Subroutine */ int igraphdgetv0_(integer *ido, char *bmat, integer *itry, logical
*initv, integer *n, integer *j, doublereal *v, integer *ldv,
doublereal *resid, doublereal *rnorm, integer *ipntr, doublereal *
workd, integer *ierr)
{
/* Initialized data */
IGRAPH_F77_SAVE logical inits = TRUE_;
/* System generated locals */
integer v_dim1, v_offset, i__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real t0, t1, t2, t3;
integer jj, nbx = 0;
extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
IGRAPH_F77_SAVE integer iter;
IGRAPH_F77_SAVE logical orth;
integer nopx = 0;
extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
IGRAPH_F77_SAVE integer iseed[4];
extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
integer idist;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
IGRAPH_F77_SAVE logical first;
real tmvbx = 0;
extern /* Subroutine */ int igraphdvout_(integer *, integer *, doublereal *,
integer *, char *, ftnlen);
integer mgetv0 = 0;
real tgetv0 = 0;
IGRAPH_F77_SAVE doublereal rnorm0;
extern /* Subroutine */ int igraphsecond_(real *);
integer logfil, ndigit;
extern /* Subroutine */ int igraphdlarnv_(integer *, integer *, integer *,
doublereal *);
IGRAPH_F77_SAVE integer msglvl;
real tmvopx = 0;
/* %----------------------------------------------------%
| Include files for debugging and timing information |
%----------------------------------------------------%
%------------------%
| Scalar Arguments |
%------------------%
%-----------------%
| Array Arguments |
%-----------------%
%------------%
| Parameters |
%------------%
%------------------------%
| Local Scalars & Arrays |
%------------------------%
%----------------------%
| External Subroutines |
%----------------------%
%--------------------%
| External Functions |
%--------------------%
%---------------------%
| Intrinsic Functions |
%---------------------%
%-----------------%
| Data Statements |
%-----------------%
Parameter adjustments */
--workd;
--resid;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--ipntr;
/* Function Body
%-----------------------%
| Executable Statements |
%-----------------------%
%-----------------------------------%
| Initialize the seed of the LAPACK |
| random number generator |
%-----------------------------------% */
if (inits) {
iseed[0] = 1;
iseed[1] = 3;
iseed[2] = 5;
iseed[3] = 7;
inits = FALSE_;
}
if (*ido == 0) {
/* %-------------------------------%
| Initialize timing statistics |
| & message level for debugging |
%-------------------------------% */
igraphsecond_(&t0);
msglvl = mgetv0;
*ierr = 0;
iter = 0;
first = FALSE_;
orth = FALSE_;
/* %-----------------------------------------------------%
| Possibly generate a random starting vector in RESID |
| Use a LAPACK random number generator used by the |
| matrix generation routines. |
| idist = 1: uniform (0,1) distribution; |
| idist = 2: uniform (-1,1) distribution; |
| idist = 3: normal (0,1) distribution; |
%-----------------------------------------------------% */
if (! (*initv)) {
idist = 2;
igraphdlarnv_(&idist, iseed, n, &resid[1]);
}
/* %----------------------------------------------------------%
| Force the starting vector into the range of OP to handle |
| the generalized problem when B is possibly (singular). |
%----------------------------------------------------------% */
igraphsecond_(&t2);
if (*(unsigned char *)bmat == 'G') {
++nopx;
ipntr[1] = 1;
ipntr[2] = *n + 1;
igraphdcopy_(n, &resid[1], &c__1, &workd[1], &c__1);
*ido = -1;
goto L9000;
}
}
/* %-----------------------------------------%
| Back from computing OP*(initial-vector) |
%-----------------------------------------% */
if (first) {
goto L20;
}
/* %-----------------------------------------------%
| Back from computing B*(orthogonalized-vector) |
%-----------------------------------------------% */
if (orth) {
goto L40;
}
if (*(unsigned char *)bmat == 'G') {
igraphsecond_(&t3);
tmvopx += t3 - t2;
}
/* %------------------------------------------------------%
| Starting vector is now in the range of OP; r = OP*r; |
| Compute B-norm of starting vector. |
%------------------------------------------------------% */
igraphsecond_(&t2);
first = TRUE_;
if (*(unsigned char *)bmat == 'G') {
++nbx;
igraphdcopy_(n, &workd[*n + 1], &c__1, &resid[1], &c__1);
ipntr[1] = *n + 1;
ipntr[2] = 1;
*ido = 2;
goto L9000;
} else if (*(unsigned char *)bmat == 'I') {
igraphdcopy_(n, &resid[1], &c__1, &workd[1], &c__1);
}
L20:
if (*(unsigned char *)bmat == 'G') {
igraphsecond_(&t3);
tmvbx += t3 - t2;
}
first = FALSE_;
if (*(unsigned char *)bmat == 'G') {
rnorm0 = igraphddot_(n, &resid[1], &c__1, &workd[1], &c__1);
rnorm0 = sqrt((abs(rnorm0)));
} else if (*(unsigned char *)bmat == 'I') {
rnorm0 = igraphdnrm2_(n, &resid[1], &c__1);
}
*rnorm = rnorm0;
/* %---------------------------------------------%
| Exit if this is the very first Arnoldi step |
%---------------------------------------------% */
if (*j == 1) {
goto L50;
}
/* %----------------------------------------------------------------
| Otherwise need to B-orthogonalize the starting vector against |
| the current Arnoldi basis using Gram-Schmidt with iter. ref. |
| This is the case where an invariant subspace is encountered |
| in the middle of the Arnoldi factorization. |
| |
| s = V^{T}*B*r; r = r - V*s; |
| |
| Stopping criteria used for iter. ref. is discussed in |
| Parlett's book, page 107 and in Gragg & Reichel TOMS paper. |
%---------------------------------------------------------------% */
orth = TRUE_;
L30:
i__1 = *j - 1;
igraphdgemv_("T", n, &i__1, &c_b24, &v[v_offset], ldv, &workd[1], &c__1, &c_b26,
&workd[*n + 1], &c__1);
i__1 = *j - 1;
igraphdgemv_("N", n, &i__1, &c_b29, &v[v_offset], ldv, &workd[*n + 1], &c__1, &
c_b24, &resid[1], &c__1);
/* %----------------------------------------------------------%
| Compute the B-norm of the orthogonalized starting vector |
%----------------------------------------------------------% */
igraphsecond_(&t2);
if (*(unsigned char *)bmat == 'G') {
++nbx;
igraphdcopy_(n, &resid[1], &c__1, &workd[*n + 1], &c__1);
ipntr[1] = *n + 1;
ipntr[2] = 1;
*ido = 2;
goto L9000;
} else if (*(unsigned char *)bmat == 'I') {
igraphdcopy_(n, &resid[1], &c__1, &workd[1], &c__1);
}
L40:
if (*(unsigned char *)bmat == 'G') {
igraphsecond_(&t3);
tmvbx += t3 - t2;
}
if (*(unsigned char *)bmat == 'G') {
*rnorm = igraphddot_(n, &resid[1], &c__1, &workd[1], &c__1);
*rnorm = sqrt((abs(*rnorm)));
} else if (*(unsigned char *)bmat == 'I') {
*rnorm = igraphdnrm2_(n, &resid[1], &c__1);
}
/* %--------------------------------------%
| Check for further orthogonalization. |
%--------------------------------------% */
if (msglvl > 2) {
igraphdvout_(&logfil, &c__1, &rnorm0, &ndigit, "_getv0: re-orthonalization"
" ; rnorm0 is", (ftnlen)38);
igraphdvout_(&logfil, &c__1, rnorm, &ndigit, "_getv0: re-orthonalization ;"
" rnorm is", (ftnlen)37);
}
if (*rnorm > rnorm0 * .717f) {
goto L50;
}
++iter;
if (iter <= 1) {
/* %-----------------------------------%
| Perform iterative refinement step |
%-----------------------------------% */
rnorm0 = *rnorm;
goto L30;
} else {
/* %------------------------------------%
| Iterative refinement step "failed" |
%------------------------------------% */
i__1 = *n;
for (jj = 1; jj <= i__1; ++jj) {
resid[jj] = 0.;
/* L45: */
}
*rnorm = 0.;
*ierr = -1;
}
L50:
if (msglvl > 0) {
igraphdvout_(&logfil, &c__1, rnorm, &ndigit, "_getv0: B-norm of initial / "
"restarted starting vector", (ftnlen)53);
}
if (msglvl > 2) {
igraphdvout_(&logfil, n, &resid[1], &ndigit, "_getv0: initial / restarted "
"starting vector", (ftnlen)43);
}
*ido = 99;
igraphsecond_(&t1);
tgetv0 += t1 - t0;
L9000:
return 0;
/* %---------------%
| End of dgetv0 |
%---------------% */
} /* igraphdgetv0_ */
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];
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_ */
/* ----------------------------------------------------------------------- */
/* Subroutine */ int igraphdneupd_(logical *rvec, char *howmny, logical *select,
doublereal *dr, doublereal *di, doublereal *z__, integer *ldz,
doublereal *sigmar, doublereal *sigmai, doublereal *workev, char *
bmat, integer *n, char *which, integer *nev, doublereal *tol,
doublereal *resid, integer *ncv, doublereal *v, integer *ldv, integer
*iparam, integer *ipntr, doublereal *workd, doublereal *workl,
integer *lworkl, integer *info)
{
/* System generated locals */
integer v_dim1, v_offset, z_dim1, z_offset, i__1;
doublereal d__1, d__2;
/* Builtin functions */
double igraphpow_dd(doublereal *, doublereal *);
integer igraphs_cmp(char *, char *, ftnlen, ftnlen);
/* Subroutine */ int igraphs_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer j, k, ih, jj, np;
static doublereal vl[1] /* was [1][1] */;
static integer ibd, ldh, ldq, iri;
static doublereal sep;
static integer irr, wri, wrr;
extern /* Subroutine */ int igraphdger_(integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
static integer mode;
static doublereal eps23;
static integer ierr;
static doublereal temp;
static integer iwev;
static char type__[6];
extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
static doublereal temp1;
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
integer *);
static integer ihbds, iconj;
extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
static doublereal conds;
static logical reord;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer nconv;
extern /* Subroutine */ int igraphdtrmm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *), igraphdmout_(
integer *, integer *, integer *, doublereal *, integer *, integer
*, char *);
static integer iwork[1];
static doublereal rnorm;
static integer ritzi;
extern /* Subroutine */ int igraphdvout_(integer *, integer *, doublereal *,
integer *, char *), igraphivout_(integer *, integer *, integer *
, integer *, char *);
static integer ritzr;
extern /* Subroutine */ int igraphdgeqr2_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
extern doublereal igraphdlapy2_(doublereal *, doublereal *);
extern /* Subroutine */ int igraphdorm2r_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
extern doublereal igraphdlamch_(char *);
static integer iheigi, iheigr, bounds, invsub, iuptri, msglvl, outncv,
ishift, numcnv;
extern /* Subroutine */ int igraphdlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
igraphdlahqr_(logical *, logical *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *, doublereal *, integer *, integer *), igraphdlaset_(char *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *), igraphdtrevc_(char *, char *, logical *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *
), igraphdtrsen_(char *, char *, logical *, integer *, doublereal
*, integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
integer *, integer *, integer *), igraphdngets_(integer
*, char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *);
/* %----------------------------------------------------% */
/* | Include files for debugging and timing information | */
/* %----------------------------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %---------------------------------% */
/* | See debug.doc for documentation | */
/* %---------------------------------% */
/* %------------------% */
/* | Scalar Arguments | */
/* %------------------% */
/* %--------------------------------% */
/* | See stat.doc for documentation | */
/* %--------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: stat.h SID: 2.2 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %-----------------% */
/* | Array Arguments | */
/* %-----------------% */
/* %------------% */
/* | Parameters | */
/* %------------% */
/* %---------------% */
/* | Local Scalars | */
/* %---------------% */
/* %----------------------% */
/* | External Subroutines | */
/* %----------------------% */
/* %--------------------% */
/* | External Functions | */
/* %--------------------% */
/* %---------------------% */
/* | Intrinsic Functions | */
/* %---------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* %------------------------% */
/* | Set default parameters | */
/* %------------------------% */
/* Parameter adjustments */
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--workd;
--resid;
--di;
--dr;
--workev;
--select;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--iparam;
--ipntr;
--workl;
/* Function Body */
msglvl = debug_1.mneupd;
mode = iparam[7];
nconv = iparam[5];
*info = 0;
/* %---------------------------------% */
/* | Get machine dependent constant. | */
/* %---------------------------------% */
eps23 = igraphdlamch_("Epsilon-Machine");
eps23 = igraphpow_dd(&eps23, &c_b3);
/* %--------------% */
/* | Quick return | */
/* %--------------% */
ierr = 0;
if (nconv <= 0) {
ierr = -14;
} else if (*n <= 0) {
ierr = -1;
} else if (*nev <= 0) {
ierr = -2;
} else if (*ncv <= *nev + 1 || *ncv > *n) {
ierr = -3;
} else if (igraphs_cmp(which, "LM", (ftnlen)2, (ftnlen)2) != 0 && igraphs_cmp(which,
"SM", (ftnlen)2, (ftnlen)2) != 0 && igraphs_cmp(which, "LR", (ftnlen)2, (ftnlen)2
) != 0 && igraphs_cmp(which, "SR", (ftnlen)2, (ftnlen)2) != 0
&& igraphs_cmp(which, "LI", (ftnlen)2, (ftnlen)2) != 0 && igraphs_cmp(which,
"SI", (ftnlen)2, (ftnlen)2) != 0) {
ierr = -5;
} else if (*(unsigned char *)bmat != 'I' && *(unsigned char *)bmat != 'G')
{
ierr = -6;
} else /* if(complicated condition) */ {
/* Computing 2nd power */
i__1 = *ncv;
if (*lworkl < i__1 * i__1 * 3 + *ncv * 6) {
ierr = -7;
} else if (*(unsigned char *)howmny != 'A' && *(unsigned char *)
howmny != 'P' && *(unsigned char *)howmny != 'S' && *rvec) {
ierr = -13;
} else if (*(unsigned char *)howmny == 'S') {
ierr = -12;
}
}
if (mode == 1 || mode == 2) {
igraphs_copy(type__, "REGULR", (ftnlen)6, (ftnlen)6);
} else if (mode == 3 && *sigmai == 0.) {
igraphs_copy(type__, "SHIFTI", (ftnlen)6, (ftnlen)6);
} else if (mode == 3) {
igraphs_copy(type__, "REALPT", (ftnlen)6, (ftnlen)6);
} else if (mode == 4) {
igraphs_copy(type__, "IMAGPT", (ftnlen)6, (ftnlen)6);
} else {
ierr = -10;
}
if (mode == 1 && *(unsigned char *)bmat == 'G') {
ierr = -11;
}
/* %------------% */
/* | Error Exit | */
/* %------------% */
if (ierr != 0) {
*info = ierr;
goto L9000;
}
/* %--------------------------------------------------------% */
/* | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | */
/* | etc... and the remaining workspace. | */
/* | Also update pointer to be used on output. | */
/* | Memory is laid out as follows: | */
/* | workl(1:ncv*ncv) := generated Hessenberg matrix | */
/* | workl(ncv*ncv+1:ncv*ncv+2*ncv) := real and imaginary | */
/* | parts of ritz values | */
/* | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds | */
/* %--------------------------------------------------------% */
/* %-----------------------------------------------------------% */
/* | The following is used and set by DNEUPD . | */
/* | workl(ncv*ncv+3*ncv+1:ncv*ncv+4*ncv) := The untransformed | */
/* | real part of the Ritz values. | */
/* | workl(ncv*ncv+4*ncv+1:ncv*ncv+5*ncv) := The untransformed | */
/* | imaginary part of the Ritz values. | */
/* | workl(ncv*ncv+5*ncv+1:ncv*ncv+6*ncv) := The untransformed | */
/* | error bounds of the Ritz values | */
/* | workl(ncv*ncv+6*ncv+1:2*ncv*ncv+6*ncv) := Holds the upper | */
/* | quasi-triangular matrix for H | */
/* | workl(2*ncv*ncv+6*ncv+1: 3*ncv*ncv+6*ncv) := Holds the | */
/* | associated matrix representation of the invariant | */
/* | subspace for H. | */
/* | GRAND total of NCV * ( 3 * NCV + 6 ) locations. | */
/* %-----------------------------------------------------------% */
ih = ipntr[5];
ritzr = ipntr[6];
ritzi = ipntr[7];
bounds = ipntr[8];
ldh = *ncv;
ldq = *ncv;
iheigr = bounds + ldh;
iheigi = iheigr + ldh;
ihbds = iheigi + ldh;
iuptri = ihbds + ldh;
invsub = iuptri + ldh * *ncv;
ipntr[9] = iheigr;
ipntr[10] = iheigi;
ipntr[11] = ihbds;
ipntr[12] = iuptri;
ipntr[13] = invsub;
wrr = 1;
wri = *ncv + 1;
iwev = wri + *ncv;
/* %-----------------------------------------% */
/* | irr points to the REAL part of the Ritz | */
/* | values computed by _neigh before | */
/* | exiting _naup2. | */
/* | iri points to the IMAGINARY part of the | */
/* | Ritz values computed by _neigh | */
/* | before exiting _naup2. | */
/* | ibd points to the Ritz estimates | */
/* | computed by _neigh before exiting | */
/* | _naup2. | */
/* %-----------------------------------------% */
irr = ipntr[14] + *ncv * *ncv;
iri = irr + *ncv;
ibd = iri + *ncv;
/* %------------------------------------% */
/* | RNORM is B-norm of the RESID(1:N). | */
/* %------------------------------------% */
rnorm = workl[ih + 2];
workl[ih + 2] = 0.;
if (msglvl > 2) {
igraphdvout_(&debug_1.logfil, ncv, &workl[irr], &debug_1.ndigit, "_neupd: "
"Real part of Ritz values passed in from _NAUPD.");
igraphdvout_(&debug_1.logfil, ncv, &workl[iri], &debug_1.ndigit, "_neupd: "
"Imag part of Ritz values passed in from _NAUPD.");
igraphdvout_(&debug_1.logfil, ncv, &workl[ibd], &debug_1.ndigit, "_neupd: "
"Ritz estimates passed in from _NAUPD.");
}
if (*rvec) {
reord = FALSE_;
/* %---------------------------------------------------% */
/* | Use the temporary bounds array to store indices | */
/* | These will be used to mark the select array later | */
/* %---------------------------------------------------% */
i__1 = *ncv;
for (j = 1; j <= i__1; ++j) {
workl[bounds + j - 1] = (doublereal) j;
select[j] = FALSE_;
/* L10: */
}
/* %-------------------------------------% */
/* | Select the wanted Ritz values. | */
/* | Sort the Ritz values so that the | */
/* | wanted ones appear at the tailing | */
/* | NEV positions of workl(irr) and | */
/* | workl(iri). Move the corresponding | */
/* | error estimates in workl(bound) | */
/* | accordingly. | */
/* %-------------------------------------% */
np = *ncv - *nev;
ishift = 0;
igraphdngets_(&ishift, which, nev, &np, &workl[irr], &workl[iri], &workl[
bounds], &workl[1], &workl[np + 1]);
if (msglvl > 2) {
igraphdvout_(&debug_1.logfil, ncv, &workl[irr], &debug_1.ndigit, "_neu"
"pd: Real part of Ritz values after calling _NGETS.");
igraphdvout_(&debug_1.logfil, ncv, &workl[iri], &debug_1.ndigit, "_neu"
"pd: Imag part of Ritz values after calling _NGETS.");
igraphdvout_(&debug_1.logfil, ncv, &workl[bounds], &debug_1.ndigit,
"_neupd: Ritz value indices after calling _NGETS.");
}
/* %-----------------------------------------------------% */
/* | Record indices of the converged wanted Ritz values | */
/* | Mark the select array for possible reordering | */
/* %-----------------------------------------------------% */
numcnv = 0;
i__1 = *ncv;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__1 = eps23, d__2 = igraphdlapy2_(&workl[irr + *ncv - j], &workl[iri +
*ncv - j]);
temp1 = max(d__1,d__2);
jj = (integer) workl[bounds + *ncv - j];
if (numcnv < nconv && workl[ibd + jj - 1] <= *tol * temp1) {
select[jj] = TRUE_;
++numcnv;
if (jj > *nev) {
reord = TRUE_;
}
}
/* L11: */
}
/* %-----------------------------------------------------------% */
/* | Check the count (numcnv) of converged Ritz values with | */
/* | the number (nconv) reported by igraphdnaupd. If these two | */
/* | are different then there has probably been an error | */
/* | caused by incorrect passing of the igraphdnaupd data. | */
/* %-----------------------------------------------------------% */
if (msglvl > 2) {
igraphivout_(&debug_1.logfil, &c__1, &numcnv, &debug_1.ndigit, "_neupd"
": Number of specified eigenvalues");
igraphivout_(&debug_1.logfil, &c__1, &nconv, &debug_1.ndigit, "_neupd:"
" Number of \"converged\" eigenvalues");
}
if (numcnv != nconv) {
*info = -15;
goto L9000;
}
/* %-----------------------------------------------------------% */
/* | Call LAPACK routine dlahqr to compute the real Schur form | */
/* | of the upper Hessenberg matrix returned by DNAUPD . | */
/* | Make a copy of the upper Hessenberg matrix. | */
/* | Initialize the Schur vector matrix Q to the identity. | */
/* %-----------------------------------------------------------% */
i__1 = ldh * *ncv;
igraphdcopy_(&i__1, &workl[ih], &c__1, &workl[iuptri], &c__1);
igraphdlaset_("All", ncv, ncv, &c_b37, &c_b38, &workl[invsub], &ldq);
igraphdlahqr_(&c_true, &c_true, ncv, &c__1, ncv, &workl[iuptri], &ldh, &
workl[iheigr], &workl[iheigi], &c__1, ncv, &workl[invsub], &
ldq, &ierr);
igraphdcopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &c__1);
if (ierr != 0) {
*info = -8;
goto L9000;
}
if (msglvl > 1) {
igraphdvout_(&debug_1.logfil, ncv, &workl[iheigr], &debug_1.ndigit,
"_neupd: Real part of the eigenvalues of H");
igraphdvout_(&debug_1.logfil, ncv, &workl[iheigi], &debug_1.ndigit,
"_neupd: Imaginary part of the Eigenvalues of H");
igraphdvout_(&debug_1.logfil, ncv, &workl[ihbds], &debug_1.ndigit,
"_neupd: Last row of the Schur vector matrix");
if (msglvl > 3) {
igraphdmout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldh, &
debug_1.ndigit, "_neupd: The upper quasi-triangular "
"matrix ");
}
}
if (reord) {
/* %-----------------------------------------------------% */
/* | Reorder the computed upper quasi-triangular matrix. | */
/* %-----------------------------------------------------% */
igraphdtrsen_("None", "V", &select[1], ncv, &workl[iuptri], &ldh, &
workl[invsub], &ldq, &workl[iheigr], &workl[iheigi], &
nconv, &conds, &sep, &workl[ihbds], ncv, iwork, &c__1, &
ierr);
if (ierr == 1) {
*info = 1;
goto L9000;
}
if (msglvl > 2) {
igraphdvout_(&debug_1.logfil, ncv, &workl[iheigr], &debug_1.ndigit,
"_neupd: Real part of the eigenvalues of H--reordered");
igraphdvout_(&debug_1.logfil, ncv, &workl[iheigi], &debug_1.ndigit,
"_neupd: Imag part of the eigenvalues of H--reordered");
if (msglvl > 3) {
igraphdmout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldq, &
debug_1.ndigit, "_neupd: Quasi-triangular matrix"
" after re-ordering");
}
}
}
/* %---------------------------------------% */
/* | Copy the last row of the Schur vector | */
/* | into workl(ihbds). This will be used | */
/* | to compute the Ritz estimates of | */
/* | converged Ritz values. | */
/* %---------------------------------------% */
igraphdcopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &c__1);
/* %----------------------------------------------------% */
/* | Place the computed eigenvalues of H into DR and DI | */
/* | if a spectral transformation was not used. | */
/* %----------------------------------------------------% */
if (igraphs_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
igraphdcopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
igraphdcopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
}
/* %----------------------------------------------------------% */
/* | Compute the QR factorization of the matrix representing | */
/* | the wanted invariant subspace located in the first NCONV | */
/* | columns of workl(invsub,ldq). | */
/* %----------------------------------------------------------% */
igraphdgeqr2_(ncv, &nconv, &workl[invsub], &ldq, &workev[1], &workev[*ncv +
1], &ierr);
/* %---------------------------------------------------------% */
/* | * Postmultiply V by Q using dorm2r . | */
/* | * Copy the first NCONV columns of VQ into Z. | */
/* | * Postmultiply Z by R. | */
/* | The N by NCONV matrix Z is now a matrix representation | */
/* | of the approximate invariant subspace associated with | */
/* | the Ritz values in workl(iheigr) and workl(iheigi) | */
/* | The first NCONV columns of V are now approximate Schur | */
/* | vectors associated with the real upper quasi-triangular | */
/* | matrix of order NCONV in workl(iuptri) | */
/* %---------------------------------------------------------% */
igraphdorm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[invsub], &ldq,
&workev[1], &v[v_offset], ldv, &workd[*n + 1], &ierr);
igraphdlacpy_("All", n, &nconv, &v[v_offset], ldv, &z__[z_offset], ldz);
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
/* %---------------------------------------------------% */
/* | Perform both a column and row scaling if the | */
/* | diagonal element of workl(invsub,ldq) is negative | */
/* | I'm lazy and don't take advantage of the upper | */
/* | quasi-triangular form of workl(iuptri,ldq) | */
/* | Note that since Q is orthogonal, R is a diagonal | */
/* | matrix consisting of plus or minus ones | */
/* %---------------------------------------------------% */
if (workl[invsub + (j - 1) * ldq + j - 1] < 0.) {
igraphdscal_(&nconv, &c_b64, &workl[iuptri + j - 1], &ldq);
igraphdscal_(&nconv, &c_b64, &workl[iuptri + (j - 1) * ldq], &c__1);
}
/* L20: */
}
if (*(unsigned char *)howmny == 'A') {
/* %--------------------------------------------% */
/* | Compute the NCONV wanted eigenvectors of T | */
/* | located in workl(iuptri,ldq). | */
/* %--------------------------------------------% */
i__1 = *ncv;
for (j = 1; j <= i__1; ++j) {
if (j <= nconv) {
select[j] = TRUE_;
} else {
select[j] = FALSE_;
}
/* L30: */
}
igraphdtrevc_("Right", "Select", &select[1], ncv, &workl[iuptri], &ldq,
vl, &c__1, &workl[invsub], &ldq, ncv, &outncv, &workev[1],
&ierr);
if (ierr != 0) {
*info = -9;
goto L9000;
}
/* %------------------------------------------------% */
/* | Scale the returning eigenvectors so that their | */
/* | Euclidean norms are all one. LAPACK subroutine | */
/* | igraphdtrevc returns each eigenvector normalized so | */
/* | that the element of largest magnitude has | */
/* | magnitude 1; | */
/* %------------------------------------------------% */
iconj = 0;
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
if (workl[iheigi + j - 1] == 0.) {
/* %----------------------% */
/* | real eigenvalue case | */
/* %----------------------% */
temp = igraphdnrm2_(ncv, &workl[invsub + (j - 1) * ldq], &c__1);
d__1 = 1. / temp;
igraphdscal_(ncv, &d__1, &workl[invsub + (j - 1) * ldq], &c__1);
} else {
/* %-------------------------------------------% */
/* | Complex conjugate pair case. Note that | */
/* | since the real and imaginary part of | */
/* | the eigenvector are stored in consecutive | */
/* | columns, we further normalize by the | */
/* | square root of two. | */
/* %-------------------------------------------% */
if (iconj == 0) {
d__1 = igraphdnrm2_(ncv, &workl[invsub + (j - 1) * ldq], &
c__1);
d__2 = igraphdnrm2_(ncv, &workl[invsub + j * ldq], &c__1);
temp = igraphdlapy2_(&d__1, &d__2);
d__1 = 1. / temp;
igraphdscal_(ncv, &d__1, &workl[invsub + (j - 1) * ldq], &
c__1);
d__1 = 1. / temp;
igraphdscal_(ncv, &d__1, &workl[invsub + j * ldq], &c__1);
iconj = 1;
} else {
iconj = 0;
}
}
/* L40: */
}
igraphdgemv_("T", ncv, &nconv, &c_b38, &workl[invsub], &ldq, &workl[
ihbds], &c__1, &c_b37, &workev[1], &c__1);
iconj = 0;
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
if (workl[iheigi + j - 1] != 0.) {
/* %-------------------------------------------% */
/* | Complex conjugate pair case. Note that | */
/* | since the real and imaginary part of | */
/* | the eigenvector are stored in consecutive | */
/* %-------------------------------------------% */
if (iconj == 0) {
workev[j] = igraphdlapy2_(&workev[j], &workev[j + 1]);
workev[j + 1] = workev[j];
iconj = 1;
} else {
iconj = 0;
}
}
/* L45: */
}
if (msglvl > 2) {
igraphdcopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &
c__1);
igraphdvout_(&debug_1.logfil, ncv, &workl[ihbds], &debug_1.ndigit,
"_neupd: Last row of the eigenvector matrix for T");
if (msglvl > 3) {
igraphdmout_(&debug_1.logfil, ncv, ncv, &workl[invsub], &ldq, &
debug_1.ndigit, "_neupd: The eigenvector matrix "
"for T");
}
}
/* %---------------------------------------% */
/* | Copy Ritz estimates into workl(ihbds) | */
/* %---------------------------------------% */
igraphdcopy_(&nconv, &workev[1], &c__1, &workl[ihbds], &c__1);
/* %---------------------------------------------------------% */
/* | Compute the QR factorization of the eigenvector matrix | */
/* | associated with leading portion of T in the first NCONV | */
/* | columns of workl(invsub,ldq). | */
/* %---------------------------------------------------------% */
igraphdgeqr2_(ncv, &nconv, &workl[invsub], &ldq, &workev[1], &workev[*
ncv + 1], &ierr);
/* %----------------------------------------------% */
/* | * Postmultiply Z by Q. | */
/* | * Postmultiply Z by R. | */
/* | The N by NCONV matrix Z is now contains the | */
/* | Ritz vectors associated with the Ritz values | */
/* | in workl(iheigr) and workl(iheigi). | */
/* %----------------------------------------------% */
igraphdorm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[invsub], &
ldq, &workev[1], &z__[z_offset], ldz, &workd[*n + 1], &
ierr);
igraphdtrmm_("Right", "Upper", "No transpose", "Non-unit", n, &nconv, &
c_b38, &workl[invsub], &ldq, &z__[z_offset], ldz);
}
} else {
/* %------------------------------------------------------% */
/* | An approximate invariant subspace is not needed. | */
/* | Place the Ritz values computed DNAUPD into DR and DI | */
/* %------------------------------------------------------% */
igraphdcopy_(&nconv, &workl[ritzr], &c__1, &dr[1], &c__1);
igraphdcopy_(&nconv, &workl[ritzi], &c__1, &di[1], &c__1);
igraphdcopy_(&nconv, &workl[ritzr], &c__1, &workl[iheigr], &c__1);
igraphdcopy_(&nconv, &workl[ritzi], &c__1, &workl[iheigi], &c__1);
igraphdcopy_(&nconv, &workl[bounds], &c__1, &workl[ihbds], &c__1);
}
/* %------------------------------------------------% */
/* | Transform the Ritz values and possibly vectors | */
/* | and corresponding error bounds of OP to those | */
/* | of A*x = lambda*B*x. | */
/* %------------------------------------------------% */
if (igraphs_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
if (*rvec) {
igraphdscal_(ncv, &rnorm, &workl[ihbds], &c__1);
}
} else {
/* %---------------------------------------% */
/* | A spectral transformation was used. | */
/* | * Determine the Ritz estimates of the | */
/* | Ritz values in the original system. | */
/* %---------------------------------------% */
if (igraphs_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
if (*rvec) {
igraphdscal_(ncv, &rnorm, &workl[ihbds], &c__1);
}
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
temp = igraphdlapy2_(&workl[iheigr + k - 1], &workl[iheigi + k - 1])
;
workl[ihbds + k - 1] = (d__1 = workl[ihbds + k - 1], abs(d__1)
) / temp / temp;
/* L50: */
}
} else if (igraphs_cmp(type__, "REALPT", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
/* L60: */
}
} else if (igraphs_cmp(type__, "IMAGPT", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
/* L70: */
}
}
/* %-----------------------------------------------------------% */
/* | * Transform the Ritz values back to the original system. | */
/* | For TYPE = 'SHIFTI' the transformation is | */
/* | lambda = 1/theta + sigma | */
/* | For TYPE = 'REALPT' or 'IMAGPT' the user must from | */
/* | Rayleigh quotients or a projection. See remark 3 above.| */
/* | NOTES: | */
/* | *The Ritz vectors are not affected by the transformation. | */
/* %-----------------------------------------------------------% */
if (igraphs_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
temp = igraphdlapy2_(&workl[iheigr + k - 1], &workl[iheigi + k - 1])
;
workl[iheigr + k - 1] = workl[iheigr + k - 1] / temp / temp +
*sigmar;
workl[iheigi + k - 1] = -workl[iheigi + k - 1] / temp / temp
+ *sigmai;
/* L80: */
}
igraphdcopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
igraphdcopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
} else if (igraphs_cmp(type__, "REALPT", (ftnlen)6, (ftnlen)6) == 0 ||
igraphs_cmp(type__, "IMAGPT", (ftnlen)6, (ftnlen)6) == 0) {
igraphdcopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
igraphdcopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
}
}
if (igraphs_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0 && msglvl > 1) {
igraphdvout_(&debug_1.logfil, &nconv, &dr[1], &debug_1.ndigit, "_neupd: Un"
"transformed real part of the Ritz valuess.");
igraphdvout_(&debug_1.logfil, &nconv, &di[1], &debug_1.ndigit, "_neupd: Un"
"transformed imag part of the Ritz valuess.");
igraphdvout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Ritz estimates of untransformed Ritz values.");
} else if (igraphs_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0 && msglvl >
1) {
igraphdvout_(&debug_1.logfil, &nconv, &dr[1], &debug_1.ndigit, "_neupd: Re"
"al parts of converged Ritz values.");
igraphdvout_(&debug_1.logfil, &nconv, &di[1], &debug_1.ndigit, "_neupd: Im"
"ag parts of converged Ritz values.");
igraphdvout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Associated Ritz estimates.");
}
/* %-------------------------------------------------% */
/* | Eigenvector Purification step. Formally perform | */
/* | one of inverse subspace iteration. Only used | */
/* | for MODE = 2. | */
/* %-------------------------------------------------% */
if (*rvec && *(unsigned char *)howmny == 'A' && igraphs_cmp(type__, "SHIFTI"
, (ftnlen)6, (ftnlen)6) == 0) {
/* %------------------------------------------------% */
/* | Purify the computed Ritz vectors by adding a | */
/* | little bit of the residual vector: | */
/* | T | */
/* | resid(:)*( e s ) / theta | */
/* | NCV | */
/* | where H s = s theta. Remember that when theta | */
/* | has nonzero imaginary part, the corresponding | */
/* | Ritz vector is stored across two columns of Z. | */
/* %------------------------------------------------% */
iconj = 0;
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
if (workl[iheigi + j - 1] == 0.) {
workev[j] = workl[invsub + (j - 1) * ldq + *ncv - 1] / workl[
iheigr + j - 1];
} else if (iconj == 0) {
temp = igraphdlapy2_(&workl[iheigr + j - 1], &workl[iheigi + j - 1])
;
workev[j] = (workl[invsub + (j - 1) * ldq + *ncv - 1] * workl[
iheigr + j - 1] + workl[invsub + j * ldq + *ncv - 1] *
workl[iheigi + j - 1]) / temp / temp;
workev[j + 1] = (workl[invsub + j * ldq + *ncv - 1] * workl[
iheigr + j - 1] - workl[invsub + (j - 1) * ldq + *ncv
- 1] * workl[iheigi + j - 1]) / temp / temp;
iconj = 1;
} else {
iconj = 0;
}
/* L110: */
}
/* %---------------------------------------% */
/* | Perform a rank one update to Z and | */
/* | purify all the Ritz vectors together. | */
/* %---------------------------------------% */
igraphdger_(n, &nconv, &c_b38, &resid[1], &c__1, &workev[1], &c__1, &z__[
z_offset], ldz);
}
L9000:
return 0;
/* %---------------% */
/* | End of DNEUPD | */
/* %---------------% */
} /* dneupd_ */
/* Subroutine */ int igraphdnaitr_(integer *ido, char *bmat, integer *n, integer *k,
integer *np, integer *nb, doublereal *resid, doublereal *rnorm,
doublereal *v, integer *ldv, doublereal *h__, integer *ldh, integer *
ipntr, doublereal *workd, integer *info)
{
/* Initialized data */
static logical first = TRUE_;
/* System generated locals */
integer h_dim1, h_offset, v_dim1, v_offset, i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__, j;
static real t0, t1, t2, t3, t4, t5;
static integer jj, ipj, irj, ivj;
static doublereal ulp, tst1;
extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static integer ierr, iter;
static doublereal unfl, ovfl;
static integer itry;
extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
static doublereal temp1;
static logical orth1, orth2, step3, step4;
static doublereal betaj;
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
integer *), igraphdgemv_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *);
static integer infol;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), igraphdaxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *), igraphdmout_(integer
*, integer *, integer *, doublereal *, integer *, integer *, char
*);
static doublereal xtemp[2];
extern /* Subroutine */ int igraphdvout_(integer *, integer *, doublereal *,
integer *, char *);
static doublereal wnorm;
extern /* Subroutine */ int igraphivout_(integer *, integer *, integer *,
integer *, char *), igraphdgetv0_(integer *, char *, integer *,
logical *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *
), igraphdlabad_(doublereal *, doublereal *);
static doublereal rnorm1;
extern doublereal igraphdlamch_(char *);
extern /* Subroutine */ int igraphdlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *);
extern doublereal igraphdlanhs_(char *, integer *, doublereal *, integer *,
doublereal *);
extern /* Subroutine */ int igraphsecond_(real *);
static logical rstart;
static integer msglvl;
static doublereal smlnum;
/* %----------------------------------------------------% */
/* | Include files for debugging and timing information | */
/* %----------------------------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %---------------------------------% */
/* | See debug.doc for documentation | */
/* %---------------------------------% */
/* %------------------% */
/* | Scalar Arguments | */
/* %------------------% */
/* %--------------------------------% */
/* | See stat.doc for documentation | */
/* %--------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: stat.h SID: 2.2 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %-----------------% */
/* | Array Arguments | */
/* %-----------------% */
/* %------------% */
/* | Parameters | */
/* %------------% */
/* %---------------% */
/* | Local Scalars | */
/* %---------------% */
/* %-----------------------% */
/* | Local Array Arguments | */
/* %-----------------------% */
/* %----------------------% */
/* | External Subroutines | */
/* %----------------------% */
/* %--------------------% */
/* | External Functions | */
/* %--------------------% */
/* %---------------------% */
/* | Intrinsic Functions | */
/* %---------------------% */
/* %-----------------% */
/* | Data statements | */
/* %-----------------% */
/* Parameter adjustments */
--workd;
--resid;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
--ipntr;
/* Function Body */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
if (first) {
/* %-----------------------------------------% */
/* | Set machine-dependent constants for the | */
/* | the splitting and deflation 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_;
}
if (*ido == 0) {
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
igraphsecond_(&t0);
msglvl = debug_1.mnaitr;
/* %------------------------------% */
/* | Initial call to this routine | */
/* %------------------------------% */
*info = 0;
step3 = FALSE_;
step4 = FALSE_;
rstart = FALSE_;
orth1 = FALSE_;
orth2 = FALSE_;
j = *k + 1;
ipj = 1;
irj = ipj + *n;
ivj = irj + *n;
}
/* %-------------------------------------------------% */
/* | When in reverse communication mode one of: | */
/* | STEP3, STEP4, ORTH1, ORTH2, RSTART | */
/* | will be .true. when .... | */
/* | STEP3: return from computing OP*v_{j}. | */
/* | STEP4: return from computing B-norm of OP*v_{j} | */
/* | ORTH1: return from computing B-norm of r_{j+1} | */
/* | ORTH2: return from computing B-norm of | */
/* | correction to the residual vector. | */
/* | RSTART: return from OP computations needed by | */
/* | dgetv0. | */
/* %-------------------------------------------------% */
if (step3) {
goto L50;
}
if (step4) {
goto L60;
}
if (orth1) {
goto L70;
}
if (orth2) {
goto L90;
}
if (rstart) {
goto L30;
}
/* %-----------------------------% */
/* | Else this is the first step | */
/* %-----------------------------% */
/* %--------------------------------------------------------------% */
/* | | */
/* | A R N O L D I I T E R A T I O N L O O P | */
/* | | */
/* | Note: B*r_{j-1} is already in WORKD(1:N)=WORKD(IPJ:IPJ+N-1) | */
/* %--------------------------------------------------------------% */
L1000:
if (msglvl > 1) {
igraphivout_(&debug_1.logfil, &c__1, &j, &debug_1.ndigit, "_naitr: generat"
"ing Arnoldi vector number");
igraphdvout_(&debug_1.logfil, &c__1, rnorm, &debug_1.ndigit, "_naitr: B-no"
"rm of the current residual is");
}
/* %---------------------------------------------------% */
/* | STEP 1: Check if the B norm of j-th residual | */
/* | vector is zero. Equivalent to determing whether | */
/* | an exact j-step Arnoldi factorization is present. | */
/* %---------------------------------------------------% */
betaj = *rnorm;
if (*rnorm > 0.) {
goto L40;
}
/* %---------------------------------------------------% */
/* | Invariant subspace found, generate a new starting | */
/* | vector which is orthogonal to the current Arnoldi | */
/* | basis and continue the iteration. | */
/* %---------------------------------------------------% */
if (msglvl > 0) {
igraphivout_(&debug_1.logfil, &c__1, &j, &debug_1.ndigit, "_naitr: ****** "
"RESTART AT STEP ******");
}
/* %---------------------------------------------% */
/* | ITRY is the loop variable that controls the | */
/* | maximum amount of times that a restart is | */
/* | attempted. NRSTRT is used by stat.h | */
/* %---------------------------------------------% */
betaj = 0.;
++timing_1.nrstrt;
itry = 1;
L20:
rstart = TRUE_;
*ido = 0;
L30:
/* %--------------------------------------% */
/* | If in reverse communication mode and | */
/* | RSTART = .true. flow returns here. | */
/* %--------------------------------------% */
igraphdgetv0_(ido, bmat, &itry, &c_false, n, &j, &v[v_offset], ldv, &resid[1],
rnorm, &ipntr[1], &workd[1], &ierr);
if (*ido != 99) {
goto L9000;
}
if (ierr < 0) {
++itry;
if (itry <= 3) {
goto L20;
}
/* %------------------------------------------------% */
/* | Give up after several restart attempts. | */
/* | Set INFO to the size of the invariant subspace | */
/* | which spans OP and exit. | */
/* %------------------------------------------------% */
*info = j - 1;
igraphsecond_(&t1);
timing_1.tnaitr += t1 - t0;
*ido = 99;
goto L9000;
}
L40:
/* %---------------------------------------------------------% */
/* | STEP 2: v_{j} = r_{j-1}/rnorm and p_{j} = p_{j}/rnorm | */
/* | Note that p_{j} = B*r_{j-1}. In order to avoid overflow | */
/* | when reciprocating a small RNORM, test against lower | */
/* | machine bound. | */
/* %---------------------------------------------------------% */
igraphdcopy_(n, &resid[1], &c__1, &v[j * v_dim1 + 1], &c__1);
if (*rnorm >= unfl) {
temp1 = 1. / *rnorm;
igraphdscal_(n, &temp1, &v[j * v_dim1 + 1], &c__1);
igraphdscal_(n, &temp1, &workd[ipj], &c__1);
} else {
/* %-----------------------------------------% */
/* | To scale both v_{j} and p_{j} carefully | */
/* | use LAPACK routine SLASCL | */
/* %-----------------------------------------% */
igraphdlascl_("General", &i__, &i__, rnorm, &c_b25, n, &c__1, &v[j * v_dim1
+ 1], n, &infol);
igraphdlascl_("General", &i__, &i__, rnorm, &c_b25, n, &c__1, &workd[ipj],
n, &infol);
}
/* %------------------------------------------------------% */
/* | STEP 3: r_{j} = OP*v_{j}; Note that p_{j} = B*v_{j} | */
/* | Note that this is not quite yet r_{j}. See STEP 4 | */
/* %------------------------------------------------------% */
step3 = TRUE_;
++timing_1.nopx;
igraphsecond_(&t2);
igraphdcopy_(n, &v[j * v_dim1 + 1], &c__1, &workd[ivj], &c__1);
ipntr[1] = ivj;
ipntr[2] = irj;
ipntr[3] = ipj;
*ido = 1;
/* %-----------------------------------% */
/* | Exit in order to compute OP*v_{j} | */
/* %-----------------------------------% */
goto L9000;
L50:
/* %----------------------------------% */
/* | Back from reverse communication; | */
/* | WORKD(IRJ:IRJ+N-1) := OP*v_{j} | */
/* | if step3 = .true. | */
/* %----------------------------------% */
igraphsecond_(&t3);
timing_1.tmvopx += t3 - t2;
step3 = FALSE_;
/* %------------------------------------------% */
/* | Put another copy of OP*v_{j} into RESID. | */
/* %------------------------------------------% */
igraphdcopy_(n, &workd[irj], &c__1, &resid[1], &c__1);
/* %---------------------------------------% */
/* | STEP 4: Finish extending the Arnoldi | */
/* | factorization to length j. | */
/* %---------------------------------------% */
igraphsecond_(&t2);
if (*(unsigned char *)bmat == 'G') {
++timing_1.nbx;
step4 = TRUE_;
ipntr[1] = irj;
ipntr[2] = ipj;
*ido = 2;
/* %-------------------------------------% */
/* | Exit in order to compute B*OP*v_{j} | */
/* %-------------------------------------% */
goto L9000;
} else if (*(unsigned char *)bmat == 'I') {
igraphdcopy_(n, &resid[1], &c__1, &workd[ipj], &c__1);
}
L60:
/* %----------------------------------% */
/* | Back from reverse communication; | */
/* | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j} | */
/* | if step4 = .true. | */
/* %----------------------------------% */
if (*(unsigned char *)bmat == 'G') {
igraphsecond_(&t3);
timing_1.tmvbx += t3 - t2;
}
step4 = FALSE_;
/* %-------------------------------------% */
/* | The following is needed for STEP 5. | */
/* | Compute the B-norm of OP*v_{j}. | */
/* %-------------------------------------% */
if (*(unsigned char *)bmat == 'G') {
wnorm = igraphddot_(n, &resid[1], &c__1, &workd[ipj], &c__1);
wnorm = sqrt((abs(wnorm)));
} else if (*(unsigned char *)bmat == 'I') {
wnorm = igraphdnrm2_(n, &resid[1], &c__1);
}
/* %-----------------------------------------% */
/* | Compute the j-th residual corresponding | */
/* | to the j step factorization. | */
/* | Use Classical Gram Schmidt and compute: | */
/* | w_{j} <- V_{j}^T * B * OP * v_{j} | */
/* | r_{j} <- OP*v_{j} - V_{j} * w_{j} | */
/* %-----------------------------------------% */
/* %------------------------------------------% */
/* | Compute the j Fourier coefficients w_{j} | */
/* | WORKD(IPJ:IPJ+N-1) contains B*OP*v_{j}. | */
/* %------------------------------------------% */
igraphdgemv_("T", n, &j, &c_b25, &v[v_offset], ldv, &workd[ipj], &c__1, &c_b47,
&h__[j * h_dim1 + 1], &c__1);
/* %--------------------------------------% */
/* | Orthogonalize r_{j} against V_{j}. | */
/* | RESID contains OP*v_{j}. See STEP 3. | */
/* %--------------------------------------% */
igraphdgemv_("N", n, &j, &c_b50, &v[v_offset], ldv, &h__[j * h_dim1 + 1], &c__1,
&c_b25, &resid[1], &c__1);
if (j > 1) {
h__[j + (j - 1) * h_dim1] = betaj;
}
igraphsecond_(&t4);
orth1 = TRUE_;
igraphsecond_(&t2);
if (*(unsigned char *)bmat == 'G') {
++timing_1.nbx;
igraphdcopy_(n, &resid[1], &c__1, &workd[irj], &c__1);
ipntr[1] = irj;
ipntr[2] = ipj;
*ido = 2;
/* %----------------------------------% */
/* | Exit in order to compute B*r_{j} | */
/* %----------------------------------% */
goto L9000;
} else if (*(unsigned char *)bmat == 'I') {
igraphdcopy_(n, &resid[1], &c__1, &workd[ipj], &c__1);
}
L70:
/* %---------------------------------------------------% */
/* | Back from reverse communication if ORTH1 = .true. | */
/* | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | */
/* %---------------------------------------------------% */
if (*(unsigned char *)bmat == 'G') {
igraphsecond_(&t3);
timing_1.tmvbx += t3 - t2;
}
orth1 = FALSE_;
/* %------------------------------% */
/* | Compute the B-norm of r_{j}. | */
/* %------------------------------% */
if (*(unsigned char *)bmat == 'G') {
*rnorm = igraphddot_(n, &resid[1], &c__1, &workd[ipj], &c__1);
*rnorm = sqrt((abs(*rnorm)));
} else if (*(unsigned char *)bmat == 'I') {
*rnorm = igraphdnrm2_(n, &resid[1], &c__1);
}
/* %-----------------------------------------------------------% */
/* | STEP 5: Re-orthogonalization / Iterative refinement phase | */
/* | Maximum NITER_ITREF tries. | */
/* | | */
/* | s = V_{j}^T * B * r_{j} | */
/* | r_{j} = r_{j} - V_{j}*s | */
/* | alphaj = alphaj + s_{j} | */
/* | | */
/* | The stopping criteria used for iterative refinement is | */
/* | discussed in Parlett's book SEP, page 107 and in Gragg & | */
/* | Reichel ACM TOMS paper; Algorithm 686, Dec. 1990. | */
/* | Determine if we need to correct the residual. The goal is | */
/* | to enforce ||v(:,1:j)^T * r_{j}|| .le. eps * || r_{j} || | */
/* | The following test determines whether the sine of the | */
/* | angle between OP*x and the computed residual is less | */
/* | than or equal to 0.717. | */
/* %-----------------------------------------------------------% */
if (*rnorm > wnorm * .717f) {
goto L100;
}
iter = 0;
++timing_1.nrorth;
/* %---------------------------------------------------% */
/* | Enter the Iterative refinement phase. If further | */
/* | refinement is necessary, loop back here. The loop | */
/* | variable is ITER. Perform a step of Classical | */
/* | Gram-Schmidt using all the Arnoldi vectors V_{j} | */
/* %---------------------------------------------------% */
L80:
if (msglvl > 2) {
xtemp[0] = wnorm;
xtemp[1] = *rnorm;
igraphdvout_(&debug_1.logfil, &c__2, xtemp, &debug_1.ndigit, "_naitr: re-o"
"rthonalization; wnorm and rnorm are");
igraphdvout_(&debug_1.logfil, &j, &h__[j * h_dim1 + 1], &debug_1.ndigit,
"_naitr: j-th column of H");
}
/* %----------------------------------------------------% */
/* | Compute V_{j}^T * B * r_{j}. | */
/* | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | */
/* %----------------------------------------------------% */
igraphdgemv_("T", n, &j, &c_b25, &v[v_offset], ldv, &workd[ipj], &c__1, &c_b47,
&workd[irj], &c__1);
/* %---------------------------------------------% */
/* | Compute the correction to the residual: | */
/* | r_{j} = r_{j} - V_{j} * WORKD(IRJ:IRJ+J-1). | */
/* | The correction to H is v(:,1:J)*H(1:J,1:J) | */
/* | + v(:,1:J)*WORKD(IRJ:IRJ+J-1)*e'_j. | */
/* %---------------------------------------------% */
igraphdgemv_("N", n, &j, &c_b50, &v[v_offset], ldv, &workd[irj], &c__1, &c_b25,
&resid[1], &c__1);
igraphdaxpy_(&j, &c_b25, &workd[irj], &c__1, &h__[j * h_dim1 + 1], &c__1);
orth2 = TRUE_;
igraphsecond_(&t2);
if (*(unsigned char *)bmat == 'G') {
++timing_1.nbx;
igraphdcopy_(n, &resid[1], &c__1, &workd[irj], &c__1);
ipntr[1] = irj;
ipntr[2] = ipj;
*ido = 2;
/* %-----------------------------------% */
/* | Exit in order to compute B*r_{j}. | */
/* | r_{j} is the corrected residual. | */
/* %-----------------------------------% */
goto L9000;
} else if (*(unsigned char *)bmat == 'I') {
igraphdcopy_(n, &resid[1], &c__1, &workd[ipj], &c__1);
}
L90:
/* %---------------------------------------------------% */
/* | Back from reverse communication if ORTH2 = .true. | */
/* %---------------------------------------------------% */
if (*(unsigned char *)bmat == 'G') {
igraphsecond_(&t3);
timing_1.tmvbx += t3 - t2;
}
/* %-----------------------------------------------------% */
/* | Compute the B-norm of the corrected residual r_{j}. | */
/* %-----------------------------------------------------% */
if (*(unsigned char *)bmat == 'G') {
rnorm1 = igraphddot_(n, &resid[1], &c__1, &workd[ipj], &c__1);
rnorm1 = sqrt((abs(rnorm1)));
} else if (*(unsigned char *)bmat == 'I') {
rnorm1 = igraphdnrm2_(n, &resid[1], &c__1);
}
if (msglvl > 0 && iter > 0) {
igraphivout_(&debug_1.logfil, &c__1, &j, &debug_1.ndigit, "_naitr: Iterati"
"ve refinement for Arnoldi residual");
if (msglvl > 2) {
xtemp[0] = *rnorm;
xtemp[1] = rnorm1;
igraphdvout_(&debug_1.logfil, &c__2, xtemp, &debug_1.ndigit, "_naitr: "
"iterative refinement ; rnorm and rnorm1 are");
}
}
/* %-----------------------------------------% */
/* | Determine if we need to perform another | */
/* | step of re-orthogonalization. | */
/* %-----------------------------------------% */
if (rnorm1 > *rnorm * .717f) {
/* %---------------------------------------% */
/* | No need for further refinement. | */
/* | The cosine of the angle between the | */
/* | corrected residual vector and the old | */
/* | residual vector is greater than 0.717 | */
/* | In other words the corrected residual | */
/* | and the old residual vector share an | */
/* | angle of less than arcCOS(0.717) | */
/* %---------------------------------------% */
*rnorm = rnorm1;
} else {
/* %-------------------------------------------% */
/* | Another step of iterative refinement step | */
/* | is required. NITREF is used by stat.h | */
/* %-------------------------------------------% */
++timing_1.nitref;
*rnorm = rnorm1;
++iter;
if (iter <= 1) {
goto L80;
}
/* %-------------------------------------------------% */
/* | Otherwise RESID is numerically in the span of V | */
/* %-------------------------------------------------% */
i__1 = *n;
for (jj = 1; jj <= i__1; ++jj) {
resid[jj] = 0.;
/* L95: */
}
*rnorm = 0.;
}
/* %----------------------------------------------% */
/* | Branch here directly if iterative refinement | */
/* | wasn't necessary or after at most NITER_REF | */
/* | steps of iterative refinement. | */
/* %----------------------------------------------% */
L100:
rstart = FALSE_;
orth2 = FALSE_;
igraphsecond_(&t5);
timing_1.titref += t5 - t4;
/* %------------------------------------% */
/* | STEP 6: Update j = j+1; Continue | */
/* %------------------------------------% */
++j;
if (j > *k + *np) {
igraphsecond_(&t1);
timing_1.tnaitr += t1 - t0;
*ido = 99;
i__1 = *k + *np - 1;
for (i__ = max(1,*k); i__ <= i__1; ++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__2 = *k + *np;
tst1 = igraphdlanhs_("1", &i__2, &h__[h_offset], ldh, &workd[*n + 1]);
}
/* Computing MAX */
d__2 = ulp * tst1;
if ((d__1 = h__[i__ + 1 + i__ * h_dim1], abs(d__1)) <= max(d__2,
smlnum)) {
h__[i__ + 1 + i__ * h_dim1] = 0.;
}
/* L110: */
}
if (msglvl > 2) {
i__1 = *k + *np;
i__2 = *k + *np;
igraphdmout_(&debug_1.logfil, &i__1, &i__2, &h__[h_offset], ldh, &
debug_1.ndigit, "_naitr: Final upper Hessenberg matrix H"
" of order K+NP");
}
goto L9000;
}
/* %--------------------------------------------------------% */
/* | Loop back to extend the factorization by another step. | */
/* %--------------------------------------------------------% */
goto L1000;
/* %---------------------------------------------------------------% */
/* | | */
/* | E N D O F M A I N I T E R A T I O N L O O P | */
/* | | */
/* %---------------------------------------------------------------% */
L9000:
return 0;
/* %---------------% */
/* | End of igraphdnaitr | */
/* %---------------% */
} /* igraphdnaitr_ */
/* ===================================================================== */
/* Subroutine */ int igraphdlarft_(char *direct, char *storev, integer *n, integer *
k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t,
integer *ldt)
{
/* System generated locals */
integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
doublereal d__1;
/* Local variables */
integer i__, j, prevlastv;
extern logical igraphlsame_(char *, char *);
extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
integer lastv;
extern /* Subroutine */ int igraphdtrmv_(char *, char *, char *, integer *,
doublereal *, integer *, doublereal *, integer *);
/* -- LAPACK auxiliary routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--tau;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
/* Function Body */
if (*n == 0) {
return 0;
}
if (igraphlsame_(direct, "F")) {
prevlastv = *n;
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
prevlastv = max(i__,prevlastv);
if (tau[i__] == 0.) {
/* H(i) = I */
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
t[j + i__ * t_dim1] = 0.;
}
} else {
/* general case */
if (igraphlsame_(storev, "C")) {
/* Skip any trailing zeros. */
lastv = *n;
L14:
if (v[lastv + i__ * v_dim1] != 0.) {
goto L15;
}
if (lastv == i__ + 1) {
goto L15;
}
--lastv;
goto L14;
L15:
/* DO LASTV = N, I+1, -1 */
/* IF( V( LASTV, I ).NE.ZERO ) EXIT */
/* END DO */
i__2 = i__ - 1;
for (j = 1; j <= i__2; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1];
}
j = min(lastv,prevlastv);
/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) */
i__2 = j - i__;
i__3 = i__ - 1;
d__1 = -tau[i__];
igraphdgemv_("Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 +
v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, &
c_b8, &t[i__ * t_dim1 + 1], &c__1);
} else {
/* Skip any trailing zeros. */
lastv = *n;
L16:
if (v[i__ + lastv * v_dim1] != 0.) {
goto L17;
}
if (lastv == i__ + 1) {
goto L17;
}
--lastv;
goto L16;
L17:
/* DO LASTV = N, I+1, -1 */
/* IF( V( I, LASTV ).NE.ZERO ) EXIT */
/* END DO */
i__2 = i__ - 1;
for (j = 1; j <= i__2; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1];
}
j = min(lastv,prevlastv);
/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T */
i__2 = i__ - 1;
i__3 = j - i__;
d__1 = -tau[i__];
igraphdgemv_("No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) *
v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1],
ldv, &c_b8, &t[i__ * t_dim1 + 1], &c__1);
}
/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
i__2 = i__ - 1;
igraphdtrmv_("Upper", "No transpose", "Non-unit", &i__2, &t[
t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
t[i__ + i__ * t_dim1] = tau[i__];
if (i__ > 1) {
prevlastv = max(prevlastv,lastv);
} else {
prevlastv = lastv;
}
}
}
} else {
prevlastv = 1;
for (i__ = *k; i__ >= 1; --i__) {
if (tau[i__] == 0.) {
/* H(i) = I */
i__1 = *k;
for (j = i__; j <= i__1; ++j) {
t[j + i__ * t_dim1] = 0.;
}
} else {
/* general case */
if (i__ < *k) {
if (igraphlsame_(storev, "C")) {
/* Skip any leading zeros. */
lastv = 1;
L34:
if (v[lastv + i__ * v_dim1] != 0.) {
goto L35;
}
if (lastv == i__ - 1) {
goto L35;
}
++lastv;
goto L34;
L35:
/* DO LASTV = 1, I-1 */
/* IF( V( LASTV, I ).NE.ZERO ) EXIT */
/* END DO */
i__1 = *k;
for (j = i__ + 1; j <= i__1; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__
+ j * v_dim1];
}
j = max(lastv,prevlastv);
/* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) */
i__1 = *n - *k + i__ - j;
i__2 = *k - i__;
d__1 = -tau[i__];
igraphdgemv_("Transpose", &i__1, &i__2, &d__1, &v[j + (i__
+ 1) * v_dim1], ldv, &v[j + i__ * v_dim1], &
c__1, &c_b8, &t[i__ + 1 + i__ * t_dim1], &
c__1);
} else {
/* Skip any leading zeros. */
lastv = 1;
/* L36: */
if (v[i__ + lastv * v_dim1] != 0.) {
goto L37;
}
if (lastv == i__ - 1) {
goto L37;
}
++lastv;
L37:
/* DO LASTV = 1, I-1 */
/* IF( V( I, LASTV ).NE.ZERO ) EXIT */
/* END DO */
i__1 = *k;
for (j = i__ + 1; j <= i__1; ++j) {
t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k
+ i__) * v_dim1];
}
j = max(lastv,prevlastv);
/* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T */
i__1 = *k - i__;
i__2 = *n - *k + i__ - j;
d__1 = -tau[i__];
igraphdgemv_("No transpose", &i__1, &i__2, &d__1, &v[i__ +
1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
ldv, &c_b8, &t[i__ + 1 + i__ * t_dim1], &c__1
);
}
/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
i__1 = *k - i__;
igraphdtrmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__
+ 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
t_dim1], &c__1)
;
if (i__ > 1) {
prevlastv = min(prevlastv,lastv);
} else {
prevlastv = lastv;
}
}
t[i__ + i__ * t_dim1] = tau[i__];
}
}
}
return 0;
/* End of DLARFT */
} /* dlarft_ */
/* Subroutine */ int igraphdlarfx_(char *side, integer *m, integer *n, doublereal *
v, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work)
{
/* System generated locals */
integer c_dim1, c_offset, i__1;
doublereal d__1;
/* Local variables */
static integer j;
static doublereal t1, t2, t3, t4, t5, t6, t7, t8, t9, v1, v2, v3, v4, v5,
v6, v7, v8, v9, t10, v10, sum;
extern /* Subroutine */ int igraphdger_(integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
extern logical igraphlsame_(char *, char *);
extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* February 29, 1992 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLARFX applies a real elementary reflector H to a real m by n */
/* matrix C, from either the left or the right. H is represented in the */
/* form */
/* H = I - tau * v * v' */
/* where tau is a real scalar and v is a real vector. */
/* If tau = 0, then H is taken to be the unit matrix */
/* This version uses inline code if H has order < 11. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': form H * C */
/* = 'R': form C * H */
/* M (input) INTEGER */
/* The number of rows of the matrix C. */
/* N (input) INTEGER */
/* The number of columns of the matrix C. */
/* V (input) DOUBLE PRECISION array, dimension (M) if SIDE = 'L' */
/* or (N) if SIDE = 'R' */
/* The vector v in the representation of H. */
/* TAU (input) DOUBLE PRECISION */
/* The value tau in the representation of H. */
/* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) */
/* On entry, the m by n matrix C. */
/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
/* or C * H if SIDE = 'R'. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDA >= (1,M). */
/* WORK (workspace) DOUBLE PRECISION array, dimension */
/* (N) if SIDE = 'L' */
/* or (M) if SIDE = 'R' */
/* WORK is not referenced if H has order < 11. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--v;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
if (*tau == 0.) {
return 0;
}
if (igraphlsame_(side, "L")) {
/* Form H * C, where H has order m. */
switch (*m) {
case 1: goto L10;
case 2: goto L30;
case 3: goto L50;
case 4: goto L70;
case 5: goto L90;
case 6: goto L110;
case 7: goto L130;
case 8: goto L150;
case 9: goto L170;
case 10: goto L190;
}
/* Code for general M */
/* w := C'*v */
igraphdgemv_("Transpose", m, n, &c_b14, &c__[c_offset], ldc, &v[1], &c__1, &
c_b16, &work[1], &c__1);
/* C := C - tau * v * w' */
d__1 = -(*tau);
igraphdger_(m, n, &d__1, &v[1], &c__1, &work[1], &c__1, &c__[c_offset], ldc)
;
goto L410;
L10:
/* Special code for 1 x 1 Householder */
t1 = 1. - *tau * v[1] * v[1];
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
c__[j * c_dim1 + 1] = t1 * c__[j * c_dim1 + 1];
/* L20: */
}
goto L410;
L30:
/* Special code for 2 x 2 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
/* L40: */
}
goto L410;
L50:
/* Special code for 3 x 3 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
/* L60: */
}
goto L410;
L70:
/* Special code for 4 x 4 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
c__[j * c_dim1 + 4] -= sum * t4;
/* L80: */
}
goto L410;
L90:
/* Special code for 5 x 5 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[
j * c_dim1 + 5];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
c__[j * c_dim1 + 4] -= sum * t4;
c__[j * c_dim1 + 5] -= sum * t5;
/* L100: */
}
goto L410;
L110:
/* Special code for 6 x 6 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[
j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
c__[j * c_dim1 + 4] -= sum * t4;
c__[j * c_dim1 + 5] -= sum * t5;
c__[j * c_dim1 + 6] -= sum * t6;
/* L120: */
}
goto L410;
L130:
/* Special code for 7 x 7 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[
j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j *
c_dim1 + 7];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
c__[j * c_dim1 + 4] -= sum * t4;
c__[j * c_dim1 + 5] -= sum * t5;
c__[j * c_dim1 + 6] -= sum * t6;
c__[j * c_dim1 + 7] -= sum * t7;
/* L140: */
}
goto L410;
L150:
/* Special code for 8 x 8 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
v8 = v[8];
t8 = *tau * v8;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[
j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j *
c_dim1 + 7] + v8 * c__[j * c_dim1 + 8];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
c__[j * c_dim1 + 4] -= sum * t4;
c__[j * c_dim1 + 5] -= sum * t5;
c__[j * c_dim1 + 6] -= sum * t6;
c__[j * c_dim1 + 7] -= sum * t7;
c__[j * c_dim1 + 8] -= sum * t8;
/* L160: */
}
goto L410;
L170:
/* Special code for 9 x 9 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
v8 = v[8];
t8 = *tau * v8;
v9 = v[9];
t9 = *tau * v9;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[
j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j *
c_dim1 + 7] + v8 * c__[j * c_dim1 + 8] + v9 * c__[j *
c_dim1 + 9];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
c__[j * c_dim1 + 4] -= sum * t4;
c__[j * c_dim1 + 5] -= sum * t5;
c__[j * c_dim1 + 6] -= sum * t6;
c__[j * c_dim1 + 7] -= sum * t7;
c__[j * c_dim1 + 8] -= sum * t8;
c__[j * c_dim1 + 9] -= sum * t9;
/* L180: */
}
goto L410;
L190:
/* Special code for 10 x 10 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
v8 = v[8];
t8 = *tau * v8;
v9 = v[9];
t9 = *tau * v9;
v10 = v[10];
t10 = *tau * v10;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 *
c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[
j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j *
c_dim1 + 7] + v8 * c__[j * c_dim1 + 8] + v9 * c__[j *
c_dim1 + 9] + v10 * c__[j * c_dim1 + 10];
c__[j * c_dim1 + 1] -= sum * t1;
c__[j * c_dim1 + 2] -= sum * t2;
c__[j * c_dim1 + 3] -= sum * t3;
c__[j * c_dim1 + 4] -= sum * t4;
c__[j * c_dim1 + 5] -= sum * t5;
c__[j * c_dim1 + 6] -= sum * t6;
c__[j * c_dim1 + 7] -= sum * t7;
c__[j * c_dim1 + 8] -= sum * t8;
c__[j * c_dim1 + 9] -= sum * t9;
c__[j * c_dim1 + 10] -= sum * t10;
/* L200: */
}
goto L410;
} else {
/* Form C * H, where H has order n. */
switch (*n) {
case 1: goto L210;
case 2: goto L230;
case 3: goto L250;
case 4: goto L270;
case 5: goto L290;
case 6: goto L310;
case 7: goto L330;
case 8: goto L350;
case 9: goto L370;
case 10: goto L390;
}
/* Code for general N */
/* w := C * v */
igraphdgemv_("No transpose", m, n, &c_b14, &c__[c_offset], ldc, &v[1], &
c__1, &c_b16, &work[1], &c__1);
/* C := C - tau * w * v' */
d__1 = -(*tau);
igraphdger_(m, n, &d__1, &work[1], &c__1, &v[1], &c__1, &c__[c_offset], ldc)
;
goto L410;
L210:
/* Special code for 1 x 1 Householder */
t1 = 1. - *tau * v[1] * v[1];
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
c__[j + c_dim1] = t1 * c__[j + c_dim1];
/* L220: */
}
goto L410;
L230:
/* Special code for 2 x 2 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
/* L240: */
}
goto L410;
L250:
/* Special code for 3 x 3 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
/* L260: */
}
goto L410;
L270:
/* Special code for 4 x 4 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
c__[j + (c_dim1 << 2)] -= sum * t4;
/* L280: */
}
goto L410;
L290:
/* Special code for 5 x 5 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 *
c__[j + c_dim1 * 5];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
c__[j + (c_dim1 << 2)] -= sum * t4;
c__[j + c_dim1 * 5] -= sum * t5;
/* L300: */
}
goto L410;
L310:
/* Special code for 6 x 6 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 *
c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
c__[j + (c_dim1 << 2)] -= sum * t4;
c__[j + c_dim1 * 5] -= sum * t5;
c__[j + c_dim1 * 6] -= sum * t6;
/* L320: */
}
goto L410;
L330:
/* Special code for 7 x 7 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 *
c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[
j + c_dim1 * 7];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
c__[j + (c_dim1 << 2)] -= sum * t4;
c__[j + c_dim1 * 5] -= sum * t5;
c__[j + c_dim1 * 6] -= sum * t6;
c__[j + c_dim1 * 7] -= sum * t7;
/* L340: */
}
goto L410;
L350:
/* Special code for 8 x 8 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
v8 = v[8];
t8 = *tau * v8;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 *
c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[
j + c_dim1 * 7] + v8 * c__[j + (c_dim1 << 3)];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
c__[j + (c_dim1 << 2)] -= sum * t4;
c__[j + c_dim1 * 5] -= sum * t5;
c__[j + c_dim1 * 6] -= sum * t6;
c__[j + c_dim1 * 7] -= sum * t7;
c__[j + (c_dim1 << 3)] -= sum * t8;
/* L360: */
}
goto L410;
L370:
/* Special code for 9 x 9 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
v8 = v[8];
t8 = *tau * v8;
v9 = v[9];
t9 = *tau * v9;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 *
c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[
j + c_dim1 * 7] + v8 * c__[j + (c_dim1 << 3)] + v9 * c__[
j + c_dim1 * 9];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
c__[j + (c_dim1 << 2)] -= sum * t4;
c__[j + c_dim1 * 5] -= sum * t5;
c__[j + c_dim1 * 6] -= sum * t6;
c__[j + c_dim1 * 7] -= sum * t7;
c__[j + (c_dim1 << 3)] -= sum * t8;
c__[j + c_dim1 * 9] -= sum * t9;
/* L380: */
}
goto L410;
L390:
/* Special code for 10 x 10 Householder */
v1 = v[1];
t1 = *tau * v1;
v2 = v[2];
t2 = *tau * v2;
v3 = v[3];
t3 = *tau * v3;
v4 = v[4];
t4 = *tau * v4;
v5 = v[5];
t5 = *tau * v5;
v6 = v[6];
t6 = *tau * v6;
v7 = v[7];
t7 = *tau * v7;
v8 = v[8];
t8 = *tau * v8;
v9 = v[9];
t9 = *tau * v9;
v10 = v[10];
t10 = *tau * v10;
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 *
c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 *
c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[
j + c_dim1 * 7] + v8 * c__[j + (c_dim1 << 3)] + v9 * c__[
j + c_dim1 * 9] + v10 * c__[j + c_dim1 * 10];
c__[j + c_dim1] -= sum * t1;
c__[j + (c_dim1 << 1)] -= sum * t2;
c__[j + c_dim1 * 3] -= sum * t3;
c__[j + (c_dim1 << 2)] -= sum * t4;
c__[j + c_dim1 * 5] -= sum * t5;
c__[j + c_dim1 * 6] -= sum * t6;
c__[j + c_dim1 * 7] -= sum * t7;
c__[j + (c_dim1 << 3)] -= sum * t8;
c__[j + c_dim1 * 9] -= sum * t9;
c__[j + c_dim1 * 10] -= sum * t10;
/* L400: */
}
goto L410;
}
L410:
return 0;
/* End of DLARFX */
} /* igraphdlarfx_ */