LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztgsja.f
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00001 *> \brief \b ZTGSJA
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZTGSJA + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgsja.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
00022 *                          LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
00023 *                          Q, LDQ, WORK, NCYCLE, INFO )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          JOBQ, JOBU, JOBV
00027 *       INTEGER            INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
00028 *      $                   NCYCLE, P
00029 *       DOUBLE PRECISION   TOLA, TOLB
00030 *       ..
00031 *       .. Array Arguments ..
00032 *       DOUBLE PRECISION   ALPHA( * ), BETA( * )
00033 *       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
00034 *      $                   U( LDU, * ), V( LDV, * ), WORK( * )
00035 *       ..
00036 *  
00037 *
00038 *> \par Purpose:
00039 *  =============
00040 *>
00041 *> \verbatim
00042 *>
00043 *> ZTGSJA computes the generalized singular value decomposition (GSVD)
00044 *> of two complex upper triangular (or trapezoidal) matrices A and B.
00045 *>
00046 *> On entry, it is assumed that matrices A and B have the following
00047 *> forms, which may be obtained by the preprocessing subroutine ZGGSVP
00048 *> from a general M-by-N matrix A and P-by-N matrix B:
00049 *>
00050 *>              N-K-L  K    L
00051 *>    A =    K ( 0    A12  A13 ) if M-K-L >= 0;
00052 *>           L ( 0     0   A23 )
00053 *>       M-K-L ( 0     0    0  )
00054 *>
00055 *>            N-K-L  K    L
00056 *>    A =  K ( 0    A12  A13 ) if M-K-L < 0;
00057 *>       M-K ( 0     0   A23 )
00058 *>
00059 *>            N-K-L  K    L
00060 *>    B =  L ( 0     0   B13 )
00061 *>       P-L ( 0     0    0  )
00062 *>
00063 *> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
00064 *> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
00065 *> otherwise A23 is (M-K)-by-L upper trapezoidal.
00066 *>
00067 *> On exit,
00068 *>
00069 *>        U**H *A*Q = D1*( 0 R ),    V**H *B*Q = D2*( 0 R ),
00070 *>
00071 *> where U, V and Q are unitary matrices.
00072 *> R is a nonsingular upper triangular matrix, and D1
00073 *> and D2 are ``diagonal'' matrices, which are of the following
00074 *> structures:
00075 *>
00076 *> If M-K-L >= 0,
00077 *>
00078 *>                     K  L
00079 *>        D1 =     K ( I  0 )
00080 *>                 L ( 0  C )
00081 *>             M-K-L ( 0  0 )
00082 *>
00083 *>                    K  L
00084 *>        D2 = L   ( 0  S )
00085 *>             P-L ( 0  0 )
00086 *>
00087 *>                N-K-L  K    L
00088 *>   ( 0 R ) = K (  0   R11  R12 ) K
00089 *>             L (  0    0   R22 ) L
00090 *>
00091 *> where
00092 *>
00093 *>   C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
00094 *>   S = diag( BETA(K+1),  ... , BETA(K+L) ),
00095 *>   C**2 + S**2 = I.
00096 *>
00097 *>   R is stored in A(1:K+L,N-K-L+1:N) on exit.
00098 *>
00099 *> If M-K-L < 0,
00100 *>
00101 *>                K M-K K+L-M
00102 *>     D1 =   K ( I  0    0   )
00103 *>          M-K ( 0  C    0   )
00104 *>
00105 *>                  K M-K K+L-M
00106 *>     D2 =   M-K ( 0  S    0   )
00107 *>          K+L-M ( 0  0    I   )
00108 *>            P-L ( 0  0    0   )
00109 *>
00110 *>                N-K-L  K   M-K  K+L-M
00111 *> ( 0 R ) =    K ( 0    R11  R12  R13  )
00112 *>           M-K ( 0     0   R22  R23  )
00113 *>         K+L-M ( 0     0    0   R33  )
00114 *>
00115 *> where
00116 *> C = diag( ALPHA(K+1), ... , ALPHA(M) ),
00117 *> S = diag( BETA(K+1),  ... , BETA(M) ),
00118 *> C**2 + S**2 = I.
00119 *>
00120 *> R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored
00121 *>     (  0  R22 R23 )
00122 *> in B(M-K+1:L,N+M-K-L+1:N) on exit.
00123 *>
00124 *> The computation of the unitary transformation matrices U, V or Q
00125 *> is optional.  These matrices may either be formed explicitly, or they
00126 *> may be postmultiplied into input matrices U1, V1, or Q1.
00127 *> \endverbatim
00128 *
00129 *  Arguments:
00130 *  ==========
00131 *
00132 *> \param[in] JOBU
00133 *> \verbatim
00134 *>          JOBU is CHARACTER*1
00135 *>          = 'U':  U must contain a unitary matrix U1 on entry, and
00136 *>                  the product U1*U is returned;
00137 *>          = 'I':  U is initialized to the unit matrix, and the
00138 *>                  unitary matrix U is returned;
00139 *>          = 'N':  U is not computed.
00140 *> \endverbatim
00141 *>
00142 *> \param[in] JOBV
00143 *> \verbatim
00144 *>          JOBV is CHARACTER*1
00145 *>          = 'V':  V must contain a unitary matrix V1 on entry, and
00146 *>                  the product V1*V is returned;
00147 *>          = 'I':  V is initialized to the unit matrix, and the
00148 *>                  unitary matrix V is returned;
00149 *>          = 'N':  V is not computed.
00150 *> \endverbatim
00151 *>
00152 *> \param[in] JOBQ
00153 *> \verbatim
00154 *>          JOBQ is CHARACTER*1
00155 *>          = 'Q':  Q must contain a unitary matrix Q1 on entry, and
00156 *>                  the product Q1*Q is returned;
00157 *>          = 'I':  Q is initialized to the unit matrix, and the
00158 *>                  unitary matrix Q is returned;
00159 *>          = 'N':  Q is not computed.
00160 *> \endverbatim
00161 *>
00162 *> \param[in] M
00163 *> \verbatim
00164 *>          M is INTEGER
00165 *>          The number of rows of the matrix A.  M >= 0.
00166 *> \endverbatim
00167 *>
00168 *> \param[in] P
00169 *> \verbatim
00170 *>          P is INTEGER
00171 *>          The number of rows of the matrix B.  P >= 0.
00172 *> \endverbatim
00173 *>
00174 *> \param[in] N
00175 *> \verbatim
00176 *>          N is INTEGER
00177 *>          The number of columns of the matrices A and B.  N >= 0.
00178 *> \endverbatim
00179 *>
00180 *> \param[in] K
00181 *> \verbatim
00182 *>          K is INTEGER
00183 *> \endverbatim
00184 *>
00185 *> \param[in] L
00186 *> \verbatim
00187 *>          L is INTEGER
00188 *>
00189 *>          K and L specify the subblocks in the input matrices A and B:
00190 *>          A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N)
00191 *>          of A and B, whose GSVD is going to be computed by ZTGSJA.
00192 *>          See Further Details.
00193 *> \endverbatim
00194 *>
00195 *> \param[in,out] A
00196 *> \verbatim
00197 *>          A is COMPLEX*16 array, dimension (LDA,N)
00198 *>          On entry, the M-by-N matrix A.
00199 *>          On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular
00200 *>          matrix R or part of R.  See Purpose for details.
00201 *> \endverbatim
00202 *>
00203 *> \param[in] LDA
00204 *> \verbatim
00205 *>          LDA is INTEGER
00206 *>          The leading dimension of the array A. LDA >= max(1,M).
00207 *> \endverbatim
00208 *>
00209 *> \param[in,out] B
00210 *> \verbatim
00211 *>          B is COMPLEX*16 array, dimension (LDB,N)
00212 *>          On entry, the P-by-N matrix B.
00213 *>          On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains
00214 *>          a part of R.  See Purpose for details.
00215 *> \endverbatim
00216 *>
00217 *> \param[in] LDB
00218 *> \verbatim
00219 *>          LDB is INTEGER
00220 *>          The leading dimension of the array B. LDB >= max(1,P).
00221 *> \endverbatim
00222 *>
00223 *> \param[in] TOLA
00224 *> \verbatim
00225 *>          TOLA is DOUBLE PRECISION
00226 *> \endverbatim
00227 *>
00228 *> \param[in] TOLB
00229 *> \verbatim
00230 *>          TOLB is DOUBLE PRECISION
00231 *>
00232 *>          TOLA and TOLB are the convergence criteria for the Jacobi-
00233 *>          Kogbetliantz iteration procedure. Generally, they are the
00234 *>          same as used in the preprocessing step, say
00235 *>              TOLA = MAX(M,N)*norm(A)*MAZHEPS,
00236 *>              TOLB = MAX(P,N)*norm(B)*MAZHEPS.
00237 *> \endverbatim
00238 *>
00239 *> \param[out] ALPHA
00240 *> \verbatim
00241 *>          ALPHA is DOUBLE PRECISION array, dimension (N)
00242 *> \endverbatim
00243 *>
00244 *> \param[out] BETA
00245 *> \verbatim
00246 *>          BETA is DOUBLE PRECISION array, dimension (N)
00247 *>
00248 *>          On exit, ALPHA and BETA contain the generalized singular
00249 *>          value pairs of A and B;
00250 *>            ALPHA(1:K) = 1,
00251 *>            BETA(1:K)  = 0,
00252 *>          and if M-K-L >= 0,
00253 *>            ALPHA(K+1:K+L) = diag(C),
00254 *>            BETA(K+1:K+L)  = diag(S),
00255 *>          or if M-K-L < 0,
00256 *>            ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0
00257 *>            BETA(K+1:M) = S, BETA(M+1:K+L) = 1.
00258 *>          Furthermore, if K+L < N,
00259 *>            ALPHA(K+L+1:N) = 0 and
00260 *>            BETA(K+L+1:N)  = 0.
00261 *> \endverbatim
00262 *>
00263 *> \param[in,out] U
00264 *> \verbatim
00265 *>          U is COMPLEX*16 array, dimension (LDU,M)
00266 *>          On entry, if JOBU = 'U', U must contain a matrix U1 (usually
00267 *>          the unitary matrix returned by ZGGSVP).
00268 *>          On exit,
00269 *>          if JOBU = 'I', U contains the unitary matrix U;
00270 *>          if JOBU = 'U', U contains the product U1*U.
00271 *>          If JOBU = 'N', U is not referenced.
00272 *> \endverbatim
00273 *>
00274 *> \param[in] LDU
00275 *> \verbatim
00276 *>          LDU is INTEGER
00277 *>          The leading dimension of the array U. LDU >= max(1,M) if
00278 *>          JOBU = 'U'; LDU >= 1 otherwise.
00279 *> \endverbatim
00280 *>
00281 *> \param[in,out] V
00282 *> \verbatim
00283 *>          V is COMPLEX*16 array, dimension (LDV,P)
00284 *>          On entry, if JOBV = 'V', V must contain a matrix V1 (usually
00285 *>          the unitary matrix returned by ZGGSVP).
00286 *>          On exit,
00287 *>          if JOBV = 'I', V contains the unitary matrix V;
00288 *>          if JOBV = 'V', V contains the product V1*V.
00289 *>          If JOBV = 'N', V is not referenced.
00290 *> \endverbatim
00291 *>
00292 *> \param[in] LDV
00293 *> \verbatim
00294 *>          LDV is INTEGER
00295 *>          The leading dimension of the array V. LDV >= max(1,P) if
00296 *>          JOBV = 'V'; LDV >= 1 otherwise.
00297 *> \endverbatim
00298 *>
00299 *> \param[in,out] Q
00300 *> \verbatim
00301 *>          Q is COMPLEX*16 array, dimension (LDQ,N)
00302 *>          On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually
00303 *>          the unitary matrix returned by ZGGSVP).
00304 *>          On exit,
00305 *>          if JOBQ = 'I', Q contains the unitary matrix Q;
00306 *>          if JOBQ = 'Q', Q contains the product Q1*Q.
00307 *>          If JOBQ = 'N', Q is not referenced.
00308 *> \endverbatim
00309 *>
00310 *> \param[in] LDQ
00311 *> \verbatim
00312 *>          LDQ is INTEGER
00313 *>          The leading dimension of the array Q. LDQ >= max(1,N) if
00314 *>          JOBQ = 'Q'; LDQ >= 1 otherwise.
00315 *> \endverbatim
00316 *>
00317 *> \param[out] WORK
00318 *> \verbatim
00319 *>          WORK is COMPLEX*16 array, dimension (2*N)
00320 *> \endverbatim
00321 *>
00322 *> \param[out] NCYCLE
00323 *> \verbatim
00324 *>          NCYCLE is INTEGER
00325 *>          The number of cycles required for convergence.
00326 *> \endverbatim
00327 *>
00328 *> \param[out] INFO
00329 *> \verbatim
00330 *>          INFO is INTEGER
00331 *>          = 0:  successful exit
00332 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
00333 *>          = 1:  the procedure does not converge after MAXIT cycles.
00334 *> \endverbatim
00335 *
00336 *> \par Internal Parameters:
00337 *  =========================
00338 *>
00339 *> \verbatim
00340 *>  MAXIT   INTEGER
00341 *>          MAXIT specifies the total loops that the iterative procedure
00342 *>          may take. If after MAXIT cycles, the routine fails to
00343 *>          converge, we return INFO = 1.
00344 *> \endverbatim
00345 *
00346 *  Authors:
00347 *  ========
00348 *
00349 *> \author Univ. of Tennessee 
00350 *> \author Univ. of California Berkeley 
00351 *> \author Univ. of Colorado Denver 
00352 *> \author NAG Ltd. 
00353 *
00354 *> \date November 2011
00355 *
00356 *> \ingroup complex16OTHERcomputational
00357 *
00358 *> \par Further Details:
00359 *  =====================
00360 *>
00361 *> \verbatim
00362 *>
00363 *>  ZTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
00364 *>  min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
00365 *>  matrix B13 to the form:
00366 *>
00367 *>           U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1,
00368 *>
00369 *>  where U1, V1 and Q1 are unitary matrix.
00370 *>  C1 and S1 are diagonal matrices satisfying
00371 *>
00372 *>                C1**2 + S1**2 = I,
00373 *>
00374 *>  and R1 is an L-by-L nonsingular upper triangular matrix.
00375 *> \endverbatim
00376 *>
00377 *  =====================================================================
00378       SUBROUTINE ZTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
00379      $                   LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
00380      $                   Q, LDQ, WORK, NCYCLE, INFO )
00381 *
00382 *  -- LAPACK computational routine (version 3.4.0) --
00383 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00384 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00385 *     November 2011
00386 *
00387 *     .. Scalar Arguments ..
00388       CHARACTER          JOBQ, JOBU, JOBV
00389       INTEGER            INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
00390      $                   NCYCLE, P
00391       DOUBLE PRECISION   TOLA, TOLB
00392 *     ..
00393 *     .. Array Arguments ..
00394       DOUBLE PRECISION   ALPHA( * ), BETA( * )
00395       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
00396      $                   U( LDU, * ), V( LDV, * ), WORK( * )
00397 *     ..
00398 *
00399 *  =====================================================================
00400 *
00401 *     .. Parameters ..
00402       INTEGER            MAXIT
00403       PARAMETER          ( MAXIT = 40 )
00404       DOUBLE PRECISION   ZERO, ONE
00405       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00406       COMPLEX*16         CZERO, CONE
00407       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ),
00408      $                   CONE = ( 1.0D+0, 0.0D+0 ) )
00409 *     ..
00410 *     .. Local Scalars ..
00411 *
00412       LOGICAL            INITQ, INITU, INITV, UPPER, WANTQ, WANTU, WANTV
00413       INTEGER            I, J, KCYCLE
00414       DOUBLE PRECISION   A1, A3, B1, B3, CSQ, CSU, CSV, ERROR, GAMMA,
00415      $                   RWK, SSMIN
00416       COMPLEX*16         A2, B2, SNQ, SNU, SNV
00417 *     ..
00418 *     .. External Functions ..
00419       LOGICAL            LSAME
00420       EXTERNAL           LSAME
00421 *     ..
00422 *     .. External Subroutines ..
00423       EXTERNAL           DLARTG, XERBLA, ZCOPY, ZDSCAL, ZLAGS2, ZLAPLL,
00424      $                   ZLASET, ZROT
00425 *     ..
00426 *     .. Intrinsic Functions ..
00427       INTRINSIC          ABS, DBLE, DCONJG, MAX, MIN
00428 *     ..
00429 *     .. Executable Statements ..
00430 *
00431 *     Decode and test the input parameters
00432 *
00433       INITU = LSAME( JOBU, 'I' )
00434       WANTU = INITU .OR. LSAME( JOBU, 'U' )
00435 *
00436       INITV = LSAME( JOBV, 'I' )
00437       WANTV = INITV .OR. LSAME( JOBV, 'V' )
00438 *
00439       INITQ = LSAME( JOBQ, 'I' )
00440       WANTQ = INITQ .OR. LSAME( JOBQ, 'Q' )
00441 *
00442       INFO = 0
00443       IF( .NOT.( INITU .OR. WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
00444          INFO = -1
00445       ELSE IF( .NOT.( INITV .OR. WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
00446          INFO = -2
00447       ELSE IF( .NOT.( INITQ .OR. WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
00448          INFO = -3
00449       ELSE IF( M.LT.0 ) THEN
00450          INFO = -4
00451       ELSE IF( P.LT.0 ) THEN
00452          INFO = -5
00453       ELSE IF( N.LT.0 ) THEN
00454          INFO = -6
00455       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00456          INFO = -10
00457       ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
00458          INFO = -12
00459       ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
00460          INFO = -18
00461       ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
00462          INFO = -20
00463       ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
00464          INFO = -22
00465       END IF
00466       IF( INFO.NE.0 ) THEN
00467          CALL XERBLA( 'ZTGSJA', -INFO )
00468          RETURN
00469       END IF
00470 *
00471 *     Initialize U, V and Q, if necessary
00472 *
00473       IF( INITU )
00474      $   CALL ZLASET( 'Full', M, M, CZERO, CONE, U, LDU )
00475       IF( INITV )
00476      $   CALL ZLASET( 'Full', P, P, CZERO, CONE, V, LDV )
00477       IF( INITQ )
00478      $   CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDQ )
00479 *
00480 *     Loop until convergence
00481 *
00482       UPPER = .FALSE.
00483       DO 40 KCYCLE = 1, MAXIT
00484 *
00485          UPPER = .NOT.UPPER
00486 *
00487          DO 20 I = 1, L - 1
00488             DO 10 J = I + 1, L
00489 *
00490                A1 = ZERO
00491                A2 = CZERO
00492                A3 = ZERO
00493                IF( K+I.LE.M )
00494      $            A1 = DBLE( A( K+I, N-L+I ) )
00495                IF( K+J.LE.M )
00496      $            A3 = DBLE( A( K+J, N-L+J ) )
00497 *
00498                B1 = DBLE( B( I, N-L+I ) )
00499                B3 = DBLE( B( J, N-L+J ) )
00500 *
00501                IF( UPPER ) THEN
00502                   IF( K+I.LE.M )
00503      $               A2 = A( K+I, N-L+J )
00504                   B2 = B( I, N-L+J )
00505                ELSE
00506                   IF( K+J.LE.M )
00507      $               A2 = A( K+J, N-L+I )
00508                   B2 = B( J, N-L+I )
00509                END IF
00510 *
00511                CALL ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
00512      $                      CSV, SNV, CSQ, SNQ )
00513 *
00514 *              Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A
00515 *
00516                IF( K+J.LE.M )
00517      $            CALL ZROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
00518      $                       LDA, CSU, DCONJG( SNU ) )
00519 *
00520 *              Update I-th and J-th rows of matrix B: V**H *B
00521 *
00522                CALL ZROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
00523      $                    CSV, DCONJG( SNV ) )
00524 *
00525 *              Update (N-L+I)-th and (N-L+J)-th columns of matrices
00526 *              A and B: A*Q and B*Q
00527 *
00528                CALL ZROT( MIN( K+L, M ), A( 1, N-L+J ), 1,
00529      $                    A( 1, N-L+I ), 1, CSQ, SNQ )
00530 *
00531                CALL ZROT( L, B( 1, N-L+J ), 1, B( 1, N-L+I ), 1, CSQ,
00532      $                    SNQ )
00533 *
00534                IF( UPPER ) THEN
00535                   IF( K+I.LE.M )
00536      $               A( K+I, N-L+J ) = CZERO
00537                   B( I, N-L+J ) = CZERO
00538                ELSE
00539                   IF( K+J.LE.M )
00540      $               A( K+J, N-L+I ) = CZERO
00541                   B( J, N-L+I ) = CZERO
00542                END IF
00543 *
00544 *              Ensure that the diagonal elements of A and B are real.
00545 *
00546                IF( K+I.LE.M )
00547      $            A( K+I, N-L+I ) = DBLE( A( K+I, N-L+I ) )
00548                IF( K+J.LE.M )
00549      $            A( K+J, N-L+J ) = DBLE( A( K+J, N-L+J ) )
00550                B( I, N-L+I ) = DBLE( B( I, N-L+I ) )
00551                B( J, N-L+J ) = DBLE( B( J, N-L+J ) )
00552 *
00553 *              Update unitary matrices U, V, Q, if desired.
00554 *
00555                IF( WANTU .AND. K+J.LE.M )
00556      $            CALL ZROT( M, U( 1, K+J ), 1, U( 1, K+I ), 1, CSU,
00557      $                       SNU )
00558 *
00559                IF( WANTV )
00560      $            CALL ZROT( P, V( 1, J ), 1, V( 1, I ), 1, CSV, SNV )
00561 *
00562                IF( WANTQ )
00563      $            CALL ZROT( N, Q( 1, N-L+J ), 1, Q( 1, N-L+I ), 1, CSQ,
00564      $                       SNQ )
00565 *
00566    10       CONTINUE
00567    20    CONTINUE
00568 *
00569          IF( .NOT.UPPER ) THEN
00570 *
00571 *           The matrices A13 and B13 were lower triangular at the start
00572 *           of the cycle, and are now upper triangular.
00573 *
00574 *           Convergence test: test the parallelism of the corresponding
00575 *           rows of A and B.
00576 *
00577             ERROR = ZERO
00578             DO 30 I = 1, MIN( L, M-K )
00579                CALL ZCOPY( L-I+1, A( K+I, N-L+I ), LDA, WORK, 1 )
00580                CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, WORK( L+1 ), 1 )
00581                CALL ZLAPLL( L-I+1, WORK, 1, WORK( L+1 ), 1, SSMIN )
00582                ERROR = MAX( ERROR, SSMIN )
00583    30       CONTINUE
00584 *
00585             IF( ABS( ERROR ).LE.MIN( TOLA, TOLB ) )
00586      $         GO TO 50
00587          END IF
00588 *
00589 *        End of cycle loop
00590 *
00591    40 CONTINUE
00592 *
00593 *     The algorithm has not converged after MAXIT cycles.
00594 *
00595       INFO = 1
00596       GO TO 100
00597 *
00598    50 CONTINUE
00599 *
00600 *     If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged.
00601 *     Compute the generalized singular value pairs (ALPHA, BETA), and
00602 *     set the triangular matrix R to array A.
00603 *
00604       DO 60 I = 1, K
00605          ALPHA( I ) = ONE
00606          BETA( I ) = ZERO
00607    60 CONTINUE
00608 *
00609       DO 70 I = 1, MIN( L, M-K )
00610 *
00611          A1 = DBLE( A( K+I, N-L+I ) )
00612          B1 = DBLE( B( I, N-L+I ) )
00613 *
00614          IF( A1.NE.ZERO ) THEN
00615             GAMMA = B1 / A1
00616 *
00617             IF( GAMMA.LT.ZERO ) THEN
00618                CALL ZDSCAL( L-I+1, -ONE, B( I, N-L+I ), LDB )
00619                IF( WANTV )
00620      $            CALL ZDSCAL( P, -ONE, V( 1, I ), 1 )
00621             END IF
00622 *
00623             CALL DLARTG( ABS( GAMMA ), ONE, BETA( K+I ), ALPHA( K+I ),
00624      $                   RWK )
00625 *
00626             IF( ALPHA( K+I ).GE.BETA( K+I ) ) THEN
00627                CALL ZDSCAL( L-I+1, ONE / ALPHA( K+I ), A( K+I, N-L+I ),
00628      $                      LDA )
00629             ELSE
00630                CALL ZDSCAL( L-I+1, ONE / BETA( K+I ), B( I, N-L+I ),
00631      $                      LDB )
00632                CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
00633      $                     LDA )
00634             END IF
00635 *
00636          ELSE
00637 *
00638             ALPHA( K+I ) = ZERO
00639             BETA( K+I ) = ONE
00640             CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
00641      $                  LDA )
00642          END IF
00643    70 CONTINUE
00644 *
00645 *     Post-assignment
00646 *
00647       DO 80 I = M + 1, K + L
00648          ALPHA( I ) = ZERO
00649          BETA( I ) = ONE
00650    80 CONTINUE
00651 *
00652       IF( K+L.LT.N ) THEN
00653          DO 90 I = K + L + 1, N
00654             ALPHA( I ) = ZERO
00655             BETA( I ) = ZERO
00656    90    CONTINUE
00657       END IF
00658 *
00659   100 CONTINUE
00660       NCYCLE = KCYCLE
00661 *
00662       RETURN
00663 *
00664 *     End of ZTGSJA
00665 *
00666       END
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