1: *> \brief \b DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.
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,out] 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 (LDU, 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 (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 array, dimension (8*N)
116: *> \endverbatim
117: *>
118: *> \param[out] WORK
119: *> \verbatim
120: *> WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M)
121: *> \endverbatim
122: *>
123: *> \param[out] INFO
124: *> \verbatim
125: *> INFO is INTEGER
126: *> = 0: successful exit.
127: *> < 0: if INFO = -i, the i-th argument had an illegal value.
128: *> > 0: if INFO = 1, a singular value did not converge
129: *> \endverbatim
130: *
131: * Authors:
132: * ========
133: *
134: *> \author Univ. of Tennessee
135: *> \author Univ. of California Berkeley
136: *> \author Univ. of Colorado Denver
137: *> \author NAG Ltd.
138: *
139: *> \ingroup OTHERauxiliary
140: *
141: *> \par Contributors:
142: * ==================
143: *>
144: *> Ming Gu and Huan Ren, Computer Science Division, University of
145: *> California at Berkeley, USA
146: *>
147: * =====================================================================
148: SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
149: $ WORK, INFO )
150: *
151: * -- LAPACK auxiliary routine --
152: * -- LAPACK is a software package provided by Univ. of Tennessee, --
153: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154: *
155: * .. Scalar Arguments ..
156: INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE
157: * ..
158: * .. Array Arguments ..
159: INTEGER IWORK( * )
160: DOUBLE PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
161: $ WORK( * )
162: * ..
163: *
164: * =====================================================================
165: *
166: * .. Local Scalars ..
167: INTEGER I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK,
168: $ J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR,
169: $ NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI
170: DOUBLE PRECISION ALPHA, BETA
171: * ..
172: * .. External Subroutines ..
173: EXTERNAL DLASD1, DLASDQ, DLASDT, XERBLA
174: * ..
175: * .. Executable Statements ..
176: *
177: * Test the input parameters.
178: *
179: INFO = 0
180: *
181: IF( N.LT.0 ) THEN
182: INFO = -1
183: ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
184: INFO = -2
185: END IF
186: *
187: M = N + SQRE
188: *
189: IF( LDU.LT.N ) THEN
190: INFO = -6
191: ELSE IF( LDVT.LT.M ) THEN
192: INFO = -8
193: ELSE IF( SMLSIZ.LT.3 ) THEN
194: INFO = -9
195: END IF
196: IF( INFO.NE.0 ) THEN
197: CALL XERBLA( 'DLASD0', -INFO )
198: RETURN
199: END IF
200: *
201: * If the input matrix is too small, call DLASDQ to find the SVD.
202: *
203: IF( N.LE.SMLSIZ ) THEN
204: CALL DLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDVT, U, LDU, U,
205: $ LDU, WORK, INFO )
206: RETURN
207: END IF
208: *
209: * Set up the computation tree.
210: *
211: INODE = 1
212: NDIML = INODE + N
213: NDIMR = NDIML + N
214: IDXQ = NDIMR + N
215: IWK = IDXQ + N
216: CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
217: $ IWORK( NDIMR ), SMLSIZ )
218: *
219: * For the nodes on bottom level of the tree, solve
220: * their subproblems by DLASDQ.
221: *
222: NDB1 = ( ND+1 ) / 2
223: NCC = 0
224: DO 30 I = NDB1, ND
225: *
226: * IC : center row of each node
227: * NL : number of rows of left subproblem
228: * NR : number of rows of right subproblem
229: * NLF: starting row of the left subproblem
230: * NRF: starting row of the right subproblem
231: *
232: I1 = I - 1
233: IC = IWORK( INODE+I1 )
234: NL = IWORK( NDIML+I1 )
235: NLP1 = NL + 1
236: NR = IWORK( NDIMR+I1 )
237: NRP1 = NR + 1
238: NLF = IC - NL
239: NRF = IC + 1
240: SQREI = 1
241: CALL DLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), E( NLF ),
242: $ VT( NLF, NLF ), LDVT, U( NLF, NLF ), LDU,
243: $ U( NLF, NLF ), LDU, WORK, INFO )
244: IF( INFO.NE.0 ) THEN
245: RETURN
246: END IF
247: ITEMP = IDXQ + NLF - 2
248: DO 10 J = 1, NL
249: IWORK( ITEMP+J ) = J
250: 10 CONTINUE
251: IF( I.EQ.ND ) THEN
252: SQREI = SQRE
253: ELSE
254: SQREI = 1
255: END IF
256: NRP1 = NR + SQREI
257: CALL DLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), E( NRF ),
258: $ VT( NRF, NRF ), LDVT, U( NRF, NRF ), LDU,
259: $ U( NRF, NRF ), LDU, WORK, INFO )
260: IF( INFO.NE.0 ) THEN
261: RETURN
262: END IF
263: ITEMP = IDXQ + IC
264: DO 20 J = 1, NR
265: IWORK( ITEMP+J-1 ) = J
266: 20 CONTINUE
267: 30 CONTINUE
268: *
269: * Now conquer each subproblem bottom-up.
270: *
271: DO 50 LVL = NLVL, 1, -1
272: *
273: * Find the first node LF and last node LL on the
274: * current level LVL.
275: *
276: IF( LVL.EQ.1 ) THEN
277: LF = 1
278: LL = 1
279: ELSE
280: LF = 2**( LVL-1 )
281: LL = 2*LF - 1
282: END IF
283: DO 40 I = LF, LL
284: IM1 = I - 1
285: IC = IWORK( INODE+IM1 )
286: NL = IWORK( NDIML+IM1 )
287: NR = IWORK( NDIMR+IM1 )
288: NLF = IC - NL
289: IF( ( SQRE.EQ.0 ) .AND. ( I.EQ.LL ) ) THEN
290: SQREI = SQRE
291: ELSE
292: SQREI = 1
293: END IF
294: IDXQC = IDXQ + NLF - 1
295: ALPHA = D( IC )
296: BETA = E( IC )
297: CALL DLASD1( NL, NR, SQREI, D( NLF ), ALPHA, BETA,
298: $ U( NLF, NLF ), LDU, VT( NLF, NLF ), LDVT,
299: $ IWORK( IDXQC ), IWORK( IWK ), WORK, INFO )
300: *
301: * Report the possible convergence failure.
302: *
303: IF( INFO.NE.0 ) THEN
304: RETURN
305: END IF
306: 40 CONTINUE
307: 50 CONTINUE
308: *
309: RETURN
310: *
311: * End of DLASD0
312: *
313: END
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