src/lapack/zhbevx.c

/* ./src_f77/zhbevx.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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static doublereal c_b16 = 1.;
static integer c__1 = 1;

/* Subroutine */ int zhbevx_(char *jobz, char *range, char *uplo, integer *n,
	integer *kd, doublecomplex *ab, integer *ldab, doublecomplex *q,
	integer *ldq, doublereal *vl, doublereal *vu, integer *il, integer *
	iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__,
	 integer *ldz, doublecomplex *work, doublereal *rwork, integer *iwork,
	 integer *ifail, integer *info, ftnlen jobz_len, ftnlen range_len,
	ftnlen uplo_len)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, q_dim1, q_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, jj;
    static doublereal eps, vll, vuu, tmp1;
    static integer indd, inde;
    static doublereal anrm;
    static integer imax;
    static doublereal rmin, rmax;
    static doublecomplex ctmp1;
    static integer itmp1, indee;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
	    integer *);
    static doublereal sigma;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    static integer iinfo;
    static char order[1];
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
	    doublereal *, integer *);
    static logical lower;
    extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *,
	    integer *, doublecomplex *, doublecomplex *, integer *, ftnlen);
    static logical wantz;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
	    doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
	    integer *, doublecomplex *, integer *);
    extern doublereal dlamch_(char *, ftnlen);
    static logical alleig, indeig;
    static integer iscale, indibl;
    static logical valeig;
    static doublereal safmin;
    extern doublereal zlanhb_(char *, char *, integer *, integer *,
	    doublecomplex *, integer *, doublereal *, ftnlen, ftnlen);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    static doublereal abstll, bignum;
    static integer indiwk, indisp;
    extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
	     integer *), zlascl_(char *, integer *, integer *, doublereal *,
	    doublereal *, integer *, integer *, doublecomplex *, integer *,
	    integer *, ftnlen), dstebz_(char *, char *, integer *, doublereal
	    *, doublereal *, integer *, integer *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *, doublereal *, integer *,
	    integer *, doublereal *, integer *, integer *, ftnlen, ftnlen),
	    zhbtrd_(char *, char *, integer *, integer *, doublecomplex *,
	    integer *, doublereal *, doublereal *, doublecomplex *, integer *,
	     doublecomplex *, integer *, ftnlen, ftnlen);
    static integer indrwk, indwrk;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
	    doublecomplex *, integer *, doublecomplex *, integer *, ftnlen);
    static integer nsplit;
    static doublereal smlnum;
    extern /* Subroutine */ int zstein_(integer *, doublereal *, doublereal *,
	     integer *, doublereal *, integer *, integer *, doublecomplex *,
	    integer *, doublereal *, integer *, integer *, integer *),
	    zsteqr_(char *, integer *, doublereal *, doublereal *,
	    doublecomplex *, integer *, doublereal *, integer *, ftnlen);


/*  -- LAPACK driver 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 */
/*  ======= */

/*  ZHBEVX computes selected eigenvalues and, optionally, eigenvectors */
/*  of a complex Hermitian band matrix A.  Eigenvalues and eigenvectors */
/*  can be selected by specifying either a range of values or a range of */
/*  indices for the desired eigenvalues. */

/*  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. */

/*  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. */

/*  KD      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0. */

/*  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the Hermitian band */
/*          matrix A, stored in the first KD+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */

/*          On exit, AB is overwritten by values generated during the */
/*          reduction to tridiagonal form. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KD + 1. */

/*  Q       (output) COMPLEX*16 array, dimension (LDQ, N) */
/*          If JOBZ = 'V', the N-by-N unitary matrix used in the */
/*                          reduction to tridiagonal form. */
/*          If JOBZ = 'N', the array Q is not referenced. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of the array Q.  If JOBZ = 'V', then */
/*          LDQ >= 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 AB to tridiagonal form. */

/*          Eigenvalues will be computed most accurately when ABSTOL is */
/*          set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
/*          If this routine returns with INFO>0, indicating that some */
/*          eigenvectors did not converge, try setting ABSTOL to */
/*          2*DLAMCH('S'). */

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

/*  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) COMPLEX*16 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 an eigenvector fails to converge, then that column of Z */
/*          contains the latest approximation to the eigenvector, and the */
/*          index of the eigenvector is returned in IFAIL. */
/*          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). */

/*  WORK    (workspace) COMPLEX*16 array, dimension (N) */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (7*N) */

/*  IWORK   (workspace) INTEGER array, dimension (5*N) */

/*  IFAIL   (output) INTEGER array, dimension (N) */
/*          If JOBZ = 'V', then if INFO = 0, the first M elements of */
/*          IFAIL are zero.  If INFO > 0, then IFAIL contains the */
/*          indices of the eigenvectors that failed to converge. */
/*          If JOBZ = 'N', then IFAIL is not referenced. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, then i eigenvectors failed to converge. */
/*                Their indices are stored in array IFAIL. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --rwork;
    --iwork;
    --ifail;

    /* 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);
    lower = lsame_(uplo, "L", (ftnlen)1, (ftnlen)1);

    *info = 0;
    if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) {
	*info = -1;
    } else if (! (alleig || valeig || indeig)) {
	*info = -2;
    } else if (! (lower || lsame_(uplo, "U", (ftnlen)1, (ftnlen)1))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*kd < 0) {
	*info = -5;
    } else if (*ldab < *kd + 1) {
	*info = -7;
    } else if (wantz && *ldq < max(1,*n)) {
	*info = -9;
    } else {
	if (valeig) {
	    if (*n > 0 && *vu <= *vl) {
		*info = -11;
	    }
	} else if (indeig) {
	    if (*il < 1 || *il > max(1,*n)) {
		*info = -12;
	    } else if (*iu < min(*n,*il) || *iu > *n) {
		*info = -13;
	    }
	}
    }
    if (*info == 0) {
	if (*ldz < 1 || wantz && *ldz < *n) {
	    *info = -18;
	}
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	*m = 1;
	if (lower) {
	    i__1 = ab_dim1 + 1;
	    ctmp1.r = ab[i__1].r, ctmp1.i = ab[i__1].i;
	} else {
	    i__1 = *kd + 1 + ab_dim1;
	    ctmp1.r = ab[i__1].r, ctmp1.i = ab[i__1].i;
	}
	tmp1 = ctmp1.r;
	if (valeig) {
	    if (! (*vl < tmp1 && *vu >= tmp1)) {
		*m = 0;
	    }
	}
	if (*m == 1) {
	    w[1] = ctmp1.r;
	    if (wantz) {
		i__1 = z_dim1 + 1;
		z__[i__1].r = 1., z__[i__1].i = 0.;
	    }
	}
	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. */

    iscale = 0;
    abstll = *abstol;
    if (valeig) {
	vll = *vl;
	vuu = *vu;
    } else {
	vll = 0.;
	vuu = 0.;
    }
    anrm = zlanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1], (ftnlen)
	    1, (ftnlen)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) {
	    zlascl_("B", kd, kd, &c_b16, &sigma, n, n, &ab[ab_offset], ldab,
		    info, (ftnlen)1);
	} else {
	    zlascl_("Q", kd, kd, &c_b16, &sigma, n, n, &ab[ab_offset], ldab,
		    info, (ftnlen)1);
	}
	if (*abstol > 0.) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }

/*     Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form. */

    indd = 1;
    inde = indd + *n;
    indrwk = inde + *n;
    indwrk = 1;
    zhbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &rwork[indd], &rwork[
	    inde], &q[q_offset], ldq, &work[indwrk], &iinfo, (ftnlen)1, (
	    ftnlen)1);

/*     If all eigenvalues are desired and ABSTOL is less than or equal */
/*     to zero, then call DSTERF or ZSTEQR.  If this fails for some */
/*     eigenvalue, then try DSTEBZ. */

    if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.) {
	dcopy_(n, &rwork[indd], &c__1, &w[1], &c__1);
	indee = indrwk + (*n << 1);
	if (! wantz) {
	    i__1 = *n - 1;
	    dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
	    dsterf_(n, &w[1], &rwork[indee], info);
	} else {
	    zlacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz, (
		    ftnlen)1);
	    i__1 = *n - 1;
	    dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
	    zsteqr_(jobz, n, &w[1], &rwork[indee], &z__[z_offset], ldz, &
		    rwork[indrwk], info, (ftnlen)1);
	    if (*info == 0) {
		i__1 = *n;
		for (i__ = 1; i__ <= i__1; ++i__) {
		    ifail[i__] = 0;
/* L10: */
		}
	    }
	}
	if (*info == 0) {
	    *m = *n;
	    goto L30;
	}
	*info = 0;
    }

/*     Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */

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

    if (wantz) {
	zstein_(n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], &
		iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[
		indiwk], &ifail[1], info);

/*        Apply unitary matrix used in reduction to tridiagonal */
/*        form to eigenvectors returned by ZSTEIN. */

	i__1 = *m;
	for (j = 1; j <= i__1; ++j) {
	    zcopy_(n, &z__[j * z_dim1 + 1], &c__1, &work[1], &c__1);
	    zgemv_("N", n, n, &c_b2, &q[q_offset], ldq, &work[1], &c__1, &
		    c_b1, &z__[j * z_dim1 + 1], &c__1, (ftnlen)1);
/* L20: */
	}
    }

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

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. */

    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) {
		itmp1 = iwork[indibl + i__ - 1];
		w[i__] = w[j];
		iwork[indibl + i__ - 1] = iwork[indibl + j - 1];
		w[j] = tmp1;
		iwork[indibl + j - 1] = itmp1;
		zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1],
			 &c__1);
		if (*info != 0) {
		    itmp1 = ifail[i__];
		    ifail[i__] = ifail[j];
		    ifail[j] = itmp1;
		}
	    }
/* L50: */
	}
    }

    return 0;

/*     End of ZHBEVX */

} /* zhbevx_ */