1 SUBROUTINE DSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
2 $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
3 $ IFAIL, INFO )
4 *
5 * -- LAPACK driver routine (version 3.3.1) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * -- April 2011 --
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, ITYPE, IU, LDZ, M, N
13 DOUBLE PRECISION ABSTOL, VL, VU
14 * ..
15 * .. Array Arguments ..
16 INTEGER IFAIL( * ), IWORK( * )
17 DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
18 $ Z( LDZ, * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * DSPGVX computes selected eigenvalues, and optionally, eigenvectors
25 * of a real generalized symmetric-definite eigenproblem, of the form
26 * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
27 * and B are assumed to be symmetric, stored in packed storage, and B
28 * is also positive definite. Eigenvalues and eigenvectors can be
29 * selected by specifying either a range of values or a range of indices
30 * for the desired eigenvalues.
31 *
32 * Arguments
33 * =========
34 *
35 * ITYPE (input) INTEGER
36 * Specifies the problem type to be solved:
37 * = 1: A*x = (lambda)*B*x
38 * = 2: A*B*x = (lambda)*x
39 * = 3: B*A*x = (lambda)*x
40 *
41 * JOBZ (input) CHARACTER*1
42 * = 'N': Compute eigenvalues only;
43 * = 'V': Compute eigenvalues and eigenvectors.
44 *
45 * RANGE (input) CHARACTER*1
46 * = 'A': all eigenvalues will be found.
47 * = 'V': all eigenvalues in the half-open interval (VL,VU]
48 * will be found.
49 * = 'I': the IL-th through IU-th eigenvalues will be found.
50 *
51 * UPLO (input) CHARACTER*1
52 * = 'U': Upper triangle of A and B are stored;
53 * = 'L': Lower triangle of A and B are stored.
54 *
55 * N (input) INTEGER
56 * The order of the matrix pencil (A,B). N >= 0.
57 *
58 * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
59 * On entry, the upper or lower triangle of the symmetric matrix
60 * A, packed columnwise in a linear array. The j-th column of A
61 * is stored in the array AP as follows:
62 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
63 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
64 *
65 * On exit, the contents of AP are destroyed.
66 *
67 * BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
68 * On entry, the upper or lower triangle of the symmetric matrix
69 * B, packed columnwise in a linear array. The j-th column of B
70 * is stored in the array BP as follows:
71 * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
72 * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
73 *
74 * On exit, the triangular factor U or L from the Cholesky
75 * factorization B = U**T*U or B = L*L**T, in the same storage
76 * format as B.
77 *
78 * VL (input) DOUBLE PRECISION
79 * VU (input) DOUBLE PRECISION
80 * If RANGE='V', the lower and upper bounds of the interval to
81 * be searched for eigenvalues. VL < VU.
82 * Not referenced if RANGE = 'A' or 'I'.
83 *
84 * IL (input) INTEGER
85 * IU (input) INTEGER
86 * If RANGE='I', the indices (in ascending order) of the
87 * smallest and largest eigenvalues to be returned.
88 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
89 * Not referenced if RANGE = 'A' or 'V'.
90 *
91 * ABSTOL (input) DOUBLE PRECISION
92 * The absolute error tolerance for the eigenvalues.
93 * An approximate eigenvalue is accepted as converged
94 * when it is determined to lie in an interval [a,b]
95 * of width less than or equal to
96 *
97 * ABSTOL + EPS * max( |a|,|b| ) ,
98 *
99 * where EPS is the machine precision. If ABSTOL is less than
100 * or equal to zero, then EPS*|T| will be used in its place,
101 * where |T| is the 1-norm of the tridiagonal matrix obtained
102 * by reducing A to tridiagonal form.
103 *
104 * Eigenvalues will be computed most accurately when ABSTOL is
105 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
106 * If this routine returns with INFO>0, indicating that some
107 * eigenvectors did not converge, try setting ABSTOL to
108 * 2*DLAMCH('S').
109 *
110 * M (output) INTEGER
111 * The total number of eigenvalues found. 0 <= M <= N.
112 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
113 *
114 * W (output) DOUBLE PRECISION array, dimension (N)
115 * On normal exit, the first M elements contain the selected
116 * eigenvalues in ascending order.
117 *
118 * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
119 * If JOBZ = 'N', then Z is not referenced.
120 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
121 * contain the orthonormal eigenvectors of the matrix A
122 * corresponding to the selected eigenvalues, with the i-th
123 * column of Z holding the eigenvector associated with W(i).
124 * The eigenvectors are normalized as follows:
125 * if ITYPE = 1 or 2, Z**T*B*Z = I;
126 * if ITYPE = 3, Z**T*inv(B)*Z = I.
127 *
128 * If an eigenvector fails to converge, then that column of Z
129 * contains the latest approximation to the eigenvector, and the
130 * index of the eigenvector is returned in IFAIL.
131 * Note: the user must ensure that at least max(1,M) columns are
132 * supplied in the array Z; if RANGE = 'V', the exact value of M
133 * is not known in advance and an upper bound must be used.
134 *
135 * LDZ (input) INTEGER
136 * The leading dimension of the array Z. LDZ >= 1, and if
137 * JOBZ = 'V', LDZ >= max(1,N).
138 *
139 * WORK (workspace) DOUBLE PRECISION array, dimension (8*N)
140 *
141 * IWORK (workspace) INTEGER array, dimension (5*N)
142 *
143 * IFAIL (output) INTEGER array, dimension (N)
144 * If JOBZ = 'V', then if INFO = 0, the first M elements of
145 * IFAIL are zero. If INFO > 0, then IFAIL contains the
146 * indices of the eigenvectors that failed to converge.
147 * If JOBZ = 'N', then IFAIL is not referenced.
148 *
149 * INFO (output) INTEGER
150 * = 0: successful exit
151 * < 0: if INFO = -i, the i-th argument had an illegal value
152 * > 0: DPPTRF or DSPEVX returned an error code:
153 * <= N: if INFO = i, DSPEVX failed to converge;
154 * i eigenvectors failed to converge. Their indices
155 * are stored in array IFAIL.
156 * > N: if INFO = N + i, for 1 <= i <= N, then the leading
157 * minor of order i of B is not positive definite.
158 * The factorization of B could not be completed and
159 * no eigenvalues or eigenvectors were computed.
160 *
161 * Further Details
162 * ===============
163 *
164 * Based on contributions by
165 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
166 *
167 * =====================================================================
168 *
169 * .. Local Scalars ..
170 LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ
171 CHARACTER TRANS
172 INTEGER J
173 * ..
174 * .. External Functions ..
175 LOGICAL LSAME
176 EXTERNAL LSAME
177 * ..
178 * .. External Subroutines ..
179 EXTERNAL DPPTRF, DSPEVX, DSPGST, DTPMV, DTPSV, XERBLA
180 * ..
181 * .. Intrinsic Functions ..
182 INTRINSIC MIN
183 * ..
184 * .. Executable Statements ..
185 *
186 * Test the input parameters.
187 *
188 UPPER = LSAME( UPLO, 'U' )
189 WANTZ = LSAME( JOBZ, 'V' )
190 ALLEIG = LSAME( RANGE, 'A' )
191 VALEIG = LSAME( RANGE, 'V' )
192 INDEIG = LSAME( RANGE, 'I' )
193 *
194 INFO = 0
195 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
196 INFO = -1
197 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
198 INFO = -2
199 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
200 INFO = -3
201 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
202 INFO = -4
203 ELSE IF( N.LT.0 ) THEN
204 INFO = -5
205 ELSE
206 IF( VALEIG ) THEN
207 IF( N.GT.0 .AND. VU.LE.VL ) THEN
208 INFO = -9
209 END IF
210 ELSE IF( INDEIG ) THEN
211 IF( IL.LT.1 ) THEN
212 INFO = -10
213 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
214 INFO = -11
215 END IF
216 END IF
217 END IF
218 IF( INFO.EQ.0 ) THEN
219 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
220 INFO = -16
221 END IF
222 END IF
223 *
224 IF( INFO.NE.0 ) THEN
225 CALL XERBLA( 'DSPGVX', -INFO )
226 RETURN
227 END IF
228 *
229 * Quick return if possible
230 *
231 M = 0
232 IF( N.EQ.0 )
233 $ RETURN
234 *
235 * Form a Cholesky factorization of B.
236 *
237 CALL DPPTRF( UPLO, N, BP, INFO )
238 IF( INFO.NE.0 ) THEN
239 INFO = N + INFO
240 RETURN
241 END IF
242 *
243 * Transform problem to standard eigenvalue problem and solve.
244 *
245 CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
246 CALL DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M,
247 $ W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
248 *
249 IF( WANTZ ) THEN
250 *
251 * Backtransform eigenvectors to the original problem.
252 *
253 IF( INFO.GT.0 )
254 $ M = INFO - 1
255 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
256 *
257 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
258 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
259 *
260 IF( UPPER ) THEN
261 TRANS = 'N'
262 ELSE
263 TRANS = 'T'
264 END IF
265 *
266 DO 10 J = 1, M
267 CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
268 $ 1 )
269 10 CONTINUE
270 *
271 ELSE IF( ITYPE.EQ.3 ) THEN
272 *
273 * For B*A*x=(lambda)*x;
274 * backtransform eigenvectors: x = L*y or U**T*y
275 *
276 IF( UPPER ) THEN
277 TRANS = 'T'
278 ELSE
279 TRANS = 'N'
280 END IF
281 *
282 DO 20 J = 1, M
283 CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
284 $ 1 )
285 20 CONTINUE
286 END IF
287 END IF
288 *
289 RETURN
290 *
291 * End of DSPGVX
292 *
293 END
2 $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
3 $ IFAIL, INFO )
4 *
5 * -- LAPACK driver routine (version 3.3.1) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * -- April 2011 --
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, ITYPE, IU, LDZ, M, N
13 DOUBLE PRECISION ABSTOL, VL, VU
14 * ..
15 * .. Array Arguments ..
16 INTEGER IFAIL( * ), IWORK( * )
17 DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
18 $ Z( LDZ, * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * DSPGVX computes selected eigenvalues, and optionally, eigenvectors
25 * of a real generalized symmetric-definite eigenproblem, of the form
26 * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
27 * and B are assumed to be symmetric, stored in packed storage, and B
28 * is also positive definite. Eigenvalues and eigenvectors can be
29 * selected by specifying either a range of values or a range of indices
30 * for the desired eigenvalues.
31 *
32 * Arguments
33 * =========
34 *
35 * ITYPE (input) INTEGER
36 * Specifies the problem type to be solved:
37 * = 1: A*x = (lambda)*B*x
38 * = 2: A*B*x = (lambda)*x
39 * = 3: B*A*x = (lambda)*x
40 *
41 * JOBZ (input) CHARACTER*1
42 * = 'N': Compute eigenvalues only;
43 * = 'V': Compute eigenvalues and eigenvectors.
44 *
45 * RANGE (input) CHARACTER*1
46 * = 'A': all eigenvalues will be found.
47 * = 'V': all eigenvalues in the half-open interval (VL,VU]
48 * will be found.
49 * = 'I': the IL-th through IU-th eigenvalues will be found.
50 *
51 * UPLO (input) CHARACTER*1
52 * = 'U': Upper triangle of A and B are stored;
53 * = 'L': Lower triangle of A and B are stored.
54 *
55 * N (input) INTEGER
56 * The order of the matrix pencil (A,B). N >= 0.
57 *
58 * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
59 * On entry, the upper or lower triangle of the symmetric matrix
60 * A, packed columnwise in a linear array. The j-th column of A
61 * is stored in the array AP as follows:
62 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
63 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
64 *
65 * On exit, the contents of AP are destroyed.
66 *
67 * BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
68 * On entry, the upper or lower triangle of the symmetric matrix
69 * B, packed columnwise in a linear array. The j-th column of B
70 * is stored in the array BP as follows:
71 * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
72 * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
73 *
74 * On exit, the triangular factor U or L from the Cholesky
75 * factorization B = U**T*U or B = L*L**T, in the same storage
76 * format as B.
77 *
78 * VL (input) DOUBLE PRECISION
79 * VU (input) DOUBLE PRECISION
80 * If RANGE='V', the lower and upper bounds of the interval to
81 * be searched for eigenvalues. VL < VU.
82 * Not referenced if RANGE = 'A' or 'I'.
83 *
84 * IL (input) INTEGER
85 * IU (input) INTEGER
86 * If RANGE='I', the indices (in ascending order) of the
87 * smallest and largest eigenvalues to be returned.
88 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
89 * Not referenced if RANGE = 'A' or 'V'.
90 *
91 * ABSTOL (input) DOUBLE PRECISION
92 * The absolute error tolerance for the eigenvalues.
93 * An approximate eigenvalue is accepted as converged
94 * when it is determined to lie in an interval [a,b]
95 * of width less than or equal to
96 *
97 * ABSTOL + EPS * max( |a|,|b| ) ,
98 *
99 * where EPS is the machine precision. If ABSTOL is less than
100 * or equal to zero, then EPS*|T| will be used in its place,
101 * where |T| is the 1-norm of the tridiagonal matrix obtained
102 * by reducing A to tridiagonal form.
103 *
104 * Eigenvalues will be computed most accurately when ABSTOL is
105 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
106 * If this routine returns with INFO>0, indicating that some
107 * eigenvectors did not converge, try setting ABSTOL to
108 * 2*DLAMCH('S').
109 *
110 * M (output) INTEGER
111 * The total number of eigenvalues found. 0 <= M <= N.
112 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
113 *
114 * W (output) DOUBLE PRECISION array, dimension (N)
115 * On normal exit, the first M elements contain the selected
116 * eigenvalues in ascending order.
117 *
118 * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
119 * If JOBZ = 'N', then Z is not referenced.
120 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
121 * contain the orthonormal eigenvectors of the matrix A
122 * corresponding to the selected eigenvalues, with the i-th
123 * column of Z holding the eigenvector associated with W(i).
124 * The eigenvectors are normalized as follows:
125 * if ITYPE = 1 or 2, Z**T*B*Z = I;
126 * if ITYPE = 3, Z**T*inv(B)*Z = I.
127 *
128 * If an eigenvector fails to converge, then that column of Z
129 * contains the latest approximation to the eigenvector, and the
130 * index of the eigenvector is returned in IFAIL.
131 * Note: the user must ensure that at least max(1,M) columns are
132 * supplied in the array Z; if RANGE = 'V', the exact value of M
133 * is not known in advance and an upper bound must be used.
134 *
135 * LDZ (input) INTEGER
136 * The leading dimension of the array Z. LDZ >= 1, and if
137 * JOBZ = 'V', LDZ >= max(1,N).
138 *
139 * WORK (workspace) DOUBLE PRECISION array, dimension (8*N)
140 *
141 * IWORK (workspace) INTEGER array, dimension (5*N)
142 *
143 * IFAIL (output) INTEGER array, dimension (N)
144 * If JOBZ = 'V', then if INFO = 0, the first M elements of
145 * IFAIL are zero. If INFO > 0, then IFAIL contains the
146 * indices of the eigenvectors that failed to converge.
147 * If JOBZ = 'N', then IFAIL is not referenced.
148 *
149 * INFO (output) INTEGER
150 * = 0: successful exit
151 * < 0: if INFO = -i, the i-th argument had an illegal value
152 * > 0: DPPTRF or DSPEVX returned an error code:
153 * <= N: if INFO = i, DSPEVX failed to converge;
154 * i eigenvectors failed to converge. Their indices
155 * are stored in array IFAIL.
156 * > N: if INFO = N + i, for 1 <= i <= N, then the leading
157 * minor of order i of B is not positive definite.
158 * The factorization of B could not be completed and
159 * no eigenvalues or eigenvectors were computed.
160 *
161 * Further Details
162 * ===============
163 *
164 * Based on contributions by
165 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
166 *
167 * =====================================================================
168 *
169 * .. Local Scalars ..
170 LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ
171 CHARACTER TRANS
172 INTEGER J
173 * ..
174 * .. External Functions ..
175 LOGICAL LSAME
176 EXTERNAL LSAME
177 * ..
178 * .. External Subroutines ..
179 EXTERNAL DPPTRF, DSPEVX, DSPGST, DTPMV, DTPSV, XERBLA
180 * ..
181 * .. Intrinsic Functions ..
182 INTRINSIC MIN
183 * ..
184 * .. Executable Statements ..
185 *
186 * Test the input parameters.
187 *
188 UPPER = LSAME( UPLO, 'U' )
189 WANTZ = LSAME( JOBZ, 'V' )
190 ALLEIG = LSAME( RANGE, 'A' )
191 VALEIG = LSAME( RANGE, 'V' )
192 INDEIG = LSAME( RANGE, 'I' )
193 *
194 INFO = 0
195 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
196 INFO = -1
197 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
198 INFO = -2
199 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
200 INFO = -3
201 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
202 INFO = -4
203 ELSE IF( N.LT.0 ) THEN
204 INFO = -5
205 ELSE
206 IF( VALEIG ) THEN
207 IF( N.GT.0 .AND. VU.LE.VL ) THEN
208 INFO = -9
209 END IF
210 ELSE IF( INDEIG ) THEN
211 IF( IL.LT.1 ) THEN
212 INFO = -10
213 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
214 INFO = -11
215 END IF
216 END IF
217 END IF
218 IF( INFO.EQ.0 ) THEN
219 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
220 INFO = -16
221 END IF
222 END IF
223 *
224 IF( INFO.NE.0 ) THEN
225 CALL XERBLA( 'DSPGVX', -INFO )
226 RETURN
227 END IF
228 *
229 * Quick return if possible
230 *
231 M = 0
232 IF( N.EQ.0 )
233 $ RETURN
234 *
235 * Form a Cholesky factorization of B.
236 *
237 CALL DPPTRF( UPLO, N, BP, INFO )
238 IF( INFO.NE.0 ) THEN
239 INFO = N + INFO
240 RETURN
241 END IF
242 *
243 * Transform problem to standard eigenvalue problem and solve.
244 *
245 CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
246 CALL DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M,
247 $ W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
248 *
249 IF( WANTZ ) THEN
250 *
251 * Backtransform eigenvectors to the original problem.
252 *
253 IF( INFO.GT.0 )
254 $ M = INFO - 1
255 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
256 *
257 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
258 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
259 *
260 IF( UPPER ) THEN
261 TRANS = 'N'
262 ELSE
263 TRANS = 'T'
264 END IF
265 *
266 DO 10 J = 1, M
267 CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
268 $ 1 )
269 10 CONTINUE
270 *
271 ELSE IF( ITYPE.EQ.3 ) THEN
272 *
273 * For B*A*x=(lambda)*x;
274 * backtransform eigenvectors: x = L*y or U**T*y
275 *
276 IF( UPPER ) THEN
277 TRANS = 'T'
278 ELSE
279 TRANS = 'N'
280 END IF
281 *
282 DO 20 J = 1, M
283 CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
284 $ 1 )
285 20 CONTINUE
286 END IF
287 END IF
288 *
289 RETURN
290 *
291 * End of DSPGVX
292 *
293 END