Annotation of rpl/lapack/lapack/ztgsja.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
! 2: $ LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
! 3: $ Q, LDQ, WORK, NCYCLE, INFO )
! 4: *
! 5: * -- LAPACK routine (version 3.2.1) --
! 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 2009 --
! 9: *
! 10: * .. Scalar Arguments ..
! 11: CHARACTER JOBQ, JOBU, JOBV
! 12: INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
! 13: $ NCYCLE, P
! 14: DOUBLE PRECISION TOLA, TOLB
! 15: * ..
! 16: * .. Array Arguments ..
! 17: DOUBLE PRECISION ALPHA( * ), BETA( * )
! 18: COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
! 19: $ U( LDU, * ), V( LDV, * ), WORK( * )
! 20: * ..
! 21: *
! 22: * Purpose
! 23: * =======
! 24: *
! 25: * ZTGSJA computes the generalized singular value decomposition (GSVD)
! 26: * of two complex upper triangular (or trapezoidal) matrices A and B.
! 27: *
! 28: * On entry, it is assumed that matrices A and B have the following
! 29: * forms, which may be obtained by the preprocessing subroutine ZGGSVP
! 30: * from a general M-by-N matrix A and P-by-N matrix B:
! 31: *
! 32: * N-K-L K L
! 33: * A = K ( 0 A12 A13 ) if M-K-L >= 0;
! 34: * L ( 0 0 A23 )
! 35: * M-K-L ( 0 0 0 )
! 36: *
! 37: * N-K-L K L
! 38: * A = K ( 0 A12 A13 ) if M-K-L < 0;
! 39: * M-K ( 0 0 A23 )
! 40: *
! 41: * N-K-L K L
! 42: * B = L ( 0 0 B13 )
! 43: * P-L ( 0 0 0 )
! 44: *
! 45: * where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
! 46: * upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
! 47: * otherwise A23 is (M-K)-by-L upper trapezoidal.
! 48: *
! 49: * On exit,
! 50: *
! 51: * U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R ),
! 52: *
! 53: * where U, V and Q are unitary matrices, Z' denotes the conjugate
! 54: * transpose of Z, R is a nonsingular upper triangular matrix, and D1
! 55: * and D2 are ``diagonal'' matrices, which are of the following
! 56: * structures:
! 57: *
! 58: * If M-K-L >= 0,
! 59: *
! 60: * K L
! 61: * D1 = K ( I 0 )
! 62: * L ( 0 C )
! 63: * M-K-L ( 0 0 )
! 64: *
! 65: * K L
! 66: * D2 = L ( 0 S )
! 67: * P-L ( 0 0 )
! 68: *
! 69: * N-K-L K L
! 70: * ( 0 R ) = K ( 0 R11 R12 ) K
! 71: * L ( 0 0 R22 ) L
! 72: *
! 73: * where
! 74: *
! 75: * C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
! 76: * S = diag( BETA(K+1), ... , BETA(K+L) ),
! 77: * C**2 + S**2 = I.
! 78: *
! 79: * R is stored in A(1:K+L,N-K-L+1:N) on exit.
! 80: *
! 81: * If M-K-L < 0,
! 82: *
! 83: * K M-K K+L-M
! 84: * D1 = K ( I 0 0 )
! 85: * M-K ( 0 C 0 )
! 86: *
! 87: * K M-K K+L-M
! 88: * D2 = M-K ( 0 S 0 )
! 89: * K+L-M ( 0 0 I )
! 90: * P-L ( 0 0 0 )
! 91: *
! 92: * N-K-L K M-K K+L-M
! 93: * ( 0 R ) = K ( 0 R11 R12 R13 )
! 94: * M-K ( 0 0 R22 R23 )
! 95: * K+L-M ( 0 0 0 R33 )
! 96: *
! 97: * where
! 98: * C = diag( ALPHA(K+1), ... , ALPHA(M) ),
! 99: * S = diag( BETA(K+1), ... , BETA(M) ),
! 100: * C**2 + S**2 = I.
! 101: *
! 102: * R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored
! 103: * ( 0 R22 R23 )
! 104: * in B(M-K+1:L,N+M-K-L+1:N) on exit.
! 105: *
! 106: * The computation of the unitary transformation matrices U, V or Q
! 107: * is optional. These matrices may either be formed explicitly, or they
! 108: * may be postmultiplied into input matrices U1, V1, or Q1.
! 109: *
! 110: * Arguments
! 111: * =========
! 112: *
! 113: * JOBU (input) CHARACTER*1
! 114: * = 'U': U must contain a unitary matrix U1 on entry, and
! 115: * the product U1*U is returned;
! 116: * = 'I': U is initialized to the unit matrix, and the
! 117: * unitary matrix U is returned;
! 118: * = 'N': U is not computed.
! 119: *
! 120: * JOBV (input) CHARACTER*1
! 121: * = 'V': V must contain a unitary matrix V1 on entry, and
! 122: * the product V1*V is returned;
! 123: * = 'I': V is initialized to the unit matrix, and the
! 124: * unitary matrix V is returned;
! 125: * = 'N': V is not computed.
! 126: *
! 127: * JOBQ (input) CHARACTER*1
! 128: * = 'Q': Q must contain a unitary matrix Q1 on entry, and
! 129: * the product Q1*Q is returned;
! 130: * = 'I': Q is initialized to the unit matrix, and the
! 131: * unitary matrix Q is returned;
! 132: * = 'N': Q is not computed.
! 133: *
! 134: * M (input) INTEGER
! 135: * The number of rows of the matrix A. M >= 0.
! 136: *
! 137: * P (input) INTEGER
! 138: * The number of rows of the matrix B. P >= 0.
! 139: *
! 140: * N (input) INTEGER
! 141: * The number of columns of the matrices A and B. N >= 0.
! 142: *
! 143: * K (input) INTEGER
! 144: * L (input) INTEGER
! 145: * K and L specify the subblocks in the input matrices A and B:
! 146: * A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N)
! 147: * of A and B, whose GSVD is going to be computed by ZTGSJA.
! 148: * See Further Details.
! 149: *
! 150: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 151: * On entry, the M-by-N matrix A.
! 152: * On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular
! 153: * matrix R or part of R. See Purpose for details.
! 154: *
! 155: * LDA (input) INTEGER
! 156: * The leading dimension of the array A. LDA >= max(1,M).
! 157: *
! 158: * B (input/output) COMPLEX*16 array, dimension (LDB,N)
! 159: * On entry, the P-by-N matrix B.
! 160: * On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains
! 161: * a part of R. See Purpose for details.
! 162: *
! 163: * LDB (input) INTEGER
! 164: * The leading dimension of the array B. LDB >= max(1,P).
! 165: *
! 166: * TOLA (input) DOUBLE PRECISION
! 167: * TOLB (input) DOUBLE PRECISION
! 168: * TOLA and TOLB are the convergence criteria for the Jacobi-
! 169: * Kogbetliantz iteration procedure. Generally, they are the
! 170: * same as used in the preprocessing step, say
! 171: * TOLA = MAX(M,N)*norm(A)*MAZHEPS,
! 172: * TOLB = MAX(P,N)*norm(B)*MAZHEPS.
! 173: *
! 174: * ALPHA (output) DOUBLE PRECISION array, dimension (N)
! 175: * BETA (output) DOUBLE PRECISION array, dimension (N)
! 176: * On exit, ALPHA and BETA contain the generalized singular
! 177: * value pairs of A and B;
! 178: * ALPHA(1:K) = 1,
! 179: * BETA(1:K) = 0,
! 180: * and if M-K-L >= 0,
! 181: * ALPHA(K+1:K+L) = diag(C),
! 182: * BETA(K+1:K+L) = diag(S),
! 183: * or if M-K-L < 0,
! 184: * ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0
! 185: * BETA(K+1:M) = S, BETA(M+1:K+L) = 1.
! 186: * Furthermore, if K+L < N,
! 187: * ALPHA(K+L+1:N) = 0
! 188: * BETA(K+L+1:N) = 0.
! 189: *
! 190: * U (input/output) COMPLEX*16 array, dimension (LDU,M)
! 191: * On entry, if JOBU = 'U', U must contain a matrix U1 (usually
! 192: * the unitary matrix returned by ZGGSVP).
! 193: * On exit,
! 194: * if JOBU = 'I', U contains the unitary matrix U;
! 195: * if JOBU = 'U', U contains the product U1*U.
! 196: * If JOBU = 'N', U is not referenced.
! 197: *
! 198: * LDU (input) INTEGER
! 199: * The leading dimension of the array U. LDU >= max(1,M) if
! 200: * JOBU = 'U'; LDU >= 1 otherwise.
! 201: *
! 202: * V (input/output) COMPLEX*16 array, dimension (LDV,P)
! 203: * On entry, if JOBV = 'V', V must contain a matrix V1 (usually
! 204: * the unitary matrix returned by ZGGSVP).
! 205: * On exit,
! 206: * if JOBV = 'I', V contains the unitary matrix V;
! 207: * if JOBV = 'V', V contains the product V1*V.
! 208: * If JOBV = 'N', V is not referenced.
! 209: *
! 210: * LDV (input) INTEGER
! 211: * The leading dimension of the array V. LDV >= max(1,P) if
! 212: * JOBV = 'V'; LDV >= 1 otherwise.
! 213: *
! 214: * Q (input/output) COMPLEX*16 array, dimension (LDQ,N)
! 215: * On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually
! 216: * the unitary matrix returned by ZGGSVP).
! 217: * On exit,
! 218: * if JOBQ = 'I', Q contains the unitary matrix Q;
! 219: * if JOBQ = 'Q', Q contains the product Q1*Q.
! 220: * If JOBQ = 'N', Q is not referenced.
! 221: *
! 222: * LDQ (input) INTEGER
! 223: * The leading dimension of the array Q. LDQ >= max(1,N) if
! 224: * JOBQ = 'Q'; LDQ >= 1 otherwise.
! 225: *
! 226: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 227: *
! 228: * NCYCLE (output) INTEGER
! 229: * The number of cycles required for convergence.
! 230: *
! 231: * INFO (output) INTEGER
! 232: * = 0: successful exit
! 233: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 234: * = 1: the procedure does not converge after MAXIT cycles.
! 235: *
! 236: * Internal Parameters
! 237: * ===================
! 238: *
! 239: * MAXIT INTEGER
! 240: * MAXIT specifies the total loops that the iterative procedure
! 241: * may take. If after MAXIT cycles, the routine fails to
! 242: * converge, we return INFO = 1.
! 243: *
! 244: * Further Details
! 245: * ===============
! 246: *
! 247: * ZTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
! 248: * min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
! 249: * matrix B13 to the form:
! 250: *
! 251: * U1'*A13*Q1 = C1*R1; V1'*B13*Q1 = S1*R1,
! 252: *
! 253: * where U1, V1 and Q1 are unitary matrix, and Z' is the conjugate
! 254: * transpose of Z. C1 and S1 are diagonal matrices satisfying
! 255: *
! 256: * C1**2 + S1**2 = I,
! 257: *
! 258: * and R1 is an L-by-L nonsingular upper triangular matrix.
! 259: *
! 260: * =====================================================================
! 261: *
! 262: * .. Parameters ..
! 263: INTEGER MAXIT
! 264: PARAMETER ( MAXIT = 40 )
! 265: DOUBLE PRECISION ZERO, ONE
! 266: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 267: COMPLEX*16 CZERO, CONE
! 268: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
! 269: $ CONE = ( 1.0D+0, 0.0D+0 ) )
! 270: * ..
! 271: * .. Local Scalars ..
! 272: *
! 273: LOGICAL INITQ, INITU, INITV, UPPER, WANTQ, WANTU, WANTV
! 274: INTEGER I, J, KCYCLE
! 275: DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV, ERROR, GAMMA,
! 276: $ RWK, SSMIN
! 277: COMPLEX*16 A2, B2, SNQ, SNU, SNV
! 278: * ..
! 279: * .. External Functions ..
! 280: LOGICAL LSAME
! 281: EXTERNAL LSAME
! 282: * ..
! 283: * .. External Subroutines ..
! 284: EXTERNAL DLARTG, XERBLA, ZCOPY, ZDSCAL, ZLAGS2, ZLAPLL,
! 285: $ ZLASET, ZROT
! 286: * ..
! 287: * .. Intrinsic Functions ..
! 288: INTRINSIC ABS, DBLE, DCONJG, MAX, MIN
! 289: * ..
! 290: * .. Executable Statements ..
! 291: *
! 292: * Decode and test the input parameters
! 293: *
! 294: INITU = LSAME( JOBU, 'I' )
! 295: WANTU = INITU .OR. LSAME( JOBU, 'U' )
! 296: *
! 297: INITV = LSAME( JOBV, 'I' )
! 298: WANTV = INITV .OR. LSAME( JOBV, 'V' )
! 299: *
! 300: INITQ = LSAME( JOBQ, 'I' )
! 301: WANTQ = INITQ .OR. LSAME( JOBQ, 'Q' )
! 302: *
! 303: INFO = 0
! 304: IF( .NOT.( INITU .OR. WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN
! 305: INFO = -1
! 306: ELSE IF( .NOT.( INITV .OR. WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN
! 307: INFO = -2
! 308: ELSE IF( .NOT.( INITQ .OR. WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN
! 309: INFO = -3
! 310: ELSE IF( M.LT.0 ) THEN
! 311: INFO = -4
! 312: ELSE IF( P.LT.0 ) THEN
! 313: INFO = -5
! 314: ELSE IF( N.LT.0 ) THEN
! 315: INFO = -6
! 316: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 317: INFO = -10
! 318: ELSE IF( LDB.LT.MAX( 1, P ) ) THEN
! 319: INFO = -12
! 320: ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN
! 321: INFO = -18
! 322: ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN
! 323: INFO = -20
! 324: ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN
! 325: INFO = -22
! 326: END IF
! 327: IF( INFO.NE.0 ) THEN
! 328: CALL XERBLA( 'ZTGSJA', -INFO )
! 329: RETURN
! 330: END IF
! 331: *
! 332: * Initialize U, V and Q, if necessary
! 333: *
! 334: IF( INITU )
! 335: $ CALL ZLASET( 'Full', M, M, CZERO, CONE, U, LDU )
! 336: IF( INITV )
! 337: $ CALL ZLASET( 'Full', P, P, CZERO, CONE, V, LDV )
! 338: IF( INITQ )
! 339: $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDQ )
! 340: *
! 341: * Loop until convergence
! 342: *
! 343: UPPER = .FALSE.
! 344: DO 40 KCYCLE = 1, MAXIT
! 345: *
! 346: UPPER = .NOT.UPPER
! 347: *
! 348: DO 20 I = 1, L - 1
! 349: DO 10 J = I + 1, L
! 350: *
! 351: A1 = ZERO
! 352: A2 = CZERO
! 353: A3 = ZERO
! 354: IF( K+I.LE.M )
! 355: $ A1 = DBLE( A( K+I, N-L+I ) )
! 356: IF( K+J.LE.M )
! 357: $ A3 = DBLE( A( K+J, N-L+J ) )
! 358: *
! 359: B1 = DBLE( B( I, N-L+I ) )
! 360: B3 = DBLE( B( J, N-L+J ) )
! 361: *
! 362: IF( UPPER ) THEN
! 363: IF( K+I.LE.M )
! 364: $ A2 = A( K+I, N-L+J )
! 365: B2 = B( I, N-L+J )
! 366: ELSE
! 367: IF( K+J.LE.M )
! 368: $ A2 = A( K+J, N-L+I )
! 369: B2 = B( J, N-L+I )
! 370: END IF
! 371: *
! 372: CALL ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
! 373: $ CSV, SNV, CSQ, SNQ )
! 374: *
! 375: * Update (K+I)-th and (K+J)-th rows of matrix A: U'*A
! 376: *
! 377: IF( K+J.LE.M )
! 378: $ CALL ZROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
! 379: $ LDA, CSU, DCONJG( SNU ) )
! 380: *
! 381: * Update I-th and J-th rows of matrix B: V'*B
! 382: *
! 383: CALL ZROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
! 384: $ CSV, DCONJG( SNV ) )
! 385: *
! 386: * Update (N-L+I)-th and (N-L+J)-th columns of matrices
! 387: * A and B: A*Q and B*Q
! 388: *
! 389: CALL ZROT( MIN( K+L, M ), A( 1, N-L+J ), 1,
! 390: $ A( 1, N-L+I ), 1, CSQ, SNQ )
! 391: *
! 392: CALL ZROT( L, B( 1, N-L+J ), 1, B( 1, N-L+I ), 1, CSQ,
! 393: $ SNQ )
! 394: *
! 395: IF( UPPER ) THEN
! 396: IF( K+I.LE.M )
! 397: $ A( K+I, N-L+J ) = CZERO
! 398: B( I, N-L+J ) = CZERO
! 399: ELSE
! 400: IF( K+J.LE.M )
! 401: $ A( K+J, N-L+I ) = CZERO
! 402: B( J, N-L+I ) = CZERO
! 403: END IF
! 404: *
! 405: * Ensure that the diagonal elements of A and B are real.
! 406: *
! 407: IF( K+I.LE.M )
! 408: $ A( K+I, N-L+I ) = DBLE( A( K+I, N-L+I ) )
! 409: IF( K+J.LE.M )
! 410: $ A( K+J, N-L+J ) = DBLE( A( K+J, N-L+J ) )
! 411: B( I, N-L+I ) = DBLE( B( I, N-L+I ) )
! 412: B( J, N-L+J ) = DBLE( B( J, N-L+J ) )
! 413: *
! 414: * Update unitary matrices U, V, Q, if desired.
! 415: *
! 416: IF( WANTU .AND. K+J.LE.M )
! 417: $ CALL ZROT( M, U( 1, K+J ), 1, U( 1, K+I ), 1, CSU,
! 418: $ SNU )
! 419: *
! 420: IF( WANTV )
! 421: $ CALL ZROT( P, V( 1, J ), 1, V( 1, I ), 1, CSV, SNV )
! 422: *
! 423: IF( WANTQ )
! 424: $ CALL ZROT( N, Q( 1, N-L+J ), 1, Q( 1, N-L+I ), 1, CSQ,
! 425: $ SNQ )
! 426: *
! 427: 10 CONTINUE
! 428: 20 CONTINUE
! 429: *
! 430: IF( .NOT.UPPER ) THEN
! 431: *
! 432: * The matrices A13 and B13 were lower triangular at the start
! 433: * of the cycle, and are now upper triangular.
! 434: *
! 435: * Convergence test: test the parallelism of the corresponding
! 436: * rows of A and B.
! 437: *
! 438: ERROR = ZERO
! 439: DO 30 I = 1, MIN( L, M-K )
! 440: CALL ZCOPY( L-I+1, A( K+I, N-L+I ), LDA, WORK, 1 )
! 441: CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, WORK( L+1 ), 1 )
! 442: CALL ZLAPLL( L-I+1, WORK, 1, WORK( L+1 ), 1, SSMIN )
! 443: ERROR = MAX( ERROR, SSMIN )
! 444: 30 CONTINUE
! 445: *
! 446: IF( ABS( ERROR ).LE.MIN( TOLA, TOLB ) )
! 447: $ GO TO 50
! 448: END IF
! 449: *
! 450: * End of cycle loop
! 451: *
! 452: 40 CONTINUE
! 453: *
! 454: * The algorithm has not converged after MAXIT cycles.
! 455: *
! 456: INFO = 1
! 457: GO TO 100
! 458: *
! 459: 50 CONTINUE
! 460: *
! 461: * If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged.
! 462: * Compute the generalized singular value pairs (ALPHA, BETA), and
! 463: * set the triangular matrix R to array A.
! 464: *
! 465: DO 60 I = 1, K
! 466: ALPHA( I ) = ONE
! 467: BETA( I ) = ZERO
! 468: 60 CONTINUE
! 469: *
! 470: DO 70 I = 1, MIN( L, M-K )
! 471: *
! 472: A1 = DBLE( A( K+I, N-L+I ) )
! 473: B1 = DBLE( B( I, N-L+I ) )
! 474: *
! 475: IF( A1.NE.ZERO ) THEN
! 476: GAMMA = B1 / A1
! 477: *
! 478: IF( GAMMA.LT.ZERO ) THEN
! 479: CALL ZDSCAL( L-I+1, -ONE, B( I, N-L+I ), LDB )
! 480: IF( WANTV )
! 481: $ CALL ZDSCAL( P, -ONE, V( 1, I ), 1 )
! 482: END IF
! 483: *
! 484: CALL DLARTG( ABS( GAMMA ), ONE, BETA( K+I ), ALPHA( K+I ),
! 485: $ RWK )
! 486: *
! 487: IF( ALPHA( K+I ).GE.BETA( K+I ) ) THEN
! 488: CALL ZDSCAL( L-I+1, ONE / ALPHA( K+I ), A( K+I, N-L+I ),
! 489: $ LDA )
! 490: ELSE
! 491: CALL ZDSCAL( L-I+1, ONE / BETA( K+I ), B( I, N-L+I ),
! 492: $ LDB )
! 493: CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
! 494: $ LDA )
! 495: END IF
! 496: *
! 497: ELSE
! 498: ALPHA( K+I ) = ZERO
! 499: BETA( K+I ) = ONE
! 500: CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
! 501: $ LDA )
! 502: END IF
! 503: 70 CONTINUE
! 504: *
! 505: * Post-assignment
! 506: *
! 507: DO 80 I = M + 1, K + L
! 508: ALPHA( I ) = ZERO
! 509: BETA( I ) = ONE
! 510: 80 CONTINUE
! 511: *
! 512: IF( K+L.LT.N ) THEN
! 513: DO 90 I = K + L + 1, N
! 514: ALPHA( I ) = ZERO
! 515: BETA( I ) = ZERO
! 516: 90 CONTINUE
! 517: END IF
! 518: *
! 519: 100 CONTINUE
! 520: NCYCLE = KCYCLE
! 521: *
! 522: RETURN
! 523: *
! 524: * End of ZTGSJA
! 525: *
! 526: END
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