/* fortran/dlaed1.f -- translated by f2c (version 20200916).
   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
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"

/* Table of constant values */

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

/* > \brief \b DLAED1 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification
 by a rank-one symmetric matrix. Used when the original matrix is tridiagonal. */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download DLAED1 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed1.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed1.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed1.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, */
/*                          INFO ) */

/*       .. Scalar Arguments .. */
/*       INTEGER            CUTPNT, INFO, LDQ, N */
/*       DOUBLE PRECISION   RHO */
/*       .. */
/*       .. Array Arguments .. */
/*       INTEGER            INDXQ( * ), IWORK( * ) */
/*       DOUBLE PRECISION   D( * ), Q( LDQ, * ), WORK( * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLAED1 computes the updated eigensystem of a diagonal */
/* > matrix after modification by a rank-one symmetric matrix.  This */
/* > routine is used only for the eigenproblem which requires all */
/* > eigenvalues and eigenvectors of a tridiagonal matrix.  DLAED7 handles */
/* > the case in which eigenvalues only or eigenvalues and eigenvectors */
/* > of a full symmetric matrix (which was reduced to tridiagonal form) */
/* > are desired. */
/* > */
/* >   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */
/* > */
/* >    where Z = Q**T*u, u is a vector of length N with ones in the */
/* >    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */
/* > */
/* >    The eigenvectors of the original matrix are stored in Q, and the */
/* >    eigenvalues are in D.  The algorithm consists of three stages: */
/* > */
/* >       The first stage consists of deflating the size of the problem */
/* >       when there are multiple eigenvalues or if there is a zero in */
/* >       the Z vector.  For each such occurrence the dimension of the */
/* >       secular equation problem is reduced by one.  This stage is */
/* >       performed by the routine DLAED2. */
/* > */
/* >       The second stage consists of calculating the updated */
/* >       eigenvalues. This is done by finding the roots of the secular */
/* >       equation via the routine DLAED4 (as called by DLAED3). */
/* >       This routine also calculates the eigenvectors of the current */
/* >       problem. */
/* > */
/* >       The final stage consists of computing the updated eigenvectors */
/* >       directly using the updated eigenvalues.  The eigenvectors for */
/* >       the current problem are multiplied with the eigenvectors from */
/* >       the overall problem. */
/* > \endverbatim */

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

/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >         The dimension of the symmetric tridiagonal matrix.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION array, dimension (N) */
/* >         On entry, the eigenvalues of the rank-1-perturbed matrix. */
/* >         On exit, the eigenvalues of the repaired matrix. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Q */
/* > \verbatim */
/* >          Q is DOUBLE PRECISION array, dimension (LDQ,N) */
/* >         On entry, the eigenvectors of the rank-1-perturbed matrix. */
/* >         On exit, the eigenvectors of the repaired tridiagonal matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* >          LDQ is INTEGER */
/* >         The leading dimension of the array Q.  LDQ >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] INDXQ */
/* > \verbatim */
/* >          INDXQ is INTEGER array, dimension (N) */
/* >         On entry, the permutation which separately sorts the two */
/* >         subproblems in D into ascending order. */
/* >         On exit, the permutation which will reintegrate the */
/* >         subproblems back into sorted order, */
/* >         i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[in] RHO */
/* > \verbatim */
/* >          RHO is DOUBLE PRECISION */
/* >         The subdiagonal entry used to create the rank-1 modification. */
/* > \endverbatim */
/* > */
/* > \param[in] CUTPNT */
/* > \verbatim */
/* >          CUTPNT is INTEGER */
/* >         The location of the last eigenvalue in the leading sub-matrix. */
/* >         min(1,N) <= CUTPNT <= N/2. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (4*N + N**2) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (4*N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit. */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/* >          > 0:  if INFO = 1, an eigenvalue did not converge */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \ingroup auxOTHERcomputational */

/* > \par Contributors: */
/*  ================== */
/* > */
/* > Jeff Rutter, Computer Science Division, University of California */
/* > at Berkeley, USA \n */
/* >  Modified by Francoise Tisseur, University of Tennessee */
/* > */
/*  ===================================================================== */
/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q,
        integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt,
        doublereal *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, i__1, i__2;

    /* Local variables */
    integer i__, k, n1, n2, is, iw, iz, iq2, zpp1, indx, indxc;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
            doublereal *, integer *);
    integer indxp;
    extern /* Subroutine */ int dlaed2_(integer *, integer *, integer *,
            doublereal *, doublereal *, integer *, integer *, doublereal *,
            doublereal *, doublereal *, doublereal *, doublereal *, integer *,
             integer *, integer *, integer *, integer *), dlaed3_(integer *,
            integer *, integer *, doublereal *, doublereal *, integer *,
            doublereal *, doublereal *, doublereal *, integer *, integer *,
            doublereal *, doublereal *, integer *);
    integer idlmda;
    extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
            integer *, integer *, integer *), xerbla_(char *, integer *,
            ftnlen);
    integer coltyp;


/*  -- LAPACK computational routine -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

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

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --indxq;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*n < 0) {
        *info = -1;
    } else if (*ldq < max(1,*n)) {
        *info = -4;
    } else /* if(complicated condition) */ {
/* Computing MIN */
        i__1 = 1, i__2 = *n / 2;
        if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) {
            *info = -7;
        }
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_((char *)"DLAED1", &i__1, (ftnlen)6);
        return 0;
    }

/*     Quick return if possible */

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

/*     The following values are integer pointers which indicate */
/*     the portion of the workspace */
/*     used by a particular array in DLAED2 and DLAED3. */

    iz = 1;
    idlmda = iz + *n;
    iw = idlmda + *n;
    iq2 = iw + *n;

    indx = 1;
    indxc = indx + *n;
    coltyp = indxc + *n;
    indxp = coltyp + *n;


/*     Form the z-vector which consists of the last row of Q_1 and the */
/*     first row of Q_2. */

    dcopy_(cutpnt, &q[*cutpnt + q_dim1], ldq, &work[iz], &c__1);
    zpp1 = *cutpnt + 1;
    i__1 = *n - *cutpnt;
    dcopy_(&i__1, &q[zpp1 + zpp1 * q_dim1], ldq, &work[iz + *cutpnt], &c__1);

/*     Deflate eigenvalues. */

    dlaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[
            iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[
            indxc], &iwork[indxp], &iwork[coltyp], info);

    if (*info != 0) {
        goto L20;
    }

/*     Solve Secular Equation. */

    if (k != 0) {
        is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp +
                1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2;
        dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda],
                 &work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[
                is], info);
        if (*info != 0) {
            goto L20;
        }

/*     Prepare the INDXQ sorting permutation. */

        n1 = k;
        n2 = *n - k;
        dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
    } else {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            indxq[i__] = i__;
/* L10: */
        }
    }

L20:
    return 0;

/*     End of DLAED1 */

} /* dlaed1_ */

#ifdef __cplusplus
        }
#endif