Annotation of rpl/lapack/lapack/dsyevr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
! 2: $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
! 3: $ IWORK, LIWORK, INFO )
! 4: *
! 5: * -- LAPACK driver routine (version 3.2) --
! 6: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 8: * November 2006
! 9: *
! 10: * .. Scalar Arguments ..
! 11: CHARACTER JOBZ, RANGE, UPLO
! 12: INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N
! 13: DOUBLE PRECISION ABSTOL, VL, VU
! 14: * ..
! 15: * .. Array Arguments ..
! 16: INTEGER ISUPPZ( * ), IWORK( * )
! 17: DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
! 18: * ..
! 19: *
! 20: * Purpose
! 21: * =======
! 22: *
! 23: * DSYEVR computes selected eigenvalues and, optionally, eigenvectors
! 24: * of a real symmetric matrix A. Eigenvalues and eigenvectors can be
! 25: * selected by specifying either a range of values or a range of
! 26: * indices for the desired eigenvalues.
! 27: *
! 28: * DSYEVR first reduces the matrix A to tridiagonal form T with a call
! 29: * to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute
! 30: * the eigenspectrum using Relatively Robust Representations. DSTEMR
! 31: * computes eigenvalues by the dqds algorithm, while orthogonal
! 32: * eigenvectors are computed from various "good" L D L^T representations
! 33: * (also known as Relatively Robust Representations). Gram-Schmidt
! 34: * orthogonalization is avoided as far as possible. More specifically,
! 35: * the various steps of the algorithm are as follows.
! 36: *
! 37: * For each unreduced block (submatrix) of T,
! 38: * (a) Compute T - sigma I = L D L^T, so that L and D
! 39: * define all the wanted eigenvalues to high relative accuracy.
! 40: * This means that small relative changes in the entries of D and L
! 41: * cause only small relative changes in the eigenvalues and
! 42: * eigenvectors. The standard (unfactored) representation of the
! 43: * tridiagonal matrix T does not have this property in general.
! 44: * (b) Compute the eigenvalues to suitable accuracy.
! 45: * If the eigenvectors are desired, the algorithm attains full
! 46: * accuracy of the computed eigenvalues only right before
! 47: * the corresponding vectors have to be computed, see steps c) and d).
! 48: * (c) For each cluster of close eigenvalues, select a new
! 49: * shift close to the cluster, find a new factorization, and refine
! 50: * the shifted eigenvalues to suitable accuracy.
! 51: * (d) For each eigenvalue with a large enough relative separation compute
! 52: * the corresponding eigenvector by forming a rank revealing twisted
! 53: * factorization. Go back to (c) for any clusters that remain.
! 54: *
! 55: * The desired accuracy of the output can be specified by the input
! 56: * parameter ABSTOL.
! 57: *
! 58: * For more details, see DSTEMR's documentation and:
! 59: * - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
! 60: * to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
! 61: * Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
! 62: * - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
! 63: * Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
! 64: * 2004. Also LAPACK Working Note 154.
! 65: * - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
! 66: * tridiagonal eigenvalue/eigenvector problem",
! 67: * Computer Science Division Technical Report No. UCB/CSD-97-971,
! 68: * UC Berkeley, May 1997.
! 69: *
! 70: *
! 71: * Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested
! 72: * on machines which conform to the ieee-754 floating point standard.
! 73: * DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and
! 74: * when partial spectrum requests are made.
! 75: *
! 76: * Normal execution of DSTEMR may create NaNs and infinities and
! 77: * hence may abort due to a floating point exception in environments
! 78: * which do not handle NaNs and infinities in the ieee standard default
! 79: * manner.
! 80: *
! 81: * Arguments
! 82: * =========
! 83: *
! 84: * JOBZ (input) CHARACTER*1
! 85: * = 'N': Compute eigenvalues only;
! 86: * = 'V': Compute eigenvalues and eigenvectors.
! 87: *
! 88: * RANGE (input) CHARACTER*1
! 89: * = 'A': all eigenvalues will be found.
! 90: * = 'V': all eigenvalues in the half-open interval (VL,VU]
! 91: * will be found.
! 92: * = 'I': the IL-th through IU-th eigenvalues will be found.
! 93: ********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and
! 94: ********** DSTEIN are called
! 95: *
! 96: * UPLO (input) CHARACTER*1
! 97: * = 'U': Upper triangle of A is stored;
! 98: * = 'L': Lower triangle of A is stored.
! 99: *
! 100: * N (input) INTEGER
! 101: * The order of the matrix A. N >= 0.
! 102: *
! 103: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
! 104: * On entry, the symmetric matrix A. If UPLO = 'U', the
! 105: * leading N-by-N upper triangular part of A contains the
! 106: * upper triangular part of the matrix A. If UPLO = 'L',
! 107: * the leading N-by-N lower triangular part of A contains
! 108: * the lower triangular part of the matrix A.
! 109: * On exit, the lower triangle (if UPLO='L') or the upper
! 110: * triangle (if UPLO='U') of A, including the diagonal, is
! 111: * destroyed.
! 112: *
! 113: * LDA (input) INTEGER
! 114: * The leading dimension of the array A. LDA >= max(1,N).
! 115: *
! 116: * VL (input) DOUBLE PRECISION
! 117: * VU (input) DOUBLE PRECISION
! 118: * If RANGE='V', the lower and upper bounds of the interval to
! 119: * be searched for eigenvalues. VL < VU.
! 120: * Not referenced if RANGE = 'A' or 'I'.
! 121: *
! 122: * IL (input) INTEGER
! 123: * IU (input) INTEGER
! 124: * If RANGE='I', the indices (in ascending order) of the
! 125: * smallest and largest eigenvalues to be returned.
! 126: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 127: * Not referenced if RANGE = 'A' or 'V'.
! 128: *
! 129: * ABSTOL (input) DOUBLE PRECISION
! 130: * The absolute error tolerance for the eigenvalues.
! 131: * An approximate eigenvalue is accepted as converged
! 132: * when it is determined to lie in an interval [a,b]
! 133: * of width less than or equal to
! 134: *
! 135: * ABSTOL + EPS * max( |a|,|b| ) ,
! 136: *
! 137: * where EPS is the machine precision. If ABSTOL is less than
! 138: * or equal to zero, then EPS*|T| will be used in its place,
! 139: * where |T| is the 1-norm of the tridiagonal matrix obtained
! 140: * by reducing A to tridiagonal form.
! 141: *
! 142: * See "Computing Small Singular Values of Bidiagonal Matrices
! 143: * with Guaranteed High Relative Accuracy," by Demmel and
! 144: * Kahan, LAPACK Working Note #3.
! 145: *
! 146: * If high relative accuracy is important, set ABSTOL to
! 147: * DLAMCH( 'Safe minimum' ). Doing so will guarantee that
! 148: * eigenvalues are computed to high relative accuracy when
! 149: * possible in future releases. The current code does not
! 150: * make any guarantees about high relative accuracy, but
! 151: * future releases will. See J. Barlow and J. Demmel,
! 152: * "Computing Accurate Eigensystems of Scaled Diagonally
! 153: * Dominant Matrices", LAPACK Working Note #7, for a discussion
! 154: * of which matrices define their eigenvalues to high relative
! 155: * accuracy.
! 156: *
! 157: * M (output) INTEGER
! 158: * The total number of eigenvalues found. 0 <= M <= N.
! 159: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 160: *
! 161: * W (output) DOUBLE PRECISION array, dimension (N)
! 162: * The first M elements contain the selected eigenvalues in
! 163: * ascending order.
! 164: *
! 165: * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
! 166: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 167: * contain the orthonormal eigenvectors of the matrix A
! 168: * corresponding to the selected eigenvalues, with the i-th
! 169: * column of Z holding the eigenvector associated with W(i).
! 170: * If JOBZ = 'N', then Z is not referenced.
! 171: * Note: the user must ensure that at least max(1,M) columns are
! 172: * supplied in the array Z; if RANGE = 'V', the exact value of M
! 173: * is not known in advance and an upper bound must be used.
! 174: * Supplying N columns is always safe.
! 175: *
! 176: * LDZ (input) INTEGER
! 177: * The leading dimension of the array Z. LDZ >= 1, and if
! 178: * JOBZ = 'V', LDZ >= max(1,N).
! 179: *
! 180: * ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) )
! 181: * The support of the eigenvectors in Z, i.e., the indices
! 182: * indicating the nonzero elements in Z. The i-th eigenvector
! 183: * is nonzero only in elements ISUPPZ( 2*i-1 ) through
! 184: * ISUPPZ( 2*i ).
! 185: ********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
! 186: *
! 187: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 188: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 189: *
! 190: * LWORK (input) INTEGER
! 191: * The dimension of the array WORK. LWORK >= max(1,26*N).
! 192: * For optimal efficiency, LWORK >= (NB+6)*N,
! 193: * where NB is the max of the blocksize for DSYTRD and DORMTR
! 194: * returned by ILAENV.
! 195: *
! 196: * If LWORK = -1, then a workspace query is assumed; the routine
! 197: * only calculates the optimal size of the WORK array, returns
! 198: * this value as the first entry of the WORK array, and no error
! 199: * message related to LWORK is issued by XERBLA.
! 200: *
! 201: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 202: * On exit, if INFO = 0, IWORK(1) returns the optimal LWORK.
! 203: *
! 204: * LIWORK (input) INTEGER
! 205: * The dimension of the array IWORK. LIWORK >= max(1,10*N).
! 206: *
! 207: * If LIWORK = -1, then a workspace query is assumed; the
! 208: * routine only calculates the optimal size of the IWORK array,
! 209: * returns this value as the first entry of the IWORK array, and
! 210: * no error message related to LIWORK is issued by XERBLA.
! 211: *
! 212: * INFO (output) INTEGER
! 213: * = 0: successful exit
! 214: * < 0: if INFO = -i, the i-th argument had an illegal value
! 215: * > 0: Internal error
! 216: *
! 217: * Further Details
! 218: * ===============
! 219: *
! 220: * Based on contributions by
! 221: * Inderjit Dhillon, IBM Almaden, USA
! 222: * Osni Marques, LBNL/NERSC, USA
! 223: * Ken Stanley, Computer Science Division, University of
! 224: * California at Berkeley, USA
! 225: * Jason Riedy, Computer Science Division, University of
! 226: * California at Berkeley, USA
! 227: *
! 228: * =====================================================================
! 229: *
! 230: * .. Parameters ..
! 231: DOUBLE PRECISION ZERO, ONE, TWO
! 232: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
! 233: * ..
! 234: * .. Local Scalars ..
! 235: LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, VALEIG, WANTZ,
! 236: $ TRYRAC
! 237: CHARACTER ORDER
! 238: INTEGER I, IEEEOK, IINFO, IMAX, INDD, INDDD, INDE,
! 239: $ INDEE, INDIBL, INDIFL, INDISP, INDIWO, INDTAU,
! 240: $ INDWK, INDWKN, ISCALE, J, JJ, LIWMIN,
! 241: $ LLWORK, LLWRKN, LWKOPT, LWMIN, NB, NSPLIT
! 242: DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
! 243: $ SIGMA, SMLNUM, TMP1, VLL, VUU
! 244: * ..
! 245: * .. External Functions ..
! 246: LOGICAL LSAME
! 247: INTEGER ILAENV
! 248: DOUBLE PRECISION DLAMCH, DLANSY
! 249: EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY
! 250: * ..
! 251: * .. External Subroutines ..
! 252: EXTERNAL DCOPY, DORMTR, DSCAL, DSTEBZ, DSTEMR, DSTEIN,
! 253: $ DSTERF, DSWAP, DSYTRD, XERBLA
! 254: * ..
! 255: * .. Intrinsic Functions ..
! 256: INTRINSIC MAX, MIN, SQRT
! 257: * ..
! 258: * .. Executable Statements ..
! 259: *
! 260: * Test the input parameters.
! 261: *
! 262: IEEEOK = ILAENV( 10, 'DSYEVR', 'N', 1, 2, 3, 4 )
! 263: *
! 264: LOWER = LSAME( UPLO, 'L' )
! 265: WANTZ = LSAME( JOBZ, 'V' )
! 266: ALLEIG = LSAME( RANGE, 'A' )
! 267: VALEIG = LSAME( RANGE, 'V' )
! 268: INDEIG = LSAME( RANGE, 'I' )
! 269: *
! 270: LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LIWORK.EQ.-1 ) )
! 271: *
! 272: LWMIN = MAX( 1, 26*N )
! 273: LIWMIN = MAX( 1, 10*N )
! 274: *
! 275: INFO = 0
! 276: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 277: INFO = -1
! 278: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 279: INFO = -2
! 280: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 281: INFO = -3
! 282: ELSE IF( N.LT.0 ) THEN
! 283: INFO = -4
! 284: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 285: INFO = -6
! 286: ELSE
! 287: IF( VALEIG ) THEN
! 288: IF( N.GT.0 .AND. VU.LE.VL )
! 289: $ INFO = -8
! 290: ELSE IF( INDEIG ) THEN
! 291: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
! 292: INFO = -9
! 293: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 294: INFO = -10
! 295: END IF
! 296: END IF
! 297: END IF
! 298: IF( INFO.EQ.0 ) THEN
! 299: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 300: INFO = -15
! 301: ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 302: INFO = -18
! 303: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 304: INFO = -20
! 305: END IF
! 306: END IF
! 307: *
! 308: IF( INFO.EQ.0 ) THEN
! 309: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
! 310: NB = MAX( NB, ILAENV( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) )
! 311: LWKOPT = MAX( ( NB+1 )*N, LWMIN )
! 312: WORK( 1 ) = LWKOPT
! 313: IWORK( 1 ) = LIWMIN
! 314: END IF
! 315: *
! 316: IF( INFO.NE.0 ) THEN
! 317: CALL XERBLA( 'DSYEVR', -INFO )
! 318: RETURN
! 319: ELSE IF( LQUERY ) THEN
! 320: RETURN
! 321: END IF
! 322: *
! 323: * Quick return if possible
! 324: *
! 325: M = 0
! 326: IF( N.EQ.0 ) THEN
! 327: WORK( 1 ) = 1
! 328: RETURN
! 329: END IF
! 330: *
! 331: IF( N.EQ.1 ) THEN
! 332: WORK( 1 ) = 7
! 333: IF( ALLEIG .OR. INDEIG ) THEN
! 334: M = 1
! 335: W( 1 ) = A( 1, 1 )
! 336: ELSE
! 337: IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN
! 338: M = 1
! 339: W( 1 ) = A( 1, 1 )
! 340: END IF
! 341: END IF
! 342: IF( WANTZ )
! 343: $ Z( 1, 1 ) = ONE
! 344: RETURN
! 345: END IF
! 346: *
! 347: * Get machine constants.
! 348: *
! 349: SAFMIN = DLAMCH( 'Safe minimum' )
! 350: EPS = DLAMCH( 'Precision' )
! 351: SMLNUM = SAFMIN / EPS
! 352: BIGNUM = ONE / SMLNUM
! 353: RMIN = SQRT( SMLNUM )
! 354: RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
! 355: *
! 356: * Scale matrix to allowable range, if necessary.
! 357: *
! 358: ISCALE = 0
! 359: ABSTLL = ABSTOL
! 360: VLL = VL
! 361: VUU = VU
! 362: ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
! 363: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 364: ISCALE = 1
! 365: SIGMA = RMIN / ANRM
! 366: ELSE IF( ANRM.GT.RMAX ) THEN
! 367: ISCALE = 1
! 368: SIGMA = RMAX / ANRM
! 369: END IF
! 370: IF( ISCALE.EQ.1 ) THEN
! 371: IF( LOWER ) THEN
! 372: DO 10 J = 1, N
! 373: CALL DSCAL( N-J+1, SIGMA, A( J, J ), 1 )
! 374: 10 CONTINUE
! 375: ELSE
! 376: DO 20 J = 1, N
! 377: CALL DSCAL( J, SIGMA, A( 1, J ), 1 )
! 378: 20 CONTINUE
! 379: END IF
! 380: IF( ABSTOL.GT.0 )
! 381: $ ABSTLL = ABSTOL*SIGMA
! 382: IF( VALEIG ) THEN
! 383: VLL = VL*SIGMA
! 384: VUU = VU*SIGMA
! 385: END IF
! 386: END IF
! 387:
! 388: * Initialize indices into workspaces. Note: The IWORK indices are
! 389: * used only if DSTERF or DSTEMR fail.
! 390:
! 391: * WORK(INDTAU:INDTAU+N-1) stores the scalar factors of the
! 392: * elementary reflectors used in DSYTRD.
! 393: INDTAU = 1
! 394: * WORK(INDD:INDD+N-1) stores the tridiagonal's diagonal entries.
! 395: INDD = INDTAU + N
! 396: * WORK(INDE:INDE+N-1) stores the off-diagonal entries of the
! 397: * tridiagonal matrix from DSYTRD.
! 398: INDE = INDD + N
! 399: * WORK(INDDD:INDDD+N-1) is a copy of the diagonal entries over
! 400: * -written by DSTEMR (the DSTERF path copies the diagonal to W).
! 401: INDDD = INDE + N
! 402: * WORK(INDEE:INDEE+N-1) is a copy of the off-diagonal entries over
! 403: * -written while computing the eigenvalues in DSTERF and DSTEMR.
! 404: INDEE = INDDD + N
! 405: * INDWK is the starting offset of the left-over workspace, and
! 406: * LLWORK is the remaining workspace size.
! 407: INDWK = INDEE + N
! 408: LLWORK = LWORK - INDWK + 1
! 409:
! 410: * IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and
! 411: * stores the block indices of each of the M<=N eigenvalues.
! 412: INDIBL = 1
! 413: * IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ and
! 414: * stores the starting and finishing indices of each block.
! 415: INDISP = INDIBL + N
! 416: * IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors
! 417: * that corresponding to eigenvectors that fail to converge in
! 418: * DSTEIN. This information is discarded; if any fail, the driver
! 419: * returns INFO > 0.
! 420: INDIFL = INDISP + N
! 421: * INDIWO is the offset of the remaining integer workspace.
! 422: INDIWO = INDISP + N
! 423:
! 424: *
! 425: * Call DSYTRD to reduce symmetric matrix to tridiagonal form.
! 426: *
! 427: CALL DSYTRD( UPLO, N, A, LDA, WORK( INDD ), WORK( INDE ),
! 428: $ WORK( INDTAU ), WORK( INDWK ), LLWORK, IINFO )
! 429: *
! 430: * If all eigenvalues are desired
! 431: * then call DSTERF or DSTEMR and DORMTR.
! 432: *
! 433: IF( ( ALLEIG .OR. ( INDEIG .AND. IL.EQ.1 .AND. IU.EQ.N ) ) .AND.
! 434: $ IEEEOK.EQ.1 ) THEN
! 435: IF( .NOT.WANTZ ) THEN
! 436: CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
! 437: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 438: CALL DSTERF( N, W, WORK( INDEE ), INFO )
! 439: ELSE
! 440: CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
! 441: CALL DCOPY( N, WORK( INDD ), 1, WORK( INDDD ), 1 )
! 442: *
! 443: IF (ABSTOL .LE. TWO*N*EPS) THEN
! 444: TRYRAC = .TRUE.
! 445: ELSE
! 446: TRYRAC = .FALSE.
! 447: END IF
! 448: CALL DSTEMR( JOBZ, 'A', N, WORK( INDDD ), WORK( INDEE ),
! 449: $ VL, VU, IL, IU, M, W, Z, LDZ, N, ISUPPZ,
! 450: $ TRYRAC, WORK( INDWK ), LWORK, IWORK, LIWORK,
! 451: $ INFO )
! 452: *
! 453: *
! 454: *
! 455: * Apply orthogonal matrix used in reduction to tridiagonal
! 456: * form to eigenvectors returned by DSTEIN.
! 457: *
! 458: IF( WANTZ .AND. INFO.EQ.0 ) THEN
! 459: INDWKN = INDE
! 460: LLWRKN = LWORK - INDWKN + 1
! 461: CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA,
! 462: $ WORK( INDTAU ), Z, LDZ, WORK( INDWKN ),
! 463: $ LLWRKN, IINFO )
! 464: END IF
! 465: END IF
! 466: *
! 467: *
! 468: IF( INFO.EQ.0 ) THEN
! 469: * Everything worked. Skip DSTEBZ/DSTEIN. IWORK(:) are
! 470: * undefined.
! 471: M = N
! 472: GO TO 30
! 473: END IF
! 474: INFO = 0
! 475: END IF
! 476: *
! 477: * Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN.
! 478: * Also call DSTEBZ and DSTEIN if DSTEMR fails.
! 479: *
! 480: IF( WANTZ ) THEN
! 481: ORDER = 'B'
! 482: ELSE
! 483: ORDER = 'E'
! 484: END IF
! 485:
! 486: CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
! 487: $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
! 488: $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWK ),
! 489: $ IWORK( INDIWO ), INFO )
! 490: *
! 491: IF( WANTZ ) THEN
! 492: CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
! 493: $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
! 494: $ WORK( INDWK ), IWORK( INDIWO ), IWORK( INDIFL ),
! 495: $ INFO )
! 496: *
! 497: * Apply orthogonal matrix used in reduction to tridiagonal
! 498: * form to eigenvectors returned by DSTEIN.
! 499: *
! 500: INDWKN = INDE
! 501: LLWRKN = LWORK - INDWKN + 1
! 502: CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
! 503: $ LDZ, WORK( INDWKN ), LLWRKN, IINFO )
! 504: END IF
! 505: *
! 506: * If matrix was scaled, then rescale eigenvalues appropriately.
! 507: *
! 508: * Jump here if DSTEMR/DSTEIN succeeded.
! 509: 30 CONTINUE
! 510: IF( ISCALE.EQ.1 ) THEN
! 511: IF( INFO.EQ.0 ) THEN
! 512: IMAX = M
! 513: ELSE
! 514: IMAX = INFO - 1
! 515: END IF
! 516: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 517: END IF
! 518: *
! 519: * If eigenvalues are not in order, then sort them, along with
! 520: * eigenvectors. Note: We do not sort the IFAIL portion of IWORK.
! 521: * It may not be initialized (if DSTEMR/DSTEIN succeeded), and we do
! 522: * not return this detailed information to the user.
! 523: *
! 524: IF( WANTZ ) THEN
! 525: DO 50 J = 1, M - 1
! 526: I = 0
! 527: TMP1 = W( J )
! 528: DO 40 JJ = J + 1, M
! 529: IF( W( JJ ).LT.TMP1 ) THEN
! 530: I = JJ
! 531: TMP1 = W( JJ )
! 532: END IF
! 533: 40 CONTINUE
! 534: *
! 535: IF( I.NE.0 ) THEN
! 536: W( I ) = W( J )
! 537: W( J ) = TMP1
! 538: CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
! 539: END IF
! 540: 50 CONTINUE
! 541: END IF
! 542: *
! 543: * Set WORK(1) to optimal workspace size.
! 544: *
! 545: WORK( 1 ) = LWKOPT
! 546: IWORK( 1 ) = LIWMIN
! 547: *
! 548: RETURN
! 549: *
! 550: * End of DSYEVR
! 551: *
! 552: END
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