#include "blaswrap.h"
/*  -- translated by f2c (version 19990503).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Table of constant values */

static integer c__1 = 1;

/* Subroutine */ int chpgvd_(integer *itype, char *jobz, char *uplo, integer *
	n, complex *ap, complex *bp, real *w, complex *z__, integer *ldz, 
	complex *work, integer *lwork, real *rwork, integer *lrwork, integer *
	iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1;
    real r__1, r__2;

    /* Local variables */
    static integer neig, j;
    extern logical lsame_(char *, char *);
    static integer lwmin;
    static char trans[1];
    extern /* Subroutine */ int ctpmv_(char *, char *, char *, integer *, 
	    complex *, complex *, integer *);
    static logical upper;
    extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *, 
	    complex *, complex *, integer *);
    static logical wantz;
    extern /* Subroutine */ int chpevd_(char *, char *, integer *, complex *, 
	    real *, complex *, integer *, complex *, integer *, real *, 
	    integer *, integer *, integer *, integer *), 
	    xerbla_(char *, integer *), chpgst_(integer *, char *, 
	    integer *, complex *, complex *, integer *), cpptrf_(char 
	    *, integer *, complex *, integer *);
    static integer liwmin, lrwmin;
    static logical lquery;


#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)]


/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1999   


    Purpose   
    =======   

    CHPGVD 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, stored in packed format, 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.   

    AP      (input/output) COMPLEX 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 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.   

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

    Z       (output) COMPLEX array, dimension (LDZ, N)   
            If JOBZ = 'V', then if INFO = 0, Z 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 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) COMPLEX array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

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

            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) REAL array, dimension (LRWORK)   
            On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.   

    LRWORK  (input) INTEGER   
            The dimension of 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 array IWORK.   
            If JOBZ  = 'N' or 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 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:  CPPTRF or CHPEVD returned an error code:   
               <= N:  if INFO = i, CHPEVD failed to converge;   
                      i off-diagonal elements of an intermediate   
                      tridiagonal form did not convergeto 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 */
    --ap;
    --bp;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --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;
	liwmin = 1;
	lrwmin = 1;
    } else {
	if (wantz) {
	    lwmin = *n << 1;
/* Computing 2nd power */
	    i__1 = *n;
	    lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
	    liwmin = *n * 5 + 3;
	} else {
	    lwmin = *n;
	    lrwmin = *n;
	    liwmin = 1;
	}
    }
    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 (*ldz < 1 || wantz && *ldz < *n) {
	*info = -9;
    } 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 = (real) lwmin, work[1].i = 0.f;
	rwork[1] = (real) lrwmin;
	iwork[1] = liwmin;
    }

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

/*     Quick return if possible */

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

/*     Form a Cholesky factorization of B. */

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

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

    chpgst_(itype, uplo, n, &ap[1], &bp[1], info);
    chpevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], 
	    lwork, &rwork[1], lrwork, &iwork[1], liwork, info);
/* Computing MAX */
    r__1 = (real) lwmin, r__2 = work[1].r;
    lwmin = dmax(r__1,r__2);
/* Computing MAX */
    r__1 = (real) lrwmin;
    lrwmin = dmax(r__1,rwork[1]);
/* Computing MAX */
    r__1 = (real) liwmin, r__2 = (real) iwork[1];
    liwmin = dmax(r__1,r__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';
	    }

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

    work[1].r = (real) lwmin, work[1].i = 0.f;
    rwork[1] = (real) lrwmin;
    iwork[1] = liwmin;
    return 0;

/*     End of CHPGVD */

} /* chpgvd_ */

#undef z___ref
#undef z___subscr



.