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Mise à jour de lapack vers la version 3.3.0.
1: RECURSIVE SUBROUTINE ZUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, 2: $ SIGNS, M, P, Q, X11, LDX11, X12, 3: $ LDX12, X21, LDX21, X22, LDX22, THETA, 4: $ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, 5: $ LDV2T, WORK, LWORK, RWORK, LRWORK, 6: $ IWORK, INFO ) 7: IMPLICIT NONE 8: * 9: * -- LAPACK routine (version 3.3.0) -- 10: * 11: * -- Contributed by Brian Sutton of the Randolph-Macon College -- 12: * -- November 2010 13: * 14: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 15: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 16: * 17: * .. Scalar Arguments .. 18: CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS 19: INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, 20: $ LDX21, LDX22, LRWORK, LWORK, M, P, Q 21: * .. 22: * .. Array Arguments .. 23: INTEGER IWORK( * ) 24: DOUBLE PRECISION THETA( * ) 25: DOUBLE PRECISION RWORK( * ) 26: COMPLEX*16 U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), 27: $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ), 28: $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22, 29: $ * ) 30: * .. 31: * 32: * Purpose 33: * ======= 34: * 35: * ZUNCSD computes the CS decomposition of an M-by-M partitioned 36: * unitary matrix X: 37: * 38: * [ I 0 0 | 0 0 0 ] 39: * [ 0 C 0 | 0 -S 0 ] 40: * [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**H 41: * X = [-----------] = [---------] [---------------------] [---------] . 42: * [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ] 43: * [ 0 S 0 | 0 C 0 ] 44: * [ 0 0 I | 0 0 0 ] 45: * 46: * X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P, 47: * (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are 48: * R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in 49: * which R = MIN(P,M-P,Q,M-Q). 50: * 51: * Arguments 52: * ========= 53: * 54: * JOBU1 (input) CHARACTER 55: * = 'Y': U1 is computed; 56: * otherwise: U1 is not computed. 57: * 58: * JOBU2 (input) CHARACTER 59: * = 'Y': U2 is computed; 60: * otherwise: U2 is not computed. 61: * 62: * JOBV1T (input) CHARACTER 63: * = 'Y': V1T is computed; 64: * otherwise: V1T is not computed. 65: * 66: * JOBV2T (input) CHARACTER 67: * = 'Y': V2T is computed; 68: * otherwise: V2T is not computed. 69: * 70: * TRANS (input) CHARACTER 71: * = 'T': X, U1, U2, V1T, and V2T are stored in row-major 72: * order; 73: * otherwise: X, U1, U2, V1T, and V2T are stored in column- 74: * major order. 75: * 76: * SIGNS (input) CHARACTER 77: * = 'O': The lower-left block is made nonpositive (the 78: * "other" convention); 79: * otherwise: The upper-right block is made nonpositive (the 80: * "default" convention). 81: * 82: * M (input) INTEGER 83: * The number of rows and columns in X. 84: * 85: * P (input) INTEGER 86: * The number of rows in X11 and X12. 0 <= P <= M. 87: * 88: * Q (input) INTEGER 89: * The number of columns in X11 and X21. 0 <= Q <= M. 90: * 91: * X (input/workspace) COMPLEX*16 array, dimension (LDX,M) 92: * On entry, the unitary matrix whose CSD is desired. 93: * 94: * LDX (input) INTEGER 95: * The leading dimension of X. LDX >= MAX(1,M). 96: * 97: * THETA (output) DOUBLE PRECISION array, dimension (R), in which R = 98: * MIN(P,M-P,Q,M-Q). 99: * C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and 100: * S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). 101: * 102: * U1 (output) COMPLEX*16 array, dimension (P) 103: * If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. 104: * 105: * LDU1 (input) INTEGER 106: * The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= 107: * MAX(1,P). 108: * 109: * U2 (output) COMPLEX*16 array, dimension (M-P) 110: * If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary 111: * matrix U2. 112: * 113: * LDU2 (input) INTEGER 114: * The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= 115: * MAX(1,M-P). 116: * 117: * V1T (output) COMPLEX*16 array, dimension (Q) 118: * If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary 119: * matrix V1**H. 120: * 121: * LDV1T (input) INTEGER 122: * The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= 123: * MAX(1,Q). 124: * 125: * V2T (output) COMPLEX*16 array, dimension (M-Q) 126: * If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary 127: * matrix V2**H. 128: * 129: * LDV2T (input) INTEGER 130: * The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >= 131: * MAX(1,M-Q). 132: * 133: * WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) 134: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 135: * 136: * LWORK (input) INTEGER 137: * The dimension of the array WORK. 138: * 139: * If LWORK = -1, then a workspace query is assumed; the routine 140: * only calculates the optimal size of the WORK array, returns 141: * this value as the first entry of the work array, and no error 142: * message related to LWORK is issued by XERBLA. 143: * 144: * RWORK (workspace) DOUBLE PRECISION array, dimension MAX(1,LRWORK) 145: * On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. 146: * If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1), 147: * ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), 148: * define the matrix in intermediate bidiagonal-block form 149: * remaining after nonconvergence. INFO specifies the number 150: * of nonzero PHI's. 151: * 152: * LRWORK (input) INTEGER 153: * The dimension of the array RWORK. 154: * 155: * If LRWORK = -1, then a workspace query is assumed; the routine 156: * only calculates the optimal size of the RWORK array, returns 157: * this value as the first entry of the work array, and no error 158: * message related to LRWORK is issued by XERBLA. 159: * 160: * IWORK (workspace) INTEGER array, dimension (M-Q) 161: * 162: * INFO (output) INTEGER 163: * = 0: successful exit. 164: * < 0: if INFO = -i, the i-th argument had an illegal value. 165: * > 0: ZBBCSD did not converge. See the description of RWORK 166: * above for details. 167: * 168: * Reference 169: * ========= 170: * 171: * [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. 172: * Algorithms, 50(1):33-65, 2009. 173: * 174: * =================================================================== 175: * 176: * .. Parameters .. 177: DOUBLE PRECISION REALONE 178: PARAMETER ( REALONE = 1.0D0 ) 179: COMPLEX*16 NEGONE, ONE, PIOVER2, ZERO 180: PARAMETER ( NEGONE = (-1.0D0,0.0D0), ONE = (1.0D0,0.0D0), 181: $ PIOVER2 = 1.57079632679489662D0, 182: $ ZERO = (0.0D0,0.0D0) ) 183: * .. 184: * .. Local Scalars .. 185: CHARACTER TRANST, SIGNST 186: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E, 187: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB, 188: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1, 189: $ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN, 190: $ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN, 191: $ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN, 192: $ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN, 193: $ LORGQRWORKOPT, LWORKMIN, LWORKOPT 194: LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2, 195: $ WANTV1T, WANTV2T 196: INTEGER LRWORKMIN, LRWORKOPT 197: LOGICAL LRQUERY 198: * .. 199: * .. External Subroutines .. 200: EXTERNAL XERBLA, ZBBCSD, ZLACPY, ZLAPMR, ZLAPMT, ZLASCL, 201: $ ZLASET, ZUNBDB, ZUNGLQ, ZUNGQR 202: * .. 203: * .. External Functions .. 204: LOGICAL LSAME 205: EXTERNAL LSAME 206: * .. 207: * .. Intrinsic Functions 208: INTRINSIC COS, INT, MAX, MIN, SIN 209: * .. 210: * .. Executable Statements .. 211: * 212: * Test input arguments 213: * 214: INFO = 0 215: WANTU1 = LSAME( JOBU1, 'Y' ) 216: WANTU2 = LSAME( JOBU2, 'Y' ) 217: WANTV1T = LSAME( JOBV1T, 'Y' ) 218: WANTV2T = LSAME( JOBV2T, 'Y' ) 219: COLMAJOR = .NOT. LSAME( TRANS, 'T' ) 220: DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' ) 221: LQUERY = LWORK .EQ. -1 222: LRQUERY = LRWORK .EQ. -1 223: IF( M .LT. 0 ) THEN 224: INFO = -7 225: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN 226: INFO = -8 227: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN 228: INFO = -9 229: ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR. 230: $ ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN 231: INFO = -11 232: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN 233: INFO = -14 234: ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN 235: INFO = -16 236: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN 237: INFO = -18 238: ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN 239: INFO = -20 240: END IF 241: * 242: * Work with transpose if convenient 243: * 244: IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN 245: IF( COLMAJOR ) THEN 246: TRANST = 'T' 247: ELSE 248: TRANST = 'N' 249: END IF 250: IF( DEFAULTSIGNS ) THEN 251: SIGNST = 'O' 252: ELSE 253: SIGNST = 'D' 254: END IF 255: CALL ZUNCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M, 256: $ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22, 257: $ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1, 258: $ U2, LDU2, WORK, LWORK, RWORK, LRWORK, IWORK, 259: $ INFO ) 260: RETURN 261: END IF 262: * 263: * Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if 264: * convenient 265: * 266: IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN 267: IF( DEFAULTSIGNS ) THEN 268: SIGNST = 'O' 269: ELSE 270: SIGNST = 'D' 271: END IF 272: CALL ZUNCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M, 273: $ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11, 274: $ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T, 275: $ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO ) 276: RETURN 277: END IF 278: * 279: * Compute workspace 280: * 281: IF( INFO .EQ. 0 ) THEN 282: * 283: * Real workspace 284: * 285: IPHI = 2 286: IB11D = IPHI + MAX( 1, Q - 1 ) 287: IB11E = IB11D + MAX( 1, Q ) 288: IB12D = IB11E + MAX( 1, Q - 1 ) 289: IB12E = IB12D + MAX( 1, Q ) 290: IB21D = IB12E + MAX( 1, Q - 1 ) 291: IB21E = IB21D + MAX( 1, Q ) 292: IB22D = IB21E + MAX( 1, Q - 1 ) 293: IB22E = IB22D + MAX( 1, Q ) 294: IBBCSD = IB22E + MAX( 1, Q - 1 ) 295: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0, 296: $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0, 297: $ 0, 0, 0, 0, 0, 0, 0, RWORK, -1, CHILDINFO ) 298: LBBCSDWORKOPT = INT( RWORK(1) ) 299: LBBCSDWORKMIN = LBBCSDWORKOPT 300: LRWORKOPT = IBBCSD + LBBCSDWORKOPT - 1 301: LRWORKMIN = IBBCSD + LBBCSDWORKMIN - 1 302: RWORK(1) = LRWORKOPT 303: * 304: * Complex workspace 305: * 306: ITAUP1 = 2 307: ITAUP2 = ITAUP1 + MAX( 1, P ) 308: ITAUQ1 = ITAUP2 + MAX( 1, M - P ) 309: ITAUQ2 = ITAUQ1 + MAX( 1, Q ) 310: IORGQR = ITAUQ2 + MAX( 1, M - Q ) 311: CALL ZUNGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1, 312: $ CHILDINFO ) 313: LORGQRWORKOPT = INT( WORK(1) ) 314: LORGQRWORKMIN = MAX( 1, M - Q ) 315: IORGLQ = ITAUQ2 + MAX( 1, M - Q ) 316: CALL ZUNGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1, 317: $ CHILDINFO ) 318: LORGLQWORKOPT = INT( WORK(1) ) 319: LORGLQWORKMIN = MAX( 1, M - Q ) 320: IORBDB = ITAUQ2 + MAX( 1, M - Q ) 321: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, 322: $ X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK, 323: $ -1, CHILDINFO ) 324: LORBDBWORKOPT = INT( WORK(1) ) 325: LORBDBWORKMIN = LORBDBWORKOPT 326: LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT, 327: $ IORBDB + LORBDBWORKOPT ) - 1 328: LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN, 329: $ IORBDB + LORBDBWORKMIN ) - 1 330: WORK(1) = LWORKOPT 331: * 332: IF( LWORK .LT. LWORKMIN 333: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN 334: INFO = -22 335: ELSE IF( LRWORK .LT. LRWORKMIN 336: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN 337: INFO = -24 338: ELSE 339: LORGQRWORK = LWORK - IORGQR + 1 340: LORGLQWORK = LWORK - IORGLQ + 1 341: LORBDBWORK = LWORK - IORBDB + 1 342: LBBCSDWORK = LRWORK - IBBCSD + 1 343: END IF 344: END IF 345: * 346: * Abort if any illegal arguments 347: * 348: IF( INFO .NE. 0 ) THEN 349: CALL XERBLA( 'ZUNCSD', -INFO ) 350: RETURN 351: ELSE IF( LQUERY .OR. LRQUERY ) THEN 352: RETURN 353: END IF 354: * 355: * Transform to bidiagonal block form 356: * 357: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, 358: $ LDX21, X22, LDX22, THETA, RWORK(IPHI), WORK(ITAUP1), 359: $ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2), 360: $ WORK(IORBDB), LORBDBWORK, CHILDINFO ) 361: * 362: * Accumulate Householder reflectors 363: * 364: IF( COLMAJOR ) THEN 365: IF( WANTU1 .AND. P .GT. 0 ) THEN 366: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 ) 367: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR), 368: $ LORGQRWORK, INFO) 369: END IF 370: IF( WANTU2 .AND. M-P .GT. 0 ) THEN 371: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 ) 372: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), 373: $ WORK(IORGQR), LORGQRWORK, INFO ) 374: END IF 375: IF( WANTV1T .AND. Q .GT. 0 ) THEN 376: CALL ZLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2), 377: $ LDV1T ) 378: V1T(1, 1) = ONE 379: DO J = 2, Q 380: V1T(1,J) = ZERO 381: V1T(J,1) = ZERO 382: END DO 383: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1), 384: $ WORK(IORGLQ), LORGLQWORK, INFO ) 385: END IF 386: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN 387: CALL ZLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T ) 388: CALL ZLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22, 389: $ V2T(P+1,P+1), LDV2T ) 390: CALL ZUNGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), 391: $ WORK(IORGLQ), LORGLQWORK, INFO ) 392: END IF 393: ELSE 394: IF( WANTU1 .AND. P .GT. 0 ) THEN 395: CALL ZLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 ) 396: CALL ZUNGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ), 397: $ LORGLQWORK, INFO) 398: END IF 399: IF( WANTU2 .AND. M-P .GT. 0 ) THEN 400: CALL ZLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 ) 401: CALL ZUNGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), 402: $ WORK(IORGLQ), LORGLQWORK, INFO ) 403: END IF 404: IF( WANTV1T .AND. Q .GT. 0 ) THEN 405: CALL ZLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2), 406: $ LDV1T ) 407: V1T(1, 1) = ONE 408: DO J = 2, Q 409: V1T(1,J) = ZERO 410: V1T(J,1) = ZERO 411: END DO 412: CALL ZUNGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1), 413: $ WORK(IORGQR), LORGQRWORK, INFO ) 414: END IF 415: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN 416: CALL ZLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T ) 417: CALL ZLACPY( 'L', M-P-Q, M-P-Q, X22(P+1,Q+1), LDX22, 418: $ V2T(P+1,P+1), LDV2T ) 419: CALL ZUNGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), 420: $ WORK(IORGQR), LORGQRWORK, INFO ) 421: END IF 422: END IF 423: * 424: * Compute the CSD of the matrix in bidiagonal-block form 425: * 426: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, 427: $ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, 428: $ LDV2T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D), 429: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E), 430: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), 431: $ LBBCSDWORK, INFO ) 432: * 433: * Permute rows and columns to place identity submatrices in top- 434: * left corner of (1,1)-block and/or bottom-right corner of (1,2)- 435: * block and/or bottom-right corner of (2,1)-block and/or top-left 436: * corner of (2,2)-block 437: * 438: IF( Q .GT. 0 .AND. WANTU2 ) THEN 439: DO I = 1, Q 440: IWORK(I) = M - P - Q + I 441: END DO 442: DO I = Q + 1, M - P 443: IWORK(I) = I - Q 444: END DO 445: IF( COLMAJOR ) THEN 446: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK ) 447: ELSE 448: CALL ZLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK ) 449: END IF 450: END IF 451: IF( M .GT. 0 .AND. WANTV2T ) THEN 452: DO I = 1, P 453: IWORK(I) = M - P - Q + I 454: END DO 455: DO I = P + 1, M - Q 456: IWORK(I) = I - P 457: END DO 458: IF( .NOT. COLMAJOR ) THEN 459: CALL ZLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK ) 460: ELSE 461: CALL ZLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK ) 462: END IF 463: END IF 464: * 465: RETURN 466: * 467: * End ZUNCSD 468: * 469: END 470: