1 SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA,
2 $ IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
3 $ LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK,
4 $ IWORK, INFO )
5 *
6 * -- LAPACK auxiliary routine (version 3.3.0) --
7 * -- LAPACK is a software package provided by Univ. of Tennessee, --
8 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
9 * November 2010
10 *
11 * .. Scalar Arguments ..
12 INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL,
13 $ NR, SQRE
14 DOUBLE PRECISION ALPHA, BETA, C, S
15 * ..
16 * .. Array Arguments ..
17 INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ),
18 $ PERM( * )
19 DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ),
20 $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ),
21 $ VF( * ), VL( * ), WORK( * ), Z( * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * DLASD6 computes the SVD of an updated upper bidiagonal matrix B
28 * obtained by merging two smaller ones by appending a row. This
29 * routine is used only for the problem which requires all singular
30 * values and optionally singular vector matrices in factored form.
31 * B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE.
32 * A related subroutine, DLASD1, handles the case in which all singular
33 * values and singular vectors of the bidiagonal matrix are desired.
34 *
35 * DLASD6 computes the SVD as follows:
36 *
37 * ( D1(in) 0 0 0 )
38 * B = U(in) * ( Z1**T a Z2**T b ) * VT(in)
39 * ( 0 0 D2(in) 0 )
40 *
41 * = U(out) * ( D(out) 0) * VT(out)
42 *
43 * where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M
44 * with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
45 * elsewhere; and the entry b is empty if SQRE = 0.
46 *
47 * The singular values of B can be computed using D1, D2, the first
48 * components of all the right singular vectors of the lower block, and
49 * the last components of all the right singular vectors of the upper
50 * block. These components are stored and updated in VF and VL,
51 * respectively, in DLASD6. Hence U and VT are not explicitly
52 * referenced.
53 *
54 * The singular values are stored in D. The algorithm consists of two
55 * stages:
56 *
57 * The first stage consists of deflating the size of the problem
58 * when there are multiple singular values or if there is a zero
59 * in the Z vector. For each such occurence the dimension of the
60 * secular equation problem is reduced by one. This stage is
61 * performed by the routine DLASD7.
62 *
63 * The second stage consists of calculating the updated
64 * singular values. This is done by finding the roots of the
65 * secular equation via the routine DLASD4 (as called by DLASD8).
66 * This routine also updates VF and VL and computes the distances
67 * between the updated singular values and the old singular
68 * values.
69 *
70 * DLASD6 is called from DLASDA.
71 *
72 * Arguments
73 * =========
74 *
75 * ICOMPQ (input) INTEGER
76 * Specifies whether singular vectors are to be computed in
77 * factored form:
78 * = 0: Compute singular values only.
79 * = 1: Compute singular vectors in factored form as well.
80 *
81 * NL (input) INTEGER
82 * The row dimension of the upper block. NL >= 1.
83 *
84 * NR (input) INTEGER
85 * The row dimension of the lower block. NR >= 1.
86 *
87 * SQRE (input) INTEGER
88 * = 0: the lower block is an NR-by-NR square matrix.
89 * = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
90 *
91 * The bidiagonal matrix has row dimension N = NL + NR + 1,
92 * and column dimension M = N + SQRE.
93 *
94 * D (input/output) DOUBLE PRECISION array, dimension ( NL+NR+1 ).
95 * On entry D(1:NL,1:NL) contains the singular values of the
96 * upper block, and D(NL+2:N) contains the singular values
97 * of the lower block. On exit D(1:N) contains the singular
98 * values of the modified matrix.
99 *
100 * VF (input/output) DOUBLE PRECISION array, dimension ( M )
101 * On entry, VF(1:NL+1) contains the first components of all
102 * right singular vectors of the upper block; and VF(NL+2:M)
103 * contains the first components of all right singular vectors
104 * of the lower block. On exit, VF contains the first components
105 * of all right singular vectors of the bidiagonal matrix.
106 *
107 * VL (input/output) DOUBLE PRECISION array, dimension ( M )
108 * On entry, VL(1:NL+1) contains the last components of all
109 * right singular vectors of the upper block; and VL(NL+2:M)
110 * contains the last components of all right singular vectors of
111 * the lower block. On exit, VL contains the last components of
112 * all right singular vectors of the bidiagonal matrix.
113 *
114 * ALPHA (input/output) DOUBLE PRECISION
115 * Contains the diagonal element associated with the added row.
116 *
117 * BETA (input/output) DOUBLE PRECISION
118 * Contains the off-diagonal element associated with the added
119 * row.
120 *
121 * IDXQ (output) INTEGER array, dimension ( N )
122 * This contains the permutation which will reintegrate the
123 * subproblem just solved back into sorted order, i.e.
124 * D( IDXQ( I = 1, N ) ) will be in ascending order.
125 *
126 * PERM (output) INTEGER array, dimension ( N )
127 * The permutations (from deflation and sorting) to be applied
128 * to each block. Not referenced if ICOMPQ = 0.
129 *
130 * GIVPTR (output) INTEGER
131 * The number of Givens rotations which took place in this
132 * subproblem. Not referenced if ICOMPQ = 0.
133 *
134 * GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 )
135 * Each pair of numbers indicates a pair of columns to take place
136 * in a Givens rotation. Not referenced if ICOMPQ = 0.
137 *
138 * LDGCOL (input) INTEGER
139 * leading dimension of GIVCOL, must be at least N.
140 *
141 * GIVNUM (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
142 * Each number indicates the C or S value to be used in the
143 * corresponding Givens rotation. Not referenced if ICOMPQ = 0.
144 *
145 * LDGNUM (input) INTEGER
146 * The leading dimension of GIVNUM and POLES, must be at least N.
147 *
148 * POLES (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
149 * On exit, POLES(1,*) is an array containing the new singular
150 * values obtained from solving the secular equation, and
151 * POLES(2,*) is an array containing the poles in the secular
152 * equation. Not referenced if ICOMPQ = 0.
153 *
154 * DIFL (output) DOUBLE PRECISION array, dimension ( N )
155 * On exit, DIFL(I) is the distance between I-th updated
156 * (undeflated) singular value and the I-th (undeflated) old
157 * singular value.
158 *
159 * DIFR (output) DOUBLE PRECISION array,
160 * dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and
161 * dimension ( N ) if ICOMPQ = 0.
162 * On exit, DIFR(I, 1) is the distance between I-th updated
163 * (undeflated) singular value and the I+1-th (undeflated) old
164 * singular value.
165 *
166 * If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
167 * normalizing factors for the right singular vector matrix.
168 *
169 * See DLASD8 for details on DIFL and DIFR.
170 *
171 * Z (output) DOUBLE PRECISION array, dimension ( M )
172 * The first elements of this array contain the components
173 * of the deflation-adjusted updating row vector.
174 *
175 * K (output) INTEGER
176 * Contains the dimension of the non-deflated matrix,
177 * This is the order of the related secular equation. 1 <= K <=N.
178 *
179 * C (output) DOUBLE PRECISION
180 * C contains garbage if SQRE =0 and the C-value of a Givens
181 * rotation related to the right null space if SQRE = 1.
182 *
183 * S (output) DOUBLE PRECISION
184 * S contains garbage if SQRE =0 and the S-value of a Givens
185 * rotation related to the right null space if SQRE = 1.
186 *
187 * WORK (workspace) DOUBLE PRECISION array, dimension ( 4 * M )
188 *
189 * IWORK (workspace) INTEGER array, dimension ( 3 * N )
190 *
191 * INFO (output) INTEGER
192 * = 0: successful exit.
193 * < 0: if INFO = -i, the i-th argument had an illegal value.
194 * > 0: if INFO = 1, a singular value did not converge
195 *
196 * Further Details
197 * ===============
198 *
199 * Based on contributions by
200 * Ming Gu and Huan Ren, Computer Science Division, University of
201 * California at Berkeley, USA
202 *
203 * =====================================================================
204 *
205 * .. Parameters ..
206 DOUBLE PRECISION ONE, ZERO
207 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
208 * ..
209 * .. Local Scalars ..
210 INTEGER I, IDX, IDXC, IDXP, ISIGMA, IVFW, IVLW, IW, M,
211 $ N, N1, N2
212 DOUBLE PRECISION ORGNRM
213 * ..
214 * .. External Subroutines ..
215 EXTERNAL DCOPY, DLAMRG, DLASCL, DLASD7, DLASD8, XERBLA
216 * ..
217 * .. Intrinsic Functions ..
218 INTRINSIC ABS, MAX
219 * ..
220 * .. Executable Statements ..
221 *
222 * Test the input parameters.
223 *
224 INFO = 0
225 N = NL + NR + 1
226 M = N + SQRE
227 *
228 IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN
229 INFO = -1
230 ELSE IF( NL.LT.1 ) THEN
231 INFO = -2
232 ELSE IF( NR.LT.1 ) THEN
233 INFO = -3
234 ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
235 INFO = -4
236 ELSE IF( LDGCOL.LT.N ) THEN
237 INFO = -14
238 ELSE IF( LDGNUM.LT.N ) THEN
239 INFO = -16
240 END IF
241 IF( INFO.NE.0 ) THEN
242 CALL XERBLA( 'DLASD6', -INFO )
243 RETURN
244 END IF
245 *
246 * The following values are for bookkeeping purposes only. They are
247 * integer pointers which indicate the portion of the workspace
248 * used by a particular array in DLASD7 and DLASD8.
249 *
250 ISIGMA = 1
251 IW = ISIGMA + N
252 IVFW = IW + M
253 IVLW = IVFW + M
254 *
255 IDX = 1
256 IDXC = IDX + N
257 IDXP = IDXC + N
258 *
259 * Scale.
260 *
261 ORGNRM = MAX( ABS( ALPHA ), ABS( BETA ) )
262 D( NL+1 ) = ZERO
263 DO 10 I = 1, N
264 IF( ABS( D( I ) ).GT.ORGNRM ) THEN
265 ORGNRM = ABS( D( I ) )
266 END IF
267 10 CONTINUE
268 CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
269 ALPHA = ALPHA / ORGNRM
270 BETA = BETA / ORGNRM
271 *
272 * Sort and Deflate singular values.
273 *
274 CALL DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, WORK( IW ), VF,
275 $ WORK( IVFW ), VL, WORK( IVLW ), ALPHA, BETA,
276 $ WORK( ISIGMA ), IWORK( IDX ), IWORK( IDXP ), IDXQ,
277 $ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, C, S,
278 $ INFO )
279 *
280 * Solve Secular Equation, compute DIFL, DIFR, and update VF, VL.
281 *
282 CALL DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDGNUM,
283 $ WORK( ISIGMA ), WORK( IW ), INFO )
284 *
285 * Handle error returned
286 *
287 IF( INFO.NE.0 ) THEN
288 CALL XERBLA( 'DLASD8', -INFO )
289 RETURN
290 END IF
291 *
292 * Save the poles if ICOMPQ = 1.
293 *
294 IF( ICOMPQ.EQ.1 ) THEN
295 CALL DCOPY( K, D, 1, POLES( 1, 1 ), 1 )
296 CALL DCOPY( K, WORK( ISIGMA ), 1, POLES( 1, 2 ), 1 )
297 END IF
298 *
299 * Unscale.
300 *
301 CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO )
302 *
303 * Prepare the IDXQ sorting permutation.
304 *
305 N1 = K
306 N2 = N - K
307 CALL DLAMRG( N1, N2, D, 1, -1, IDXQ )
308 *
309 RETURN
310 *
311 * End of DLASD6
312 *
313 END
2 $ IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM,
3 $ LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK,
4 $ IWORK, INFO )
5 *
6 * -- LAPACK auxiliary routine (version 3.3.0) --
7 * -- LAPACK is a software package provided by Univ. of Tennessee, --
8 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
9 * November 2010
10 *
11 * .. Scalar Arguments ..
12 INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL,
13 $ NR, SQRE
14 DOUBLE PRECISION ALPHA, BETA, C, S
15 * ..
16 * .. Array Arguments ..
17 INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ),
18 $ PERM( * )
19 DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ),
20 $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ),
21 $ VF( * ), VL( * ), WORK( * ), Z( * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * DLASD6 computes the SVD of an updated upper bidiagonal matrix B
28 * obtained by merging two smaller ones by appending a row. This
29 * routine is used only for the problem which requires all singular
30 * values and optionally singular vector matrices in factored form.
31 * B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE.
32 * A related subroutine, DLASD1, handles the case in which all singular
33 * values and singular vectors of the bidiagonal matrix are desired.
34 *
35 * DLASD6 computes the SVD as follows:
36 *
37 * ( D1(in) 0 0 0 )
38 * B = U(in) * ( Z1**T a Z2**T b ) * VT(in)
39 * ( 0 0 D2(in) 0 )
40 *
41 * = U(out) * ( D(out) 0) * VT(out)
42 *
43 * where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M
44 * with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
45 * elsewhere; and the entry b is empty if SQRE = 0.
46 *
47 * The singular values of B can be computed using D1, D2, the first
48 * components of all the right singular vectors of the lower block, and
49 * the last components of all the right singular vectors of the upper
50 * block. These components are stored and updated in VF and VL,
51 * respectively, in DLASD6. Hence U and VT are not explicitly
52 * referenced.
53 *
54 * The singular values are stored in D. The algorithm consists of two
55 * stages:
56 *
57 * The first stage consists of deflating the size of the problem
58 * when there are multiple singular values or if there is a zero
59 * in the Z vector. For each such occurence the dimension of the
60 * secular equation problem is reduced by one. This stage is
61 * performed by the routine DLASD7.
62 *
63 * The second stage consists of calculating the updated
64 * singular values. This is done by finding the roots of the
65 * secular equation via the routine DLASD4 (as called by DLASD8).
66 * This routine also updates VF and VL and computes the distances
67 * between the updated singular values and the old singular
68 * values.
69 *
70 * DLASD6 is called from DLASDA.
71 *
72 * Arguments
73 * =========
74 *
75 * ICOMPQ (input) INTEGER
76 * Specifies whether singular vectors are to be computed in
77 * factored form:
78 * = 0: Compute singular values only.
79 * = 1: Compute singular vectors in factored form as well.
80 *
81 * NL (input) INTEGER
82 * The row dimension of the upper block. NL >= 1.
83 *
84 * NR (input) INTEGER
85 * The row dimension of the lower block. NR >= 1.
86 *
87 * SQRE (input) INTEGER
88 * = 0: the lower block is an NR-by-NR square matrix.
89 * = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
90 *
91 * The bidiagonal matrix has row dimension N = NL + NR + 1,
92 * and column dimension M = N + SQRE.
93 *
94 * D (input/output) DOUBLE PRECISION array, dimension ( NL+NR+1 ).
95 * On entry D(1:NL,1:NL) contains the singular values of the
96 * upper block, and D(NL+2:N) contains the singular values
97 * of the lower block. On exit D(1:N) contains the singular
98 * values of the modified matrix.
99 *
100 * VF (input/output) DOUBLE PRECISION array, dimension ( M )
101 * On entry, VF(1:NL+1) contains the first components of all
102 * right singular vectors of the upper block; and VF(NL+2:M)
103 * contains the first components of all right singular vectors
104 * of the lower block. On exit, VF contains the first components
105 * of all right singular vectors of the bidiagonal matrix.
106 *
107 * VL (input/output) DOUBLE PRECISION array, dimension ( M )
108 * On entry, VL(1:NL+1) contains the last components of all
109 * right singular vectors of the upper block; and VL(NL+2:M)
110 * contains the last components of all right singular vectors of
111 * the lower block. On exit, VL contains the last components of
112 * all right singular vectors of the bidiagonal matrix.
113 *
114 * ALPHA (input/output) DOUBLE PRECISION
115 * Contains the diagonal element associated with the added row.
116 *
117 * BETA (input/output) DOUBLE PRECISION
118 * Contains the off-diagonal element associated with the added
119 * row.
120 *
121 * IDXQ (output) INTEGER array, dimension ( N )
122 * This contains the permutation which will reintegrate the
123 * subproblem just solved back into sorted order, i.e.
124 * D( IDXQ( I = 1, N ) ) will be in ascending order.
125 *
126 * PERM (output) INTEGER array, dimension ( N )
127 * The permutations (from deflation and sorting) to be applied
128 * to each block. Not referenced if ICOMPQ = 0.
129 *
130 * GIVPTR (output) INTEGER
131 * The number of Givens rotations which took place in this
132 * subproblem. Not referenced if ICOMPQ = 0.
133 *
134 * GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 )
135 * Each pair of numbers indicates a pair of columns to take place
136 * in a Givens rotation. Not referenced if ICOMPQ = 0.
137 *
138 * LDGCOL (input) INTEGER
139 * leading dimension of GIVCOL, must be at least N.
140 *
141 * GIVNUM (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
142 * Each number indicates the C or S value to be used in the
143 * corresponding Givens rotation. Not referenced if ICOMPQ = 0.
144 *
145 * LDGNUM (input) INTEGER
146 * The leading dimension of GIVNUM and POLES, must be at least N.
147 *
148 * POLES (output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
149 * On exit, POLES(1,*) is an array containing the new singular
150 * values obtained from solving the secular equation, and
151 * POLES(2,*) is an array containing the poles in the secular
152 * equation. Not referenced if ICOMPQ = 0.
153 *
154 * DIFL (output) DOUBLE PRECISION array, dimension ( N )
155 * On exit, DIFL(I) is the distance between I-th updated
156 * (undeflated) singular value and the I-th (undeflated) old
157 * singular value.
158 *
159 * DIFR (output) DOUBLE PRECISION array,
160 * dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and
161 * dimension ( N ) if ICOMPQ = 0.
162 * On exit, DIFR(I, 1) is the distance between I-th updated
163 * (undeflated) singular value and the I+1-th (undeflated) old
164 * singular value.
165 *
166 * If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
167 * normalizing factors for the right singular vector matrix.
168 *
169 * See DLASD8 for details on DIFL and DIFR.
170 *
171 * Z (output) DOUBLE PRECISION array, dimension ( M )
172 * The first elements of this array contain the components
173 * of the deflation-adjusted updating row vector.
174 *
175 * K (output) INTEGER
176 * Contains the dimension of the non-deflated matrix,
177 * This is the order of the related secular equation. 1 <= K <=N.
178 *
179 * C (output) DOUBLE PRECISION
180 * C contains garbage if SQRE =0 and the C-value of a Givens
181 * rotation related to the right null space if SQRE = 1.
182 *
183 * S (output) DOUBLE PRECISION
184 * S contains garbage if SQRE =0 and the S-value of a Givens
185 * rotation related to the right null space if SQRE = 1.
186 *
187 * WORK (workspace) DOUBLE PRECISION array, dimension ( 4 * M )
188 *
189 * IWORK (workspace) INTEGER array, dimension ( 3 * N )
190 *
191 * INFO (output) INTEGER
192 * = 0: successful exit.
193 * < 0: if INFO = -i, the i-th argument had an illegal value.
194 * > 0: if INFO = 1, a singular value did not converge
195 *
196 * Further Details
197 * ===============
198 *
199 * Based on contributions by
200 * Ming Gu and Huan Ren, Computer Science Division, University of
201 * California at Berkeley, USA
202 *
203 * =====================================================================
204 *
205 * .. Parameters ..
206 DOUBLE PRECISION ONE, ZERO
207 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
208 * ..
209 * .. Local Scalars ..
210 INTEGER I, IDX, IDXC, IDXP, ISIGMA, IVFW, IVLW, IW, M,
211 $ N, N1, N2
212 DOUBLE PRECISION ORGNRM
213 * ..
214 * .. External Subroutines ..
215 EXTERNAL DCOPY, DLAMRG, DLASCL, DLASD7, DLASD8, XERBLA
216 * ..
217 * .. Intrinsic Functions ..
218 INTRINSIC ABS, MAX
219 * ..
220 * .. Executable Statements ..
221 *
222 * Test the input parameters.
223 *
224 INFO = 0
225 N = NL + NR + 1
226 M = N + SQRE
227 *
228 IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN
229 INFO = -1
230 ELSE IF( NL.LT.1 ) THEN
231 INFO = -2
232 ELSE IF( NR.LT.1 ) THEN
233 INFO = -3
234 ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
235 INFO = -4
236 ELSE IF( LDGCOL.LT.N ) THEN
237 INFO = -14
238 ELSE IF( LDGNUM.LT.N ) THEN
239 INFO = -16
240 END IF
241 IF( INFO.NE.0 ) THEN
242 CALL XERBLA( 'DLASD6', -INFO )
243 RETURN
244 END IF
245 *
246 * The following values are for bookkeeping purposes only. They are
247 * integer pointers which indicate the portion of the workspace
248 * used by a particular array in DLASD7 and DLASD8.
249 *
250 ISIGMA = 1
251 IW = ISIGMA + N
252 IVFW = IW + M
253 IVLW = IVFW + M
254 *
255 IDX = 1
256 IDXC = IDX + N
257 IDXP = IDXC + N
258 *
259 * Scale.
260 *
261 ORGNRM = MAX( ABS( ALPHA ), ABS( BETA ) )
262 D( NL+1 ) = ZERO
263 DO 10 I = 1, N
264 IF( ABS( D( I ) ).GT.ORGNRM ) THEN
265 ORGNRM = ABS( D( I ) )
266 END IF
267 10 CONTINUE
268 CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO )
269 ALPHA = ALPHA / ORGNRM
270 BETA = BETA / ORGNRM
271 *
272 * Sort and Deflate singular values.
273 *
274 CALL DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, WORK( IW ), VF,
275 $ WORK( IVFW ), VL, WORK( IVLW ), ALPHA, BETA,
276 $ WORK( ISIGMA ), IWORK( IDX ), IWORK( IDXP ), IDXQ,
277 $ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, C, S,
278 $ INFO )
279 *
280 * Solve Secular Equation, compute DIFL, DIFR, and update VF, VL.
281 *
282 CALL DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDGNUM,
283 $ WORK( ISIGMA ), WORK( IW ), INFO )
284 *
285 * Handle error returned
286 *
287 IF( INFO.NE.0 ) THEN
288 CALL XERBLA( 'DLASD8', -INFO )
289 RETURN
290 END IF
291 *
292 * Save the poles if ICOMPQ = 1.
293 *
294 IF( ICOMPQ.EQ.1 ) THEN
295 CALL DCOPY( K, D, 1, POLES( 1, 1 ), 1 )
296 CALL DCOPY( K, WORK( ISIGMA ), 1, POLES( 1, 2 ), 1 )
297 END IF
298 *
299 * Unscale.
300 *
301 CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO )
302 *
303 * Prepare the IDXQ sorting permutation.
304 *
305 N1 = K
306 N2 = N - K
307 CALL DLAMRG( N1, N2, D, 1, -1, IDXQ )
308 *
309 RETURN
310 *
311 * End of DLASD6
312 *
313 END