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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, 2: $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, 3: $ RWORK, LRWORK, IWORK, LIWORK, INFO ) 4: * 5: * -- LAPACK driver 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: CHARACTER JOBZ, RANGE, UPLO 12: INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK, 13: $ M, N 14: DOUBLE PRECISION ABSTOL, VL, VU 15: * .. 16: * .. Array Arguments .. 17: INTEGER ISUPPZ( * ), IWORK( * ) 18: DOUBLE PRECISION RWORK( * ), W( * ) 19: COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * ) 20: * .. 21: * 22: * Purpose 23: * ======= 24: * 25: * ZHEEVR computes selected eigenvalues and, optionally, eigenvectors 26: * of a complex Hermitian matrix A. Eigenvalues and eigenvectors can 27: * be selected by specifying either a range of values or a range of 28: * indices for the desired eigenvalues. 29: * 30: * ZHEEVR first reduces the matrix A to tridiagonal form T with a call 31: * to ZHETRD. Then, whenever possible, ZHEEVR calls ZSTEMR to compute 32: * eigenspectrum using Relatively Robust Representations. ZSTEMR 33: * computes eigenvalues by the dqds algorithm, while orthogonal 34: * eigenvectors are computed from various "good" L D L^T representations 35: * (also known as Relatively Robust Representations). Gram-Schmidt 36: * orthogonalization is avoided as far as possible. More specifically, 37: * the various steps of the algorithm are as follows. 38: * 39: * For each unreduced block (submatrix) of T, 40: * (a) Compute T - sigma I = L D L^T, so that L and D 41: * define all the wanted eigenvalues to high relative accuracy. 42: * This means that small relative changes in the entries of D and L 43: * cause only small relative changes in the eigenvalues and 44: * eigenvectors. The standard (unfactored) representation of the 45: * tridiagonal matrix T does not have this property in general. 46: * (b) Compute the eigenvalues to suitable accuracy. 47: * If the eigenvectors are desired, the algorithm attains full 48: * accuracy of the computed eigenvalues only right before 49: * the corresponding vectors have to be computed, see steps c) and d). 50: * (c) For each cluster of close eigenvalues, select a new 51: * shift close to the cluster, find a new factorization, and refine 52: * the shifted eigenvalues to suitable accuracy. 53: * (d) For each eigenvalue with a large enough relative separation compute 54: * the corresponding eigenvector by forming a rank revealing twisted 55: * factorization. Go back to (c) for any clusters that remain. 56: * 57: * The desired accuracy of the output can be specified by the input 58: * parameter ABSTOL. 59: * 60: * For more details, see DSTEMR's documentation and: 61: * - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations 62: * to compute orthogonal eigenvectors of symmetric tridiagonal matrices," 63: * Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. 64: * - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and 65: * Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, 66: * 2004. Also LAPACK Working Note 154. 67: * - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric 68: * tridiagonal eigenvalue/eigenvector problem", 69: * Computer Science Division Technical Report No. UCB/CSD-97-971, 70: * UC Berkeley, May 1997. 71: * 72: * 73: * Note 1 : ZHEEVR calls ZSTEMR when the full spectrum is requested 74: * on machines which conform to the ieee-754 floating point standard. 75: * ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and 76: * when partial spectrum requests are made. 77: * 78: * Normal execution of ZSTEMR may create NaNs and infinities and 79: * hence may abort due to a floating point exception in environments 80: * which do not handle NaNs and infinities in the ieee standard default 81: * manner. 82: * 83: * Arguments 84: * ========= 85: * 86: * JOBZ (input) CHARACTER*1 87: * = 'N': Compute eigenvalues only; 88: * = 'V': Compute eigenvalues and eigenvectors. 89: * 90: * RANGE (input) CHARACTER*1 91: * = 'A': all eigenvalues will be found. 92: * = 'V': all eigenvalues in the half-open interval (VL,VU] 93: * will be found. 94: * = 'I': the IL-th through IU-th eigenvalues will be found. 95: ********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and 96: ********** ZSTEIN are called 97: * 98: * UPLO (input) CHARACTER*1 99: * = 'U': Upper triangle of A is stored; 100: * = 'L': Lower triangle of A is stored. 101: * 102: * N (input) INTEGER 103: * The order of the matrix A. N >= 0. 104: * 105: * A (input/output) COMPLEX*16 array, dimension (LDA, N) 106: * On entry, the Hermitian matrix A. If UPLO = 'U', the 107: * leading N-by-N upper triangular part of A contains the 108: * upper triangular part of the matrix A. If UPLO = 'L', 109: * the leading N-by-N lower triangular part of A contains 110: * the lower triangular part of the matrix A. 111: * On exit, the lower triangle (if UPLO='L') or the upper 112: * triangle (if UPLO='U') of A, including the diagonal, is 113: * destroyed. 114: * 115: * LDA (input) INTEGER 116: * The leading dimension of the array A. LDA >= max(1,N). 117: * 118: * VL (input) DOUBLE PRECISION 119: * VU (input) DOUBLE PRECISION 120: * If RANGE='V', the lower and upper bounds of the interval to 121: * be searched for eigenvalues. VL < VU. 122: * Not referenced if RANGE = 'A' or 'I'. 123: * 124: * IL (input) INTEGER 125: * IU (input) INTEGER 126: * If RANGE='I', the indices (in ascending order) of the 127: * smallest and largest eigenvalues to be returned. 128: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. 129: * Not referenced if RANGE = 'A' or 'V'. 130: * 131: * ABSTOL (input) DOUBLE PRECISION 132: * The absolute error tolerance for the eigenvalues. 133: * An approximate eigenvalue is accepted as converged 134: * when it is determined to lie in an interval [a,b] 135: * of width less than or equal to 136: * 137: * ABSTOL + EPS * max( |a|,|b| ) , 138: * 139: * where EPS is the machine precision. If ABSTOL is less than 140: * or equal to zero, then EPS*|T| will be used in its place, 141: * where |T| is the 1-norm of the tridiagonal matrix obtained 142: * by reducing A to tridiagonal form. 143: * 144: * See "Computing Small Singular Values of Bidiagonal Matrices 145: * with Guaranteed High Relative Accuracy," by Demmel and 146: * Kahan, LAPACK Working Note #3. 147: * 148: * If high relative accuracy is important, set ABSTOL to 149: * DLAMCH( 'Safe minimum' ). Doing so will guarantee that 150: * eigenvalues are computed to high relative accuracy when 151: * possible in future releases. The current code does not 152: * make any guarantees about high relative accuracy, but 153: * furutre releases will. See J. Barlow and J. Demmel, 154: * "Computing Accurate Eigensystems of Scaled Diagonally 155: * Dominant Matrices", LAPACK Working Note #7, for a discussion 156: * of which matrices define their eigenvalues to high relative 157: * accuracy. 158: * 159: * M (output) INTEGER 160: * The total number of eigenvalues found. 0 <= M <= N. 161: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. 162: * 163: * W (output) DOUBLE PRECISION array, dimension (N) 164: * The first M elements contain the selected eigenvalues in 165: * ascending order. 166: * 167: * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M)) 168: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z 169: * contain the orthonormal eigenvectors of the matrix A 170: * corresponding to the selected eigenvalues, with the i-th 171: * column of Z holding the eigenvector associated with W(i). 172: * If JOBZ = 'N', then Z is not referenced. 173: * Note: the user must ensure that at least max(1,M) columns are 174: * supplied in the array Z; if RANGE = 'V', the exact value of M 175: * is not known in advance and an upper bound must be used. 176: * 177: * LDZ (input) INTEGER 178: * The leading dimension of the array Z. LDZ >= 1, and if 179: * JOBZ = 'V', LDZ >= max(1,N). 180: * 181: * ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) ) 182: * The support of the eigenvectors in Z, i.e., the indices 183: * indicating the nonzero elements in Z. The i-th eigenvector 184: * is nonzero only in elements ISUPPZ( 2*i-1 ) through 185: * ISUPPZ( 2*i ). 186: ********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 187: * 188: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 189: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 190: * 191: * LWORK (input) INTEGER 192: * The length of the array WORK. LWORK >= max(1,2*N). 193: * For optimal efficiency, LWORK >= (NB+1)*N, 194: * where NB is the max of the blocksize for ZHETRD and for 195: * ZUNMTR as returned by ILAENV. 196: * 197: * If LWORK = -1, then a workspace query is assumed; the routine 198: * only calculates the optimal sizes of the WORK, RWORK and 199: * IWORK arrays, returns these values as the first entries of 200: * the WORK, RWORK and IWORK arrays, and no error message 201: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 202: * 203: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) 204: * On exit, if INFO = 0, RWORK(1) returns the optimal 205: * (and minimal) LRWORK. 206: * 207: * LRWORK (input) INTEGER 208: * The length of the array RWORK. LRWORK >= max(1,24*N). 209: * 210: * If LRWORK = -1, then a workspace query is assumed; the 211: * routine only calculates the optimal sizes of the WORK, RWORK 212: * and IWORK arrays, returns these values as the first entries 213: * of the WORK, RWORK and IWORK arrays, and no error message 214: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 215: * 216: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 217: * On exit, if INFO = 0, IWORK(1) returns the optimal 218: * (and minimal) LIWORK. 219: * 220: * LIWORK (input) INTEGER 221: * The dimension of the array IWORK. LIWORK >= max(1,10*N). 222: * 223: * If LIWORK = -1, then a workspace query is assumed; the 224: * routine only calculates the optimal sizes of the WORK, RWORK 225: * and IWORK arrays, returns these values as the first entries 226: * of the WORK, RWORK and IWORK arrays, and no error message 227: * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 228: * 229: * INFO (output) INTEGER 230: * = 0: successful exit 231: * < 0: if INFO = -i, the i-th argument had an illegal value 232: * > 0: Internal error 233: * 234: * Further Details 235: * =============== 236: * 237: * Based on contributions by 238: * Inderjit Dhillon, IBM Almaden, USA 239: * Osni Marques, LBNL/NERSC, USA 240: * Ken Stanley, Computer Science Division, University of 241: * California at Berkeley, USA 242: * Jason Riedy, Computer Science Division, University of 243: * California at Berkeley, USA 244: * 245: * ===================================================================== 246: * 247: * .. Parameters .. 248: DOUBLE PRECISION ZERO, ONE, TWO 249: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) 250: * .. 251: * .. Local Scalars .. 252: LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG, 253: $ WANTZ, TRYRAC 254: CHARACTER ORDER 255: INTEGER I, IEEEOK, IINFO, IMAX, INDIBL, INDIFL, INDISP, 256: $ INDIWO, INDRD, INDRDD, INDRE, INDREE, INDRWK, 257: $ INDTAU, INDWK, INDWKN, ISCALE, ITMP1, J, JJ, 258: $ LIWMIN, LLWORK, LLRWORK, LLWRKN, LRWMIN, 259: $ LWKOPT, LWMIN, NB, NSPLIT 260: DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, 261: $ SIGMA, SMLNUM, TMP1, VLL, VUU 262: * .. 263: * .. External Functions .. 264: LOGICAL LSAME 265: INTEGER ILAENV 266: DOUBLE PRECISION DLAMCH, ZLANSY 267: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANSY 268: * .. 269: * .. External Subroutines .. 270: EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZDSCAL, 271: $ ZHETRD, ZSTEMR, ZSTEIN, ZSWAP, ZUNMTR 272: * .. 273: * .. Intrinsic Functions .. 274: INTRINSIC DBLE, MAX, MIN, SQRT 275: * .. 276: * .. Executable Statements .. 277: * 278: * Test the input parameters. 279: * 280: IEEEOK = ILAENV( 10, 'ZHEEVR', 'N', 1, 2, 3, 4 ) 281: * 282: LOWER = LSAME( UPLO, 'L' ) 283: WANTZ = LSAME( JOBZ, 'V' ) 284: ALLEIG = LSAME( RANGE, 'A' ) 285: VALEIG = LSAME( RANGE, 'V' ) 286: INDEIG = LSAME( RANGE, 'I' ) 287: * 288: LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LRWORK.EQ.-1 ) .OR. 289: $ ( LIWORK.EQ.-1 ) ) 290: * 291: LRWMIN = MAX( 1, 24*N ) 292: LIWMIN = MAX( 1, 10*N ) 293: LWMIN = MAX( 1, 2*N ) 294: * 295: INFO = 0 296: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 297: INFO = -1 298: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN 299: INFO = -2 300: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN 301: INFO = -3 302: ELSE IF( N.LT.0 ) THEN 303: INFO = -4 304: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 305: INFO = -6 306: ELSE 307: IF( VALEIG ) THEN 308: IF( N.GT.0 .AND. VU.LE.VL ) 309: $ INFO = -8 310: ELSE IF( INDEIG ) THEN 311: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN 312: INFO = -9 313: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN 314: INFO = -10 315: END IF 316: END IF 317: END IF 318: IF( INFO.EQ.0 ) THEN 319: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 320: INFO = -15 321: END IF 322: END IF 323: * 324: IF( INFO.EQ.0 ) THEN 325: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) 326: NB = MAX( NB, ILAENV( 1, 'ZUNMTR', UPLO, N, -1, -1, -1 ) ) 327: LWKOPT = MAX( ( NB+1 )*N, LWMIN ) 328: WORK( 1 ) = LWKOPT 329: RWORK( 1 ) = LRWMIN 330: IWORK( 1 ) = LIWMIN 331: * 332: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 333: INFO = -18 334: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 335: INFO = -20 336: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 337: INFO = -22 338: END IF 339: END IF 340: * 341: IF( INFO.NE.0 ) THEN 342: CALL XERBLA( 'ZHEEVR', -INFO ) 343: RETURN 344: ELSE IF( LQUERY ) THEN 345: RETURN 346: END IF 347: * 348: * Quick return if possible 349: * 350: M = 0 351: IF( N.EQ.0 ) THEN 352: WORK( 1 ) = 1 353: RETURN 354: END IF 355: * 356: IF( N.EQ.1 ) THEN 357: WORK( 1 ) = 2 358: IF( ALLEIG .OR. INDEIG ) THEN 359: M = 1 360: W( 1 ) = DBLE( A( 1, 1 ) ) 361: ELSE 362: IF( VL.LT.DBLE( A( 1, 1 ) ) .AND. VU.GE.DBLE( A( 1, 1 ) ) ) 363: $ THEN 364: M = 1 365: W( 1 ) = DBLE( A( 1, 1 ) ) 366: END IF 367: END IF 368: IF( WANTZ ) THEN 369: Z( 1, 1 ) = ONE 370: ISUPPZ( 1 ) = 1 371: ISUPPZ( 2 ) = 1 372: END IF 373: RETURN 374: END IF 375: * 376: * Get machine constants. 377: * 378: SAFMIN = DLAMCH( 'Safe minimum' ) 379: EPS = DLAMCH( 'Precision' ) 380: SMLNUM = SAFMIN / EPS 381: BIGNUM = ONE / SMLNUM 382: RMIN = SQRT( SMLNUM ) 383: RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) 384: * 385: * Scale matrix to allowable range, if necessary. 386: * 387: ISCALE = 0 388: ABSTLL = ABSTOL 389: IF (VALEIG) THEN 390: VLL = VL 391: VUU = VU 392: END IF 393: ANRM = ZLANSY( 'M', UPLO, N, A, LDA, RWORK ) 394: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN 395: ISCALE = 1 396: SIGMA = RMIN / ANRM 397: ELSE IF( ANRM.GT.RMAX ) THEN 398: ISCALE = 1 399: SIGMA = RMAX / ANRM 400: END IF 401: IF( ISCALE.EQ.1 ) THEN 402: IF( LOWER ) THEN 403: DO 10 J = 1, N 404: CALL ZDSCAL( N-J+1, SIGMA, A( J, J ), 1 ) 405: 10 CONTINUE 406: ELSE 407: DO 20 J = 1, N 408: CALL ZDSCAL( J, SIGMA, A( 1, J ), 1 ) 409: 20 CONTINUE 410: END IF 411: IF( ABSTOL.GT.0 ) 412: $ ABSTLL = ABSTOL*SIGMA 413: IF( VALEIG ) THEN 414: VLL = VL*SIGMA 415: VUU = VU*SIGMA 416: END IF 417: END IF 418: 419: * Initialize indices into workspaces. Note: The IWORK indices are 420: * used only if DSTERF or ZSTEMR fail. 421: 422: * WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the 423: * elementary reflectors used in ZHETRD. 424: INDTAU = 1 425: * INDWK is the starting offset of the remaining complex workspace, 426: * and LLWORK is the remaining complex workspace size. 427: INDWK = INDTAU + N 428: LLWORK = LWORK - INDWK + 1 429: 430: * RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal 431: * entries. 432: INDRD = 1 433: * RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the 434: * tridiagonal matrix from ZHETRD. 435: INDRE = INDRD + N 436: * RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over 437: * -written by ZSTEMR (the DSTERF path copies the diagonal to W). 438: INDRDD = INDRE + N 439: * RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over 440: * -written while computing the eigenvalues in DSTERF and ZSTEMR. 441: INDREE = INDRDD + N 442: * INDRWK is the starting offset of the left-over real workspace, and 443: * LLRWORK is the remaining workspace size. 444: INDRWK = INDREE + N 445: LLRWORK = LRWORK - INDRWK + 1 446: 447: * IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and 448: * stores the block indices of each of the M<=N eigenvalues. 449: INDIBL = 1 450: * IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ and 451: * stores the starting and finishing indices of each block. 452: INDISP = INDIBL + N 453: * IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors 454: * that corresponding to eigenvectors that fail to converge in 455: * DSTEIN. This information is discarded; if any fail, the driver 456: * returns INFO > 0. 457: INDIFL = INDISP + N 458: * INDIWO is the offset of the remaining integer workspace. 459: INDIWO = INDISP + N 460: 461: * 462: * Call ZHETRD to reduce Hermitian matrix to tridiagonal form. 463: * 464: CALL ZHETRD( UPLO, N, A, LDA, RWORK( INDRD ), RWORK( INDRE ), 465: $ WORK( INDTAU ), WORK( INDWK ), LLWORK, IINFO ) 466: * 467: * If all eigenvalues are desired 468: * then call DSTERF or ZSTEMR and ZUNMTR. 469: * 470: TEST = .FALSE. 471: IF( INDEIG ) THEN 472: IF( IL.EQ.1 .AND. IU.EQ.N ) THEN 473: TEST = .TRUE. 474: END IF 475: END IF 476: IF( ( ALLEIG.OR.TEST ) .AND. ( IEEEOK.EQ.1 ) ) THEN 477: IF( .NOT.WANTZ ) THEN 478: CALL DCOPY( N, RWORK( INDRD ), 1, W, 1 ) 479: CALL DCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 ) 480: CALL DSTERF( N, W, RWORK( INDREE ), INFO ) 481: ELSE 482: CALL DCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 ) 483: CALL DCOPY( N, RWORK( INDRD ), 1, RWORK( INDRDD ), 1 ) 484: * 485: IF (ABSTOL .LE. TWO*N*EPS) THEN 486: TRYRAC = .TRUE. 487: ELSE 488: TRYRAC = .FALSE. 489: END IF 490: CALL ZSTEMR( JOBZ, 'A', N, RWORK( INDRDD ), 491: $ RWORK( INDREE ), VL, VU, IL, IU, M, W, 492: $ Z, LDZ, N, ISUPPZ, TRYRAC, 493: $ RWORK( INDRWK ), LLRWORK, 494: $ IWORK, LIWORK, INFO ) 495: * 496: * Apply unitary matrix used in reduction to tridiagonal 497: * form to eigenvectors returned by ZSTEIN. 498: * 499: IF( WANTZ .AND. INFO.EQ.0 ) THEN 500: INDWKN = INDWK 501: LLWRKN = LWORK - INDWKN + 1 502: CALL ZUNMTR( 'L', UPLO, 'N', N, M, A, LDA, 503: $ WORK( INDTAU ), Z, LDZ, WORK( INDWKN ), 504: $ LLWRKN, IINFO ) 505: END IF 506: END IF 507: * 508: * 509: IF( INFO.EQ.0 ) THEN 510: M = N 511: GO TO 30 512: END IF 513: INFO = 0 514: END IF 515: * 516: * Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. 517: * Also call DSTEBZ and ZSTEIN if ZSTEMR fails. 518: * 519: IF( WANTZ ) THEN 520: ORDER = 'B' 521: ELSE 522: ORDER = 'E' 523: END IF 524: 525: CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, 526: $ RWORK( INDRD ), RWORK( INDRE ), M, NSPLIT, W, 527: $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ), 528: $ IWORK( INDIWO ), INFO ) 529: * 530: IF( WANTZ ) THEN 531: CALL ZSTEIN( N, RWORK( INDRD ), RWORK( INDRE ), M, W, 532: $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, 533: $ RWORK( INDRWK ), IWORK( INDIWO ), IWORK( INDIFL ), 534: $ INFO ) 535: * 536: * Apply unitary matrix used in reduction to tridiagonal 537: * form to eigenvectors returned by ZSTEIN. 538: * 539: INDWKN = INDWK 540: LLWRKN = LWORK - INDWKN + 1 541: CALL ZUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z, 542: $ LDZ, WORK( INDWKN ), LLWRKN, IINFO ) 543: END IF 544: * 545: * If matrix was scaled, then rescale eigenvalues appropriately. 546: * 547: 30 CONTINUE 548: IF( ISCALE.EQ.1 ) THEN 549: IF( INFO.EQ.0 ) THEN 550: IMAX = M 551: ELSE 552: IMAX = INFO - 1 553: END IF 554: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) 555: END IF 556: * 557: * If eigenvalues are not in order, then sort them, along with 558: * eigenvectors. 559: * 560: IF( WANTZ ) THEN 561: DO 50 J = 1, M - 1 562: I = 0 563: TMP1 = W( J ) 564: DO 40 JJ = J + 1, M 565: IF( W( JJ ).LT.TMP1 ) THEN 566: I = JJ 567: TMP1 = W( JJ ) 568: END IF 569: 40 CONTINUE 570: * 571: IF( I.NE.0 ) THEN 572: ITMP1 = IWORK( INDIBL+I-1 ) 573: W( I ) = W( J ) 574: IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 ) 575: W( J ) = TMP1 576: IWORK( INDIBL+J-1 ) = ITMP1 577: CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) 578: END IF 579: 50 CONTINUE 580: END IF 581: * 582: * Set WORK(1) to optimal workspace size. 583: * 584: WORK( 1 ) = LWKOPT 585: RWORK( 1 ) = LRWMIN 586: IWORK( 1 ) = LIWMIN 587: * 588: RETURN 589: * 590: * End of ZHEEVR 591: * 592: END