cheevx.c

Go to the documentation of this file.

/* cheevx.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

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

/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;

/* Subroutine */ int cheevx_(char *jobz, char *range, char *uplo, integer *n, 
        complex *a, integer *lda, real *vl, real *vu, integer *il, integer *
        iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, 
        complex *work, integer *lwork, real *rwork, integer *iwork, integer *
        ifail, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
    real r__1, r__2;

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

    /* Local variables */
    integer i__, j, nb, 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 cswap_(integer *, complex *, integer *, 
            complex *, integer *);
    logical lower;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
            integer *);
    logical wantz;
    extern doublereal clanhe_(char *, char *, integer *, complex *, integer *, 
             real *);
    logical alleig, indeig;
    integer iscale, indibl;
    logical valeig;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer 
            *, real *, real *, complex *, complex *, integer *, integer *), csscal_(integer *, real *, complex *, integer *), 
            clacpy_(char *, integer *, integer *, complex *, integer *, 
            complex *, integer *);
    real safmin;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real abstll, bignum;
    integer indiwk, indisp, indtau;
    extern /* Subroutine */ int cstein_(integer *, real *, real *, integer *, 
            real *, integer *, integer *, complex *, integer *, real *, 
            integer *, integer *, integer *);
    integer indrwk, indwrk, lwkmin;
    extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, 
            complex *, integer *, real *, integer *), cungtr_(char *, 
            integer *, complex *, integer *, complex *, complex *, integer *, 
            integer *), ssterf_(integer *, real *, real *, integer *),
             cunmtr_(char *, char *, char *, integer *, integer *, complex *, 
            integer *, complex *, complex *, integer *, complex *, integer *, 
            integer *);
    integer nsplit, llwork;
    real smlnum;
    extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, 
            real *, integer *, integer *, real *, real *, real *, integer *, 
            integer *, real *, integer *, integer *, real *, integer *, 
            integer *);
    integer lwkopt;
    logical lquery;


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

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

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

/*  CHEEVX computes selected eigenvalues and, optionally, eigenvectors */
/*  of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can */
/*  be selected by specifying either a range of values or a range of */
/*  indices for the desired eigenvalues. */

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

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

/*  RANGE   (input) CHARACTER*1 */
/*          = 'A': all eigenvalues will be found. */
/*          = 'V': all eigenvalues in the half-open interval (VL,VU] */
/*                 will be found. */
/*          = 'I': the IL-th through IU-th eigenvalues will be found. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

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

/*  A       (input/output) COMPLEX array, dimension (LDA, N) */
/*          On entry, the Hermitian matrix A.  If UPLO = 'U', the */
/*          leading N-by-N upper triangular part of A contains the */
/*          upper triangular part of the matrix A.  If UPLO = 'L', */
/*          the leading N-by-N lower triangular part of A contains */
/*          the lower triangular part of the matrix A. */
/*          On exit, the lower triangle (if UPLO='L') or the upper */
/*          triangle (if UPLO='U') of A, including the diagonal, is */
/*          destroyed. */

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

/*  VL      (input) 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 A 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) */
/*          On normal exit, the first M elements contain 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/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The length of the array WORK.  LWORK >= 1, when N <= 1; */
/*          otherwise 2*N. */
/*          For optimal efficiency, LWORK >= (NB+1)*N, */
/*          where NB is the max of the blocksize for CHETRD and for */
/*          CUNMTR as returned by ILAENV. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal size of the WORK array, returns */
/*          this value as the first entry of the WORK array, and no error */
/*          message related to LWORK is issued by XERBLA. */

/*  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. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --rwork;
    --iwork;
    --ifail;

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

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
        *info = -1;
    } else if (! (alleig || valeig || indeig)) {
        *info = -2;
    } else if (! (lower || lsame_(uplo, "U"))) {
        *info = -3;
    } else if (*n < 0) {
        *info = -4;
    } else if (*lda < max(1,*n)) {
        *info = -6;
    } else {
        if (valeig) {
            if (*n > 0 && *vu <= *vl) {
                *info = -8;
            }
        } else if (indeig) {
            if (*il < 1 || *il > max(1,*n)) {
                *info = -9;
            } else if (*iu < min(*n,*il) || *iu > *n) {
                *info = -10;
            }
        }
    }
    if (*info == 0) {
        if (*ldz < 1 || wantz && *ldz < *n) {
            *info = -15;
        }
    }

    if (*info == 0) {
        if (*n <= 1) {
            lwkmin = 1;
            work[1].r = (real) lwkmin, work[1].i = 0.f;
        } else {
            lwkmin = *n << 1;
            nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
            i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMTR", uplo, n, &c_n1, &c_n1, 
                    &c_n1);
            nb = max(i__1,i__2);
/* Computing MAX */
            i__1 = 1, i__2 = (nb + 1) * *n;
            lwkopt = max(i__1,i__2);
            work[1].r = (real) lwkopt, work[1].i = 0.f;
        }

        if (*lwork < lwkmin && ! lquery) {
            *info = -17;
        }
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
        if (alleig || indeig) {
            *m = 1;
            i__1 = a_dim1 + 1;
            w[1] = a[i__1].r;
        } else if (valeig) {
            i__1 = a_dim1 + 1;
            i__2 = a_dim1 + 1;
            if (*vl < a[i__1].r && *vu >= a[i__2].r) {
                *m = 1;
                i__1 = a_dim1 + 1;
                w[1] = a[i__1].r;
            }
        }
        if (wantz) {
            i__1 = z_dim1 + 1;
            z__[i__1].r = 1.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;
    }
    anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &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) {
        if (lower) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = *n - j + 1;
                csscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1);
/* L10: */
            }
        } else {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                csscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1);
/* L20: */
            }
        }
        if (*abstol > 0.f) {
            abstll = *abstol * sigma;
        }
        if (valeig) {
            vll = *vl * sigma;
            vuu = *vu * sigma;
        }
    }

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

    indd = 1;
    inde = indd + *n;
    indrwk = inde + *n;
    indtau = 1;
    indwrk = indtau + *n;
    llwork = *lwork - indwrk + 1;
    chetrd_(uplo, n, &a[a_offset], lda, &rwork[indd], &rwork[inde], &work[
            indtau], &work[indwrk], &llwork, &iinfo);

/*     If all eigenvalues are desired and ABSTOL is less than or equal to */
/*     zero, then call SSTERF or CUNGTR and CSTEQR.  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, &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 {
            clacpy_("A", n, n, &a[a_offset], lda, &z__[z_offset], ldz);
            cungtr_(uplo, n, &z__[z_offset], ldz, &work[indtau], &work[indwrk]
, &llwork, &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;
/* L30: */
                }
            }
        }
        if (*info == 0) {
            *m = *n;
            goto L40;
        }
        *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. */

        cunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[
                z_offset], ldz, &work[indwrk], &llwork, &iinfo);
    }

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

L40:
    if (iscale == 1) {
        if (*info == 0) {
            imax = *m;
        } else {
            imax = *info - 1;
        }
        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];
                }
/* L50: */
            }

            if (i__ != 0) {
                itmp1 = iwork[indibl + i__ - 1];
                w[i__] = w[j];
                iwork[indibl + i__ - 1] = iwork[indibl + j - 1];
                w[j] = tmp1;
                iwork[indibl + j - 1] = itmp1;
                cswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], 
                         &c__1);
                if (*info != 0) {
                    itmp1 = ifail[i__];
                    ifail[i__] = ifail[j];
                    ifail[j] = itmp1;
                }
            }
/* L60: */
        }
    }

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

    work[1].r = (real) lwkopt, work[1].i = 0.f;

    return 0;

/*     End of CHEEVX */

} /* cheevx_ */