/*  -- translated by f2c (version 20191129).
   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"

/* Table of constant values */

static doublereal c_b5 = 0.;
static doublereal c_b6 = 1.;
static integer c__1 = 1;
static doublereal c_b43 = -1.;

/* -----------------------------------------------------------------------   
   \BeginDoc   

   \Name: dnapps   

   \Description:   
    Given the Arnoldi factorization   

       A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T,   

    apply NP implicit shifts resulting in   

       A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q   

    where Q is an orthogonal matrix which is the product of rotations   
    and reflections resulting from the NP bulge chage sweeps.   
    The updated Arnoldi factorization becomes:   

       A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T.   

   \Usage:   
    call dnapps   
       ( N, KEV, NP, SHIFTR, SHIFTI, V, LDV, H, LDH, RESID, Q, LDQ,   
         WORKL, WORKD )   

   \Arguments   
    N       Integer.  (INPUT)   
            Problem size, i.e. size of matrix A.   

    KEV     Integer.  (INPUT/OUTPUT)   
            KEV+NP is the size of the input matrix H.   
            KEV is the size of the updated matrix HNEW.  KEV is only   
            updated on ouput when fewer than NP shifts are applied in   
            order to keep the conjugate pair together.   

    NP      Integer.  (INPUT)   
            Number of implicit shifts to be applied.   

    SHIFTR, Double precision array of length NP.  (INPUT)   
    SHIFTI  Real and imaginary part of the shifts to be applied.   
            Upon, entry to dnapps, the shifts must be sorted so that the   
            conjugate pairs are in consecutive locations.   

    V       Double precision N by (KEV+NP) array.  (INPUT/OUTPUT)   
            On INPUT, V contains the current KEV+NP Arnoldi vectors.   
            On OUTPUT, V contains the updated KEV Arnoldi vectors   
            in the first KEV columns of V.   

    LDV     Integer.  (INPUT)   
            Leading dimension of V exactly as declared in the calling   
            program.   

    H       Double precision (KEV+NP) by (KEV+NP) array.  (INPUT/OUTPUT)   
            On INPUT, H contains the current KEV+NP by KEV+NP upper   
            Hessenber matrix of the Arnoldi factorization.   
            On OUTPUT, H contains the updated KEV by KEV upper Hessenberg   
            matrix in the KEV leading submatrix.   

    LDH     Integer.  (INPUT)   
            Leading dimension of H exactly as declared in the calling   
            program.   

    RESID   Double precision array of length N.  (INPUT/OUTPUT)   
            On INPUT, RESID contains the the residual vector r_{k+p}.   
            On OUTPUT, RESID is the update residual vector rnew_{k}   
            in the first KEV locations.   

    Q       Double precision KEV+NP by KEV+NP work array.  (WORKSPACE)   
            Work array used to accumulate the rotations and reflections   
            during the bulge chase sweep.   

    LDQ     Integer.  (INPUT)   
            Leading dimension of Q exactly as declared in the calling   
            program.   

    WORKL   Double precision work array of length (KEV+NP).  (WORKSPACE)   
            Private (replicated) array on each PE or array allocated on   
            the front end.   

    WORKD   Double precision work array of length 2*N.  (WORKSPACE)   
            Distributed array used in the application of the accumulated   
            orthogonal matrix Q.   

   \EndDoc   

   -----------------------------------------------------------------------   

   \BeginLib   

   \Local variables:   
       xxxxxx  real   

   \References:   
    1. D.C. Sorensen, "Implicit Application of Polynomial Filters in   
       a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),   
       pp 357-385.   

   \Routines called:   
       ivout   ARPACK utility routine that prints integers.   
       second  ARPACK utility routine for timing.   
       dmout   ARPACK utility routine that prints matrices.   
       dvout   ARPACK utility routine that prints vectors.   
       dlabad  LAPACK routine that computes machine constants.   
       dlacpy  LAPACK matrix copy routine.   
       dlamch  LAPACK routine that determines machine constants.   
       dlanhs  LAPACK routine that computes various norms of a matrix.   
       dlapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.   
       dlarf   LAPACK routine that applies Householder reflection to   
               a matrix.   
       dlarfg  LAPACK Householder reflection construction routine.   
       dlartg  LAPACK Givens rotation construction routine.   
       dlaset  LAPACK matrix initialization routine.   
       dgemv   Level 2 BLAS routine for matrix vector multiplication.   
       daxpy   Level 1 BLAS that computes a vector triad.   
       dcopy   Level 1 BLAS that copies one vector to another .   
       dscal   Level 1 BLAS that scales a vector.   

   \Author   
       Danny Sorensen               Phuong Vu   
       Richard Lehoucq              CRPC / Rice University   
       Dept. of Computational &     Houston, Texas   
       Applied Mathematics   
       Rice University   
       Houston, Texas   

   \Revision history:   
       xx/xx/92: Version ' 2.1'   

   \SCCS Information: @(#)   
   FILE: napps.F   SID: 2.3   DATE OF SID: 4/20/96   RELEASE: 2   

   \Remarks   
    1. In this version, each shift is applied to all the sublocks of   
       the Hessenberg matrix H and not just to the submatrix that it   
       comes from. Deflation as in LAPACK routine dlahqr (QR algorithm   
       for upper Hessenberg matrices ) is used.   
       The subdiagonals of H are enforced to be non-negative.   

   \EndLib   

   -----------------------------------------------------------------------   

   Subroutine */ int igraphdnapps_(integer *n, integer *kev, integer *np, 
	doublereal *shiftr, doublereal *shifti, doublereal *v, integer *ldv, 
	doublereal *h__, integer *ldh, doublereal *resid, doublereal *q, 
	integer *ldq, doublereal *workl, doublereal *workd)
{
    /* Initialized data */

    IGRAPH_F77_SAVE logical first = TRUE_;

    /* System generated locals */
    integer h_dim1, h_offset, v_dim1, v_offset, q_dim1, q_offset, i__1, i__2, 
	    i__3, i__4;
    doublereal d__1, d__2;

    /* Local variables */
    doublereal c__, f, g;
    integer i__, j;
    doublereal r__, s, t, u[3];
    IGRAPH_F77_SAVE real t0, t1;
    doublereal h11, h12, h21, h22, h32;
    integer jj, ir, nr;
    doublereal tau;
    IGRAPH_F77_SAVE doublereal ulp;
    doublereal tst1;
    integer iend;
    IGRAPH_F77_SAVE doublereal unfl, ovfl;
    extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *, 
	    integer *), igraphdlarf_(char *, integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *);
    logical cconj;
    extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *), igraphdcopy_(integer *, 
	    doublereal *, integer *, doublereal *, integer *), igraphdaxpy_(integer 
	    *, doublereal *, doublereal *, integer *, doublereal *, integer *)
	    , igraphdmout_(integer *, integer *, integer *, doublereal *, integer *,
	     integer *, char *, ftnlen), igraphdvout_(integer *, integer *, 
	    doublereal *, integer *, char *, ftnlen), igraphivout_(integer *, 
	    integer *, integer *, integer *, char *, ftnlen);
    extern doublereal igraphdlapy2_(doublereal *, doublereal *);
    extern /* Subroutine */ int igraphdlabad_(doublereal *, doublereal *);
    extern doublereal igraphdlamch_(char *);
    extern /* Subroutine */ int igraphdlarfg_(integer *, doublereal *, doublereal *,
	     integer *, doublereal *);
    doublereal sigmai;
    extern doublereal igraphdlanhs_(char *, integer *, doublereal *, integer *, 
	    doublereal *);
    extern /* Subroutine */ int igraphsecond_(real *), igraphdlacpy_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, integer *), igraphdlaset_(char *, integer *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *), igraphdlartg_(
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *);
    integer logfil, ndigit;
    doublereal sigmar;
    integer mnapps = 0, msglvl;
    real tnapps = 0.;
    integer istart;
    IGRAPH_F77_SAVE doublereal smlnum;
    integer kplusp;


/*     %----------------------------------------------------%   
       | Include files for debugging and timing information |   
       %----------------------------------------------------%   


       %------------------%   
       | Scalar Arguments |   
       %------------------%   


       %-----------------%   
       | Array Arguments |   
       %-----------------%   


       %------------%   
       | Parameters |   
       %------------%   


       %------------------------%   
       | Local Scalars & Arrays |   
       %------------------------%   


       %----------------------%   
       | External Subroutines |   
       %----------------------%   


       %--------------------%   
       | External Functions |   
       %--------------------%   


       %----------------------%   
       | Intrinsics Functions |   
       %----------------------%   


       %----------------%   
       | Data statments |   
       %----------------%   

       Parameter adjustments */
    --workd;
    --resid;
    --workl;
    --shifti;
    --shiftr;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    h_dim1 = *ldh;
    h_offset = 1 + h_dim1;
    h__ -= h_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;

    /* Function Body   

       %-----------------------%   
       | Executable Statements |   
       %-----------------------% */

    if (first) {

/*        %-----------------------------------------------%   
          | Set machine-dependent constants for the       |   
          | stopping criterion. If norm(H) <= sqrt(OVFL), |   
          | overflow should not occur.                    |   
          | REFERENCE: LAPACK subroutine dlahqr           |   
          %-----------------------------------------------% */

	unfl = igraphdlamch_("safe minimum");
	ovfl = 1. / unfl;
	igraphdlabad_(&unfl, &ovfl);
	ulp = igraphdlamch_("precision");
	smlnum = unfl * (*n / ulp);
	first = FALSE_;
    }

/*     %-------------------------------%   
       | Initialize timing statistics  |   
       | & message level for debugging |   
       %-------------------------------% */

    igraphsecond_(&t0);
    msglvl = mnapps;
    kplusp = *kev + *np;

/*     %--------------------------------------------%   
       | Initialize Q to the identity to accumulate |   
       | the rotations and reflections              |   
       %--------------------------------------------% */

    igraphdlaset_("All", &kplusp, &kplusp, &c_b5, &c_b6, &q[q_offset], ldq);

/*     %----------------------------------------------%   
       | Quick return if there are no shifts to apply |   
       %----------------------------------------------% */

    if (*np == 0) {
	goto L9000;
    }

/*     %----------------------------------------------%   
       | Chase the bulge with the application of each |   
       | implicit shift. Each shift is applied to the |   
       | whole matrix including each block.           |   
       %----------------------------------------------% */

    cconj = FALSE_;
    i__1 = *np;
    for (jj = 1; jj <= i__1; ++jj) {
	sigmar = shiftr[jj];
	sigmai = shifti[jj];

	if (msglvl > 2) {
	    igraphivout_(&logfil, &c__1, &jj, &ndigit, "_napps: shift number.", (
		    ftnlen)21);
	    igraphdvout_(&logfil, &c__1, &sigmar, &ndigit, "_napps: The real part "
		    "of the shift ", (ftnlen)35);
	    igraphdvout_(&logfil, &c__1, &sigmai, &ndigit, "_napps: The imaginary "
		    "part of the shift ", (ftnlen)40);
	}

/*        %-------------------------------------------------%   
          | The following set of conditionals is necessary  |   
          | in order that complex conjugate pairs of shifts |   
          | are applied together or not at all.             |   
          %-------------------------------------------------% */

	if (cconj) {

/*           %-----------------------------------------%   
             | cconj = .true. means the previous shift |   
             | had non-zero imaginary part.            |   
             %-----------------------------------------% */

	    cconj = FALSE_;
	    goto L110;
	} else if (jj < *np && abs(sigmai) > 0.) {

/*           %------------------------------------%   
             | Start of a complex conjugate pair. |   
             %------------------------------------% */

	    cconj = TRUE_;
	} else if (jj == *np && abs(sigmai) > 0.) {

/*           %----------------------------------------------%   
             | The last shift has a nonzero imaginary part. |   
             | Don't apply it; thus the order of the        |   
             | compressed H is order KEV+1 since only np-1  |   
             | were applied.                                |   
             %----------------------------------------------% */

	    ++(*kev);
	    goto L110;
	}
	istart = 1;
L20:

/*        %--------------------------------------------------%   
          | if sigmai = 0 then                               |   
          |    Apply the jj-th shift ...                     |   
          | else                                             |   
          |    Apply the jj-th and (jj+1)-th together ...    |   
          |    (Note that jj < np at this point in the code) |   
          | end                                              |   
          | to the current block of H. The next do loop      |   
          | determines the current block ;                   |   
          %--------------------------------------------------% */

	i__2 = kplusp - 1;
	for (i__ = istart; i__ <= i__2; ++i__) {

/*           %----------------------------------------%   
             | Check for splitting and deflation. Use |   
             | a standard test as in the QR algorithm |   
             | REFERENCE: LAPACK subroutine dlahqr    |   
             %----------------------------------------% */

	    tst1 = (d__1 = h__[i__ + i__ * h_dim1], abs(d__1)) + (d__2 = h__[
		    i__ + 1 + (i__ + 1) * h_dim1], abs(d__2));
	    if (tst1 == 0.) {
		i__3 = kplusp - jj + 1;
		tst1 = igraphdlanhs_("1", &i__3, &h__[h_offset], ldh, &workl[1]);
	    }
/* Computing MAX */
	    d__2 = ulp * tst1;
	    if ((d__1 = h__[i__ + 1 + i__ * h_dim1], abs(d__1)) <= max(d__2,
		    smlnum)) {
		if (msglvl > 0) {
		    igraphivout_(&logfil, &c__1, &i__, &ndigit, "_napps: matrix sp"
			    "litting at row/column no.", (ftnlen)42);
		    igraphivout_(&logfil, &c__1, &jj, &ndigit, "_napps: matrix spl"
			    "itting with shift number.", (ftnlen)43);
		    igraphdvout_(&logfil, &c__1, &h__[i__ + 1 + i__ * h_dim1], &
			    ndigit, "_napps: off diagonal element.", (ftnlen)
			    29);
		}
		iend = i__;
		h__[i__ + 1 + i__ * h_dim1] = 0.;
		goto L40;
	    }
/* L30: */
	}
	iend = kplusp;
L40:

	if (msglvl > 2) {
	    igraphivout_(&logfil, &c__1, &istart, &ndigit, "_napps: Start of curre"
		    "nt block ", (ftnlen)31);
	    igraphivout_(&logfil, &c__1, &iend, &ndigit, "_napps: End of current b"
		    "lock ", (ftnlen)29);
	}

/*        %------------------------------------------------%   
          | No reason to apply a shift to block of order 1 |   
          %------------------------------------------------% */

	if (istart == iend) {
	    goto L100;
	}

/*        %------------------------------------------------------%   
          | If istart + 1 = iend then no reason to apply a       |   
          | complex conjugate pair of shifts on a 2 by 2 matrix. |   
          %------------------------------------------------------% */

	if (istart + 1 == iend && abs(sigmai) > 0.) {
	    goto L100;
	}

	h11 = h__[istart + istart * h_dim1];
	h21 = h__[istart + 1 + istart * h_dim1];
	if (abs(sigmai) <= 0.) {

/*           %---------------------------------------------%   
             | Real-valued shift ==> apply single shift QR |   
             %---------------------------------------------% */

	    f = h11 - sigmar;
	    g = h21;

	    i__2 = iend - 1;
	    for (i__ = istart; i__ <= i__2; ++i__) {

/*              %-----------------------------------------------------%   
                | Contruct the plane rotation G to zero out the bulge |   
                %-----------------------------------------------------% */

		igraphdlartg_(&f, &g, &c__, &s, &r__);
		if (i__ > istart) {

/*                 %-------------------------------------------%   
                   | The following ensures that h(1:iend-1,1), |   
                   | the first iend-2 off diagonal of elements |   
                   | H, remain non negative.                   |   
                   %-------------------------------------------% */

		    if (r__ < 0.) {
			r__ = -r__;
			c__ = -c__;
			s = -s;
		    }
		    h__[i__ + (i__ - 1) * h_dim1] = r__;
		    h__[i__ + 1 + (i__ - 1) * h_dim1] = 0.;
		}

/*              %---------------------------------------------%   
                | Apply rotation to the left of H;  H <- G'*H |   
                %---------------------------------------------% */

		i__3 = kplusp;
		for (j = i__; j <= i__3; ++j) {
		    t = c__ * h__[i__ + j * h_dim1] + s * h__[i__ + 1 + j * 
			    h_dim1];
		    h__[i__ + 1 + j * h_dim1] = -s * h__[i__ + j * h_dim1] + 
			    c__ * h__[i__ + 1 + j * h_dim1];
		    h__[i__ + j * h_dim1] = t;
/* L50: */
		}

/*              %---------------------------------------------%   
                | Apply rotation to the right of H;  H <- H*G |   
                %---------------------------------------------%   

   Computing MIN */
		i__4 = i__ + 2;
		i__3 = min(i__4,iend);
		for (j = 1; j <= i__3; ++j) {
		    t = c__ * h__[j + i__ * h_dim1] + s * h__[j + (i__ + 1) * 
			    h_dim1];
		    h__[j + (i__ + 1) * h_dim1] = -s * h__[j + i__ * h_dim1] 
			    + c__ * h__[j + (i__ + 1) * h_dim1];
		    h__[j + i__ * h_dim1] = t;
/* L60: */
		}

/*              %----------------------------------------------------%   
                | Accumulate the rotation in the matrix Q;  Q <- Q*G |   
                %----------------------------------------------------%   

   Computing MIN */
		i__4 = j + jj;
		i__3 = min(i__4,kplusp);
		for (j = 1; j <= i__3; ++j) {
		    t = c__ * q[j + i__ * q_dim1] + s * q[j + (i__ + 1) * 
			    q_dim1];
		    q[j + (i__ + 1) * q_dim1] = -s * q[j + i__ * q_dim1] + 
			    c__ * q[j + (i__ + 1) * q_dim1];
		    q[j + i__ * q_dim1] = t;
/* L70: */
		}

/*              %---------------------------%   
                | Prepare for next rotation |   
                %---------------------------% */

		if (i__ < iend - 1) {
		    f = h__[i__ + 1 + i__ * h_dim1];
		    g = h__[i__ + 2 + i__ * h_dim1];
		}
/* L80: */
	    }

/*           %-----------------------------------%   
             | Finished applying the real shift. |   
             %-----------------------------------% */

	} else {

/*           %----------------------------------------------------%   
             | Complex conjugate shifts ==> apply double shift QR |   
             %----------------------------------------------------% */

	    h12 = h__[istart + (istart + 1) * h_dim1];
	    h22 = h__[istart + 1 + (istart + 1) * h_dim1];
	    h32 = h__[istart + 2 + (istart + 1) * h_dim1];

/*           %---------------------------------------------------------%   
             | Compute 1st column of (H - shift*I)*(H - conj(shift)*I) |   
             %---------------------------------------------------------% */

	    s = sigmar * 2.f;
	    t = igraphdlapy2_(&sigmar, &sigmai);
	    u[0] = (h11 * (h11 - s) + t * t) / h21 + h12;
	    u[1] = h11 + h22 - s;
	    u[2] = h32;

	    i__2 = iend - 1;
	    for (i__ = istart; i__ <= i__2; ++i__) {

/* Computing MIN */
		i__3 = 3, i__4 = iend - i__ + 1;
		nr = min(i__3,i__4);

/*              %-----------------------------------------------------%   
                | Construct Householder reflector G to zero out u(1). |   
                | G is of the form I - tau*( 1 u )' * ( 1 u' ).       |   
                %-----------------------------------------------------% */

		igraphdlarfg_(&nr, u, &u[1], &c__1, &tau);

		if (i__ > istart) {
		    h__[i__ + (i__ - 1) * h_dim1] = u[0];
		    h__[i__ + 1 + (i__ - 1) * h_dim1] = 0.;
		    if (i__ < iend - 1) {
			h__[i__ + 2 + (i__ - 1) * h_dim1] = 0.;
		    }
		}
		u[0] = 1.;

/*              %--------------------------------------%   
                | Apply the reflector to the left of H |   
                %--------------------------------------% */

		i__3 = kplusp - i__ + 1;
		igraphdlarf_("Left", &nr, &i__3, u, &c__1, &tau, &h__[i__ + i__ * 
			h_dim1], ldh, &workl[1]);

/*              %---------------------------------------%   
                | Apply the reflector to the right of H |   
                %---------------------------------------%   

   Computing MIN */
		i__3 = i__ + 3;
		ir = min(i__3,iend);
		igraphdlarf_("Right", &ir, &nr, u, &c__1, &tau, &h__[i__ * h_dim1 + 
			1], ldh, &workl[1]);

/*              %-----------------------------------------------------%   
                | Accumulate the reflector in the matrix Q;  Q <- Q*G |   
                %-----------------------------------------------------% */

		igraphdlarf_("Right", &kplusp, &nr, u, &c__1, &tau, &q[i__ * q_dim1 
			+ 1], ldq, &workl[1]);

/*              %----------------------------%   
                | Prepare for next reflector |   
                %----------------------------% */

		if (i__ < iend - 1) {
		    u[0] = h__[i__ + 1 + i__ * h_dim1];
		    u[1] = h__[i__ + 2 + i__ * h_dim1];
		    if (i__ < iend - 2) {
			u[2] = h__[i__ + 3 + i__ * h_dim1];
		    }
		}

/* L90: */
	    }

/*           %--------------------------------------------%   
             | Finished applying a complex pair of shifts |   
             | to the current block                       |   
             %--------------------------------------------% */

	}

L100:

/*        %---------------------------------------------------------%   
          | Apply the same shift to the next block if there is any. |   
          %---------------------------------------------------------% */

	istart = iend + 1;
	if (iend < kplusp) {
	    goto L20;
	}

/*        %---------------------------------------------%   
          | Loop back to the top to get the next shift. |   
          %---------------------------------------------% */

L110:
	;
    }

/*     %--------------------------------------------------%   
       | Perform a similarity transformation that makes   |   
       | sure that H will have non negative sub diagonals |   
       %--------------------------------------------------% */

    i__1 = *kev;
    for (j = 1; j <= i__1; ++j) {
	if (h__[j + 1 + j * h_dim1] < 0.) {
	    i__2 = kplusp - j + 1;
	    igraphdscal_(&i__2, &c_b43, &h__[j + 1 + j * h_dim1], ldh);
/* Computing MIN */
	    i__3 = j + 2;
	    i__2 = min(i__3,kplusp);
	    igraphdscal_(&i__2, &c_b43, &h__[(j + 1) * h_dim1 + 1], &c__1);
/* Computing MIN */
	    i__3 = j + *np + 1;
	    i__2 = min(i__3,kplusp);
	    igraphdscal_(&i__2, &c_b43, &q[(j + 1) * q_dim1 + 1], &c__1);
	}
/* L120: */
    }

    i__1 = *kev;
    for (i__ = 1; i__ <= i__1; ++i__) {

/*        %--------------------------------------------%   
          | Final check for splitting and deflation.   |   
          | Use a standard test as in the QR algorithm |   
          | REFERENCE: LAPACK subroutine dlahqr        |   
          %--------------------------------------------% */

	tst1 = (d__1 = h__[i__ + i__ * h_dim1], abs(d__1)) + (d__2 = h__[i__ 
		+ 1 + (i__ + 1) * h_dim1], abs(d__2));
	if (tst1 == 0.) {
	    tst1 = igraphdlanhs_("1", kev, &h__[h_offset], ldh, &workl[1]);
	}
/* Computing MAX */
	d__1 = ulp * tst1;
	if (h__[i__ + 1 + i__ * h_dim1] <= max(d__1,smlnum)) {
	    h__[i__ + 1 + i__ * h_dim1] = 0.;
	}
/* L130: */
    }

/*     %-------------------------------------------------%   
       | Compute the (kev+1)-st column of (V*Q) and      |   
       | temporarily store the result in WORKD(N+1:2*N). |   
       | This is needed in the residual update since we  |   
       | cannot GUARANTEE that the corresponding entry   |   
       | of H would be zero as in exact arithmetic.      |   
       %-------------------------------------------------% */

    if (h__[*kev + 1 + *kev * h_dim1] > 0.) {
	igraphdgemv_("N", n, &kplusp, &c_b6, &v[v_offset], ldv, &q[(*kev + 1) * 
		q_dim1 + 1], &c__1, &c_b5, &workd[*n + 1], &c__1);
    }

/*     %----------------------------------------------------------%   
       | Compute column 1 to kev of (V*Q) in backward order       |   
       | taking advantage of the upper Hessenberg structure of Q. |   
       %----------------------------------------------------------% */

    i__1 = *kev;
    for (i__ = 1; i__ <= i__1; ++i__) {
	i__2 = kplusp - i__ + 1;
	igraphdgemv_("N", n, &i__2, &c_b6, &v[v_offset], ldv, &q[(*kev - i__ + 1) * 
		q_dim1 + 1], &c__1, &c_b5, &workd[1], &c__1);
	igraphdcopy_(n, &workd[1], &c__1, &v[(kplusp - i__ + 1) * v_dim1 + 1], &
		c__1);
/* L140: */
    }

/*     %-------------------------------------------------%   
       |  Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). |   
       %-------------------------------------------------% */

    igraphdlacpy_("A", n, kev, &v[(kplusp - *kev + 1) * v_dim1 + 1], ldv, &v[
	    v_offset], ldv);

/*     %--------------------------------------------------------------%   
       | Copy the (kev+1)-st column of (V*Q) in the appropriate place |   
       %--------------------------------------------------------------% */

    if (h__[*kev + 1 + *kev * h_dim1] > 0.) {
	igraphdcopy_(n, &workd[*n + 1], &c__1, &v[(*kev + 1) * v_dim1 + 1], &c__1);
    }

/*     %-------------------------------------%   
       | Update the residual vector:         |   
       |    r <- sigmak*r + betak*v(:,kev+1) |   
       | where                               |   
       |    sigmak = (e_{kplusp}'*Q)*e_{kev} |   
       |    betak = e_{kev+1}'*H*e_{kev}     |   
       %-------------------------------------% */

    igraphdscal_(n, &q[kplusp + *kev * q_dim1], &resid[1], &c__1);
    if (h__[*kev + 1 + *kev * h_dim1] > 0.) {
	igraphdaxpy_(n, &h__[*kev + 1 + *kev * h_dim1], &v[(*kev + 1) * v_dim1 + 1],
		 &c__1, &resid[1], &c__1);
    }

    if (msglvl > 1) {
	igraphdvout_(&logfil, &c__1, &q[kplusp + *kev * q_dim1], &ndigit, "_napps:"
		" sigmak = (e_{kev+p}^T*Q)*e_{kev}", (ftnlen)40);
	igraphdvout_(&logfil, &c__1, &h__[*kev + 1 + *kev * h_dim1], &ndigit, "_na"
		"pps: betak = e_{kev+1}^T*H*e_{kev}", (ftnlen)37);
	igraphivout_(&logfil, &c__1, kev, &ndigit, "_napps: Order of the final Hes"
		"senberg matrix ", (ftnlen)45);
	if (msglvl > 2) {
	    igraphdmout_(&logfil, kev, kev, &h__[h_offset], ldh, &ndigit, "_napps:"
		    " updated Hessenberg matrix H for next iteration", (ftnlen)
		    54);
	}

    }

L9000:
    igraphsecond_(&t1);
    tnapps += t1 - t0;

    return 0;

/*     %---------------%   
       | End of dnapps |   
       %---------------% */

} /* igraphdnapps_ */

