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

/* Subroutine */ int chegvd_(integer *itype, char *jobz, char *uplo, integer *
	n, complex *a, integer *lda, complex *b, integer *ldb, real *w, 
	complex *work, integer *lwork, real *rwork, integer *lrwork, integer *
	iwork, integer *liwork, integer *info  	)
{
/*  -- LAPACK driver routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    Purpose   
    =======   

    CHEGVD 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 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 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) REAL array, dimension (N)   
            If INFO = 0, the eigenvalues in ascending order.   

    WORK    (workspace/output) COMPLEX array, dimension (MAX(1,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 sizes of the WORK, RWORK and   
            IWORK arrays, returns these values as the first entries of   
            the WORK, RWORK and IWORK arrays, and no error message   
            related to LWORK or LRWORK or LIWORK is issued by XERBLA.   

    RWORK   (workspace/output) REAL array, dimension (MAX(1,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 sizes of the WORK, RWORK   
            and IWORK arrays, returns these values as the first entries   
            of the WORK, RWORK and IWORK arrays, and no error message   
            related to LWORK or LRWORK or LIWORK is issued by XERBLA.   

    IWORK   (workspace/output) INTEGER array, dimension (MAX(1,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.   

            If LIWORK = -1, then a workspace query is assumed; the   
            routine only calculates the optimal sizes of the WORK, RWORK   
            and IWORK arrays, returns these values as the first entries   
            of the WORK, RWORK and IWORK arrays, and no error message   
            related to LWORK or LRWORK or LIWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   
            > 0:  CPOTRF or CHEEVD returned an error code:   
               <= N:  if INFO = i and JOBZ = 'N', then the algorithm   
                      failed to converge; i off-diagonal elements of an   
                      intermediate tridiagonal form did not converge to   
                      zero;   
                      if INFO = i and JOBZ = 'V', then the algorithm   
                      failed to compute an eigenvalue while working on   
                      the submatrix lying in rows and columns INFO/(N+1)   
                      through mod(INFO,N+1);   
               > 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   

    Modified so that no backsubstitution is performed if CHEEVD fails to   
    converge (NEIG in old code could be greater than N causing out of   
    bounds reference to A - reported by Ralf Meyer).  Also corrected the   
    description of INFO and the test on ITYPE. Sven, 16 Feb 05.   
    =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    /* Table of constant values */
    static complex c_b1 = {1.f,0.f};
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1;
    real r__1, r__2;
    /* Local variables */
    static integer lopt;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, 
	    integer *, integer *, complex *, complex *, integer *, complex *, 
	    integer *);
    static integer lwmin;
    static char trans[1];
    static integer liopt;
    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
	    integer *, integer *, complex *, complex *, integer *, complex *, 
	    integer *);
    static logical upper;
    static integer lropt;
    static logical wantz;
    extern /* Subroutine */ int cheevd_(char *, char *, integer *, complex *, 
	    integer *, real *, complex *, integer *, real *, integer *, 
	    integer *, integer *, integer *), chegst_(integer 
	    *, char *, integer *, complex *, integer *, complex *, integer *, 
	    integer *), xerbla_(char *, integer *), cpotrf_(
	    char *, integer *, complex *, integer *, integer *);
    static integer liwmin, lrwmin;
    static logical lquery;


    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    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;
    } 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 < 1 || *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;
    }

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

	if (*lwork < lwmin && ! lquery) {
	    *info = -11;
	} else if (*lrwork < lrwmin && ! lquery) {
	    *info = -13;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -15;
	}
    }

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

/*     Quick return if possible */

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

/*     Form a Cholesky factorization of B. */

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

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

    chegst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    cheevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &rwork[
	    1], lrwork, &iwork[1], liwork, info);
/* Computing MAX */
    r__1 = (real) lopt, r__2 = work[1].r;
    lopt = dmax(r__1,r__2);
/* Computing MAX */
    r__1 = (real) lropt;
    lropt = dmax(r__1,rwork[1]);
/* Computing MAX */
    r__1 = (real) liopt, r__2 = (real) iwork[1];
    liopt = dmax(r__1,r__2);

    if (wantz && *info == 0) {

/*        Backtransform eigenvectors to the original problem. */

	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';
	    }

	    ctrsm_("Left", uplo, trans, "Non-unit", n, n, &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';
	    }

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

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

    return 0;

/*     End of CHEGVD */

} /* chegvd_ */