Annotation of rpl/lapack/lapack/dlasd0.f, revision 1.11
1.10 bertrand 1: *> \brief \b DLASD0
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLASD0 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd0.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd0.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd0.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
22: * WORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IWORK( * )
29: * DOUBLE PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
30: * $ WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> Using a divide and conquer approach, DLASD0 computes the singular
40: *> value decomposition (SVD) of a real upper bidiagonal N-by-M
41: *> matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
42: *> The algorithm computes orthogonal matrices U and VT such that
43: *> B = U * S * VT. The singular values S are overwritten on D.
44: *>
45: *> A related subroutine, DLASDA, computes only the singular values,
46: *> and optionally, the singular vectors in compact form.
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] N
53: *> \verbatim
54: *> N is INTEGER
55: *> On entry, the row dimension of the upper bidiagonal matrix.
56: *> This is also the dimension of the main diagonal array D.
57: *> \endverbatim
58: *>
59: *> \param[in] SQRE
60: *> \verbatim
61: *> SQRE is INTEGER
62: *> Specifies the column dimension of the bidiagonal matrix.
63: *> = 0: The bidiagonal matrix has column dimension M = N;
64: *> = 1: The bidiagonal matrix has column dimension M = N+1;
65: *> \endverbatim
66: *>
67: *> \param[in,out] D
68: *> \verbatim
69: *> D is DOUBLE PRECISION array, dimension (N)
70: *> On entry D contains the main diagonal of the bidiagonal
71: *> matrix.
72: *> On exit D, if INFO = 0, contains its singular values.
73: *> \endverbatim
74: *>
75: *> \param[in] E
76: *> \verbatim
77: *> E is DOUBLE PRECISION array, dimension (M-1)
78: *> Contains the subdiagonal entries of the bidiagonal matrix.
79: *> On exit, E has been destroyed.
80: *> \endverbatim
81: *>
82: *> \param[out] U
83: *> \verbatim
84: *> U is DOUBLE PRECISION array, dimension at least (LDQ, N)
85: *> On exit, U contains the left singular vectors.
86: *> \endverbatim
87: *>
88: *> \param[in] LDU
89: *> \verbatim
90: *> LDU is INTEGER
91: *> On entry, leading dimension of U.
92: *> \endverbatim
93: *>
94: *> \param[out] VT
95: *> \verbatim
96: *> VT is DOUBLE PRECISION array, dimension at least (LDVT, M)
97: *> On exit, VT**T contains the right singular vectors.
98: *> \endverbatim
99: *>
100: *> \param[in] LDVT
101: *> \verbatim
102: *> LDVT is INTEGER
103: *> On entry, leading dimension of VT.
104: *> \endverbatim
105: *>
106: *> \param[in] SMLSIZ
107: *> \verbatim
108: *> SMLSIZ is INTEGER
109: *> On entry, maximum size of the subproblems at the
110: *> bottom of the computation tree.
111: *> \endverbatim
112: *>
113: *> \param[out] IWORK
114: *> \verbatim
115: *> IWORK is INTEGER work array.
116: *> Dimension must be at least (8 * N)
117: *> \endverbatim
118: *>
119: *> \param[out] WORK
120: *> \verbatim
121: *> WORK is DOUBLE PRECISION work array.
122: *> Dimension must be at least (3 * M**2 + 2 * M)
123: *> \endverbatim
124: *>
125: *> \param[out] INFO
126: *> \verbatim
127: *> INFO is INTEGER
128: *> = 0: successful exit.
129: *> < 0: if INFO = -i, the i-th argument had an illegal value.
130: *> > 0: if INFO = 1, a singular value did not converge
131: *> \endverbatim
132: *
133: * Authors:
134: * ========
135: *
136: *> \author Univ. of Tennessee
137: *> \author Univ. of California Berkeley
138: *> \author Univ. of Colorado Denver
139: *> \author NAG Ltd.
140: *
141: *> \date November 2011
142: *
143: *> \ingroup auxOTHERauxiliary
144: *
145: *> \par Contributors:
146: * ==================
147: *>
148: *> Ming Gu and Huan Ren, Computer Science Division, University of
149: *> California at Berkeley, USA
150: *>
151: * =====================================================================
1.1 bertrand 152: SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
153: $ WORK, INFO )
154: *
1.10 bertrand 155: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 156: * -- LAPACK is a software package provided by Univ. of Tennessee, --
157: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 bertrand 158: * November 2011
1.1 bertrand 159: *
160: * .. Scalar Arguments ..
161: INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE
162: * ..
163: * .. Array Arguments ..
164: INTEGER IWORK( * )
165: DOUBLE PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
166: $ WORK( * )
167: * ..
168: *
169: * =====================================================================
170: *
171: * .. Local Scalars ..
172: INTEGER I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK,
173: $ J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR,
174: $ NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI
175: DOUBLE PRECISION ALPHA, BETA
176: * ..
177: * .. External Subroutines ..
178: EXTERNAL DLASD1, DLASDQ, DLASDT, XERBLA
179: * ..
180: * .. Executable Statements ..
181: *
182: * Test the input parameters.
183: *
184: INFO = 0
185: *
186: IF( N.LT.0 ) THEN
187: INFO = -1
188: ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
189: INFO = -2
190: END IF
191: *
192: M = N + SQRE
193: *
194: IF( LDU.LT.N ) THEN
195: INFO = -6
196: ELSE IF( LDVT.LT.M ) THEN
197: INFO = -8
198: ELSE IF( SMLSIZ.LT.3 ) THEN
199: INFO = -9
200: END IF
201: IF( INFO.NE.0 ) THEN
202: CALL XERBLA( 'DLASD0', -INFO )
203: RETURN
204: END IF
205: *
206: * If the input matrix is too small, call DLASDQ to find the SVD.
207: *
208: IF( N.LE.SMLSIZ ) THEN
209: CALL DLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDVT, U, LDU, U,
210: $ LDU, WORK, INFO )
211: RETURN
212: END IF
213: *
214: * Set up the computation tree.
215: *
216: INODE = 1
217: NDIML = INODE + N
218: NDIMR = NDIML + N
219: IDXQ = NDIMR + N
220: IWK = IDXQ + N
221: CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
222: $ IWORK( NDIMR ), SMLSIZ )
223: *
224: * For the nodes on bottom level of the tree, solve
225: * their subproblems by DLASDQ.
226: *
227: NDB1 = ( ND+1 ) / 2
228: NCC = 0
229: DO 30 I = NDB1, ND
230: *
231: * IC : center row of each node
232: * NL : number of rows of left subproblem
233: * NR : number of rows of right subproblem
234: * NLF: starting row of the left subproblem
235: * NRF: starting row of the right subproblem
236: *
237: I1 = I - 1
238: IC = IWORK( INODE+I1 )
239: NL = IWORK( NDIML+I1 )
240: NLP1 = NL + 1
241: NR = IWORK( NDIMR+I1 )
242: NRP1 = NR + 1
243: NLF = IC - NL
244: NRF = IC + 1
245: SQREI = 1
246: CALL DLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), E( NLF ),
247: $ VT( NLF, NLF ), LDVT, U( NLF, NLF ), LDU,
248: $ U( NLF, NLF ), LDU, WORK, INFO )
249: IF( INFO.NE.0 ) THEN
250: RETURN
251: END IF
252: ITEMP = IDXQ + NLF - 2
253: DO 10 J = 1, NL
254: IWORK( ITEMP+J ) = J
255: 10 CONTINUE
256: IF( I.EQ.ND ) THEN
257: SQREI = SQRE
258: ELSE
259: SQREI = 1
260: END IF
261: NRP1 = NR + SQREI
262: CALL DLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), E( NRF ),
263: $ VT( NRF, NRF ), LDVT, U( NRF, NRF ), LDU,
264: $ U( NRF, NRF ), LDU, WORK, INFO )
265: IF( INFO.NE.0 ) THEN
266: RETURN
267: END IF
268: ITEMP = IDXQ + IC
269: DO 20 J = 1, NR
270: IWORK( ITEMP+J-1 ) = J
271: 20 CONTINUE
272: 30 CONTINUE
273: *
274: * Now conquer each subproblem bottom-up.
275: *
276: DO 50 LVL = NLVL, 1, -1
277: *
278: * Find the first node LF and last node LL on the
279: * current level LVL.
280: *
281: IF( LVL.EQ.1 ) THEN
282: LF = 1
283: LL = 1
284: ELSE
285: LF = 2**( LVL-1 )
286: LL = 2*LF - 1
287: END IF
288: DO 40 I = LF, LL
289: IM1 = I - 1
290: IC = IWORK( INODE+IM1 )
291: NL = IWORK( NDIML+IM1 )
292: NR = IWORK( NDIMR+IM1 )
293: NLF = IC - NL
294: IF( ( SQRE.EQ.0 ) .AND. ( I.EQ.LL ) ) THEN
295: SQREI = SQRE
296: ELSE
297: SQREI = 1
298: END IF
299: IDXQC = IDXQ + NLF - 1
300: ALPHA = D( IC )
301: BETA = E( IC )
302: CALL DLASD1( NL, NR, SQREI, D( NLF ), ALPHA, BETA,
303: $ U( NLF, NLF ), LDU, VT( NLF, NLF ), LDVT,
304: $ IWORK( IDXQC ), IWORK( IWK ), WORK, INFO )
305: IF( INFO.NE.0 ) THEN
306: RETURN
307: END IF
308: 40 CONTINUE
309: 50 CONTINUE
310: *
311: RETURN
312: *
313: * End of DLASD0
314: *
315: END
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