but we know of
36 none. See SLASD3 for details.
37 The code currently calls SLASDQ if singular values only are desired.
39 However, it can be slightly modified to compute singular values using
40 the divide and conquer method.
41
44 UPLO (input) CHARACTER*1
45 = 'U': B is upper bidiagonal.
46 = 'L': B is lower bidiagonal.
47 COMPQ (input) CHARACTER*1
49 Specifies whether singular vectors are to be computed as fol‐
50 lows:
51 = 'N': Compute singular values only;
52 = 'P': Compute singular values and compute singular vectors in
53 compact form; = 'I': Compute singular values and singular vec‐
54 tors.
55 N (input) INTEGER
57 The order of the matrix B. N >= 0.
58 D (input/output) REAL array, dimension (N)
60 On entry, the n diagonal elements of the bidiagonal matrix B.
61 On exit, if INFO=0, the singular values of B.
62 E (input/output) REAL array, dimension (N-1)
64 On entry, the elements of E contain the offdiagonal elements of
65 the bidiagonal matrix whose SVD is desired. On exit, E has
66 been destroyed.
67 U (output) REAL array, dimension (LDU,N)
69 If COMPQ = 'I', then: On exit, if INFO = 0, U contains the
70 left singular vectors of the bidiagonal matrix. For other val‐
71 ues of COMPQ, U is not referenced.
72 LDU (input) INTEGER
74 The leading dimension of the array U. LDU >= 1. If singular
75 vectors are desired, then LDU >= max( 1, N ).
76 VT (output) REAL array, dimension (LDVT,N)
78 If COMPQ = 'I', then: On exit, if INFO = 0, VT' contains the
79 right singular vectors of the bidiagonal matrix. For other
80 values of COMPQ, VT is not referenced.
81 LDVT (input) INTEGER
83 The leading dimension of the array VT. LDVT >= 1. If singular
84 vectors are desired, then LDVT >= max( 1, N ).
85 Q (output) REAL array, dimension (LDQ)
87 If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain
88 the left and right singular vectors in a compact form, requir‐
89 ing O(N log N) space instead of 2*N**2. In particular, Q con‐
90 tains all the REAL data in LDQ >= N*(11 + 2*SMLSIZ +
91 8*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is
92 returned by ILAENV and is equal to the maximum size of the sub‐
93 problems at the bottom of the computation tree (usually about
94 25). For other values of COMPQ, Q is not referenced.
95 IQ (output) INTEGER array, dimension (LDIQ)
97 If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain
98 the left and right singular vectors in a compact form, requir‐
99 ing O(N log N) space instead of 2*N**2. In particular, IQ con‐
100 tains all INTEGER data in LDIQ >= N*(3 + 3*INT(LOG_2(N/(SML‐
101 SIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV
102 and is equal to the maximum size of the subproblems at the bot‐
103 tom of the computation tree (usually about 25). For other val‐
104 ues of COMPQ, IQ is not referenced.
105 WORK (workspace) REAL array, dimension (MAX(1,LWORK))
107 If COMPQ = 'N' then LWORK >= (4 * N). If COMPQ = 'P' then
108 LWORK >= (6 * N). If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 *
109 N).
110 IWORK (workspace) INTEGER array, dimension (8*N)
112 INFO (output) INTEGER
114 = 0: successful exit.
115 < 0: if INFO = -i, the i-th argument had an illegal value.
116 > 0: The algorithm failed to compute an singular value. The
117 update process of divide and conquer failed.
118
120 Based on contributions by
121 Ming Gu and Huan Ren, Computer Science Division, University of
122 California at Berkeley, USA
123 LAPACK routine (version 3.1) November 2006 SBDSDC(1)