#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int dsbevd_(char *jobz, char *uplo, integer *n, integer *kd, 
	doublereal *ab, integer *ldab, doublereal *w, doublereal *z__, 
	integer *ldz, doublereal *work, integer *lwork, integer *iwork, 
	integer *liwork, integer *info)
{
/*  -- 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   


    Purpose   
    =======   

    DSBEVD computes all the eigenvalues and, optionally, eigenvectors of   
    a real symmetric band matrix A. If eigenvectors are desired, it uses   
    a divide and conquer algorithm.   

    The divide and conquer algorithm makes very mild assumptions about   
    floating point arithmetic. It will work on machines with a guard   
    digit in add/subtract, or on those binary machines without guard   
    digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or   
    Cray-2. It could conceivably fail on hexadecimal or decimal machines   
    without guard digits, but we know of none.   

    Arguments   
    =========   

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

    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) DOUBLE PRECISION array, dimension (LDAB, N)   
            On entry, the upper or lower triangle of the symmetric 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.  If UPLO = 'U', the first   
            superdiagonal and the diagonal of the tridiagonal matrix T   
            are returned in rows KD and KD+1 of AB, and if UPLO = 'L',   
            the diagonal and first subdiagonal of T are returned in the   
            first two rows of AB.   

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

    W       (output) DOUBLE PRECISION array, dimension (N)   
            If INFO = 0, the eigenvalues in ascending order.   

    Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)   
            If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal   
            eigenvectors of the matrix A, with the i-th column of Z   
            holding the eigenvector associated with W(i).   
            If JOBZ = 'N', then Z is not referenced.   

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

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

    LWORK   (input) INTEGER   
            The dimension of the array WORK.   
            IF N <= 1,                LWORK must be at least 1.   
            If JOBZ  = 'N' and N > 2, LWORK must be at least 2*N.   
            If JOBZ  = 'V' and N > 2, LWORK must be at least   
                           ( 1 + 5*N + 2*N**2 ).   

            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 LIWORK.   
            If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.   
            If JOBZ  = 'V' and N > 2, LIWORK must be at least 3 + 5*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 = i, the algorithm failed to converge; i   
                  off-diagonal elements of an intermediate tridiagonal   
                  form did not converge to zero.   

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


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static doublereal c_b11 = 1.;
    static doublereal c_b18 = 0.;
    static integer c__1 = 1;
    
    /* System generated locals */
    integer ab_dim1, ab_offset, z_dim1, z_offset, i__1;
    doublereal d__1;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer inde;
    static doublereal anrm, rmin, rmax;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *), dgemm_(char *, char *, integer *, integer *, integer *
	    , doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *);
    static doublereal sigma;
    extern logical lsame_(char *, char *);
    static integer iinfo, lwmin;
    static logical lower, wantz;
    static integer indwk2, llwrk2;
    extern doublereal dlamch_(char *);
    static integer iscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *);
    extern doublereal dlansb_(char *, char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dstedc_(char *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    integer *, integer *, integer *), dlacpy_(char *, integer 
	    *, integer *, doublereal *, integer *, doublereal *, integer *);
    static doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static doublereal bignum;
    extern /* Subroutine */ int dsbtrd_(char *, char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *,
	     integer *, doublereal *, integer *), dsterf_(
	    integer *, doublereal *, doublereal *, integer *);
    static integer indwrk, liwmin;
    static doublereal smlnum;
    static logical lquery;
    static doublereal eps;
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1]


    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --iwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    lower = lsame_(uplo, "L");
    lquery = *lwork == -1 || *liwork == -1;

    *info = 0;
    if (*n <= 1) {
	liwmin = 1;
	lwmin = 1;
    } else {
	if (wantz) {
	    liwmin = *n * 5 + 3;
/* Computing 2nd power */
	    i__1 = *n;
	    lwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
	} else {
	    liwmin = 1;
	    lwmin = *n << 1;
	}
    }
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lower || lsame_(uplo, "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*kd < 0) {
	*info = -4;
    } else if (*ldab < *kd + 1) {
	*info = -6;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -9;
    } else if (*lwork < lwmin && ! lquery) {
	*info = -11;
    } else if (*liwork < liwmin && ! lquery) {
	*info = -13;
    }

    if (*info == 0) {
	work[1] = (doublereal) lwmin;
	iwork[1] = liwmin;
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	w[1] = ab_ref(1, 1);
	if (wantz) {
	    z___ref(1, 1) = 1.;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = dlamch_("Safe minimum");
    eps = dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
    rmax = sqrt(bignum);

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

    anrm = dlansb_("M", uplo, n, kd, &ab[ab_offset], ldab, &work[1]);
    iscale = 0;
    if (anrm > 0. && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    dlascl_("B", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	} else {
	    dlascl_("Q", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	}
    }

/*     Call DSBTRD to reduce symmetric band matrix to tridiagonal form. */

    inde = 1;
    indwrk = inde + *n;
    indwk2 = indwrk + *n * *n;
    llwrk2 = *lwork - indwk2 + 1;
    dsbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &work[inde], &z__[
	    z_offset], ldz, &work[indwrk], &iinfo);

/*     For eigenvalues only, call DSTERF.  For eigenvectors, call SSTEDC. */

    if (! wantz) {
	dsterf_(n, &w[1], &work[inde], info);
    } else {
	dstedc_("I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], &
		llwrk2, &iwork[1], liwork, info);
	dgemm_("N", "N", n, n, n, &c_b11, &z__[z_offset], ldz, &work[indwrk], 
		n, &c_b18, &work[indwk2], n);
	dlacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
    }

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

    if (iscale == 1) {
	d__1 = 1. / sigma;
	dscal_(n, &d__1, &w[1], &c__1);
    }

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

/*     End of DSBEVD */

} /* dsbevd_ */

#undef ab_ref
#undef z___ref


