Exemplo n.º 1
0
/* Subroutine */ int zhbgv_(char *jobz, char *uplo, integer *n, integer *ka, 
	integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, 
	integer *ldbb, doublereal *w, doublecomplex *z__, integer *ldz, 
	doublecomplex *work, doublereal *rwork, integer *info, ftnlen 
	jobz_len, ftnlen uplo_len)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1;

    /* Local variables */
    static integer inde;
    static char vect[1];
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    static integer iinfo;
    static logical upper, wantz;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dsterf_(
	    integer *, doublereal *, doublereal *, integer *), zhbtrd_(char *,
	     char *, integer *, integer *, doublecomplex *, integer *, 
	    doublereal *, doublereal *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, ftnlen, ftnlen);
    static integer indwrk;
    extern /* Subroutine */ int zhbgst_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *,
	     doublecomplex *, integer *, doublecomplex *, doublereal *, 
	    integer *, ftnlen, ftnlen), zpbstf_(char *, integer *, integer *, 
	    doublecomplex *, integer *, integer *, ftnlen), zsteqr_(char *, 
	    integer *, doublereal *, doublereal *, doublecomplex *, integer *,
	     doublereal *, integer *, ftnlen);


/*  -- LAPACK driver routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     September 30, 1994 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZHBGV computes all the eigenvalues, and optionally, the eigenvectors */
/*  of a complex generalized Hermitian-definite banded eigenproblem, of */
/*  the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian */
/*  and banded, and B is also positive definite. */

/*  Arguments */
/*  ========= */

/*  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. */

/*  KA      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'. KA >= 0. */

/*  KB      (input) INTEGER */
/*          The number of superdiagonals of the matrix B if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'. KB >= 0. */

/*  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the Hermitian band */
/*          matrix A, stored in the first ka+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka). */

/*          On exit, the contents of AB are destroyed. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KA+1. */

/*  BB      (input/output) COMPLEX*16 array, dimension (LDBB, N) */
/*          On entry, the upper or lower triangle of the Hermitian band */
/*          matrix B, stored in the first kb+1 rows of the array.  The */
/*          j-th column of B is stored in the j-th column of the array BB */
/*          as follows: */
/*          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; */
/*          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb). */

/*          On exit, the factor S from the split Cholesky factorization */
/*          B = S**H*S, as returned by ZPBSTF. */

/*  LDBB    (input) INTEGER */
/*          The leading dimension of the array BB.  LDBB >= KB+1. */

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

/*  Z       (output) COMPLEX*16 array, dimension (LDZ, N) */
/*          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
/*          eigenvectors, with the i-th column of Z holding the */
/*          eigenvector associated with W(i). The eigenvectors are */
/*          normalized so that Z**H*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 >= N. */

/*  WORK    (workspace) COMPLEX*16 array, dimension (N) */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (3*N) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, and i is: */
/*             <= N:  the algorithm 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 ZPBSTF */
/*                    returned INFO = i: B is not positive definite. */
/*                    The factorization of B could not be completed and */
/*                    no eigenvalues or eigenvectors were computed. */

/*  ===================================================================== */

/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    bb_dim1 = *ldbb;
    bb_offset = 1 + bb_dim1;
    bb -= bb_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --rwork;

    /* Function Body */
    wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1);
    upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);

    *info = 0;
    if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) {
	*info = -1;
    } else if (! (upper || lsame_(uplo, "L", (ftnlen)1, (ftnlen)1))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*ka < 0) {
	*info = -4;
    } else if (*kb < 0 || *kb > *ka) {
	*info = -5;
    } else if (*ldab < *ka + 1) {
	*info = -7;
    } else if (*ldbb < *kb + 1) {
	*info = -9;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -12;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZHBGV ", &i__1, (ftnlen)6);
	return 0;
    }

/*     Quick return if possible */

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

/*     Form a split Cholesky factorization of B. */

    zpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info, (ftnlen)1);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem. */

    inde = 1;
    indwrk = inde + *n;
    zhbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb,
	     &z__[z_offset], ldz, &work[1], &rwork[indwrk], &iinfo, (ftnlen)1,
	     (ftnlen)1);

/*     Reduce to tridiagonal form. */

    if (wantz) {
	*(unsigned char *)vect = 'U';
    } else {
	*(unsigned char *)vect = 'N';
    }
    zhbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
	    z__[z_offset], ldz, &work[1], &iinfo, (ftnlen)1, (ftnlen)1);

/*     For eigenvalues only, call DSTERF.  For eigenvectors, call ZSTEQR. */

    if (! wantz) {
	dsterf_(n, &w[1], &rwork[inde], info);
    } else {
	zsteqr_(jobz, n, &w[1], &rwork[inde], &z__[z_offset], ldz, &rwork[
		indwrk], info, (ftnlen)1);
    }
    return 0;

/*     End of ZHBGV */

} /* zhbgv_ */
Exemplo n.º 2
0
/* Subroutine */ int zhbgvd_(char *jobz, char *uplo, integer *n, integer *ka, 
	integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, 
	integer *ldbb, doublereal *w, doublecomplex *z__, integer *ldz, 
	doublecomplex *work, integer *lwork, doublereal *rwork, integer *
	lrwork, integer *iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1;

    /* Local variables */
    static integer inde;
    static char vect[1];
    static integer llwk2;
    extern logical lsame_(char *, char *);
    static integer iinfo;
    extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *);
    static integer lwmin;
    static logical upper;
    static integer llrwk;
    static logical wantz;
    static integer indwk2;
    extern /* Subroutine */ int xerbla_(char *, integer *), dsterf_(
	    integer *, doublereal *, doublereal *, integer *), zstedc_(char *,
	     integer *, doublereal *, doublereal *, doublecomplex *, integer *
	    , doublecomplex *, integer *, doublereal *, integer *, integer *, 
	    integer *, integer *), zhbtrd_(char *, char *, integer *, 
	    integer *, doublecomplex *, integer *, doublereal *, doublereal *,
	     doublecomplex *, integer *, doublecomplex *, integer *);
    static integer indwrk, liwmin;
    extern /* Subroutine */ int zhbgst_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *,
	     doublecomplex *, integer *, doublecomplex *, doublereal *, 
	    integer *), zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    static integer lrwmin;
    extern /* Subroutine */ int zpbstf_(char *, integer *, integer *, 
	    doublecomplex *, integer *, integer *);
    static logical lquery;


/*  -- 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   
    =======   

    ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors   
    of a complex generalized Hermitian-definite banded eigenproblem, of   
    the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian   
    and banded, 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   
    =========   

    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.   

    KA      (input) INTEGER   
            The number of superdiagonals of the matrix A if UPLO = 'U',   
            or the number of subdiagonals if UPLO = 'L'. KA >= 0.   

    KB      (input) INTEGER   
            The number of superdiagonals of the matrix B if UPLO = 'U',   
            or the number of subdiagonals if UPLO = 'L'. KB >= 0.   

    AB      (input/output) COMPLEX*16 array, dimension (LDAB, N)   
            On entry, the upper or lower triangle of the Hermitian band   
            matrix A, stored in the first ka+1 rows of the array.  The   
            j-th column of A is stored in the j-th column of the array AB   
            as follows:   
            if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;   
            if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).   

            On exit, the contents of AB are destroyed.   

    LDAB    (input) INTEGER   
            The leading dimension of the array AB.  LDAB >= KA+1.   

    BB      (input/output) COMPLEX*16 array, dimension (LDBB, N)   
            On entry, the upper or lower triangle of the Hermitian band   
            matrix B, stored in the first kb+1 rows of the array.  The   
            j-th column of B is stored in the j-th column of the array BB   
            as follows:   
            if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;   
            if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).   

            On exit, the factor S from the split Cholesky factorization   
            B = S**H*S, as returned by ZPBSTF.   

    LDBB    (input) INTEGER   
            The leading dimension of the array BB.  LDBB >= KB+1.   

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

    Z       (output) COMPLEX*16 array, dimension (LDZ, N)   
            If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of   
            eigenvectors, with the i-th column of Z holding the   
            eigenvector associated with W(i). The eigenvectors are   
            normalized so that Z**H*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 >= N.   

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

    LWORK   (input) INTEGER   
            The dimension of the array WORK.   
            If N <= 1,               LWORK >= 1.   
            If JOBZ = 'N' and N > 1, LWORK >= N.   
            If JOBZ = 'V' and N > 1, LWORK >= 2*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 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:  if INFO = i, and i is:   
               <= N:  the algorithm 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 ZPBSTF   
                      returned INFO = i: 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 */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1 * 1;
    ab -= ab_offset;
    bb_dim1 = *ldbb;
    bb_offset = 1 + bb_dim1 * 1;
    bb -= bb_offset;
    --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;
	lrwmin = 1;
	liwmin = 1;
    } else {
	if (wantz) {
/* Computing 2nd power */
	    i__1 = *n;
	    lwmin = i__1 * i__1 << 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 (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*ka < 0) {
	*info = -4;
    } else if (*kb < 0 || *kb > *ka) {
	*info = -5;
    } else if (*ldab < *ka + 1) {
	*info = -7;
    } else if (*ldbb < *kb + 1) {
	*info = -9;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -12;
    } else if (*lwork < lwmin && ! lquery) {
	*info = -14;
    } else if (*lrwork < lrwmin && ! lquery) {
	*info = -16;
    } else if (*liwork < liwmin && ! lquery) {
	*info = -18;
    }

    if (*info == 0) {
	work[1].r = (doublereal) lwmin, work[1].i = 0.;
	rwork[1] = (doublereal) lrwmin;
	iwork[1] = liwmin;
    }

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

/*     Quick return if possible */

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

/*     Form a split Cholesky factorization of B. */

    zpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem. */

    inde = 1;
    indwrk = inde + *n;
    indwk2 = *n * *n + 1;
    llwk2 = *lwork - indwk2 + 2;
    llrwk = *lrwork - indwrk + 2;
    zhbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb,
	     &z__[z_offset], ldz, &work[1], &rwork[indwrk], &iinfo);

/*     Reduce Hermitian band matrix to tridiagonal form. */

    if (wantz) {
	*(unsigned char *)vect = 'U';
    } else {
	*(unsigned char *)vect = 'N';
    }
    zhbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
	    z__[z_offset], ldz, &work[1], &iinfo);

/*     For eigenvalues only, call DSTERF.  For eigenvectors, call ZSTEDC. */

    if (! wantz) {
	dsterf_(n, &w[1], &rwork[inde], info);
    } else {
	zstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], &
		llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info);
	zgemm_("N", "N", n, n, n, &c_b1, &z__[z_offset], ldz, &work[1], n, &
		c_b2, &work[indwk2], n);
	zlacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
    }

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

/*     End of ZHBGVD */

} /* zhbgvd_ */
Exemplo n.º 3
0
/* Subroutine */ int zhbgvx_(char *jobz, char *range, char *uplo, integer *n, 
	integer *ka, integer *kb, doublecomplex *ab, integer *ldab, 
	doublecomplex *bb, integer *ldbb, doublecomplex *q, integer *ldq, 
	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)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, bb_dim1, bb_offset, q_dim1, q_offset, z_dim1, 
	    z_offset, i__1, i__2;

    /* Local variables */
    integer i__, j, jj;
    doublereal tmp1;
    integer indd, inde;
    char vect[1];
    logical test;
    integer itmp1, indee;
    extern logical lsame_(char *, char *);
    integer iinfo;
    char order[1];
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *), zgemv_(char *, integer *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, doublecomplex *, integer *);
    logical upper, wantz;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), zswap_(integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *);
    logical alleig, indeig;
    integer indibl;
    logical valeig;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    integer indiwk, indisp;
    extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, 
	     integer *), dstebz_(char *, char *, integer *, doublereal *, 
	    doublereal *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *, integer *, doublereal *, integer *, 
	    integer *, doublereal *, integer *, integer *), 
	    zhbtrd_(char *, char *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *, doublereal *, doublecomplex *, integer *, 
	     doublecomplex *, integer *);
    integer indrwk, indwrk;
    extern /* Subroutine */ int zhbgst_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *, 
	     doublecomplex *, integer *, doublecomplex *, doublereal *, 
	    integer *), zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    integer nsplit;
    extern /* Subroutine */ int zpbstf_(char *, integer *, integer *, 
	    doublecomplex *, integer *, integer *), zstein_(integer *, 
	     doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    integer *, doublecomplex *, integer *, doublereal *, integer *, 
	    integer *, integer *), zsteqr_(char *, integer *, doublereal *, 
	    doublereal *, doublecomplex *, integer *, doublereal *, integer *);


/*  -- LAPACK driver routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

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

/*  Arguments */
/*  ========= */

/*  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. */

/*  KA      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'. KA >= 0. */

/*  KB      (input) INTEGER */
/*          The number of superdiagonals of the matrix B if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'. KB >= 0. */

/*  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the Hermitian band */
/*          matrix A, stored in the first ka+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka). */

/*          On exit, the contents of AB are destroyed. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KA+1. */

/*  BB      (input/output) COMPLEX*16 array, dimension (LDBB, N) */
/*          On entry, the upper or lower triangle of the Hermitian band */
/*          matrix B, stored in the first kb+1 rows of the array.  The */
/*          j-th column of B is stored in the j-th column of the array BB */
/*          as follows: */
/*          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; */
/*          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb). */

/*          On exit, the factor S from the split Cholesky factorization */
/*          B = S**H*S, as returned by ZPBSTF. */

/*  LDBB    (input) INTEGER */
/*          The leading dimension of the array BB.  LDBB >= KB+1. */

/*  Q       (output) COMPLEX*16 array, dimension (LDQ, N) */
/*          If JOBZ = 'V', the n-by-n matrix used in the reduction of */
/*          A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, */
/*          and consequently C to tridiagonal form. */
/*          If JOBZ = 'N', the array Q is not referenced. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of the array Q.  If JOBZ = 'N', */
/*          LDQ >= 1. If JOBZ = 'V', LDQ >= 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 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) */
/*          If INFO = 0, the eigenvalues in ascending order. */

/*  Z       (output) COMPLEX*16 array, dimension (LDZ, N) */
/*          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
/*          eigenvectors, with the i-th column of Z holding the */
/*          eigenvector associated with W(i). The eigenvectors are */
/*          normalized so that Z**H*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 >= N. */

/*  WORK    (workspace) COMPLEX*16 array, dimension (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:  if INFO = i, and i is: */
/*             <= N:  then i eigenvectors failed to converge.  Their */
/*                    indices are stored in array IFAIL. */
/*             > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF */
/*                    returned INFO = i: 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 */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    bb_dim1 = *ldbb;
    bb_offset = 1 + bb_dim1;
    bb -= bb_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    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 (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (alleig || valeig || indeig)) {
	*info = -2;
    } else if (! (upper || lsame_(uplo, "L"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*ka < 0) {
	*info = -5;
    } else if (*kb < 0 || *kb > *ka) {
	*info = -6;
    } else if (*ldab < *ka + 1) {
	*info = -8;
    } else if (*ldbb < *kb + 1) {
	*info = -10;
    } else if (*ldq < 1 || wantz && *ldq < *n) {
	*info = -12;
    } else {
	if (valeig) {
	    if (*n > 0 && *vu <= *vl) {
		*info = -14;
	    }
	} else if (indeig) {
	    if (*il < 1 || *il > max(1,*n)) {
		*info = -15;
	    } else if (*iu < min(*n,*il) || *iu > *n) {
		*info = -16;
	    }
	}
    }
    if (*info == 0) {
	if (*ldz < 1 || wantz && *ldz < *n) {
	    *info = -21;
	}
    }

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

/*     Quick return if possible */

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

/*     Form a split Cholesky factorization of B. */

    zpbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info);
    if (*info != 0) {
	*info = *n + *info;
	return 0;
    }

/*     Transform problem to standard eigenvalue problem. */

    zhbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, 
	     &q[q_offset], ldq, &work[1], &rwork[1], &iinfo);

/*     Solve the standard eigenvalue problem. */
/*     Reduce Hermitian band matrix to tridiagonal form. */

    indd = 1;
    inde = indd + *n;
    indrwk = inde + *n;
    indwrk = 1;
    if (wantz) {
	*(unsigned char *)vect = 'U';
    } else {
	*(unsigned char *)vect = 'N';
    }
    zhbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &rwork[indd], &rwork[
	    inde], &q[q_offset], ldq, &work[indwrk], &iinfo);

/*     If all eigenvalues are desired and ABSTOL is less than or equal */
/*     to zero, then call DSTERF or ZSTEQR.  If this fails for some */
/*     eigenvalue, then try DSTEBZ. */

    test = FALSE_;
    if (indeig) {
	if (*il == 1 && *iu == *n) {
	    test = TRUE_;
	}
    }
    if ((alleig || test) && *abstol <= 0.) {
	dcopy_(n, &rwork[indd], &c__1, &w[1], &c__1);
	indee = indrwk + (*n << 1);
	i__1 = *n - 1;
	dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
	if (! wantz) {
	    dsterf_(n, &w[1], &rwork[indee], info);
	} else {
	    zlacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz);
	    zsteqr_(jobz, n, &w[1], &rwork[indee], &z__[z_offset], ldz, &
		    rwork[indrwk], info);
	    if (*info == 0) {
		i__1 = *n;
		for (i__ = 1; i__ <= i__1; ++i__) {
		    ifail[i__] = 0;
/* L10: */
		}
	    }
	}
	if (*info == 0) {
	    *m = *n;
	    goto L30;
	}
	*info = 0;
    }

/*     Otherwise, call DSTEBZ and, if eigenvectors are desired, */
/*     call ZSTEIN. */

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    indibl = 1;
    indisp = indibl + *n;
    indiwk = indisp + *n;
    dstebz_(range, order, n, vl, vu, il, iu, abstol, &rwork[indd], &rwork[
	    inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &rwork[
	    indrwk], &iwork[indiwk], info);

    if (wantz) {
	zstein_(n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], &
		iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[
		indiwk], &ifail[1], info);

/*        Apply unitary matrix used in reduction to tridiagonal */
/*        form to eigenvectors returned by ZSTEIN. */

	i__1 = *m;
	for (j = 1; j <= i__1; ++j) {
	    zcopy_(n, &z__[j * z_dim1 + 1], &c__1, &work[1], &c__1);
	    zgemv_("N", n, n, &c_b2, &q[q_offset], ldq, &work[1], &c__1, &
		    c_b1, &z__[j * z_dim1 + 1], &c__1);
/* L20: */
	}
    }

L30:

/*     If eigenvalues are not in order, then sort them, along with */
/*     eigenvectors. */

    if (wantz) {
	i__1 = *m - 1;
	for (j = 1; j <= i__1; ++j) {
	    i__ = 0;
	    tmp1 = w[j];
	    i__2 = *m;
	    for (jj = j + 1; jj <= i__2; ++jj) {
		if (w[jj] < tmp1) {
		    i__ = jj;
		    tmp1 = w[jj];
		}
/* L40: */
	    }

	    if (i__ != 0) {
		itmp1 = iwork[indibl + i__ - 1];
		w[i__] = w[j];
		iwork[indibl + i__ - 1] = iwork[indibl + j - 1];
		w[j] = tmp1;
		iwork[indibl + j - 1] = itmp1;
		zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], 
			 &c__1);
		if (*info != 0) {
		    itmp1 = ifail[i__];
		    ifail[i__] = ifail[j];
		    ifail[j] = itmp1;
		}
	    }
/* L50: */
	}
    }

    return 0;

/*     End of ZHBGVX */

} /* zhbgvx_ */