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

/* Subroutine */ int zhpgvx_(integer *itype, char *jobz, char *range, char *
	uplo, integer *n, doublecomplex *ap, doublecomplex *bp, 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)
{
/*  -- 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   
    =======   

    ZHPGVX computes selected eigenvalues and, optionally, eigenvectors   
    of a complex generalized Hermitian-definite eigenproblem, of the form   
    A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and   
    B are assumed to be Hermitian, stored in packed format, and B is also   
    positive definite.  Eigenvalues and eigenvectors can be selected by   
    specifying either a range of values or a range of indices for the   
    desired eigenvalues.   

    Arguments   
    =========   

    ITYPE   (input) INTEGER   
            Specifies the problem type to be solved:   
            = 1:  A*x = (lambda)*B*x   
            = 2:  A*B*x = (lambda)*x   
            = 3:  B*A*x = (lambda)*x   

    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.   

    AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)   
            On entry, the upper or lower triangle of the Hermitian matrix   
            A, packed columnwise in a linear array.  The j-th column of A   
            is stored in the array AP as follows:   
            if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;   
            if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.   

            On exit, the contents of AP are destroyed.   

    BP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)   
            On entry, the upper or lower triangle of the Hermitian matrix   
            B, packed columnwise in a linear array.  The j-th column of B   
            is stored in the array BP as follows:   
            if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;   
            if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.   

            On exit, the triangular factor U or L from the Cholesky   
            factorization B = U**H*U or B = L*L**H, in the same storage   
            format as B.   

    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 AP 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)   
            On normal exit, the first M elements contain the selected   
            eigenvalues in ascending order.   

    Z       (output) COMPLEX*16 array, dimension (LDZ, N)   
            If JOBZ = 'N', then Z is not referenced.   
            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).   
            The eigenvectors are normalized as follows:   
            if ITYPE = 1 or 2, Z**H*B*Z = I;   
            if ITYPE = 3, Z**H*inv(B)*Z = 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.   
            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 (2*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:  ZPPTRF or ZHPEVX returned an error code:   
               <= N:  if INFO = i, ZHPEVX failed to converge;   
                      i eigenvectors failed to converge.  Their indices   
                      are stored in array IFAIL.   
               > N:   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;
    
    /* System generated locals */
    integer z_dim1, z_offset, i__1;
    /* Local variables */
    static integer j;
    extern logical lsame_(char *, char *);
    static char trans[1];
    static logical upper, wantz;
    extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, 
	    doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex *
	    , doublecomplex *, integer *);
    static logical alleig, indeig, valeig;
    extern /* Subroutine */ int xerbla_(char *, integer *), zhpgst_(
	    integer *, char *, integer *, doublecomplex *, doublecomplex *, 
	    integer *), zhpevx_(char *, char *, char *, integer *, 
	    doublecomplex *, doublereal *, doublereal *, integer *, integer *,
	     doublereal *, integer *, doublereal *, doublecomplex *, integer *
	    , doublecomplex *, doublereal *, integer *, integer *, integer *), zpptrf_(char *, integer *, doublecomplex 
	    *, integer *);
#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)]


    --ap;
    --bp;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --rwork;
    --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 (*itype < 0 || *itype > 3) {
	*info = -1;
    } else if (! (wantz || lsame_(jobz, "N"))) {
	*info = -2;
    } else if (! (alleig || valeig || indeig)) {
	*info = -3;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (valeig && *n > 0 && *vu <= *vl) {
	*info = -9;
    } else if (indeig && *il < 1) {
	*info = -10;
    } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) {
	*info = -11;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -16;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZHPGVX", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Form a Cholesky factorization of B. */

    zpptrf_(uplo, n, &bp[1], info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem and solve. */

    zhpgst_(itype, uplo, n, &ap[1], &bp[1], info);
    zhpevx_(jobz, range, uplo, n, &ap[1], vl, vu, il, iu, abstol, m, &w[1], &
	    z__[z_offset], ldz, &work[1], &rwork[1], &iwork[1], &ifail[1], 
	    info);

    if (wantz) {

/*        Backtransform eigenvectors to the original problem. */

	if (*info > 0) {
	    *m = *info - 1;
	}
	if (*itype == 1 || *itype == 2) {

/*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;   
             backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */

	    if (upper) {
		*(unsigned char *)trans = 'N';
	    } else {
		*(unsigned char *)trans = 'C';
	    }

	    i__1 = *m;
	    for (j = 1; j <= i__1; ++j) {
		ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z___ref(1, j), &
			c__1);
/* L10: */
	    }

	} else if (*itype == 3) {

/*           For B*A*x=(lambda)*x;   
             backtransform eigenvectors: x = L*y or U'*y */

	    if (upper) {
		*(unsigned char *)trans = 'C';
	    } else {
		*(unsigned char *)trans = 'N';
	    }

	    i__1 = *m;
	    for (j = 1; j <= i__1; ++j) {
		ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z___ref(1, j), &
			c__1);
/* L20: */
	    }
	}
    }

    return 0;

/*     End of ZHPGVX */

} /* zhpgvx_ */

#undef z___ref
#undef z___subscr


