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

/* Subroutine */ int zhegvd_(integer *itype, char *jobz, char *uplo, integer *
	n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork,
	 integer *lrwork, 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   
    =======   

    ZHEGVD computes all the eigenvalues, and optionally, the 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 and B is also positive definite.   
    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   
    =========   

    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.   

    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.   

    A       (input/output) COMPLEX*16 array, dimension (LDA, N)   
            On entry, the Hermitian matrix A.  If UPLO = 'U', the   
            leading N-by-N upper triangular part of A contains the   
            upper triangular part of the matrix A.  If UPLO = 'L',   
            the leading N-by-N lower triangular part of A contains   
            the lower triangular part of the matrix A.   

            On exit, if JOBZ = 'V', then if INFO = 0, A contains the   
            matrix Z of eigenvectors.  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 JOBZ = 'N', then on exit the upper triangle (if UPLO='U')   
            or the lower triangle (if UPLO='L') of A, including the   
            diagonal, is destroyed.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.  LDA >= max(1,N).   

    B       (input/output) COMPLEX*16 array, dimension (LDB, N)   
            On entry, the Hermitian matrix B.  If UPLO = 'U', the   
            leading N-by-N upper triangular part of B contains the   
            upper triangular part of the matrix B.  If UPLO = 'L',   
            the leading N-by-N lower triangular part of B contains   
            the lower triangular part of the matrix B.   

            On exit, if INFO <= N, the part of B containing the matrix is   
            overwritten by the triangular factor U or L from the Cholesky   
            factorization B = U**H*U or B = L*L**H.   

    LDB     (input) INTEGER   
            The leading dimension of the array B.  LDB >= max(1,N).   

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

    WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The length of the array WORK.   
            If N <= 1,                LWORK >= 1.   
            If JOBZ  = 'N' and N > 1, LWORK >= N + 1.   
            If JOBZ  = 'V' and N > 1, LWORK >= 2*N + 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.   

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

    LRWORK  (input) INTEGER   
            The dimension of the array RWORK.   
            If N <= 1,                LRWORK >= 1.   
            If JOBZ  = 'N' and N > 1, LRWORK >= N.   
            If JOBZ  = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.   

            If LRWORK = -1, then a workspace query is assumed; the   
            routine only calculates the optimal size of the RWORK array,   
            returns this value as the first entry of the RWORK array, and   
            no error message related to LRWORK 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.   
            If N <= 1,                LIWORK >= 1.   
            If JOBZ  = 'N' and N > 1, LIWORK >= 1.   
            If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  ZPOTRF or ZHEEVD returned an error code:   
               <= N:  if INFO = i, ZHEEVD failed to converge;   
                      i off-diagonal elements of an intermediate   
                      tridiagonal form did not converge to zero;   
               > 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 doublecomplex c_b1 = {1.,0.};
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1;
    doublereal d__1, d__2;
    /* Local variables */
    static integer neig, lopt;
    extern logical lsame_(char *, char *);
    static integer lwmin;
    static char trans[1];
    static integer liopt;
    static logical upper;
    static integer lropt;
    static logical wantz;
    extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *, 
	    integer *, integer *, doublecomplex *, doublecomplex *, integer *,
	     doublecomplex *, integer *), 
	    ztrsm_(char *, char *, char *, char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *), xerbla_(char *, 
	    integer *), zheevd_(char *, char *, integer *, 
	    doublecomplex *, integer *, doublereal *, doublecomplex *, 
	    integer *, doublereal *, integer *, integer *, integer *, integer 
	    *);
    static integer liwmin;
    extern /* Subroutine */ int zhegst_(integer *, char *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    static integer lrwmin;
    static logical lquery;
    extern /* Subroutine */ int zpotrf_(char *, integer *, doublecomplex *, 
	    integer *, integer *);


    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --w;
    --work;
    --rwork;
    --iwork;

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

    *info = 0;
    if (*n <= 1) {
	lwmin = 1;
	lrwmin = 1;
	liwmin = 1;
	lopt = lwmin;
	lropt = lrwmin;
	liopt = liwmin;
    } else {
	if (wantz) {
	    lwmin = (*n << 1) + *n * *n;
	    lrwmin = *n * 5 + 1 + (*n << 1) * *n;
	    liwmin = *n * 5 + 3;
	} else {
	    lwmin = *n + 1;
	    lrwmin = *n;
	    liwmin = 1;
	}
	lopt = lwmin;
	lropt = lrwmin;
	liopt = liwmin;
    }
    if (*itype < 0 || *itype > 3) {
	*info = -1;
    } else if (! (wantz || lsame_(jobz, "N"))) {
	*info = -2;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    } else if (*lwork < lwmin && ! lquery) {
	*info = -11;
    } else if (*lrwork < lrwmin && ! lquery) {
	*info = -13;
    } else if (*liwork < liwmin && ! lquery) {
	*info = -15;
    }

    if (*info == 0) {
	work[1].r = (doublereal) lopt, work[1].i = 0.;
	rwork[1] = (doublereal) lropt;
	iwork[1] = liopt;
    }

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

/*     Quick return if possible */

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

/*     Form a Cholesky factorization of B. */

    zpotrf_(uplo, n, &b[b_offset], ldb, info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

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

    zhegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    zheevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[
	    1], lrwork, &iwork[1], liwork, info);
/* Computing MAX */
    d__1 = (doublereal) lopt, d__2 = work[1].r;
    lopt = (integer) max(d__1,d__2);
/* Computing MAX */
    d__1 = (doublereal) lropt;
    lropt = (integer) max(d__1,rwork[1]);
/* Computing MAX */
    d__1 = (doublereal) liopt, d__2 = (doublereal) iwork[1];
    liopt = (integer) max(d__1,d__2);

    if (wantz) {

/*        Backtransform eigenvectors to the original problem. */

	neig = *n;
	if (*info > 0) {
	    neig = *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';
	    }

	    ztrsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
		    b_offset], ldb, &a[a_offset], lda);

	} 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';
	    }

	    ztrmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b1, &b[
		    b_offset], ldb, &a[a_offset], lda);
	}
    }

    work[1].r = (doublereal) lopt, work[1].i = 0.;
    rwork[1] = (doublereal) lropt;
    iwork[1] = liopt;

    return 0;

/*     End of ZHEGVD */

} /* zhegvd_ */

