Annotation of rpl/lapack/lapack/dggsvp3.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DGGSVP3
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGGSVP3 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggsvp3.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggsvp3.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggsvp3.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGGSVP3( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
! 22: * TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
! 23: * IWORK, TAU, WORK, LWORK, INFO )
! 24: *
! 25: * .. Scalar Arguments ..
! 26: * CHARACTER JOBQ, JOBU, JOBV
! 27: * INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P, LWORK
! 28: * DOUBLE PRECISION TOLA, TOLB
! 29: * ..
! 30: * .. Array Arguments ..
! 31: * INTEGER IWORK( * )
! 32: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
! 33: * $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
! 34: * ..
! 35: *
! 36: *
! 37: *> \par Purpose:
! 38: * =============
! 39: *>
! 40: *> \verbatim
! 41: *>
! 42: *> DGGSVP3 computes orthogonal matrices U, V and Q such that
! 43: *>
! 44: *> N-K-L K L
! 45: *> U**T*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
! 46: *> L ( 0 0 A23 )
! 47: *> M-K-L ( 0 0 0 )
! 48: *>
! 49: *> N-K-L K L
! 50: *> = K ( 0 A12 A13 ) if M-K-L < 0;
! 51: *> M-K ( 0 0 A23 )
! 52: *>
! 53: *> N-K-L K L
! 54: *> V**T*B*Q = L ( 0 0 B13 )
! 55: *> P-L ( 0 0 0 )
! 56: *>
! 57: *> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
! 58: *> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
! 59: *> otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
! 60: *> numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T.
! 61: *>
! 62: *> This decomposition is the preprocessing step for computing the
! 63: *> Generalized Singular Value Decomposition (GSVD), see subroutine
! 64: *> DGGSVD3.
! 65: *> \endverbatim
! 66: *
! 67: * Arguments:
! 68: * ==========
! 69: *
! 70: *> \param[in] JOBU
! 71: *> \verbatim
! 72: *> JOBU is CHARACTER*1
! 73: *> = 'U': Orthogonal matrix U is computed;
! 74: *> = 'N': U is not computed.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] JOBV
! 78: *> \verbatim
! 79: *> JOBV is CHARACTER*1
! 80: *> = 'V': Orthogonal matrix V is computed;
! 81: *> = 'N': V is not computed.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] JOBQ
! 85: *> \verbatim
! 86: *> JOBQ is CHARACTER*1
! 87: *> = 'Q': Orthogonal matrix Q is computed;
! 88: *> = 'N': Q is not computed.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[in] M
! 92: *> \verbatim
! 93: *> M is INTEGER
! 94: *> The number of rows of the matrix A. M >= 0.
! 95: *> \endverbatim
! 96: *>
! 97: *> \param[in] P
! 98: *> \verbatim
! 99: *> P is INTEGER
! 100: *> The number of rows of the matrix B. P >= 0.
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] N
! 104: *> \verbatim
! 105: *> N is INTEGER
! 106: *> The number of columns of the matrices A and B. N >= 0.
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[in,out] A
! 110: *> \verbatim
! 111: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 112: *> On entry, the M-by-N matrix A.
! 113: *> On exit, A contains the triangular (or trapezoidal) matrix
! 114: *> described in the Purpose section.
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] LDA
! 118: *> \verbatim
! 119: *> LDA is INTEGER
! 120: *> The leading dimension of the array A. LDA >= max(1,M).
! 121: *> \endverbatim
! 122: *>
! 123: *> \param[in,out] B
! 124: *> \verbatim
! 125: *> B is DOUBLE PRECISION array, dimension (LDB,N)
! 126: *> On entry, the P-by-N matrix B.
! 127: *> On exit, B contains the triangular matrix described in
! 128: *> the Purpose section.
! 129: *> \endverbatim
! 130: *>
! 131: *> \param[in] LDB
! 132: *> \verbatim
! 133: *> LDB is INTEGER
! 134: *> The leading dimension of the array B. LDB >= max(1,P).
! 135: *> \endverbatim
! 136: *>
! 137: *> \param[in] TOLA
! 138: *> \verbatim
! 139: *> TOLA is DOUBLE PRECISION
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] TOLB
! 143: *> \verbatim
! 144: *> TOLB is DOUBLE PRECISION
! 145: *>
! 146: *> TOLA and TOLB are the thresholds to determine the effective
! 147: *> numerical rank of matrix B and a subblock of A. Generally,
! 148: *> they are set to
! 149: *> TOLA = MAX(M,N)*norm(A)*MACHEPS,
! 150: *> TOLB = MAX(P,N)*norm(B)*MACHEPS.
! 151: *> The size of TOLA and TOLB may affect the size of backward
! 152: *> errors of the decomposition.
! 153: *> \endverbatim
! 154: *>
! 155: *> \param[out] K
! 156: *> \verbatim
! 157: *> K is INTEGER
! 158: *> \endverbatim
! 159: *>
! 160: *> \param[out] L
! 161: *> \verbatim
! 162: *> L is INTEGER
! 163: *>
! 164: *> On exit, K and L specify the dimension of the subblocks
! 165: *> described in Purpose section.
! 166: *> K + L = effective numerical rank of (A**T,B**T)**T.
! 167: *> \endverbatim
! 168: *>
! 169: *> \param[out] U
! 170: *> \verbatim
! 171: *> U is DOUBLE PRECISION array, dimension (LDU,M)
! 172: *> If JOBU = 'U', U contains the orthogonal matrix U.
! 173: *> If JOBU = 'N', U is not referenced.
! 174: *> \endverbatim
! 175: *>
! 176: *> \param[in] LDU
! 177: *> \verbatim
! 178: *> LDU is INTEGER
! 179: *> The leading dimension of the array U. LDU >= max(1,M) if
! 180: *> JOBU = 'U'; LDU >= 1 otherwise.
! 181: *> \endverbatim
! 182: *>
! 183: *> \param[out] V
! 184: *> \verbatim
! 185: *> V is DOUBLE PRECISION array, dimension (LDV,P)
! 186: *> If JOBV = 'V', V contains the orthogonal matrix V.
! 187: *> If JOBV = 'N', V is not referenced.
! 188: *> \endverbatim
! 189: *>
! 190: *> \param[in] LDV
! 191: *> \verbatim
! 192: *> LDV is INTEGER
! 193: *> The leading dimension of the array V. LDV >= max(1,P) if
! 194: *> JOBV = 'V'; LDV >= 1 otherwise.
! 195: *> \endverbatim
! 196: *>
! 197: *> \param[out] Q
! 198: *> \verbatim
! 199: *> Q is DOUBLE PRECISION array, dimension (LDQ,N)
! 200: *> If JOBQ = 'Q', Q contains the orthogonal matrix Q.
! 201: *> If JOBQ = 'N', Q is not referenced.
! 202: *> \endverbatim
! 203: *>
! 204: *> \param[in] LDQ
! 205: *> \verbatim
! 206: *> LDQ is INTEGER
! 207: *> The leading dimension of the array Q. LDQ >= max(1,N) if
! 208: *> JOBQ = 'Q'; LDQ >= 1 otherwise.
! 209: *> \endverbatim
! 210: *>
! 211: *> \param[out] IWORK
! 212: *> \verbatim
! 213: *> IWORK is INTEGER array, dimension (N)
! 214: *> \endverbatim
! 215: *>
! 216: *> \param[out] TAU
! 217: *> \verbatim
! 218: *> TAU is DOUBLE PRECISION array, dimension (N)
! 219: *> \endverbatim
! 220: *>
! 221: *> \param[out] WORK
! 222: *> \verbatim
! 223: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 224: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 225: *> \endverbatim
! 226: *>
! 227: *> \param[in] LWORK
! 228: *> \verbatim
! 229: *> LWORK is INTEGER
! 230: *> The dimension of the array WORK.
! 231: *>
! 232: *> If LWORK = -1, then a workspace query is assumed; the routine
! 233: *> only calculates the optimal size of the WORK array, returns
! 234: *> this value as the first entry of the WORK array, and no error
! 235: *> message related to LWORK is issued by XERBLA.
! 236: *> \endverbatim
! 237: *>
! 238: *> \param[out] INFO
! 239: *> \verbatim
! 240: *> INFO is INTEGER
! 241: *> = 0: successful exit
! 242: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 243: *> \endverbatim
! 244: *
! 245: * Authors:
! 246: * ========
! 247: *
! 248: *> \author Univ. of Tennessee
! 249: *> \author Univ. of California Berkeley
! 250: *> \author Univ. of Colorado Denver
! 251: *> \author NAG Ltd.
! 252: *
! 253: *> \date August 2015
! 254: *
! 255: *> \ingroup doubleOTHERcomputational
! 256: *
! 257: *> \par Further Details:
! 258: * =====================
! 259: *>
! 260: *> \verbatim
! 261: *>
! 262: *> The subroutine uses LAPACK subroutine DGEQP3 for the QR factorization
! 263: *> with column pivoting to detect the effective numerical rank of the
! 264: *> a matrix. It may be replaced by a better rank determination strategy.
! 265: *>
! 266: *> DGGSVP3 replaces the deprecated subroutine DGGSVP.
! 267: *>
! 268: *> \endverbatim
! 269: *>
! 270: * =====================================================================
! 271: SUBROUTINE DGGSVP3( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB,
! 272: $ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ,
! 273: $ IWORK, TAU, WORK, LWORK, INFO )
! 274: *
! 275: * -- LAPACK computational routine (version 3.6.0) --
! 276: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 277: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 278: * August 2015
! 279: *
! 280: IMPLICIT NONE
! 281: *
! 282: * .. Scalar Arguments ..
! 283: CHARACTER JOBQ, JOBU, JOBV
! 284: INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P,
! 285: $ LWORK
! 286: DOUBLE PRECISION TOLA, TOLB
! 287: * ..
! 288: * .. Array Arguments ..
! 289: INTEGER IWORK( * )
! 290: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
! 291: $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * )
! 292: * ..
! 293: *
! 294: * =====================================================================
! 295: *
! 296: * .. Parameters ..
! 297: DOUBLE PRECISION ZERO, ONE
! 298: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 299: * ..
! 300: * .. Local Scalars ..
! 301: LOGICAL FORWRD, WANTQ, WANTU, WANTV, LQUERY
! 302: INTEGER I, J, LWKOPT
! 303: * ..
! 304: * .. External Functions ..
! 305: LOGICAL LSAME
! 306: EXTERNAL LSAME
! 307: * ..
! 308: * .. External Subroutines ..
! 309: EXTERNAL DGEQP3, DGEQR2, DGERQ2, DLACPY, DLAPMT,
! 310: $ DLASET, DORG2R, DORM2R, DORMR2, XERBLA
! 311: * ..
! 312: * .. Intrinsic Functions ..
! 313: INTRINSIC ABS, MAX, MIN
! 314: * ..
! 315: * .. Executable Statements ..
! 316: *
! 317: * Test the input parameters
! 318: *
! 319: WANTU = LSAME( JOBU, 'U' )
! 320: WANTV = LSAME( JOBV, 'V' )
! 321: WANTQ = LSAME( JOBQ, 'Q' )
! 322: FORWRD = .TRUE.
! 323: LQUERY = ( LWORK.EQ.-1 )
! 324: LWKOPT = 1
! 325: *
! 326: * Test the input arguments
! 327: *
! 328: INFO = 0
! 329: IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
! 330: INFO = -1
! 331: ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
! 332: INFO = -2
! 333: ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
! 334: INFO = -3
! 335: ELSE IF( M.LT.0 ) THEN
! 336: INFO = -4
! 337: ELSE IF( P.LT.0 ) THEN
! 338: INFO = -5
! 339: ELSE IF( N.LT.0 ) THEN
! 340: INFO = -6
! 341: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 342: INFO = -8
! 343: ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
! 344: INFO = -10
! 345: ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
! 346: INFO = -16
! 347: ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
! 348: INFO = -18
! 349: ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
! 350: INFO = -20
! 351: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
! 352: INFO = -24
! 353: END IF
! 354: *
! 355: * Compute workspace
! 356: *
! 357: IF( INFO.EQ.0 ) THEN
! 358: CALL DGEQP3( P, N, B, LDB, IWORK, TAU, WORK, -1, INFO )
! 359: LWKOPT = INT( WORK ( 1 ) )
! 360: IF( WANTV ) THEN
! 361: LWKOPT = MAX( LWKOPT, P )
! 362: END IF
! 363: LWKOPT = MAX( LWKOPT, MIN( N, P ) )
! 364: LWKOPT = MAX( LWKOPT, M )
! 365: IF( WANTQ ) THEN
! 366: LWKOPT = MAX( LWKOPT, N )
! 367: END IF
! 368: CALL DGEQP3( M, N, A, LDA, IWORK, TAU, WORK, -1, INFO )
! 369: LWKOPT = MAX( LWKOPT, INT( WORK ( 1 ) ) )
! 370: LWKOPT = MAX( 1, LWKOPT )
! 371: WORK( 1 ) = DBLE( LWKOPT )
! 372: END IF
! 373: *
! 374: IF( INFO.NE.0 ) THEN
! 375: CALL XERBLA( 'DGGSVP3', -INFO )
! 376: RETURN
! 377: END IF
! 378: IF( LQUERY ) THEN
! 379: RETURN
! 380: ENDIF
! 381: *
! 382: * QR with column pivoting of B: B*P = V*( S11 S12 )
! 383: * ( 0 0 )
! 384: *
! 385: DO 10 I = 1, N
! 386: IWORK( I ) = 0
! 387: 10 CONTINUE
! 388: CALL DGEQP3( P, N, B, LDB, IWORK, TAU, WORK, LWORK, INFO )
! 389: *
! 390: * Update A := A*P
! 391: *
! 392: CALL DLAPMT( FORWRD, M, N, A, LDA, IWORK )
! 393: *
! 394: * Determine the effective rank of matrix B.
! 395: *
! 396: L = 0
! 397: DO 20 I = 1, MIN( P, N )
! 398: IF( ABS( B( I, I ) ).GT.TOLB )
! 399: $ L = L + 1
! 400: 20 CONTINUE
! 401: *
! 402: IF( WANTV ) THEN
! 403: *
! 404: * Copy the details of V, and form V.
! 405: *
! 406: CALL DLASET( 'Full', P, P, ZERO, ZERO, V, LDV )
! 407: IF( P.GT.1 )
! 408: $ CALL DLACPY( 'Lower', P-1, N, B( 2, 1 ), LDB, V( 2, 1 ),
! 409: $ LDV )
! 410: CALL DORG2R( P, P, MIN( P, N ), V, LDV, TAU, WORK, INFO )
! 411: END IF
! 412: *
! 413: * Clean up B
! 414: *
! 415: DO 40 J = 1, L - 1
! 416: DO 30 I = J + 1, L
! 417: B( I, J ) = ZERO
! 418: 30 CONTINUE
! 419: 40 CONTINUE
! 420: IF( P.GT.L )
! 421: $ CALL DLASET( 'Full', P-L, N, ZERO, ZERO, B( L+1, 1 ), LDB )
! 422: *
! 423: IF( WANTQ ) THEN
! 424: *
! 425: * Set Q = I and Update Q := Q*P
! 426: *
! 427: CALL DLASET( 'Full', N, N, ZERO, ONE, Q, LDQ )
! 428: CALL DLAPMT( FORWRD, N, N, Q, LDQ, IWORK )
! 429: END IF
! 430: *
! 431: IF( P.GE.L .AND. N.NE.L ) THEN
! 432: *
! 433: * RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z
! 434: *
! 435: CALL DGERQ2( L, N, B, LDB, TAU, WORK, INFO )
! 436: *
! 437: * Update A := A*Z**T
! 438: *
! 439: CALL DORMR2( 'Right', 'Transpose', M, N, L, B, LDB, TAU, A,
! 440: $ LDA, WORK, INFO )
! 441: *
! 442: IF( WANTQ ) THEN
! 443: *
! 444: * Update Q := Q*Z**T
! 445: *
! 446: CALL DORMR2( 'Right', 'Transpose', N, N, L, B, LDB, TAU, Q,
! 447: $ LDQ, WORK, INFO )
! 448: END IF
! 449: *
! 450: * Clean up B
! 451: *
! 452: CALL DLASET( 'Full', L, N-L, ZERO, ZERO, B, LDB )
! 453: DO 60 J = N - L + 1, N
! 454: DO 50 I = J - N + L + 1, L
! 455: B( I, J ) = ZERO
! 456: 50 CONTINUE
! 457: 60 CONTINUE
! 458: *
! 459: END IF
! 460: *
! 461: * Let N-L L
! 462: * A = ( A11 A12 ) M,
! 463: *
! 464: * then the following does the complete QR decomposition of A11:
! 465: *
! 466: * A11 = U*( 0 T12 )*P1**T
! 467: * ( 0 0 )
! 468: *
! 469: DO 70 I = 1, N - L
! 470: IWORK( I ) = 0
! 471: 70 CONTINUE
! 472: CALL DGEQP3( M, N-L, A, LDA, IWORK, TAU, WORK, LWORK, INFO )
! 473: *
! 474: * Determine the effective rank of A11
! 475: *
! 476: K = 0
! 477: DO 80 I = 1, MIN( M, N-L )
! 478: IF( ABS( A( I, I ) ).GT.TOLA )
! 479: $ K = K + 1
! 480: 80 CONTINUE
! 481: *
! 482: * Update A12 := U**T*A12, where A12 = A( 1:M, N-L+1:N )
! 483: *
! 484: CALL DORM2R( 'Left', 'Transpose', M, L, MIN( M, N-L ), A, LDA,
! 485: $ TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
! 486: *
! 487: IF( WANTU ) THEN
! 488: *
! 489: * Copy the details of U, and form U
! 490: *
! 491: CALL DLASET( 'Full', M, M, ZERO, ZERO, U, LDU )
! 492: IF( M.GT.1 )
! 493: $ CALL DLACPY( 'Lower', M-1, N-L, A( 2, 1 ), LDA, U( 2, 1 ),
! 494: $ LDU )
! 495: CALL DORG2R( M, M, MIN( M, N-L ), U, LDU, TAU, WORK, INFO )
! 496: END IF
! 497: *
! 498: IF( WANTQ ) THEN
! 499: *
! 500: * Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1
! 501: *
! 502: CALL DLAPMT( FORWRD, N, N-L, Q, LDQ, IWORK )
! 503: END IF
! 504: *
! 505: * Clean up A: set the strictly lower triangular part of
! 506: * A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0.
! 507: *
! 508: DO 100 J = 1, K - 1
! 509: DO 90 I = J + 1, K
! 510: A( I, J ) = ZERO
! 511: 90 CONTINUE
! 512: 100 CONTINUE
! 513: IF( M.GT.K )
! 514: $ CALL DLASET( 'Full', M-K, N-L, ZERO, ZERO, A( K+1, 1 ), LDA )
! 515: *
! 516: IF( N-L.GT.K ) THEN
! 517: *
! 518: * RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1
! 519: *
! 520: CALL DGERQ2( K, N-L, A, LDA, TAU, WORK, INFO )
! 521: *
! 522: IF( WANTQ ) THEN
! 523: *
! 524: * Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**T
! 525: *
! 526: CALL DORMR2( 'Right', 'Transpose', N, N-L, K, A, LDA, TAU,
! 527: $ Q, LDQ, WORK, INFO )
! 528: END IF
! 529: *
! 530: * Clean up A
! 531: *
! 532: CALL DLASET( 'Full', K, N-L-K, ZERO, ZERO, A, LDA )
! 533: DO 120 J = N - L - K + 1, N - L
! 534: DO 110 I = J - N + L + K + 1, K
! 535: A( I, J ) = ZERO
! 536: 110 CONTINUE
! 537: 120 CONTINUE
! 538: *
! 539: END IF
! 540: *
! 541: IF( M.GT.K ) THEN
! 542: *
! 543: * QR factorization of A( K+1:M,N-L+1:N )
! 544: *
! 545: CALL DGEQR2( M-K, L, A( K+1, N-L+1 ), LDA, TAU, WORK, INFO )
! 546: *
! 547: IF( WANTU ) THEN
! 548: *
! 549: * Update U(:,K+1:M) := U(:,K+1:M)*U1
! 550: *
! 551: CALL DORM2R( 'Right', 'No transpose', M, M-K, MIN( M-K, L ),
! 552: $ A( K+1, N-L+1 ), LDA, TAU, U( 1, K+1 ), LDU,
! 553: $ WORK, INFO )
! 554: END IF
! 555: *
! 556: * Clean up
! 557: *
! 558: DO 140 J = N - L + 1, N
! 559: DO 130 I = J - N + K + L + 1, M
! 560: A( I, J ) = ZERO
! 561: 130 CONTINUE
! 562: 140 CONTINUE
! 563: *
! 564: END IF
! 565: *
! 566: WORK( 1 ) = DBLE( LWKOPT )
! 567: RETURN
! 568: *
! 569: * End of DGGSVP3
! 570: *
! 571: END
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