1 SUBROUTINE ZGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
2 $ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
3 $ IWORK, RWORK, TAU, WORK, INFO )
4 *
5 * -- LAPACK 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 DOUBLE PRECISION TOLA, TOLB
14 * ..
15 * .. Array Arguments ..
16 INTEGER IWORK( * )
17 DOUBLE PRECISION RWORK( * )
18 COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
19 $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * ZGGSVP computes unitary matrices U, V and Q such that
26 *
27 * N-K-L K L
28 * U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
29 * L ( 0 0 A23 )
30 * M-K-L ( 0 0 0 )
31 *
32 * N-K-L K L
33 * = K ( 0 A12 A13 ) if M-K-L < 0;
34 * M-K ( 0 0 A23 )
35 *
36 * N-K-L K L
37 * V**H*B*Q = L ( 0 0 B13 )
38 * P-L ( 0 0 0 )
39 *
40 * where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
41 * upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
42 * otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
43 * numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.
44 *
45 * This decomposition is the preprocessing step for computing the
46 * Generalized Singular Value Decomposition (GSVD), see subroutine
47 * ZGGSVD.
48 *
49 * Arguments
50 * =========
51 *
52 * JOBU (input) CHARACTER*1
53 * = 'U': Unitary matrix U is computed;
54 * = 'N': U is not computed.
55 *
56 * JOBV (input) CHARACTER*1
57 * = 'V': Unitary matrix V is computed;
58 * = 'N': V is not computed.
59 *
60 * JOBQ (input) CHARACTER*1
61 * = 'Q': Unitary matrix Q is computed;
62 * = 'N': Q is not computed.
63 *
64 * M (input) INTEGER
65 * The number of rows of the matrix A. M >= 0.
66 *
67 * P (input) INTEGER
68 * The number of rows of the matrix B. P >= 0.
69 *
70 * N (input) INTEGER
71 * The number of columns of the matrices A and B. N >= 0.
72 *
73 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
74 * On entry, the M-by-N matrix A.
75 * On exit, A contains the triangular (or trapezoidal) matrix
76 * described in the Purpose section.
77 *
78 * LDA (input) INTEGER
79 * The leading dimension of the array A. LDA >= max(1,M).
80 *
81 * B (input/output) COMPLEX*16 array, dimension (LDB,N)
82 * On entry, the P-by-N matrix B.
83 * On exit, B contains the triangular matrix described in
84 * the Purpose section.
85 *
86 * LDB (input) INTEGER
87 * The leading dimension of the array B. LDB >= max(1,P).
88 *
89 * TOLA (input) DOUBLE PRECISION
90 * TOLB (input) DOUBLE PRECISION
91 * TOLA and TOLB are the thresholds to determine the effective
92 * numerical rank of matrix B and a subblock of A. Generally,
93 * they are set to
94 * TOLA = MAX(M,N)*norm(A)*MAZHEPS,
95 * TOLB = MAX(P,N)*norm(B)*MAZHEPS.
96 * The size of TOLA and TOLB may affect the size of backward
97 * errors of the decomposition.
98 *
99 * K (output) INTEGER
100 * L (output) INTEGER
101 * On exit, K and L specify the dimension of the subblocks
102 * described in Purpose section.
103 * K + L = effective numerical rank of (A**H,B**H)**H.
104 *
105 * U (output) COMPLEX*16 array, dimension (LDU,M)
106 * If JOBU = 'U', U contains the unitary matrix U.
107 * If JOBU = 'N', U is not referenced.
108 *
109 * LDU (input) INTEGER
110 * The leading dimension of the array U. LDU >= max(1,M) if
111 * JOBU = 'U'; LDU >= 1 otherwise.
112 *
113 * V (output) COMPLEX*16 array, dimension (LDV,P)
114 * If JOBV = 'V', V contains the unitary matrix V.
115 * If JOBV = 'N', V is not referenced.
116 *
117 * LDV (input) INTEGER
118 * The leading dimension of the array V. LDV >= max(1,P) if
119 * JOBV = 'V'; LDV >= 1 otherwise.
120 *
121 * Q (output) COMPLEX*16 array, dimension (LDQ,N)
122 * If JOBQ = 'Q', Q contains the unitary matrix Q.
123 * If JOBQ = 'N', Q is not referenced.
124 *
125 * LDQ (input) INTEGER
126 * The leading dimension of the array Q. LDQ >= max(1,N) if
127 * JOBQ = 'Q'; LDQ >= 1 otherwise.
128 *
129 * IWORK (workspace) INTEGER array, dimension (N)
130 *
131 * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
132 *
133 * TAU (workspace) COMPLEX*16 array, dimension (N)
134 *
135 * WORK (workspace) COMPLEX*16 array, dimension (max(3*N,M,P))
136 *
137 * INFO (output) INTEGER
138 * = 0: successful exit
139 * < 0: if INFO = -i, the i-th argument had an illegal value.
140 *
141 * Further Details
142 * ===============
143 *
144 * The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization
145 * with column pivoting to detect the effective numerical rank of the
146 * a matrix. It may be replaced by a better rank determination strategy.
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151 COMPLEX*16 CZERO, CONE
152 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
153 $ CONE = ( 1.0D+0, 0.0D+0 ) )
154 * ..
155 * .. Local Scalars ..
156 LOGICAL FORWRD, WANTQ, WANTU, WANTV
157 INTEGER I, J
158 COMPLEX*16 T
159 * ..
160 * .. External Functions ..
161 LOGICAL LSAME
162 EXTERNAL LSAME
163 * ..
164 * .. External Subroutines ..
165 EXTERNAL XERBLA, ZGEQPF, ZGEQR2, ZGERQ2, ZLACPY, ZLAPMT,
166 $ ZLASET, ZUNG2R, ZUNM2R, ZUNMR2
167 * ..
168 * .. Intrinsic Functions ..
169 INTRINSIC ABS, DBLE, DIMAG, MAX, MIN
170 * ..
171 * .. Statement Functions ..
172 DOUBLE PRECISION CABS1
173 * ..
174 * .. Statement Function definitions ..
175 CABS1( T ) = ABS( DBLE( T ) ) + ABS( DIMAG( T ) )
176 * ..
177 * .. Executable Statements ..
178 *
179 * Test the input parameters
180 *
181 WANTU = LSAME( JOBU, 'U' )
182 WANTV = LSAME( JOBV, 'V' )
183 WANTQ = LSAME( JOBQ, 'Q' )
184 FORWRD = .TRUE.
185 *
186 INFO = 0
187 IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
188 INFO = -1
189 ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
190 INFO = -2
191 ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
192 INFO = -3
193 ELSE IF( M.LT.0 ) THEN
194 INFO = -4
195 ELSE IF( P.LT.0 ) THEN
196 INFO = -5
197 ELSE IF( N.LT.0 ) THEN
198 INFO = -6
199 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
200 INFO = -8
201 ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
202 INFO = -10
203 ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
204 INFO = -16
205 ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
206 INFO = -18
207 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
208 INFO = -20
209 END IF
210 IF( INFO.NE.0 ) THEN
211 CALL XERBLA( 'ZGGSVP', -INFO )
212 RETURN
213 END IF
214 *
215 * QR with column pivoting of B: B*P = V*( S11 S12 )
216 * ( 0 0 )
217 *
218 DO 10 I = 1, N
219 IWORK( I ) = 0
220 10 CONTINUE
221 CALL ZGEQPF( P, N, B, LDB, IWORK, TAU, WORK, RWORK, INFO )
222 *
223 * Update A := A*P
224 *
225 CALL ZLAPMT( FORWRD, M, N, A, LDA, IWORK )
226 *
227 * Determine the effective rank of matrix B.
228 *
229 L = 0
230 DO 20 I = 1, MIN( P, N )
231 IF( CABS1( B( I, I ) ).GT.TOLB )
232 $ L = L + 1
233 20 CONTINUE
234 *
235 IF( WANTV ) THEN
236 *
237 * Copy the details of V, and form V.
238 *
239 CALL ZLASET( 'Full', P, P, CZERO, CZERO, V, LDV )
240 IF( P.GT.1 )
241 $ CALL ZLACPY( 'Lower', P-1, N, B( 2, 1 ), LDB, V( 2, 1 ),
242 $ LDV )
243 CALL ZUNG2R( P, P, MIN( P, N ), V, LDV, TAU, WORK, INFO )
244 END IF
245 *
246 * Clean up B
247 *
248 DO 40 J = 1, L - 1
249 DO 30 I = J + 1, L
250 B( I, J ) = CZERO
251 30 CONTINUE
252 40 CONTINUE
253 IF( P.GT.L )
254 $ CALL ZLASET( 'Full', P-L, N, CZERO, CZERO, B( L+1, 1 ), LDB )
255 *
256 IF( WANTQ ) THEN
257 *
258 * Set Q = I and Update Q := Q*P
259 *
260 CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDQ )
261 CALL ZLAPMT( FORWRD, N, N, Q, LDQ, IWORK )
262 END IF
263 *
264 IF( P.GE.L .AND. N.NE.L ) THEN
265 *
266 * RQ factorization of ( S11 S12 ) = ( 0 S12 )*Z
267 *
268 CALL ZGERQ2( L, N, B, LDB, TAU, WORK, INFO )
269 *
270 * Update A := A*Z**H
271 *
272 CALL ZUNMR2( 'Right', 'Conjugate transpose', M, N, L, B, LDB,
273 $ TAU, A, LDA, WORK, INFO )
274 IF( WANTQ ) THEN
275 *
276 * Update Q := Q*Z**H
277 *
278 CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N, L, B,
279 $ LDB, TAU, Q, LDQ, WORK, INFO )
280 END IF
281 *
282 * Clean up B
283 *
284 CALL ZLASET( 'Full', L, N-L, CZERO, CZERO, B, LDB )
285 DO 60 J = N - L + 1, N
286 DO 50 I = J - N + L + 1, L
287 B( I, J ) = CZERO
288 50 CONTINUE
289 60 CONTINUE
290 *
291 END IF
292 *
293 * Let N-L L
294 * A = ( A11 A12 ) M,
295 *
296 * then the following does the complete QR decomposition of A11:
297 *
298 * A11 = U*( 0 T12 )*P1**H
299 * ( 0 0 )
300 *
301 DO 70 I = 1, N - L
302 IWORK( I ) = 0
303 70 CONTINUE
304 CALL ZGEQPF( M, N-L, A, LDA, IWORK, TAU, WORK, RWORK, INFO )
305 *
306 * Determine the effective rank of A11
307 *
308 K = 0
309 DO 80 I = 1, MIN( M, N-L )
310 IF( CABS1( A( I, I ) ).GT.TOLA )
311 $ K = K + 1
312 80 CONTINUE
313 *
314 * Update A12 := U**H*A12, where A12 = A( 1:M, N-L+1:N )
315 *
316 CALL ZUNM2R( 'Left', 'Conjugate transpose', M, L, MIN( M, N-L ),
317 $ A, LDA, TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
318 *
319 IF( WANTU ) THEN
320 *
321 * Copy the details of U, and form U
322 *
323 CALL ZLASET( 'Full', M, M, CZERO, CZERO, U, LDU )
324 IF( M.GT.1 )
325 $ CALL ZLACPY( 'Lower', M-1, N-L, A( 2, 1 ), LDA, U( 2, 1 ),
326 $ LDU )
327 CALL ZUNG2R( M, M, MIN( M, N-L ), U, LDU, TAU, WORK, INFO )
328 END IF
329 *
330 IF( WANTQ ) THEN
331 *
332 * Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1
333 *
334 CALL ZLAPMT( FORWRD, N, N-L, Q, LDQ, IWORK )
335 END IF
336 *
337 * Clean up A: set the strictly lower triangular part of
338 * A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0.
339 *
340 DO 100 J = 1, K - 1
341 DO 90 I = J + 1, K
342 A( I, J ) = CZERO
343 90 CONTINUE
344 100 CONTINUE
345 IF( M.GT.K )
346 $ CALL ZLASET( 'Full', M-K, N-L, CZERO, CZERO, A( K+1, 1 ), LDA )
347 *
348 IF( N-L.GT.K ) THEN
349 *
350 * RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1
351 *
352 CALL ZGERQ2( K, N-L, A, LDA, TAU, WORK, INFO )
353 *
354 IF( WANTQ ) THEN
355 *
356 * Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**H
357 *
358 CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N-L, K, A,
359 $ LDA, TAU, Q, LDQ, WORK, INFO )
360 END IF
361 *
362 * Clean up A
363 *
364 CALL ZLASET( 'Full', K, N-L-K, CZERO, CZERO, A, LDA )
365 DO 120 J = N - L - K + 1, N - L
366 DO 110 I = J - N + L + K + 1, K
367 A( I, J ) = CZERO
368 110 CONTINUE
369 120 CONTINUE
370 *
371 END IF
372 *
373 IF( M.GT.K ) THEN
374 *
375 * QR factorization of A( K+1:M,N-L+1:N )
376 *
377 CALL ZGEQR2( M-K, L, A( K+1, N-L+1 ), LDA, TAU, WORK, INFO )
378 *
379 IF( WANTU ) THEN
380 *
381 * Update U(:,K+1:M) := U(:,K+1:M)*U1
382 *
383 CALL ZUNM2R( 'Right', 'No transpose', M, M-K, MIN( M-K, L ),
384 $ A( K+1, N-L+1 ), LDA, TAU, U( 1, K+1 ), LDU,
385 $ WORK, INFO )
386 END IF
387 *
388 * Clean up
389 *
390 DO 140 J = N - L + 1, N
391 DO 130 I = J - N + K + L + 1, M
392 A( I, J ) = CZERO
393 130 CONTINUE
394 140 CONTINUE
395 *
396 END IF
397 *
398 RETURN
399 *
400 * End of ZGGSVP
401 *
402 END
2 $ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
3 $ IWORK, RWORK, TAU, WORK, INFO )
4 *
5 * -- LAPACK 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 DOUBLE PRECISION TOLA, TOLB
14 * ..
15 * .. Array Arguments ..
16 INTEGER IWORK( * )
17 DOUBLE PRECISION RWORK( * )
18 COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
19 $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * ZGGSVP computes unitary matrices U, V and Q such that
26 *
27 * N-K-L K L
28 * U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
29 * L ( 0 0 A23 )
30 * M-K-L ( 0 0 0 )
31 *
32 * N-K-L K L
33 * = K ( 0 A12 A13 ) if M-K-L < 0;
34 * M-K ( 0 0 A23 )
35 *
36 * N-K-L K L
37 * V**H*B*Q = L ( 0 0 B13 )
38 * P-L ( 0 0 0 )
39 *
40 * where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
41 * upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
42 * otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
43 * numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.
44 *
45 * This decomposition is the preprocessing step for computing the
46 * Generalized Singular Value Decomposition (GSVD), see subroutine
47 * ZGGSVD.
48 *
49 * Arguments
50 * =========
51 *
52 * JOBU (input) CHARACTER*1
53 * = 'U': Unitary matrix U is computed;
54 * = 'N': U is not computed.
55 *
56 * JOBV (input) CHARACTER*1
57 * = 'V': Unitary matrix V is computed;
58 * = 'N': V is not computed.
59 *
60 * JOBQ (input) CHARACTER*1
61 * = 'Q': Unitary matrix Q is computed;
62 * = 'N': Q is not computed.
63 *
64 * M (input) INTEGER
65 * The number of rows of the matrix A. M >= 0.
66 *
67 * P (input) INTEGER
68 * The number of rows of the matrix B. P >= 0.
69 *
70 * N (input) INTEGER
71 * The number of columns of the matrices A and B. N >= 0.
72 *
73 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
74 * On entry, the M-by-N matrix A.
75 * On exit, A contains the triangular (or trapezoidal) matrix
76 * described in the Purpose section.
77 *
78 * LDA (input) INTEGER
79 * The leading dimension of the array A. LDA >= max(1,M).
80 *
81 * B (input/output) COMPLEX*16 array, dimension (LDB,N)
82 * On entry, the P-by-N matrix B.
83 * On exit, B contains the triangular matrix described in
84 * the Purpose section.
85 *
86 * LDB (input) INTEGER
87 * The leading dimension of the array B. LDB >= max(1,P).
88 *
89 * TOLA (input) DOUBLE PRECISION
90 * TOLB (input) DOUBLE PRECISION
91 * TOLA and TOLB are the thresholds to determine the effective
92 * numerical rank of matrix B and a subblock of A. Generally,
93 * they are set to
94 * TOLA = MAX(M,N)*norm(A)*MAZHEPS,
95 * TOLB = MAX(P,N)*norm(B)*MAZHEPS.
96 * The size of TOLA and TOLB may affect the size of backward
97 * errors of the decomposition.
98 *
99 * K (output) INTEGER
100 * L (output) INTEGER
101 * On exit, K and L specify the dimension of the subblocks
102 * described in Purpose section.
103 * K + L = effective numerical rank of (A**H,B**H)**H.
104 *
105 * U (output) COMPLEX*16 array, dimension (LDU,M)
106 * If JOBU = 'U', U contains the unitary matrix U.
107 * If JOBU = 'N', U is not referenced.
108 *
109 * LDU (input) INTEGER
110 * The leading dimension of the array U. LDU >= max(1,M) if
111 * JOBU = 'U'; LDU >= 1 otherwise.
112 *
113 * V (output) COMPLEX*16 array, dimension (LDV,P)
114 * If JOBV = 'V', V contains the unitary matrix V.
115 * If JOBV = 'N', V is not referenced.
116 *
117 * LDV (input) INTEGER
118 * The leading dimension of the array V. LDV >= max(1,P) if
119 * JOBV = 'V'; LDV >= 1 otherwise.
120 *
121 * Q (output) COMPLEX*16 array, dimension (LDQ,N)
122 * If JOBQ = 'Q', Q contains the unitary matrix Q.
123 * If JOBQ = 'N', Q is not referenced.
124 *
125 * LDQ (input) INTEGER
126 * The leading dimension of the array Q. LDQ >= max(1,N) if
127 * JOBQ = 'Q'; LDQ >= 1 otherwise.
128 *
129 * IWORK (workspace) INTEGER array, dimension (N)
130 *
131 * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
132 *
133 * TAU (workspace) COMPLEX*16 array, dimension (N)
134 *
135 * WORK (workspace) COMPLEX*16 array, dimension (max(3*N,M,P))
136 *
137 * INFO (output) INTEGER
138 * = 0: successful exit
139 * < 0: if INFO = -i, the i-th argument had an illegal value.
140 *
141 * Further Details
142 * ===============
143 *
144 * The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization
145 * with column pivoting to detect the effective numerical rank of the
146 * a matrix. It may be replaced by a better rank determination strategy.
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151 COMPLEX*16 CZERO, CONE
152 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
153 $ CONE = ( 1.0D+0, 0.0D+0 ) )
154 * ..
155 * .. Local Scalars ..
156 LOGICAL FORWRD, WANTQ, WANTU, WANTV
157 INTEGER I, J
158 COMPLEX*16 T
159 * ..
160 * .. External Functions ..
161 LOGICAL LSAME
162 EXTERNAL LSAME
163 * ..
164 * .. External Subroutines ..
165 EXTERNAL XERBLA, ZGEQPF, ZGEQR2, ZGERQ2, ZLACPY, ZLAPMT,
166 $ ZLASET, ZUNG2R, ZUNM2R, ZUNMR2
167 * ..
168 * .. Intrinsic Functions ..
169 INTRINSIC ABS, DBLE, DIMAG, MAX, MIN
170 * ..
171 * .. Statement Functions ..
172 DOUBLE PRECISION CABS1
173 * ..
174 * .. Statement Function definitions ..
175 CABS1( T ) = ABS( DBLE( T ) ) + ABS( DIMAG( T ) )
176 * ..
177 * .. Executable Statements ..
178 *
179 * Test the input parameters
180 *
181 WANTU = LSAME( JOBU, 'U' )
182 WANTV = LSAME( JOBV, 'V' )
183 WANTQ = LSAME( JOBQ, 'Q' )
184 FORWRD = .TRUE.
185 *
186 INFO = 0
187 IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
188 INFO = -1
189 ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
190 INFO = -2
191 ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
192 INFO = -3
193 ELSE IF( M.LT.0 ) THEN
194 INFO = -4
195 ELSE IF( P.LT.0 ) THEN
196 INFO = -5
197 ELSE IF( N.LT.0 ) THEN
198 INFO = -6
199 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
200 INFO = -8
201 ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
202 INFO = -10
203 ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
204 INFO = -16
205 ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
206 INFO = -18
207 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
208 INFO = -20
209 END IF
210 IF( INFO.NE.0 ) THEN
211 CALL XERBLA( 'ZGGSVP', -INFO )
212 RETURN
213 END IF
214 *
215 * QR with column pivoting of B: B*P = V*( S11 S12 )
216 * ( 0 0 )
217 *
218 DO 10 I = 1, N
219 IWORK( I ) = 0
220 10 CONTINUE
221 CALL ZGEQPF( P, N, B, LDB, IWORK, TAU, WORK, RWORK, INFO )
222 *
223 * Update A := A*P
224 *
225 CALL ZLAPMT( FORWRD, M, N, A, LDA, IWORK )
226 *
227 * Determine the effective rank of matrix B.
228 *
229 L = 0
230 DO 20 I = 1, MIN( P, N )
231 IF( CABS1( B( I, I ) ).GT.TOLB )
232 $ L = L + 1
233 20 CONTINUE
234 *
235 IF( WANTV ) THEN
236 *
237 * Copy the details of V, and form V.
238 *
239 CALL ZLASET( 'Full', P, P, CZERO, CZERO, V, LDV )
240 IF( P.GT.1 )
241 $ CALL ZLACPY( 'Lower', P-1, N, B( 2, 1 ), LDB, V( 2, 1 ),
242 $ LDV )
243 CALL ZUNG2R( P, P, MIN( P, N ), V, LDV, TAU, WORK, INFO )
244 END IF
245 *
246 * Clean up B
247 *
248 DO 40 J = 1, L - 1
249 DO 30 I = J + 1, L
250 B( I, J ) = CZERO
251 30 CONTINUE
252 40 CONTINUE
253 IF( P.GT.L )
254 $ CALL ZLASET( 'Full', P-L, N, CZERO, CZERO, B( L+1, 1 ), LDB )
255 *
256 IF( WANTQ ) THEN
257 *
258 * Set Q = I and Update Q := Q*P
259 *
260 CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDQ )
261 CALL ZLAPMT( FORWRD, N, N, Q, LDQ, IWORK )
262 END IF
263 *
264 IF( P.GE.L .AND. N.NE.L ) THEN
265 *
266 * RQ factorization of ( S11 S12 ) = ( 0 S12 )*Z
267 *
268 CALL ZGERQ2( L, N, B, LDB, TAU, WORK, INFO )
269 *
270 * Update A := A*Z**H
271 *
272 CALL ZUNMR2( 'Right', 'Conjugate transpose', M, N, L, B, LDB,
273 $ TAU, A, LDA, WORK, INFO )
274 IF( WANTQ ) THEN
275 *
276 * Update Q := Q*Z**H
277 *
278 CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N, L, B,
279 $ LDB, TAU, Q, LDQ, WORK, INFO )
280 END IF
281 *
282 * Clean up B
283 *
284 CALL ZLASET( 'Full', L, N-L, CZERO, CZERO, B, LDB )
285 DO 60 J = N - L + 1, N
286 DO 50 I = J - N + L + 1, L
287 B( I, J ) = CZERO
288 50 CONTINUE
289 60 CONTINUE
290 *
291 END IF
292 *
293 * Let N-L L
294 * A = ( A11 A12 ) M,
295 *
296 * then the following does the complete QR decomposition of A11:
297 *
298 * A11 = U*( 0 T12 )*P1**H
299 * ( 0 0 )
300 *
301 DO 70 I = 1, N - L
302 IWORK( I ) = 0
303 70 CONTINUE
304 CALL ZGEQPF( M, N-L, A, LDA, IWORK, TAU, WORK, RWORK, INFO )
305 *
306 * Determine the effective rank of A11
307 *
308 K = 0
309 DO 80 I = 1, MIN( M, N-L )
310 IF( CABS1( A( I, I ) ).GT.TOLA )
311 $ K = K + 1
312 80 CONTINUE
313 *
314 * Update A12 := U**H*A12, where A12 = A( 1:M, N-L+1:N )
315 *
316 CALL ZUNM2R( 'Left', 'Conjugate transpose', M, L, MIN( M, N-L ),
317 $ A, LDA, TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
318 *
319 IF( WANTU ) THEN
320 *
321 * Copy the details of U, and form U
322 *
323 CALL ZLASET( 'Full', M, M, CZERO, CZERO, U, LDU )
324 IF( M.GT.1 )
325 $ CALL ZLACPY( 'Lower', M-1, N-L, A( 2, 1 ), LDA, U( 2, 1 ),
326 $ LDU )
327 CALL ZUNG2R( M, M, MIN( M, N-L ), U, LDU, TAU, WORK, INFO )
328 END IF
329 *
330 IF( WANTQ ) THEN
331 *
332 * Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1
333 *
334 CALL ZLAPMT( FORWRD, N, N-L, Q, LDQ, IWORK )
335 END IF
336 *
337 * Clean up A: set the strictly lower triangular part of
338 * A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0.
339 *
340 DO 100 J = 1, K - 1
341 DO 90 I = J + 1, K
342 A( I, J ) = CZERO
343 90 CONTINUE
344 100 CONTINUE
345 IF( M.GT.K )
346 $ CALL ZLASET( 'Full', M-K, N-L, CZERO, CZERO, A( K+1, 1 ), LDA )
347 *
348 IF( N-L.GT.K ) THEN
349 *
350 * RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1
351 *
352 CALL ZGERQ2( K, N-L, A, LDA, TAU, WORK, INFO )
353 *
354 IF( WANTQ ) THEN
355 *
356 * Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**H
357 *
358 CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N-L, K, A,
359 $ LDA, TAU, Q, LDQ, WORK, INFO )
360 END IF
361 *
362 * Clean up A
363 *
364 CALL ZLASET( 'Full', K, N-L-K, CZERO, CZERO, A, LDA )
365 DO 120 J = N - L - K + 1, N - L
366 DO 110 I = J - N + L + K + 1, K
367 A( I, J ) = CZERO
368 110 CONTINUE
369 120 CONTINUE
370 *
371 END IF
372 *
373 IF( M.GT.K ) THEN
374 *
375 * QR factorization of A( K+1:M,N-L+1:N )
376 *
377 CALL ZGEQR2( M-K, L, A( K+1, N-L+1 ), LDA, TAU, WORK, INFO )
378 *
379 IF( WANTU ) THEN
380 *
381 * Update U(:,K+1:M) := U(:,K+1:M)*U1
382 *
383 CALL ZUNM2R( 'Right', 'No transpose', M, M-K, MIN( M-K, L ),
384 $ A( K+1, N-L+1 ), LDA, TAU, U( 1, K+1 ), LDU,
385 $ WORK, INFO )
386 END IF
387 *
388 * Clean up
389 *
390 DO 140 J = N - L + 1, N
391 DO 130 I = J - N + K + L + 1, M
392 A( I, J ) = CZERO
393 130 CONTINUE
394 140 CONTINUE
395 *
396 END IF
397 *
398 RETURN
399 *
400 * End of ZGGSVP
401 *
402 END