コード例 #1
0
ファイル: zheevx.c プロジェクト: flame/libflame
/* Subroutine */
int zheevx_(char *jobz, char *range, char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer *m, doublereal * w, doublecomplex *z__, integer *ldz, doublecomplex *work, integer * lwork, doublereal *rwork, integer *iwork, integer *ifail, integer * info)
{
    /* System generated locals */
    integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
    doublereal d__1, d__2;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    integer i__, j, nb, jj;
    doublereal eps, vll, vuu, tmp1;
    integer indd, inde;
    doublereal anrm;
    integer imax;
    doublereal rmin, rmax;
    logical test;
    integer itmp1, indee;
    extern /* Subroutine */
    int dscal_(integer *, doublereal *, doublereal *, integer *);
    doublereal sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    char order[1];
    extern /* Subroutine */
    int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *);
    logical lower, wantz;
    extern /* Subroutine */
    int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dlamch_(char *);
    logical alleig, indeig;
    integer iscale, indibl;
    logical valeig;
    doublereal safmin;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
    extern /* Subroutine */
    int xerbla_(char *, integer *), zdscal_( integer *, doublereal *, doublecomplex *, integer *);
    doublereal abstll, bignum;
    extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *);
    integer indiwk, indisp, indtau;
    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 *);
    integer indrwk, indwrk;
    extern /* Subroutine */
    int zhetrd_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublecomplex *, integer *, integer *);
    integer lwkmin;
    extern /* Subroutine */
    int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *);
    integer llwork, nsplit;
    doublereal smlnum;
    extern /* Subroutine */
    int zstein_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, integer *, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */
    int zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *), zungtr_(char *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zunmtr_(char *, char *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    /* -- LAPACK driver routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Test the input parameters. */
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --rwork;
    --iwork;
    --ifail;
    /* Function Body */
    lower = lsame_(uplo, "L");
    wantz = lsame_(jobz, "V");
    alleig = lsame_(range, "A");
    valeig = lsame_(range, "V");
    indeig = lsame_(range, "I");
    lquery = *lwork == -1;
    *info = 0;
    if (! (wantz || lsame_(jobz, "N")))
    {
        *info = -1;
    }
    else if (! (alleig || valeig || indeig))
    {
        *info = -2;
    }
    else if (! (lower || lsame_(uplo, "U")))
    {
        *info = -3;
    }
    else if (*n < 0)
    {
        *info = -4;
    }
    else if (*lda < max(1,*n))
    {
        *info = -6;
    }
    else
    {
        if (valeig)
        {
            if (*n > 0 && *vu <= *vl)
            {
                *info = -8;
            }
        }
        else if (indeig)
        {
            if (*il < 1 || *il > max(1,*n))
            {
                *info = -9;
            }
            else if (*iu < min(*n,*il) || *iu > *n)
            {
                *info = -10;
            }
        }
    }
    if (*info == 0)
    {
        if (*ldz < 1 || wantz && *ldz < *n)
        {
            *info = -15;
        }
    }
    if (*info == 0)
    {
        if (*n <= 1)
        {
            lwkmin = 1;
            work[1].r = (doublereal) lwkmin;
            work[1].i = 0.; // , expr subst
        }
        else
        {
            lwkmin = *n << 1;
            nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1);
            /* Computing MAX */
            i__1 = nb;
            i__2 = ilaenv_(&c__1, "ZUNMTR", uplo, n, &c_n1, &c_n1, &c_n1); // , expr subst
            nb = max(i__1,i__2);
            /* Computing MAX */
            i__1 = 1;
            i__2 = (nb + 1) * *n; // , expr subst
            lwkopt = max(i__1,i__2);
            work[1].r = (doublereal) lwkopt;
            work[1].i = 0.; // , expr subst
        }
        if (*lwork < lwkmin && ! lquery)
        {
            *info = -17;
        }
    }
    if (*info != 0)
    {
        i__1 = -(*info);
        xerbla_("ZHEEVX", &i__1);
        return 0;
    }
    else if (lquery)
    {
        return 0;
    }
    /* Quick return if possible */
    *m = 0;
    if (*n == 0)
    {
        return 0;
    }
    if (*n == 1)
    {
        if (alleig || indeig)
        {
            *m = 1;
            i__1 = a_dim1 + 1;
            w[1] = a[i__1].r;
        }
        else if (valeig)
        {
            i__1 = a_dim1 + 1;
            i__2 = a_dim1 + 1;
            if (*vl < a[i__1].r && *vu >= a[i__2].r)
            {
                *m = 1;
                i__1 = a_dim1 + 1;
                w[1] = a[i__1].r;
            }
        }
        if (wantz)
        {
            i__1 = z_dim1 + 1;
            z__[i__1].r = 1.;
            z__[i__1].i = 0.; // , expr subst
        }
        return 0;
    }
    /* Get machine constants. */
    safmin = dlamch_("Safe minimum");
    eps = dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
    /* Computing MIN */
    d__1 = sqrt(bignum);
    d__2 = 1. / sqrt(sqrt(safmin)); // , expr subst
    rmax = min(d__1,d__2);
    /* Scale matrix to allowable range, if necessary. */
    iscale = 0;
    abstll = *abstol;
    if (valeig)
    {
        vll = *vl;
        vuu = *vu;
    }
    anrm = zlanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
    if (anrm > 0. && anrm < rmin)
    {
        iscale = 1;
        sigma = rmin / anrm;
    }
    else if (anrm > rmax)
    {
        iscale = 1;
        sigma = rmax / anrm;
    }
    if (iscale == 1)
    {
        if (lower)
        {
            i__1 = *n;
            for (j = 1;
                    j <= i__1;
                    ++j)
            {
                i__2 = *n - j + 1;
                zdscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1);
                /* L10: */
            }
        }
        else
        {
            i__1 = *n;
            for (j = 1;
                    j <= i__1;
                    ++j)
            {
                zdscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1);
                /* L20: */
            }
        }
        if (*abstol > 0.)
        {
            abstll = *abstol * sigma;
        }
        if (valeig)
        {
            vll = *vl * sigma;
            vuu = *vu * sigma;
        }
    }
    /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
    indd = 1;
    inde = indd + *n;
    indrwk = inde + *n;
    indtau = 1;
    indwrk = indtau + *n;
    llwork = *lwork - indwrk + 1;
    zhetrd_(uplo, n, &a[a_offset], lda, &rwork[indd], &rwork[inde], &work[ indtau], &work[indwrk], &llwork, &iinfo);
    /* If all eigenvalues are desired and ABSTOL is less than or equal to */
    /* zero, then call DSTERF or ZUNGTR and 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);
        if (! wantz)
        {
            i__1 = *n - 1;
            dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
            dsterf_(n, &w[1], &rwork[indee], info);
        }
        else
        {
            zlacpy_("A", n, n, &a[a_offset], lda, &z__[z_offset], ldz);
            zungtr_(uplo, n, &z__[z_offset], ldz, &work[indtau], &work[indwrk] , &llwork, &iinfo);
            i__1 = *n - 1;
            dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
            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;
                    /* L30: */
                }
            }
        }
        if (*info == 0)
        {
            *m = *n;
            goto L40;
        }
        *info = 0;
    }
    /* Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. */
    if (wantz)
    {
        *(unsigned char *)order = 'B';
    }
    else
    {
        *(unsigned char *)order = 'E';
    }
    indibl = 1;
    indisp = indibl + *n;
    indiwk = indisp + *n;
    dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &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. */
        zunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[ z_offset], ldz, &work[indwrk], &llwork, &iinfo);
    }
    /* If matrix was scaled, then rescale eigenvalues appropriately. */
L40:
    if (iscale == 1)
    {
        if (*info == 0)
        {
            imax = *m;
        }
        else
        {
            imax = *info - 1;
        }
        d__1 = 1. / sigma;
        dscal_(&imax, &d__1, &w[1], &c__1);
    }
    /* 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];
                }
                /* L50: */
            }
            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;
                }
            }
            /* L60: */
        }
    }
    /* Set WORK(1) to optimal complex workspace size. */
    work[1].r = (doublereal) lwkopt;
    work[1].i = 0.; // , expr subst
    return 0;
    /* End of ZHEEVX */
}
コード例 #2
0
ファイル: zheevx.c プロジェクト: deepakantony/vispack
/* Subroutine */ int zheevx_(char *jobz, char *range, char *uplo, integer *n, 
	doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, 
	integer *il, integer *iu, doublereal *abstol, integer *m, doublereal *
	w, doublecomplex *z, integer *ldz, doublecomplex *work, integer *
	lwork, doublereal *rwork, integer *iwork, integer *ifail, integer *
	info)
{
/*  -- LAPACK driver routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    ZHEEVX computes selected eigenvalues and, optionally, eigenvectors   
    of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can   
    be selected by specifying either 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 triangle of A is stored;   
            = 'L':  Lower triangle of A is stored.   

    N       (input) INTEGER   
            The order of the matrix A.  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, 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).   

    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').   

            See "Computing Small Singular Values of Bidiagonal Matrices   
            with Guaranteed High Relative Accuracy," by Demmel and   
            Kahan, LAPACK Working Note #3.   

    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) COMPLEX*16 array, dimension (LDZ, max(1,M))   
            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).   
            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.   
            If JOBZ = 'N', then Z is not referenced.   
            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) 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.  LWORK >= max(1,2*N-1).   
            For optimal efficiency, LWORK >= (NB+1)*N,   
            where NB is the blocksize for ZHETRD returned by ILAENV.   

    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, then i eigenvectors failed to converge.   
                  Their indices are stored in array IFAIL.   

    ===================================================================== 
  


       Test the input parameters.   

    
   Parameter adjustments   
       Function Body */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* System generated locals */
    integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
    doublereal d__1, d__2;
    doublecomplex z__1;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer indd, inde;
    static doublereal anrm;
    static integer imax;
    static doublereal rmin, rmax;
    static integer lopt, itmp1, i, j, indee;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    static doublereal sigma;
    extern logical lsame_(char *, char *);
    static integer iinfo;
    static char order[1];
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static logical lower, wantz;
    extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *);
    static integer jj;
    extern doublereal dlamch_(char *);
    static logical alleig, indeig;
    static integer iscale, indibl;
    static logical valeig;
    static doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
	    integer *, doublereal *, doublecomplex *, integer *);
    static doublereal abstll, bignum;
    extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    static integer indiwk, indisp, indtau;
    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 *);
    static integer indrwk, indwrk;
    extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, 
	    integer *, doublereal *, doublereal *, doublecomplex *, 
	    doublecomplex *, integer *, integer *), zlacpy_(char *, 
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *,
	     integer *);
    static integer llwork, nsplit;
    static doublereal smlnum;
    extern /* Subroutine */ int zstein_(integer *, doublereal *, doublereal *,
	     integer *, doublereal *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *, integer *, integer *, integer *), 
	    zsteqr_(char *, integer *, doublereal *, doublereal *, 
	    doublecomplex *, integer *, doublereal *, integer *), 
	    zungtr_(char *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, doublecomplex *, integer *, integer *), 
	    zunmtr_(char *, char *, char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, integer *);
    static doublereal eps, vll, vuu, tmp1;



#define W(I) w[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define IWORK(I) iwork[(I)-1]
#define IFAIL(I) ifail[(I)-1]

#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define Z(I,J) z[(I)-1 + ((J)-1)* ( *ldz)]

    lower = lsame_(uplo, "L");
    wantz = lsame_(jobz, "V");
    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 (! (lower || lsame_(uplo, "U"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (valeig && *n > 0 && *vu <= *vl) {
	*info = -8;
    } else if (indeig && *il < 1) {
	*info = -9;
    } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) {
	*info = -10;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -15;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 1) - 1;
	if (*lwork < max(i__1,i__2)) {
	    *info = -17;
	}
    }

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

/*     Quick return if possible */

    *m = 0;
    if (*n == 0) {
	WORK(1).r = 1., WORK(1).i = 0.;
	return 0;
    }

    if (*n == 1) {
	WORK(1).r = 1., WORK(1).i = 0.;
	if (alleig || indeig) {
	    *m = 1;
	    i__1 = a_dim1 + 1;
	    W(1) = A(1,1).r;
	} else if (valeig) {
	    i__1 = a_dim1 + 1;
	    i__2 = a_dim1 + 1;
	    if (*vl < A(1,1).r && *vu >= A(1,1).r) {
		*m = 1;
		i__1 = a_dim1 + 1;
		W(1) = A(1,1).r;
	    }
	}
	if (wantz) {
	    i__1 = z_dim1 + 1;
	    Z(1,1).r = 1., Z(1,1).i = 0.;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = dlamch_("Safe minimum");
    eps = dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
/* Computing MIN */
    d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin));
    rmax = min(d__1,d__2);

/*     Scale matrix to allowable range, if necessary. */

    iscale = 0;
    abstll = *abstol;
    if (valeig) {
	vll = *vl;
	vuu = *vu;
    }
    anrm = zlanhe_("M", uplo, n, &A(1,1), lda, &RWORK(1));
    if (anrm > 0. && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		i__2 = *n - j + 1;
		zdscal_(&i__2, &sigma, &A(j,j), &c__1);
/* L10: */
	    }
	} else {
	    i__1 = *n;
	    for (j = 1; j <= *n; ++j) {
		zdscal_(&j, &sigma, &A(1,j), &c__1);
/* L20: */
	    }
	}
	if (*abstol > 0.) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }

/*     Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */

    indd = 1;
    inde = indd + *n;
    indrwk = inde + *n;
    indtau = 1;
    indwrk = indtau + *n;
    llwork = *lwork - indwrk + 1;
    zhetrd_(uplo, n, &A(1,1), lda, &RWORK(indd), &RWORK(inde), &WORK(
	    indtau), &WORK(indwrk), &llwork, &iinfo);
    i__1 = indwrk;
    z__1.r = *n + WORK(indwrk).r, z__1.i = WORK(indwrk).i;
    lopt = (integer) z__1.r;

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

    if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.) {
	dcopy_(n, &RWORK(indd), &c__1, &W(1), &c__1);
	indee = indrwk + (*n << 1);
	if (! wantz) {
	    i__1 = *n - 1;
	    dcopy_(&i__1, &RWORK(inde), &c__1, &RWORK(indee), &c__1);
	    dsterf_(n, &W(1), &RWORK(indee), info);
	} else {
	    zlacpy_("A", n, n, &A(1,1), lda, &Z(1,1), ldz);
	    zungtr_(uplo, n, &Z(1,1), ldz, &WORK(indtau), &WORK(indwrk), 
		    &llwork, &iinfo);
	    i__1 = *n - 1;
	    dcopy_(&i__1, &RWORK(inde), &c__1, &RWORK(indee), &c__1);
	    zsteqr_(jobz, n, &W(1), &RWORK(indee), &Z(1,1), ldz, &RWORK(
		    indrwk), info);
	    if (*info == 0) {
		i__1 = *n;
		for (i = 1; i <= *n; ++i) {
		    IFAIL(i) = 0;
/* L30: */
		}
	    }
	}
	if (*info == 0) {
	    *m = *n;
	    goto L40;
	}
	*info = 0;
    }

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

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    indibl = 1;
    indisp = indibl + *n;
    indiwk = indisp + *n;
    dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &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(1,1), ldz, &RWORK(indrwk), &IWORK(
		indiwk), &IFAIL(1), info);

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

	zunmtr_("L", uplo, "N", n, m, &A(1,1), lda, &WORK(indtau), &Z(1,1), ldz, &WORK(indwrk), &llwork, &iinfo);
    }

/*     If matrix was scaled, then rescale eigenvalues appropriately. */

L40:
    if (iscale == 1) {
	if (*info == 0) {
	    imax = *m;
	} else {
	    imax = *info - 1;
	}
	d__1 = 1. / sigma;
	dscal_(&imax, &d__1, &W(1), &c__1);
    }

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

    if (wantz) {
	i__1 = *m - 1;
	for (j = 1; j <= *m-1; ++j) {
	    i = 0;
	    tmp1 = W(j);
	    i__2 = *m;
	    for (jj = j + 1; jj <= *m; ++jj) {
		if (W(jj) < tmp1) {
		    i = jj;
		    tmp1 = W(jj);
		}
/* L50: */
	    }

	    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(1,i), &c__1, &Z(1,j), &
			c__1);
		if (*info != 0) {
		    itmp1 = IFAIL(i);
		    IFAIL(i) = IFAIL(j);
		    IFAIL(j) = itmp1;
		}
	    }
/* L60: */
	}
    }

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

   Computing MAX */
    i__1 = (*n << 1) - 1;
    d__1 = (doublereal) max(i__1,lopt);
    WORK(1).r = d__1, WORK(1).i = 0.;

    return 0;

/*     End of ZHEEVX */

} /* zheevx_ */
コード例 #3
0
ファイル: zhpevx.c プロジェクト: 0u812/roadrunner-backup
/* Subroutine */ int zhpevx_(char *jobz, char *range, char *uplo, integer *n, 
	doublecomplex *ap, 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 z_dim1, z_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer i__, j, jj;
    doublereal eps, vll, vuu, tmp1;
    integer indd, inde;
    doublereal anrm;
    integer imax;
    doublereal rmin, rmax;
    logical test;
    integer itmp1, indee;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    doublereal sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    char order[1];
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    logical wantz;
    extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *);
    extern doublereal dlamch_(char *);
    logical alleig, indeig;
    integer iscale, indibl;
    logical valeig;
    doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_(
	    integer *, doublereal *, doublecomplex *, integer *);
    doublereal abstll, bignum;
    integer indiwk, indisp, indtau;
    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 *);
    extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *, 
	    doublereal *);
    integer indrwk, indwrk, nsplit;
    doublereal smlnum;
    extern /* Subroutine */ int zhptrd_(char *, integer *, doublecomplex *, 
	    doublereal *, doublereal *, doublecomplex *, integer *), 
	    zstein_(integer *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *, integer *, doublecomplex *, integer *, 
	    doublereal *, integer *, integer *, integer *), zsteqr_(char *, 
	    integer *, doublereal *, doublereal *, doublecomplex *, integer *, 
	     doublereal *, integer *), zupgtr_(char *, integer *, 
	    doublecomplex *, doublecomplex *, doublecomplex *, integer *, 
	    doublecomplex *, integer *), zupmtr_(char *, char *, char 
	    *, integer *, integer *, doublecomplex *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);


/*  -- LAPACK driver routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  ZHPEVX computes selected eigenvalues and, optionally, eigenvectors */
/*  of a complex Hermitian matrix A in packed storage. */
/*  Eigenvalues/vectors can be selected by specifying either 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 triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  AP      (input/output) COMPLEX*16 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, AP is overwritten by values generated during the */
/*          reduction to tridiagonal form.  If UPLO = 'U', the diagonal */
/*          and first superdiagonal of the tridiagonal matrix T overwrite */
/*          the corresponding elements of A, and if UPLO = 'L', the */
/*          diagonal and first subdiagonal of T overwrite the */
/*          corresponding elements of A. */

/*  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'). */

/*          See "Computing Small Singular Values of Bidiagonal Matrices */
/*          with Guaranteed High Relative Accuracy," by Demmel and */
/*          Kahan, LAPACK Working Note #3. */

/*  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 selected eigenvalues in ascending order. */

/*  Z       (output) COMPLEX*16 array, dimension (LDZ, max(1,M)) */
/*          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). */
/*          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. */
/*          If JOBZ = 'N', then Z is not referenced. */
/*          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) COMPLEX*16 array, dimension (2*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, then i eigenvectors failed to converge. */
/*                Their indices are stored in array IFAIL. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --ap;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --rwork;
    --iwork;
    --ifail;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    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 (! (lsame_(uplo, "L") || lsame_(uplo, 
	    "U"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else {
	if (valeig) {
	    if (*n > 0 && *vu <= *vl) {
		*info = -7;
	    }
	} else if (indeig) {
	    if (*il < 1 || *il > max(1,*n)) {
		*info = -8;
	    } else if (*iu < min(*n,*il) || *iu > *n) {
		*info = -9;
	    }
	}
    }
    if (*info == 0) {
	if (*ldz < 1 || wantz && *ldz < *n) {
	    *info = -14;
	}
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	if (alleig || indeig) {
	    *m = 1;
	    w[1] = ap[1].r;
	} else {
	    if (*vl < ap[1].r && *vu >= ap[1].r) {
		*m = 1;
		w[1] = ap[1].r;
	    }
	}
	if (wantz) {
	    i__1 = z_dim1 + 1;
	    z__[i__1].r = 1., z__[i__1].i = 0.;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = dlamch_("Safe minimum");
    eps = dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
/* Computing MIN */
    d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin));
    rmax = min(d__1,d__2);

/*     Scale matrix to allowable range, if necessary. */

    iscale = 0;
    abstll = *abstol;
    if (valeig) {
	vll = *vl;
	vuu = *vu;
    } else {
	vll = 0.;
	vuu = 0.;
    }
    anrm = zlanhp_("M", uplo, n, &ap[1], &rwork[1]);
    if (anrm > 0. && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	i__1 = *n * (*n + 1) / 2;
	zdscal_(&i__1, &sigma, &ap[1], &c__1);
	if (*abstol > 0.) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }

/*     Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. */

    indd = 1;
    inde = indd + *n;
    indrwk = inde + *n;
    indtau = 1;
    indwrk = indtau + *n;
    zhptrd_(uplo, n, &ap[1], &rwork[indd], &rwork[inde], &work[indtau], &
	    iinfo);

/*     If all eigenvalues are desired and ABSTOL is less than or equal */
/*     to zero, then call DSTERF or ZUPGTR and 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);
	if (! wantz) {
	    i__1 = *n - 1;
	    dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
	    dsterf_(n, &w[1], &rwork[indee], info);
	} else {
	    zupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &
		    work[indwrk], &iinfo);
	    i__1 = *n - 1;
	    dcopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
	    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 L20;
	}
	*info = 0;
    }

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

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    indibl = 1;
    indisp = indibl + *n;
    indiwk = indisp + *n;
    dstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &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. */

	indwrk = indtau + *n;
	zupmtr_("L", uplo, "N", n, m, &ap[1], &work[indtau], &z__[z_offset], 
		ldz, &work[indwrk], &iinfo);
    }

/*     If matrix was scaled, then rescale eigenvalues appropriately. */

L20:
    if (iscale == 1) {
	if (*info == 0) {
	    imax = *m;
	} else {
	    imax = *info - 1;
	}
	d__1 = 1. / sigma;
	dscal_(&imax, &d__1, &w[1], &c__1);
    }

/*     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];
		}
/* L30: */
	    }

	    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;
		}
	    }
/* L40: */
	}
    }

    return 0;

/*     End of ZHPEVX */

} /* zhpevx_ */
コード例 #4
0
ファイル: zhbgvx.c プロジェクト: dacap/loseface
/* 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_ */