src/lapack/dstegr.c

/* ./src_f77/dstegr.f -- translated by f2c (version 20030320).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include <punc/vf2c.h>

/* Table of constant values */

static integer c__1 = 1;
static doublereal c_b14 = 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,
	ftnlen jobz_len, ftnlen range_len)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    static integer i__, j, jj;
    static doublereal eps, tol, tmp;
    static integer iend;
    static doublereal rmin, rmax;
    static integer itmp;
    static doublereal tnrm;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
	    integer *);
    static doublereal scale;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    static integer iinfo;
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
	    doublereal *, integer *);
    static integer lwmin;
    static logical wantz;
    extern doublereal dlamch_(char *, ftnlen);
    static logical alleig;
    static integer ibegin;
    static logical indeig;
    static integer iindbl;
    static logical valeig;
    extern /* Subroutine */ int dlarre_(integer *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *, integer *, doublereal *,
	    doublereal *, doublereal *, doublereal *, integer *), dlaset_(
	    char *, integer *, integer *, doublereal *, doublereal *,
	    doublereal *, integer *, ftnlen);
    static doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    static doublereal bignum;
    static integer iindwk, indgrs, indwof;
    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *,
	    ftnlen);
    extern /* Subroutine */ int dlarrv_(integer *, doublereal *, doublereal *,
	     integer *, integer *, doublereal *, integer *, doublereal *,
	    doublereal *, doublereal *, integer *, integer *, doublereal *,
	    integer *, integer *);
    static doublereal thresh;
    static integer iinspl, indwrk, liwmin, nsplit;
    static doublereal smlnum;
    static logical lquery;


/*  -- LAPACK computational routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     June 30, 1999 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

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

/* DSTEGR computes selected eigenvalues and, optionally, eigenvectors */
/* of a real symmetric tridiagonal matrix T.  Eigenvalues and */
/* eigenvectors can be selected by specifying either a range of values */
/* or a range of indices for the desired eigenvalues. The eigenvalues */
/* are computed 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 the i-th unreduced block of T, */
/*     (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T */
/*         is a relatively robust representation, */
/*     (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high */
/*         relative accuracy by the dqds algorithm, */
/*     (c) If there is a cluster of close eigenvalues, "choose" sigma_i */
/*         close to the cluster, and go to step (a), */
/*     (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T, */
/*         compute the corresponding eigenvector by forming a */
/*         rank-revealing twisted factorization. */
/*  The desired accuracy of the output can be specified by the input */
/*  parameter ABSTOL. */

/*  For more details, see "A new O(n^2) algorithm for the symmetric */
/*  tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon, */
/*  Computer Science Division Technical Report No. UCB/CSD-97-971, */
/*  UC Berkeley, May 1997. */

/*  Note 1 : Currently DSTEGR is only set up to find ALL the n */
/*  eigenvalues and eigenvectors of T in O(n^2) time */
/*  Note 2 : Currently the routine DSTEIN is called when an appropriate */
/*  sigma_i cannot be chosen in step (c) above. DSTEIN invokes modified */
/*  Gram-Schmidt when eigenvalues are close. */
/*  Note 3 : DSTEGR works only on machines which follow ieee-754 */
/*  floating-point standard in their handling of infinities and NaNs. */
/*  Normal execution of DSTEGR may create NaNs and infinities and hence */
/*  may abort due to a floating point exception in environments which */
/*  do not conform to the ieee 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. */
/* ********* Only RANGE = 'A' is currently supported ********************* */

/*  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 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; 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/eigenvectors. IF JOBZ = 'V', the eigenvalues and */
/*          eigenvectors output have residual norms bounded by ABSTOL, */
/*          and the dot products between different eigenvectors are */
/*          bounded by ABSTOL. If ABSTOL is less than N*EPS*|T|, then */
/*          N*EPS*|T| will be used in its place, where EPS is the */
/*          machine precision and |T| is the 1-norm of the tridiagonal */
/*          matrix. The eigenvalues are computed to an accuracy of */
/*          EPS*|T| irrespective of ABSTOL. If high relative accuracy */
/*          is important, set ABSTOL to DLAMCH( 'Safe minimum' ). */
/*          See Barlow and 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 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. */

/*  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 ). */

/*  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 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 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:  if INFO = 1, internal error in DLARRE, */
/*                if INFO = 2, internal error in DLARRV. */

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

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

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

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

    /* Function Body */
    wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1);
    alleig = lsame_(range, "A", (ftnlen)1, (ftnlen)1);
    valeig = lsame_(range, "V", (ftnlen)1, (ftnlen)1);
    indeig = lsame_(range, "I", (ftnlen)1, (ftnlen)1);

    lquery = *lwork == -1 || *liwork == -1;
    lwmin = *n * 18;
    liwmin = *n * 10;

    *info = 0;
    if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) {
	*info = -1;
    } else if (! (alleig || valeig || indeig)) {
	*info = -2;

/*     The following two lines need to be removed once the */
/*     RANGE = 'V' and RANGE = 'I' options are provided. */

    } else if (valeig || indeig) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (valeig && *n > 0 && *vu <= *vl) {
	*info = -7;
    } else if (indeig && *il < 1) {
	*info = -8;
/*     The following change should be made in DSTEVX also, otherwise */
/*     IL can be specified as N+1 and IU as N. */
/*     ELSE IF( INDEIG .AND. ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) ) THEN */
    } else if (indeig && (*iu < *il || *iu > *n)) {
	*info = -9;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -14;
    } else if (*lwork < lwmin && ! lquery) {
	*info = -17;
    } else if (*liwork < liwmin && ! lquery) {
	*info = -19;
    }
    if (*info == 0) {
	work[1] = (doublereal) lwmin;
	iwork[1] = liwmin;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DSTEGR", &i__1, (ftnlen)6);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    *m = 0;
    if (*n == 0) {
	return 0;
    }

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

/*     Get machine constants. */

    safmin = dlamch_("Safe minimum", (ftnlen)12);
    eps = dlamch_("Precision", (ftnlen)9);
    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. */

    scale = 1.;
    tnrm = dlanst_("M", n, &d__[1], &e[1], (ftnlen)1);
    if (tnrm > 0. && tnrm < rmin) {
	scale = rmin / tnrm;
    } else if (tnrm > rmax) {
	scale = rmax / tnrm;
    }
    if (scale != 1.) {
	dscal_(n, &scale, &d__[1], &c__1);
	i__1 = *n - 1;
	dscal_(&i__1, &scale, &e[1], &c__1);
	tnrm *= scale;
    }
    indgrs = 1;
    indwof = (*n << 1) + 1;
    indwrk = *n * 3 + 1;

    iinspl = 1;
    iindbl = *n + 1;
    iindwk = (*n << 1) + 1;

    dlaset_("Full", n, n, &c_b14, &c_b14, &z__[z_offset], ldz, (ftnlen)4);

/*     Compute the desired eigenvalues of the tridiagonal after splitting */
/*     into smaller subblocks if the corresponding of-diagonal elements */
/*     are small */

    thresh = eps * tnrm;
    dlarre_(n, &d__[1], &e[1], &thresh, &nsplit, &iwork[iinspl], m, &w[1], &
	    work[indwof], &work[indgrs], &work[indwrk], &iinfo);
    if (iinfo != 0) {
	*info = 1;
	return 0;
    }

    if (wantz) {

/*        Compute the desired eigenvectors corresponding to the computed */
/*        eigenvalues */

/* Computing MAX */
	d__1 = *abstol, d__2 = (doublereal) (*n) * thresh;
	tol = max(d__1,d__2);
	ibegin = 1;
	i__1 = nsplit;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    iend = iwork[iinspl + i__ - 1];
	    i__2 = iend;
	    for (j = ibegin; j <= i__2; ++j) {
		iwork[iindbl + j - 1] = i__;
/* L10: */
	    }
	    ibegin = iend + 1;
/* L20: */
	}

	dlarrv_(n, &d__[1], &e[1], &iwork[iinspl], m, &w[1], &iwork[iindbl], &
		work[indgrs], &tol, &z__[z_offset], ldz, &isuppz[1], &work[
		indwrk], &iwork[iindwk], &iinfo);
	if (iinfo != 0) {
	    *info = 2;
	    return 0;
	}

    }

    ibegin = 1;
    i__1 = nsplit;
    for (i__ = 1; i__ <= i__1; ++i__) {
	iend = iwork[iinspl + i__ - 1];
	i__2 = iend;
	for (j = ibegin; j <= i__2; ++j) {
	    w[j] += work[indwof + i__ - 1];
/* L30: */
	}
	ibegin = iend + 1;
/* L40: */
    }

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

    if (scale != 1.) {
	d__1 = 1. / scale;
	dscal_(m, &d__1, &w[1], &c__1);
    }

/*     If eigenvalues are not in order, then sort them, along with */
/*     eigenvectors. */

    if (nsplit > 1) {
	i__1 = *m - 1;
	for (j = 1; j <= i__1; ++j) {
	    i__ = 0;
	    tmp = w[j];
	    i__2 = *m;
	    for (jj = j + 1; jj <= i__2; ++jj) {
		if (w[jj] < tmp) {
		    i__ = jj;
		    tmp = w[jj];
		}
/* L50: */
	    }
	    if (i__ != 0) {
		w[i__] = w[j];
		w[j] = tmp;
		if (wantz) {
		    dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1
			    + 1], &c__1);
		    itmp = isuppz[(i__ << 1) - 1];
		    isuppz[(i__ << 1) - 1] = isuppz[(j << 1) - 1];
		    isuppz[(j << 1) - 1] = itmp;
		    itmp = isuppz[i__ * 2];
		    isuppz[i__ * 2] = isuppz[j * 2];
		    isuppz[j * 2] = itmp;
		}
	    }
/* L60: */
	}
    }

    work[1] = (doublereal) lwmin;
    iwork[1] = liwmin;
    return 0;

/*     End of DSTEGR */

} /* dstegr_ */