Annotation of rpl/lapack/lapack/ztgsja.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZTGSJA
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZTGSJA + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgsja.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgsja.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgsja.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
! 22: * LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
! 23: * Q, LDQ, WORK, NCYCLE, INFO )
! 24: *
! 25: * .. Scalar Arguments ..
! 26: * CHARACTER JOBQ, JOBU, JOBV
! 27: * INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
! 28: * $ NCYCLE, P
! 29: * DOUBLE PRECISION TOLA, TOLB
! 30: * ..
! 31: * .. Array Arguments ..
! 32: * DOUBLE PRECISION ALPHA( * ), BETA( * )
! 33: * COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
! 34: * $ U( LDU, * ), V( LDV, * ), WORK( * )
! 35: * ..
! 36: *
! 37: *
! 38: *> \par Purpose:
! 39: * =============
! 40: *>
! 41: *> \verbatim
! 42: *>
! 43: *> ZTGSJA computes the generalized singular value decomposition (GSVD)
! 44: *> of two complex upper triangular (or trapezoidal) matrices A and B.
! 45: *>
! 46: *> On entry, it is assumed that matrices A and B have the following
! 47: *> forms, which may be obtained by the preprocessing subroutine ZGGSVP
! 48: *> from a general M-by-N matrix A and P-by-N matrix B:
! 49: *>
! 50: *> N-K-L K L
! 51: *> A = K ( 0 A12 A13 ) if M-K-L >= 0;
! 52: *> L ( 0 0 A23 )
! 53: *> M-K-L ( 0 0 0 )
! 54: *>
! 55: *> N-K-L K L
! 56: *> A = K ( 0 A12 A13 ) if M-K-L < 0;
! 57: *> M-K ( 0 0 A23 )
! 58: *>
! 59: *> N-K-L K L
! 60: *> B = L ( 0 0 B13 )
! 61: *> P-L ( 0 0 0 )
! 62: *>
! 63: *> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
! 64: *> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
! 65: *> otherwise A23 is (M-K)-by-L upper trapezoidal.
! 66: *>
! 67: *> On exit,
! 68: *>
! 69: *> U**H *A*Q = D1*( 0 R ), V**H *B*Q = D2*( 0 R ),
! 70: *>
! 71: *> where U, V and Q are unitary matrices.
! 72: *> R is a nonsingular upper triangular matrix, and D1
! 73: *> and D2 are ``diagonal'' matrices, which are of the following
! 74: *> structures:
! 75: *>
! 76: *> If M-K-L >= 0,
! 77: *>
! 78: *> K L
! 79: *> D1 = K ( I 0 )
! 80: *> L ( 0 C )
! 81: *> M-K-L ( 0 0 )
! 82: *>
! 83: *> K L
! 84: *> D2 = L ( 0 S )
! 85: *> P-L ( 0 0 )
! 86: *>
! 87: *> N-K-L K L
! 88: *> ( 0 R ) = K ( 0 R11 R12 ) K
! 89: *> L ( 0 0 R22 ) L
! 90: *>
! 91: *> where
! 92: *>
! 93: *> C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
! 94: *> S = diag( BETA(K+1), ... , BETA(K+L) ),
! 95: *> C**2 + S**2 = I.
! 96: *>
! 97: *> R is stored in A(1:K+L,N-K-L+1:N) on exit.
! 98: *>
! 99: *> If M-K-L < 0,
! 100: *>
! 101: *> K M-K K+L-M
! 102: *> D1 = K ( I 0 0 )
! 103: *> M-K ( 0 C 0 )
! 104: *>
! 105: *> K M-K K+L-M
! 106: *> D2 = M-K ( 0 S 0 )
! 107: *> K+L-M ( 0 0 I )
! 108: *> P-L ( 0 0 0 )
! 109: *>
! 110: *> N-K-L K M-K K+L-M
! 111: *> ( 0 R ) = K ( 0 R11 R12 R13 )
! 112: *> M-K ( 0 0 R22 R23 )
! 113: *> K+L-M ( 0 0 0 R33 )
! 114: *>
! 115: *> where
! 116: *> C = diag( ALPHA(K+1), ... , ALPHA(M) ),
! 117: *> S = diag( BETA(K+1), ... , BETA(M) ),
! 118: *> C**2 + S**2 = I.
! 119: *>
! 120: *> R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored
! 121: *> ( 0 R22 R23 )
! 122: *> in B(M-K+1:L,N+M-K-L+1:N) on exit.
! 123: *>
! 124: *> The computation of the unitary transformation matrices U, V or Q
! 125: *> is optional. These matrices may either be formed explicitly, or they
! 126: *> may be postmultiplied into input matrices U1, V1, or Q1.
! 127: *> \endverbatim
! 128: *
! 129: * Arguments:
! 130: * ==========
! 131: *
! 132: *> \param[in] JOBU
! 133: *> \verbatim
! 134: *> JOBU is CHARACTER*1
! 135: *> = 'U': U must contain a unitary matrix U1 on entry, and
! 136: *> the product U1*U is returned;
! 137: *> = 'I': U is initialized to the unit matrix, and the
! 138: *> unitary matrix U is returned;
! 139: *> = 'N': U is not computed.
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] JOBV
! 143: *> \verbatim
! 144: *> JOBV is CHARACTER*1
! 145: *> = 'V': V must contain a unitary matrix V1 on entry, and
! 146: *> the product V1*V is returned;
! 147: *> = 'I': V is initialized to the unit matrix, and the
! 148: *> unitary matrix V is returned;
! 149: *> = 'N': V is not computed.
! 150: *> \endverbatim
! 151: *>
! 152: *> \param[in] JOBQ
! 153: *> \verbatim
! 154: *> JOBQ is CHARACTER*1
! 155: *> = 'Q': Q must contain a unitary matrix Q1 on entry, and
! 156: *> the product Q1*Q is returned;
! 157: *> = 'I': Q is initialized to the unit matrix, and the
! 158: *> unitary matrix Q is returned;
! 159: *> = 'N': Q is not computed.
! 160: *> \endverbatim
! 161: *>
! 162: *> \param[in] M
! 163: *> \verbatim
! 164: *> M is INTEGER
! 165: *> The number of rows of the matrix A. M >= 0.
! 166: *> \endverbatim
! 167: *>
! 168: *> \param[in] P
! 169: *> \verbatim
! 170: *> P is INTEGER
! 171: *> The number of rows of the matrix B. P >= 0.
! 172: *> \endverbatim
! 173: *>
! 174: *> \param[in] N
! 175: *> \verbatim
! 176: *> N is INTEGER
! 177: *> The number of columns of the matrices A and B. N >= 0.
! 178: *> \endverbatim
! 179: *>
! 180: *> \param[in] K
! 181: *> \verbatim
! 182: *> K is INTEGER
! 183: *> \endverbatim
! 184: *>
! 185: *> \param[in] L
! 186: *> \verbatim
! 187: *> L is INTEGER
! 188: *>
! 189: *> K and L specify the subblocks in the input matrices A and B:
! 190: *> A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N)
! 191: *> of A and B, whose GSVD is going to be computed by ZTGSJA.
! 192: *> See Further Details.
! 193: *> \endverbatim
! 194: *>
! 195: *> \param[in,out] A
! 196: *> \verbatim
! 197: *> A is COMPLEX*16 array, dimension (LDA,N)
! 198: *> On entry, the M-by-N matrix A.
! 199: *> On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular
! 200: *> matrix R or part of R. See Purpose for details.
! 201: *> \endverbatim
! 202: *>
! 203: *> \param[in] LDA
! 204: *> \verbatim
! 205: *> LDA is INTEGER
! 206: *> The leading dimension of the array A. LDA >= max(1,M).
! 207: *> \endverbatim
! 208: *>
! 209: *> \param[in,out] B
! 210: *> \verbatim
! 211: *> B is COMPLEX*16 array, dimension (LDB,N)
! 212: *> On entry, the P-by-N matrix B.
! 213: *> On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains
! 214: *> a part of R. See Purpose for details.
! 215: *> \endverbatim
! 216: *>
! 217: *> \param[in] LDB
! 218: *> \verbatim
! 219: *> LDB is INTEGER
! 220: *> The leading dimension of the array B. LDB >= max(1,P).
! 221: *> \endverbatim
! 222: *>
! 223: *> \param[in] TOLA
! 224: *> \verbatim
! 225: *> TOLA is DOUBLE PRECISION
! 226: *> \endverbatim
! 227: *>
! 228: *> \param[in] TOLB
! 229: *> \verbatim
! 230: *> TOLB is DOUBLE PRECISION
! 231: *>
! 232: *> TOLA and TOLB are the convergence criteria for the Jacobi-
! 233: *> Kogbetliantz iteration procedure. Generally, they are the
! 234: *> same as used in the preprocessing step, say
! 235: *> TOLA = MAX(M,N)*norm(A)*MAZHEPS,
! 236: *> TOLB = MAX(P,N)*norm(B)*MAZHEPS.
! 237: *> \endverbatim
! 238: *>
! 239: *> \param[out] ALPHA
! 240: *> \verbatim
! 241: *> ALPHA is DOUBLE PRECISION array, dimension (N)
! 242: *> \endverbatim
! 243: *>
! 244: *> \param[out] BETA
! 245: *> \verbatim
! 246: *> BETA is DOUBLE PRECISION array, dimension (N)
! 247: *>
! 248: *> On exit, ALPHA and BETA contain the generalized singular
! 249: *> value pairs of A and B;
! 250: *> ALPHA(1:K) = 1,
! 251: *> BETA(1:K) = 0,
! 252: *> and if M-K-L >= 0,
! 253: *> ALPHA(K+1:K+L) = diag(C),
! 254: *> BETA(K+1:K+L) = diag(S),
! 255: *> or if M-K-L < 0,
! 256: *> ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0
! 257: *> BETA(K+1:M) = S, BETA(M+1:K+L) = 1.
! 258: *> Furthermore, if K+L < N,
! 259: *> ALPHA(K+L+1:N) = 0 and
! 260: *> BETA(K+L+1:N) = 0.
! 261: *> \endverbatim
! 262: *>
! 263: *> \param[in,out] U
! 264: *> \verbatim
! 265: *> U is COMPLEX*16 array, dimension (LDU,M)
! 266: *> On entry, if JOBU = 'U', U must contain a matrix U1 (usually
! 267: *> the unitary matrix returned by ZGGSVP).
! 268: *> On exit,
! 269: *> if JOBU = 'I', U contains the unitary matrix U;
! 270: *> if JOBU = 'U', U contains the product U1*U.
! 271: *> If JOBU = 'N', U is not referenced.
! 272: *> \endverbatim
! 273: *>
! 274: *> \param[in] LDU
! 275: *> \verbatim
! 276: *> LDU is INTEGER
! 277: *> The leading dimension of the array U. LDU >= max(1,M) if
! 278: *> JOBU = 'U'; LDU >= 1 otherwise.
! 279: *> \endverbatim
! 280: *>
! 281: *> \param[in,out] V
! 282: *> \verbatim
! 283: *> V is COMPLEX*16 array, dimension (LDV,P)
! 284: *> On entry, if JOBV = 'V', V must contain a matrix V1 (usually
! 285: *> the unitary matrix returned by ZGGSVP).
! 286: *> On exit,
! 287: *> if JOBV = 'I', V contains the unitary matrix V;
! 288: *> if JOBV = 'V', V contains the product V1*V.
! 289: *> If JOBV = 'N', V is not referenced.
! 290: *> \endverbatim
! 291: *>
! 292: *> \param[in] LDV
! 293: *> \verbatim
! 294: *> LDV is INTEGER
! 295: *> The leading dimension of the array V. LDV >= max(1,P) if
! 296: *> JOBV = 'V'; LDV >= 1 otherwise.
! 297: *> \endverbatim
! 298: *>
! 299: *> \param[in,out] Q
! 300: *> \verbatim
! 301: *> Q is COMPLEX*16 array, dimension (LDQ,N)
! 302: *> On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually
! 303: *> the unitary matrix returned by ZGGSVP).
! 304: *> On exit,
! 305: *> if JOBQ = 'I', Q contains the unitary matrix Q;
! 306: *> if JOBQ = 'Q', Q contains the product Q1*Q.
! 307: *> If JOBQ = 'N', Q is not referenced.
! 308: *> \endverbatim
! 309: *>
! 310: *> \param[in] LDQ
! 311: *> \verbatim
! 312: *> LDQ is INTEGER
! 313: *> The leading dimension of the array Q. LDQ >= max(1,N) if
! 314: *> JOBQ = 'Q'; LDQ >= 1 otherwise.
! 315: *> \endverbatim
! 316: *>
! 317: *> \param[out] WORK
! 318: *> \verbatim
! 319: *> WORK is COMPLEX*16 array, dimension (2*N)
! 320: *> \endverbatim
! 321: *>
! 322: *> \param[out] NCYCLE
! 323: *> \verbatim
! 324: *> NCYCLE is INTEGER
! 325: *> The number of cycles required for convergence.
! 326: *> \endverbatim
! 327: *>
! 328: *> \param[out] INFO
! 329: *> \verbatim
! 330: *> INFO is INTEGER
! 331: *> = 0: successful exit
! 332: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 333: *> = 1: the procedure does not converge after MAXIT cycles.
! 334: *> \endverbatim
! 335: *
! 336: *> \par Internal Parameters:
! 337: * =========================
! 338: *>
! 339: *> \verbatim
! 340: *> MAXIT INTEGER
! 341: *> MAXIT specifies the total loops that the iterative procedure
! 342: *> may take. If after MAXIT cycles, the routine fails to
! 343: *> converge, we return INFO = 1.
! 344: *> \endverbatim
! 345: *
! 346: * Authors:
! 347: * ========
! 348: *
! 349: *> \author Univ. of Tennessee
! 350: *> \author Univ. of California Berkeley
! 351: *> \author Univ. of Colorado Denver
! 352: *> \author NAG Ltd.
! 353: *
! 354: *> \date November 2011
! 355: *
! 356: *> \ingroup complex16OTHERcomputational
! 357: *
! 358: *> \par Further Details:
! 359: * =====================
! 360: *>
! 361: *> \verbatim
! 362: *>
! 363: *> ZTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
! 364: *> min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
! 365: *> matrix B13 to the form:
! 366: *>
! 367: *> U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1,
! 368: *>
! 369: *> where U1, V1 and Q1 are unitary matrix.
! 370: *> C1 and S1 are diagonal matrices satisfying
! 371: *>
! 372: *> C1**2 + S1**2 = I,
! 373: *>
! 374: *> and R1 is an L-by-L nonsingular upper triangular matrix.
! 375: *> \endverbatim
! 376: *>
! 377: * =====================================================================
1.1 bertrand 378: SUBROUTINE ZTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
379: $ LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
380: $ Q, LDQ, WORK, NCYCLE, INFO )
381: *
1.9 ! bertrand 382: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 383: * -- LAPACK is a software package provided by Univ. of Tennessee, --
384: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 385: * November 2011
1.1 bertrand 386: *
387: * .. Scalar Arguments ..
388: CHARACTER JOBQ, JOBU, JOBV
389: INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
390: $ NCYCLE, P
391: DOUBLE PRECISION TOLA, TOLB
392: * ..
393: * .. Array Arguments ..
394: DOUBLE PRECISION ALPHA( * ), BETA( * )
395: COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
396: $ U( LDU, * ), V( LDV, * ), WORK( * )
397: * ..
398: *
399: * =====================================================================
400: *
401: * .. Parameters ..
402: INTEGER MAXIT
403: PARAMETER ( MAXIT = 40 )
404: DOUBLE PRECISION ZERO, ONE
405: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
406: COMPLEX*16 CZERO, CONE
407: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
408: $ CONE = ( 1.0D+0, 0.0D+0 ) )
409: * ..
410: * .. Local Scalars ..
411: *
412: LOGICAL INITQ, INITU, INITV, UPPER, WANTQ, WANTU, WANTV
413: INTEGER I, J, KCYCLE
414: DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV, ERROR, GAMMA,
415: $ RWK, SSMIN
416: COMPLEX*16 A2, B2, SNQ, SNU, SNV
417: * ..
418: * .. External Functions ..
419: LOGICAL LSAME
420: EXTERNAL LSAME
421: * ..
422: * .. External Subroutines ..
423: EXTERNAL DLARTG, XERBLA, ZCOPY, ZDSCAL, ZLAGS2, ZLAPLL,
424: $ ZLASET, ZROT
425: * ..
426: * .. Intrinsic Functions ..
427: INTRINSIC ABS, DBLE, DCONJG, MAX, MIN
428: * ..
429: * .. Executable Statements ..
430: *
431: * Decode and test the input parameters
432: *
433: INITU = LSAME( JOBU, 'I' )
434: WANTU = INITU .OR. LSAME( JOBU, 'U' )
435: *
436: INITV = LSAME( JOBV, 'I' )
437: WANTV = INITV .OR. LSAME( JOBV, 'V' )
438: *
439: INITQ = LSAME( JOBQ, 'I' )
440: WANTQ = INITQ .OR. LSAME( JOBQ, 'Q' )
441: *
442: INFO = 0
443: IF( .NOT.( INITU .OR. WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
444: INFO = -1
445: ELSE IF( .NOT.( INITV .OR. WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
446: INFO = -2
447: ELSE IF( .NOT.( INITQ .OR. WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
448: INFO = -3
449: ELSE IF( M.LT.0 ) THEN
450: INFO = -4
451: ELSE IF( P.LT.0 ) THEN
452: INFO = -5
453: ELSE IF( N.LT.0 ) THEN
454: INFO = -6
455: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
456: INFO = -10
457: ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
458: INFO = -12
459: ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
460: INFO = -18
461: ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
462: INFO = -20
463: ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
464: INFO = -22
465: END IF
466: IF( INFO.NE.0 ) THEN
467: CALL XERBLA( 'ZTGSJA', -INFO )
468: RETURN
469: END IF
470: *
471: * Initialize U, V and Q, if necessary
472: *
473: IF( INITU )
474: $ CALL ZLASET( 'Full', M, M, CZERO, CONE, U, LDU )
475: IF( INITV )
476: $ CALL ZLASET( 'Full', P, P, CZERO, CONE, V, LDV )
477: IF( INITQ )
478: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDQ )
479: *
480: * Loop until convergence
481: *
482: UPPER = .FALSE.
483: DO 40 KCYCLE = 1, MAXIT
484: *
485: UPPER = .NOT.UPPER
486: *
487: DO 20 I = 1, L - 1
488: DO 10 J = I + 1, L
489: *
490: A1 = ZERO
491: A2 = CZERO
492: A3 = ZERO
493: IF( K+I.LE.M )
494: $ A1 = DBLE( A( K+I, N-L+I ) )
495: IF( K+J.LE.M )
496: $ A3 = DBLE( A( K+J, N-L+J ) )
497: *
498: B1 = DBLE( B( I, N-L+I ) )
499: B3 = DBLE( B( J, N-L+J ) )
500: *
501: IF( UPPER ) THEN
502: IF( K+I.LE.M )
503: $ A2 = A( K+I, N-L+J )
504: B2 = B( I, N-L+J )
505: ELSE
506: IF( K+J.LE.M )
507: $ A2 = A( K+J, N-L+I )
508: B2 = B( J, N-L+I )
509: END IF
510: *
511: CALL ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
512: $ CSV, SNV, CSQ, SNQ )
513: *
1.8 bertrand 514: * Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A
1.1 bertrand 515: *
516: IF( K+J.LE.M )
517: $ CALL ZROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
518: $ LDA, CSU, DCONJG( SNU ) )
519: *
1.8 bertrand 520: * Update I-th and J-th rows of matrix B: V**H *B
1.1 bertrand 521: *
522: CALL ZROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
523: $ CSV, DCONJG( SNV ) )
524: *
525: * Update (N-L+I)-th and (N-L+J)-th columns of matrices
526: * A and B: A*Q and B*Q
527: *
528: CALL ZROT( MIN( K+L, M ), A( 1, N-L+J ), 1,
529: $ A( 1, N-L+I ), 1, CSQ, SNQ )
530: *
531: CALL ZROT( L, B( 1, N-L+J ), 1, B( 1, N-L+I ), 1, CSQ,
532: $ SNQ )
533: *
534: IF( UPPER ) THEN
535: IF( K+I.LE.M )
536: $ A( K+I, N-L+J ) = CZERO
537: B( I, N-L+J ) = CZERO
538: ELSE
539: IF( K+J.LE.M )
540: $ A( K+J, N-L+I ) = CZERO
541: B( J, N-L+I ) = CZERO
542: END IF
543: *
544: * Ensure that the diagonal elements of A and B are real.
545: *
546: IF( K+I.LE.M )
547: $ A( K+I, N-L+I ) = DBLE( A( K+I, N-L+I ) )
548: IF( K+J.LE.M )
549: $ A( K+J, N-L+J ) = DBLE( A( K+J, N-L+J ) )
550: B( I, N-L+I ) = DBLE( B( I, N-L+I ) )
551: B( J, N-L+J ) = DBLE( B( J, N-L+J ) )
552: *
553: * Update unitary matrices U, V, Q, if desired.
554: *
555: IF( WANTU .AND. K+J.LE.M )
556: $ CALL ZROT( M, U( 1, K+J ), 1, U( 1, K+I ), 1, CSU,
557: $ SNU )
558: *
559: IF( WANTV )
560: $ CALL ZROT( P, V( 1, J ), 1, V( 1, I ), 1, CSV, SNV )
561: *
562: IF( WANTQ )
563: $ CALL ZROT( N, Q( 1, N-L+J ), 1, Q( 1, N-L+I ), 1, CSQ,
564: $ SNQ )
565: *
566: 10 CONTINUE
567: 20 CONTINUE
568: *
569: IF( .NOT.UPPER ) THEN
570: *
571: * The matrices A13 and B13 were lower triangular at the start
572: * of the cycle, and are now upper triangular.
573: *
574: * Convergence test: test the parallelism of the corresponding
575: * rows of A and B.
576: *
577: ERROR = ZERO
578: DO 30 I = 1, MIN( L, M-K )
579: CALL ZCOPY( L-I+1, A( K+I, N-L+I ), LDA, WORK, 1 )
580: CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, WORK( L+1 ), 1 )
581: CALL ZLAPLL( L-I+1, WORK, 1, WORK( L+1 ), 1, SSMIN )
582: ERROR = MAX( ERROR, SSMIN )
583: 30 CONTINUE
584: *
585: IF( ABS( ERROR ).LE.MIN( TOLA, TOLB ) )
586: $ GO TO 50
587: END IF
588: *
589: * End of cycle loop
590: *
591: 40 CONTINUE
592: *
593: * The algorithm has not converged after MAXIT cycles.
594: *
595: INFO = 1
596: GO TO 100
597: *
598: 50 CONTINUE
599: *
600: * If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged.
601: * Compute the generalized singular value pairs (ALPHA, BETA), and
602: * set the triangular matrix R to array A.
603: *
604: DO 60 I = 1, K
605: ALPHA( I ) = ONE
606: BETA( I ) = ZERO
607: 60 CONTINUE
608: *
609: DO 70 I = 1, MIN( L, M-K )
610: *
611: A1 = DBLE( A( K+I, N-L+I ) )
612: B1 = DBLE( B( I, N-L+I ) )
613: *
614: IF( A1.NE.ZERO ) THEN
615: GAMMA = B1 / A1
616: *
617: IF( GAMMA.LT.ZERO ) THEN
618: CALL ZDSCAL( L-I+1, -ONE, B( I, N-L+I ), LDB )
619: IF( WANTV )
620: $ CALL ZDSCAL( P, -ONE, V( 1, I ), 1 )
621: END IF
622: *
623: CALL DLARTG( ABS( GAMMA ), ONE, BETA( K+I ), ALPHA( K+I ),
624: $ RWK )
625: *
626: IF( ALPHA( K+I ).GE.BETA( K+I ) ) THEN
627: CALL ZDSCAL( L-I+1, ONE / ALPHA( K+I ), A( K+I, N-L+I ),
628: $ LDA )
629: ELSE
630: CALL ZDSCAL( L-I+1, ONE / BETA( K+I ), B( I, N-L+I ),
631: $ LDB )
632: CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
633: $ LDA )
634: END IF
635: *
636: ELSE
1.8 bertrand 637: *
1.1 bertrand 638: ALPHA( K+I ) = ZERO
639: BETA( K+I ) = ONE
640: CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
641: $ LDA )
642: END IF
643: 70 CONTINUE
644: *
645: * Post-assignment
646: *
647: DO 80 I = M + 1, K + L
648: ALPHA( I ) = ZERO
649: BETA( I ) = ONE
650: 80 CONTINUE
651: *
652: IF( K+L.LT.N ) THEN
653: DO 90 I = K + L + 1, N
654: ALPHA( I ) = ZERO
655: BETA( I ) = ZERO
656: 90 CONTINUE
657: END IF
658: *
659: 100 CONTINUE
660: NCYCLE = KCYCLE
661: *
662: RETURN
663: *
664: * End of ZTGSJA
665: *
666: END
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