Exemplo n.º 1
0
/* Subroutine */ int dstegr_(char *jobz, char *range, integer *n, doublereal *
	d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, 
	integer *iu, doublereal *abstol, integer *m, doublereal *w, 
	doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, 
	integer *lwork, integer *iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset;

    /* Local variables */
    logical tryrac;

/*  -- LAPACK computational routine (version 3.2) -- */
/*     November 2006 */

/*  Purpose */
/*  ======= */

/*  DSTEGR computes selected eigenvalues and, optionally, eigenvectors */
/*  of a real symmetric tridiagonal matrix T. Any such unreduced matrix has */
/*  a well defined set of pairwise different real eigenvalues, the corresponding */
/*  real eigenvectors are pairwise orthogonal. */

/*  The spectrum may be computed either completely or partially by specifying */
/*  either an interval (VL,VU] or a range of indices IL:IU for the desired */
/*  eigenvalues. */

/*  DSTEGR is a compatability wrapper around the improved DSTEMR routine. */
/*  See DSTEMR for further details. */

/*  One important change is that the ABSTOL parameter no longer provides any */
/*  benefit and hence is no longer used. */

/*  Note : DSTEGR and DSTEMR work only on machines which follow */
/*  IEEE-754 floating-point standard in their handling of infinities and */
/*  NaNs.  Normal execution may create these exceptiona values and hence */
/*  may abort due to a floating point exception in environments which */
/*  do not conform to the IEEE-754 standard. */

/*  Arguments */
/*  ========= */

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  RANGE   (input) CHARACTER*1 */
/*          = 'A': all eigenvalues will be found. */
/*          = 'V': all eigenvalues in the half-open interval (VL,VU] */
/*                 will be found. */
/*          = 'I': the IL-th through IU-th eigenvalues will be found. */

/*  N       (input) INTEGER */
/*          The order of the matrix.  N >= 0. */

/*  D       (input/output) DOUBLE PRECISION array, dimension (N) */
/*          On entry, the N diagonal elements of the tridiagonal matrix */
/*          T. On exit, D is overwritten. */

/*  E       (input/output) DOUBLE PRECISION array, dimension (N) */
/*          On entry, the (N-1) subdiagonal elements of the tridiagonal */
/*          matrix T in elements 1 to N-1 of E. E(N) need not be set on */
/*          input, but is used internally as workspace. */
/*          On exit, E is overwritten. */

/*  VL      (input) DOUBLE PRECISION */
/*  VU      (input) DOUBLE PRECISION */
/*          If RANGE='V', the lower and upper bounds of the interval to */
/*          be searched for eigenvalues. VL < VU. */
/*          Not referenced if RANGE = 'A' or 'I'. */

/*  IL      (input) INTEGER */
/*  IU      (input) INTEGER */
/*          If RANGE='I', the indices (in ascending order) of the */
/*          smallest and largest eigenvalues to be returned. */
/*          1 <= IL <= IU <= N, if N > 0. */
/*          Not referenced if RANGE = 'A' or 'V'. */

/*  ABSTOL  (input) DOUBLE PRECISION */
/*          Unused.  Was the absolute error tolerance for the */
/*          eigenvalues/eigenvectors in previous versions. */

/*  M       (output) INTEGER */
/*          The total number of eigenvalues found.  0 <= M <= N. */
/*          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */

/*  W       (output) DOUBLE PRECISION array, dimension (N) */
/*          The first M elements contain the selected eigenvalues in */
/*          ascending order. */

/*  Z       (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) */
/*          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z */
/*          contain the orthonormal eigenvectors of the matrix T */
/*          corresponding to the selected eigenvalues, with the i-th */
/*          column of Z holding the eigenvector associated with W(i). */
/*          If JOBZ = 'N', then Z is not referenced. */
/*          Note: the user must ensure that at least max(1,M) columns are */
/*          supplied in the array Z; if RANGE = 'V', the exact value of M */
/*          is not known in advance and an upper bound must be used. */
/*          Supplying N columns is always safe. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z.  LDZ >= 1, and if */
/*          JOBZ = 'V', then LDZ >= max(1,N). */

/*  ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) ) */
/*          The support of the eigenvectors in Z, i.e., the indices */
/*          indicating the nonzero elements in Z. The i-th computed eigenvector */
/*          is nonzero only in elements ISUPPZ( 2*i-1 ) through */
/*          ISUPPZ( 2*i ). This is relevant in the case when the matrix */
/*          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. */

/*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal */
/*          (and minimal) LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. LWORK >= max(1,18*N) */
/*          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. */
/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal size of the WORK array, returns */
/*          this value as the first entry of the WORK array, and no error */
/*          message related to LWORK is issued by XERBLA. */

/*  IWORK   (workspace/output) INTEGER array, dimension (LIWORK) */
/*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */

/*  LIWORK  (input) INTEGER */
/*          The dimension of the array IWORK.  LIWORK >= max(1,10*N) */
/*          if the eigenvectors are desired, and LIWORK >= max(1,8*N) */
/*          if only the eigenvalues are to be computed. */
/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal size of the IWORK array, */
/*          returns this value as the first entry of the IWORK array, and */
/*          no error message related to LIWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          On exit, INFO */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = 1X, internal error in DLARRE, */
/*                if INFO = 2X, internal error in DLARRV. */
/*                Here, the digit X = ABS( IINFO ) < 10, where IINFO is */
/*                the nonzero error code returned by DLARRE or */
/*                DLARRV, respectively. */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Inderjit Dhillon, IBM Almaden, USA */
/*     Osni Marques, LBNL/NERSC, USA */
/*     Christof Voemel, LBNL/NERSC, USA */

/*  ===================================================================== */

    /* Parameter adjustments */
    --d__;
    --e;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --isuppz;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    tryrac = FALSE_;
    dstemr_(jobz, range, n, &d__[1], &e[1], vl, vu, il, iu, m, &w[1], &z__[
	    z_offset], ldz, n, &isuppz[1], &tryrac, &work[1], lwork, &iwork[1]
, liwork, info);

/*     End of DSTEGR */

    return 0;
} /* dstegr_ */
Exemplo n.º 2
0
/* Subroutine */ int dsyevr_(char *jobz, char *range, char *uplo, integer *n, 
	doublereal *a, integer *lda, doublereal *vl, doublereal *vu, integer *
	il, integer *iu, doublereal *abstol, integer *m, doublereal *w, 
	doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, 
	integer *lwork, integer *iwork, integer *liwork, integer *info)
{
/*  -- LAPACK driver routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    Purpose   
    =======   

    DSYEVR computes selected eigenvalues and, optionally, eigenvectors   
    of a real symmetric matrix A.  Eigenvalues and eigenvectors can be   
    selected by specifying either a range of values or a range of   
    indices for the desired eigenvalues.   

    DSYEVR first reduces the matrix A to tridiagonal form T with a call   
    to DSYTRD.  Then, whenever possible, DSYEVR calls DSTEMR to compute   
    the eigenspectrum using Relatively Robust Representations.  DSTEMR   
    computes eigenvalues by the dqds algorithm, while orthogonal   
    eigenvectors are computed from various "good" L D L^T representations   
    (also known as Relatively Robust Representations). Gram-Schmidt   
    orthogonalization is avoided as far as possible. More specifically,   
    the various steps of the algorithm are as follows.   

    For each unreduced block (submatrix) of T,   
       (a) Compute T - sigma I  = L D L^T, so that L and D   
           define all the wanted eigenvalues to high relative accuracy.   
           This means that small relative changes in the entries of D and L   
           cause only small relative changes in the eigenvalues and   
           eigenvectors. The standard (unfactored) representation of the   
           tridiagonal matrix T does not have this property in general.   
       (b) Compute the eigenvalues to suitable accuracy.   
           If the eigenvectors are desired, the algorithm attains full   
           accuracy of the computed eigenvalues only right before   
           the corresponding vectors have to be computed, see steps c) and d).   
       (c) For each cluster of close eigenvalues, select a new   
           shift close to the cluster, find a new factorization, and refine   
           the shifted eigenvalues to suitable accuracy.   
       (d) For each eigenvalue with a large enough relative separation compute   
           the corresponding eigenvector by forming a rank revealing twisted   
           factorization. Go back to (c) for any clusters that remain.   

    The desired accuracy of the output can be specified by the input   
    parameter ABSTOL.   

    For more details, see DSTEMR's documentation and:   
    - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations   
      to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"   
      Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.   
    - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and   
      Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,   
      2004.  Also LAPACK Working Note 154.   
    - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric   
      tridiagonal eigenvalue/eigenvector problem",   
      Computer Science Division Technical Report No. UCB/CSD-97-971,   
      UC Berkeley, May 1997.   


    Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested   
    on machines which conform to the ieee-754 floating point standard.   
    DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and   
    when partial spectrum requests are made.   

    Normal execution of DSTEMR may create NaNs and infinities and   
    hence may abort due to a floating point exception in environments   
    which do not handle NaNs and infinities in the ieee standard default   
    manner.   

    Arguments   
    =========   

    JOBZ    (input) CHARACTER*1   
            = 'N':  Compute eigenvalues only;   
            = 'V':  Compute eigenvalues and eigenvectors.   

    RANGE   (input) CHARACTER*1   
            = 'A': all eigenvalues will be found.   
            = 'V': all eigenvalues in the half-open interval (VL,VU]   
                   will be found.   
            = 'I': the IL-th through IU-th eigenvalues will be found.   
   ********* For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and   
   ********* DSTEIN are called   

    UPLO    (input) CHARACTER*1   
            = 'U':  Upper triangle of A is stored;   
            = 'L':  Lower triangle of A is stored.   

    N       (input) INTEGER   
            The order of the matrix A.  N >= 0.   

    A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)   
            On entry, the symmetric matrix A.  If UPLO = 'U', the   
            leading N-by-N upper triangular part of A contains the   
            upper triangular part of the matrix A.  If UPLO = 'L',   
            the leading N-by-N lower triangular part of A contains   
            the lower triangular part of the matrix A.   
            On exit, the lower triangle (if UPLO='L') or the upper   
            triangle (if UPLO='U') of A, including the diagonal, is   
            destroyed.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.  LDA >= max(1,N).   

    VL      (input) DOUBLE PRECISION   
    VU      (input) DOUBLE PRECISION   
            If RANGE='V', the lower and upper bounds of the interval to   
            be searched for eigenvalues. VL < VU.   
            Not referenced if RANGE = 'A' or 'I'.   

    IL      (input) INTEGER   
    IU      (input) INTEGER   
            If RANGE='I', the indices (in ascending order) of the   
            smallest and largest eigenvalues to be returned.   
            1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.   
            Not referenced if RANGE = 'A' or 'V'.   

    ABSTOL  (input) DOUBLE PRECISION   
            The absolute error tolerance for the eigenvalues.   
            An approximate eigenvalue is accepted as converged   
            when it is determined to lie in an interval [a,b]   
            of width less than or equal to   

                    ABSTOL + EPS *   max( |a|,|b| ) ,   

            where EPS is the machine precision.  If ABSTOL is less than   
            or equal to zero, then  EPS*|T|  will be used in its place,   
            where |T| is the 1-norm of the tridiagonal matrix obtained   
            by reducing A to tridiagonal form.   

            See "Computing Small Singular Values of Bidiagonal Matrices   
            with Guaranteed High Relative Accuracy," by Demmel and   
            Kahan, LAPACK Working Note #3.   

            If high relative accuracy is important, set ABSTOL to   
            DLAMCH( 'Safe minimum' ).  Doing so will guarantee that   
            eigenvalues are computed to high relative accuracy when   
            possible in future releases.  The current code does not   
            make any guarantees about high relative accuracy, but   
            future releases will. See J. Barlow and J. Demmel,   
            "Computing Accurate Eigensystems of Scaled Diagonally   
            Dominant Matrices", LAPACK Working Note #7, for a discussion   
            of which matrices define their eigenvalues to high relative   
            accuracy.   

    M       (output) INTEGER   
            The total number of eigenvalues found.  0 <= M <= N.   
            If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.   

    W       (output) DOUBLE PRECISION array, dimension (N)   
            The first M elements contain the selected eigenvalues in   
            ascending order.   

    Z       (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))   
            If JOBZ = 'V', then if INFO = 0, the first M columns of Z   
            contain the orthonormal eigenvectors of the matrix A   
            corresponding to the selected eigenvalues, with the i-th   
            column of Z holding the eigenvector associated with W(i).   
            If JOBZ = 'N', then Z is not referenced.   
            Note: the user must ensure that at least max(1,M) columns are   
            supplied in the array Z; if RANGE = 'V', the exact value of M   
            is not known in advance and an upper bound must be used.   
            Supplying N columns is always safe.   

    LDZ     (input) INTEGER   
            The leading dimension of the array Z.  LDZ >= 1, and if   
            JOBZ = 'V', LDZ >= max(1,N).   

    ISUPPZ  (output) INTEGER array, dimension ( 2*max(1,M) )   
            The support of the eigenvectors in Z, i.e., the indices   
            indicating the nonzero elements in Z. The i-th eigenvector   
            is nonzero only in elements ISUPPZ( 2*i-1 ) through   
            ISUPPZ( 2*i ).   
   ********* Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1   

    WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK.  LWORK >= max(1,26*N).   
            For optimal efficiency, LWORK >= (NB+6)*N,   
            where NB is the max of the blocksize for DSYTRD and DORMTR   
            returned by ILAENV.   

            If LWORK = -1, then a workspace query is assumed; the routine   
            only calculates the optimal size of the WORK array, returns   
            this value as the first entry of the WORK array, and no error   
            message related to LWORK is issued by XERBLA.   

    IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))   
            On exit, if INFO = 0, IWORK(1) returns the optimal LWORK.   

    LIWORK  (input) INTEGER   
            The dimension of the array IWORK.  LIWORK >= max(1,10*N).   

            If LIWORK = -1, then a workspace query is assumed; the   
            routine only calculates the optimal size of the IWORK array,   
            returns this value as the first entry of the IWORK array, and   
            no error message related to LIWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  Internal error   

    Further Details   
    ===============   

    Based on contributions by   
       Inderjit Dhillon, IBM Almaden, USA   
       Osni Marques, LBNL/NERSC, USA   
       Ken Stanley, Computer Science Division, University of   
         California at Berkeley, USA   
       Jason Riedy, Computer Science Division, University of   
         California at Berkeley, USA   

   =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__10 = 10;
    static integer c__1 = 1;
    static integer c__2 = 2;
    static integer c__3 = 3;
    static integer c__4 = 4;
    static integer c_n1 = -1;
    
    /* System generated locals */
    integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
    doublereal d__1, d__2;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer i__, j, nb, jj;
    static doublereal eps, vll, vuu, tmp1;
    static integer indd, inde;
    static doublereal anrm;
    static integer imax;
    static doublereal rmin, rmax;
    static integer inddd, indee;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    static doublereal sigma;
    extern logical lsame_(char *, char *);
    static integer iinfo;
    static char order[1];
    static integer indwk;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *), dswap_(integer *, doublereal *, integer 
	    *, doublereal *, integer *);
    static integer lwmin;
    static logical lower, wantz;
    extern doublereal dlamch_(char *);
    static logical alleig, indeig;
    static integer iscale, ieeeok, indibl, indifl;
    static logical valeig;
    static doublereal safmin;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static doublereal abstll, bignum;
    static integer indtau, indisp;
    extern /* Subroutine */ int dstein_(integer *, doublereal *, doublereal *,
	     integer *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, doublereal *, integer *, integer *, integer *), 
	    dsterf_(integer *, doublereal *, doublereal *, integer *);
    static integer indiwo, indwkn;
    extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
	    integer *, doublereal *);
    extern /* Subroutine */ int dstebz_(char *, char *, integer *, doublereal 
	    *, doublereal *, integer *, integer *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *, doublereal *, integer *, 
	    integer *, doublereal *, integer *, integer *), 
	    dstemr_(char *, char *, integer *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, integer *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, integer *, 
	    logical *, doublereal *, integer *, integer *, integer *, integer 
	    *);
    static integer liwmin;
    static logical tryrac;
    extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static integer llwrkn, llwork, nsplit;
    static doublereal smlnum;
    extern /* Subroutine */ int dsytrd_(char *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     integer *, integer *);
    static integer lwkopt;
    static logical lquery;


    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --isuppz;
    --work;
    --iwork;

    /* Function Body */
    ieeeok = ilaenv_(&c__10, "DSYEVR", "N", &c__1, &c__2, &c__3, &c__4, (
	    ftnlen)6, (ftnlen)1);

    lower = lsame_(uplo, "L");
    wantz = lsame_(jobz, "V");
    alleig = lsame_(range, "A");
    valeig = lsame_(range, "V");
    indeig = lsame_(range, "I");

    lquery = *lwork == -1 || *liwork == -1;

/* Computing MAX */
    i__1 = 1, i__2 = *n * 26;
    lwmin = max(i__1,i__2);
/* Computing MAX */
    i__1 = 1, i__2 = *n * 10;
    liwmin = max(i__1,i__2);

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (alleig || valeig || indeig)) {
	*info = -2;
    } else if (! (lower || lsame_(uplo, "U"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else {
	if (valeig) {
	    if (*n > 0 && *vu <= *vl) {
		*info = -8;
	    }
	} else if (indeig) {
	    if (*il < 1 || *il > max(1,*n)) {
		*info = -9;
	    } else if (*iu < min(*n,*il) || *iu > *n) {
		*info = -10;
	    }
	}
    }
    if (*info == 0) {
	if (*ldz < 1 || wantz && *ldz < *n) {
	    *info = -15;
	} else if (*lwork < lwmin && ! lquery) {
	    *info = -18;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -20;
	}
    }

    if (*info == 0) {
	nb = ilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
		 (ftnlen)1);
/* Computing MAX */
	i__1 = nb, i__2 = ilaenv_(&c__1, "DORMTR", uplo, n, &c_n1, &c_n1, &
		c_n1, (ftnlen)6, (ftnlen)1);
	nb = max(i__1,i__2);
/* Computing MAX */
	i__1 = (nb + 1) * *n;
	lwkopt = max(i__1,lwmin);
	work[1] = (doublereal) lwkopt;
	iwork[1] = liwmin;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DSYEVR", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    *m = 0;
    if (*n == 0) {
	work[1] = 1.;
	return 0;
    }

    if (*n == 1) {
	work[1] = 7.;
	if (alleig || indeig) {
	    *m = 1;
	    w[1] = a[a_dim1 + 1];
	} else {
	    if (*vl < a[a_dim1 + 1] && *vu >= a[a_dim1 + 1]) {
		*m = 1;
		w[1] = a[a_dim1 + 1];
	    }
	}
	if (wantz) {
	    z__[z_dim1 + 1] = 1.;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = dlamch_("Safe minimum");
    eps = dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
/* Computing MIN */
    d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin));
    rmax = min(d__1,d__2);

/*     Scale matrix to allowable range, if necessary. */

    iscale = 0;
    abstll = *abstol;
    vll = *vl;
    vuu = *vu;
    anrm = dlansy_("M", uplo, n, &a[a_offset], lda, &work[1]);
    if (anrm > 0. && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *n - j + 1;
		dscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1);
/* L10: */
	    }
	} else {
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		dscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1);
/* L20: */
	    }
	}
	if (*abstol > 0.) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }
/*     Initialize indices into workspaces.  Note: The IWORK indices are   
       used only if DSTERF or DSTEMR fail.   
       WORK(INDTAU:INDTAU+N-1) stores the scalar factors of the   
       elementary reflectors used in DSYTRD. */
    indtau = 1;
/*     WORK(INDD:INDD+N-1) stores the tridiagonal's diagonal entries. */
    indd = indtau + *n;
/*     WORK(INDE:INDE+N-1) stores the off-diagonal entries of the   
       tridiagonal matrix from DSYTRD. */
    inde = indd + *n;
/*     WORK(INDDD:INDDD+N-1) is a copy of the diagonal entries over   
       -written by DSTEMR (the DSTERF path copies the diagonal to W). */
    inddd = inde + *n;
/*     WORK(INDEE:INDEE+N-1) is a copy of the off-diagonal entries over   
       -written while computing the eigenvalues in DSTERF and DSTEMR. */
    indee = inddd + *n;
/*     INDWK is the starting offset of the left-over workspace, and   
       LLWORK is the remaining workspace size. */
    indwk = indee + *n;
    llwork = *lwork - indwk + 1;
/*     IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and   
       stores the block indices of each of the M<=N eigenvalues. */
    indibl = 1;
/*     IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ and   
       stores the starting and finishing indices of each block. */
    indisp = indibl + *n;
/*     IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors   
       that corresponding to eigenvectors that fail to converge in   
       DSTEIN.  This information is discarded; if any fail, the driver   
       returns INFO > 0. */
    indifl = indisp + *n;
/*     INDIWO is the offset of the remaining integer workspace. */
    indiwo = indisp + *n;

/*     Call DSYTRD to reduce symmetric matrix to tridiagonal form. */

    dsytrd_(uplo, n, &a[a_offset], lda, &work[indd], &work[inde], &work[
	    indtau], &work[indwk], &llwork, &iinfo);

/*     If all eigenvalues are desired   
       then call DSTERF or DSTEMR and DORMTR. */

    if ((alleig || indeig && *il == 1 && *iu == *n) && ieeeok == 1) {
	if (! wantz) {
	    dcopy_(n, &work[indd], &c__1, &w[1], &c__1);
	    i__1 = *n - 1;
	    dcopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
	    dsterf_(n, &w[1], &work[indee], info);
	} else {
	    i__1 = *n - 1;
	    dcopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
	    dcopy_(n, &work[indd], &c__1, &work[inddd], &c__1);

	    if (*abstol <= *n * 0. * eps) {
		tryrac = TRUE_;
	    } else {
		tryrac = FALSE_;
	    }
	    dstemr_(jobz, "A", n, &work[inddd], &work[indee], vl, vu, il, iu, 
		    m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac, &
		    work[indwk], lwork, &iwork[1], liwork, info);



/*        Apply orthogonal matrix used in reduction to tridiagonal   
          form to eigenvectors returned by DSTEIN. */

	    if (wantz && *info == 0) {
		indwkn = inde;
		llwrkn = *lwork - indwkn + 1;
		dormtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau]
			, &z__[z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
	    }
	}


	if (*info == 0) {
/*           Everything worked.  Skip DSTEBZ/DSTEIN.  IWORK(:) are   
             undefined. */
	    *m = *n;
	    goto L30;
	}
	*info = 0;
    }

/*     Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN.   
       Also call DSTEBZ and DSTEIN if DSTEMR fails. */

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[
	    inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[
	    indwk], &iwork[indiwo], info);

    if (wantz) {
	dstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[
		indisp], &z__[z_offset], ldz, &work[indwk], &iwork[indiwo], &
		iwork[indifl], info);

/*        Apply orthogonal matrix used in reduction to tridiagonal   
          form to eigenvectors returned by DSTEIN. */

	indwkn = inde;
	llwrkn = *lwork - indwkn + 1;
	dormtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[
		z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
    }

/*     If matrix was scaled, then rescale eigenvalues appropriately.   

    Jump here if DSTEMR/DSTEIN succeeded. */
L30:
    if (iscale == 1) {
	if (*info == 0) {
	    imax = *m;
	} else {
	    imax = *info - 1;
	}
	d__1 = 1. / sigma;
	dscal_(&imax, &d__1, &w[1], &c__1);
    }

/*     If eigenvalues are not in order, then sort them, along with   
       eigenvectors.  Note: We do not sort the IFAIL portion of IWORK.   
       It may not be initialized (if DSTEMR/DSTEIN succeeded), and we do   
       not return this detailed information to the user. */

    if (wantz) {
	i__1 = *m - 1;
	for (j = 1; j <= i__1; ++j) {
	    i__ = 0;
	    tmp1 = w[j];
	    i__2 = *m;
	    for (jj = j + 1; jj <= i__2; ++jj) {
		if (w[jj] < tmp1) {
		    i__ = jj;
		    tmp1 = w[jj];
		}
/* L40: */
	    }

	    if (i__ != 0) {
		w[i__] = w[j];
		w[j] = tmp1;
		dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], 
			 &c__1);
	    }
/* L50: */
	}
    }

/*     Set WORK(1) to optimal workspace size. */

    work[1] = (doublereal) lwkopt;
    iwork[1] = liwmin;

    return 0;

/*     End of DSYEVR */

} /* dsyevr_ */