1 SUBROUTINE DGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B,
2 $ LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
3 $ IWORK, 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 JOBQ, JOBU, JOBV
12 INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P
13 * ..
14 * .. Array Arguments ..
15 INTEGER IWORK( * )
16 DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ),
17 $ BETA( * ), Q( LDQ, * ), U( LDU, * ),
18 $ V( LDV, * ), WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * DGGSVD computes the generalized singular value decomposition (GSVD)
25 * of an M-by-N real matrix A and P-by-N real matrix B:
26 *
27 * U**T*A*Q = D1*( 0 R ), V**T*B*Q = D2*( 0 R )
28 *
29 * where U, V and Q are orthogonal matrices.
30 * Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T,
31 * then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and
32 * D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the
33 * following structures, respectively:
34 *
35 * If M-K-L >= 0,
36 *
37 * K L
38 * D1 = K ( I 0 )
39 * L ( 0 C )
40 * M-K-L ( 0 0 )
41 *
42 * K L
43 * D2 = L ( 0 S )
44 * P-L ( 0 0 )
45 *
46 * N-K-L K L
47 * ( 0 R ) = K ( 0 R11 R12 )
48 * L ( 0 0 R22 )
49 *
50 * where
51 *
52 * C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
53 * S = diag( BETA(K+1), ... , BETA(K+L) ),
54 * C**2 + S**2 = I.
55 *
56 * R is stored in A(1:K+L,N-K-L+1:N) on exit.
57 *
58 * If M-K-L < 0,
59 *
60 * K M-K K+L-M
61 * D1 = K ( I 0 0 )
62 * M-K ( 0 C 0 )
63 *
64 * K M-K K+L-M
65 * D2 = M-K ( 0 S 0 )
66 * K+L-M ( 0 0 I )
67 * P-L ( 0 0 0 )
68 *
69 * N-K-L K M-K K+L-M
70 * ( 0 R ) = K ( 0 R11 R12 R13 )
71 * M-K ( 0 0 R22 R23 )
72 * K+L-M ( 0 0 0 R33 )
73 *
74 * where
75 *
76 * C = diag( ALPHA(K+1), ... , ALPHA(M) ),
77 * S = diag( BETA(K+1), ... , BETA(M) ),
78 * C**2 + S**2 = I.
79 *
80 * (R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored
81 * ( 0 R22 R23 )
82 * in B(M-K+1:L,N+M-K-L+1:N) on exit.
83 *
84 * The routine computes C, S, R, and optionally the orthogonal
85 * transformation matrices U, V and Q.
86 *
87 * In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
88 * A and B implicitly gives the SVD of A*inv(B):
89 * A*inv(B) = U*(D1*inv(D2))*V**T.
90 * If ( A**T,B**T)**T has orthonormal columns, then the GSVD of A and B is
91 * also equal to the CS decomposition of A and B. Furthermore, the GSVD
92 * can be used to derive the solution of the eigenvalue problem:
93 * A**T*A x = lambda* B**T*B x.
94 * In some literature, the GSVD of A and B is presented in the form
95 * U**T*A*X = ( 0 D1 ), V**T*B*X = ( 0 D2 )
96 * where U and V are orthogonal and X is nonsingular, D1 and D2 are
97 * ``diagonal''. The former GSVD form can be converted to the latter
98 * form by taking the nonsingular matrix X as
99 *
100 * X = Q*( I 0 )
101 * ( 0 inv(R) ).
102 *
103 * Arguments
104 * =========
105 *
106 * JOBU (input) CHARACTER*1
107 * = 'U': Orthogonal matrix U is computed;
108 * = 'N': U is not computed.
109 *
110 * JOBV (input) CHARACTER*1
111 * = 'V': Orthogonal matrix V is computed;
112 * = 'N': V is not computed.
113 *
114 * JOBQ (input) CHARACTER*1
115 * = 'Q': Orthogonal matrix Q is computed;
116 * = 'N': Q is not computed.
117 *
118 * M (input) INTEGER
119 * The number of rows of the matrix A. M >= 0.
120 *
121 * N (input) INTEGER
122 * The number of columns of the matrices A and B. N >= 0.
123 *
124 * P (input) INTEGER
125 * The number of rows of the matrix B. P >= 0.
126 *
127 * K (output) INTEGER
128 * L (output) INTEGER
129 * On exit, K and L specify the dimension of the subblocks
130 * described in the Purpose section.
131 * K + L = effective numerical rank of (A**T,B**T)**T.
132 *
133 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
134 * On entry, the M-by-N matrix A.
135 * On exit, A contains the triangular matrix R, or part of R.
136 * See Purpose for details.
137 *
138 * LDA (input) INTEGER
139 * The leading dimension of the array A. LDA >= max(1,M).
140 *
141 * B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
142 * On entry, the P-by-N matrix B.
143 * On exit, B contains the triangular matrix R if M-K-L < 0.
144 * See Purpose for details.
145 *
146 * LDB (input) INTEGER
147 * The leading dimension of the array B. LDB >= max(1,P).
148 *
149 * ALPHA (output) DOUBLE PRECISION array, dimension (N)
150 * BETA (output) DOUBLE PRECISION array, dimension (N)
151 * On exit, ALPHA and BETA contain the generalized singular
152 * value pairs of A and B;
153 * ALPHA(1:K) = 1,
154 * BETA(1:K) = 0,
155 * and if M-K-L >= 0,
156 * ALPHA(K+1:K+L) = C,
157 * BETA(K+1:K+L) = S,
158 * or if M-K-L < 0,
159 * ALPHA(K+1:M)=C, ALPHA(M+1:K+L)=0
160 * BETA(K+1:M) =S, BETA(M+1:K+L) =1
161 * and
162 * ALPHA(K+L+1:N) = 0
163 * BETA(K+L+1:N) = 0
164 *
165 * U (output) DOUBLE PRECISION array, dimension (LDU,M)
166 * If JOBU = 'U', U contains the M-by-M orthogonal matrix U.
167 * If JOBU = 'N', U is not referenced.
168 *
169 * LDU (input) INTEGER
170 * The leading dimension of the array U. LDU >= max(1,M) if
171 * JOBU = 'U'; LDU >= 1 otherwise.
172 *
173 * V (output) DOUBLE PRECISION array, dimension (LDV,P)
174 * If JOBV = 'V', V contains the P-by-P orthogonal matrix V.
175 * If JOBV = 'N', V is not referenced.
176 *
177 * LDV (input) INTEGER
178 * The leading dimension of the array V. LDV >= max(1,P) if
179 * JOBV = 'V'; LDV >= 1 otherwise.
180 *
181 * Q (output) DOUBLE PRECISION array, dimension (LDQ,N)
182 * If JOBQ = 'Q', Q contains the N-by-N orthogonal matrix Q.
183 * If JOBQ = 'N', Q is not referenced.
184 *
185 * LDQ (input) INTEGER
186 * The leading dimension of the array Q. LDQ >= max(1,N) if
187 * JOBQ = 'Q'; LDQ >= 1 otherwise.
188 *
189 * WORK (workspace) DOUBLE PRECISION array,
190 * dimension (max(3*N,M,P)+N)
191 *
192 * IWORK (workspace/output) INTEGER array, dimension (N)
193 * On exit, IWORK stores the sorting information. More
194 * precisely, the following loop will sort ALPHA
195 * for I = K+1, min(M,K+L)
196 * swap ALPHA(I) and ALPHA(IWORK(I))
197 * endfor
198 * such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N).
199 *
200 * INFO (output) INTEGER
201 * = 0: successful exit
202 * < 0: if INFO = -i, the i-th argument had an illegal value.
203 * > 0: if INFO = 1, the Jacobi-type procedure failed to
204 * converge. For further details, see subroutine DTGSJA.
205 *
206 * Internal Parameters
207 * ===================
208 *
209 * TOLA DOUBLE PRECISION
210 * TOLB DOUBLE PRECISION
211 * TOLA and TOLB are the thresholds to determine the effective
212 * rank of (A',B')**T. Generally, they are set to
213 * TOLA = MAX(M,N)*norm(A)*MAZHEPS,
214 * TOLB = MAX(P,N)*norm(B)*MAZHEPS.
215 * The size of TOLA and TOLB may affect the size of backward
216 * errors of the decomposition.
217 *
218 * Further Details
219 * ===============
220 *
221 * 2-96 Based on modifications by
222 * Ming Gu and Huan Ren, Computer Science Division, University of
223 * California at Berkeley, USA
224 *
225 * =====================================================================
226 *
227 * .. Local Scalars ..
228 LOGICAL WANTQ, WANTU, WANTV
229 INTEGER I, IBND, ISUB, J, NCYCLE
230 DOUBLE PRECISION ANORM, BNORM, SMAX, TEMP, TOLA, TOLB, ULP, UNFL
231 * ..
232 * .. External Functions ..
233 LOGICAL LSAME
234 DOUBLE PRECISION DLAMCH, DLANGE
235 EXTERNAL LSAME, DLAMCH, DLANGE
236 * ..
237 * .. External Subroutines ..
238 EXTERNAL DCOPY, DGGSVP, DTGSJA, XERBLA
239 * ..
240 * .. Intrinsic Functions ..
241 INTRINSIC MAX, MIN
242 * ..
243 * .. Executable Statements ..
244 *
245 * Test the input parameters
246 *
247 WANTU = LSAME( JOBU, 'U' )
248 WANTV = LSAME( JOBV, 'V' )
249 WANTQ = LSAME( JOBQ, 'Q' )
250 *
251 INFO = 0
252 IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
253 INFO = -1
254 ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
255 INFO = -2
256 ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
257 INFO = -3
258 ELSE IF( M.LT.0 ) THEN
259 INFO = -4
260 ELSE IF( N.LT.0 ) THEN
261 INFO = -5
262 ELSE IF( P.LT.0 ) THEN
263 INFO = -6
264 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
265 INFO = -10
266 ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
267 INFO = -12
268 ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
269 INFO = -16
270 ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
271 INFO = -18
272 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
273 INFO = -20
274 END IF
275 IF( INFO.NE.0 ) THEN
276 CALL XERBLA( 'DGGSVD', -INFO )
277 RETURN
278 END IF
279 *
280 * Compute the Frobenius norm of matrices A and B
281 *
282 ANORM = DLANGE( '1', M, N, A, LDA, WORK )
283 BNORM = DLANGE( '1', P, N, B, LDB, WORK )
284 *
285 * Get machine precision and set up threshold for determining
286 * the effective numerical rank of the matrices A and B.
287 *
288 ULP = DLAMCH( 'Precision' )
289 UNFL = DLAMCH( 'Safe Minimum' )
290 TOLA = MAX( M, N )*MAX( ANORM, UNFL )*ULP
291 TOLB = MAX( P, N )*MAX( BNORM, UNFL )*ULP
292 *
293 * Preprocessing
294 *
295 CALL DGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA,
296 $ TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, WORK,
297 $ WORK( N+1 ), INFO )
298 *
299 * Compute the GSVD of two upper "triangular" matrices
300 *
301 CALL DTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, LDB,
302 $ TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ,
303 $ WORK, NCYCLE, INFO )
304 *
305 * Sort the singular values and store the pivot indices in IWORK
306 * Copy ALPHA to WORK, then sort ALPHA in WORK
307 *
308 CALL DCOPY( N, ALPHA, 1, WORK, 1 )
309 IBND = MIN( L, M-K )
310 DO 20 I = 1, IBND
311 *
312 * Scan for largest ALPHA(K+I)
313 *
314 ISUB = I
315 SMAX = WORK( K+I )
316 DO 10 J = I + 1, IBND
317 TEMP = WORK( K+J )
318 IF( TEMP.GT.SMAX ) THEN
319 ISUB = J
320 SMAX = TEMP
321 END IF
322 10 CONTINUE
323 IF( ISUB.NE.I ) THEN
324 WORK( K+ISUB ) = WORK( K+I )
325 WORK( K+I ) = SMAX
326 IWORK( K+I ) = K + ISUB
327 ELSE
328 IWORK( K+I ) = K + I
329 END IF
330 20 CONTINUE
331 *
332 RETURN
333 *
334 * End of DGGSVD
335 *
336 END
2 $ LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK,
3 $ IWORK, 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 JOBQ, JOBU, JOBV
12 INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P
13 * ..
14 * .. Array Arguments ..
15 INTEGER IWORK( * )
16 DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ),
17 $ BETA( * ), Q( LDQ, * ), U( LDU, * ),
18 $ V( LDV, * ), WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * DGGSVD computes the generalized singular value decomposition (GSVD)
25 * of an M-by-N real matrix A and P-by-N real matrix B:
26 *
27 * U**T*A*Q = D1*( 0 R ), V**T*B*Q = D2*( 0 R )
28 *
29 * where U, V and Q are orthogonal matrices.
30 * Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T,
31 * then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and
32 * D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the
33 * following structures, respectively:
34 *
35 * If M-K-L >= 0,
36 *
37 * K L
38 * D1 = K ( I 0 )
39 * L ( 0 C )
40 * M-K-L ( 0 0 )
41 *
42 * K L
43 * D2 = L ( 0 S )
44 * P-L ( 0 0 )
45 *
46 * N-K-L K L
47 * ( 0 R ) = K ( 0 R11 R12 )
48 * L ( 0 0 R22 )
49 *
50 * where
51 *
52 * C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
53 * S = diag( BETA(K+1), ... , BETA(K+L) ),
54 * C**2 + S**2 = I.
55 *
56 * R is stored in A(1:K+L,N-K-L+1:N) on exit.
57 *
58 * If M-K-L < 0,
59 *
60 * K M-K K+L-M
61 * D1 = K ( I 0 0 )
62 * M-K ( 0 C 0 )
63 *
64 * K M-K K+L-M
65 * D2 = M-K ( 0 S 0 )
66 * K+L-M ( 0 0 I )
67 * P-L ( 0 0 0 )
68 *
69 * N-K-L K M-K K+L-M
70 * ( 0 R ) = K ( 0 R11 R12 R13 )
71 * M-K ( 0 0 R22 R23 )
72 * K+L-M ( 0 0 0 R33 )
73 *
74 * where
75 *
76 * C = diag( ALPHA(K+1), ... , ALPHA(M) ),
77 * S = diag( BETA(K+1), ... , BETA(M) ),
78 * C**2 + S**2 = I.
79 *
80 * (R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored
81 * ( 0 R22 R23 )
82 * in B(M-K+1:L,N+M-K-L+1:N) on exit.
83 *
84 * The routine computes C, S, R, and optionally the orthogonal
85 * transformation matrices U, V and Q.
86 *
87 * In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
88 * A and B implicitly gives the SVD of A*inv(B):
89 * A*inv(B) = U*(D1*inv(D2))*V**T.
90 * If ( A**T,B**T)**T has orthonormal columns, then the GSVD of A and B is
91 * also equal to the CS decomposition of A and B. Furthermore, the GSVD
92 * can be used to derive the solution of the eigenvalue problem:
93 * A**T*A x = lambda* B**T*B x.
94 * In some literature, the GSVD of A and B is presented in the form
95 * U**T*A*X = ( 0 D1 ), V**T*B*X = ( 0 D2 )
96 * where U and V are orthogonal and X is nonsingular, D1 and D2 are
97 * ``diagonal''. The former GSVD form can be converted to the latter
98 * form by taking the nonsingular matrix X as
99 *
100 * X = Q*( I 0 )
101 * ( 0 inv(R) ).
102 *
103 * Arguments
104 * =========
105 *
106 * JOBU (input) CHARACTER*1
107 * = 'U': Orthogonal matrix U is computed;
108 * = 'N': U is not computed.
109 *
110 * JOBV (input) CHARACTER*1
111 * = 'V': Orthogonal matrix V is computed;
112 * = 'N': V is not computed.
113 *
114 * JOBQ (input) CHARACTER*1
115 * = 'Q': Orthogonal matrix Q is computed;
116 * = 'N': Q is not computed.
117 *
118 * M (input) INTEGER
119 * The number of rows of the matrix A. M >= 0.
120 *
121 * N (input) INTEGER
122 * The number of columns of the matrices A and B. N >= 0.
123 *
124 * P (input) INTEGER
125 * The number of rows of the matrix B. P >= 0.
126 *
127 * K (output) INTEGER
128 * L (output) INTEGER
129 * On exit, K and L specify the dimension of the subblocks
130 * described in the Purpose section.
131 * K + L = effective numerical rank of (A**T,B**T)**T.
132 *
133 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
134 * On entry, the M-by-N matrix A.
135 * On exit, A contains the triangular matrix R, or part of R.
136 * See Purpose for details.
137 *
138 * LDA (input) INTEGER
139 * The leading dimension of the array A. LDA >= max(1,M).
140 *
141 * B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
142 * On entry, the P-by-N matrix B.
143 * On exit, B contains the triangular matrix R if M-K-L < 0.
144 * See Purpose for details.
145 *
146 * LDB (input) INTEGER
147 * The leading dimension of the array B. LDB >= max(1,P).
148 *
149 * ALPHA (output) DOUBLE PRECISION array, dimension (N)
150 * BETA (output) DOUBLE PRECISION array, dimension (N)
151 * On exit, ALPHA and BETA contain the generalized singular
152 * value pairs of A and B;
153 * ALPHA(1:K) = 1,
154 * BETA(1:K) = 0,
155 * and if M-K-L >= 0,
156 * ALPHA(K+1:K+L) = C,
157 * BETA(K+1:K+L) = S,
158 * or if M-K-L < 0,
159 * ALPHA(K+1:M)=C, ALPHA(M+1:K+L)=0
160 * BETA(K+1:M) =S, BETA(M+1:K+L) =1
161 * and
162 * ALPHA(K+L+1:N) = 0
163 * BETA(K+L+1:N) = 0
164 *
165 * U (output) DOUBLE PRECISION array, dimension (LDU,M)
166 * If JOBU = 'U', U contains the M-by-M orthogonal matrix U.
167 * If JOBU = 'N', U is not referenced.
168 *
169 * LDU (input) INTEGER
170 * The leading dimension of the array U. LDU >= max(1,M) if
171 * JOBU = 'U'; LDU >= 1 otherwise.
172 *
173 * V (output) DOUBLE PRECISION array, dimension (LDV,P)
174 * If JOBV = 'V', V contains the P-by-P orthogonal matrix V.
175 * If JOBV = 'N', V is not referenced.
176 *
177 * LDV (input) INTEGER
178 * The leading dimension of the array V. LDV >= max(1,P) if
179 * JOBV = 'V'; LDV >= 1 otherwise.
180 *
181 * Q (output) DOUBLE PRECISION array, dimension (LDQ,N)
182 * If JOBQ = 'Q', Q contains the N-by-N orthogonal matrix Q.
183 * If JOBQ = 'N', Q is not referenced.
184 *
185 * LDQ (input) INTEGER
186 * The leading dimension of the array Q. LDQ >= max(1,N) if
187 * JOBQ = 'Q'; LDQ >= 1 otherwise.
188 *
189 * WORK (workspace) DOUBLE PRECISION array,
190 * dimension (max(3*N,M,P)+N)
191 *
192 * IWORK (workspace/output) INTEGER array, dimension (N)
193 * On exit, IWORK stores the sorting information. More
194 * precisely, the following loop will sort ALPHA
195 * for I = K+1, min(M,K+L)
196 * swap ALPHA(I) and ALPHA(IWORK(I))
197 * endfor
198 * such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N).
199 *
200 * INFO (output) INTEGER
201 * = 0: successful exit
202 * < 0: if INFO = -i, the i-th argument had an illegal value.
203 * > 0: if INFO = 1, the Jacobi-type procedure failed to
204 * converge. For further details, see subroutine DTGSJA.
205 *
206 * Internal Parameters
207 * ===================
208 *
209 * TOLA DOUBLE PRECISION
210 * TOLB DOUBLE PRECISION
211 * TOLA and TOLB are the thresholds to determine the effective
212 * rank of (A',B')**T. Generally, they are set to
213 * TOLA = MAX(M,N)*norm(A)*MAZHEPS,
214 * TOLB = MAX(P,N)*norm(B)*MAZHEPS.
215 * The size of TOLA and TOLB may affect the size of backward
216 * errors of the decomposition.
217 *
218 * Further Details
219 * ===============
220 *
221 * 2-96 Based on modifications by
222 * Ming Gu and Huan Ren, Computer Science Division, University of
223 * California at Berkeley, USA
224 *
225 * =====================================================================
226 *
227 * .. Local Scalars ..
228 LOGICAL WANTQ, WANTU, WANTV
229 INTEGER I, IBND, ISUB, J, NCYCLE
230 DOUBLE PRECISION ANORM, BNORM, SMAX, TEMP, TOLA, TOLB, ULP, UNFL
231 * ..
232 * .. External Functions ..
233 LOGICAL LSAME
234 DOUBLE PRECISION DLAMCH, DLANGE
235 EXTERNAL LSAME, DLAMCH, DLANGE
236 * ..
237 * .. External Subroutines ..
238 EXTERNAL DCOPY, DGGSVP, DTGSJA, XERBLA
239 * ..
240 * .. Intrinsic Functions ..
241 INTRINSIC MAX, MIN
242 * ..
243 * .. Executable Statements ..
244 *
245 * Test the input parameters
246 *
247 WANTU = LSAME( JOBU, 'U' )
248 WANTV = LSAME( JOBV, 'V' )
249 WANTQ = LSAME( JOBQ, 'Q' )
250 *
251 INFO = 0
252 IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
253 INFO = -1
254 ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
255 INFO = -2
256 ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
257 INFO = -3
258 ELSE IF( M.LT.0 ) THEN
259 INFO = -4
260 ELSE IF( N.LT.0 ) THEN
261 INFO = -5
262 ELSE IF( P.LT.0 ) THEN
263 INFO = -6
264 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
265 INFO = -10
266 ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
267 INFO = -12
268 ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
269 INFO = -16
270 ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
271 INFO = -18
272 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
273 INFO = -20
274 END IF
275 IF( INFO.NE.0 ) THEN
276 CALL XERBLA( 'DGGSVD', -INFO )
277 RETURN
278 END IF
279 *
280 * Compute the Frobenius norm of matrices A and B
281 *
282 ANORM = DLANGE( '1', M, N, A, LDA, WORK )
283 BNORM = DLANGE( '1', P, N, B, LDB, WORK )
284 *
285 * Get machine precision and set up threshold for determining
286 * the effective numerical rank of the matrices A and B.
287 *
288 ULP = DLAMCH( 'Precision' )
289 UNFL = DLAMCH( 'Safe Minimum' )
290 TOLA = MAX( M, N )*MAX( ANORM, UNFL )*ULP
291 TOLB = MAX( P, N )*MAX( BNORM, UNFL )*ULP
292 *
293 * Preprocessing
294 *
295 CALL DGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA,
296 $ TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, WORK,
297 $ WORK( N+1 ), INFO )
298 *
299 * Compute the GSVD of two upper "triangular" matrices
300 *
301 CALL DTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, LDB,
302 $ TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ,
303 $ WORK, NCYCLE, INFO )
304 *
305 * Sort the singular values and store the pivot indices in IWORK
306 * Copy ALPHA to WORK, then sort ALPHA in WORK
307 *
308 CALL DCOPY( N, ALPHA, 1, WORK, 1 )
309 IBND = MIN( L, M-K )
310 DO 20 I = 1, IBND
311 *
312 * Scan for largest ALPHA(K+I)
313 *
314 ISUB = I
315 SMAX = WORK( K+I )
316 DO 10 J = I + 1, IBND
317 TEMP = WORK( K+J )
318 IF( TEMP.GT.SMAX ) THEN
319 ISUB = J
320 SMAX = TEMP
321 END IF
322 10 CONTINUE
323 IF( ISUB.NE.I ) THEN
324 WORK( K+ISUB ) = WORK( K+I )
325 WORK( K+I ) = SMAX
326 IWORK( K+I ) = K + ISUB
327 ELSE
328 IWORK( K+I ) = K + I
329 END IF
330 20 CONTINUE
331 *
332 RETURN
333 *
334 * End of DGGSVD
335 *
336 END