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

/* Subroutine */ int dsbgvx_(char *jobz, char *range, char *uplo, integer *n, 
	integer *ka, integer *kb, doublereal *ab, integer *ldab, doublereal *
	bb, integer *ldbb, doublereal *q, integer *ldq, doublereal *vl, 
	doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer 
	*m, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, 
	integer *iwork, integer *ifail, 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   
    =======   

    DSBGVX computes selected eigenvalues, and optionally, eigenvectors   
    of a real generalized symmetric-definite banded eigenproblem, of   
    the form A*x=(lambda)*B*x.  Here A and B are assumed to be symmetric   
    and banded, and B is also positive definite.  Eigenvalues and   
    eigenvectors can be selected by specifying either all eigenvalues,   
    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 triangles of A and B are stored;   
            = 'L':  Lower triangles of A and B are stored.   

    N       (input) INTEGER   
            The order of the matrices A and B.  N >= 0.   

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

    KB      (input) INTEGER   
            The number of superdiagonals of the matrix B if UPLO = 'U',   
            or the number of subdiagonals if UPLO = 'L'.  KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;   
            if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).   

            On exit, the contents of AB are destroyed.   

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

    BB      (input/output) DOUBLE PRECISION array, dimension (LDBB, N)   
            On entry, the upper or lower triangle of the symmetric band   
            matrix B, stored in the first kb+1 rows of the array.  The   
            j-th column of B is stored in the j-th column of the array BB   
            as follows:   
            if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;   
            if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).   

            On exit, the factor S from the split Cholesky factorization   
            B = S**T*S, as returned by DPBSTF.   

    LDBB    (input) INTEGER   
            The leading dimension of the array BB.  LDBB >= KB+1.   

    Q       (output) DOUBLE PRECISION array, dimension (LDQ, N)   
            If JOBZ = 'V', the n-by-n matrix used in the reduction of   
            A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,   
            and consequently C to tridiagonal form.   
            If JOBZ = 'N', the array Q is not referenced.   

    LDQ     (input) INTEGER   
            The leading dimension of the array Q.  If JOBZ = 'N',   
            LDQ >= 1. If JOBZ = 'V', 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 A 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').   

    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)   
            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 matrix Z of   
            eigenvectors, with the i-th column of Z holding the   
            eigenvector associated with W(i).  The eigenvectors are   
            normalized so Z**T*B*Z = 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 (7N)   

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

    IFAIL   (input) INTEGER array, dimension (M)   
            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 eigenvalues 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   
            <= N: if INFO = i, then i eigenvectors failed to converge.   
                    Their indices are stored in IFAIL.   
            > N : DPBSTF returned an error code; i.e.,   
                  if INFO = N + i, for 1 <= i <= N, then the leading   
                  minor of order i of B is not positive definite.   
                  The factorization of B could not be completed and   
                  no eigenvalues or eigenvectors were computed.   

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

    Based on contributions by   
       Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA   

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


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static doublereal c_b25 = 1.;
    static doublereal c_b27 = 0.;
    
    /* System generated locals */
    integer ab_dim1, ab_offset, bb_dim1, bb_offset, q_dim1, q_offset, z_dim1, 
	    z_offset, i__1, i__2;
    /* Local variables */
    static integer indd, inde;
    static char vect[1];
    static integer itmp1, i__, j, indee;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *);
    static integer iinfo;
    static char order[1];
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *), dswap_(integer *, doublereal *, integer 
	    *, doublereal *, integer *);
    static logical upper, wantz;
    static integer jj;
    static logical alleig, indeig;
    static integer indibl;
    static logical valeig;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    xerbla_(char *, integer *), dpbstf_(char *, integer *, 
	    integer *, doublereal *, integer *, integer *), dsbtrd_(
	    char *, char *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *, doublereal *,
	     integer *);
    static integer indisp;
    extern /* Subroutine */ int dsbgst_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, integer *),
	     dstein_(integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, integer *, integer *, integer *);
    static integer indiwo;
    extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
	     integer *), dstebz_(char *, char *, integer *, doublereal *, 
	    doublereal *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *, integer *, doublereal *, integer *, 
	    integer *, doublereal *, integer *, integer *);
    static integer indwrk;
    extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *);
    static integer nsplit;
    static doublereal tmp1;
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]


    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    bb_dim1 = *ldbb;
    bb_offset = 1 + bb_dim1 * 1;
    bb -= bb_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --iwork;
    --ifail;

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

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (alleig || valeig || indeig)) {
	*info = -2;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*ka < 0) {
	*info = -5;
    } else if (*kb < 0 || *kb > *ka) {
	*info = -6;
    } else if (*ldab < *ka + 1) {
	*info = -8;
    } else if (*ldbb < *kb + 1) {
	*info = -10;
    } else if (*ldq < 1) {
	*info = -12;
    } else if (valeig && *n > 0 && *vu <= *vl) {
	*info = -14;
    } else if (indeig && *il < 1) {
	*info = -15;
    } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) {
	*info = -16;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -21;
    }

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

/*     Quick return if possible */

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

/*     Form a split Cholesky factorization of B. */

    dpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem. */

    dsbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb,
	     &q[q_offset], ldq, &work[1], &iinfo);

/*     Reduce symmetric band matrix to tridiagonal form. */

    indd = 1;
    inde = indd + *n;
    indwrk = inde + *n;
    if (wantz) {
	*(unsigned char *)vect = 'U';
    } else {
	*(unsigned char *)vect = 'N';
    }
    dsbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &work[indd], &work[inde],
	     &q[q_offset], ldq, &work[indwrk], &iinfo);

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

    if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.) {
	dcopy_(n, &work[indd], &c__1, &w[1], &c__1);
	indee = indwrk + (*n << 1);
	i__1 = *n - 1;
	dcopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
	if (! wantz) {
	    dsterf_(n, &w[1], &work[indee], info);
	} else {
	    dlacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz);
	    dsteqr_(jobz, n, &w[1], &work[indee], &z__[z_offset], ldz, &work[
		    indwrk], info);
	    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,   
       call DSTEIN. */

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

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

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

	i__1 = *m;
	for (j = 1; j <= i__1; ++j) {
	    dcopy_(n, &z___ref(1, j), &c__1, &work[1], &c__1);
	    dgemv_("N", n, n, &c_b25, &q[q_offset], ldq, &work[1], &c__1, &
		    c_b27, &z___ref(1, j), &c__1);
/* L20: */
	}
    }

L30:

/*     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;
		dswap_(n, &z___ref(1, i__), &c__1, &z___ref(1, j), &c__1);
		if (*info != 0) {
		    itmp1 = ifail[i__];
		    ifail[i__] = ifail[j];
		    ifail[j] = itmp1;
		}
	    }
/* L50: */
	}
    }

    return 0;

/*     End of DSBGVX */

} /* dsbgvx_ */

#undef z___ref


