1 SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
2 $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
3 $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,
4 $ INFO )
5 *
6 * -- LAPACK routine (version 3.3.1) --
7 * -- LAPACK is a software package provided by Univ. of Tennessee, --
8 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
9 * -- April 2011 --
10 *
11 * .. Scalar Arguments ..
12 INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,
13 $ QSIZ, TLVLS
14 DOUBLE PRECISION RHO
15 * ..
16 * .. Array Arguments ..
17 INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ),
18 $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
19 DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ),
20 $ QSTORE( * ), WORK( * )
21 * ..
22 *
23 * Purpose
24 * =======
25 *
26 * DLAED7 computes the updated eigensystem of a diagonal
27 * matrix after modification by a rank-one symmetric matrix. This
28 * routine is used only for the eigenproblem which requires all
29 * eigenvalues and optionally eigenvectors of a dense symmetric matrix
30 * that has been reduced to tridiagonal form. DLAED1 handles
31 * the case in which all eigenvalues and eigenvectors of a symmetric
32 * tridiagonal matrix are desired.
33 *
34 * T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
35 *
36 * where Z = Q**Tu, u is a vector of length N with ones in the
37 * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
38 *
39 * The eigenvectors of the original matrix are stored in Q, and the
40 * eigenvalues are in D. The algorithm consists of three stages:
41 *
42 * The first stage consists of deflating the size of the problem
43 * when there are multiple eigenvalues or if there is a zero in
44 * the Z vector. For each such occurence the dimension of the
45 * secular equation problem is reduced by one. This stage is
46 * performed by the routine DLAED8.
47 *
48 * The second stage consists of calculating the updated
49 * eigenvalues. This is done by finding the roots of the secular
50 * equation via the routine DLAED4 (as called by DLAED9).
51 * This routine also calculates the eigenvectors of the current
52 * problem.
53 *
54 * The final stage consists of computing the updated eigenvectors
55 * directly using the updated eigenvalues. The eigenvectors for
56 * the current problem are multiplied with the eigenvectors from
57 * the overall problem.
58 *
59 * Arguments
60 * =========
61 *
62 * ICOMPQ (input) INTEGER
63 * = 0: Compute eigenvalues only.
64 * = 1: Compute eigenvectors of original dense symmetric matrix
65 * also. On entry, Q contains the orthogonal matrix used
66 * to reduce the original matrix to tridiagonal form.
67 *
68 * N (input) INTEGER
69 * The dimension of the symmetric tridiagonal matrix. N >= 0.
70 *
71 * QSIZ (input) INTEGER
72 * The dimension of the orthogonal matrix used to reduce
73 * the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
74 *
75 * TLVLS (input) INTEGER
76 * The total number of merging levels in the overall divide and
77 * conquer tree.
78 *
79 * CURLVL (input) INTEGER
80 * The current level in the overall merge routine,
81 * 0 <= CURLVL <= TLVLS.
82 *
83 * CURPBM (input) INTEGER
84 * The current problem in the current level in the overall
85 * merge routine (counting from upper left to lower right).
86 *
87 * D (input/output) DOUBLE PRECISION array, dimension (N)
88 * On entry, the eigenvalues of the rank-1-perturbed matrix.
89 * On exit, the eigenvalues of the repaired matrix.
90 *
91 * Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
92 * On entry, the eigenvectors of the rank-1-perturbed matrix.
93 * On exit, the eigenvectors of the repaired tridiagonal matrix.
94 *
95 * LDQ (input) INTEGER
96 * The leading dimension of the array Q. LDQ >= max(1,N).
97 *
98 * INDXQ (output) INTEGER array, dimension (N)
99 * The permutation which will reintegrate the subproblem just
100 * solved back into sorted order, i.e., D( INDXQ( I = 1, N ) )
101 * will be in ascending order.
102 *
103 * RHO (input) DOUBLE PRECISION
104 * The subdiagonal element used to create the rank-1
105 * modification.
106 *
107 * CUTPNT (input) INTEGER
108 * Contains the location of the last eigenvalue in the leading
109 * sub-matrix. min(1,N) <= CUTPNT <= N.
110 *
111 * QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1)
112 * Stores eigenvectors of submatrices encountered during
113 * divide and conquer, packed together. QPTR points to
114 * beginning of the submatrices.
115 *
116 * QPTR (input/output) INTEGER array, dimension (N+2)
117 * List of indices pointing to beginning of submatrices stored
118 * in QSTORE. The submatrices are numbered starting at the
119 * bottom left of the divide and conquer tree, from left to
120 * right and bottom to top.
121 *
122 * PRMPTR (input) INTEGER array, dimension (N lg N)
123 * Contains a list of pointers which indicate where in PERM a
124 * level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)
125 * indicates the size of the permutation and also the size of
126 * the full, non-deflated problem.
127 *
128 * PERM (input) INTEGER array, dimension (N lg N)
129 * Contains the permutations (from deflation and sorting) to be
130 * applied to each eigenblock.
131 *
132 * GIVPTR (input) INTEGER array, dimension (N lg N)
133 * Contains a list of pointers which indicate where in GIVCOL a
134 * level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)
135 * indicates the number of Givens rotations.
136 *
137 * GIVCOL (input) INTEGER array, dimension (2, N lg N)
138 * Each pair of numbers indicates a pair of columns to take place
139 * in a Givens rotation.
140 *
141 * GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N)
142 * Each number indicates the S value to be used in the
143 * corresponding Givens rotation.
144 *
145 * WORK (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)
146 *
147 * IWORK (workspace) INTEGER array, dimension (4*N)
148 *
149 * INFO (output) INTEGER
150 * = 0: successful exit.
151 * < 0: if INFO = -i, the i-th argument had an illegal value.
152 * > 0: if INFO = 1, an eigenvalue did not converge
153 *
154 * Further Details
155 * ===============
156 *
157 * Based on contributions by
158 * Jeff Rutter, Computer Science Division, University of California
159 * at Berkeley, USA
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164 DOUBLE PRECISION ONE, ZERO
165 PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 )
166 * ..
167 * .. Local Scalars ..
168 INTEGER COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP,
169 $ IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR
170 * ..
171 * .. External Subroutines ..
172 EXTERNAL DGEMM, DLAED8, DLAED9, DLAEDA, DLAMRG, XERBLA
173 * ..
174 * .. Intrinsic Functions ..
175 INTRINSIC MAX, MIN
176 * ..
177 * .. Executable Statements ..
178 *
179 * Test the input parameters.
180 *
181 INFO = 0
182 *
183 IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN
184 INFO = -1
185 ELSE IF( N.LT.0 ) THEN
186 INFO = -2
187 ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN
188 INFO = -4
189 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
190 INFO = -9
191 ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN
192 INFO = -12
193 END IF
194 IF( INFO.NE.0 ) THEN
195 CALL XERBLA( 'DLAED7', -INFO )
196 RETURN
197 END IF
198 *
199 * Quick return if possible
200 *
201 IF( N.EQ.0 )
202 $ RETURN
203 *
204 * The following values are for bookkeeping purposes only. They are
205 * integer pointers which indicate the portion of the workspace
206 * used by a particular array in DLAED8 and DLAED9.
207 *
208 IF( ICOMPQ.EQ.1 ) THEN
209 LDQ2 = QSIZ
210 ELSE
211 LDQ2 = N
212 END IF
213 *
214 IZ = 1
215 IDLMDA = IZ + N
216 IW = IDLMDA + N
217 IQ2 = IW + N
218 IS = IQ2 + N*LDQ2
219 *
220 INDX = 1
221 INDXC = INDX + N
222 COLTYP = INDXC + N
223 INDXP = COLTYP + N
224 *
225 * Form the z-vector which consists of the last row of Q_1 and the
226 * first row of Q_2.
227 *
228 PTR = 1 + 2**TLVLS
229 DO 10 I = 1, CURLVL - 1
230 PTR = PTR + 2**( TLVLS-I )
231 10 CONTINUE
232 CURR = PTR + CURPBM
233 CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
234 $ GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ),
235 $ WORK( IZ+N ), INFO )
236 *
237 * When solving the final problem, we no longer need the stored data,
238 * so we will overwrite the data from this level onto the previously
239 * used storage space.
240 *
241 IF( CURLVL.EQ.TLVLS ) THEN
242 QPTR( CURR ) = 1
243 PRMPTR( CURR ) = 1
244 GIVPTR( CURR ) = 1
245 END IF
246 *
247 * Sort and Deflate eigenvalues.
248 *
249 CALL DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT,
250 $ WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2,
251 $ WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ),
252 $ GIVCOL( 1, GIVPTR( CURR ) ),
253 $ GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ),
254 $ IWORK( INDX ), INFO )
255 PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N
256 GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR )
257 *
258 * Solve Secular Equation.
259 *
260 IF( K.NE.0 ) THEN
261 CALL DLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ),
262 $ WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO )
263 IF( INFO.NE.0 )
264 $ GO TO 30
265 IF( ICOMPQ.EQ.1 ) THEN
266 CALL DGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2,
267 $ QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ )
268 END IF
269 QPTR( CURR+1 ) = QPTR( CURR ) + K**2
270 *
271 * Prepare the INDXQ sorting permutation.
272 *
273 N1 = K
274 N2 = N - K
275 CALL DLAMRG( N1, N2, D, 1, -1, INDXQ )
276 ELSE
277 QPTR( CURR+1 ) = QPTR( CURR )
278 DO 20 I = 1, N
279 INDXQ( I ) = I
280 20 CONTINUE
281 END IF
282 *
283 30 CONTINUE
284 RETURN
285 *
286 * End of DLAED7
287 *
288 END
2 $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR,
3 $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK,
4 $ INFO )
5 *
6 * -- LAPACK routine (version 3.3.1) --
7 * -- LAPACK is a software package provided by Univ. of Tennessee, --
8 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
9 * -- April 2011 --
10 *
11 * .. Scalar Arguments ..
12 INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N,
13 $ QSIZ, TLVLS
14 DOUBLE PRECISION RHO
15 * ..
16 * .. Array Arguments ..
17 INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ),
18 $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
19 DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ),
20 $ QSTORE( * ), WORK( * )
21 * ..
22 *
23 * Purpose
24 * =======
25 *
26 * DLAED7 computes the updated eigensystem of a diagonal
27 * matrix after modification by a rank-one symmetric matrix. This
28 * routine is used only for the eigenproblem which requires all
29 * eigenvalues and optionally eigenvectors of a dense symmetric matrix
30 * that has been reduced to tridiagonal form. DLAED1 handles
31 * the case in which all eigenvalues and eigenvectors of a symmetric
32 * tridiagonal matrix are desired.
33 *
34 * T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
35 *
36 * where Z = Q**Tu, u is a vector of length N with ones in the
37 * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
38 *
39 * The eigenvectors of the original matrix are stored in Q, and the
40 * eigenvalues are in D. The algorithm consists of three stages:
41 *
42 * The first stage consists of deflating the size of the problem
43 * when there are multiple eigenvalues or if there is a zero in
44 * the Z vector. For each such occurence the dimension of the
45 * secular equation problem is reduced by one. This stage is
46 * performed by the routine DLAED8.
47 *
48 * The second stage consists of calculating the updated
49 * eigenvalues. This is done by finding the roots of the secular
50 * equation via the routine DLAED4 (as called by DLAED9).
51 * This routine also calculates the eigenvectors of the current
52 * problem.
53 *
54 * The final stage consists of computing the updated eigenvectors
55 * directly using the updated eigenvalues. The eigenvectors for
56 * the current problem are multiplied with the eigenvectors from
57 * the overall problem.
58 *
59 * Arguments
60 * =========
61 *
62 * ICOMPQ (input) INTEGER
63 * = 0: Compute eigenvalues only.
64 * = 1: Compute eigenvectors of original dense symmetric matrix
65 * also. On entry, Q contains the orthogonal matrix used
66 * to reduce the original matrix to tridiagonal form.
67 *
68 * N (input) INTEGER
69 * The dimension of the symmetric tridiagonal matrix. N >= 0.
70 *
71 * QSIZ (input) INTEGER
72 * The dimension of the orthogonal matrix used to reduce
73 * the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
74 *
75 * TLVLS (input) INTEGER
76 * The total number of merging levels in the overall divide and
77 * conquer tree.
78 *
79 * CURLVL (input) INTEGER
80 * The current level in the overall merge routine,
81 * 0 <= CURLVL <= TLVLS.
82 *
83 * CURPBM (input) INTEGER
84 * The current problem in the current level in the overall
85 * merge routine (counting from upper left to lower right).
86 *
87 * D (input/output) DOUBLE PRECISION array, dimension (N)
88 * On entry, the eigenvalues of the rank-1-perturbed matrix.
89 * On exit, the eigenvalues of the repaired matrix.
90 *
91 * Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
92 * On entry, the eigenvectors of the rank-1-perturbed matrix.
93 * On exit, the eigenvectors of the repaired tridiagonal matrix.
94 *
95 * LDQ (input) INTEGER
96 * The leading dimension of the array Q. LDQ >= max(1,N).
97 *
98 * INDXQ (output) INTEGER array, dimension (N)
99 * The permutation which will reintegrate the subproblem just
100 * solved back into sorted order, i.e., D( INDXQ( I = 1, N ) )
101 * will be in ascending order.
102 *
103 * RHO (input) DOUBLE PRECISION
104 * The subdiagonal element used to create the rank-1
105 * modification.
106 *
107 * CUTPNT (input) INTEGER
108 * Contains the location of the last eigenvalue in the leading
109 * sub-matrix. min(1,N) <= CUTPNT <= N.
110 *
111 * QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1)
112 * Stores eigenvectors of submatrices encountered during
113 * divide and conquer, packed together. QPTR points to
114 * beginning of the submatrices.
115 *
116 * QPTR (input/output) INTEGER array, dimension (N+2)
117 * List of indices pointing to beginning of submatrices stored
118 * in QSTORE. The submatrices are numbered starting at the
119 * bottom left of the divide and conquer tree, from left to
120 * right and bottom to top.
121 *
122 * PRMPTR (input) INTEGER array, dimension (N lg N)
123 * Contains a list of pointers which indicate where in PERM a
124 * level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)
125 * indicates the size of the permutation and also the size of
126 * the full, non-deflated problem.
127 *
128 * PERM (input) INTEGER array, dimension (N lg N)
129 * Contains the permutations (from deflation and sorting) to be
130 * applied to each eigenblock.
131 *
132 * GIVPTR (input) INTEGER array, dimension (N lg N)
133 * Contains a list of pointers which indicate where in GIVCOL a
134 * level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)
135 * indicates the number of Givens rotations.
136 *
137 * GIVCOL (input) INTEGER array, dimension (2, N lg N)
138 * Each pair of numbers indicates a pair of columns to take place
139 * in a Givens rotation.
140 *
141 * GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N)
142 * Each number indicates the S value to be used in the
143 * corresponding Givens rotation.
144 *
145 * WORK (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)
146 *
147 * IWORK (workspace) INTEGER array, dimension (4*N)
148 *
149 * INFO (output) INTEGER
150 * = 0: successful exit.
151 * < 0: if INFO = -i, the i-th argument had an illegal value.
152 * > 0: if INFO = 1, an eigenvalue did not converge
153 *
154 * Further Details
155 * ===============
156 *
157 * Based on contributions by
158 * Jeff Rutter, Computer Science Division, University of California
159 * at Berkeley, USA
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164 DOUBLE PRECISION ONE, ZERO
165 PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 )
166 * ..
167 * .. Local Scalars ..
168 INTEGER COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP,
169 $ IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR
170 * ..
171 * .. External Subroutines ..
172 EXTERNAL DGEMM, DLAED8, DLAED9, DLAEDA, DLAMRG, XERBLA
173 * ..
174 * .. Intrinsic Functions ..
175 INTRINSIC MAX, MIN
176 * ..
177 * .. Executable Statements ..
178 *
179 * Test the input parameters.
180 *
181 INFO = 0
182 *
183 IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN
184 INFO = -1
185 ELSE IF( N.LT.0 ) THEN
186 INFO = -2
187 ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN
188 INFO = -4
189 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
190 INFO = -9
191 ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN
192 INFO = -12
193 END IF
194 IF( INFO.NE.0 ) THEN
195 CALL XERBLA( 'DLAED7', -INFO )
196 RETURN
197 END IF
198 *
199 * Quick return if possible
200 *
201 IF( N.EQ.0 )
202 $ RETURN
203 *
204 * The following values are for bookkeeping purposes only. They are
205 * integer pointers which indicate the portion of the workspace
206 * used by a particular array in DLAED8 and DLAED9.
207 *
208 IF( ICOMPQ.EQ.1 ) THEN
209 LDQ2 = QSIZ
210 ELSE
211 LDQ2 = N
212 END IF
213 *
214 IZ = 1
215 IDLMDA = IZ + N
216 IW = IDLMDA + N
217 IQ2 = IW + N
218 IS = IQ2 + N*LDQ2
219 *
220 INDX = 1
221 INDXC = INDX + N
222 COLTYP = INDXC + N
223 INDXP = COLTYP + N
224 *
225 * Form the z-vector which consists of the last row of Q_1 and the
226 * first row of Q_2.
227 *
228 PTR = 1 + 2**TLVLS
229 DO 10 I = 1, CURLVL - 1
230 PTR = PTR + 2**( TLVLS-I )
231 10 CONTINUE
232 CURR = PTR + CURPBM
233 CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
234 $ GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ),
235 $ WORK( IZ+N ), INFO )
236 *
237 * When solving the final problem, we no longer need the stored data,
238 * so we will overwrite the data from this level onto the previously
239 * used storage space.
240 *
241 IF( CURLVL.EQ.TLVLS ) THEN
242 QPTR( CURR ) = 1
243 PRMPTR( CURR ) = 1
244 GIVPTR( CURR ) = 1
245 END IF
246 *
247 * Sort and Deflate eigenvalues.
248 *
249 CALL DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT,
250 $ WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2,
251 $ WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ),
252 $ GIVCOL( 1, GIVPTR( CURR ) ),
253 $ GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ),
254 $ IWORK( INDX ), INFO )
255 PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N
256 GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR )
257 *
258 * Solve Secular Equation.
259 *
260 IF( K.NE.0 ) THEN
261 CALL DLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ),
262 $ WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO )
263 IF( INFO.NE.0 )
264 $ GO TO 30
265 IF( ICOMPQ.EQ.1 ) THEN
266 CALL DGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2,
267 $ QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ )
268 END IF
269 QPTR( CURR+1 ) = QPTR( CURR ) + K**2
270 *
271 * Prepare the INDXQ sorting permutation.
272 *
273 N1 = K
274 N2 = N - K
275 CALL DLAMRG( N1, N2, D, 1, -1, INDXQ )
276 ELSE
277 QPTR( CURR+1 ) = QPTR( CURR )
278 DO 20 I = 1, N
279 INDXQ( I ) = I
280 20 CONTINUE
281 END IF
282 *
283 30 CONTINUE
284 RETURN
285 *
286 * End of DLAED7
287 *
288 END