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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, 2: $ LDZ, J1, N1, N2, WORK, LWORK, INFO ) 3: * 4: * -- LAPACK auxiliary routine (version 3.2.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * June 2010 8: * 9: * .. Scalar Arguments .. 10: LOGICAL WANTQ, WANTZ 11: INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 12: * .. 13: * .. Array Arguments .. 14: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), 15: $ WORK( * ), Z( LDZ, * ) 16: * .. 17: * 18: * Purpose 19: * ======= 20: * 21: * DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) 22: * of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair 23: * (A, B) by an orthogonal equivalence transformation. 24: * 25: * (A, B) must be in generalized real Schur canonical form (as returned 26: * by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 27: * diagonal blocks. B is upper triangular. 28: * 29: * Optionally, the matrices Q and Z of generalized Schur vectors are 30: * updated. 31: * 32: * Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' 33: * Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' 34: * 35: * 36: * Arguments 37: * ========= 38: * 39: * WANTQ (input) LOGICAL 40: * .TRUE. : update the left transformation matrix Q; 41: * .FALSE.: do not update Q. 42: * 43: * WANTZ (input) LOGICAL 44: * .TRUE. : update the right transformation matrix Z; 45: * .FALSE.: do not update Z. 46: * 47: * N (input) INTEGER 48: * The order of the matrices A and B. N >= 0. 49: * 50: * A (input/output) DOUBLE PRECISION array, dimensions (LDA,N) 51: * On entry, the matrix A in the pair (A, B). 52: * On exit, the updated matrix A. 53: * 54: * LDA (input) INTEGER 55: * The leading dimension of the array A. LDA >= max(1,N). 56: * 57: * B (input/output) DOUBLE PRECISION array, dimensions (LDB,N) 58: * On entry, the matrix B in the pair (A, B). 59: * On exit, the updated matrix B. 60: * 61: * LDB (input) INTEGER 62: * The leading dimension of the array B. LDB >= max(1,N). 63: * 64: * Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) 65: * On entry, if WANTQ = .TRUE., the orthogonal matrix Q. 66: * On exit, the updated matrix Q. 67: * Not referenced if WANTQ = .FALSE.. 68: * 69: * LDQ (input) INTEGER 70: * The leading dimension of the array Q. LDQ >= 1. 71: * If WANTQ = .TRUE., LDQ >= N. 72: * 73: * Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N) 74: * On entry, if WANTZ =.TRUE., the orthogonal matrix Z. 75: * On exit, the updated matrix Z. 76: * Not referenced if WANTZ = .FALSE.. 77: * 78: * LDZ (input) INTEGER 79: * The leading dimension of the array Z. LDZ >= 1. 80: * If WANTZ = .TRUE., LDZ >= N. 81: * 82: * J1 (input) INTEGER 83: * The index to the first block (A11, B11). 1 <= J1 <= N. 84: * 85: * N1 (input) INTEGER 86: * The order of the first block (A11, B11). N1 = 0, 1 or 2. 87: * 88: * N2 (input) INTEGER 89: * The order of the second block (A22, B22). N2 = 0, 1 or 2. 90: * 91: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)). 92: * 93: * LWORK (input) INTEGER 94: * The dimension of the array WORK. 95: * LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 ) 96: * 97: * INFO (output) INTEGER 98: * =0: Successful exit 99: * >0: If INFO = 1, the transformed matrix (A, B) would be 100: * too far from generalized Schur form; the blocks are 101: * not swapped and (A, B) and (Q, Z) are unchanged. 102: * The problem of swapping is too ill-conditioned. 103: * <0: If INFO = -16: LWORK is too small. Appropriate value 104: * for LWORK is returned in WORK(1). 105: * 106: * Further Details 107: * =============== 108: * 109: * Based on contributions by 110: * Bo Kagstrom and Peter Poromaa, Department of Computing Science, 111: * Umea University, S-901 87 Umea, Sweden. 112: * 113: * In the current code both weak and strong stability tests are 114: * performed. The user can omit the strong stability test by changing 115: * the internal logical parameter WANDS to .FALSE.. See ref. [2] for 116: * details. 117: * 118: * [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the 119: * Generalized Real Schur Form of a Regular Matrix Pair (A, B), in 120: * M.S. Moonen et al (eds), Linear Algebra for Large Scale and 121: * Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. 122: * 123: * [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified 124: * Eigenvalues of a Regular Matrix Pair (A, B) and Condition 125: * Estimation: Theory, Algorithms and Software, 126: * Report UMINF - 94.04, Department of Computing Science, Umea 127: * University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working 128: * Note 87. To appear in Numerical Algorithms, 1996. 129: * 130: * ===================================================================== 131: * Replaced various illegal calls to DCOPY by calls to DLASET, or by DO 132: * loops. Sven Hammarling, 1/5/02. 133: * 134: * .. Parameters .. 135: DOUBLE PRECISION ZERO, ONE 136: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 137: DOUBLE PRECISION TWENTY 138: PARAMETER ( TWENTY = 2.0D+01 ) 139: INTEGER LDST 140: PARAMETER ( LDST = 4 ) 141: LOGICAL WANDS 142: PARAMETER ( WANDS = .TRUE. ) 143: * .. 144: * .. Local Scalars .. 145: LOGICAL DTRONG, WEAK 146: INTEGER I, IDUM, LINFO, M 147: DOUBLE PRECISION BQRA21, BRQA21, DDUM, DNORM, DSCALE, DSUM, EPS, 148: $ F, G, SA, SB, SCALE, SMLNUM, SS, THRESH, WS 149: * .. 150: * .. Local Arrays .. 151: INTEGER IWORK( LDST ) 152: DOUBLE PRECISION AI( 2 ), AR( 2 ), BE( 2 ), IR( LDST, LDST ), 153: $ IRCOP( LDST, LDST ), LI( LDST, LDST ), 154: $ LICOP( LDST, LDST ), S( LDST, LDST ), 155: $ SCPY( LDST, LDST ), T( LDST, LDST ), 156: $ TAUL( LDST ), TAUR( LDST ), TCPY( LDST, LDST ) 157: * .. 158: * .. External Functions .. 159: DOUBLE PRECISION DLAMCH 160: EXTERNAL DLAMCH 161: * .. 162: * .. External Subroutines .. 163: EXTERNAL DGEMM, DGEQR2, DGERQ2, DLACPY, DLAGV2, DLARTG, 164: $ DLASET, DLASSQ, DORG2R, DORGR2, DORM2R, DORMR2, 165: $ DROT, DSCAL, DTGSY2 166: * .. 167: * .. Intrinsic Functions .. 168: INTRINSIC ABS, MAX, SQRT 169: * .. 170: * .. Executable Statements .. 171: * 172: INFO = 0 173: * 174: * Quick return if possible 175: * 176: IF( N.LE.1 .OR. N1.LE.0 .OR. N2.LE.0 ) 177: $ RETURN 178: IF( N1.GT.N .OR. ( J1+N1 ).GT.N ) 179: $ RETURN 180: M = N1 + N2 181: IF( LWORK.LT.MAX( 1, N*M, M*M*2 ) ) THEN 182: INFO = -16 183: WORK( 1 ) = MAX( 1, N*M, M*M*2 ) 184: RETURN 185: END IF 186: * 187: WEAK = .FALSE. 188: DTRONG = .FALSE. 189: * 190: * Make a local copy of selected block 191: * 192: CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, LI, LDST ) 193: CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, IR, LDST ) 194: CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST ) 195: CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST ) 196: * 197: * Compute threshold for testing acceptance of swapping. 198: * 199: EPS = DLAMCH( 'P' ) 200: SMLNUM = DLAMCH( 'S' ) / EPS 201: DSCALE = ZERO 202: DSUM = ONE 203: CALL DLACPY( 'Full', M, M, S, LDST, WORK, M ) 204: CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) 205: CALL DLACPY( 'Full', M, M, T, LDST, WORK, M ) 206: CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) 207: DNORM = DSCALE*SQRT( DSUM ) 208: * 209: * THRES has been changed from 210: * THRESH = MAX( TEN*EPS*SA, SMLNUM ) 211: * to 212: * THRESH = MAX( TWENTY*EPS*SA, SMLNUM ) 213: * on 04/01/10. 214: * "Bug" reported by Ondra Kamenik, confirmed by Julie Langou, fixed by 215: * Jim Demmel and Guillaume Revy. See forum post 1783. 216: * 217: THRESH = MAX( TWENTY*EPS*DNORM, SMLNUM ) 218: * 219: IF( M.EQ.2 ) THEN 220: * 221: * CASE 1: Swap 1-by-1 and 1-by-1 blocks. 222: * 223: * Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks 224: * using Givens rotations and perform the swap tentatively. 225: * 226: F = S( 2, 2 )*T( 1, 1 ) - T( 2, 2 )*S( 1, 1 ) 227: G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 ) 228: SB = ABS( T( 2, 2 ) ) 229: SA = ABS( S( 2, 2 ) ) 230: CALL DLARTG( F, G, IR( 1, 2 ), IR( 1, 1 ), DDUM ) 231: IR( 2, 1 ) = -IR( 1, 2 ) 232: IR( 2, 2 ) = IR( 1, 1 ) 233: CALL DROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, IR( 1, 1 ), 234: $ IR( 2, 1 ) ) 235: CALL DROT( 2, T( 1, 1 ), 1, T( 1, 2 ), 1, IR( 1, 1 ), 236: $ IR( 2, 1 ) ) 237: IF( SA.GE.SB ) THEN 238: CALL DLARTG( S( 1, 1 ), S( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ), 239: $ DDUM ) 240: ELSE 241: CALL DLARTG( T( 1, 1 ), T( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ), 242: $ DDUM ) 243: END IF 244: CALL DROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, LI( 1, 1 ), 245: $ LI( 2, 1 ) ) 246: CALL DROT( 2, T( 1, 1 ), LDST, T( 2, 1 ), LDST, LI( 1, 1 ), 247: $ LI( 2, 1 ) ) 248: LI( 2, 2 ) = LI( 1, 1 ) 249: LI( 1, 2 ) = -LI( 2, 1 ) 250: * 251: * Weak stability test: 252: * |S21| + |T21| <= O(EPS * F-norm((S, T))) 253: * 254: WS = ABS( S( 2, 1 ) ) + ABS( T( 2, 1 ) ) 255: WEAK = WS.LE.THRESH 256: IF( .NOT.WEAK ) 257: $ GO TO 70 258: * 259: IF( WANDS ) THEN 260: * 261: * Strong stability test: 262: * F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B))) 263: * 264: CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ), 265: $ M ) 266: CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, 267: $ WORK, M ) 268: CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 269: $ WORK( M*M+1 ), M ) 270: DSCALE = ZERO 271: DSUM = ONE 272: CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 273: * 274: CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ), 275: $ M ) 276: CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, 277: $ WORK, M ) 278: CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 279: $ WORK( M*M+1 ), M ) 280: CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 281: SS = DSCALE*SQRT( DSUM ) 282: DTRONG = SS.LE.THRESH 283: IF( .NOT.DTRONG ) 284: $ GO TO 70 285: END IF 286: * 287: * Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and 288: * (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). 289: * 290: CALL DROT( J1+1, A( 1, J1 ), 1, A( 1, J1+1 ), 1, IR( 1, 1 ), 291: $ IR( 2, 1 ) ) 292: CALL DROT( J1+1, B( 1, J1 ), 1, B( 1, J1+1 ), 1, IR( 1, 1 ), 293: $ IR( 2, 1 ) ) 294: CALL DROT( N-J1+1, A( J1, J1 ), LDA, A( J1+1, J1 ), LDA, 295: $ LI( 1, 1 ), LI( 2, 1 ) ) 296: CALL DROT( N-J1+1, B( J1, J1 ), LDB, B( J1+1, J1 ), LDB, 297: $ LI( 1, 1 ), LI( 2, 1 ) ) 298: * 299: * Set N1-by-N2 (2,1) - blocks to ZERO. 300: * 301: A( J1+1, J1 ) = ZERO 302: B( J1+1, J1 ) = ZERO 303: * 304: * Accumulate transformations into Q and Z if requested. 305: * 306: IF( WANTZ ) 307: $ CALL DROT( N, Z( 1, J1 ), 1, Z( 1, J1+1 ), 1, IR( 1, 1 ), 308: $ IR( 2, 1 ) ) 309: IF( WANTQ ) 310: $ CALL DROT( N, Q( 1, J1 ), 1, Q( 1, J1+1 ), 1, LI( 1, 1 ), 311: $ LI( 2, 1 ) ) 312: * 313: * Exit with INFO = 0 if swap was successfully performed. 314: * 315: RETURN 316: * 317: ELSE 318: * 319: * CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2 320: * and 2-by-2 blocks. 321: * 322: * Solve the generalized Sylvester equation 323: * S11 * R - L * S22 = SCALE * S12 324: * T11 * R - L * T22 = SCALE * T12 325: * for R and L. Solutions in LI and IR. 326: * 327: CALL DLACPY( 'Full', N1, N2, T( 1, N1+1 ), LDST, LI, LDST ) 328: CALL DLACPY( 'Full', N1, N2, S( 1, N1+1 ), LDST, 329: $ IR( N2+1, N1+1 ), LDST ) 330: CALL DTGSY2( 'N', 0, N1, N2, S, LDST, S( N1+1, N1+1 ), LDST, 331: $ IR( N2+1, N1+1 ), LDST, T, LDST, T( N1+1, N1+1 ), 332: $ LDST, LI, LDST, SCALE, DSUM, DSCALE, IWORK, IDUM, 333: $ LINFO ) 334: * 335: * Compute orthogonal matrix QL: 336: * 337: * QL' * LI = [ TL ] 338: * [ 0 ] 339: * where 340: * LI = [ -L ] 341: * [ SCALE * identity(N2) ] 342: * 343: DO 10 I = 1, N2 344: CALL DSCAL( N1, -ONE, LI( 1, I ), 1 ) 345: LI( N1+I, I ) = SCALE 346: 10 CONTINUE 347: CALL DGEQR2( M, N2, LI, LDST, TAUL, WORK, LINFO ) 348: IF( LINFO.NE.0 ) 349: $ GO TO 70 350: CALL DORG2R( M, M, N2, LI, LDST, TAUL, WORK, LINFO ) 351: IF( LINFO.NE.0 ) 352: $ GO TO 70 353: * 354: * Compute orthogonal matrix RQ: 355: * 356: * IR * RQ' = [ 0 TR], 357: * 358: * where IR = [ SCALE * identity(N1), R ] 359: * 360: DO 20 I = 1, N1 361: IR( N2+I, I ) = SCALE 362: 20 CONTINUE 363: CALL DGERQ2( N1, M, IR( N2+1, 1 ), LDST, TAUR, WORK, LINFO ) 364: IF( LINFO.NE.0 ) 365: $ GO TO 70 366: CALL DORGR2( M, M, N1, IR, LDST, TAUR, WORK, LINFO ) 367: IF( LINFO.NE.0 ) 368: $ GO TO 70 369: * 370: * Perform the swapping tentatively: 371: * 372: CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, 373: $ WORK, M ) 374: CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, S, 375: $ LDST ) 376: CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, 377: $ WORK, M ) 378: CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, T, 379: $ LDST ) 380: CALL DLACPY( 'F', M, M, S, LDST, SCPY, LDST ) 381: CALL DLACPY( 'F', M, M, T, LDST, TCPY, LDST ) 382: CALL DLACPY( 'F', M, M, IR, LDST, IRCOP, LDST ) 383: CALL DLACPY( 'F', M, M, LI, LDST, LICOP, LDST ) 384: * 385: * Triangularize the B-part by an RQ factorization. 386: * Apply transformation (from left) to A-part, giving S. 387: * 388: CALL DGERQ2( M, M, T, LDST, TAUR, WORK, LINFO ) 389: IF( LINFO.NE.0 ) 390: $ GO TO 70 391: CALL DORMR2( 'R', 'T', M, M, M, T, LDST, TAUR, S, LDST, WORK, 392: $ LINFO ) 393: IF( LINFO.NE.0 ) 394: $ GO TO 70 395: CALL DORMR2( 'L', 'N', M, M, M, T, LDST, TAUR, IR, LDST, WORK, 396: $ LINFO ) 397: IF( LINFO.NE.0 ) 398: $ GO TO 70 399: * 400: * Compute F-norm(S21) in BRQA21. (T21 is 0.) 401: * 402: DSCALE = ZERO 403: DSUM = ONE 404: DO 30 I = 1, N2 405: CALL DLASSQ( N1, S( N2+1, I ), 1, DSCALE, DSUM ) 406: 30 CONTINUE 407: BRQA21 = DSCALE*SQRT( DSUM ) 408: * 409: * Triangularize the B-part by a QR factorization. 410: * Apply transformation (from right) to A-part, giving S. 411: * 412: CALL DGEQR2( M, M, TCPY, LDST, TAUL, WORK, LINFO ) 413: IF( LINFO.NE.0 ) 414: $ GO TO 70 415: CALL DORM2R( 'L', 'T', M, M, M, TCPY, LDST, TAUL, SCPY, LDST, 416: $ WORK, INFO ) 417: CALL DORM2R( 'R', 'N', M, M, M, TCPY, LDST, TAUL, LICOP, LDST, 418: $ WORK, INFO ) 419: IF( LINFO.NE.0 ) 420: $ GO TO 70 421: * 422: * Compute F-norm(S21) in BQRA21. (T21 is 0.) 423: * 424: DSCALE = ZERO 425: DSUM = ONE 426: DO 40 I = 1, N2 427: CALL DLASSQ( N1, SCPY( N2+1, I ), 1, DSCALE, DSUM ) 428: 40 CONTINUE 429: BQRA21 = DSCALE*SQRT( DSUM ) 430: * 431: * Decide which method to use. 432: * Weak stability test: 433: * F-norm(S21) <= O(EPS * F-norm((S, T))) 434: * 435: IF( BQRA21.LE.BRQA21 .AND. BQRA21.LE.THRESH ) THEN 436: CALL DLACPY( 'F', M, M, SCPY, LDST, S, LDST ) 437: CALL DLACPY( 'F', M, M, TCPY, LDST, T, LDST ) 438: CALL DLACPY( 'F', M, M, IRCOP, LDST, IR, LDST ) 439: CALL DLACPY( 'F', M, M, LICOP, LDST, LI, LDST ) 440: ELSE IF( BRQA21.GE.THRESH ) THEN 441: GO TO 70 442: END IF 443: * 444: * Set lower triangle of B-part to zero 445: * 446: CALL DLASET( 'Lower', M-1, M-1, ZERO, ZERO, T(2,1), LDST ) 447: * 448: IF( WANDS ) THEN 449: * 450: * Strong stability test: 451: * F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B))) 452: * 453: CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ), 454: $ M ) 455: CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, 456: $ WORK, M ) 457: CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 458: $ WORK( M*M+1 ), M ) 459: DSCALE = ZERO 460: DSUM = ONE 461: CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 462: * 463: CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ), 464: $ M ) 465: CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, 466: $ WORK, M ) 467: CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE, 468: $ WORK( M*M+1 ), M ) 469: CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) 470: SS = DSCALE*SQRT( DSUM ) 471: DTRONG = ( SS.LE.THRESH ) 472: IF( .NOT.DTRONG ) 473: $ GO TO 70 474: * 475: END IF 476: * 477: * If the swap is accepted ("weakly" and "strongly"), apply the 478: * transformations and set N1-by-N2 (2,1)-block to zero. 479: * 480: CALL DLASET( 'Full', N1, N2, ZERO, ZERO, S(N2+1,1), LDST ) 481: * 482: * copy back M-by-M diagonal block starting at index J1 of (A, B) 483: * 484: CALL DLACPY( 'F', M, M, S, LDST, A( J1, J1 ), LDA ) 485: CALL DLACPY( 'F', M, M, T, LDST, B( J1, J1 ), LDB ) 486: CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, T, LDST ) 487: * 488: * Standardize existing 2-by-2 blocks. 489: * 490: DO 50 I = 1, M*M 491: WORK(I) = ZERO 492: 50 CONTINUE 493: WORK( 1 ) = ONE 494: T( 1, 1 ) = ONE 495: IDUM = LWORK - M*M - 2 496: IF( N2.GT.1 ) THEN 497: CALL DLAGV2( A( J1, J1 ), LDA, B( J1, J1 ), LDB, AR, AI, BE, 498: $ WORK( 1 ), WORK( 2 ), T( 1, 1 ), T( 2, 1 ) ) 499: WORK( M+1 ) = -WORK( 2 ) 500: WORK( M+2 ) = WORK( 1 ) 501: T( N2, N2 ) = T( 1, 1 ) 502: T( 1, 2 ) = -T( 2, 1 ) 503: END IF 504: WORK( M*M ) = ONE 505: T( M, M ) = ONE 506: * 507: IF( N1.GT.1 ) THEN 508: CALL DLAGV2( A( J1+N2, J1+N2 ), LDA, B( J1+N2, J1+N2 ), LDB, 509: $ TAUR, TAUL, WORK( M*M+1 ), WORK( N2*M+N2+1 ), 510: $ WORK( N2*M+N2+2 ), T( N2+1, N2+1 ), 511: $ T( M, M-1 ) ) 512: WORK( M*M ) = WORK( N2*M+N2+1 ) 513: WORK( M*M-1 ) = -WORK( N2*M+N2+2 ) 514: T( M, M ) = T( N2+1, N2+1 ) 515: T( M-1, M ) = -T( M, M-1 ) 516: END IF 517: CALL DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, A( J1, J1+N2 ), 518: $ LDA, ZERO, WORK( M*M+1 ), N2 ) 519: CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, A( J1, J1+N2 ), 520: $ LDA ) 521: CALL DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, B( J1, J1+N2 ), 522: $ LDB, ZERO, WORK( M*M+1 ), N2 ) 523: CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, B( J1, J1+N2 ), 524: $ LDB ) 525: CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, WORK, M, ZERO, 526: $ WORK( M*M+1 ), M ) 527: CALL DLACPY( 'Full', M, M, WORK( M*M+1 ), M, LI, LDST ) 528: CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, A( J1, J1+N2 ), LDA, 529: $ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 ) 530: CALL DLACPY( 'Full', N2, N1, WORK, N2, A( J1, J1+N2 ), LDA ) 531: CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, B( J1, J1+N2 ), LDB, 532: $ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 ) 533: CALL DLACPY( 'Full', N2, N1, WORK, N2, B( J1, J1+N2 ), LDB ) 534: CALL DGEMM( 'T', 'N', M, M, M, ONE, IR, LDST, T, LDST, ZERO, 535: $ WORK, M ) 536: CALL DLACPY( 'Full', M, M, WORK, M, IR, LDST ) 537: * 538: * Accumulate transformations into Q and Z if requested. 539: * 540: IF( WANTQ ) THEN 541: CALL DGEMM( 'N', 'N', N, M, M, ONE, Q( 1, J1 ), LDQ, LI, 542: $ LDST, ZERO, WORK, N ) 543: CALL DLACPY( 'Full', N, M, WORK, N, Q( 1, J1 ), LDQ ) 544: * 545: END IF 546: * 547: IF( WANTZ ) THEN 548: CALL DGEMM( 'N', 'N', N, M, M, ONE, Z( 1, J1 ), LDZ, IR, 549: $ LDST, ZERO, WORK, N ) 550: CALL DLACPY( 'Full', N, M, WORK, N, Z( 1, J1 ), LDZ ) 551: * 552: END IF 553: * 554: * Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and 555: * (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). 556: * 557: I = J1 + M 558: IF( I.LE.N ) THEN 559: CALL DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST, 560: $ A( J1, I ), LDA, ZERO, WORK, M ) 561: CALL DLACPY( 'Full', M, N-I+1, WORK, M, A( J1, I ), LDA ) 562: CALL DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST, 563: $ B( J1, I ), LDA, ZERO, WORK, M ) 564: CALL DLACPY( 'Full', M, N-I+1, WORK, M, B( J1, I ), LDB ) 565: END IF 566: I = J1 - 1 567: IF( I.GT.0 ) THEN 568: CALL DGEMM( 'N', 'N', I, M, M, ONE, A( 1, J1 ), LDA, IR, 569: $ LDST, ZERO, WORK, I ) 570: CALL DLACPY( 'Full', I, M, WORK, I, A( 1, J1 ), LDA ) 571: CALL DGEMM( 'N', 'N', I, M, M, ONE, B( 1, J1 ), LDB, IR, 572: $ LDST, ZERO, WORK, I ) 573: CALL DLACPY( 'Full', I, M, WORK, I, B( 1, J1 ), LDB ) 574: END IF 575: * 576: * Exit with INFO = 0 if swap was successfully performed. 577: * 578: RETURN 579: * 580: END IF 581: * 582: * Exit with INFO = 1 if swap was rejected. 583: * 584: 70 CONTINUE 585: * 586: INFO = 1 587: RETURN 588: * 589: * End of DTGEX2 590: * 591: END