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

/* Subroutine */ int dsygvx_(integer *itype, char *jobz, char *range, char *
	uplo, integer *n, doublereal *a, integer *lda, doublereal *b, integer 
	*ldb, doublereal *vl, doublereal *vu, integer *il, integer *iu, 
	doublereal *abstol, integer *m, doublereal *w, doublereal *z__, 
	integer *ldz, doublereal *work, integer *lwork, 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   
    =======   

    DSYGVX computes selected eigenvalues, and optionally, eigenvectors   
    of a real generalized symmetric-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 symmetric 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 triangle of A and B are stored;   
            = 'L':  Lower triangle of A and B are stored.   

    N       (input) INTEGER   
            The order of the matrix pencil (A,B).  N >= 0.   

    A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)   
            On entry, the symmetric 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, the lower triangle (if UPLO='L') or the upper   
            triangle (if UPLO='U') of A, including the diagonal, is   
            destroyed.   

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

    B       (input/output) DOUBLE PRECISION array, dimension (LDA, N)   
            On entry, the symmetric 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**T*U or B = L*L**T.   

    LDB     (input) INTEGER   
            The leading dimension of the array B.  LDB >= 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)   
            On normal exit, the first M elements contain the selected   
            eigenvalues in ascending order.   

    Z       (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))   
            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**T*B*Z = I;   
            if ITYPE = 3, Z**T*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/output) DOUBLE PRECISION array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The length of the array WORK.  LWORK >= max(1,8*N).   
            For optimal efficiency, LWORK >= (NB+3)*N,   
            where NB is the blocksize for DSYTRD returned by ILAENV.   

            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.   

    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:  DPOTRF or DSYEVX returned an error code:   
               <= N:  if INFO = i, DSYEVX 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;
    static integer c_n1 = -1;
    static doublereal c_b19 = 1.;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset, i__1, i__2;
    /* Local variables */
    static integer lopt;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, 
	    integer *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *);
    static char trans[1];
    extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, 
	    integer *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *);
    static logical upper, wantz;
    static integer nb;
    static logical alleig, indeig, valeig;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *, 
	    integer *, integer *), dsygst_(integer *, char *, integer 
	    *, doublereal *, integer *, doublereal *, integer *, integer *);
    static integer lwkopt;
    static logical lquery;
    extern /* Subroutine */ int dsyevx_(char *, char *, char *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *, 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;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --work;
    --iwork;
    --ifail;

    /* Function Body */
    upper = lsame_(uplo, "U");
    wantz = lsame_(jobz, "V");
    alleig = lsame_(range, "A");
    valeig = lsame_(range, "V");
    indeig = lsame_(range, "I");
    lquery = *lwork == -1;

    *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 (*lda < max(1,*n)) {
	*info = -7;
    } else if (*ldb < max(1,*n)) {
	*info = -9;
    } else if (valeig && *n > 0) {
	if (*vu <= *vl) {
	    *info = -11;
	}
    } else if (indeig && *il < 1) {
	*info = -12;
    } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) {
	*info = -13;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -18;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = *n << 3;
	if (*lwork < max(i__1,i__2) && ! lquery) {
	    *info = -20;
	}
    }

    if (*info == 0) {
	nb = ilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
		 (ftnlen)1);
	lwkopt = (nb + 3) * *n;
	work[1] = (doublereal) lwkopt;
    }

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

/*     Quick return if possible */

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

/*     Form a Cholesky factorization of B. */

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

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

    dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
    dsyevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol, 
	    m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], &ifail[
	    1], info);
    lopt = (integer) work[1];

    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 = 'T';
	    }

	    dtrsm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
		    , ldb, &z__[z_offset], ldz);

	} else if (*itype == 3) {

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

	    if (upper) {
		*(unsigned char *)trans = 'T';
	    } else {
		*(unsigned char *)trans = 'N';
	    }

	    dtrmm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
		    , ldb, &z__[z_offset], ldz);
	}
    }

/*     Set WORK(1) to optimal workspace size. */

    work[1] = (doublereal) lwkopt;

    return 0;

/*     End of DSYGVX */

} /* dsygvx_ */

