Beispiel #1
0
/* Subroutine */ int chpev_(char *jobz, char *uplo, integer *n, complex *ap, 
	real *w, complex *z, integer *ldz, complex *work, real *rwork, 
	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   
       March 31, 1993   


    Purpose   
    =======   

    CHPEV computes all the eigenvalues and, optionally, eigenvectors of a 
  
    complex Hermitian matrix in packed storage.   

    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.   

    AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)   
            On entry, the upper or lower triangle of the Hermitian matrix 
  
            A, packed columnwise in a linear array.  The j-th column of A 
  
            is stored in the array AP as follows:   
            if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;   
            if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 
  

            On exit, 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.   

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

    Z       (output) COMPLEX array, dimension (LDZ, N)   
            If JOBZ = 'V', then if INFO = 0, Z contains the 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) COMPLEX array, dimension (max(1, 2*N-1))   

    RWORK   (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.   

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


       Test the input parameters.   

    
   Parameter adjustments   
       Function Body */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* System generated locals */
    integer z_dim1, z_offset, i__1;
    real r__1;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer inde;
    static real anrm;
    static integer imax;
    static real rmin, rmax, sigma;
    extern logical lsame_(char *, char *);
    static integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static logical wantz;
    static integer iscale;
    extern doublereal clanhp_(char *, char *, integer *, complex *, real *), slamch_(char *);
    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
	    *);
    static real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real bignum;
    static integer indtau;
    extern /* Subroutine */ int chptrd_(char *, integer *, complex *, real *, 
	    real *, complex *, integer *);
    static integer indrwk, indwrk;
    extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, 
	    complex *, integer *, real *, integer *), cupgtr_(char *, 
	    integer *, complex *, complex *, complex *, integer *, complex *, 
	    integer *), ssterf_(integer *, real *, real *, integer *);
    static real smlnum, eps;



#define AP(I) ap[(I)-1]
#define W(I) w[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]

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

    wantz = lsame_(jobz, "V");

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lsame_(uplo, "L") || lsame_(uplo, "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -7;
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	W(1) = AP(1).r;
	RWORK(1) = 1.f;
	if (wantz) {
	    i__1 = z_dim1 + 1;
	    Z(1,1).r = 1.f, Z(1,1).i = 0.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 = clanhp_("M", uplo, n, &AP(1), &RWORK(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) {
	i__1 = *n * (*n + 1) / 2;
	csscal_(&i__1, &sigma, &AP(1), &c__1);
    }

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

    inde = 1;
    indtau = 1;
    chptrd_(uplo, n, &AP(1), &W(1), &RWORK(inde), &WORK(indtau), &iinfo);

/*     For eigenvalues only, call SSTERF.  For eigenvectors, first call   
       CUPGTR to generate the orthogonal matrix, then call CSTEQR. */

    if (! wantz) {
	ssterf_(n, &W(1), &RWORK(inde), info);
    } else {
	indwrk = indtau + *n;
	cupgtr_(uplo, n, &AP(1), &WORK(indtau), &Z(1,1), ldz, &WORK(
		indwrk), &iinfo);
	indrwk = inde + *n;
	csteqr_(jobz, n, &W(1), &RWORK(inde), &Z(1,1), ldz, &RWORK(
		indrwk), 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 CHPEV */

} /* chpev_ */
Beispiel #2
0
/* Subroutine */ int chpev_(char *jobz, char *uplo, integer *n, complex *ap, 
	real *w, complex *z__, integer *ldz, complex *work, real *rwork, 
	integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1;
    real r__1;

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

    /* Local variables */
    real eps;
    integer inde;
    real anrm;
    integer imax;
    real rmin, rmax, sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    logical wantz;
    integer iscale;
    extern doublereal clanhp_(char *, char *, integer *, complex *, real *), slamch_(char *);
    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
	    *);
    real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real bignum;
    integer indtau;
    extern /* Subroutine */ int chptrd_(char *, integer *, complex *, real *, 
	    real *, complex *, integer *);
    integer indrwk, indwrk;
    extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, 
	    complex *, integer *, real *, integer *), cupgtr_(char *, 
	    integer *, complex *, complex *, complex *, integer *, complex *, 
	    integer *), ssterf_(integer *, real *, real *, integer *);
    real smlnum;


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

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

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

/*  CHPEV computes all the eigenvalues and, optionally, eigenvectors of a */
/*  complex Hermitian matrix in packed storage. */

/*  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. */

/*  AP      (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/*          On entry, the upper or lower triangle of the Hermitian matrix */
/*          A, packed columnwise in a linear array.  The j-th column of A */
/*          is stored in the array AP as follows: */
/*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/*          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */

/*          On exit, 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. */

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

/*  Z       (output) COMPLEX array, dimension (LDZ, N) */
/*          If JOBZ = 'V', then if INFO = 0, Z contains the 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) COMPLEX array, dimension (max(1, 2*N-1)) */

/*  RWORK   (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 */
    --ap;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --rwork;

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

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lsame_(uplo, "L") || lsame_(uplo, 
	    "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -7;
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	w[1] = ap[1].r;
	rwork[1] = 1.f;
	if (wantz) {
	    i__1 = z_dim1 + 1;
	    z__[i__1].r = 1.f, z__[i__1].i = 0.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 = clanhp_("M", uplo, n, &ap[1], &rwork[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) {
	i__1 = *n * (*n + 1) / 2;
	csscal_(&i__1, &sigma, &ap[1], &c__1);
    }

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

    inde = 1;
    indtau = 1;
    chptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo);

/*     For eigenvalues only, call SSTERF.  For eigenvectors, first call */
/*     CUPGTR to generate the orthogonal matrix, then call CSTEQR. */

    if (! wantz) {
	ssterf_(n, &w[1], &rwork[inde], info);
    } else {
	indwrk = indtau + *n;
	cupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[
		indwrk], &iinfo);
	indrwk = inde + *n;
	csteqr_(jobz, n, &w[1], &rwork[inde], &z__[z_offset], ldz, &rwork[
		indrwk], 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 CHPEV */

} /* chpev_ */
/* Subroutine */ int chpevx_(char *jobz, char *range, char *uplo, integer *n, 
	complex *ap, real *vl, real *vu, integer *il, integer *iu, real *
	abstol, integer *m, real *w, complex *z__, integer *ldz, complex *
	work, real *rwork, integer *iwork, integer *ifail, integer *info)
{
/*  -- LAPACK driver routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    CHPEVX 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 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) 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 AP 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)   
            If INFO = 0, the selected eigenvalues in ascending order.   

    Z       (output) COMPLEX 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 array, dimension (2*N)   

    RWORK   (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 */
    /* Table of constant values */
    static integer c__1 = 1;
    
    /* System generated locals */
    integer 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 cswap_(integer *, complex *, integer *, 
	    complex *, integer *), scopy_(integer *, real *, integer *, real *
	    , integer *);
    static logical wantz;
    static integer jj;
    static logical alleig, indeig;
    static integer iscale, indibl;
    extern doublereal clanhp_(char *, char *, integer *, complex *, real *);
    static logical valeig;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
	    *);
    static real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    static real abstll, bignum;
    static integer indiwk, indisp, indtau;
    extern /* Subroutine */ int chptrd_(char *, integer *, complex *, real *, 
	    real *, complex *, integer *), cstein_(integer *, real *, 
	    real *, integer *, real *, integer *, integer *, complex *, 
	    integer *, real *, integer *, integer *, integer *);
    static integer indrwk, indwrk;
    extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, 
	    complex *, integer *, real *, integer *), cupgtr_(char *, 
	    integer *, complex *, complex *, complex *, integer *, complex *, 
	    integer *), ssterf_(integer *, real *, real *, integer *);
    static integer nsplit;
    extern /* Subroutine */ int cupmtr_(char *, char *, char *, integer *, 
	    integer *, complex *, complex *, complex *, integer *, complex *, 
	    integer *);
    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 *);
    static real eps, vll, vuu, tmp1;
#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)]


    --ap;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    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_("CHPEVX", &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___subscr(1, 1);
	    z__[i__1].r = 1.f, z__[i__1].i = 0.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 = clanhp_("M", uplo, n, &ap[1], &rwork[1]);
    if (anrm > 0.f && 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;
	csscal_(&i__1, &sigma, &ap[1], &c__1);
	if (*abstol > 0.f) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }

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

    indd = 1;
    inde = indd + *n;
    indrwk = inde + *n;
    indtau = 1;
    indwrk = indtau + *n;
    chptrd_(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 SSTERF or CUPGTR and CSTEQR.  If this fails   
       for some eigenvalue, then try SSTEBZ. */

    if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.f) {
	scopy_(n, &rwork[indd], &c__1, &w[1], &c__1);
	indee = indrwk + (*n << 1);
	if (! wantz) {
	    i__1 = *n - 1;
	    scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
	    ssterf_(n, &w[1], &rwork[indee], info);
	} else {
	    cupgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &
		    work[indwrk], &iinfo);
	    i__1 = *n - 1;
	    scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1);
	    csteqr_(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 SSTEBZ and, if eigenvectors are desired, CSTEIN. */

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    indibl = 1;
    indisp = indibl + *n;
    indiwk = indisp + *n;
    sstebz_(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) {
	cstein_(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 CSTEIN. */

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

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

L20:
    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];
		}
/* 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;
		cswap_(n, &z___ref(1, i__), &c__1, &z___ref(1, j), &c__1);
		if (*info != 0) {
		    itmp1 = ifail[i__];
		    ifail[i__] = ifail[j];
		    ifail[j] = itmp1;
		}
	    }
/* L40: */
	}
    }

    return 0;

/*     End of CHPEVX */

} /* chpevx_ */
Beispiel #4
0
/* Subroutine */ int chpevd_(char *jobz, char *uplo, integer *n, complex *ap, 
	real *w, complex *z__, integer *ldz, complex *work, integer *lwork, 
	real *rwork, integer *lrwork, integer *iwork, integer *liwork, 
	integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1;
    real r__1;

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

    /* Local variables */
    real eps;
    integer inde;
    real anrm;
    integer imax;
    real rmin, rmax, sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    integer lwmin, llrwk, llwrk;
    logical wantz;
    integer iscale;
    extern doublereal clanhp_(char *, char *, integer *, complex *, real *);
    extern /* Subroutine */ int cstedc_(char *, integer *, real *, real *, 
	    complex *, integer *, complex *, integer *, real *, integer *, 
	    integer *, integer *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
	    *);
    real safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real bignum;
    integer indtau;
    extern /* Subroutine */ int chptrd_(char *, integer *, complex *, real *, 
	    real *, complex *, integer *);
    integer indrwk, indwrk, liwmin;
    extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
    integer lrwmin;
    extern /* Subroutine */ int cupmtr_(char *, char *, char *, integer *, 
	    integer *, complex *, complex *, complex *, integer *, complex *, 
	    integer *);
    real smlnum;
    logical lquery;


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

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

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

/*  CHPEVD computes all the eigenvalues and, optionally, eigenvectors of */
/*  a complex Hermitian matrix A in packed storage.  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 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 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. */

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

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

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

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

/*  RWORK   (workspace/output) REAL array, dimension (MAX(1,LRWORK)) */
/*          On exit, if INFO = 0, RWORK(1) returns the required LRWORK. */

/*  LRWORK  (input) INTEGER */
/*          The dimension of array RWORK. */
/*          If N <= 1,               LRWORK must be at least 1. */
/*          If JOBZ = 'N' and N > 1, LRWORK must be at least N. */
/*          If JOBZ = 'V' and N > 1, LRWORK must be at least */
/*                    1 + 5*N + 2*N**2. */

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

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

/*  LIWORK  (input) INTEGER */
/*          The dimension of array IWORK. */
/*          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1. */
/*          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */

/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the required sizes of the WORK, RWORK */
/*          and IWORK arrays, returns these values as the first entries */
/*          of the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK 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, 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 */
    --ap;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --rwork;
    --iwork;

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

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lsame_(uplo, "L") || lsame_(uplo, 
	    "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
	*info = -7;
    }

    if (*info == 0) {
	if (*n <= 1) {
	    lwmin = 1;
	    liwmin = 1;
	    lrwmin = 1;
	} else {
	    if (wantz) {
		lwmin = *n << 1;
/* Computing 2nd power */
		i__1 = *n;
		lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
		liwmin = *n * 5 + 3;
	    } else {
		lwmin = *n;
		lrwmin = *n;
		liwmin = 1;
	    }
	}
	work[1].r = (real) lwmin, work[1].i = 0.f;
	rwork[1] = (real) lrwmin;
	iwork[1] = liwmin;

	if (*lwork < lwmin && ! lquery) {
	    *info = -9;
	} else if (*lrwork < lrwmin && ! lquery) {
	    *info = -11;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -13;
	}
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
	w[1] = ap[1].r;
	if (wantz) {
	    i__1 = z_dim1 + 1;
	    z__[i__1].r = 1.f, z__[i__1].i = 0.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 = clanhp_("M", uplo, n, &ap[1], &rwork[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) {
	i__1 = *n * (*n + 1) / 2;
	csscal_(&i__1, &sigma, &ap[1], &c__1);
    }

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

    inde = 1;
    indtau = 1;
    indrwk = inde + *n;
    indwrk = indtau + *n;
    llwrk = *lwork - indwrk + 1;
    llrwk = *lrwork - indrwk + 1;
    chptrd_(uplo, n, &ap[1], &w[1], &rwork[inde], &work[indtau], &iinfo);

/*     For eigenvalues only, call SSTERF.  For eigenvectors, first call */
/*     CUPGTR to generate the orthogonal matrix, then call CSTEDC. */

    if (! wantz) {
	ssterf_(n, &w[1], &rwork[inde], info);
    } else {
	cstedc_("I", n, &w[1], &rwork[inde], &z__[z_offset], ldz, &work[
		indwrk], &llwrk, &rwork[indrwk], &llrwk, &iwork[1], liwork, 
		info);
	cupmtr_("L", uplo, "N", n, n, &ap[1], &work[indtau], &z__[z_offset], 
		ldz, &work[indwrk], &iinfo);
    }

/*     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);
    }

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

/*     End of CHPEVD */

} /* chpevd_ */