Ejemplo n.º 1
0
/* Subroutine */ int ssbgv_(char *jobz, char *uplo, integer *n, integer *ka, 
	integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real *
	w, real *z__, integer *ldz, real *work, integer *info)
{
/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    SSBGV computes all the eigenvalues, and optionally, the eigenvectors   
    of a real generalized symmetric-definite banded eigenproblem, of   
    the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric   
    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) REAL array, dimension (LDAB, N)   
            On entry, the upper or lower triangle of the symmetric 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) REAL array, dimension (LDBB, N)   
            On entry, the upper or lower triangle of the symmetric 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**T*S, as returned by SPBSTF.   

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

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

    Z       (output) REAL 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**T*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) REAL 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 SPBSTF   
                      returned INFO = i: B is not positive definite.   
                      The factorization of B could not be completed and   
                      no eigenvalues or eigenvectors were computed.   

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


       Test the input parameters.   

       Parameter adjustments */
    /* 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 *);
    static integer iinfo;
    static logical upper, wantz;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static integer indwrk;
    extern /* Subroutine */ int spbstf_(char *, integer *, integer *, real *, 
	    integer *, integer *), ssbtrd_(char *, char *, integer *, 
	    integer *, real *, integer *, real *, real *, real *, integer *, 
	    real *, integer *), ssbgst_(char *, char *, 
	    integer *, integer *, integer *, real *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *), 
	    ssterf_(integer *, real *, real *, integer *), ssteqr_(char *, 
	    integer *, real *, real *, real *, integer *, real *, integer *);

    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;

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

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

/*     Quick return if possible */

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

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

    spbstf_(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;
    ssbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb,
	     &z__[z_offset], ldz, &work[indwrk], &iinfo)
	    ;

/*     Reduce to tridiagonal form. */

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

/*     For eigenvalues only, call SSTERF.  For eigenvectors, call SSTEQR. */

    if (! wantz) {
	ssterf_(n, &w[1], &work[inde], info);
    } else {
	ssteqr_(jobz, n, &w[1], &work[inde], &z__[z_offset], ldz, &work[
		indwrk], info);
    }
    return 0;

/*     End of SSBGV */

} /* ssbgv_ */
Ejemplo n.º 2
0
/* Subroutine */ int ssbevx_(char *jobz, char *range, char *uplo, integer *n, 
	integer *kd, real *ab, integer *ldab, real *q, integer *ldq, real *vl, 
	 real *vu, integer *il, integer *iu, real *abstol, integer *m, real *
	w, real *z__, integer *ldz, real *work, integer *iwork, integer *
	ifail, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, 
	    i__2;
    real r__1, r__2;

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

    /* Local variables */
    integer i__, j, jj;
    real eps, vll, vuu, tmp1;
    integer indd, inde;
    real anrm;
    integer imax;
    real rmin, rmax;
    logical test;
    integer itmp1, indee;
    real sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    char order[1];
    extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, 
	    real *, integer *, real *, integer *, real *, real *, integer *);
    logical lower;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *), sswap_(integer *, real *, integer *, real *, integer *
);
    logical wantz, alleig, indeig;
    integer iscale, indibl;
    logical valeig;
    extern doublereal slamch_(char *);
    real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real abstll, bignum;
    extern doublereal slansb_(char *, char *, integer *, integer *, real *, 
	    integer *, real *);
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    integer indisp, indiwo;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *);
    integer indwrk;
    extern /* Subroutine */ int ssbtrd_(char *, char *, integer *, integer *, 
	    real *, integer *, real *, real *, real *, integer *, real *, 
	    integer *), sstein_(integer *, real *, real *, 
	    integer *, real *, integer *, integer *, real *, integer *, real *
, integer *, integer *, integer *), ssterf_(integer *, real *, 
	    real *, integer *);
    integer nsplit;
    real smlnum;
    extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, 
	    real *, integer *, integer *, real *, real *, real *, integer *, 
	    integer *, real *, integer *, integer *, real *, integer *, 
	    integer *), ssteqr_(char *, integer *, real *, 
	    real *, real *, integer *, real *, integer *);


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

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

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

/*  SSBEVX computes selected eigenvalues and, optionally, eigenvectors */
/*  of a real symmetric band 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. */

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

/*  AB      (input/output) REAL array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */

/*          On exit, AB is overwritten by values generated during the */
/*          reduction to tridiagonal form.  If UPLO = 'U', the first */
/*          superdiagonal and the diagonal of the tridiagonal matrix T */
/*          are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */
/*          the diagonal and first subdiagonal of T are returned in the */
/*          first two rows of AB. */

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

/*  Q       (output) REAL array, dimension (LDQ, N) */
/*          If JOBZ = 'V', the N-by-N orthogonal matrix used in the */
/*                         reduction to tridiagonal form. */
/*          If JOBZ = 'N', the array Q is not referenced. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of the array Q.  If JOBZ = 'V', then */
/*          LDQ >= max(1,N). */

/*  VL      (input) REAL */
/*  VU      (input) REAL */
/*          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) REAL */
/*          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 AB to tridiagonal form. */

/*          Eigenvalues will be computed most accurately when ABSTOL is */
/*          set to twice the underflow threshold 2*SLAMCH('S'), not zero. */
/*          If this routine returns with INFO>0, indicating that some */
/*          eigenvectors did not converge, try setting ABSTOL to */
/*          2*SLAMCH('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) REAL array, dimension (N) */
/*          The first M elements contain the selected eigenvalues in */
/*          ascending order. */

/*  Z       (output) REAL 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) REAL 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 */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_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;
    --iwork;
    --ifail;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    alleig = lsame_(range, "A");
    valeig = lsame_(range, "V");
    indeig = lsame_(range, "I");
    lower = lsame_(uplo, "L");

    *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 (*kd < 0) {
	*info = -5;
    } else if (*ldab < *kd + 1) {
	*info = -7;
    } else if (wantz && *ldq < max(1,*n)) {
	*info = -9;
    } else {
	if (valeig) {
	    if (*n > 0 && *vu <= *vl) {
		*info = -11;
	    }
	} else if (indeig) {
	    if (*il < 1 || *il > max(1,*n)) {
		*info = -12;
	    } else if (*iu < min(*n,*il) || *iu > *n) {
		*info = -13;
	    }
	}
    }
    if (*info == 0) {
	if (*ldz < 1 || wantz && *ldz < *n) {
	    *info = -18;
	}
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	*m = 1;
	if (lower) {
	    tmp1 = ab[ab_dim1 + 1];
	} else {
	    tmp1 = ab[*kd + 1 + ab_dim1];
	}
	if (valeig) {
	    if (! (*vl < tmp1 && *vu >= tmp1)) {
		*m = 0;
	    }
	}
	if (*m == 1) {
	    w[1] = tmp1;
	    if (wantz) {
		z__[z_dim1 + 1] = 1.f;
	    }
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = slamch_("Safe minimum");
    eps = slamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1.f / smlnum;
    rmin = sqrt(smlnum);
/* Computing MIN */
    r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));
    rmax = dmin(r__1,r__2);

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

    iscale = 0;
    abstll = *abstol;
    if (valeig) {
	vll = *vl;
	vuu = *vu;
    } else {
	vll = 0.f;
	vuu = 0.f;
    }
    anrm = slansb_("M", uplo, n, kd, &ab[ab_offset], ldab, &work[1]);
    if (anrm > 0.f && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    slascl_("B", kd, kd, &c_b14, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	} else {
	    slascl_("Q", kd, kd, &c_b14, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	}
	if (*abstol > 0.f) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }

/*     Call SSBTRD to reduce symmetric band matrix to tridiagonal form. */

    indd = 1;
    inde = indd + *n;
    indwrk = inde + *n;
    ssbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &work[indd], &work[inde], 
	     &q[q_offset], ldq, &work[indwrk], &iinfo);

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

    test = FALSE_;
    if (indeig) {
	if (*il == 1 && *iu == *n) {
	    test = TRUE_;
	}
    }
    if ((alleig || test) && *abstol <= 0.f) {
	scopy_(n, &work[indd], &c__1, &w[1], &c__1);
	indee = indwrk + (*n << 1);
	if (! wantz) {
	    i__1 = *n - 1;
	    scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
	    ssterf_(n, &w[1], &work[indee], info);
	} else {
	    slacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz);
	    i__1 = *n - 1;
	    scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
	    ssteqr_(jobz, n, &w[1], &work[indee], &z__[z_offset], ldz, &work[
		    indwrk], 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 SSTEBZ and, if eigenvectors are desired, SSTEIN. */

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    indibl = 1;
    indisp = indibl + *n;
    indiwo = indisp + *n;
    sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[
	    inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[
	    indwrk], &iwork[indiwo], info);

    if (wantz) {
	sstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[
		indisp], &z__[z_offset], ldz, &work[indwrk], &iwork[indiwo], &
		ifail[1], info);

/*        Apply orthogonal matrix used in reduction to tridiagonal */
/*        form to eigenvectors returned by SSTEIN. */

	i__1 = *m;
	for (j = 1; j <= i__1; ++j) {
	    scopy_(n, &z__[j * z_dim1 + 1], &c__1, &work[1], &c__1);
	    sgemv_("N", n, n, &c_b14, &q[q_offset], ldq, &work[1], &c__1, &
		    c_b34, &z__[j * z_dim1 + 1], &c__1);
/* L20: */
	}
    }

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

L30:
    if (iscale == 1) {
	if (*info == 0) {
	    imax = *m;
	} else {
	    imax = *info - 1;
	}
	r__1 = 1.f / sigma;
	sscal_(&imax, &r__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];
		}
/* 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;
		sswap_(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 SSBEVX */

} /* ssbevx_ */
Ejemplo n.º 3
0
 int ssbgv_(char *jobz, char *uplo, int *n, int *ka, 
	int *kb, float *ab, int *ldab, float *bb, int *ldbb, float *
	w, float *z__, int *ldz, float *work, int *info)
{
    /* System generated locals */
    int ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1;

    /* Local variables */
    int inde;
    char vect[1];
    extern int lsame_(char *, char *);
    int iinfo;
    int upper, wantz;
    extern  int xerbla_(char *, int *);
    int indwrk;
    extern  int spbstf_(char *, int *, int *, float *, 
	    int *, int *), ssbtrd_(char *, char *, int *, 
	    int *, float *, int *, float *, float *, float *, int *, 
	    float *, int *), ssbgst_(char *, char *, 
	    int *, int *, int *, float *, int *, float *, 
	    int *, float *, int *, float *, int *), 
	    ssterf_(int *, float *, float *, int *), ssteqr_(char *, 
	    int *, float *, float *, float *, int *, float *, int *);


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

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

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

/*  SSBGV computes all the eigenvalues, and optionally, the eigenvectors */
/*  of a float generalized symmetric-definite banded eigenproblem, of */
/*  the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric */
/*  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) REAL array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the symmetric 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) REAL array, dimension (LDBB, N) */
/*          On entry, the upper or lower triangle of the symmetric 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**T*S, as returned by SPBSTF. */

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

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

/*  Z       (output) REAL 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**T*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) REAL 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 SPBSTF */
/*                    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;

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

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

/*     Quick return if possible */

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

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

    spbstf_(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;
    ssbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, 
	     &z__[z_offset], ldz, &work[indwrk], &iinfo)
	    ;

/*     Reduce to tridiagonal form. */

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

/*     For eigenvalues only, call SSTERF.  For eigenvectors, call SSTEQR. */

    if (! wantz) {
	ssterf_(n, &w[1], &work[inde], info);
    } else {
	ssteqr_(jobz, n, &w[1], &work[inde], &z__[z_offset], ldz, &work[
		indwrk], info);
    }
    return 0;

/*     End of SSBGV */

} /* ssbgv_ */
Ejemplo n.º 4
0
 int ssbev_(char *jobz, char *uplo, int *n, int *kd, 
	float *ab, int *ldab, float *w, float *z__, int *ldz, float *work, 
	 int *info)
{
    /* System generated locals */
    int ab_dim1, ab_offset, z_dim1, z_offset, i__1;
    float r__1;

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

    /* Local variables */
    float eps;
    int inde;
    float anrm;
    int imax;
    float rmin, rmax, sigma;
    extern int lsame_(char *, char *);
    int iinfo;
    extern  int sscal_(int *, float *, float *, int *);
    int lower, wantz;
    int iscale;
    extern double slamch_(char *);
    float safmin;
    extern  int xerbla_(char *, int *);
    float bignum;
    extern double slansb_(char *, char *, int *, int *, float *, 
	    int *, float *);
    extern  int slascl_(char *, int *, int *, float *, 
	    float *, int *, int *, float *, int *, int *);
    int indwrk;
    extern  int ssbtrd_(char *, char *, int *, int *, 
	    float *, int *, float *, float *, float *, int *, float *, 
	    int *), ssterf_(int *, float *, float *, 
	    int *);
    float smlnum;
    extern  int ssteqr_(char *, int *, float *, float *, 
	    float *, int *, float *, int *);


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

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

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

/*  SSBEV computes all the eigenvalues and, optionally, eigenvectors of */
/*  a float symmetric band matrix A. */

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

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  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. */

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

/*  AB      (input/output) REAL array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for MAX(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=MIN(n,j+kd). */

/*          On exit, AB is overwritten by values generated during the */
/*          reduction to tridiagonal form.  If UPLO = 'U', the first */
/*          superdiagonal and the diagonal of the tridiagonal matrix T */
/*          are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */
/*          the diagonal and first subdiagonal of T are returned in the */
/*          first two rows of AB. */

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

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

/*  Z       (output) REAL array, dimension (LDZ, N) */
/*          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */
/*          eigenvectors of the matrix A, with the i-th column of Z */
/*          holding the eigenvector associated with W(i). */
/*          If JOBZ = 'N', then Z is not referenced. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z.  LDZ >= 1, and if */
/*          JOBZ = 'V', LDZ >= MAX(1,N). */

/*  WORK    (workspace) REAL array, dimension (MAX(1,3*N-2)) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, the algorithm failed to converge; i */
/*                off-diagonal elements of an intermediate tridiagonal */
/*                form did not converge to zero. */

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

/*     .. 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;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    lower = lsame_(uplo, "L");

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lower || lsame_(uplo, "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*kd < 0) {
	*info = -4;
    } else if (*ldab < *kd + 1) {
	*info = -6;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -9;
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	if (lower) {
	    w[1] = ab[ab_dim1 + 1];
	} else {
	    w[1] = ab[*kd + 1 + ab_dim1];
	}
	if (wantz) {
	    z__[z_dim1 + 1] = 1.f;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = slamch_("Safe minimum");
    eps = slamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1.f / smlnum;
    rmin = sqrt(smlnum);
    rmax = sqrt(bignum);

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

    anrm = slansb_("M", uplo, n, kd, &ab[ab_offset], ldab, &work[1]);
    iscale = 0;
    if (anrm > 0.f && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    slascl_("B", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	} else {
	    slascl_("Q", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, 
		    info);
	}
    }

/*     Call SSBTRD to reduce symmetric band matrix to tridiagonal form. */

    inde = 1;
    indwrk = inde + *n;
    ssbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &work[inde], &z__[
	    z_offset], ldz, &work[indwrk], &iinfo);

/*     For eigenvalues only, call SSTERF.  For eigenvectors, call SSTEQR. */

    if (! wantz) {
	ssterf_(n, &w[1], &work[inde], info);
    } else {
	ssteqr_(jobz, n, &w[1], &work[inde], &z__[z_offset], ldz, &work[
		indwrk], info);
    }

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

    if (iscale == 1) {
	if (*info == 0) {
	    imax = *n;
	} else {
	    imax = *info - 1;
	}
	r__1 = 1.f / sigma;
	sscal_(&imax, &r__1, &w[1], &c__1);
    }

    return 0;

/*     End of SSBEV */

} /* ssbev_ */
Ejemplo n.º 5
0
int main(void)
{
    /* Local scalars */
    char vect, vect_i;
    char uplo, uplo_i;
    lapack_int n, n_i;
    lapack_int kd, kd_i;
    lapack_int ldab, ldab_i;
    lapack_int ldab_r;
    lapack_int ldq, ldq_i;
    lapack_int ldq_r;
    lapack_int info, info_i;
    lapack_int i;
    int failed;

    /* Local arrays */
    float *ab = NULL, *ab_i = NULL;
    float *d = NULL, *d_i = NULL;
    float *e = NULL, *e_i = NULL;
    float *q = NULL, *q_i = NULL;
    float *work = NULL, *work_i = NULL;
    float *ab_save = NULL;
    float *d_save = NULL;
    float *e_save = NULL;
    float *q_save = NULL;
    float *ab_r = NULL;
    float *q_r = NULL;

    /* Iniitialize the scalar parameters */
    init_scalars_ssbtrd( &vect, &uplo, &n, &kd, &ldab, &ldq );
    ldab_r = n+2;
    ldq_r = n+2;
    vect_i = vect;
    uplo_i = uplo;
    n_i = n;
    kd_i = kd;
    ldab_i = ldab;
    ldq_i = ldq;

    /* Allocate memory for the LAPACK routine arrays */
    ab = (float *)LAPACKE_malloc( ldab*n * sizeof(float) );
    d = (float *)LAPACKE_malloc( n * sizeof(float) );
    e = (float *)LAPACKE_malloc( (n-1) * sizeof(float) );
    q = (float *)LAPACKE_malloc( ldq*n * sizeof(float) );
    work = (float *)LAPACKE_malloc( n * sizeof(float) );

    /* Allocate memory for the C interface function arrays */
    ab_i = (float *)LAPACKE_malloc( ldab*n * sizeof(float) );
    d_i = (float *)LAPACKE_malloc( n * sizeof(float) );
    e_i = (float *)LAPACKE_malloc( (n-1) * sizeof(float) );
    q_i = (float *)LAPACKE_malloc( ldq*n * sizeof(float) );
    work_i = (float *)LAPACKE_malloc( n * sizeof(float) );

    /* Allocate memory for the backup arrays */
    ab_save = (float *)LAPACKE_malloc( ldab*n * sizeof(float) );
    d_save = (float *)LAPACKE_malloc( n * sizeof(float) );
    e_save = (float *)LAPACKE_malloc( (n-1) * sizeof(float) );
    q_save = (float *)LAPACKE_malloc( ldq*n * sizeof(float) );

    /* Allocate memory for the row-major arrays */
    ab_r = (float *)LAPACKE_malloc( (kd+1)*(n+2) * sizeof(float) );
    q_r = (float *)LAPACKE_malloc( n*(n+2) * sizeof(float) );

    /* Initialize input arrays */
    init_ab( ldab*n, ab );
    init_d( n, d );
    init_e( (n-1), e );
    init_q( ldq*n, q );
    init_work( n, work );

    /* Backup the ouptut arrays */
    for( i = 0; i < ldab*n; i++ ) {
        ab_save[i] = ab[i];
    }
    for( i = 0; i < n; i++ ) {
        d_save[i] = d[i];
    }
    for( i = 0; i < (n-1); i++ ) {
        e_save[i] = e[i];
    }
    for( i = 0; i < ldq*n; i++ ) {
        q_save[i] = q[i];
    }

    /* Call the LAPACK routine */
    ssbtrd_( &vect, &uplo, &n, &kd, ab, &ldab, d, e, q, &ldq, work, &info );

    /* Initialize input data, call the column-major middle-level
     * interface to LAPACK routine and check the results */
    for( i = 0; i < ldab*n; i++ ) {
        ab_i[i] = ab_save[i];
    }
    for( i = 0; i < n; i++ ) {
        d_i[i] = d_save[i];
    }
    for( i = 0; i < (n-1); i++ ) {
        e_i[i] = e_save[i];
    }
    for( i = 0; i < ldq*n; i++ ) {
        q_i[i] = q_save[i];
    }
    for( i = 0; i < n; i++ ) {
        work_i[i] = work[i];
    }
    info_i = LAPACKE_ssbtrd_work( LAPACK_COL_MAJOR, vect_i, uplo_i, n_i, kd_i,
                                  ab_i, ldab_i, d_i, e_i, q_i, ldq_i, work_i );

    failed = compare_ssbtrd( ab, ab_i, d, d_i, e, e_i, q, q_i, info, info_i,
                             ldab, ldq, n, vect );
    if( failed == 0 ) {
        printf( "PASSED: column-major middle-level interface to ssbtrd\n" );
    } else {
        printf( "FAILED: column-major middle-level interface to ssbtrd\n" );
    }

    /* Initialize input data, call the column-major high-level
     * interface to LAPACK routine and check the results */
    for( i = 0; i < ldab*n; i++ ) {
        ab_i[i] = ab_save[i];
    }
    for( i = 0; i < n; i++ ) {
        d_i[i] = d_save[i];
    }
    for( i = 0; i < (n-1); i++ ) {
        e_i[i] = e_save[i];
    }
    for( i = 0; i < ldq*n; i++ ) {
        q_i[i] = q_save[i];
    }
    for( i = 0; i < n; i++ ) {
        work_i[i] = work[i];
    }
    info_i = LAPACKE_ssbtrd( LAPACK_COL_MAJOR, vect_i, uplo_i, n_i, kd_i, ab_i,
                             ldab_i, d_i, e_i, q_i, ldq_i );

    failed = compare_ssbtrd( ab, ab_i, d, d_i, e, e_i, q, q_i, info, info_i,
                             ldab, ldq, n, vect );
    if( failed == 0 ) {
        printf( "PASSED: column-major high-level interface to ssbtrd\n" );
    } else {
        printf( "FAILED: column-major high-level interface to ssbtrd\n" );
    }

    /* Initialize input data, call the row-major middle-level
     * interface to LAPACK routine and check the results */
    for( i = 0; i < ldab*n; i++ ) {
        ab_i[i] = ab_save[i];
    }
    for( i = 0; i < n; i++ ) {
        d_i[i] = d_save[i];
    }
    for( i = 0; i < (n-1); i++ ) {
        e_i[i] = e_save[i];
    }
    for( i = 0; i < ldq*n; i++ ) {
        q_i[i] = q_save[i];
    }
    for( i = 0; i < n; i++ ) {
        work_i[i] = work[i];
    }

    LAPACKE_sge_trans( LAPACK_COL_MAJOR, kd+1, n, ab_i, ldab, ab_r, n+2 );
    if( LAPACKE_lsame( vect, 'u' ) || LAPACKE_lsame( vect, 'v' ) ) {
        LAPACKE_sge_trans( LAPACK_COL_MAJOR, n, n, q_i, ldq, q_r, n+2 );
    }
    info_i = LAPACKE_ssbtrd_work( LAPACK_ROW_MAJOR, vect_i, uplo_i, n_i, kd_i,
                                  ab_r, ldab_r, d_i, e_i, q_r, ldq_r, work_i );

    LAPACKE_sge_trans( LAPACK_ROW_MAJOR, kd+1, n, ab_r, n+2, ab_i, ldab );
    if( LAPACKE_lsame( vect, 'u' ) || LAPACKE_lsame( vect, 'v' ) ) {
        LAPACKE_sge_trans( LAPACK_ROW_MAJOR, n, n, q_r, n+2, q_i, ldq );
    }

    failed = compare_ssbtrd( ab, ab_i, d, d_i, e, e_i, q, q_i, info, info_i,
                             ldab, ldq, n, vect );
    if( failed == 0 ) {
        printf( "PASSED: row-major middle-level interface to ssbtrd\n" );
    } else {
        printf( "FAILED: row-major middle-level interface to ssbtrd\n" );
    }

    /* Initialize input data, call the row-major high-level
     * interface to LAPACK routine and check the results */
    for( i = 0; i < ldab*n; i++ ) {
        ab_i[i] = ab_save[i];
    }
    for( i = 0; i < n; i++ ) {
        d_i[i] = d_save[i];
    }
    for( i = 0; i < (n-1); i++ ) {
        e_i[i] = e_save[i];
    }
    for( i = 0; i < ldq*n; i++ ) {
        q_i[i] = q_save[i];
    }
    for( i = 0; i < n; i++ ) {
        work_i[i] = work[i];
    }

    /* Init row_major arrays */
    LAPACKE_sge_trans( LAPACK_COL_MAJOR, kd+1, n, ab_i, ldab, ab_r, n+2 );
    if( LAPACKE_lsame( vect, 'u' ) || LAPACKE_lsame( vect, 'v' ) ) {
        LAPACKE_sge_trans( LAPACK_COL_MAJOR, n, n, q_i, ldq, q_r, n+2 );
    }
    info_i = LAPACKE_ssbtrd( LAPACK_ROW_MAJOR, vect_i, uplo_i, n_i, kd_i, ab_r,
                             ldab_r, d_i, e_i, q_r, ldq_r );

    LAPACKE_sge_trans( LAPACK_ROW_MAJOR, kd+1, n, ab_r, n+2, ab_i, ldab );
    if( LAPACKE_lsame( vect, 'u' ) || LAPACKE_lsame( vect, 'v' ) ) {
        LAPACKE_sge_trans( LAPACK_ROW_MAJOR, n, n, q_r, n+2, q_i, ldq );
    }

    failed = compare_ssbtrd( ab, ab_i, d, d_i, e, e_i, q, q_i, info, info_i,
                             ldab, ldq, n, vect );
    if( failed == 0 ) {
        printf( "PASSED: row-major high-level interface to ssbtrd\n" );
    } else {
        printf( "FAILED: row-major high-level interface to ssbtrd\n" );
    }

    /* Release memory */
    if( ab != NULL ) {
        LAPACKE_free( ab );
    }
    if( ab_i != NULL ) {
        LAPACKE_free( ab_i );
    }
    if( ab_r != NULL ) {
        LAPACKE_free( ab_r );
    }
    if( ab_save != NULL ) {
        LAPACKE_free( ab_save );
    }
    if( d != NULL ) {
        LAPACKE_free( d );
    }
    if( d_i != NULL ) {
        LAPACKE_free( d_i );
    }
    if( d_save != NULL ) {
        LAPACKE_free( d_save );
    }
    if( e != NULL ) {
        LAPACKE_free( e );
    }
    if( e_i != NULL ) {
        LAPACKE_free( e_i );
    }
    if( e_save != NULL ) {
        LAPACKE_free( e_save );
    }
    if( q != NULL ) {
        LAPACKE_free( q );
    }
    if( q_i != NULL ) {
        LAPACKE_free( q_i );
    }
    if( q_r != NULL ) {
        LAPACKE_free( q_r );
    }
    if( q_save != NULL ) {
        LAPACKE_free( q_save );
    }
    if( work != NULL ) {
        LAPACKE_free( work );
    }
    if( work_i != NULL ) {
        LAPACKE_free( work_i );
    }

    return 0;
}
Ejemplo n.º 6
0
/* Subroutine */ int ssbevx_(char *jobz, char *range, char *uplo, integer *n, 
	integer *kd, real *ab, integer *ldab, real *q, integer *ldq, real *vl,
	 real *vu, integer *il, integer *iu, real *abstol, integer *m, real *
	w, real *z, integer *ldz, real *work, 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   
    =======   

    SSBEVX computes selected eigenvalues and, optionally, eigenvectors   
    of a real symmetric band 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.   

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

    AB      (input/output) REAL array, dimension (LDAB, N)   
            On entry, the upper or lower triangle of the symmetric band   
            matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 
  
            if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). 
  

            On exit, AB is overwritten by values generated during the   
            reduction to tridiagonal form.  If UPLO = 'U', the first   
            superdiagonal and the diagonal of the tridiagonal matrix T   
            are returned in rows KD and KD+1 of AB, and if UPLO = 'L',   
            the diagonal and first subdiagonal of T are returned in the   
            first two rows of AB.   

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

    Q       (output) REAL array, dimension (LDQ, N)   
            If JOBZ = 'V', the N-by-N orthogonal matrix used in the   
                           reduction to tridiagonal form.   
            If JOBZ = 'N', the array Q is not referenced.   

    LDQ     (input) INTEGER   
            The leading dimension of the array Q.  If JOBZ = 'V', then   
            LDQ >= max(1,N).   

    VL      (input) REAL   
    VU      (input) REAL   
            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) REAL   
            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 AB to tridiagonal form.   

            Eigenvalues will be computed most accurately when ABSTOL is   
            set to twice the underflow threshold 2*SLAMCH('S'), not zero. 
  
            If this routine returns with INFO>0, indicating that some   
            eigenvectors did not converge, try setting ABSTOL to   
            2*SLAMCH('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) REAL array, dimension (N)   
            The first M elements contain the selected eigenvalues in   
            ascending order.   

    Z       (output) REAL 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) REAL 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 real c_b14 = 1.f;
    static integer c__1 = 1;
    static real c_b34 = 0.f;
    
    /* System generated locals */
    integer ab_dim1, ab_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, 
	    i__2;
    real r__1, r__2;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer indd, inde;
    static real anrm;
    static integer imax;
    static real rmin, rmax;
    static integer itmp1, i, j, indee;
    static real sigma;
    extern logical lsame_(char *, char *);
    static integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static char order[1];
    extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, 
	    real *, integer *, real *, integer *, real *, real *, integer *);
    static logical lower;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *), sswap_(integer *, real *, integer *, real *, integer *
	    );
    static logical wantz;
    static integer jj;
    static logical alleig, indeig;
    static integer iscale, indibl;
    static logical valeig;
    extern doublereal slamch_(char *);
    static real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real abstll, bignum;
    extern doublereal slansb_(char *, char *, integer *, integer *, real *, 
	    integer *, real *);
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *);
    static integer indisp, indiwo;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *);
    static integer indwrk;
    extern /* Subroutine */ int ssbtrd_(char *, char *, integer *, integer *, 
	    real *, integer *, real *, real *, real *, integer *, real *, 
	    integer *), sstein_(integer *, real *, real *, 
	    integer *, real *, integer *, integer *, real *, integer *, real *
	    , integer *, integer *, integer *), ssterf_(integer *, real *, 
	    real *, integer *);
    static integer nsplit;
    static real smlnum;
    extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, 
	    real *, integer *, integer *, real *, real *, real *, integer *, 
	    integer *, real *, integer *, integer *, real *, integer *, 
	    integer *), ssteqr_(char *, integer *, real *, 
	    real *, real *, integer *, real *, integer *);
    static real eps, vll, vuu, tmp1;



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

#define AB(I,J) ab[(I)-1 + ((J)-1)* ( *ldab)]
#define Q(I,J) q[(I)-1 + ((J)-1)* ( *ldq)]
#define Z(I,J) z[(I)-1 + ((J)-1)* ( *ldz)]

    wantz = lsame_(jobz, "V");
    alleig = lsame_(range, "A");
    valeig = lsame_(range, "V");
    indeig = lsame_(range, "I");
    lower = lsame_(uplo, "L");

    *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 (*kd < 0) {
	*info = -5;
    } else if (*ldab < *kd + 1) {
	*info = -7;
    } else if (*ldq < *n) {
	*info = -9;
    } else if (valeig && *n > 0 && *vu <= *vl) {
	*info = -11;
    } else if (indeig && *il < 1) {
	*info = -12;
    } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) {
	*info = -13;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -18;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SSBEVX", &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) = AB(1,1);
	} else {
	    if (*vl < AB(1,1) && *vu >= AB(1,1)) {
		*m = 1;
		W(1) = AB(1,1);
	    }
	}
	if (wantz) {
	    Z(1,1) = 1.f;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = slamch_("Safe minimum");
    eps = slamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1.f / smlnum;
    rmin = sqrt(smlnum);
/* Computing MIN */
    r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));
    rmax = dmin(r__1,r__2);

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

    iscale = 0;
    abstll = *abstol;
    if (valeig) {
	vll = *vl;
	vuu = *vu;
    }
    anrm = slansb_("M", uplo, n, kd, &AB(1,1), ldab, &WORK(1));
    if (anrm > 0.f && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    slascl_("B", kd, kd, &c_b14, &sigma, n, n, &AB(1,1), ldab, 
		    info);
	} else {
	    slascl_("Q", kd, kd, &c_b14, &sigma, n, n, &AB(1,1), ldab, 
		    info);
	}
	if (*abstol > 0.f) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }

/*     Call SSBTRD to reduce symmetric band matrix to tridiagonal form. */

    indd = 1;
    inde = indd + *n;
    indwrk = inde + *n;
    ssbtrd_(jobz, uplo, n, kd, &AB(1,1), ldab, &WORK(indd), &WORK(inde),
	     &Q(1,1), ldq, &WORK(indwrk), &iinfo);

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

    if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.f) {
	scopy_(n, &WORK(indd), &c__1, &W(1), &c__1);
	indee = indwrk + (*n << 1);
	if (! wantz) {
	    i__1 = *n - 1;
	    scopy_(&i__1, &WORK(inde), &c__1, &WORK(indee), &c__1);
	    ssterf_(n, &W(1), &WORK(indee), info);
	} else {
	    slacpy_("A", n, n, &Q(1,1), ldq, &Z(1,1), ldz);
	    i__1 = *n - 1;
	    scopy_(&i__1, &WORK(inde), &c__1, &WORK(indee), &c__1);
	    ssteqr_(jobz, n, &W(1), &WORK(indee), &Z(1,1), ldz, &WORK(
		    indwrk), info);
	    if (*info == 0) {
		i__1 = *n;
		for (i = 1; i <= *n; ++i) {
		    IFAIL(i) = 0;
/* L10: */
		}
	    }
	}
	if (*info == 0) {
	    *m = *n;
	    goto L30;
	}
	*info = 0;
    }

/*     Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    indibl = 1;
    indisp = indibl + *n;
    indiwo = indisp + *n;
    sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &WORK(indd), &WORK(
	    inde), m, &nsplit, &W(1), &IWORK(indibl), &IWORK(indisp), &WORK(
	    indwrk), &IWORK(indiwo), info);

    if (wantz) {
	sstein_(n, &WORK(indd), &WORK(inde), m, &W(1), &IWORK(indibl), &IWORK(
		indisp), &Z(1,1), ldz, &WORK(indwrk), &IWORK(indiwo), &
		IFAIL(1), info);

/*        Apply orthogonal matrix used in reduction to tridiagonal   
          form to eigenvectors returned by SSTEIN. */

	i__1 = *m;
	for (j = 1; j <= *m; ++j) {
	    scopy_(n, &Z(1,j), &c__1, &WORK(1), &c__1);
	    sgemv_("N", n, n, &c_b14, &Q(1,1), ldq, &WORK(1), &c__1, &
		    c_b34, &Z(1,j), &c__1);
/* L20: */
	}
    }

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

L30:
    if (iscale == 1) {
	if (*info == 0) {
	    imax = *m;
	} else {
	    imax = *info - 1;
	}
	r__1 = 1.f / sigma;
	sscal_(&imax, &r__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);
		}
/* 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;
		sswap_(n, &Z(1,i), &c__1, &Z(1,j), &
			c__1);
		if (*info != 0) {
		    itmp1 = IFAIL(i);
		    IFAIL(i) = IFAIL(j);
		    IFAIL(j) = itmp1;
		}
	    }
/* L50: */
	}
    }

    return 0;

/*     End of SSBEVX */

} /* ssbevx_ */
Ejemplo n.º 7
0
 int ssbgvd_(char *jobz, char *uplo, int *n, int *ka, 
	int *kb, float *ab, int *ldab, float *bb, int *ldbb, float *
	w, float *z__, int *ldz, float *work, int *lwork, int *
	iwork, int *liwork, int *info)
{
    /* System generated locals */
    int ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1;

    /* Local variables */
    int inde;
    char vect[1];
    extern int lsame_(char *, char *);
    int iinfo;
    extern  int sgemm_(char *, char *, int *, int *, 
	    int *, float *, float *, int *, float *, int *, float *, 
	    float *, int *);
    int lwmin;
    int upper, wantz;
    int indwk2, llwrk2;
    extern  int xerbla_(char *, int *), sstedc_(
	    char *, int *, float *, float *, float *, int *, float *, 
	    int *, int *, int *, int *), slacpy_(char 
	    *, int *, int *, float *, int *, float *, int *);
    int indwrk, liwmin;
    extern  int spbstf_(char *, int *, int *, float *, 
	    int *, int *), ssbtrd_(char *, char *, int *, 
	    int *, float *, int *, float *, float *, float *, int *, 
	    float *, int *), ssbgst_(char *, char *, 
	    int *, int *, int *, float *, int *, float *, 
	    int *, float *, int *, float *, int *), 
	    ssterf_(int *, float *, float *, int *);
    int lquery;


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

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

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

/*  SSBGVD computes all the eigenvalues, and optionally, the eigenvectors */
/*  of a float generalized symmetric-definite banded eigenproblem, of the */
/*  form A*x=(lambda)*B*x.  Here A and B are assumed to be symmetric 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) REAL array, dimension (LDAB, N) */
/*          On entry, the upper or lower triangle of the symmetric 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) REAL array, dimension (LDBB, N) */
/*          On entry, the upper or lower triangle of the symmetric 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(ka+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**T*S, as returned by SPBSTF. */

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

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

/*  Z       (output) REAL 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 Z**T*B*Z = I. */
/*          If JOBZ = 'N', then Z is not referenced. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z.  LDZ >= 1, and if */
/*          JOBZ = 'V', LDZ >= MAX(1,N). */

/*  WORK    (workspace/output) REAL array, dimension (MAX(1,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 >= 3*N. */
/*          If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2. */

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

/*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/*          On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK. */

/*  LIWORK  (input) INTEGER */
/*          The dimension of the 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 sizes of the WORK and */
/*          IWORK arrays, returns these values as the first entries of */
/*          the WORK and IWORK arrays, and no error message related to */
/*          LWORK or LIWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  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 SPBSTF */
/*                    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 .. */
/*     .. */
/*     .. 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;
    --iwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1 || *liwork == -1;

    *info = 0;
    if (*n <= 1) {
	liwmin = 1;
	lwmin = 1;
    } else if (wantz) {
	liwmin = *n * 5 + 3;
/* Computing 2nd power */
	i__1 = *n;
	lwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
    } else {
	liwmin = 1;
	lwmin = *n << 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;
    }

    if (*info == 0) {
	work[1] = (float) lwmin;
	iwork[1] = liwmin;

	if (*lwork < lwmin && ! lquery) {
	    *info = -14;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -16;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SSBGVD", &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. */

    spbstf_(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 = indwrk + *n * *n;
    llwrk2 = *lwork - indwk2 + 1;
    ssbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, 
	     &z__[z_offset], ldz, &work[indwrk], &iinfo)
	    ;

/*     Reduce to tridiagonal form. */

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

/*     For eigenvalues only, call SSTERF. For eigenvectors, call SSTEDC. */

    if (! wantz) {
	ssterf_(n, &w[1], &work[inde], info);
    } else {
	sstedc_("I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], &
		llwrk2, &iwork[1], liwork, info);
	sgemm_("N", "N", n, n, n, &c_b12, &z__[z_offset], ldz, &work[indwrk], 
		n, &c_b13, &work[indwk2], n);
	slacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz);
    }

    work[1] = (float) lwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of SSBGVD */

} /* ssbgvd_ */