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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, 2: $ DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, 3: $ PERM, GIVNUM, C, S, WORK, IWORK, INFO ) 4: * 5: * -- LAPACK auxiliary routine (version 3.2.2) -- 6: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 8: * June 2010 9: * 10: * .. Scalar Arguments .. 11: INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE 12: * .. 13: * .. Array Arguments .. 14: INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), 15: $ K( * ), PERM( LDGCOL, * ) 16: DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), 17: $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), 18: $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), 19: $ Z( LDU, * ) 20: * .. 21: * 22: * Purpose 23: * ======= 24: * 25: * Using a divide and conquer approach, DLASDA computes the singular 26: * value decomposition (SVD) of a real upper bidiagonal N-by-M matrix 27: * B with diagonal D and offdiagonal E, where M = N + SQRE. The 28: * algorithm computes the singular values in the SVD B = U * S * VT. 29: * The orthogonal matrices U and VT are optionally computed in 30: * compact form. 31: * 32: * A related subroutine, DLASD0, computes the singular values and 33: * the singular vectors in explicit form. 34: * 35: * Arguments 36: * ========= 37: * 38: * ICOMPQ (input) INTEGER 39: * Specifies whether singular vectors are to be computed 40: * in compact form, as follows 41: * = 0: Compute singular values only. 42: * = 1: Compute singular vectors of upper bidiagonal 43: * matrix in compact form. 44: * 45: * SMLSIZ (input) INTEGER 46: * The maximum size of the subproblems at the bottom of the 47: * computation tree. 48: * 49: * N (input) INTEGER 50: * The row dimension of the upper bidiagonal matrix. This is 51: * also the dimension of the main diagonal array D. 52: * 53: * SQRE (input) INTEGER 54: * Specifies the column dimension of the bidiagonal matrix. 55: * = 0: The bidiagonal matrix has column dimension M = N; 56: * = 1: The bidiagonal matrix has column dimension M = N + 1. 57: * 58: * D (input/output) DOUBLE PRECISION array, dimension ( N ) 59: * On entry D contains the main diagonal of the bidiagonal 60: * matrix. On exit D, if INFO = 0, contains its singular values. 61: * 62: * E (input) DOUBLE PRECISION array, dimension ( M-1 ) 63: * Contains the subdiagonal entries of the bidiagonal matrix. 64: * On exit, E has been destroyed. 65: * 66: * U (output) DOUBLE PRECISION array, 67: * dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced 68: * if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left 69: * singular vector matrices of all subproblems at the bottom 70: * level. 71: * 72: * LDU (input) INTEGER, LDU = > N. 73: * The leading dimension of arrays U, VT, DIFL, DIFR, POLES, 74: * GIVNUM, and Z. 75: * 76: * VT (output) DOUBLE PRECISION array, 77: * dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced 78: * if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right 79: * singular vector matrices of all subproblems at the bottom 80: * level. 81: * 82: * K (output) INTEGER array, 83: * dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. 84: * If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th 85: * secular equation on the computation tree. 86: * 87: * DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ), 88: * where NLVL = floor(log_2 (N/SMLSIZ))). 89: * 90: * DIFR (output) DOUBLE PRECISION array, 91: * dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and 92: * dimension ( N ) if ICOMPQ = 0. 93: * If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) 94: * record distances between singular values on the I-th 95: * level and singular values on the (I -1)-th level, and 96: * DIFR(1:N, 2 * I ) contains the normalizing factors for 97: * the right singular vector matrix. See DLASD8 for details. 98: * 99: * Z (output) DOUBLE PRECISION array, 100: * dimension ( LDU, NLVL ) if ICOMPQ = 1 and 101: * dimension ( N ) if ICOMPQ = 0. 102: * The first K elements of Z(1, I) contain the components of 103: * the deflation-adjusted updating row vector for subproblems 104: * on the I-th level. 105: * 106: * POLES (output) DOUBLE PRECISION array, 107: * dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced 108: * if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and 109: * POLES(1, 2*I) contain the new and old singular values 110: * involved in the secular equations on the I-th level. 111: * 112: * GIVPTR (output) INTEGER array, 113: * dimension ( N ) if ICOMPQ = 1, and not referenced if 114: * ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records 115: * the number of Givens rotations performed on the I-th 116: * problem on the computation tree. 117: * 118: * GIVCOL (output) INTEGER array, 119: * dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not 120: * referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, 121: * GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations 122: * of Givens rotations performed on the I-th level on the 123: * computation tree. 124: * 125: * LDGCOL (input) INTEGER, LDGCOL = > N. 126: * The leading dimension of arrays GIVCOL and PERM. 127: * 128: * PERM (output) INTEGER array, 129: * dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced 130: * if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records 131: * permutations done on the I-th level of the computation tree. 132: * 133: * GIVNUM (output) DOUBLE PRECISION array, 134: * dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not 135: * referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, 136: * GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- 137: * values of Givens rotations performed on the I-th level on 138: * the computation tree. 139: * 140: * C (output) DOUBLE PRECISION array, 141: * dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. 142: * If ICOMPQ = 1 and the I-th subproblem is not square, on exit, 143: * C( I ) contains the C-value of a Givens rotation related to 144: * the right null space of the I-th subproblem. 145: * 146: * S (output) DOUBLE PRECISION array, dimension ( N ) if 147: * ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 148: * and the I-th subproblem is not square, on exit, S( I ) 149: * contains the S-value of a Givens rotation related to 150: * the right null space of the I-th subproblem. 151: * 152: * WORK (workspace) DOUBLE PRECISION array, dimension 153: * (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). 154: * 155: * IWORK (workspace) INTEGER array. 156: * Dimension must be at least (7 * N). 157: * 158: * INFO (output) INTEGER 159: * = 0: successful exit. 160: * < 0: if INFO = -i, the i-th argument had an illegal value. 161: * > 0: if INFO = 1, a singular value did not converge 162: * 163: * Further Details 164: * =============== 165: * 166: * Based on contributions by 167: * Ming Gu and Huan Ren, Computer Science Division, University of 168: * California at Berkeley, USA 169: * 170: * ===================================================================== 171: * 172: * .. Parameters .. 173: DOUBLE PRECISION ZERO, ONE 174: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 175: * .. 176: * .. Local Scalars .. 177: INTEGER I, I1, IC, IDXQ, IDXQI, IM1, INODE, ITEMP, IWK, 178: $ J, LF, LL, LVL, LVL2, M, NCC, ND, NDB1, NDIML, 179: $ NDIMR, NL, NLF, NLP1, NLVL, NR, NRF, NRP1, NRU, 180: $ NWORK1, NWORK2, SMLSZP, SQREI, VF, VFI, VL, VLI 181: DOUBLE PRECISION ALPHA, BETA 182: * .. 183: * .. External Subroutines .. 184: EXTERNAL DCOPY, DLASD6, DLASDQ, DLASDT, DLASET, XERBLA 185: * .. 186: * .. Executable Statements .. 187: * 188: * Test the input parameters. 189: * 190: INFO = 0 191: * 192: IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN 193: INFO = -1 194: ELSE IF( SMLSIZ.LT.3 ) THEN 195: INFO = -2 196: ELSE IF( N.LT.0 ) THEN 197: INFO = -3 198: ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN 199: INFO = -4 200: ELSE IF( LDU.LT.( N+SQRE ) ) THEN 201: INFO = -8 202: ELSE IF( LDGCOL.LT.N ) THEN 203: INFO = -17 204: END IF 205: IF( INFO.NE.0 ) THEN 206: CALL XERBLA( 'DLASDA', -INFO ) 207: RETURN 208: END IF 209: * 210: M = N + SQRE 211: * 212: * If the input matrix is too small, call DLASDQ to find the SVD. 213: * 214: IF( N.LE.SMLSIZ ) THEN 215: IF( ICOMPQ.EQ.0 ) THEN 216: CALL DLASDQ( 'U', SQRE, N, 0, 0, 0, D, E, VT, LDU, U, LDU, 217: $ U, LDU, WORK, INFO ) 218: ELSE 219: CALL DLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDU, U, LDU, 220: $ U, LDU, WORK, INFO ) 221: END IF 222: RETURN 223: END IF 224: * 225: * Book-keeping and set up the computation tree. 226: * 227: INODE = 1 228: NDIML = INODE + N 229: NDIMR = NDIML + N 230: IDXQ = NDIMR + N 231: IWK = IDXQ + N 232: * 233: NCC = 0 234: NRU = 0 235: * 236: SMLSZP = SMLSIZ + 1 237: VF = 1 238: VL = VF + M 239: NWORK1 = VL + M 240: NWORK2 = NWORK1 + SMLSZP*SMLSZP 241: * 242: CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ), 243: $ IWORK( NDIMR ), SMLSIZ ) 244: * 245: * for the nodes on bottom level of the tree, solve 246: * their subproblems by DLASDQ. 247: * 248: NDB1 = ( ND+1 ) / 2 249: DO 30 I = NDB1, ND 250: * 251: * IC : center row of each node 252: * NL : number of rows of left subproblem 253: * NR : number of rows of right subproblem 254: * NLF: starting row of the left subproblem 255: * NRF: starting row of the right subproblem 256: * 257: I1 = I - 1 258: IC = IWORK( INODE+I1 ) 259: NL = IWORK( NDIML+I1 ) 260: NLP1 = NL + 1 261: NR = IWORK( NDIMR+I1 ) 262: NLF = IC - NL 263: NRF = IC + 1 264: IDXQI = IDXQ + NLF - 2 265: VFI = VF + NLF - 1 266: VLI = VL + NLF - 1 267: SQREI = 1 268: IF( ICOMPQ.EQ.0 ) THEN 269: CALL DLASET( 'A', NLP1, NLP1, ZERO, ONE, WORK( NWORK1 ), 270: $ SMLSZP ) 271: CALL DLASDQ( 'U', SQREI, NL, NLP1, NRU, NCC, D( NLF ), 272: $ E( NLF ), WORK( NWORK1 ), SMLSZP, 273: $ WORK( NWORK2 ), NL, WORK( NWORK2 ), NL, 274: $ WORK( NWORK2 ), INFO ) 275: ITEMP = NWORK1 + NL*SMLSZP 276: CALL DCOPY( NLP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 ) 277: CALL DCOPY( NLP1, WORK( ITEMP ), 1, WORK( VLI ), 1 ) 278: ELSE 279: CALL DLASET( 'A', NL, NL, ZERO, ONE, U( NLF, 1 ), LDU ) 280: CALL DLASET( 'A', NLP1, NLP1, ZERO, ONE, VT( NLF, 1 ), LDU ) 281: CALL DLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), 282: $ E( NLF ), VT( NLF, 1 ), LDU, U( NLF, 1 ), LDU, 283: $ U( NLF, 1 ), LDU, WORK( NWORK1 ), INFO ) 284: CALL DCOPY( NLP1, VT( NLF, 1 ), 1, WORK( VFI ), 1 ) 285: CALL DCOPY( NLP1, VT( NLF, NLP1 ), 1, WORK( VLI ), 1 ) 286: END IF 287: IF( INFO.NE.0 ) THEN 288: RETURN 289: END IF 290: DO 10 J = 1, NL 291: IWORK( IDXQI+J ) = J 292: 10 CONTINUE 293: IF( ( I.EQ.ND ) .AND. ( SQRE.EQ.0 ) ) THEN 294: SQREI = 0 295: ELSE 296: SQREI = 1 297: END IF 298: IDXQI = IDXQI + NLP1 299: VFI = VFI + NLP1 300: VLI = VLI + NLP1 301: NRP1 = NR + SQREI 302: IF( ICOMPQ.EQ.0 ) THEN 303: CALL DLASET( 'A', NRP1, NRP1, ZERO, ONE, WORK( NWORK1 ), 304: $ SMLSZP ) 305: CALL DLASDQ( 'U', SQREI, NR, NRP1, NRU, NCC, D( NRF ), 306: $ E( NRF ), WORK( NWORK1 ), SMLSZP, 307: $ WORK( NWORK2 ), NR, WORK( NWORK2 ), NR, 308: $ WORK( NWORK2 ), INFO ) 309: ITEMP = NWORK1 + ( NRP1-1 )*SMLSZP 310: CALL DCOPY( NRP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 ) 311: CALL DCOPY( NRP1, WORK( ITEMP ), 1, WORK( VLI ), 1 ) 312: ELSE 313: CALL DLASET( 'A', NR, NR, ZERO, ONE, U( NRF, 1 ), LDU ) 314: CALL DLASET( 'A', NRP1, NRP1, ZERO, ONE, VT( NRF, 1 ), LDU ) 315: CALL DLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), 316: $ E( NRF ), VT( NRF, 1 ), LDU, U( NRF, 1 ), LDU, 317: $ U( NRF, 1 ), LDU, WORK( NWORK1 ), INFO ) 318: CALL DCOPY( NRP1, VT( NRF, 1 ), 1, WORK( VFI ), 1 ) 319: CALL DCOPY( NRP1, VT( NRF, NRP1 ), 1, WORK( VLI ), 1 ) 320: END IF 321: IF( INFO.NE.0 ) THEN 322: RETURN 323: END IF 324: DO 20 J = 1, NR 325: IWORK( IDXQI+J ) = J 326: 20 CONTINUE 327: 30 CONTINUE 328: * 329: * Now conquer each subproblem bottom-up. 330: * 331: J = 2**NLVL 332: DO 50 LVL = NLVL, 1, -1 333: LVL2 = LVL*2 - 1 334: * 335: * Find the first node LF and last node LL on 336: * the current level LVL. 337: * 338: IF( LVL.EQ.1 ) THEN 339: LF = 1 340: LL = 1 341: ELSE 342: LF = 2**( LVL-1 ) 343: LL = 2*LF - 1 344: END IF 345: DO 40 I = LF, LL 346: IM1 = I - 1 347: IC = IWORK( INODE+IM1 ) 348: NL = IWORK( NDIML+IM1 ) 349: NR = IWORK( NDIMR+IM1 ) 350: NLF = IC - NL 351: NRF = IC + 1 352: IF( I.EQ.LL ) THEN 353: SQREI = SQRE 354: ELSE 355: SQREI = 1 356: END IF 357: VFI = VF + NLF - 1 358: VLI = VL + NLF - 1 359: IDXQI = IDXQ + NLF - 1 360: ALPHA = D( IC ) 361: BETA = E( IC ) 362: IF( ICOMPQ.EQ.0 ) THEN 363: CALL DLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ), 364: $ WORK( VFI ), WORK( VLI ), ALPHA, BETA, 365: $ IWORK( IDXQI ), PERM, GIVPTR( 1 ), GIVCOL, 366: $ LDGCOL, GIVNUM, LDU, POLES, DIFL, DIFR, Z, 367: $ K( 1 ), C( 1 ), S( 1 ), WORK( NWORK1 ), 368: $ IWORK( IWK ), INFO ) 369: ELSE 370: J = J - 1 371: CALL DLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ), 372: $ WORK( VFI ), WORK( VLI ), ALPHA, BETA, 373: $ IWORK( IDXQI ), PERM( NLF, LVL ), 374: $ GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL, 375: $ GIVNUM( NLF, LVL2 ), LDU, 376: $ POLES( NLF, LVL2 ), DIFL( NLF, LVL ), 377: $ DIFR( NLF, LVL2 ), Z( NLF, LVL ), K( J ), 378: $ C( J ), S( J ), WORK( NWORK1 ), 379: $ IWORK( IWK ), INFO ) 380: END IF 381: IF( INFO.NE.0 ) THEN 382: RETURN 383: END IF 384: 40 CONTINUE 385: 50 CONTINUE 386: * 387: RETURN 388: * 389: * End of DLASDA 390: * 391: END