/* Subroutine */ int znaitr_(integer *ido, char *bmat, integer *n, integer *k,
integer *np, integer *nb, doublecomplex *resid, doublereal *rnorm,
doublecomplex *v, integer *ldv, doublecomplex *h__, integer *ldh,
integer *ipntr, doublecomplex *workd, integer *info, ftnlen bmat_len)
{
/* Initialized data */
static logical first = TRUE_;
/* System generated locals */
integer h_dim1, h_offset, v_dim1, v_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *), 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;
static integer ierr, iter;
static doublereal unfl, ovfl;
static integer itry;
static doublereal temp1;
static logical orth1, orth2, step3, step4;
static doublereal betaj;
static integer infol;
static doublecomplex cnorm;
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static doublereal rtemp[2];
extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, ftnlen);
static doublereal wnorm;
extern /* Subroutine */ int dvout_(integer *, integer *, doublereal *,
integer *, char *, ftnlen), zcopy_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *), ivout_(integer *, integer
*, integer *, integer *, char *, ftnlen), zaxpy_(integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), zmout_(integer *, integer *, integer *, doublecomplex
*, integer *, integer *, char *, ftnlen), zvout_(integer *,
integer *, doublecomplex *, integer *, char *, ftnlen);
extern doublereal dlapy2_(doublereal *, doublereal *);
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
static doublereal rnorm1;
extern /* Subroutine */ int zgetv0_(integer *, char *, integer *, logical
*, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublereal *, integer *, doublecomplex *,
integer *, ftnlen);
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int second_(real *), zdscal_(integer *,
doublereal *, doublecomplex *, integer *);
static logical rstart;
static integer msglvl;
static doublereal smlnum;
extern doublereal zlanhs_(char *, integer *, doublecomplex *, integer *,
doublecomplex *, ftnlen);
extern /* Subroutine */ int zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 Arrays | */
/* %--------------% */
/* %---------------% */
/* | Local Scalars | */
/* %---------------% */
/* %----------------------% */
/* | 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 zlahqr | */
/* %-----------------------------------------% */
unfl = dlamch_("safe minimum", (ftnlen)12);
z__1.r = 1. / unfl, z__1.i = 0. / unfl;
ovfl = z__1.r;
dlabad_(&unfl, &ovfl);
ulp = dlamch_("precision", (ftnlen)9);
smlnum = unfl * (*n / ulp);
first = FALSE_;
}
if (*ido == 0) {
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
second_(&t0);
msglvl = debug_1.mcaitr;
/* %------------------------------% */
/* | 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 | */
/* | zgetv0. | */
/* %-------------------------------------------------% */
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) {
ivout_(&debug_1.logfil, &c__1, &j, &debug_1.ndigit, "_naitr: generat"
"ing Arnoldi vector number", (ftnlen)40);
dvout_(&debug_1.logfil, &c__1, rnorm, &debug_1.ndigit, "_naitr: B-no"
"rm of the current residual is", (ftnlen)41);
}
/* %---------------------------------------------------% */
/* | STEP 1: Check if the B norm of j-th residual | */
/* | vector is zero. Equivalent to determine 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) {
ivout_(&debug_1.logfil, &c__1, &j, &debug_1.ndigit, "_naitr: ****** "
"RESTART AT STEP ******", (ftnlen)37);
}
/* %---------------------------------------------% */
/* | 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. | */
/* %--------------------------------------% */
zgetv0_(ido, bmat, &itry, &c_false, n, &j, &v[v_offset], ldv, &resid[1],
rnorm, &ipntr[1], &workd[1], &ierr, (ftnlen)1);
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;
second_(&t1);
timing_1.tcaitr += 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. | */
/* %---------------------------------------------------------% */
zcopy_(n, &resid[1], &c__1, &v[j * v_dim1 + 1], &c__1);
if (*rnorm >= unfl) {
temp1 = 1. / *rnorm;
zdscal_(n, &temp1, &v[j * v_dim1 + 1], &c__1);
zdscal_(n, &temp1, &workd[ipj], &c__1);
} else {
/* %-----------------------------------------% */
/* | To scale both v_{j} and p_{j} carefully | */
/* | use LAPACK routine zlascl | */
/* %-----------------------------------------% */
zlascl_("General", &i__, &i__, rnorm, &c_b27, n, &c__1, &v[j * v_dim1
+ 1], n, &infol, (ftnlen)7);
zlascl_("General", &i__, &i__, rnorm, &c_b27, n, &c__1, &workd[ipj],
n, &infol, (ftnlen)7);
}
/* %------------------------------------------------------% */
/* | 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;
second_(&t2);
zcopy_(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. | */
/* %----------------------------------% */
second_(&t3);
timing_1.tmvopx += t3 - t2;
step3 = FALSE_;
/* %------------------------------------------% */
/* | Put another copy of OP*v_{j} into RESID. | */
/* %------------------------------------------% */
zcopy_(n, &workd[irj], &c__1, &resid[1], &c__1);
/* %---------------------------------------% */
/* | STEP 4: Finish extending the Arnoldi | */
/* | factorization to length j. | */
/* %---------------------------------------% */
second_(&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') {
zcopy_(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') {
second_(&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') {
zdotc_(&z__1, n, &resid[1], &c__1, &workd[ipj], &c__1);
cnorm.r = z__1.r, cnorm.i = z__1.i;
d__1 = cnorm.r;
d__2 = d_imag(&cnorm);
wnorm = sqrt(dlapy2_(&d__1, &d__2));
} else if (*(unsigned char *)bmat == 'I') {
wnorm = dznrm2_(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}. | */
/* %------------------------------------------% */
zgemv_("C", n, &j, &c_b1, &v[v_offset], ldv, &workd[ipj], &c__1, &c_b2, &
h__[j * h_dim1 + 1], &c__1, (ftnlen)1);
/* %--------------------------------------% */
/* | Orthogonalize r_{j} against V_{j}. | */
/* | RESID contains OP*v_{j}. See STEP 3. | */
/* %--------------------------------------% */
z__1.r = -1., z__1.i = -0.;
zgemv_("N", n, &j, &z__1, &v[v_offset], ldv, &h__[j * h_dim1 + 1], &c__1,
&c_b1, &resid[1], &c__1, (ftnlen)1);
if (j > 1) {
i__1 = j + (j - 1) * h_dim1;
z__1.r = betaj, z__1.i = 0.;
h__[i__1].r = z__1.r, h__[i__1].i = z__1.i;
}
second_(&t4);
orth1 = TRUE_;
second_(&t2);
if (*(unsigned char *)bmat == 'G') {
++timing_1.nbx;
zcopy_(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') {
zcopy_(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') {
second_(&t3);
timing_1.tmvbx += t3 - t2;
}
orth1 = FALSE_;
/* %------------------------------% */
/* | Compute the B-norm of r_{j}. | */
/* %------------------------------% */
if (*(unsigned char *)bmat == 'G') {
zdotc_(&z__1, n, &resid[1], &c__1, &workd[ipj], &c__1);
cnorm.r = z__1.r, cnorm.i = z__1.i;
d__1 = cnorm.r;
d__2 = d_imag(&cnorm);
*rnorm = sqrt(dlapy2_(&d__1, &d__2));
} else if (*(unsigned char *)bmat == 'I') {
*rnorm = dznrm2_(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) {
rtemp[0] = wnorm;
rtemp[1] = *rnorm;
dvout_(&debug_1.logfil, &c__2, rtemp, &debug_1.ndigit, "_naitr: re-o"
"rthogonalization; wnorm and rnorm are", (ftnlen)49);
zvout_(&debug_1.logfil, &j, &h__[j * h_dim1 + 1], &debug_1.ndigit,
"_naitr: j-th column of H", (ftnlen)24);
}
/* %----------------------------------------------------% */
/* | Compute V_{j}^T * B * r_{j}. | */
/* | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | */
/* %----------------------------------------------------% */
zgemv_("C", n, &j, &c_b1, &v[v_offset], ldv, &workd[ipj], &c__1, &c_b2, &
workd[irj], &c__1, (ftnlen)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. | */
/* %---------------------------------------------% */
z__1.r = -1., z__1.i = -0.;
zgemv_("N", n, &j, &z__1, &v[v_offset], ldv, &workd[irj], &c__1, &c_b1, &
resid[1], &c__1, (ftnlen)1);
zaxpy_(&j, &c_b1, &workd[irj], &c__1, &h__[j * h_dim1 + 1], &c__1);
orth2 = TRUE_;
second_(&t2);
if (*(unsigned char *)bmat == 'G') {
++timing_1.nbx;
zcopy_(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') {
zcopy_(n, &resid[1], &c__1, &workd[ipj], &c__1);
}
L90:
/* %---------------------------------------------------% */
/* | Back from reverse communication if ORTH2 = .true. | */
/* %---------------------------------------------------% */
if (*(unsigned char *)bmat == 'G') {
second_(&t3);
timing_1.tmvbx += t3 - t2;
}
/* %-----------------------------------------------------% */
/* | Compute the B-norm of the corrected residual r_{j}. | */
/* %-----------------------------------------------------% */
if (*(unsigned char *)bmat == 'G') {
zdotc_(&z__1, n, &resid[1], &c__1, &workd[ipj], &c__1);
cnorm.r = z__1.r, cnorm.i = z__1.i;
d__1 = cnorm.r;
d__2 = d_imag(&cnorm);
rnorm1 = sqrt(dlapy2_(&d__1, &d__2));
} else if (*(unsigned char *)bmat == 'I') {
rnorm1 = dznrm2_(n, &resid[1], &c__1);
}
if (msglvl > 0 && iter > 0) {
ivout_(&debug_1.logfil, &c__1, &j, &debug_1.ndigit, "_naitr: Iterati"
"ve refinement for Arnoldi residual", (ftnlen)49);
if (msglvl > 2) {
rtemp[0] = *rnorm;
rtemp[1] = rnorm1;
dvout_(&debug_1.logfil, &c__2, rtemp, &debug_1.ndigit, "_naitr: "
"iterative refinement ; rnorm and rnorm1 are", (ftnlen)51);
}
}
/* %-----------------------------------------% */
/* | 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) {
i__2 = jj;
resid[i__2].r = 0., resid[i__2].i = 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_;
second_(&t5);
timing_1.titref += t5 - t4;
/* %------------------------------------% */
/* | STEP 6: Update j = j+1; Continue | */
/* %------------------------------------% */
++j;
if (j > *k + *np) {
second_(&t1);
timing_1.tcaitr += 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 zlahqr | */
/* %--------------------------------------------% */
i__2 = i__ + i__ * h_dim1;
d__1 = h__[i__2].r;
d__2 = d_imag(&h__[i__ + i__ * h_dim1]);
i__3 = i__ + 1 + (i__ + 1) * h_dim1;
d__3 = h__[i__3].r;
d__4 = d_imag(&h__[i__ + 1 + (i__ + 1) * h_dim1]);
tst1 = dlapy2_(&d__1, &d__2) + dlapy2_(&d__3, &d__4);
if (tst1 == 0.) {
i__2 = *k + *np;
tst1 = zlanhs_("1", &i__2, &h__[h_offset], ldh, &workd[*n + 1]
, (ftnlen)1);
}
i__2 = i__ + 1 + i__ * h_dim1;
d__1 = h__[i__2].r;
d__2 = d_imag(&h__[i__ + 1 + i__ * h_dim1]);
/* Computing MAX */
d__3 = ulp * tst1;
if (dlapy2_(&d__1, &d__2) <= max(d__3,smlnum)) {
i__3 = i__ + 1 + i__ * h_dim1;
h__[i__3].r = 0., h__[i__3].i = 0.;
}
/* L110: */
}
if (msglvl > 2) {
i__1 = *k + *np;
i__2 = *k + *np;
zmout_(&debug_1.logfil, &i__1, &i__2, &h__[h_offset], ldh, &
debug_1.ndigit, "_naitr: Final upper Hessenberg matrix H"
" of order K+NP", (ftnlen)53);
}
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 znaitr | */
/* %---------------% */
} /* znaitr_ */
/* DECK DBOLSM */
/* Subroutine */ int dbolsm_(doublereal *w, integer *mdw, integer *minput,
integer *ncols, doublereal *bl, doublereal *bu, integer *ind, integer
*iopt, doublereal *x, doublereal *rnorm, integer *mode, doublereal *
rw, doublereal *ww, doublereal *scl, integer *ibasis, integer *ibb)
{
/* System generated locals */
address a__1[3], a__2[4], a__3[6], a__4[5], a__5[2], a__6[7];
integer w_dim1, w_offset, i__1[3], i__2[4], i__3, i__4[6], i__5[5], i__6[
2], i__7[7], i__8, i__9, i__10;
doublereal d__1, d__2;
char ch__1[47], ch__2[50], ch__3[79], ch__4[53], ch__5[94], ch__6[75],
ch__7[83], ch__8[92], ch__9[105], ch__10[102], ch__11[61], ch__12[
110], ch__13[134], ch__14[44], ch__15[76];
/* Local variables */
static integer i__, j;
static doublereal t, t1, t2, sc;
static integer ip, jp, lp;
static doublereal ss, wt, cl1, cl2, cl3, fac, big;
static integer lds;
static doublereal bou, beta;
static integer jbig, jmag, ioff, jcol;
static doublereal wbig;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static doublereal wmag;
static integer mval, iter;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
static doublereal xnew;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static char xern1[8], xern2[8], xern3[16], xern4[16];
static doublereal alpha;
static logical found;
static integer nsetb;
extern /* Subroutine */ int drotg_(doublereal *, doublereal *, doublereal
*, doublereal *), dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer igopr, itmax, itemp;
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
static integer lgopr;
extern /* Subroutine */ int dmout_(integer *, integer *, integer *,
doublereal *, char *, integer *, ftnlen);
static integer jdrop;
extern doublereal d1mach_(integer *);
extern /* Subroutine */ int dvout_(integer *, doublereal *, char *,
integer *, ftnlen), ivout_(integer *, integer *, char *, integer *
, ftnlen);
static integer mrows, jdrop1, jdrop2, jlarge;
static doublereal colabv, colblo, wlarge, tolind;
extern /* Subroutine */ int xermsg_(char *, char *, char *, integer *,
integer *, ftnlen, ftnlen, ftnlen);
static integer iprint;
static logical constr;
static doublereal tolsze;
/* Fortran I/O blocks */
static icilist io___2 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___3 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___4 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___6 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___8 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___9 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___10 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___12 = { 0, xern3, 0, "(1PD15.6)", 16, 1 };
static icilist io___14 = { 0, xern4, 0, "(1PD15.6)", 16, 1 };
static icilist io___15 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___16 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___17 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___18 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___31 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___32 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___33 = { 0, xern3, 0, "(1PD15.6)", 16, 1 };
static icilist io___34 = { 0, xern4, 0, "(1PD15.6)", 16, 1 };
static icilist io___35 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___36 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___37 = { 0, xern3, 0, "(1PD15.6)", 16, 1 };
static icilist io___38 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___39 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___40 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___41 = { 0, xern3, 0, "(1PD15.6)", 16, 1 };
static icilist io___42 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___43 = { 0, xern2, 0, "(I8)", 8, 1 };
static icilist io___44 = { 0, xern3, 0, "(1PD15.6)", 16, 1 };
static icilist io___45 = { 0, xern1, 0, "(I8)", 8, 1 };
static icilist io___54 = { 0, xern1, 0, "(I8)", 8, 1 };
/* ***BEGIN PROLOGUE DBOLSM */
/* ***SUBSIDIARY */
/* ***PURPOSE Subsidiary to DBOCLS and DBOLS */
/* ***LIBRARY SLATEC */
/* ***TYPE DOUBLE PRECISION (SBOLSM-S, DBOLSM-D) */
/* ***AUTHOR (UNKNOWN) */
/* ***DESCRIPTION */
/* **** Double Precision Version of SBOLSM **** */
/* **** All INPUT and OUTPUT real variables are DOUBLE PRECISION **** */
/* Solve E*X = F (least squares sense) with bounds on */
/* selected X values. */
/* The user must have DIMENSION statements of the form: */
/* DIMENSION W(MDW,NCOLS+1), BL(NCOLS), BU(NCOLS), */
/* * X(NCOLS+NX), RW(NCOLS), WW(NCOLS), SCL(NCOLS) */
/* INTEGER IND(NCOLS), IOPT(1+NI), IBASIS(NCOLS), IBB(NCOLS) */
/* (Here NX=number of extra locations required for options 1,...,7; */
/* NX=0 for no options; here NI=number of extra locations possibly */
/* required for options 1-7; NI=0 for no options; NI=14 if all the */
/* options are simultaneously in use.) */
/* INPUT */
/* ----- */
/* -------------------- */
/* W(MDW,*),MINPUT,NCOLS */
/* -------------------- */
/* The array W(*,*) contains the matrix [E:F] on entry. The matrix */
/* [E:F] has MINPUT rows and NCOLS+1 columns. This data is placed in */
/* the array W(*,*) with E occupying the first NCOLS columns and the */
/* right side vector F in column NCOLS+1. The row dimension, MDW, of */
/* the array W(*,*) must satisfy the inequality MDW .ge. MINPUT. */
/* Other values of MDW are errors. The values of MINPUT and NCOLS */
/* must be positive. Other values are errors. */
/* ------------------ */
/* BL(*),BU(*),IND(*) */
/* ------------------ */
/* These arrays contain the information about the bounds that the */
/* solution values are to satisfy. The value of IND(J) tells the */
/* type of bound and BL(J) and BU(J) give the explicit values for */
/* the respective upper and lower bounds. */
/* 1. For IND(J)=1, require X(J) .ge. BL(J). */
/* 2. For IND(J)=2, require X(J) .le. BU(J). */
/* 3. For IND(J)=3, require X(J) .ge. BL(J) and */
/* X(J) .le. BU(J). */
/* 4. For IND(J)=4, no bounds on X(J) are required. */
/* The values of BL(*),BL(*) are modified by the subprogram. Values */
/* other than 1,2,3 or 4 for IND(J) are errors. In the case IND(J)=3 */
/* (upper and lower bounds) the condition BL(J) .gt. BU(J) is an */
/* error. */
/* ------- */
/* IOPT(*) */
/* ------- */
/* This is the array where the user can specify nonstandard options */
/* for DBOLSM. Most of the time this feature can be ignored by */
/* setting the input value IOPT(1)=99. Occasionally users may have */
/* needs that require use of the following subprogram options. For */
/* details about how to use the options see below: IOPT(*) CONTENTS. */
/* Option Number Brief Statement of Purpose */
/* ----- ------ ----- --------- -- ------- */
/* 1 Move the IOPT(*) processing pointer. */
/* 2 Change rank determination tolerance. */
/* 3 Change blow-up factor that determines the */
/* size of variables being dropped from active */
/* status. */
/* 4 Reset the maximum number of iterations to use */
/* in solving the problem. */
/* 5 The data matrix is triangularized before the */
/* problem is solved whenever (NCOLS/MINPUT) .lt. */
/* FAC. Change the value of FAC. */
/* 6 Redefine the weighting matrix used for */
/* linear independence checking. */
/* 7 Debug output is desired. */
/* 99 No more options to change. */
/* ---- */
/* X(*) */
/* ---- */
/* This array is used to pass data associated with options 1,2,3 and */
/* 5. Ignore this input parameter if none of these options are used. */
/* Otherwise see below: IOPT(*) CONTENTS. */
/* ---------------- */
/* IBASIS(*),IBB(*) */
/* ---------------- */
/* These arrays must be initialized by the user. The values */
/* IBASIS(J)=J, J=1,...,NCOLS */
/* IBB(J) =1, J=1,...,NCOLS */
/* are appropriate except when using nonstandard features. */
/* ------ */
/* SCL(*) */
/* ------ */
/* This is the array of scaling factors to use on the columns of the */
/* matrix E. These values must be defined by the user. To suppress */
/* any column scaling set SCL(J)=1.0, J=1,...,NCOLS. */
/* OUTPUT */
/* ------ */
/* ---------- */
/* X(*),RNORM */
/* ---------- */
/* The array X(*) contains a solution (if MODE .ge. 0 or .eq. -22) */
/* for the constrained least squares problem. The value RNORM is the */
/* minimum residual vector length. */
/* ---- */
/* MODE */
/* ---- */
/* The sign of mode determines whether the subprogram has completed */
/* normally, or encountered an error condition or abnormal status. */
/* A value of MODE .ge. 0 signifies that the subprogram has completed */
/* normally. The value of MODE (.ge. 0) is the number of variables */
/* in an active status: not at a bound nor at the value ZERO, for */
/* the case of free variables. A negative value of MODE will be one */
/* of the 18 cases -38,-37,...,-22, or -1. Values .lt. -1 correspond */
/* to an abnormal completion of the subprogram. To understand the */
/* abnormal completion codes see below: ERROR MESSAGES for DBOLSM */
/* An approximate solution will be returned to the user only when */
/* maximum iterations is reached, MODE=-22. */
/* ----------- */
/* RW(*),WW(*) */
/* ----------- */
/* These are working arrays each with NCOLS entries. The array RW(*) */
/* contains the working (scaled, nonactive) solution values. The */
/* array WW(*) contains the working (scaled, active) gradient vector */
/* values. */
/* ---------------- */
/* IBASIS(*),IBB(*) */
/* ---------------- */
/* These arrays contain information about the status of the solution */
/* when MODE .ge. 0. The indices IBASIS(K), K=1,...,MODE, show the */
/* nonactive variables; indices IBASIS(K), K=MODE+1,..., NCOLS are */
/* the active variables. The value (IBB(J)-1) is the number of times */
/* variable J was reflected from its upper bound. (Normally the user */
/* can ignore these parameters.) */
/* IOPT(*) CONTENTS */
/* ------- -------- */
/* The option array allows a user to modify internal variables in */
/* the subprogram without recompiling the source code. A central */
/* goal of the initial software design was to do a good job for most */
/* people. Thus the use of options will be restricted to a select */
/* group of users. The processing of the option array proceeds as */
/* follows: a pointer, here called LP, is initially set to the value */
/* 1. The value is updated as the options are processed. At the */
/* pointer position the option number is extracted and used for */
/* locating other information that allows for options to be changed. */
/* The portion of the array IOPT(*) that is used for each option is */
/* fixed; the user and the subprogram both know how many locations */
/* are needed for each option. A great deal of error checking is */
/* done by the subprogram on the contents of the option array. */
/* Nevertheless it is still possible to give the subprogram optional */
/* input that is meaningless. For example, some of the options use */
/* the location X(NCOLS+IOFF) for passing data. The user must manage */
/* the allocation of these locations when more than one piece of */
/* option data is being passed to the subprogram. */
/* 1 */
/* - */
/* Move the processing pointer (either forward or backward) to the */
/* location IOPT(LP+1). The processing pointer is moved to location */
/* LP+2 of IOPT(*) in case IOPT(LP)=-1. For example to skip over */
/* locations 3,...,NCOLS+2 of IOPT(*), */
/* IOPT(1)=1 */
/* IOPT(2)=NCOLS+3 */
/* (IOPT(I), I=3,...,NCOLS+2 are not defined here.) */
/* IOPT(NCOLS+3)=99 */
/* CALL DBOLSM */
/* CAUTION: Misuse of this option can yield some very hard-to-find */
/* bugs. Use it with care. */
/* 2 */
/* - */
/* The algorithm that solves the bounded least squares problem */
/* iteratively drops columns from the active set. This has the */
/* effect of joining a new column vector to the QR factorization of */
/* the rectangular matrix consisting of the partially triangularized */
/* nonactive columns. After triangularizing this matrix a test is */
/* made on the size of the pivot element. The column vector is */
/* rejected as dependent if the magnitude of the pivot element is */
/* .le. TOL* magnitude of the column in components strictly above */
/* the pivot element. Nominally the value of this (rank) tolerance */
/* is TOL = SQRT(R1MACH(4)). To change only the value of TOL, for */
/* example, */
/* X(NCOLS+1)=TOL */
/* IOPT(1)=2 */
/* IOPT(2)=1 */
/* IOPT(3)=99 */
/* CALL DBOLSM */
/* Generally, if LP is the processing pointer for IOPT(*), */
/* X(NCOLS+IOFF)=TOL */
/* IOPT(LP)=2 */
/* IOPT(LP+1)=IOFF */
/* . */
/* CALL DBOLSM */
/* The required length of IOPT(*) is increased by 2 if option 2 is */
/* used; The required length of X(*) is increased by 1. A value of */
/* IOFF .le. 0 is an error. A value of TOL .le. R1MACH(4) gives a */
/* warning message; it is not considered an error. */
/* 3 */
/* - */
/* A solution component is left active (not used) if, roughly */
/* speaking, it seems too large. Mathematically the new component is */
/* left active if the magnitude is .ge.((vector norm of F)/(matrix */
/* norm of E))/BLOWUP. Nominally the factor BLOWUP = SQRT(R1MACH(4)). */
/* To change only the value of BLOWUP, for example, */
/* X(NCOLS+2)=BLOWUP */
/* IOPT(1)=3 */
/* IOPT(2)=2 */
/* IOPT(3)=99 */
/* CALL DBOLSM */
/* Generally, if LP is the processing pointer for IOPT(*), */
/* X(NCOLS+IOFF)=BLOWUP */
/* IOPT(LP)=3 */
/* IOPT(LP+1)=IOFF */
/* . */
/* CALL DBOLSM */
/* The required length of IOPT(*) is increased by 2 if option 3 is */
/* used; the required length of X(*) is increased by 1. A value of */
/* IOFF .le. 0 is an error. A value of BLOWUP .le. 0.0 is an error. */
/* 4 */
/* - */
/* Normally the algorithm for solving the bounded least squares */
/* problem requires between NCOLS/3 and NCOLS drop-add steps to */
/* converge. (this remark is based on examining a small number of */
/* test cases.) The amount of arithmetic for such problems is */
/* typically about twice that required for linear least squares if */
/* there are no bounds and if plane rotations are used in the */
/* solution method. Convergence of the algorithm, while */
/* mathematically certain, can be much slower than indicated. To */
/* avoid this potential but unlikely event ITMAX drop-add steps are */
/* permitted. Nominally ITMAX=5*(MAX(MINPUT,NCOLS)). To change the */
/* value of ITMAX, for example, */
/* IOPT(1)=4 */
/* IOPT(2)=ITMAX */
/* IOPT(3)=99 */
/* CALL DBOLSM */
/* Generally, if LP is the processing pointer for IOPT(*), */
/* IOPT(LP)=4 */
/* IOPT(LP+1)=ITMAX */
/* . */
/* CALL DBOLSM */
/* The value of ITMAX must be .gt. 0. Other values are errors. Use */
/* of this option increases the required length of IOPT(*) by 2. */
/* 5 */
/* - */
/* For purposes of increased efficiency the MINPUT by NCOLS+1 data */
/* matrix [E:F] is triangularized as a first step whenever MINPUT */
/* satisfies FAC*MINPUT .gt. NCOLS. Nominally FAC=0.75. To change the */
/* value of FAC, */
/* X(NCOLS+3)=FAC */
/* IOPT(1)=5 */
/* IOPT(2)=3 */
/* IOPT(3)=99 */
/* CALL DBOLSM */
/* Generally, if LP is the processing pointer for IOPT(*), */
/* X(NCOLS+IOFF)=FAC */
/* IOPT(LP)=5 */
/* IOPT(LP+1)=IOFF */
/* . */
/* CALL DBOLSM */
/* The value of FAC must be nonnegative. Other values are errors. */
/* Resetting FAC=0.0 suppresses the initial triangularization step. */
/* Use of this option increases the required length of IOPT(*) by 2; */
/* The required length of of X(*) is increased by 1. */
/* 6 */
/* - */
/* The norm used in testing the magnitudes of the pivot element */
/* compared to the mass of the column above the pivot line can be */
/* changed. The type of change that this option allows is to weight */
/* the components with an index larger than MVAL by the parameter */
/* WT. Normally MVAL=0 and WT=1. To change both the values MVAL and */
/* WT, where LP is the processing pointer for IOPT(*), */
/* X(NCOLS+IOFF)=WT */
/* IOPT(LP)=6 */
/* IOPT(LP+1)=IOFF */
/* IOPT(LP+2)=MVAL */
/* Use of this option increases the required length of IOPT(*) by 3. */
/* The length of X(*) is increased by 1. Values of MVAL must be */
/* nonnegative and not greater than MINPUT. Other values are errors. */
/* The value of WT must be positive. Any other value is an error. If */
/* either error condition is present a message will be printed. */
/* 7 */
/* - */
/* Debug output, showing the detailed add-drop steps for the */
/* constrained least squares problem, is desired. This option is */
/* intended to be used to locate suspected bugs. */
/* 99 */
/* -- */
/* There are no more options to change. */
/* The values for options are 1,...,7,99, and are the only ones */
/* permitted. Other values are errors. Options -99,-1,...,-7 mean */
/* that the repective options 99,1,...,7 are left at their default */
/* values. An example is the option to modify the (rank) tolerance: */
/* X(NCOLS+1)=TOL */
/* IOPT(1)=-2 */
/* IOPT(2)=1 */
/* IOPT(3)=99 */
/* Error Messages for DBOLSM */
/* ----- -------- --- --------- */
/* -22 MORE THAN ITMAX = ... ITERATIONS SOLVING BOUNDED LEAST */
/* SQUARES PROBLEM. */
/* -23 THE OPTION NUMBER = ... IS NOT DEFINED. */
/* -24 THE OFFSET = ... BEYOND POSTION NCOLS = ... MUST BE POSITIVE */
/* FOR OPTION NUMBER 2. */
/* -25 THE TOLERANCE FOR RANK DETERMINATION = ... IS LESS THAN */
/* MACHINE PRECISION = .... */
/* -26 THE OFFSET = ... BEYOND POSITION NCOLS = ... MUST BE POSTIVE */
/* FOR OPTION NUMBER 3. */
/* -27 THE RECIPROCAL OF THE BLOW-UP FACTOR FOR REJECTING VARIABLES */
/* MUST BE POSITIVE. NOW = .... */
/* -28 THE MAXIMUM NUMBER OF ITERATIONS = ... MUST BE POSITIVE. */
/* -29 THE OFFSET = ... BEYOND POSITION NCOLS = ... MUST BE POSTIVE */
/* FOR OPTION NUMBER 5. */
/* -30 THE FACTOR (NCOLS/MINPUT) WHERE PRETRIANGULARIZING IS */
/* PERFORMED MUST BE NONNEGATIVE. NOW = .... */
/* -31 THE NUMBER OF ROWS = ... MUST BE POSITIVE. */
/* -32 THE NUMBER OF COLUMNS = ... MUST BE POSTIVE. */
/* -33 THE ROW DIMENSION OF W(,) = ... MUST BE .GE. THE NUMBER OF */
/* ROWS = .... */
/* -34 FOR J = ... THE CONSTRAINT INDICATOR MUST BE 1-4. */
/* -35 FOR J = ... THE LOWER BOUND = ... IS .GT. THE UPPER BOUND = */
/* .... */
/* -36 THE INPUT ORDER OF COLUMNS = ... IS NOT BETWEEN 1 AND NCOLS */
/* = .... */
/* -37 THE BOUND POLARITY FLAG IN COMPONENT J = ... MUST BE */
/* POSITIVE. NOW = .... */
/* -38 THE ROW SEPARATOR TO APPLY WEIGHTING (...) MUST LIE BETWEEN */
/* 0 AND MINPUT = .... WEIGHT = ... MUST BE POSITIVE. */
/* ***SEE ALSO DBOCLS, DBOLS */
/* ***ROUTINES CALLED D1MACH, DAXPY, DCOPY, DDOT, DMOUT, DNRM2, DROT, */
/* DROTG, DSWAP, DVOUT, IVOUT, XERMSG */
/* ***REVISION HISTORY (YYMMDD) */
/* 821220 DATE WRITTEN */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900328 Added TYPE section. (WRB) */
/* 900510 Convert XERRWV calls to XERMSG calls. (RWC) */
/* 920422 Fixed usage of MINPUT. (WRB) */
/* 901009 Editorial changes, code now reads from top to bottom. (RWC) */
/* ***END PROLOGUE DBOLSM */
/* PURPOSE */
/* ------- */
/* THIS IS THE MAIN SUBPROGRAM THAT SOLVES THE BOUNDED */
/* LEAST SQUARES PROBLEM. THE PROBLEM SOLVED HERE IS: */
/* SOLVE E*X = F (LEAST SQUARES SENSE) */
/* WITH BOUNDS ON SELECTED X VALUES. */
/* TO CHANGE THIS SUBPROGRAM FROM SINGLE TO DOUBLE PRECISION BEGIN */
/* EDITING AT THE CARD 'C++'. */
/* CHANGE THE SUBPROGRAM NAME TO DBOLSM AND THE STRINGS */
/* /SAXPY/ TO /DAXPY/, /SCOPY/ TO /DCOPY/, */
/* /SDOT/ TO /DDOT/, /SNRM2/ TO /DNRM2/, */
/* /SROT/ TO /DROT/, /SROTG/ TO /DROTG/, /R1MACH/ TO /D1MACH/, */
/* /SVOUT/ TO /DVOUT/, /SMOUT/ TO /DMOUT/, */
/* /SSWAP/ TO /DSWAP/, /E0/ TO /D0/, */
/* /REAL / TO /DOUBLE PRECISION/. */
/* ++ */
/* ***FIRST EXECUTABLE STATEMENT DBOLSM */
/* Verify that the problem dimensions are defined properly. */
/* Parameter adjustments */
w_dim1 = *mdw;
w_offset = 1 + w_dim1;
w -= w_offset;
--bl;
--bu;
--ind;
--iopt;
--x;
--rw;
--ww;
--scl;
--ibasis;
--ibb;
/* Function Body */
if (*minput <= 0) {
s_wsfi(&io___2);
do_fio(&c__1, (char *)&(*minput), (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__1[0] = 21, a__1[0] = "THE NUMBER OF ROWS = ";
i__1[1] = 8, a__1[1] = xern1;
i__1[2] = 18, a__1[2] = " MUST BE POSITIVE.";
s_cat(ch__1, a__1, i__1, &c__3, (ftnlen)47);
xermsg_("SLATEC", "DBOLSM", ch__1, &c__31, &c__1, (ftnlen)6, (ftnlen)
6, (ftnlen)47);
*mode = -31;
return 0;
}
if (*ncols <= 0) {
s_wsfi(&io___3);
do_fio(&c__1, (char *)&(*ncols), (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__1[0] = 24, a__1[0] = "THE NUMBER OF COLUMNS = ";
i__1[1] = 8, a__1[1] = xern1;
i__1[2] = 18, a__1[2] = " MUST BE POSITIVE.";
s_cat(ch__2, a__1, i__1, &c__3, (ftnlen)50);
xermsg_("SLATEC", "DBOLSM", ch__2, &c__32, &c__1, (ftnlen)6, (ftnlen)
6, (ftnlen)50);
*mode = -32;
return 0;
}
if (*mdw < *minput) {
s_wsfi(&io___4);
do_fio(&c__1, (char *)&(*mdw), (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___6);
do_fio(&c__1, (char *)&(*minput), (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__2[0] = 28, a__2[0] = "THE ROW DIMENSION OF W(,) = ";
i__2[1] = 8, a__2[1] = xern1;
i__2[2] = 35, a__2[2] = " MUST BE .GE. THE NUMBER OF ROWS = ";
i__2[3] = 8, a__2[3] = xern2;
s_cat(ch__3, a__2, i__2, &c__4, (ftnlen)79);
xermsg_("SLATEC", "DBOLSM", ch__3, &c__33, &c__1, (ftnlen)6, (ftnlen)
6, (ftnlen)79);
*mode = -33;
return 0;
}
/* Verify that bound information is correct. */
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
if (ind[j] < 1 || ind[j] > 4) {
s_wsfi(&io___8);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___9);
do_fio(&c__1, (char *)&ind[j], (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__1[0] = 8, a__1[0] = "FOR J = ";
i__1[1] = 8, a__1[1] = xern1;
i__1[2] = 37, a__1[2] = " THE CONSTRAINT INDICATOR MUST BE 1-4";
s_cat(ch__4, a__1, i__1, &c__3, (ftnlen)53);
xermsg_("SLATEC", "DBOLSM", ch__4, &c__34, &c__1, (ftnlen)6, (
ftnlen)6, (ftnlen)53);
*mode = -34;
return 0;
}
/* L10: */
}
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
if (ind[j] == 3) {
if (bu[j] < bl[j]) {
s_wsfi(&io___10);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___12);
do_fio(&c__1, (char *)&bl[j], (ftnlen)sizeof(doublereal));
e_wsfi();
s_wsfi(&io___14);
do_fio(&c__1, (char *)&bu[j], (ftnlen)sizeof(doublereal));
e_wsfi();
/* Writing concatenation */
i__4[0] = 8, a__3[0] = "FOR J = ";
i__4[1] = 8, a__3[1] = xern1;
i__4[2] = 19, a__3[2] = " THE LOWER BOUND = ";
i__4[3] = 16, a__3[3] = xern3;
i__4[4] = 27, a__3[4] = " IS .GT. THE UPPER BOUND = ";
i__4[5] = 16, a__3[5] = xern4;
s_cat(ch__5, a__3, i__4, &c__6, (ftnlen)94);
xermsg_("SLATEC", "DBOLSM", ch__5, &c__35, &c__1, (ftnlen)6, (
ftnlen)6, (ftnlen)94);
*mode = -35;
return 0;
}
}
/* L20: */
}
/* Check that permutation and polarity arrays have been set. */
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
if (ibasis[j] < 1 || ibasis[j] > *ncols) {
s_wsfi(&io___15);
do_fio(&c__1, (char *)&ibasis[j], (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___16);
do_fio(&c__1, (char *)&(*ncols), (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__2[0] = 29, a__2[0] = "THE INPUT ORDER OF COLUMNS = ";
i__2[1] = 8, a__2[1] = xern1;
i__2[2] = 30, a__2[2] = " IS NOT BETWEEN 1 AND NCOLS = ";
i__2[3] = 8, a__2[3] = xern2;
s_cat(ch__6, a__2, i__2, &c__4, (ftnlen)75);
xermsg_("SLATEC", "DBOLSM", ch__6, &c__36, &c__1, (ftnlen)6, (
ftnlen)6, (ftnlen)75);
*mode = -36;
return 0;
}
if (ibb[j] <= 0) {
s_wsfi(&io___17);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___18);
do_fio(&c__1, (char *)&ibb[j], (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__2[0] = 41, a__2[0] = "THE BOUND POLARITY FLAG IN COMPONENT J "
"= ";
i__2[1] = 8, a__2[1] = xern1;
i__2[2] = 26, a__2[2] = " MUST BE POSITIVE.$$NOW = ";
i__2[3] = 8, a__2[3] = xern2;
s_cat(ch__7, a__2, i__2, &c__4, (ftnlen)83);
xermsg_("SLATEC", "DBOLSM", ch__7, &c__37, &c__1, (ftnlen)6, (
ftnlen)6, (ftnlen)83);
*mode = -37;
return 0;
}
/* L30: */
}
/* Process the option array. */
fac = .75;
tolind = sqrt(d1mach_(&c__4));
tolsze = sqrt(d1mach_(&c__4));
itmax = max(*minput,*ncols) * 5;
wt = 1.;
mval = 0;
iprint = 0;
/* Changes to some parameters can occur through the option array, */
/* IOPT(*). Process this array looking carefully for input data */
/* errors. */
lp = 0;
lds = 0;
/* Test for no more options. */
L590:
lp += lds;
ip = iopt[lp + 1];
jp = abs(ip);
if (ip == 99) {
goto L470;
} else if (jp == 99) {
lds = 1;
} else if (jp == 1) {
/* Move the IOPT(*) processing pointer. */
if (ip > 0) {
lp = iopt[lp + 2] - 1;
lds = 0;
} else {
lds = 2;
}
} else if (jp == 2) {
/* Change tolerance for rank determination. */
if (ip > 0) {
ioff = iopt[lp + 2];
if (ioff <= 0) {
s_wsfi(&io___31);
do_fio(&c__1, (char *)&ioff, (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___32);
do_fio(&c__1, (char *)&(*ncols), (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__5[0] = 13, a__4[0] = "THE OFFSET = ";
i__5[1] = 8, a__4[1] = xern1;
i__5[2] = 25, a__4[2] = " BEYOND POSITION NCOLS = ";
i__5[3] = 8, a__4[3] = xern2;
i__5[4] = 38, a__4[4] = " MUST BE POSITIVE FOR OPTION NUMBER"
" 2.";
s_cat(ch__8, a__4, i__5, &c__5, (ftnlen)92);
xermsg_("SLATEC", "DBOLSM", ch__8, &c__24, &c__1, (ftnlen)6, (
ftnlen)6, (ftnlen)92);
*mode = -24;
return 0;
}
tolind = x[*ncols + ioff];
if (tolind < d1mach_(&c__4)) {
s_wsfi(&io___33);
do_fio(&c__1, (char *)&tolind, (ftnlen)sizeof(doublereal));
e_wsfi();
s_wsfi(&io___34);
d__1 = d1mach_(&c__4);
do_fio(&c__1, (char *)&d__1, (ftnlen)sizeof(doublereal));
e_wsfi();
/* Writing concatenation */
i__2[0] = 39, a__2[0] = "THE TOLERANCE FOR RANK DETERMINATIO"
"N = ";
i__2[1] = 16, a__2[1] = xern3;
i__2[2] = 34, a__2[2] = " IS LESS THAN MACHINE PRECISION = ";
i__2[3] = 16, a__2[3] = xern4;
s_cat(ch__9, a__2, i__2, &c__4, (ftnlen)105);
xermsg_("SLATEC", "DBOLSM", ch__9, &c__25, &c__0, (ftnlen)6, (
ftnlen)6, (ftnlen)105);
*mode = -25;
}
}
lds = 2;
} else if (jp == 3) {
/* Change blowup factor for allowing variables to become */
/* inactive. */
if (ip > 0) {
ioff = iopt[lp + 2];
if (ioff <= 0) {
s_wsfi(&io___35);
do_fio(&c__1, (char *)&ioff, (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___36);
do_fio(&c__1, (char *)&(*ncols), (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__5[0] = 13, a__4[0] = "THE OFFSET = ";
i__5[1] = 8, a__4[1] = xern1;
i__5[2] = 25, a__4[2] = " BEYOND POSITION NCOLS = ";
i__5[3] = 8, a__4[3] = xern2;
i__5[4] = 38, a__4[4] = " MUST BE POSITIVE FOR OPTION NUMBER"
" 3.";
s_cat(ch__8, a__4, i__5, &c__5, (ftnlen)92);
xermsg_("SLATEC", "DBOLSM", ch__8, &c__26, &c__1, (ftnlen)6, (
ftnlen)6, (ftnlen)92);
*mode = -26;
return 0;
}
tolsze = x[*ncols + ioff];
if (tolsze <= 0.) {
s_wsfi(&io___37);
do_fio(&c__1, (char *)&tolsze, (ftnlen)sizeof(doublereal));
e_wsfi();
/* Writing concatenation */
i__6[0] = 86, a__5[0] = "THE RECIPROCAL OF THE BLOW-UP FACTO"
"R FOR REJECTING VARIABLES MUST BE POSITIVE.$$NOW = ";
i__6[1] = 16, a__5[1] = xern3;
s_cat(ch__10, a__5, i__6, &c__2, (ftnlen)102);
xermsg_("SLATEC", "DBOLSM", ch__10, &c__27, &c__1, (ftnlen)6,
(ftnlen)6, (ftnlen)102);
*mode = -27;
return 0;
}
}
lds = 2;
} else if (jp == 4) {
/* Change the maximum number of iterations allowed. */
if (ip > 0) {
itmax = iopt[lp + 2];
if (itmax <= 0) {
s_wsfi(&io___38);
do_fio(&c__1, (char *)&itmax, (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__1[0] = 35, a__1[0] = "THE MAXIMUM NUMBER OF ITERATIONS = ";
i__1[1] = 8, a__1[1] = xern1;
i__1[2] = 18, a__1[2] = " MUST BE POSITIVE.";
s_cat(ch__11, a__1, i__1, &c__3, (ftnlen)61);
xermsg_("SLATEC", "DBOLSM", ch__11, &c__28, &c__1, (ftnlen)6,
(ftnlen)6, (ftnlen)61);
*mode = -28;
return 0;
}
}
lds = 2;
} else if (jp == 5) {
/* Change the factor for pretriangularizing the data matrix. */
if (ip > 0) {
ioff = iopt[lp + 2];
if (ioff <= 0) {
s_wsfi(&io___39);
do_fio(&c__1, (char *)&ioff, (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___40);
do_fio(&c__1, (char *)&(*ncols), (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__5[0] = 13, a__4[0] = "THE OFFSET = ";
i__5[1] = 8, a__4[1] = xern1;
i__5[2] = 25, a__4[2] = " BEYOND POSITION NCOLS = ";
i__5[3] = 8, a__4[3] = xern2;
i__5[4] = 38, a__4[4] = " MUST BE POSITIVE FOR OPTION NUMBER"
" 5.";
s_cat(ch__8, a__4, i__5, &c__5, (ftnlen)92);
xermsg_("SLATEC", "DBOLSM", ch__8, &c__29, &c__1, (ftnlen)6, (
ftnlen)6, (ftnlen)92);
*mode = -29;
return 0;
}
fac = x[*ncols + ioff];
if (fac < 0.) {
s_wsfi(&io___41);
do_fio(&c__1, (char *)&fac, (ftnlen)sizeof(doublereal));
e_wsfi();
/* Writing concatenation */
i__6[0] = 94, a__5[0] = "THE FACTOR (NCOLS/MINPUT) WHERE PRE"
"-TRIANGULARIZING IS PERFORMED MUST BE NON-NEGATIVE.$"
"$NOW = ";
i__6[1] = 16, a__5[1] = xern3;
s_cat(ch__12, a__5, i__6, &c__2, (ftnlen)110);
xermsg_("SLATEC", "DBOLSM", ch__12, &c__30, &c__0, (ftnlen)6,
(ftnlen)6, (ftnlen)110);
*mode = -30;
return 0;
}
}
lds = 2;
} else if (jp == 6) {
/* Change the weighting factor (from 1.0) to apply to components */
/* numbered .gt. MVAL (initially set to 1.) This trick is needed */
/* for applications of this subprogram to the heavily weighted */
/* least squares problem that come from equality constraints. */
if (ip > 0) {
ioff = iopt[lp + 2];
mval = iopt[lp + 3];
wt = x[*ncols + ioff];
}
if (mval < 0 || mval > *minput || wt <= 0.) {
s_wsfi(&io___42);
do_fio(&c__1, (char *)&mval, (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___43);
do_fio(&c__1, (char *)&(*minput), (ftnlen)sizeof(integer));
e_wsfi();
s_wsfi(&io___44);
do_fio(&c__1, (char *)&wt, (ftnlen)sizeof(doublereal));
e_wsfi();
/* Writing concatenation */
i__7[0] = 38, a__6[0] = "THE ROW SEPARATOR TO APPLY WEIGHTING (";
i__7[1] = 8, a__6[1] = xern1;
i__7[2] = 34, a__6[2] = ") MUST LIE BETWEEN 0 AND MINPUT = ";
i__7[3] = 8, a__6[3] = xern2;
i__7[4] = 12, a__6[4] = ".$$WEIGHT = ";
i__7[5] = 16, a__6[5] = xern3;
i__7[6] = 18, a__6[6] = " MUST BE POSITIVE.";
s_cat(ch__13, a__6, i__7, &c__7, (ftnlen)134);
xermsg_("SLATEC", "DBOLSM", ch__13, &c__38, &c__0, (ftnlen)6, (
ftnlen)6, (ftnlen)134);
*mode = -38;
return 0;
}
lds = 3;
} else if (jp == 7) {
/* Turn on debug output. */
if (ip > 0) {
iprint = 1;
}
lds = 2;
} else {
s_wsfi(&io___45);
do_fio(&c__1, (char *)&ip, (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__1[0] = 20, a__1[0] = "THE OPTION NUMBER = ";
i__1[1] = 8, a__1[1] = xern1;
i__1[2] = 16, a__1[2] = " IS NOT DEFINED.";
s_cat(ch__14, a__1, i__1, &c__3, (ftnlen)44);
xermsg_("SLATEC", "DBOLSM", ch__14, &c__23, &c__1, (ftnlen)6, (ftnlen)
6, (ftnlen)44);
*mode = -23;
return 0;
}
goto L590;
/* Pretriangularize rectangular arrays of certain sizes for */
/* increased efficiency. */
L470:
if (fac * *minput > (doublereal) (*ncols)) {
i__3 = *ncols + 1;
for (j = 1; j <= i__3; ++j) {
i__8 = j + mval + 1;
for (i__ = *minput; i__ >= i__8; --i__) {
drotg_(&w[i__ - 1 + j * w_dim1], &w[i__ + j * w_dim1], &sc, &
ss);
w[i__ + j * w_dim1] = 0.;
i__9 = *ncols - j + 1;
drot_(&i__9, &w[i__ - 1 + (j + 1) * w_dim1], mdw, &w[i__ + (j
+ 1) * w_dim1], mdw, &sc, &ss);
/* L480: */
}
/* L490: */
}
mrows = *ncols + mval + 1;
} else {
mrows = *minput;
}
/* Set the X(*) array to zero so all components are defined. */
dcopy_(ncols, &c_b185, &c__0, &x[1], &c__1);
/* The arrays IBASIS(*) and IBB(*) are initialized by the calling */
/* program and the column scaling is defined in the calling program. */
/* 'BIG' is plus infinity on this machine. */
big = d1mach_(&c__2);
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
if (ind[j] == 1) {
bu[j] = big;
} else if (ind[j] == 2) {
bl[j] = -big;
} else if (ind[j] == 4) {
bl[j] = -big;
bu[j] = big;
}
/* L550: */
}
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
if (bl[j] <= 0. && 0. <= bu[j] && (d__1 = bu[j], abs(d__1)) < (d__2 =
bl[j], abs(d__2)) || bu[j] < 0.) {
t = bu[j];
bu[j] = -bl[j];
bl[j] = -t;
scl[j] = -scl[j];
i__8 = mrows;
for (i__ = 1; i__ <= i__8; ++i__) {
w[i__ + j * w_dim1] = -w[i__ + j * w_dim1];
/* L560: */
}
}
/* Indices in set T(=TIGHT) are denoted by negative values */
/* of IBASIS(*). */
if (bl[j] >= 0.) {
ibasis[j] = -ibasis[j];
t = -bl[j];
bu[j] += t;
daxpy_(&mrows, &t, &w[j * w_dim1 + 1], &c__1, &w[(*ncols + 1) *
w_dim1 + 1], &c__1);
}
/* L570: */
}
nsetb = 0;
iter = 0;
if (iprint > 0) {
i__3 = *ncols + 1;
dmout_(&mrows, &i__3, mdw, &w[w_offset], "(' PRETRI. INPUT MATRIX')",
&c_n4, (ftnlen)25);
dvout_(ncols, &bl[1], "(' LOWER BOUNDS')", &c_n4, (ftnlen)17);
dvout_(ncols, &bu[1], "(' UPPER BOUNDS')", &c_n4, (ftnlen)17);
}
L580:
++iter;
if (iter > itmax) {
s_wsfi(&io___54);
do_fio(&c__1, (char *)&itmax, (ftnlen)sizeof(integer));
e_wsfi();
/* Writing concatenation */
i__1[0] = 18, a__1[0] = "MORE THAN ITMAX = ";
i__1[1] = 8, a__1[1] = xern1;
i__1[2] = 50, a__1[2] = " ITERATIONS SOLVING BOUNDED LEAST SQUARES P"
"ROBLEM.";
s_cat(ch__15, a__1, i__1, &c__3, (ftnlen)76);
xermsg_("SLATEC", "DBOLSM", ch__15, &c__22, &c__1, (ftnlen)6, (ftnlen)
6, (ftnlen)76);
*mode = -22;
/* Rescale and translate variables. */
igopr = 1;
goto L130;
}
/* Find a variable to become non-active. */
/* T */
/* Compute (negative) of gradient vector, W = E *(F-E*X). */
dcopy_(ncols, &c_b185, &c__0, &ww[1], &c__1);
i__3 = *ncols;
for (j = nsetb + 1; j <= i__3; ++j) {
jcol = (i__8 = ibasis[j], abs(i__8));
i__8 = mrows - nsetb;
/* Computing MIN */
i__9 = nsetb + 1;
/* Computing MIN */
i__10 = nsetb + 1;
ww[j] = ddot_(&i__8, &w[min(i__9,mrows) + j * w_dim1], &c__1, &w[min(
i__10,mrows) + (*ncols + 1) * w_dim1], &c__1) * (d__1 = scl[
jcol], abs(d__1));
/* L200: */
}
if (iprint > 0) {
dvout_(ncols, &ww[1], "(' GRADIENT VALUES')", &c_n4, (ftnlen)20);
ivout_(ncols, &ibasis[1], "(' INTERNAL VARIABLE ORDER')", &c_n4, (
ftnlen)28);
ivout_(ncols, &ibb[1], "(' BOUND POLARITY')", &c_n4, (ftnlen)19);
}
/* If active set = number of total rows, quit. */
L210:
if (nsetb == mrows) {
found = FALSE_;
goto L120;
}
/* Choose an extremal component of gradient vector for a candidate */
/* to become non-active. */
wlarge = -big;
wmag = -big;
i__3 = *ncols;
for (j = nsetb + 1; j <= i__3; ++j) {
t = ww[j];
if (t == big) {
goto L220;
}
itemp = ibasis[j];
jcol = abs(itemp);
i__8 = mval - nsetb;
/* Computing MIN */
i__9 = nsetb + 1;
t1 = dnrm2_(&i__8, &w[min(i__9,mrows) + j * w_dim1], &c__1);
if (itemp < 0) {
if (ibb[jcol] % 2 == 0) {
t = -t;
}
if (t < 0.) {
goto L220;
}
if (mval > nsetb) {
t = t1;
}
if (t > wlarge) {
wlarge = t;
jlarge = j;
}
} else {
if (mval > nsetb) {
t = t1;
}
if (abs(t) > wmag) {
wmag = abs(t);
jmag = j;
}
}
L220:
;
}
/* Choose magnitude of largest component of gradient for candidate. */
jbig = 0;
wbig = 0.;
if (wlarge > 0.) {
jbig = jlarge;
wbig = wlarge;
}
if (wmag >= wbig) {
jbig = jmag;
wbig = wmag;
}
if (jbig == 0) {
found = FALSE_;
if (iprint > 0) {
ivout_(&c__0, &i__, "(' FOUND NO VARIABLE TO ENTER')", &c_n4, (
ftnlen)31);
}
goto L120;
}
/* See if the incoming column is sufficiently independent. This */
/* test is made before an elimination is performed. */
if (iprint > 0) {
ivout_(&c__1, &jbig, "(' TRY TO BRING IN THIS COL.')", &c_n4, (ftnlen)
30);
}
if (mval <= nsetb) {
cl1 = dnrm2_(&mval, &w[jbig * w_dim1 + 1], &c__1);
i__3 = nsetb - mval;
/* Computing MIN */
i__8 = mval + 1;
cl2 = abs(wt) * dnrm2_(&i__3, &w[min(i__8,mrows) + jbig * w_dim1], &
c__1);
i__3 = mrows - nsetb;
/* Computing MIN */
i__8 = nsetb + 1;
cl3 = abs(wt) * dnrm2_(&i__3, &w[min(i__8,mrows) + jbig * w_dim1], &
c__1);
drotg_(&cl1, &cl2, &sc, &ss);
colabv = abs(cl1);
colblo = cl3;
} else {
cl1 = dnrm2_(&nsetb, &w[jbig * w_dim1 + 1], &c__1);
i__3 = mval - nsetb;
/* Computing MIN */
i__8 = nsetb + 1;
cl2 = dnrm2_(&i__3, &w[min(i__8,mrows) + jbig * w_dim1], &c__1);
i__3 = mrows - mval;
/* Computing MIN */
i__8 = mval + 1;
cl3 = abs(wt) * dnrm2_(&i__3, &w[min(i__8,mrows) + jbig * w_dim1], &
c__1);
colabv = cl1;
drotg_(&cl2, &cl3, &sc, &ss);
colblo = abs(cl2);
}
if (colblo <= tolind * colabv) {
ww[jbig] = big;
if (iprint > 0) {
ivout_(&c__0, &i__, "(' VARIABLE IS DEPENDENT, NOT USED.')", &
c_n4, (ftnlen)37);
}
goto L210;
}
/* Swap matrix columns NSETB+1 and JBIG, plus pointer information, */
/* and gradient values. */
++nsetb;
if (nsetb != jbig) {
dswap_(&mrows, &w[nsetb * w_dim1 + 1], &c__1, &w[jbig * w_dim1 + 1], &
c__1);
dswap_(&c__1, &ww[nsetb], &c__1, &ww[jbig], &c__1);
itemp = ibasis[nsetb];
ibasis[nsetb] = ibasis[jbig];
ibasis[jbig] = itemp;
}
/* Eliminate entries below the pivot line in column NSETB. */
if (mrows > nsetb) {
i__3 = nsetb + 1;
for (i__ = mrows; i__ >= i__3; --i__) {
if (i__ == mval + 1) {
goto L230;
}
drotg_(&w[i__ - 1 + nsetb * w_dim1], &w[i__ + nsetb * w_dim1], &
sc, &ss);
w[i__ + nsetb * w_dim1] = 0.;
i__8 = *ncols - nsetb + 1;
drot_(&i__8, &w[i__ - 1 + (nsetb + 1) * w_dim1], mdw, &w[i__ + (
nsetb + 1) * w_dim1], mdw, &sc, &ss);
L230:
;
}
if (mval >= nsetb && mval < mrows) {
drotg_(&w[nsetb + nsetb * w_dim1], &w[mval + 1 + nsetb * w_dim1],
&sc, &ss);
w[mval + 1 + nsetb * w_dim1] = 0.;
i__3 = *ncols - nsetb + 1;
drot_(&i__3, &w[nsetb + (nsetb + 1) * w_dim1], mdw, &w[mval + 1 +
(nsetb + 1) * w_dim1], mdw, &sc, &ss);
}
}
if (w[nsetb + nsetb * w_dim1] == 0.) {
ww[nsetb] = big;
--nsetb;
if (iprint > 0) {
ivout_(&c__0, &i__, "(' PIVOT IS ZERO, NOT USED.')", &c_n4, (
ftnlen)29);
}
goto L210;
}
/* Check that new variable is moving in the right direction. */
itemp = ibasis[nsetb];
jcol = abs(itemp);
xnew = w[nsetb + (*ncols + 1) * w_dim1] / w[nsetb + nsetb * w_dim1] / (
d__1 = scl[jcol], abs(d__1));
if (itemp < 0) {
/* IF(WW(NSETB).GE.ZERO.AND.XNEW.LE.ZERO) exit(quit) */
/* IF(WW(NSETB).LE.ZERO.AND.XNEW.GE.ZERO) exit(quit) */
if (ww[nsetb] >= 0. && xnew <= 0. || ww[nsetb] <= 0. && xnew >= 0.) {
goto L240;
}
}
found = TRUE_;
goto L120;
L240:
ww[nsetb] = big;
--nsetb;
if (iprint > 0) {
ivout_(&c__0, &i__, "(' VARIABLE HAS BAD DIRECTION, NOT USED.')", &
c_n4, (ftnlen)42);
}
goto L210;
/* Solve the triangular system. */
L270:
dcopy_(&nsetb, &w[(*ncols + 1) * w_dim1 + 1], &c__1, &rw[1], &c__1);
for (j = nsetb; j >= 1; --j) {
rw[j] /= w[j + j * w_dim1];
jcol = (i__3 = ibasis[j], abs(i__3));
t = rw[j];
if (ibb[jcol] % 2 == 0) {
rw[j] = -rw[j];
}
i__3 = j - 1;
d__1 = -t;
daxpy_(&i__3, &d__1, &w[j * w_dim1 + 1], &c__1, &rw[1], &c__1);
rw[j] /= (d__1 = scl[jcol], abs(d__1));
/* L280: */
}
if (iprint > 0) {
dvout_(&nsetb, &rw[1], "(' SOLN. VALUES')", &c_n4, (ftnlen)17);
ivout_(&nsetb, &ibasis[1], "(' COLS. USED')", &c_n4, (ftnlen)15);
}
if (lgopr == 2) {
dcopy_(&nsetb, &rw[1], &c__1, &x[1], &c__1);
i__3 = nsetb;
for (j = 1; j <= i__3; ++j) {
itemp = ibasis[j];
jcol = abs(itemp);
if (itemp < 0) {
bou = 0.;
} else {
bou = bl[jcol];
}
if (-bou != big) {
bou /= (d__1 = scl[jcol], abs(d__1));
}
if (x[j] <= bou) {
jdrop1 = j;
goto L340;
}
bou = bu[jcol];
if (bou != big) {
bou /= (d__1 = scl[jcol], abs(d__1));
}
if (x[j] >= bou) {
jdrop2 = j;
goto L340;
}
/* L450: */
}
goto L340;
}
/* See if the unconstrained solution (obtained by solving the */
/* triangular system) satisfies the problem bounds. */
alpha = 2.;
beta = 2.;
x[nsetb] = 0.;
i__3 = nsetb;
for (j = 1; j <= i__3; ++j) {
itemp = ibasis[j];
jcol = abs(itemp);
t1 = 2.;
t2 = 2.;
if (itemp < 0) {
bou = 0.;
} else {
bou = bl[jcol];
}
if (-bou != big) {
bou /= (d__1 = scl[jcol], abs(d__1));
}
if (rw[j] <= bou) {
t1 = (x[j] - bou) / (x[j] - rw[j]);
}
bou = bu[jcol];
if (bou != big) {
bou /= (d__1 = scl[jcol], abs(d__1));
}
if (rw[j] >= bou) {
t2 = (bou - x[j]) / (rw[j] - x[j]);
}
/* If not, then compute a step length so that the variables remain */
/* feasible. */
if (t1 < alpha) {
alpha = t1;
jdrop1 = j;
}
if (t2 < beta) {
beta = t2;
jdrop2 = j;
}
/* L310: */
}
constr = alpha < 2. || beta < 2.;
if (! constr) {
/* Accept the candidate because it satisfies the stated bounds */
/* on the variables. */
dcopy_(&nsetb, &rw[1], &c__1, &x[1], &c__1);
goto L580;
}
/* Take a step that is as large as possible with all variables */
/* remaining feasible. */
i__3 = nsetb;
for (j = 1; j <= i__3; ++j) {
x[j] += min(alpha,beta) * (rw[j] - x[j]);
/* L330: */
}
if (alpha <= beta) {
jdrop2 = 0;
} else {
jdrop1 = 0;
}
L340:
if (jdrop1 + jdrop2 <= 0 || nsetb <= 0) {
goto L580;
}
/* L350: */
jdrop = jdrop1 + jdrop2;
itemp = ibasis[jdrop];
jcol = abs(itemp);
if (jdrop2 > 0) {
/* Variable is at an upper bound. Subtract multiple of this */
/* column from right hand side. */
t = bu[jcol];
if (itemp > 0) {
bu[jcol] = t - bl[jcol];
bl[jcol] = -t;
itemp = -itemp;
scl[jcol] = -scl[jcol];
i__3 = jdrop;
for (i__ = 1; i__ <= i__3; ++i__) {
w[i__ + jdrop * w_dim1] = -w[i__ + jdrop * w_dim1];
/* L360: */
}
} else {
++ibb[jcol];
if (ibb[jcol] % 2 == 0) {
t = -t;
}
}
/* Variable is at a lower bound. */
} else {
if ((doublereal) itemp < 0.) {
t = 0.;
} else {
t = -bl[jcol];
bu[jcol] += t;
itemp = -itemp;
}
}
daxpy_(&jdrop, &t, &w[jdrop * w_dim1 + 1], &c__1, &w[(*ncols + 1) *
w_dim1 + 1], &c__1);
/* Move certain columns left to achieve upper Hessenberg form. */
dcopy_(&jdrop, &w[jdrop * w_dim1 + 1], &c__1, &rw[1], &c__1);
i__3 = nsetb;
for (j = jdrop + 1; j <= i__3; ++j) {
ibasis[j - 1] = ibasis[j];
x[j - 1] = x[j];
dcopy_(&j, &w[j * w_dim1 + 1], &c__1, &w[(j - 1) * w_dim1 + 1], &c__1)
;
/* L370: */
}
ibasis[nsetb] = itemp;
w[nsetb * w_dim1 + 1] = 0.;
i__3 = mrows - jdrop;
dcopy_(&i__3, &w[nsetb * w_dim1 + 1], &c__0, &w[jdrop + 1 + nsetb *
w_dim1], &c__1);
dcopy_(&jdrop, &rw[1], &c__1, &w[nsetb * w_dim1 + 1], &c__1);
/* Transform the matrix from upper Hessenberg form to upper */
/* triangular form. */
--nsetb;
i__3 = nsetb;
for (i__ = jdrop; i__ <= i__3; ++i__) {
/* Look for small pivots and avoid mixing weighted and */
/* nonweighted rows. */
if (i__ == mval) {
t = 0.;
i__8 = nsetb;
for (j = i__; j <= i__8; ++j) {
jcol = (i__9 = ibasis[j], abs(i__9));
t1 = (d__1 = w[i__ + j * w_dim1] * scl[jcol], abs(d__1));
if (t1 > t) {
jbig = j;
t = t1;
}
/* L380: */
}
goto L400;
}
drotg_(&w[i__ + i__ * w_dim1], &w[i__ + 1 + i__ * w_dim1], &sc, &ss);
w[i__ + 1 + i__ * w_dim1] = 0.;
i__8 = *ncols - i__ + 1;
drot_(&i__8, &w[i__ + (i__ + 1) * w_dim1], mdw, &w[i__ + 1 + (i__ + 1)
* w_dim1], mdw, &sc, &ss);
/* L390: */
}
goto L430;
/* The triangularization is completed by giving up the Hessenberg */
/* form and triangularizing a rectangular matrix. */
L400:
dswap_(&mrows, &w[i__ * w_dim1 + 1], &c__1, &w[jbig * w_dim1 + 1], &c__1);
dswap_(&c__1, &ww[i__], &c__1, &ww[jbig], &c__1);
dswap_(&c__1, &x[i__], &c__1, &x[jbig], &c__1);
itemp = ibasis[i__];
ibasis[i__] = ibasis[jbig];
ibasis[jbig] = itemp;
jbig = i__;
i__3 = nsetb;
for (j = jbig; j <= i__3; ++j) {
i__8 = mrows;
for (i__ = j + 1; i__ <= i__8; ++i__) {
drotg_(&w[j + j * w_dim1], &w[i__ + j * w_dim1], &sc, &ss);
w[i__ + j * w_dim1] = 0.;
i__9 = *ncols - j + 1;
drot_(&i__9, &w[j + (j + 1) * w_dim1], mdw, &w[i__ + (j + 1) *
w_dim1], mdw, &sc, &ss);
/* L410: */
}
/* L420: */
}
/* See if the remaining coefficients are feasible. They should be */
/* because of the way MIN(ALPHA,BETA) was chosen. Any that are not */
/* feasible will be set to their bounds and appropriately translated. */
L430:
jdrop1 = 0;
jdrop2 = 0;
lgopr = 2;
goto L270;
/* Find a variable to become non-active. */
L120:
if (found) {
lgopr = 1;
goto L270;
}
/* Rescale and translate variables. */
igopr = 2;
L130:
dcopy_(&nsetb, &x[1], &c__1, &rw[1], &c__1);
dcopy_(ncols, &c_b185, &c__0, &x[1], &c__1);
i__3 = nsetb;
for (j = 1; j <= i__3; ++j) {
jcol = (i__8 = ibasis[j], abs(i__8));
x[jcol] = rw[j] * (d__1 = scl[jcol], abs(d__1));
/* L140: */
}
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
if (ibb[j] % 2 == 0) {
x[j] = bu[j] - x[j];
}
/* L150: */
}
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
jcol = ibasis[j];
if (jcol < 0) {
x[-jcol] = bl[-jcol] + x[-jcol];
}
/* L160: */
}
i__3 = *ncols;
for (j = 1; j <= i__3; ++j) {
if (scl[j] < 0.) {
x[j] = -x[j];
}
/* L170: */
}
i__ = max(nsetb,mval);
i__3 = mrows - i__;
/* Computing MIN */
i__8 = i__ + 1;
*rnorm = dnrm2_(&i__3, &w[min(i__8,mrows) + (*ncols + 1) * w_dim1], &c__1)
;
if (igopr == 2) {
*mode = nsetb;
}
return 0;
} /* dbolsm_ */
/* Subroutine */ int cnaupd_(integer *ido, char *bmat, integer *n, char *
which, integer *nev, real *tol, complex *resid, integer *ncv, complex
*v, integer *ldv, integer *iparam, integer *ipntr, complex *workd,
complex *workl, integer *lworkl, real *rwork, integer *info, ftnlen
bmat_len, ftnlen which_len)
{
/* Format strings */
static char fmt_1000[] = "(//,5x,\002==================================="
"==========\002,/5x,\002= Complex implicit Arnoldi update code "
" =\002,/5x,\002= Version Number: \002,\002 2.3\002,21x,\002 "
"=\002,/5x,\002= Version Date: \002,\002 07/31/96\002,16x,\002 ="
"\002,/5x,\002=============================================\002,/"
"5x,\002= Summary of timing statistics =\002,/5x,"
"\002=============================================\002,//)";
static char fmt_1100[] = "(5x,\002Total number update iterations "
" = \002,i5,/5x,\002Total number of OP*x operations "
" = \002,i5,/5x,\002Total number of B*x operations = "
"\002,i5,/5x,\002Total number of reorthogonalization steps = "
"\002,i5,/5x,\002Total number of iterative refinement steps = "
"\002,i5,/5x,\002Total number of restart steps = "
"\002,i5,/5x,\002Total time in user OP*x operation = "
"\002,f12.6,/5x,\002Total time in user B*x operation ="
" \002,f12.6,/5x,\002Total time in Arnoldi update routine = "
"\002,f12.6,/5x,\002Total time in naup2 routine ="
" \002,f12.6,/5x,\002Total time in basic Arnoldi iteration loop = "
"\002,f12.6,/5x,\002Total time in reorthogonalization phase ="
" \002,f12.6,/5x,\002Total time in (re)start vector generation = "
"\002,f12.6,/5x,\002Total time in Hessenberg eig. subproblem ="
" \002,f12.6,/5x,\002Total time in getting the shifts = "
"\002,f12.6,/5x,\002Total time in applying the shifts ="
" \002,f12.6,/5x,\002Total time in convergence testing = "
"\002,f12.6,/5x,\002Total time in computing final Ritz vectors ="
" \002,f12.6/)";
/* System generated locals */
integer v_dim1, v_offset, i__1, i__2;
/* Builtin functions */
integer s_cmp(char *, char *, ftnlen, ftnlen), s_wsfe(cilist *), e_wsfe(
void), do_fio(integer *, char *, ftnlen);
/* Local variables */
static integer j;
static real t0, t1;
static integer nb, ih, iq, np, iw, ldh, ldq, nev0, mode, ierr, iupd, next,
ritz;
extern /* Subroutine */ int cvout_(integer *, integer *, complex *,
integer *, char *, ftnlen), ivout_(integer *, integer *, integer *
, integer *, char *, ftnlen), cnaup2_(integer *, char *, integer *
, char *, integer *, integer *, real *, complex *, integer *,
integer *, integer *, integer *, complex *, integer *, complex *,
integer *, complex *, complex *, complex *, integer *, complex *,
integer *, complex *, real *, integer *, ftnlen, ftnlen);
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int second_(real *);
static integer bounds, ishift, msglvl, mxiter;
extern /* Subroutine */ int cstatn_(void);
/* Fortran I/O blocks */
static cilist io___21 = { 0, 6, 0, fmt_1000, 0 };
static cilist io___22 = { 0, 6, 0, fmt_1100, 0 };
/* %----------------------------------------------------% */
/* | 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 | */
/* %--------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* Parameter adjustments */
--workd;
--resid;
--rwork;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--iparam;
--ipntr;
--workl;
/* Function Body */
if (*ido == 0) {
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
cstatn_();
second_(&t0);
msglvl = debug_1.mcaupd;
/* %----------------% */
/* | Error checking | */
/* %----------------% */
ierr = 0;
ishift = iparam[1];
/* levec = iparam(2) */
mxiter = iparam[3];
/* nb = iparam(4) */
nb = 1;
/* %--------------------------------------------% */
/* | Revision 2 performs only implicit restart. | */
/* %--------------------------------------------% */
iupd = 1;
mode = iparam[7];
if (*n <= 0) {
ierr = -1;
} else if (*nev <= 0) {
ierr = -2;
} else if (*ncv <= *nev || *ncv > *n) {
ierr = -3;
} else if (mxiter <= 0) {
ierr = -4;
} else if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(
which, "SM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which, "LR",
(ftnlen)2, (ftnlen)2) != 0 && s_cmp(which, "SR", (ftnlen)2, (
ftnlen)2) != 0 && s_cmp(which, "LI", (ftnlen)2, (ftnlen)2) !=
0 && s_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 * 5) {
ierr = -7;
} else if (mode < 1 || mode > 3) {
ierr = -10;
} else if (mode == 1 && *(unsigned char *)bmat == 'G') {
ierr = -11;
}
}
/* %------------% */
/* | Error Exit | */
/* %------------% */
if (ierr != 0) {
*info = ierr;
*ido = 99;
goto L9000;
}
/* %------------------------% */
/* | Set default parameters | */
/* %------------------------% */
if (nb <= 0) {
nb = 1;
}
if (*tol <= 0.f) {
*tol = slamch_("EpsMach", (ftnlen)7);
}
if (ishift != 0 && ishift != 1 && ishift != 2) {
ishift = 1;
}
/* %----------------------------------------------% */
/* | NP is the number of additional steps to | */
/* | extend the length NEV Lanczos factorization. | */
/* | NEV0 is the local variable designating the | */
/* | size of the invariant subspace desired. | */
/* %----------------------------------------------% */
np = *ncv - *nev;
nev0 = *nev;
/* %-----------------------------% */
/* | Zero out internal workspace | */
/* %-----------------------------% */
/* Computing 2nd power */
i__2 = *ncv;
i__1 = i__2 * i__2 * 3 + *ncv * 5;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
workl[i__2].r = 0.f, workl[i__2].i = 0.f;
/* L10: */
}
/* %-------------------------------------------------------------% */
/* | 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+ncv) := the ritz values | */
/* | workl(ncv*ncv+ncv+1:ncv*ncv+2*ncv) := error bounds | */
/* | workl(ncv*ncv+2*ncv+1:2*ncv*ncv+2*ncv) := rotation matrix Q | */
/* | workl(2*ncv*ncv+2*ncv+1:3*ncv*ncv+5*ncv) := workspace | */
/* | The final workspace is needed by subroutine cneigh called | */
/* | by cnaup2. Subroutine cneigh calls LAPACK routines for | */
/* | calculating eigenvalues and the last row of the eigenvector | */
/* | matrix. | */
/* %-------------------------------------------------------------% */
ldh = *ncv;
ldq = *ncv;
ih = 1;
ritz = ih + ldh * *ncv;
bounds = ritz + *ncv;
iq = bounds + *ncv;
iw = iq + ldq * *ncv;
/* Computing 2nd power */
i__1 = *ncv;
next = iw + i__1 * i__1 + *ncv * 3;
ipntr[4] = next;
ipntr[5] = ih;
ipntr[6] = ritz;
ipntr[7] = iq;
ipntr[8] = bounds;
ipntr[14] = iw;
}
/* %-------------------------------------------------------% */
/* | Carry out the Implicitly restarted Arnoldi Iteration. | */
/* %-------------------------------------------------------% */
cnaup2_(ido, bmat, n, which, &nev0, &np, tol, &resid[1], &mode, &iupd, &
ishift, &mxiter, &v[v_offset], ldv, &workl[ih], &ldh, &workl[ritz]
, &workl[bounds], &workl[iq], &ldq, &workl[iw], &ipntr[1], &workd[
1], &rwork[1], info, (ftnlen)1, (ftnlen)2);
/* %--------------------------------------------------% */
/* | ido .ne. 99 implies use of reverse communication | */
/* | to compute operations involving OP. | */
/* %--------------------------------------------------% */
if (*ido == 3) {
iparam[8] = np;
}
if (*ido != 99) {
goto L9000;
}
iparam[3] = mxiter;
iparam[5] = np;
iparam[9] = timing_1.nopx;
iparam[10] = timing_1.nbx;
iparam[11] = timing_1.nrorth;
/* %------------------------------------% */
/* | Exit if there was an informational | */
/* | error within cnaup2. | */
/* %------------------------------------% */
if (*info < 0) {
goto L9000;
}
if (*info == 2) {
*info = 3;
}
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &mxiter, &debug_1.ndigit, "_naupd: Nu"
"mber of update iterations taken", (ftnlen)41);
ivout_(&debug_1.logfil, &c__1, &np, &debug_1.ndigit, "_naupd: Number"
" of wanted \"converged\" Ritz values", (ftnlen)48);
cvout_(&debug_1.logfil, &np, &workl[ritz], &debug_1.ndigit, "_naupd:"
" The final Ritz values", (ftnlen)29);
cvout_(&debug_1.logfil, &np, &workl[bounds], &debug_1.ndigit, "_naup"
"d: Associated Ritz estimates", (ftnlen)33);
}
second_(&t1);
timing_1.tcaupd = t1 - t0;
if (msglvl > 0) {
/* %--------------------------------------------------------% */
/* | Version Number & Version Date are defined in version.h | */
/* %--------------------------------------------------------% */
s_wsfe(&io___21);
e_wsfe();
s_wsfe(&io___22);
do_fio(&c__1, (char *)&mxiter, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&timing_1.nopx, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&timing_1.nbx, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&timing_1.nrorth, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&timing_1.nitref, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&timing_1.nrstrt, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&timing_1.tmvopx, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tmvbx, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tcaupd, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tcaup2, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tcaitr, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.titref, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tgetv0, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tceigh, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tcgets, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tcapps, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.tcconv, (ftnlen)sizeof(real));
do_fio(&c__1, (char *)&timing_1.trvec, (ftnlen)sizeof(real));
e_wsfe();
}
L9000:
return 0;
/* %---------------% */
/* | End of cnaupd | */
/* %---------------% */
} /* cnaupd_ */
/* Subroutine */ int zngets_(integer *ishift, char *which, integer *kev,
integer *np, doublecomplex *ritz, doublecomplex *bounds, ftnlen
which_len)
{
/* System generated locals */
integer i__1;
/* Local variables */
static real t0, t1;
extern /* Subroutine */ int ivout_(integer *, integer *, integer *,
integer *, char *, ftnlen), zvout_(integer *, integer *,
doublecomplex *, integer *, char *, ftnlen), arscnd_(real *);
static integer msglvl;
extern /* Subroutine */ int zsortc_(char *, logical *, integer *,
doublecomplex *, doublecomplex *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 | */
/* %----------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
/* Parameter adjustments */
--bounds;
--ritz;
/* Function Body */
arscnd_(&t0);
msglvl = debug_1.mcgets;
i__1 = *kev + *np;
zsortc_(which, &c_true, &i__1, &ritz[1], &bounds[1], (ftnlen)2);
if (*ishift == 1) {
/* %-------------------------------------------------------% */
/* | Sort the unwanted Ritz values used as shifts so that | */
/* | the ones with largest Ritz estimates are first | */
/* | This will tend to minimize the effects of the | */
/* | forward instability of the iteration when the shifts | */
/* | are applied in subroutine znapps. | */
/* | Be careful and use 'SM' since we want to sort BOUNDS! | */
/* %-------------------------------------------------------% */
zsortc_("SM", &c_true, np, &bounds[1], &ritz[1], (ftnlen)2);
}
arscnd_(&t1);
timing_1.tcgets += t1 - t0;
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, kev, &debug_1.ndigit, "_ngets: KEV is",
(ftnlen)14);
ivout_(&debug_1.logfil, &c__1, np, &debug_1.ndigit, "_ngets: NP is", (
ftnlen)13);
i__1 = *kev + *np;
zvout_(&debug_1.logfil, &i__1, &ritz[1], &debug_1.ndigit, "_ngets: E"
"igenvalues of current H matrix ", (ftnlen)40);
i__1 = *kev + *np;
zvout_(&debug_1.logfil, &i__1, &bounds[1], &debug_1.ndigit, "_ngets:"
" Ritz estimates of the current KEV+NP Ritz values", (ftnlen)
56);
}
return 0;
/* %---------------% */
/* | End of zngets | */
/* %---------------% */
} /* zngets_ */
/* Subroutine */ int ssapps_(integer *n, integer *kev, integer *np, real *
shift, real *v, integer *ldv, real *h__, integer *ldh, real *resid,
real *q, integer *ldq, real *workd)
{
/* Initialized data */
static logical first = TRUE_;
/* System generated locals */
integer h_dim1, h_offset, q_dim1, q_offset, v_dim1, v_offset, i__1, i__2,
i__3, i__4;
real r__1, r__2;
/* Local variables */
static real c__, f, g;
static integer i__, j;
static real r__, s, a1, a2, a3, a4, t0, t1;
static integer jj;
static real big;
static integer iend, itop;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
sgemv_(char *, integer *, integer *, real *, real *, integer *,
real *, integer *, real *, real *, integer *, ftnlen), scopy_(
integer *, real *, integer *, real *, integer *), saxpy_(integer *
, real *, real *, integer *, real *, integer *), ivout_(integer *,
integer *, integer *, integer *, char *, ftnlen), svout_(integer
*, integer *, real *, integer *, char *, ftnlen);
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int arscnd_(real *);
static real epsmch;
static integer istart, kplusp, msglvl;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen), slartg_(real *, real *,
real *, real *, real *), slaset_(char *, integer *, integer *,
real *, real *, real *, integer *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 | */
/* %--------------------% */
/* %----------------------% */
/* | Intrinsics Functions | */
/* %----------------------% */
/* %----------------% */
/* | Data statments | */
/* %----------------% */
/* Parameter adjustments */
--workd;
--resid;
--shift;
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) {
epsmch = slamch_("Epsilon-Machine", (ftnlen)15);
first = FALSE_;
}
itop = 1;
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
arscnd_(&t0);
msglvl = debug_1.msapps;
kplusp = *kev + *np;
/* %----------------------------------------------% */
/* | Initialize Q to the identity matrix of order | */
/* | kplusp used to accumulate the rotations. | */
/* %----------------------------------------------% */
slaset_("All", &kplusp, &kplusp, &c_b4, &c_b5, &q[q_offset], ldq, (ftnlen)
3);
/* %----------------------------------------------% */
/* | Quick return if there are no shifts to apply | */
/* %----------------------------------------------% */
if (*np == 0) {
goto L9000;
}
/* %----------------------------------------------------------% */
/* | Apply the np shifts implicitly. Apply each shift to the | */
/* | whole matrix and not just to the submatrix from which it | */
/* | comes. | */
/* %----------------------------------------------------------% */
i__1 = *np;
for (jj = 1; jj <= i__1; ++jj) {
istart = itop;
/* %----------------------------------------------------------% */
/* | Check for splitting and deflation. Currently we consider | */
/* | an off-diagonal element h(i+1,1) negligible if | */
/* | h(i+1,1) .le. epsmch*( |h(i,2)| + |h(i+1,2)| ) | */
/* | for i=1:KEV+NP-1. | */
/* | If above condition tests true then we set h(i+1,1) = 0. | */
/* | Note that h(1:KEV+NP,1) are assumed to be non negative. | */
/* %----------------------------------------------------------% */
L20:
/* %------------------------------------------------% */
/* | The following loop exits early if we encounter | */
/* | a negligible off diagonal element. | */
/* %------------------------------------------------% */
i__2 = kplusp - 1;
for (i__ = istart; i__ <= i__2; ++i__) {
big = (r__1 = h__[i__ + (h_dim1 << 1)], dabs(r__1)) + (r__2 = h__[
i__ + 1 + (h_dim1 << 1)], dabs(r__2));
if (h__[i__ + 1 + h_dim1] <= epsmch * big) {
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &i__, &debug_1.ndigit,
"_sapps: deflation at row/column no.", (ftnlen)35)
;
ivout_(&debug_1.logfil, &c__1, &jj, &debug_1.ndigit,
"_sapps: occured before shift number.", (ftnlen)
36);
svout_(&debug_1.logfil, &c__1, &h__[i__ + 1 + h_dim1], &
debug_1.ndigit, "_sapps: the corresponding off d"
"iagonal element", (ftnlen)46);
}
h__[i__ + 1 + h_dim1] = 0.f;
iend = i__;
goto L40;
}
/* L30: */
}
iend = kplusp;
L40:
if (istart < iend) {
/* %--------------------------------------------------------% */
/* | Construct the plane rotation G'(istart,istart+1,theta) | */
/* | that attempts to drive h(istart+1,1) to zero. | */
/* %--------------------------------------------------------% */
f = h__[istart + (h_dim1 << 1)] - shift[jj];
g = h__[istart + 1 + h_dim1];
slartg_(&f, &g, &c__, &s, &r__);
/* %-------------------------------------------------------% */
/* | Apply rotation to the left and right of H; | */
/* | H <- G' * H * G, where G = G(istart,istart+1,theta). | */
/* | This will create a "bulge". | */
/* %-------------------------------------------------------% */
a1 = c__ * h__[istart + (h_dim1 << 1)] + s * h__[istart + 1 +
h_dim1];
a2 = c__ * h__[istart + 1 + h_dim1] + s * h__[istart + 1 + (
h_dim1 << 1)];
a4 = c__ * h__[istart + 1 + (h_dim1 << 1)] - s * h__[istart + 1 +
h_dim1];
a3 = c__ * h__[istart + 1 + h_dim1] - s * h__[istart + (h_dim1 <<
1)];
h__[istart + (h_dim1 << 1)] = c__ * a1 + s * a2;
h__[istart + 1 + (h_dim1 << 1)] = c__ * a4 - s * a3;
h__[istart + 1 + h_dim1] = c__ * a3 + s * a4;
/* %----------------------------------------------------% */
/* | Accumulate the rotation in the matrix Q; Q <- Q*G | */
/* %----------------------------------------------------% */
/* Computing MIN */
i__3 = istart + jj;
i__2 = min(i__3,kplusp);
for (j = 1; j <= i__2; ++j) {
a1 = c__ * q[j + istart * q_dim1] + s * q[j + (istart + 1) *
q_dim1];
q[j + (istart + 1) * q_dim1] = -s * q[j + istart * q_dim1] +
c__ * q[j + (istart + 1) * q_dim1];
q[j + istart * q_dim1] = a1;
/* L60: */
}
/* %----------------------------------------------% */
/* | The following loop chases the bulge created. | */
/* | Note that the previous rotation may also be | */
/* | done within the following loop. But it is | */
/* | kept separate to make the distinction among | */
/* | the bulge chasing sweeps and the first plane | */
/* | rotation designed to drive h(istart+1,1) to | */
/* | zero. | */
/* %----------------------------------------------% */
i__2 = iend - 1;
for (i__ = istart + 1; i__ <= i__2; ++i__) {
/* %----------------------------------------------% */
/* | Construct the plane rotation G'(i,i+1,theta) | */
/* | that zeros the i-th bulge that was created | */
/* | by G(i-1,i,theta). g represents the bulge. | */
/* %----------------------------------------------% */
f = h__[i__ + h_dim1];
g = s * h__[i__ + 1 + h_dim1];
/* %----------------------------------% */
/* | Final update with G(i-1,i,theta) | */
/* %----------------------------------% */
h__[i__ + 1 + h_dim1] = c__ * h__[i__ + 1 + h_dim1];
slartg_(&f, &g, &c__, &s, &r__);
/* %-------------------------------------------% */
/* | The following ensures that h(1:iend-1,1), | */
/* | the first iend-2 off diagonal of elements | */
/* | H, remain non negative. | */
/* %-------------------------------------------% */
if (r__ < 0.f) {
r__ = -r__;
c__ = -c__;
s = -s;
}
/* %--------------------------------------------% */
/* | Apply rotation to the left and right of H; | */
/* | H <- G * H * G', where G = G(i,i+1,theta) | */
/* %--------------------------------------------% */
h__[i__ + h_dim1] = r__;
a1 = c__ * h__[i__ + (h_dim1 << 1)] + s * h__[i__ + 1 +
h_dim1];
a2 = c__ * h__[i__ + 1 + h_dim1] + s * h__[i__ + 1 + (h_dim1
<< 1)];
a3 = c__ * h__[i__ + 1 + h_dim1] - s * h__[i__ + (h_dim1 << 1)
];
a4 = c__ * h__[i__ + 1 + (h_dim1 << 1)] - s * h__[i__ + 1 +
h_dim1];
h__[i__ + (h_dim1 << 1)] = c__ * a1 + s * a2;
h__[i__ + 1 + (h_dim1 << 1)] = c__ * a4 - s * a3;
h__[i__ + 1 + h_dim1] = c__ * a3 + s * a4;
/* %----------------------------------------------------% */
/* | Accumulate the rotation in the matrix Q; Q <- Q*G | */
/* %----------------------------------------------------% */
/* Computing MIN */
i__4 = i__ + jj;
i__3 = min(i__4,kplusp);
for (j = 1; j <= i__3; ++j) {
a1 = 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] = a1;
/* L50: */
}
/* L70: */
}
}
/* %--------------------------% */
/* | Update the block pointer | */
/* %--------------------------% */
istart = iend + 1;
/* %------------------------------------------% */
/* | Make sure that h(iend,1) is non-negative | */
/* | If not then set h(iend,1) <-- -h(iend,1) | */
/* | and negate the last column of Q. | */
/* | We have effectively carried out a | */
/* | similarity on transformation H | */
/* %------------------------------------------% */
if (h__[iend + h_dim1] < 0.f) {
h__[iend + h_dim1] = -h__[iend + h_dim1];
sscal_(&kplusp, &c_b20, &q[iend * q_dim1 + 1], &c__1);
}
/* %--------------------------------------------------------% */
/* | Apply the same shift to the next block if there is any | */
/* %--------------------------------------------------------% */
if (iend < kplusp) {
goto L20;
}
/* %-----------------------------------------------------% */
/* | Check if we can increase the the start of the block | */
/* %-----------------------------------------------------% */
i__2 = kplusp - 1;
for (i__ = itop; i__ <= i__2; ++i__) {
if (h__[i__ + 1 + h_dim1] > 0.f) {
goto L90;
}
++itop;
/* L80: */
}
/* %-----------------------------------% */
/* | Finished applying the jj-th shift | */
/* %-----------------------------------% */
L90:
;
}
/* %------------------------------------------% */
/* | All shifts have been applied. Check for | */
/* | more possible deflation that might occur | */
/* | after the last shift is applied. | */
/* %------------------------------------------% */
i__1 = kplusp - 1;
for (i__ = itop; i__ <= i__1; ++i__) {
big = (r__1 = h__[i__ + (h_dim1 << 1)], dabs(r__1)) + (r__2 = h__[i__
+ 1 + (h_dim1 << 1)], dabs(r__2));
if (h__[i__ + 1 + h_dim1] <= epsmch * big) {
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &i__, &debug_1.ndigit, "_sapp"
"s: deflation at row/column no.", (ftnlen)35);
svout_(&debug_1.logfil, &c__1, &h__[i__ + 1 + h_dim1], &
debug_1.ndigit, "_sapps: the corresponding off diago"
"nal element", (ftnlen)46);
}
h__[i__ + 1 + h_dim1] = 0.f;
}
/* L100: */
}
/* %-------------------------------------------------% */
/* | Compute the (kev+1)-st column of (V*Q) and | */
/* | temporarily store the result in WORKD(N+1:2*N). | */
/* | This is not necessary if h(kev+1,1) = 0. | */
/* %-------------------------------------------------% */
if (h__[*kev + 1 + h_dim1] > 0.f) {
sgemv_("N", n, &kplusp, &c_b5, &v[v_offset], ldv, &q[(*kev + 1) *
q_dim1 + 1], &c__1, &c_b4, &workd[*n + 1], &c__1, (ftnlen)1);
}
/* %-------------------------------------------------------% */
/* | Compute column 1 to kev of (V*Q) in backward order | */
/* | taking advantage that Q is an upper triangular matrix | */
/* | with lower bandwidth np. | */
/* | Place results in v(:,kplusp-kev:kplusp) temporarily. | */
/* %-------------------------------------------------------% */
i__1 = *kev;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = kplusp - i__ + 1;
sgemv_("N", n, &i__2, &c_b5, &v[v_offset], ldv, &q[(*kev - i__ + 1) *
q_dim1 + 1], &c__1, &c_b4, &workd[1], &c__1, (ftnlen)1);
scopy_(n, &workd[1], &c__1, &v[(kplusp - i__ + 1) * v_dim1 + 1], &
c__1);
/* L130: */
}
/* %-------------------------------------------------% */
/* | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | */
/* %-------------------------------------------------% */
slacpy_("All", n, kev, &v[(*np + 1) * v_dim1 + 1], ldv, &v[v_offset], ldv,
(ftnlen)3);
/* %--------------------------------------------% */
/* | Copy the (kev+1)-st column of (V*Q) in the | */
/* | appropriate place if h(kev+1,1) .ne. zero. | */
/* %--------------------------------------------% */
if (h__[*kev + 1 + h_dim1] > 0.f) {
scopy_(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_{kev+p}'*Q)*e_{kev} | */
/* | betak = e_{kev+1}'*H*e_{kev} | */
/* %-------------------------------------% */
sscal_(n, &q[kplusp + *kev * q_dim1], &resid[1], &c__1);
if (h__[*kev + 1 + h_dim1] > 0.f) {
saxpy_(n, &h__[*kev + 1 + h_dim1], &v[(*kev + 1) * v_dim1 + 1], &c__1,
&resid[1], &c__1);
}
if (msglvl > 1) {
svout_(&debug_1.logfil, &c__1, &q[kplusp + *kev * q_dim1], &
debug_1.ndigit, "_sapps: sigmak of the updated residual vect"
"or", (ftnlen)45);
svout_(&debug_1.logfil, &c__1, &h__[*kev + 1 + h_dim1], &
debug_1.ndigit, "_sapps: betak of the updated residual vector"
, (ftnlen)44);
svout_(&debug_1.logfil, kev, &h__[(h_dim1 << 1) + 1], &debug_1.ndigit,
"_sapps: updated main diagonal of H for next iteration", (
ftnlen)53);
if (*kev > 1) {
i__1 = *kev - 1;
svout_(&debug_1.logfil, &i__1, &h__[h_dim1 + 2], &debug_1.ndigit,
"_sapps: updated sub diagonal of H for next iteration", (
ftnlen)52);
}
}
arscnd_(&t1);
timing_1.tsapps += t1 - t0;
L9000:
return 0;
/* %---------------% */
/* | End of ssapps | */
/* %---------------% */
} /* ssapps_ */
/* Subroutine */ int dsaup2_(integer *ido, char *bmat, integer *n, char *
which, integer *nev, integer *np, doublereal *tol, doublereal *resid,
integer *mode, integer *iupd, integer *ishift, integer *mxiter,
doublereal *v, integer *ldv, doublereal *h__, integer *ldh,
doublereal *ritz, doublereal *bounds, doublereal *q, integer *ldq,
doublereal *workl, integer *ipntr, doublereal *workd, integer *info,
ftnlen bmat_len, ftnlen which_len)
{
/* System generated locals */
integer h_dim1, h_offset, q_dim1, q_offset, v_dim1, v_offset, i__1, i__2,
i__3;
doublereal d__1, d__2, d__3;
/* Local variables */
static integer j;
static real t0, t1, t2, t3;
static integer kp[3], np0, nev0;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static doublereal eps23;
static integer ierr, iter;
static doublereal temp;
static integer nevd2;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static logical getv0;
static integer nevm2;
static logical cnorm;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), dswap_(integer *, doublereal *, integer
*, doublereal *, integer *);
static integer nconv;
static logical initv;
static doublereal rnorm;
extern /* Subroutine */ int dvout_(integer *, integer *, doublereal *,
integer *, char *, ftnlen), ivout_(integer *, integer *, integer *
, integer *, char *, ftnlen), dgetv0_(integer *, char *, integer *
, logical *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
ftnlen);
extern doublereal dlamch_(char *, ftnlen);
static integer nevbef;
extern /* Subroutine */ int arscnd_(real *);
static logical update;
static char wprime[2];
static logical ushift;
static integer kplusp, msglvl, nptemp;
extern /* Subroutine */ int dsaitr_(integer *, char *, integer *, integer
*, integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *, doublereal *,
integer *, ftnlen), dsconv_(integer *, doublereal *, doublereal *,
doublereal *, integer *), dseigt_(doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *), dsgets_(integer *, char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, ftnlen), dsapps_(
integer *, integer *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *), dsortr_(char *, logical *, integer *,
doublereal *, doublereal *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 | */
/* %-----------------------% */
/* Parameter adjustments */
--workd;
--resid;
--workl;
--bounds;
--ritz;
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;
--ipntr;
/* Function Body */
if (*ido == 0) {
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
arscnd_(&t0);
msglvl = debug_1.msaup2;
/* %---------------------------------% */
/* | Set machine dependent constant. | */
/* %---------------------------------% */
eps23 = dlamch_("Epsilon-Machine", (ftnlen)15);
eps23 = pow_dd(&eps23, &c_b3);
/* %-------------------------------------% */
/* | nev0 and np0 are integer variables | */
/* | hold the initial values of NEV & NP | */
/* %-------------------------------------% */
nev0 = *nev;
np0 = *np;
/* %-------------------------------------% */
/* | kplusp is the bound on the largest | */
/* | Lanczos factorization built. | */
/* | nconv is the current number of | */
/* | "converged" eigenvlues. | */
/* | iter is the counter on the current | */
/* | iteration step. | */
/* %-------------------------------------% */
kplusp = nev0 + np0;
nconv = 0;
iter = 0;
/* %--------------------------------------------% */
/* | Set flags for computing the first NEV steps | */
/* | of the Lanczos factorization. | */
/* %--------------------------------------------% */
getv0 = TRUE_;
update = FALSE_;
ushift = FALSE_;
cnorm = FALSE_;
if (*info != 0) {
/* %--------------------------------------------% */
/* | User provides the initial residual vector. | */
/* %--------------------------------------------% */
initv = TRUE_;
*info = 0;
} else {
initv = FALSE_;
}
}
/* %---------------------------------------------% */
/* | Get a possibly random starting vector and | */
/* | force it into the range of the operator OP. | */
/* %---------------------------------------------% */
/* L10: */
if (getv0) {
dgetv0_(ido, bmat, &c__1, &initv, n, &c__1, &v[v_offset], ldv, &resid[
1], &rnorm, &ipntr[1], &workd[1], info, (ftnlen)1);
if (*ido != 99) {
goto L9000;
}
if (rnorm == 0.) {
/* %-----------------------------------------% */
/* | The initial vector is zero. Error exit. | */
/* %-----------------------------------------% */
*info = -9;
goto L1200;
}
getv0 = FALSE_;
*ido = 0;
}
/* %------------------------------------------------------------% */
/* | Back from reverse communication: continue with update step | */
/* %------------------------------------------------------------% */
if (update) {
goto L20;
}
/* %-------------------------------------------% */
/* | Back from computing user specified shifts | */
/* %-------------------------------------------% */
if (ushift) {
goto L50;
}
/* %-------------------------------------% */
/* | Back from computing residual norm | */
/* | at the end of the current iteration | */
/* %-------------------------------------% */
if (cnorm) {
goto L100;
}
/* %----------------------------------------------------------% */
/* | Compute the first NEV steps of the Lanczos factorization | */
/* %----------------------------------------------------------% */
dsaitr_(ido, bmat, n, &c__0, &nev0, mode, &resid[1], &rnorm, &v[v_offset],
ldv, &h__[h_offset], ldh, &ipntr[1], &workd[1], info, (ftnlen)1);
/* %---------------------------------------------------% */
/* | ido .ne. 99 implies use of reverse communication | */
/* | to compute operations involving OP and possibly B | */
/* %---------------------------------------------------% */
if (*ido != 99) {
goto L9000;
}
if (*info > 0) {
/* %-----------------------------------------------------% */
/* | dsaitr was unable to build an Lanczos factorization | */
/* | of length NEV0. INFO is returned with the size of | */
/* | the factorization built. Exit main loop. | */
/* %-----------------------------------------------------% */
*np = *info;
*mxiter = iter;
*info = -9999;
goto L1200;
}
/* %--------------------------------------------------------------% */
/* | | */
/* | M A I N LANCZOS I T E R A T I O N L O O P | */
/* | Each iteration implicitly restarts the Lanczos | */
/* | factorization in place. | */
/* | | */
/* %--------------------------------------------------------------% */
L1000:
++iter;
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &iter, &debug_1.ndigit, "_saup2: ****"
" Start of major iteration number ****", (ftnlen)49);
}
if (msglvl > 1) {
ivout_(&debug_1.logfil, &c__1, nev, &debug_1.ndigit, "_saup2: The le"
"ngth of the current Lanczos factorization", (ftnlen)55);
ivout_(&debug_1.logfil, &c__1, np, &debug_1.ndigit, "_saup2: Extend "
"the Lanczos factorization by", (ftnlen)43);
}
/* %------------------------------------------------------------% */
/* | Compute NP additional steps of the Lanczos factorization. | */
/* %------------------------------------------------------------% */
*ido = 0;
L20:
update = TRUE_;
dsaitr_(ido, bmat, n, nev, np, mode, &resid[1], &rnorm, &v[v_offset], ldv,
&h__[h_offset], ldh, &ipntr[1], &workd[1], info, (ftnlen)1);
/* %---------------------------------------------------% */
/* | ido .ne. 99 implies use of reverse communication | */
/* | to compute operations involving OP and possibly B | */
/* %---------------------------------------------------% */
if (*ido != 99) {
goto L9000;
}
if (*info > 0) {
/* %-----------------------------------------------------% */
/* | dsaitr was unable to build an Lanczos factorization | */
/* | of length NEV0+NP0. INFO is returned with the size | */
/* | of the factorization built. Exit main loop. | */
/* %-----------------------------------------------------% */
*np = *info;
*mxiter = iter;
*info = -9999;
goto L1200;
}
update = FALSE_;
if (msglvl > 1) {
dvout_(&debug_1.logfil, &c__1, &rnorm, &debug_1.ndigit, "_saup2: Cur"
"rent B-norm of residual for factorization", (ftnlen)52);
}
/* %--------------------------------------------------------% */
/* | Compute the eigenvalues and corresponding error bounds | */
/* | of the current symmetric tridiagonal matrix. | */
/* %--------------------------------------------------------% */
dseigt_(&rnorm, &kplusp, &h__[h_offset], ldh, &ritz[1], &bounds[1], &
workl[1], &ierr);
if (ierr != 0) {
*info = -8;
goto L1200;
}
/* %----------------------------------------------------% */
/* | Make a copy of eigenvalues and corresponding error | */
/* | bounds obtained from _seigt. | */
/* %----------------------------------------------------% */
dcopy_(&kplusp, &ritz[1], &c__1, &workl[kplusp + 1], &c__1);
dcopy_(&kplusp, &bounds[1], &c__1, &workl[(kplusp << 1) + 1], &c__1);
/* %---------------------------------------------------% */
/* | Select the wanted Ritz values and their bounds | */
/* | to be used in the convergence test. | */
/* | The selection is based on the requested number of | */
/* | eigenvalues instead of the current NEV and NP to | */
/* | prevent possible misconvergence. | */
/* | * Wanted Ritz values := RITZ(NP+1:NEV+NP) | */
/* | * Shifts := RITZ(1:NP) := WORKL(1:NP) | */
/* %---------------------------------------------------% */
*nev = nev0;
*np = np0;
dsgets_(ishift, which, nev, np, &ritz[1], &bounds[1], &workl[1], (ftnlen)
2);
/* %-------------------% */
/* | Convergence test. | */
/* %-------------------% */
dcopy_(nev, &bounds[*np + 1], &c__1, &workl[*np + 1], &c__1);
dsconv_(nev, &ritz[*np + 1], &workl[*np + 1], tol, &nconv);
if (msglvl > 2) {
kp[0] = *nev;
kp[1] = *np;
kp[2] = nconv;
ivout_(&debug_1.logfil, &c__3, kp, &debug_1.ndigit, "_saup2: NEV, NP"
", NCONV are", (ftnlen)26);
dvout_(&debug_1.logfil, &kplusp, &ritz[1], &debug_1.ndigit, "_saup2:"
" The eigenvalues of H", (ftnlen)28);
dvout_(&debug_1.logfil, &kplusp, &bounds[1], &debug_1.ndigit, "_saup"
"2: Ritz estimates of the current NCV Ritz values", (ftnlen)53)
;
}
/* %---------------------------------------------------------% */
/* | Count the number of unwanted Ritz values that have zero | */
/* | Ritz estimates. If any Ritz estimates are equal to zero | */
/* | then a leading block of H of order equal to at least | */
/* | the number of Ritz values with zero Ritz estimates has | */
/* | split off. None of these Ritz values may be removed by | */
/* | shifting. Decrease NP the number of shifts to apply. If | */
/* | no shifts may be applied, then prepare to exit | */
/* %---------------------------------------------------------% */
nptemp = *np;
i__1 = nptemp;
for (j = 1; j <= i__1; ++j) {
if (bounds[j] == 0.) {
--(*np);
++(*nev);
}
/* L30: */
}
if (nconv >= nev0 || iter > *mxiter || *np == 0) {
/* %------------------------------------------------% */
/* | Prepare to exit. Put the converged Ritz values | */
/* | and corresponding bounds in RITZ(1:NCONV) and | */
/* | BOUNDS(1:NCONV) respectively. Then sort. Be | */
/* | careful when NCONV > NP since we don't want to | */
/* | swap overlapping locations. | */
/* %------------------------------------------------% */
if (s_cmp(which, "BE", (ftnlen)2, (ftnlen)2) == 0) {
/* %-----------------------------------------------------% */
/* | Both ends of the spectrum are requested. | */
/* | Sort the eigenvalues into algebraically decreasing | */
/* | order first then swap low end of the spectrum next | */
/* | to high end in appropriate locations. | */
/* | NOTE: when np < floor(nev/2) be careful not to swap | */
/* | overlapping locations. | */
/* %-----------------------------------------------------% */
s_copy(wprime, "SA", (ftnlen)2, (ftnlen)2);
dsortr_(wprime, &c_true, &kplusp, &ritz[1], &bounds[1], (ftnlen)2)
;
nevd2 = nev0 / 2;
nevm2 = nev0 - nevd2;
if (*nev > 1) {
i__1 = min(nevd2,*np);
/* Computing MAX */
i__2 = kplusp - nevd2 + 1, i__3 = kplusp - *np + 1;
dswap_(&i__1, &ritz[nevm2 + 1], &c__1, &ritz[max(i__2,i__3)],
&c__1);
i__1 = min(nevd2,*np);
/* Computing MAX */
i__2 = kplusp - nevd2 + 1, i__3 = kplusp - *np + 1;
dswap_(&i__1, &bounds[nevm2 + 1], &c__1, &bounds[max(i__2,
i__3)], &c__1);
}
} else {
/* %--------------------------------------------------% */
/* | LM, SM, LA, SA case. | */
/* | Sort the eigenvalues of H into the an order that | */
/* | is opposite to WHICH, and apply the resulting | */
/* | order to BOUNDS. The eigenvalues are sorted so | */
/* | that the wanted part are always within the first | */
/* | NEV locations. | */
/* %--------------------------------------------------% */
if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SM", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LM", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "LA", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SA", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SA", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LA", (ftnlen)2, (ftnlen)2);
}
dsortr_(wprime, &c_true, &kplusp, &ritz[1], &bounds[1], (ftnlen)2)
;
}
/* %--------------------------------------------------% */
/* | Scale the Ritz estimate of each Ritz value | */
/* | by 1 / max(eps23,magnitude of the Ritz value). | */
/* %--------------------------------------------------% */
i__1 = nev0;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__2 = eps23, d__3 = (d__1 = ritz[j], abs(d__1));
temp = max(d__2,d__3);
bounds[j] /= temp;
/* L35: */
}
/* %----------------------------------------------------% */
/* | Sort the Ritz values according to the scaled Ritz | */
/* | esitmates. This will push all the converged ones | */
/* | towards the front of ritzr, ritzi, bounds | */
/* | (in the case when NCONV < NEV.) | */
/* %----------------------------------------------------% */
s_copy(wprime, "LA", (ftnlen)2, (ftnlen)2);
dsortr_(wprime, &c_true, &nev0, &bounds[1], &ritz[1], (ftnlen)2);
/* %----------------------------------------------% */
/* | Scale the Ritz estimate back to its original | */
/* | value. | */
/* %----------------------------------------------% */
i__1 = nev0;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__2 = eps23, d__3 = (d__1 = ritz[j], abs(d__1));
temp = max(d__2,d__3);
bounds[j] *= temp;
/* L40: */
}
/* %--------------------------------------------------% */
/* | Sort the "converged" Ritz values again so that | */
/* | the "threshold" values and their associated Ritz | */
/* | estimates appear at the appropriate position in | */
/* | ritz and bound. | */
/* %--------------------------------------------------% */
if (s_cmp(which, "BE", (ftnlen)2, (ftnlen)2) == 0) {
/* %------------------------------------------------% */
/* | Sort the "converged" Ritz values in increasing | */
/* | order. The "threshold" values are in the | */
/* | middle. | */
/* %------------------------------------------------% */
s_copy(wprime, "LA", (ftnlen)2, (ftnlen)2);
dsortr_(wprime, &c_true, &nconv, &ritz[1], &bounds[1], (ftnlen)2);
} else {
/* %----------------------------------------------% */
/* | In LM, SM, LA, SA case, sort the "converged" | */
/* | Ritz values according to WHICH so that the | */
/* | "threshold" value appears at the front of | */
/* | ritz. | */
/* %----------------------------------------------% */
dsortr_(which, &c_true, &nconv, &ritz[1], &bounds[1], (ftnlen)2);
}
/* %------------------------------------------% */
/* | Use h( 1,1 ) as storage to communicate | */
/* | rnorm to _seupd if needed | */
/* %------------------------------------------% */
h__[h_dim1 + 1] = rnorm;
if (msglvl > 1) {
dvout_(&debug_1.logfil, &kplusp, &ritz[1], &debug_1.ndigit, "_sa"
"up2: Sorted Ritz values.", (ftnlen)27);
dvout_(&debug_1.logfil, &kplusp, &bounds[1], &debug_1.ndigit,
"_saup2: Sorted ritz estimates.", (ftnlen)30);
}
/* %------------------------------------% */
/* | Max iterations have been exceeded. | */
/* %------------------------------------% */
if (iter > *mxiter && nconv < *nev) {
*info = 1;
}
/* %---------------------% */
/* | No shifts to apply. | */
/* %---------------------% */
if (*np == 0 && nconv < nev0) {
*info = 2;
}
*np = nconv;
goto L1100;
} else if (nconv < *nev && *ishift == 1) {
/* %---------------------------------------------------% */
/* | Do not have all the requested eigenvalues yet. | */
/* | To prevent possible stagnation, adjust the number | */
/* | of Ritz values and the shifts. | */
/* %---------------------------------------------------% */
nevbef = *nev;
/* Computing MIN */
i__1 = nconv, i__2 = *np / 2;
*nev += min(i__1,i__2);
if (*nev == 1 && kplusp >= 6) {
*nev = kplusp / 2;
} else if (*nev == 1 && kplusp > 2) {
*nev = 2;
}
*np = kplusp - *nev;
/* %---------------------------------------% */
/* | If the size of NEV was just increased | */
/* | resort the eigenvalues. | */
/* %---------------------------------------% */
if (nevbef < *nev) {
dsgets_(ishift, which, nev, np, &ritz[1], &bounds[1], &workl[1], (
ftnlen)2);
}
}
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &nconv, &debug_1.ndigit, "_saup2: no."
" of \"converged\" Ritz values at this iter.", (ftnlen)52);
if (msglvl > 1) {
kp[0] = *nev;
kp[1] = *np;
ivout_(&debug_1.logfil, &c__2, kp, &debug_1.ndigit, "_saup2: NEV"
" and NP are", (ftnlen)22);
dvout_(&debug_1.logfil, nev, &ritz[*np + 1], &debug_1.ndigit,
"_saup2: \"wanted\" Ritz values.", (ftnlen)29);
dvout_(&debug_1.logfil, nev, &bounds[*np + 1], &debug_1.ndigit,
"_saup2: Ritz estimates of the \"wanted\" values ", (
ftnlen)46);
}
}
if (*ishift == 0) {
/* %-----------------------------------------------------% */
/* | User specified shifts: reverse communication to | */
/* | compute the shifts. They are returned in the first | */
/* | NP locations of WORKL. | */
/* %-----------------------------------------------------% */
ushift = TRUE_;
*ido = 3;
goto L9000;
}
L50:
/* %------------------------------------% */
/* | Back from reverse communication; | */
/* | User specified shifts are returned | */
/* | in WORKL(1:*NP) | */
/* %------------------------------------% */
ushift = FALSE_;
/* %---------------------------------------------------------% */
/* | Move the NP shifts to the first NP locations of RITZ to | */
/* | free up WORKL. This is for the non-exact shift case; | */
/* | in the exact shift case, dsgets already handles this. | */
/* %---------------------------------------------------------% */
if (*ishift == 0) {
dcopy_(np, &workl[1], &c__1, &ritz[1], &c__1);
}
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, np, &debug_1.ndigit, "_saup2: The num"
"ber of shifts to apply ", (ftnlen)38);
dvout_(&debug_1.logfil, np, &workl[1], &debug_1.ndigit, "_saup2: shi"
"fts selected", (ftnlen)23);
if (*ishift == 1) {
dvout_(&debug_1.logfil, np, &bounds[1], &debug_1.ndigit, "_saup2"
": corresponding Ritz estimates", (ftnlen)36);
}
}
/* %---------------------------------------------------------% */
/* | Apply the NP0 implicit shifts by QR bulge chasing. | */
/* | Each shift is applied to the entire tridiagonal matrix. | */
/* | The first 2*N locations of WORKD are used as workspace. | */
/* | After dsapps is done, we have a Lanczos | */
/* | factorization of length NEV. | */
/* %---------------------------------------------------------% */
dsapps_(n, nev, np, &ritz[1], &v[v_offset], ldv, &h__[h_offset], ldh, &
resid[1], &q[q_offset], ldq, &workd[1]);
/* %---------------------------------------------% */
/* | Compute the B-norm of the updated residual. | */
/* | Keep B*RESID in WORKD(1:N) to be used in | */
/* | the first step of the next call to dsaitr. | */
/* %---------------------------------------------% */
cnorm = TRUE_;
arscnd_(&t2);
if (*(unsigned char *)bmat == 'G') {
++timing_1.nbx;
dcopy_(n, &resid[1], &c__1, &workd[*n + 1], &c__1);
ipntr[1] = *n + 1;
ipntr[2] = 1;
*ido = 2;
/* %----------------------------------% */
/* | Exit in order to compute B*RESID | */
/* %----------------------------------% */
goto L9000;
} else if (*(unsigned char *)bmat == 'I') {
dcopy_(n, &resid[1], &c__1, &workd[1], &c__1);
}
L100:
/* %----------------------------------% */
/* | Back from reverse communication; | */
/* | WORKD(1:N) := B*RESID | */
/* %----------------------------------% */
if (*(unsigned char *)bmat == 'G') {
arscnd_(&t3);
timing_1.tmvbx += t3 - t2;
}
if (*(unsigned char *)bmat == 'G') {
rnorm = ddot_(n, &resid[1], &c__1, &workd[1], &c__1);
rnorm = sqrt((abs(rnorm)));
} else if (*(unsigned char *)bmat == 'I') {
rnorm = dnrm2_(n, &resid[1], &c__1);
}
cnorm = FALSE_;
/* L130: */
if (msglvl > 2) {
dvout_(&debug_1.logfil, &c__1, &rnorm, &debug_1.ndigit, "_saup2: B-n"
"orm of residual for NEV factorization", (ftnlen)48);
dvout_(&debug_1.logfil, nev, &h__[(h_dim1 << 1) + 1], &debug_1.ndigit,
"_saup2: main diagonal of compressed H matrix", (ftnlen)44);
i__1 = *nev - 1;
dvout_(&debug_1.logfil, &i__1, &h__[h_dim1 + 2], &debug_1.ndigit,
"_saup2: subdiagonal of compressed H matrix", (ftnlen)42);
}
goto L1000;
/* %---------------------------------------------------------------% */
/* | | */
/* | E N D O F M A I N I T E R A T I O N L O O P | */
/* | | */
/* %---------------------------------------------------------------% */
L1100:
*mxiter = iter;
*nev = nconv;
L1200:
*ido = 99;
/* %------------% */
/* | Error exit | */
/* %------------% */
arscnd_(&t1);
timing_1.tsaup2 = t1 - t0;
L9000:
return 0;
/* %---------------% */
/* | End of dsaup2 | */
/* %---------------% */
} /* dsaup2_ */
/* ----------------------------------------------------------------------- */
/* Subroutine */ int sneupd_(logical *rvec, char *howmny, logical *select,
real *dr, real *di, real *z__, integer *ldz, real *sigmar, real *
sigmai, real *workev, char *bmat, integer *n, char *which, integer *
nev, real *tol, real *resid, integer *ncv, real *v, integer *ldv,
integer *iparam, integer *ipntr, real *workd, real *workl, integer *
lworkl, integer *info, ftnlen howmny_len, ftnlen bmat_len, ftnlen
which_len)
{
/* System generated locals */
integer v_dim1, v_offset, z_dim1, z_offset, i__1;
real r__1, r__2;
doublereal d__1;
/* Local variables */
static integer j, k, ih, jj, np;
static real vl[1] /* was [1][1] */;
static integer ibd, ldh, ldq, iri;
static real sep;
static integer irr, wri, wrr, mode;
static real eps23;
extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *);
static integer ierr;
static real temp;
static integer iwev;
static char type__[6];
static real temp1;
extern doublereal snrm2_(integer *, real *, integer *);
static integer ihbds, iconj;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
static real conds;
static logical reord;
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *,
ftnlen);
static integer nconv, iwork[1];
static real rnorm;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
static integer ritzi;
extern /* Subroutine */ int strmm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
, ftnlen, ftnlen, ftnlen, ftnlen), ivout_(integer *, integer *,
integer *, integer *, char *, ftnlen), smout_(integer *, integer *
, integer *, real *, integer *, integer *, char *, ftnlen);
static integer ritzr;
extern /* Subroutine */ int svout_(integer *, integer *, real *, integer *
, char *, ftnlen), sgeqr2_(integer *, integer *, real *, integer *
, real *, real *, integer *);
static integer nconv2;
extern doublereal slapy2_(real *, real *);
extern /* Subroutine */ int sorm2r_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, ftnlen, ftnlen);
static integer iheigi, iheigr, bounds, invsub, iuptri, msglvl, outncv,
ishift, numcnv;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen), slahqr_(logical *, logical
*, integer *, integer *, integer *, real *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *),
slaset_(char *, integer *, integer *, real *, real *, real *,
integer *, ftnlen), strevc_(char *, char *, logical *, integer *,
real *, integer *, real *, integer *, real *, integer *, integer *
, integer *, real *, integer *, ftnlen, ftnlen), strsen_(char *,
char *, logical *, integer *, real *, integer *, real *, integer *
, real *, real *, integer *, real *, real *, real *, integer *,
integer *, integer *, integer *, ftnlen, ftnlen);
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int sngets_(integer *, char *, integer *, integer
*, real *, real *, real *, real *, real *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 = slamch_("Epsilon-Machine", (ftnlen)15);
d__1 = (doublereal) eps23;
eps23 = pow_dd(&d__1, &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 (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which,
"SM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which, "LR", (ftnlen)2,
(ftnlen)2) != 0 && s_cmp(which, "SR", (ftnlen)2, (ftnlen)2) != 0
&& s_cmp(which, "LI", (ftnlen)2, (ftnlen)2) != 0 && s_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) {
s_copy(type__, "REGULR", (ftnlen)6, (ftnlen)6);
} else if (mode == 3 && *sigmai == 0.f) {
s_copy(type__, "SHIFTI", (ftnlen)6, (ftnlen)6);
} else if (mode == 3) {
s_copy(type__, "REALPT", (ftnlen)6, (ftnlen)6);
} else if (mode == 4) {
s_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 SNEUPD. | */
/* | 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.f;
if (msglvl > 2) {
svout_(&debug_1.logfil, ncv, &workl[irr], &debug_1.ndigit, "_neupd: "
"Real part of Ritz values passed in from _NAUPD.", (ftnlen)55);
svout_(&debug_1.logfil, ncv, &workl[iri], &debug_1.ndigit, "_neupd: "
"Imag part of Ritz values passed in from _NAUPD.", (ftnlen)55);
svout_(&debug_1.logfil, ncv, &workl[ibd], &debug_1.ndigit, "_neupd: "
"Ritz estimates passed in from _NAUPD.", (ftnlen)45);
}
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] = (real) 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;
sngets_(&ishift, which, nev, &np, &workl[irr], &workl[iri], &workl[
bounds], &workl[1], &workl[np + 1], (ftnlen)2);
if (msglvl > 2) {
svout_(&debug_1.logfil, ncv, &workl[irr], &debug_1.ndigit, "_neu"
"pd: Real part of Ritz values after calling _NGETS.", (
ftnlen)54);
svout_(&debug_1.logfil, ncv, &workl[iri], &debug_1.ndigit, "_neu"
"pd: Imag part of Ritz values after calling _NGETS.", (
ftnlen)54);
svout_(&debug_1.logfil, ncv, &workl[bounds], &debug_1.ndigit,
"_neupd: Ritz value indices after calling _NGETS.", (
ftnlen)48);
}
/* %-----------------------------------------------------% */
/* | 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 */
r__1 = eps23, r__2 = slapy2_(&workl[irr + *ncv - j], &workl[iri +
*ncv - j]);
temp1 = dmax(r__1,r__2);
jj = workl[bounds + *ncv - j];
if (numcnv < nconv && workl[ibd + jj - 1] <= *tol * temp1) {
select[jj] = TRUE_;
++numcnv;
if (jj > nconv) {
reord = TRUE_;
}
}
/* L11: */
}
/* %-----------------------------------------------------------% */
/* | Check the count (numcnv) of converged Ritz values with | */
/* | the number (nconv) reported by dnaupd. If these two | */
/* | are different then there has probably been an error | */
/* | caused by incorrect passing of the dnaupd data. | */
/* %-----------------------------------------------------------% */
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, &numcnv, &debug_1.ndigit, "_neupd"
": Number of specified eigenvalues", (ftnlen)39);
ivout_(&debug_1.logfil, &c__1, &nconv, &debug_1.ndigit, "_neupd:"
" Number of \"converged\" eigenvalues", (ftnlen)41);
}
if (numcnv != nconv) {
*info = -15;
goto L9000;
}
/* %-----------------------------------------------------------% */
/* | Call LAPACK routine slahqr to compute the real Schur form | */
/* | of the upper Hessenberg matrix returned by SNAUPD. | */
/* | Make a copy of the upper Hessenberg matrix. | */
/* | Initialize the Schur vector matrix Q to the identity. | */
/* %-----------------------------------------------------------% */
i__1 = ldh * *ncv;
scopy_(&i__1, &workl[ih], &c__1, &workl[iuptri], &c__1);
slaset_("All", ncv, ncv, &c_b37, &c_b38, &workl[invsub], &ldq, (
ftnlen)3);
slahqr_(&c_true, &c_true, ncv, &c__1, ncv, &workl[iuptri], &ldh, &
workl[iheigr], &workl[iheigi], &c__1, ncv, &workl[invsub], &
ldq, &ierr);
scopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &c__1);
if (ierr != 0) {
*info = -8;
goto L9000;
}
if (msglvl > 1) {
svout_(&debug_1.logfil, ncv, &workl[iheigr], &debug_1.ndigit,
"_neupd: Real part of the eigenvalues of H", (ftnlen)41);
svout_(&debug_1.logfil, ncv, &workl[iheigi], &debug_1.ndigit,
"_neupd: Imaginary part of the Eigenvalues of H", (ftnlen)
46);
svout_(&debug_1.logfil, ncv, &workl[ihbds], &debug_1.ndigit,
"_neupd: Last row of the Schur vector matrix", (ftnlen)43)
;
if (msglvl > 3) {
smout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldh, &
debug_1.ndigit, "_neupd: The upper quasi-triangular "
"matrix ", (ftnlen)42);
}
}
if (reord) {
/* %-----------------------------------------------------% */
/* | Reorder the computed upper quasi-triangular matrix. | */
/* %-----------------------------------------------------% */
strsen_("None", "V", &select[1], ncv, &workl[iuptri], &ldh, &
workl[invsub], &ldq, &workl[iheigr], &workl[iheigi], &
nconv2, &conds, &sep, &workl[ihbds], ncv, iwork, &c__1, &
ierr, (ftnlen)4, (ftnlen)1);
if (nconv2 < nconv) {
nconv = nconv2;
}
if (ierr == 1) {
*info = 1;
goto L9000;
}
if (msglvl > 2) {
svout_(&debug_1.logfil, ncv, &workl[iheigr], &debug_1.ndigit,
"_neupd: Real part of the eigenvalues of H--reordered"
, (ftnlen)52);
svout_(&debug_1.logfil, ncv, &workl[iheigi], &debug_1.ndigit,
"_neupd: Imag part of the eigenvalues of H--reordered"
, (ftnlen)52);
if (msglvl > 3) {
smout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldq, &
debug_1.ndigit, "_neupd: Quasi-triangular matrix"
" after re-ordering", (ftnlen)49);
}
}
}
/* %---------------------------------------% */
/* | Copy the last row of the Schur vector | */
/* | into workl(ihbds). This will be used | */
/* | to compute the Ritz estimates of | */
/* | converged Ritz values. | */
/* %---------------------------------------% */
scopy_(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 (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
scopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
scopy_(&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). | */
/* %----------------------------------------------------------% */
sgeqr2_(ncv, &nconv, &workl[invsub], &ldq, &workev[1], &workev[*ncv +
1], &ierr);
/* %---------------------------------------------------------% */
/* | * Postmultiply V by Q using sorm2r. | */
/* | * 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) | */
/* %---------------------------------------------------------% */
sorm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[invsub], &ldq,
&workev[1], &v[v_offset], ldv, &workd[*n + 1], &ierr, (ftnlen)
5, (ftnlen)11);
slacpy_("All", n, &nconv, &v[v_offset], ldv, &z__[z_offset], ldz, (
ftnlen)3);
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.f) {
sscal_(&nconv, &c_b64, &workl[iuptri + j - 1], &ldq);
sscal_(&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: */
}
strevc_("Right", "Select", &select[1], ncv, &workl[iuptri], &ldq,
vl, &c__1, &workl[invsub], &ldq, ncv, &outncv, &workev[1],
&ierr, (ftnlen)5, (ftnlen)6);
if (ierr != 0) {
*info = -9;
goto L9000;
}
/* %------------------------------------------------% */
/* | Scale the returning eigenvectors so that their | */
/* | Euclidean norms are all one. LAPACK subroutine | */
/* | strevc 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.f) {
/* %----------------------% */
/* | real eigenvalue case | */
/* %----------------------% */
temp = snrm2_(ncv, &workl[invsub + (j - 1) * ldq], &c__1);
r__1 = 1.f / temp;
sscal_(ncv, &r__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) {
r__1 = snrm2_(ncv, &workl[invsub + (j - 1) * ldq], &
c__1);
r__2 = snrm2_(ncv, &workl[invsub + j * ldq], &c__1);
temp = slapy2_(&r__1, &r__2);
r__1 = 1.f / temp;
sscal_(ncv, &r__1, &workl[invsub + (j - 1) * ldq], &
c__1);
r__1 = 1.f / temp;
sscal_(ncv, &r__1, &workl[invsub + j * ldq], &c__1);
iconj = 1;
} else {
iconj = 0;
}
}
/* L40: */
}
sgemv_("T", ncv, &nconv, &c_b38, &workl[invsub], &ldq, &workl[
ihbds], &c__1, &c_b37, &workev[1], &c__1, (ftnlen)1);
iconj = 0;
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
if (workl[iheigi + j - 1] != 0.f) {
/* %-------------------------------------------% */
/* | Complex conjugate pair case. Note that | */
/* | since the real and imaginary part of | */
/* | the eigenvector are stored in consecutive | */
/* %-------------------------------------------% */
if (iconj == 0) {
workev[j] = slapy2_(&workev[j], &workev[j + 1]);
workev[j + 1] = workev[j];
iconj = 1;
} else {
iconj = 0;
}
}
/* L45: */
}
if (msglvl > 2) {
scopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &
c__1);
svout_(&debug_1.logfil, ncv, &workl[ihbds], &debug_1.ndigit,
"_neupd: Last row of the eigenvector matrix for T", (
ftnlen)48);
if (msglvl > 3) {
smout_(&debug_1.logfil, ncv, ncv, &workl[invsub], &ldq, &
debug_1.ndigit, "_neupd: The eigenvector matrix "
"for T", (ftnlen)36);
}
}
/* %---------------------------------------% */
/* | Copy Ritz estimates into workl(ihbds) | */
/* %---------------------------------------% */
scopy_(&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). | */
/* %---------------------------------------------------------% */
sgeqr2_(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). | */
/* %----------------------------------------------% */
sorm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[invsub], &
ldq, &workev[1], &z__[z_offset], ldz, &workd[*n + 1], &
ierr, (ftnlen)5, (ftnlen)11);
strmm_("Right", "Upper", "No transpose", "Non-unit", n, &nconv, &
c_b38, &workl[invsub], &ldq, &z__[z_offset], ldz, (ftnlen)
5, (ftnlen)5, (ftnlen)12, (ftnlen)8);
}
} else {
/* %------------------------------------------------------% */
/* | An approximate invariant subspace is not needed. | */
/* | Place the Ritz values computed SNAUPD into DR and DI | */
/* %------------------------------------------------------% */
scopy_(&nconv, &workl[ritzr], &c__1, &dr[1], &c__1);
scopy_(&nconv, &workl[ritzi], &c__1, &di[1], &c__1);
scopy_(&nconv, &workl[ritzr], &c__1, &workl[iheigr], &c__1);
scopy_(&nconv, &workl[ritzi], &c__1, &workl[iheigi], &c__1);
scopy_(&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 (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
if (*rvec) {
sscal_(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 (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
if (*rvec) {
sscal_(ncv, &rnorm, &workl[ihbds], &c__1);
}
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
temp = slapy2_(&workl[iheigr + k - 1], &workl[iheigi + k - 1])
;
workl[ihbds + k - 1] = (r__1 = workl[ihbds + k - 1], dabs(
r__1)) / temp / temp;
/* L50: */
}
} else if (s_cmp(type__, "REALPT", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
/* L60: */
}
} else if (s_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 (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
temp = slapy2_(&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: */
}
scopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
scopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
} else if (s_cmp(type__, "REALPT", (ftnlen)6, (ftnlen)6) == 0 ||
s_cmp(type__, "IMAGPT", (ftnlen)6, (ftnlen)6) == 0) {
scopy_(&nconv, &workl[iheigr], &c__1, &dr[1], &c__1);
scopy_(&nconv, &workl[iheigi], &c__1, &di[1], &c__1);
}
}
if (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0 && msglvl > 1) {
svout_(&debug_1.logfil, &nconv, &dr[1], &debug_1.ndigit, "_neupd: Un"
"transformed real part of the Ritz valuess.", (ftnlen)52);
svout_(&debug_1.logfil, &nconv, &di[1], &debug_1.ndigit, "_neupd: Un"
"transformed imag part of the Ritz valuess.", (ftnlen)52);
svout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Ritz estimates of untransformed Ritz values.", (ftnlen)
52);
} else if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0 && msglvl >
1) {
svout_(&debug_1.logfil, &nconv, &dr[1], &debug_1.ndigit, "_neupd: Re"
"al parts of converged Ritz values.", (ftnlen)44);
svout_(&debug_1.logfil, &nconv, &di[1], &debug_1.ndigit, "_neupd: Im"
"ag parts of converged Ritz values.", (ftnlen)44);
svout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Associated Ritz estimates.", (ftnlen)34);
}
/* %-------------------------------------------------% */
/* | Eigenvector Purification step. Formally perform | */
/* | one of inverse subspace iteration. Only used | */
/* | for MODE = 2. | */
/* %-------------------------------------------------% */
if (*rvec && *(unsigned char *)howmny == 'A' && s_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.f) {
workev[j] = workl[invsub + (j - 1) * ldq + *ncv - 1] / workl[
iheigr + j - 1];
} else if (iconj == 0) {
temp = slapy2_(&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. | */
/* %---------------------------------------% */
sger_(n, &nconv, &c_b38, &resid[1], &c__1, &workev[1], &c__1, &z__[
z_offset], ldz);
}
L9000:
return 0;
/* %---------------% */
/* | End of SNEUPD | */
/* %---------------% */
} /* sneupd_ */
/* Subroutine */ int cnapps_(integer *n, integer *kev, integer *np, complex *
shift, complex *v, integer *ldv, complex *h__, integer *ldh, complex *
resid, complex *q, integer *ldq, complex *workl, complex *workd)
{
/* Initialized data */
static 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, i__5, i__6;
real r__1, r__2, r__3, r__4;
complex q__1, q__2, q__3, q__4, q__5;
/* Builtin functions */
double r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
static real c__;
static complex f, g;
static integer i__, j;
static complex r__, s, t;
static real t0, t1;
static complex h11, h21;
static integer jj;
static real ulp, tst1;
static integer iend;
static real unfl, ovfl;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
static complex sigma;
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *, ftnlen), ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), cmout_(integer *, integer *,
integer *, complex *, integer *, integer *, char *, ftnlen),
cvout_(integer *, integer *, complex *, integer *, char *, ftnlen)
, ivout_(integer *, integer *, integer *, integer *, char *,
ftnlen);
extern doublereal slapy2_(real *, real *);
extern /* Subroutine */ int slabad_(real *, real *);
extern doublereal clanhs_(char *, integer *, complex *, integer *,
complex *, ftnlen), slamch_(char *, ftnlen);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, ftnlen);
static integer istart, kplusp, msglvl;
static real smlnum;
extern /* Subroutine */ int clartg_(complex *, complex *, real *, complex
*, complex *), claset_(char *, integer *, integer *, complex *,
complex *, complex *, integer *, ftnlen), second_(real *);
/* %----------------------------------------------------% */
/* | 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 & Arrays | */
/* %------------------------% */
/* %----------------------% */
/* | External Subroutines | */
/* %----------------------% */
/* %--------------------% */
/* | External Functions | */
/* %--------------------% */
/* %----------------------% */
/* | Intrinsics Functions | */
/* %----------------------% */
/* %---------------------% */
/* | Statement Functions | */
/* %---------------------% */
/* %----------------% */
/* | Data statments | */
/* %----------------% */
/* Parameter adjustments */
--workd;
--resid;
--workl;
--shift;
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 clahqr | */
/* %-----------------------------------------------% */
unfl = slamch_("safe minimum", (ftnlen)12);
q__1.r = 1.f / unfl, q__1.i = 0.f / unfl;
ovfl = q__1.r;
slabad_(&unfl, &ovfl);
ulp = slamch_("precision", (ftnlen)9);
smlnum = unfl * (*n / ulp);
first = FALSE_;
}
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
second_(&t0);
msglvl = debug_1.mcapps;
kplusp = *kev + *np;
/* %--------------------------------------------% */
/* | Initialize Q to the identity to accumulate | */
/* | the rotations and reflections | */
/* %--------------------------------------------% */
claset_("All", &kplusp, &kplusp, &c_b2, &c_b1, &q[q_offset], ldq, (ftnlen)
3);
/* %----------------------------------------------% */
/* | 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. | */
/* %----------------------------------------------% */
i__1 = *np;
for (jj = 1; jj <= i__1; ++jj) {
i__2 = jj;
sigma.r = shift[i__2].r, sigma.i = shift[i__2].i;
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, &jj, &debug_1.ndigit, "_napps: sh"
"ift number.", (ftnlen)21);
cvout_(&debug_1.logfil, &c__1, &sigma, &debug_1.ndigit, "_napps:"
" Value of the shift ", (ftnlen)27);
}
istart = 1;
L20:
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 clahqr | */
/* %----------------------------------------% */
i__3 = i__ + i__ * h_dim1;
i__4 = i__ + 1 + (i__ + 1) * h_dim1;
tst1 = (r__1 = h__[i__3].r, dabs(r__1)) + (r__2 = r_imag(&h__[i__
+ i__ * h_dim1]), dabs(r__2)) + ((r__3 = h__[i__4].r,
dabs(r__3)) + (r__4 = r_imag(&h__[i__ + 1 + (i__ + 1) *
h_dim1]), dabs(r__4)));
if (tst1 == 0.f) {
i__3 = kplusp - jj + 1;
tst1 = clanhs_("1", &i__3, &h__[h_offset], ldh, &workl[1], (
ftnlen)1);
}
i__3 = i__ + 1 + i__ * h_dim1;
/* Computing MAX */
r__2 = ulp * tst1;
if ((r__1 = h__[i__3].r, dabs(r__1)) <= dmax(r__2,smlnum)) {
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &i__, &debug_1.ndigit,
"_napps: matrix splitting at row/column no.", (
ftnlen)42);
ivout_(&debug_1.logfil, &c__1, &jj, &debug_1.ndigit,
"_napps: matrix splitting with shift number.", (
ftnlen)43);
cvout_(&debug_1.logfil, &c__1, &h__[i__ + 1 + i__ *
h_dim1], &debug_1.ndigit, "_napps: off diagonal "
"element.", (ftnlen)29);
}
iend = i__;
i__3 = i__ + 1 + i__ * h_dim1;
h__[i__3].r = 0.f, h__[i__3].i = 0.f;
goto L40;
}
/* L30: */
}
iend = kplusp;
L40:
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, &istart, &debug_1.ndigit, "_napps"
": Start of current block ", (ftnlen)31);
ivout_(&debug_1.logfil, &c__1, &iend, &debug_1.ndigit, "_napps: "
"End of current block ", (ftnlen)29);
}
/* %------------------------------------------------% */
/* | No reason to apply a shift to block of order 1 | */
/* | or if the current block starts after the point | */
/* | of compression since we'll discard this stuff | */
/* %------------------------------------------------% */
if (istart == iend || istart > *kev) {
goto L100;
}
i__2 = istart + istart * h_dim1;
h11.r = h__[i__2].r, h11.i = h__[i__2].i;
i__2 = istart + 1 + istart * h_dim1;
h21.r = h__[i__2].r, h21.i = h__[i__2].i;
q__1.r = h11.r - sigma.r, q__1.i = h11.i - sigma.i;
f.r = q__1.r, f.i = q__1.i;
g.r = h21.r, g.i = h21.i;
i__2 = iend - 1;
for (i__ = istart; i__ <= i__2; ++i__) {
/* %------------------------------------------------------% */
/* | Construct the plane rotation G to zero out the bulge | */
/* %------------------------------------------------------% */
clartg_(&f, &g, &c__, &s, &r__);
if (i__ > istart) {
i__3 = i__ + (i__ - 1) * h_dim1;
h__[i__3].r = r__.r, h__[i__3].i = r__.i;
i__3 = i__ + 1 + (i__ - 1) * h_dim1;
h__[i__3].r = 0.f, h__[i__3].i = 0.f;
}
/* %---------------------------------------------% */
/* | Apply rotation to the left of H; H <- G'*H | */
/* %---------------------------------------------% */
i__3 = kplusp;
for (j = i__; j <= i__3; ++j) {
i__4 = i__ + j * h_dim1;
q__2.r = c__ * h__[i__4].r, q__2.i = c__ * h__[i__4].i;
i__5 = i__ + 1 + j * h_dim1;
q__3.r = s.r * h__[i__5].r - s.i * h__[i__5].i, q__3.i = s.r *
h__[i__5].i + s.i * h__[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
t.r = q__1.r, t.i = q__1.i;
i__4 = i__ + 1 + j * h_dim1;
r_cnjg(&q__4, &s);
q__3.r = -q__4.r, q__3.i = -q__4.i;
i__5 = i__ + j * h_dim1;
q__2.r = q__3.r * h__[i__5].r - q__3.i * h__[i__5].i, q__2.i =
q__3.r * h__[i__5].i + q__3.i * h__[i__5].r;
i__6 = i__ + 1 + j * h_dim1;
q__5.r = c__ * h__[i__6].r, q__5.i = c__ * h__[i__6].i;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
h__[i__4].r = q__1.r, h__[i__4].i = q__1.i;
i__4 = i__ + j * h_dim1;
h__[i__4].r = t.r, h__[i__4].i = t.i;
/* 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) {
i__4 = j + i__ * h_dim1;
q__2.r = c__ * h__[i__4].r, q__2.i = c__ * h__[i__4].i;
r_cnjg(&q__4, &s);
i__5 = j + (i__ + 1) * h_dim1;
q__3.r = q__4.r * h__[i__5].r - q__4.i * h__[i__5].i, q__3.i =
q__4.r * h__[i__5].i + q__4.i * h__[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
t.r = q__1.r, t.i = q__1.i;
i__4 = j + (i__ + 1) * h_dim1;
q__3.r = -s.r, q__3.i = -s.i;
i__5 = j + i__ * h_dim1;
q__2.r = q__3.r * h__[i__5].r - q__3.i * h__[i__5].i, q__2.i =
q__3.r * h__[i__5].i + q__3.i * h__[i__5].r;
i__6 = j + (i__ + 1) * h_dim1;
q__4.r = c__ * h__[i__6].r, q__4.i = c__ * h__[i__6].i;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
h__[i__4].r = q__1.r, h__[i__4].i = q__1.i;
i__4 = j + i__ * h_dim1;
h__[i__4].r = t.r, h__[i__4].i = t.i;
/* L60: */
}
/* %-----------------------------------------------------% */
/* | Accumulate the rotation in the matrix Q; Q <- Q*G' | */
/* %-----------------------------------------------------% */
/* Computing MIN */
i__4 = i__ + jj;
i__3 = min(i__4,kplusp);
for (j = 1; j <= i__3; ++j) {
i__4 = j + i__ * q_dim1;
q__2.r = c__ * q[i__4].r, q__2.i = c__ * q[i__4].i;
r_cnjg(&q__4, &s);
i__5 = j + (i__ + 1) * q_dim1;
q__3.r = q__4.r * q[i__5].r - q__4.i * q[i__5].i, q__3.i =
q__4.r * q[i__5].i + q__4.i * q[i__5].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
t.r = q__1.r, t.i = q__1.i;
i__4 = j + (i__ + 1) * q_dim1;
q__3.r = -s.r, q__3.i = -s.i;
i__5 = j + i__ * q_dim1;
q__2.r = q__3.r * q[i__5].r - q__3.i * q[i__5].i, q__2.i =
q__3.r * q[i__5].i + q__3.i * q[i__5].r;
i__6 = j + (i__ + 1) * q_dim1;
q__4.r = c__ * q[i__6].r, q__4.i = c__ * q[i__6].i;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
q[i__4].r = q__1.r, q[i__4].i = q__1.i;
i__4 = j + i__ * q_dim1;
q[i__4].r = t.r, q[i__4].i = t.i;
/* L70: */
}
/* %---------------------------% */
/* | Prepare for next rotation | */
/* %---------------------------% */
if (i__ < iend - 1) {
i__3 = i__ + 1 + i__ * h_dim1;
f.r = h__[i__3].r, f.i = h__[i__3].i;
i__3 = i__ + 2 + i__ * h_dim1;
g.r = h__[i__3].r, g.i = h__[i__3].i;
}
/* L80: */
}
/* %-------------------------------% */
/* | Finished applying the shift. | */
/* %-------------------------------% */
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 the compressed H will have non-negative | */
/* | real subdiagonal elements. | */
/* %---------------------------------------------------% */
i__1 = *kev;
for (j = 1; j <= i__1; ++j) {
i__2 = j + 1 + j * h_dim1;
if (h__[i__2].r < 0.f || r_imag(&h__[j + 1 + j * h_dim1]) != 0.f) {
i__2 = j + 1 + j * h_dim1;
i__3 = j + 1 + j * h_dim1;
r__2 = h__[i__3].r;
r__3 = r_imag(&h__[j + 1 + j * h_dim1]);
r__1 = slapy2_(&r__2, &r__3);
q__1.r = h__[i__2].r / r__1, q__1.i = h__[i__2].i / r__1;
t.r = q__1.r, t.i = q__1.i;
i__2 = kplusp - j + 1;
r_cnjg(&q__1, &t);
cscal_(&i__2, &q__1, &h__[j + 1 + j * h_dim1], ldh);
/* Computing MIN */
i__3 = j + 2;
i__2 = min(i__3,kplusp);
cscal_(&i__2, &t, &h__[(j + 1) * h_dim1 + 1], &c__1);
/* Computing MIN */
i__3 = j + *np + 1;
i__2 = min(i__3,kplusp);
cscal_(&i__2, &t, &q[(j + 1) * q_dim1 + 1], &c__1);
i__2 = j + 1 + j * h_dim1;
i__3 = j + 1 + j * h_dim1;
r__1 = h__[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
h__[i__2].r = q__1.r, h__[i__2].i = q__1.i;
}
/* 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 clahqr. | */
/* | Note: Since the subdiagonals of the | */
/* | compressed H are nonnegative real numbers, | */
/* | we take advantage of this. | */
/* %--------------------------------------------% */
i__2 = i__ + i__ * h_dim1;
i__3 = i__ + 1 + (i__ + 1) * h_dim1;
tst1 = (r__1 = h__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&h__[i__ +
i__ * h_dim1]), dabs(r__2)) + ((r__3 = h__[i__3].r, dabs(r__3)
) + (r__4 = r_imag(&h__[i__ + 1 + (i__ + 1) * h_dim1]), dabs(
r__4)));
if (tst1 == 0.f) {
tst1 = clanhs_("1", kev, &h__[h_offset], ldh, &workl[1], (ftnlen)
1);
}
i__2 = i__ + 1 + i__ * h_dim1;
/* Computing MAX */
r__1 = ulp * tst1;
if (h__[i__2].r <= dmax(r__1,smlnum)) {
i__3 = i__ + 1 + i__ * h_dim1;
h__[i__3].r = 0.f, h__[i__3].i = 0.f;
}
/* 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. | */
/* %-------------------------------------------------% */
i__1 = *kev + 1 + *kev * h_dim1;
if (h__[i__1].r > 0.f) {
cgemv_("N", n, &kplusp, &c_b1, &v[v_offset], ldv, &q[(*kev + 1) *
q_dim1 + 1], &c__1, &c_b2, &workd[*n + 1], &c__1, (ftnlen)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;
cgemv_("N", n, &i__2, &c_b1, &v[v_offset], ldv, &q[(*kev - i__ + 1) *
q_dim1 + 1], &c__1, &c_b2, &workd[1], &c__1, (ftnlen)1);
ccopy_(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). | */
/* %-------------------------------------------------% */
clacpy_("A", n, kev, &v[(kplusp - *kev + 1) * v_dim1 + 1], ldv, &v[
v_offset], ldv, (ftnlen)1);
/* %--------------------------------------------------------------% */
/* | Copy the (kev+1)-st column of (V*Q) in the appropriate place | */
/* %--------------------------------------------------------------% */
i__1 = *kev + 1 + *kev * h_dim1;
if (h__[i__1].r > 0.f) {
ccopy_(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_{kev+p}'*Q)*e_{kev} | */
/* | betak = e_{kev+1}'*H*e_{kev} | */
/* %-------------------------------------% */
cscal_(n, &q[kplusp + *kev * q_dim1], &resid[1], &c__1);
i__1 = *kev + 1 + *kev * h_dim1;
if (h__[i__1].r > 0.f) {
caxpy_(n, &h__[*kev + 1 + *kev * h_dim1], &v[(*kev + 1) * v_dim1 + 1],
&c__1, &resid[1], &c__1);
}
if (msglvl > 1) {
cvout_(&debug_1.logfil, &c__1, &q[kplusp + *kev * q_dim1], &
debug_1.ndigit, "_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}", (
ftnlen)40);
cvout_(&debug_1.logfil, &c__1, &h__[*kev + 1 + *kev * h_dim1], &
debug_1.ndigit, "_napps: betak = e_{kev+1}^T*H*e_{kev}", (
ftnlen)37);
ivout_(&debug_1.logfil, &c__1, kev, &debug_1.ndigit, "_napps: Order "
"of the final Hessenberg matrix ", (ftnlen)45);
if (msglvl > 2) {
cmout_(&debug_1.logfil, kev, kev, &h__[h_offset], ldh, &
debug_1.ndigit, "_napps: updated Hessenberg matrix H for"
" next iteration", (ftnlen)54);
}
}
L9000:
second_(&t1);
timing_1.tcapps += t1 - t0;
return 0;
/* %---------------% */
/* | End of cnapps | */
/* %---------------% */
} /* cnapps_ */
/* Subroutine */ int snaup2_(integer *ido, char *bmat, integer *n, char *
which, integer *nev, integer *np, real *tol, real *resid, integer *
mode, integer *iupd, integer *ishift, integer *mxiter, real *v,
integer *ldv, real *h__, integer *ldh, real *ritzr, real *ritzi, real
*bounds, real *q, integer *ldq, real *workl, integer *ipntr, real *
workd, integer *info, ftnlen bmat_len, ftnlen which_len)
{
/* System generated locals */
integer h_dim1, h_offset, q_dim1, q_offset, v_dim1, v_offset, i__1, i__2;
real r__1, r__2;
doublereal d__1;
/* Builtin functions */
double pow_dd(doublereal *, doublereal *);
integer s_cmp(char *, char *, ftnlen, ftnlen);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double sqrt(doublereal);
/* Local variables */
static integer j;
static real t0, t1, t2, t3;
static integer kp[4], np0, nev0;
static real eps23;
static integer ierr, iter;
static real temp;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
static logical getv0;
extern doublereal snrm2_(integer *, real *, integer *);
static logical cnorm;
static integer nconv;
static logical initv;
static real rnorm;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), ivout_(integer *, integer *, integer *, integer *,
char *, ftnlen), smout_(integer *, integer *, integer *, real *,
integer *, integer *, char *, ftnlen), svout_(integer *, integer *
, real *, integer *, char *, ftnlen), sgetv0_(integer *, char *,
integer *, logical *, integer *, integer *, real *, integer *,
real *, real *, integer *, real *, integer *, ftnlen);
extern doublereal slapy2_(real *, real *);
static integer nevbef;
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int second_(real *);
static logical update;
static char wprime[2];
static logical ushift;
static integer kplusp, msglvl, nptemp, numcnv;
extern /* Subroutine */ int snaitr_(integer *, char *, integer *, integer
*, integer *, integer *, real *, real *, real *, integer *, real *
, integer *, integer *, real *, integer *, ftnlen), snconv_(
integer *, real *, real *, real *, real *, integer *), sneigh_(
real *, integer *, real *, integer *, real *, real *, real *,
real *, integer *, real *, integer *), sngets_(integer *, char *,
integer *, integer *, real *, real *, real *, real *, real *,
ftnlen), snapps_(integer *, integer *, integer *, real *, real *,
real *, integer *, real *, integer *, real *, real *, integer *,
real *, real *), ssortc_(char *, logical *, integer *, real *,
real *, real *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 | */
/* %---------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* Parameter adjustments */
--workd;
--resid;
--workl;
--bounds;
--ritzi;
--ritzr;
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;
--ipntr;
/* Function Body */
if (*ido == 0) {
second_(&t0);
msglvl = debug_1.mnaup2;
/* %-------------------------------------% */
/* | Get the machine dependent constant. | */
/* %-------------------------------------% */
eps23 = slamch_("Epsilon-Machine", (ftnlen)15);
d__1 = (doublereal) eps23;
eps23 = pow_dd(&d__1, &c_b3);
nev0 = *nev;
np0 = *np;
/* %-------------------------------------% */
/* | kplusp is the bound on the largest | */
/* | Lanczos factorization built. | */
/* | nconv is the current number of | */
/* | "converged" eigenvlues. | */
/* | iter is the counter on the current | */
/* | iteration step. | */
/* %-------------------------------------% */
kplusp = *nev + *np;
nconv = 0;
iter = 0;
/* %---------------------------------------% */
/* | Set flags for computing the first NEV | */
/* | steps of the Arnoldi factorization. | */
/* %---------------------------------------% */
getv0 = TRUE_;
update = FALSE_;
ushift = FALSE_;
cnorm = FALSE_;
if (*info != 0) {
/* %--------------------------------------------% */
/* | User provides the initial residual vector. | */
/* %--------------------------------------------% */
initv = TRUE_;
*info = 0;
} else {
initv = FALSE_;
}
}
/* %---------------------------------------------% */
/* | Get a possibly random starting vector and | */
/* | force it into the range of the operator OP. | */
/* %---------------------------------------------% */
/* L10: */
if (getv0) {
sgetv0_(ido, bmat, &c__1, &initv, n, &c__1, &v[v_offset], ldv, &resid[
1], &rnorm, &ipntr[1], &workd[1], info, (ftnlen)1);
if (*ido != 99) {
goto L9000;
}
if (rnorm == 0.f) {
/* %-----------------------------------------% */
/* | The initial vector is zero. Error exit. | */
/* %-----------------------------------------% */
*info = -9;
goto L1100;
}
getv0 = FALSE_;
*ido = 0;
}
/* %-----------------------------------% */
/* | Back from reverse communication : | */
/* | continue with update step | */
/* %-----------------------------------% */
if (update) {
goto L20;
}
/* %-------------------------------------------% */
/* | Back from computing user specified shifts | */
/* %-------------------------------------------% */
if (ushift) {
goto L50;
}
/* %-------------------------------------% */
/* | Back from computing residual norm | */
/* | at the end of the current iteration | */
/* %-------------------------------------% */
if (cnorm) {
goto L100;
}
/* %----------------------------------------------------------% */
/* | Compute the first NEV steps of the Arnoldi factorization | */
/* %----------------------------------------------------------% */
snaitr_(ido, bmat, n, &c__0, nev, mode, &resid[1], &rnorm, &v[v_offset],
ldv, &h__[h_offset], ldh, &ipntr[1], &workd[1], info, (ftnlen)1);
/* %---------------------------------------------------% */
/* | ido .ne. 99 implies use of reverse communication | */
/* | to compute operations involving OP and possibly B | */
/* %---------------------------------------------------% */
if (*ido != 99) {
goto L9000;
}
if (*info > 0) {
*np = *info;
*mxiter = iter;
*info = -9999;
goto L1200;
}
/* %--------------------------------------------------------------% */
/* | | */
/* | M A I N ARNOLDI I T E R A T I O N L O O P | */
/* | Each iteration implicitly restarts the Arnoldi | */
/* | factorization in place. | */
/* | | */
/* %--------------------------------------------------------------% */
L1000:
++iter;
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &iter, &debug_1.ndigit, "_naup2: ****"
" Start of major iteration number ****", (ftnlen)49);
}
/* %-----------------------------------------------------------% */
/* | Compute NP additional steps of the Arnoldi factorization. | */
/* | Adjust NP since NEV might have been updated by last call | */
/* | to the shift application routine snapps. | */
/* %-----------------------------------------------------------% */
*np = kplusp - *nev;
if (msglvl > 1) {
ivout_(&debug_1.logfil, &c__1, nev, &debug_1.ndigit, "_naup2: The le"
"ngth of the current Arnoldi factorization", (ftnlen)55);
ivout_(&debug_1.logfil, &c__1, np, &debug_1.ndigit, "_naup2: Extend "
"the Arnoldi factorization by", (ftnlen)43);
}
/* %-----------------------------------------------------------% */
/* | Compute NP additional steps of the Arnoldi factorization. | */
/* %-----------------------------------------------------------% */
*ido = 0;
L20:
update = TRUE_;
snaitr_(ido, bmat, n, nev, np, mode, &resid[1], &rnorm, &v[v_offset], ldv,
&h__[h_offset], ldh, &ipntr[1], &workd[1], info, (ftnlen)1);
/* %---------------------------------------------------% */
/* | ido .ne. 99 implies use of reverse communication | */
/* | to compute operations involving OP and possibly B | */
/* %---------------------------------------------------% */
if (*ido != 99) {
goto L9000;
}
if (*info > 0) {
*np = *info;
*mxiter = iter;
*info = -9999;
goto L1200;
}
update = FALSE_;
if (msglvl > 1) {
svout_(&debug_1.logfil, &c__1, &rnorm, &debug_1.ndigit, "_naup2: Cor"
"responding B-norm of the residual", (ftnlen)44);
}
/* %--------------------------------------------------------% */
/* | Compute the eigenvalues and corresponding error bounds | */
/* | of the current upper Hessenberg matrix. | */
/* %--------------------------------------------------------% */
sneigh_(&rnorm, &kplusp, &h__[h_offset], ldh, &ritzr[1], &ritzi[1], &
bounds[1], &q[q_offset], ldq, &workl[1], &ierr);
if (ierr != 0) {
*info = -8;
goto L1200;
}
/* %----------------------------------------------------% */
/* | Make a copy of eigenvalues and corresponding error | */
/* | bounds obtained from sneigh. | */
/* %----------------------------------------------------% */
/* Computing 2nd power */
i__1 = kplusp;
scopy_(&kplusp, &ritzr[1], &c__1, &workl[i__1 * i__1 + 1], &c__1);
/* Computing 2nd power */
i__1 = kplusp;
scopy_(&kplusp, &ritzi[1], &c__1, &workl[i__1 * i__1 + kplusp + 1], &c__1)
;
/* Computing 2nd power */
i__1 = kplusp;
scopy_(&kplusp, &bounds[1], &c__1, &workl[i__1 * i__1 + (kplusp << 1) + 1]
, &c__1);
/* %---------------------------------------------------% */
/* | Select the wanted Ritz values and their bounds | */
/* | to be used in the convergence test. | */
/* | The wanted part of the spectrum and corresponding | */
/* | error bounds are in the last NEV loc. of RITZR, | */
/* | RITZI and BOUNDS respectively. The variables NEV | */
/* | and NP may be updated if the NEV-th wanted Ritz | */
/* | value has a non zero imaginary part. In this case | */
/* | NEV is increased by one and NP decreased by one. | */
/* | NOTE: The last two arguments of sngets are no | */
/* | longer used as of version 2.1. | */
/* %---------------------------------------------------% */
*nev = nev0;
*np = np0;
numcnv = *nev;
sngets_(ishift, which, nev, np, &ritzr[1], &ritzi[1], &bounds[1], &workl[
1], &workl[*np + 1], (ftnlen)2);
if (*nev == nev0 + 1) {
numcnv = nev0 + 1;
}
/* %-------------------% */
/* | Convergence test. | */
/* %-------------------% */
scopy_(nev, &bounds[*np + 1], &c__1, &workl[(*np << 1) + 1], &c__1);
snconv_(nev, &ritzr[*np + 1], &ritzi[*np + 1], &workl[(*np << 1) + 1],
tol, &nconv);
if (msglvl > 2) {
kp[0] = *nev;
kp[1] = *np;
kp[2] = numcnv;
kp[3] = nconv;
ivout_(&debug_1.logfil, &c__4, kp, &debug_1.ndigit, "_naup2: NEV, NP"
", NUMCNV, NCONV are", (ftnlen)34);
svout_(&debug_1.logfil, &kplusp, &ritzr[1], &debug_1.ndigit, "_naup2"
": Real part of the eigenvalues of H", (ftnlen)41);
svout_(&debug_1.logfil, &kplusp, &ritzi[1], &debug_1.ndigit, "_naup2"
": Imaginary part of the eigenvalues of H", (ftnlen)46);
svout_(&debug_1.logfil, &kplusp, &bounds[1], &debug_1.ndigit, "_naup"
"2: Ritz estimates of the current NCV Ritz values", (ftnlen)53)
;
}
/* %---------------------------------------------------------% */
/* | Count the number of unwanted Ritz values that have zero | */
/* | Ritz estimates. If any Ritz estimates are equal to zero | */
/* | then a leading block of H of order equal to at least | */
/* | the number of Ritz values with zero Ritz estimates has | */
/* | split off. None of these Ritz values may be removed by | */
/* | shifting. Decrease NP the number of shifts to apply. If | */
/* | no shifts may be applied, then prepare to exit | */
/* %---------------------------------------------------------% */
nptemp = *np;
i__1 = nptemp;
for (j = 1; j <= i__1; ++j) {
if (bounds[j] == 0.f) {
--(*np);
++(*nev);
}
/* L30: */
}
if (nconv >= numcnv || iter > *mxiter || *np == 0) {
if (msglvl > 4) {
/* Computing 2nd power */
i__1 = kplusp;
svout_(&debug_1.logfil, &kplusp, &workl[i__1 * i__1 + 1], &
debug_1.ndigit, "_naup2: Real part of the eig computed b"
"y _neigh:", (ftnlen)48);
/* Computing 2nd power */
i__1 = kplusp;
svout_(&debug_1.logfil, &kplusp, &workl[i__1 * i__1 + kplusp + 1],
&debug_1.ndigit, "_naup2: Imag part of the eig computed"
" by _neigh:", (ftnlen)48);
/* Computing 2nd power */
i__1 = kplusp;
svout_(&debug_1.logfil, &kplusp, &workl[i__1 * i__1 + (kplusp <<
1) + 1], &debug_1.ndigit, "_naup2: Ritz eistmates comput"
"ed by _neigh:", (ftnlen)42);
}
/* %------------------------------------------------% */
/* | Prepare to exit. Put the converged Ritz values | */
/* | and corresponding bounds in RITZ(1:NCONV) and | */
/* | BOUNDS(1:NCONV) respectively. Then sort. Be | */
/* | careful when NCONV > NP | */
/* %------------------------------------------------% */
/* %------------------------------------------% */
/* | Use h( 3,1 ) as storage to communicate | */
/* | rnorm to _neupd if needed | */
/* %------------------------------------------% */
h__[h_dim1 + 3] = rnorm;
/* %----------------------------------------------% */
/* | To be consistent with sngets, we first do a | */
/* | pre-processing sort in order to keep complex | */
/* | conjugate pairs together. This is similar | */
/* | to the pre-processing sort used in sngets | */
/* | except that the sort is done in the opposite | */
/* | order. | */
/* %----------------------------------------------% */
if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SR", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LR", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "LR", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SM", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SR", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LM", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "LI", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SM", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SI", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LM", (ftnlen)2, (ftnlen)2);
}
ssortc_(wprime, &c_true, &kplusp, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
/* %----------------------------------------------% */
/* | Now sort Ritz values so that converged Ritz | */
/* | values appear within the first NEV locations | */
/* | of ritzr, ritzi and bounds, and the most | */
/* | desired one appears at the front. | */
/* %----------------------------------------------% */
if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SM", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SM", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LM", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "LR", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SR", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SR", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LR", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "LI", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "SI", (ftnlen)2, (ftnlen)2);
}
if (s_cmp(which, "SI", (ftnlen)2, (ftnlen)2) == 0) {
s_copy(wprime, "LI", (ftnlen)2, (ftnlen)2);
}
ssortc_(wprime, &c_true, &kplusp, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
/* %--------------------------------------------------% */
/* | Scale the Ritz estimate of each Ritz value | */
/* | by 1 / max(eps23,magnitude of the Ritz value). | */
/* %--------------------------------------------------% */
i__1 = numcnv;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
r__1 = eps23, r__2 = slapy2_(&ritzr[j], &ritzi[j]);
temp = dmax(r__1,r__2);
bounds[j] /= temp;
/* L35: */
}
/* %----------------------------------------------------% */
/* | Sort the Ritz values according to the scaled Ritz | */
/* | esitmates. This will push all the converged ones | */
/* | towards the front of ritzr, ritzi, bounds | */
/* | (in the case when NCONV < NEV.) | */
/* %----------------------------------------------------% */
s_copy(wprime, "LR", (ftnlen)2, (ftnlen)2);
ssortc_(wprime, &c_true, &numcnv, &bounds[1], &ritzr[1], &ritzi[1], (
ftnlen)2);
/* %----------------------------------------------% */
/* | Scale the Ritz estimate back to its original | */
/* | value. | */
/* %----------------------------------------------% */
i__1 = numcnv;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
r__1 = eps23, r__2 = slapy2_(&ritzr[j], &ritzi[j]);
temp = dmax(r__1,r__2);
bounds[j] *= temp;
/* L40: */
}
/* %------------------------------------------------% */
/* | Sort the converged Ritz values again so that | */
/* | the "threshold" value appears at the front of | */
/* | ritzr, ritzi and bound. | */
/* %------------------------------------------------% */
ssortc_(which, &c_true, &nconv, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
if (msglvl > 1) {
svout_(&debug_1.logfil, &kplusp, &ritzr[1], &debug_1.ndigit,
"_naup2: Sorted real part of the eigenvalues", (ftnlen)43)
;
svout_(&debug_1.logfil, &kplusp, &ritzi[1], &debug_1.ndigit,
"_naup2: Sorted imaginary part of the eigenvalues", (
ftnlen)48);
svout_(&debug_1.logfil, &kplusp, &bounds[1], &debug_1.ndigit,
"_naup2: Sorted ritz estimates.", (ftnlen)30);
}
/* %------------------------------------% */
/* | Max iterations have been exceeded. | */
/* %------------------------------------% */
if (iter > *mxiter && nconv < numcnv) {
*info = 1;
}
/* %---------------------% */
/* | No shifts to apply. | */
/* %---------------------% */
if (*np == 0 && nconv < numcnv) {
*info = 2;
}
*np = nconv;
goto L1100;
} else if (nconv < numcnv && *ishift == 1) {
/* %-------------------------------------------------% */
/* | Do not have all the requested eigenvalues yet. | */
/* | To prevent possible stagnation, adjust the size | */
/* | of NEV. | */
/* %-------------------------------------------------% */
nevbef = *nev;
/* Computing MIN */
i__1 = nconv, i__2 = *np / 2;
*nev += min(i__1,i__2);
if (*nev == 1 && kplusp >= 6) {
*nev = kplusp / 2;
} else if (*nev == 1 && kplusp > 3) {
*nev = 2;
}
*np = kplusp - *nev;
/* %---------------------------------------% */
/* | If the size of NEV was just increased | */
/* | resort the eigenvalues. | */
/* %---------------------------------------% */
if (nevbef < *nev) {
sngets_(ishift, which, nev, np, &ritzr[1], &ritzi[1], &bounds[1],
&workl[1], &workl[*np + 1], (ftnlen)2);
}
}
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &nconv, &debug_1.ndigit, "_naup2: no."
" of \"converged\" Ritz values at this iter.", (ftnlen)52);
if (msglvl > 1) {
kp[0] = *nev;
kp[1] = *np;
ivout_(&debug_1.logfil, &c__2, kp, &debug_1.ndigit, "_naup2: NEV"
" and NP are", (ftnlen)22);
svout_(&debug_1.logfil, nev, &ritzr[*np + 1], &debug_1.ndigit,
"_naup2: \"wanted\" Ritz values -- real part", (ftnlen)41)
;
svout_(&debug_1.logfil, nev, &ritzi[*np + 1], &debug_1.ndigit,
"_naup2: \"wanted\" Ritz values -- imag part", (ftnlen)41)
;
svout_(&debug_1.logfil, nev, &bounds[*np + 1], &debug_1.ndigit,
"_naup2: Ritz estimates of the \"wanted\" values ", (
ftnlen)46);
}
}
if (*ishift == 0) {
/* %-------------------------------------------------------% */
/* | User specified shifts: reverse comminucation to | */
/* | compute the shifts. They are returned in the first | */
/* | 2*NP locations of WORKL. | */
/* %-------------------------------------------------------% */
ushift = TRUE_;
*ido = 3;
goto L9000;
}
L50:
/* %------------------------------------% */
/* | Back from reverse communication; | */
/* | User specified shifts are returned | */
/* | in WORKL(1:2*NP) | */
/* %------------------------------------% */
ushift = FALSE_;
if (*ishift == 0) {
/* %----------------------------------% */
/* | Move the NP shifts from WORKL to | */
/* | RITZR, RITZI to free up WORKL | */
/* | for non-exact shift case. | */
/* %----------------------------------% */
scopy_(np, &workl[1], &c__1, &ritzr[1], &c__1);
scopy_(np, &workl[*np + 1], &c__1, &ritzi[1], &c__1);
}
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, np, &debug_1.ndigit, "_naup2: The num"
"ber of shifts to apply ", (ftnlen)38);
svout_(&debug_1.logfil, np, &ritzr[1], &debug_1.ndigit, "_naup2: Rea"
"l part of the shifts", (ftnlen)31);
svout_(&debug_1.logfil, np, &ritzi[1], &debug_1.ndigit, "_naup2: Ima"
"ginary part of the shifts", (ftnlen)36);
if (*ishift == 1) {
svout_(&debug_1.logfil, np, &bounds[1], &debug_1.ndigit, "_naup2"
": Ritz estimates of the shifts", (ftnlen)36);
}
}
/* %---------------------------------------------------------% */
/* | Apply the NP implicit shifts by QR bulge chasing. | */
/* | Each shift is applied to the whole upper Hessenberg | */
/* | matrix H. | */
/* | The first 2*N locations of WORKD are used as workspace. | */
/* %---------------------------------------------------------% */
snapps_(n, nev, np, &ritzr[1], &ritzi[1], &v[v_offset], ldv, &h__[
h_offset], ldh, &resid[1], &q[q_offset], ldq, &workl[1], &workd[1]
);
/* %---------------------------------------------% */
/* | Compute the B-norm of the updated residual. | */
/* | Keep B*RESID in WORKD(1:N) to be used in | */
/* | the first step of the next call to snaitr. | */
/* %---------------------------------------------% */
cnorm = TRUE_;
second_(&t2);
if (*(unsigned char *)bmat == 'G') {
++timing_1.nbx;
scopy_(n, &resid[1], &c__1, &workd[*n + 1], &c__1);
ipntr[1] = *n + 1;
ipntr[2] = 1;
*ido = 2;
/* %----------------------------------% */
/* | Exit in order to compute B*RESID | */
/* %----------------------------------% */
goto L9000;
} else if (*(unsigned char *)bmat == 'I') {
scopy_(n, &resid[1], &c__1, &workd[1], &c__1);
}
L100:
/* %----------------------------------% */
/* | Back from reverse communication; | */
/* | WORKD(1:N) := B*RESID | */
/* %----------------------------------% */
if (*(unsigned char *)bmat == 'G') {
second_(&t3);
timing_1.tmvbx += t3 - t2;
}
if (*(unsigned char *)bmat == 'G') {
rnorm = sdot_(n, &resid[1], &c__1, &workd[1], &c__1);
rnorm = sqrt((dabs(rnorm)));
} else if (*(unsigned char *)bmat == 'I') {
rnorm = snrm2_(n, &resid[1], &c__1);
}
cnorm = FALSE_;
if (msglvl > 2) {
svout_(&debug_1.logfil, &c__1, &rnorm, &debug_1.ndigit, "_naup2: B-n"
"orm of residual for compressed factorization", (ftnlen)55);
smout_(&debug_1.logfil, nev, nev, &h__[h_offset], ldh, &
debug_1.ndigit, "_naup2: Compressed upper Hessenberg matrix H"
, (ftnlen)44);
}
goto L1000;
/* %---------------------------------------------------------------% */
/* | | */
/* | E N D O F M A I N I T E R A T I O N L O O P | */
/* | | */
/* %---------------------------------------------------------------% */
L1100:
*mxiter = iter;
*nev = numcnv;
L1200:
*ido = 99;
/* %------------% */
/* | Error Exit | */
/* %------------% */
second_(&t1);
timing_1.tnaup2 = t1 - t0;
L9000:
/* %---------------% */
/* | End of snaup2 | */
/* %---------------% */
return 0;
} /* snaup2_ */
/* ----------------------------------------------------------------------- */
/* Subroutine */ int dseupd_(logical *rvec, char *howmny, logical *select,
doublereal *d__, doublereal *z__, integer *ldz, doublereal *sigma,
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, ftnlen howmny_len, ftnlen bmat_len,
ftnlen which_len)
{
/* System generated locals */
integer v_dim1, v_offset, z_dim1, z_offset, i__1;
doublereal d__1, d__2, d__3;
/* Builtin functions */
integer s_cmp(char *, char *, ftnlen, ftnlen);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double pow_dd(doublereal *, doublereal *);
/* Local variables */
static integer j, k, ih, jj, iq, np, iw, ibd, ihb, ihd, ldh, ldq, irz;
extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
static integer mode;
static doublereal eps23;
static integer ierr;
static doublereal temp;
static integer next;
static char type__[6];
static integer ritz;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static doublereal temp1;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static logical reord;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer nconv;
static doublereal rnorm;
extern /* Subroutine */ int dvout_(integer *, integer *, doublereal *,
integer *, char *, ftnlen), ivout_(integer *, integer *, integer *
, integer *, char *, ftnlen), dgeqr2_(integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *);
static doublereal bnorm2;
extern /* Subroutine */ int dorm2r_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, ftnlen, ftnlen);
extern doublereal dlamch_(char *, ftnlen);
static integer bounds, msglvl, ishift, numcnv;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, ftnlen),
dsesrt_(char *, logical *, integer *, doublereal *, integer *,
doublereal *, integer *, ftnlen), dsteqr_(char *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, ftnlen), dsortr_(char *, logical *, integer *,
doublereal *, doublereal *, ftnlen), dsgets_(integer *, char *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
ftnlen);
static integer leftptr, rghtptr;
/* %----------------------------------------------------% */
/* | 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 */
--workd;
--resid;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--d__;
--select;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--iparam;
--ipntr;
--workl;
/* Function Body */
msglvl = debug_1.mseupd;
mode = iparam[7];
nconv = iparam[5];
*info = 0;
/* %--------------% */
/* | Quick return | */
/* %--------------% */
if (nconv == 0) {
goto L9000;
}
ierr = 0;
if (nconv <= 0) {
ierr = -14;
}
if (*n <= 0) {
ierr = -1;
}
if (*nev <= 0) {
ierr = -2;
}
if (*ncv <= *nev || *ncv > *n) {
ierr = -3;
}
if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which, "SM", (
ftnlen)2, (ftnlen)2) != 0 && s_cmp(which, "LA", (ftnlen)2, (
ftnlen)2) != 0 && s_cmp(which, "SA", (ftnlen)2, (ftnlen)2) != 0 &&
s_cmp(which, "BE", (ftnlen)2, (ftnlen)2) != 0) {
ierr = -5;
}
if (*(unsigned char *)bmat != 'I' && *(unsigned char *)bmat != 'G') {
ierr = -6;
}
if (*(unsigned char *)howmny != 'A' && *(unsigned char *)howmny != 'P' &&
*(unsigned char *)howmny != 'S' && *rvec) {
ierr = -15;
}
if (*rvec && *(unsigned char *)howmny == 'S') {
ierr = -16;
}
/* Computing 2nd power */
i__1 = *ncv;
if (*rvec && *lworkl < i__1 * i__1 + (*ncv << 3)) {
ierr = -7;
}
if (mode == 1 || mode == 2) {
s_copy(type__, "REGULR", (ftnlen)6, (ftnlen)6);
} else if (mode == 3) {
s_copy(type__, "SHIFTI", (ftnlen)6, (ftnlen)6);
} else if (mode == 4) {
s_copy(type__, "BUCKLE", (ftnlen)6, (ftnlen)6);
} else if (mode == 5) {
s_copy(type__, "CAYLEY", (ftnlen)6, (ftnlen)6);
} else {
ierr = -10;
}
if (mode == 1 && *(unsigned char *)bmat == 'G') {
ierr = -11;
}
if (*nev == 1 && s_cmp(which, "BE", (ftnlen)2, (ftnlen)2) == 0) {
ierr = -12;
}
/* %------------% */
/* | 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(1:2*ncv) := generated tridiagonal matrix H | */
/* | The subdiagonal is stored in workl(2:ncv). | */
/* | The dead spot is workl(1) but upon exiting | */
/* | dsaupd stores the B-norm of the last residual | */
/* | vector in workl(1). We use this !!! | */
/* | workl(2*ncv+1:2*ncv+ncv) := ritz values | */
/* | The wanted values are in the first NCONV spots. | */
/* | workl(3*ncv+1:3*ncv+ncv) := computed Ritz estimates | */
/* | The wanted values are in the first NCONV spots. | */
/* | NOTE: workl(1:4*ncv) is set by dsaupd and is not | */
/* | modified by dseupd . | */
/* %-------------------------------------------------------% */
/* %-------------------------------------------------------% */
/* | The following is used and set by dseupd . | */
/* | workl(4*ncv+1:4*ncv+ncv) := used as workspace during | */
/* | computation of the eigenvectors of H. Stores | */
/* | the diagonal of H. Upon EXIT contains the NCV | */
/* | Ritz values of the original system. The first | */
/* | NCONV spots have the wanted values. If MODE = | */
/* | 1 or 2 then will equal workl(2*ncv+1:3*ncv). | */
/* | workl(5*ncv+1:5*ncv+ncv) := used as workspace during | */
/* | computation of the eigenvectors of H. Stores | */
/* | the subdiagonal of H. Upon EXIT contains the | */
/* | NCV corresponding Ritz estimates of the | */
/* | original system. The first NCONV spots have the | */
/* | wanted values. If MODE = 1,2 then will equal | */
/* | workl(3*ncv+1:4*ncv). | */
/* | workl(6*ncv+1:6*ncv+ncv*ncv) := orthogonal Q that is | */
/* | the eigenvector matrix for H as returned by | */
/* | dsteqr . Not referenced if RVEC = .False. | */
/* | Ordering follows that of workl(4*ncv+1:5*ncv) | */
/* | workl(6*ncv+ncv*ncv+1:6*ncv+ncv*ncv+2*ncv) := | */
/* | Workspace. Needed by dsteqr and by dseupd . | */
/* | GRAND total of NCV*(NCV+8) locations. | */
/* %-------------------------------------------------------% */
ih = ipntr[5];
ritz = ipntr[6];
bounds = ipntr[7];
ldh = *ncv;
ldq = *ncv;
ihd = bounds + ldh;
ihb = ihd + ldh;
iq = ihb + ldh;
iw = iq + ldh * *ncv;
next = iw + (*ncv << 1);
ipntr[4] = next;
ipntr[8] = ihd;
ipntr[9] = ihb;
ipntr[10] = iq;
/* %----------------------------------------% */
/* | irz points to the Ritz values computed | */
/* | by _seigt before exiting _saup2. | */
/* | ibd points to the Ritz estimates | */
/* | computed by _seigt before exiting | */
/* | _saup2. | */
/* %----------------------------------------% */
irz = ipntr[11] + *ncv;
ibd = irz + *ncv;
/* %---------------------------------% */
/* | Set machine dependent constant. | */
/* %---------------------------------% */
eps23 = dlamch_("Epsilon-Machine", (ftnlen)15);
eps23 = pow_dd(&eps23, &c_b21);
/* %---------------------------------------% */
/* | RNORM is B-norm of the RESID(1:N). | */
/* | BNORM2 is the 2 norm of B*RESID(1:N). | */
/* | Upon exit of dsaupd WORKD(1:N) has | */
/* | B*RESID(1:N). | */
/* %---------------------------------------% */
rnorm = workl[ih];
if (*(unsigned char *)bmat == 'I') {
bnorm2 = rnorm;
} else if (*(unsigned char *)bmat == 'G') {
bnorm2 = dnrm2_(n, &workd[1], &c__1);
}
if (msglvl > 2) {
dvout_(&debug_1.logfil, ncv, &workl[irz], &debug_1.ndigit, "_seupd: "
"Ritz values passed in from _SAUPD.", (ftnlen)42);
dvout_(&debug_1.logfil, ncv, &workl[ibd], &debug_1.ndigit, "_seupd: "
"Ritz estimates passed in from _SAUPD.", (ftnlen)45);
}
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;
dsgets_(&ishift, which, nev, &np, &workl[irz], &workl[bounds], &workl[
1], (ftnlen)2);
if (msglvl > 2) {
dvout_(&debug_1.logfil, ncv, &workl[irz], &debug_1.ndigit, "_seu"
"pd: Ritz values after calling _SGETS.", (ftnlen)41);
dvout_(&debug_1.logfil, ncv, &workl[bounds], &debug_1.ndigit,
"_seupd: Ritz value indices after calling _SGETS.", (
ftnlen)48);
}
/* %-----------------------------------------------------% */
/* | 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__2 = eps23, d__3 = (d__1 = workl[irz + *ncv - j], abs(d__1));
temp1 = max(d__2,d__3);
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 _saupd. If these two | */
/* | are different then there has probably been an error | */
/* | caused by incorrect passing of the _saupd data. | */
/* %-----------------------------------------------------------% */
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, &numcnv, &debug_1.ndigit, "_seupd"
": Number of specified eigenvalues", (ftnlen)39);
ivout_(&debug_1.logfil, &c__1, &nconv, &debug_1.ndigit, "_seupd:"
" Number of \"converged\" eigenvalues", (ftnlen)41);
}
if (numcnv != nconv) {
*info = -17;
goto L9000;
}
/* %-----------------------------------------------------------% */
/* | Call LAPACK routine _steqr to compute the eigenvalues and | */
/* | eigenvectors of the final symmetric tridiagonal matrix H. | */
/* | Initialize the eigenvector matrix Q to the identity. | */
/* %-----------------------------------------------------------% */
i__1 = *ncv - 1;
dcopy_(&i__1, &workl[ih + 1], &c__1, &workl[ihb], &c__1);
dcopy_(ncv, &workl[ih + ldh], &c__1, &workl[ihd], &c__1);
dsteqr_("Identity", ncv, &workl[ihd], &workl[ihb], &workl[iq], &ldq, &
workl[iw], &ierr, (ftnlen)8);
if (ierr != 0) {
*info = -8;
goto L9000;
}
if (msglvl > 1) {
dcopy_(ncv, &workl[iq + *ncv - 1], &ldq, &workl[iw], &c__1);
dvout_(&debug_1.logfil, ncv, &workl[ihd], &debug_1.ndigit, "_seu"
"pd: NCV Ritz values of the final H matrix", (ftnlen)45);
dvout_(&debug_1.logfil, ncv, &workl[iw], &debug_1.ndigit, "_seup"
"d: last row of the eigenvector matrix for H", (ftnlen)48);
}
if (reord) {
/* %---------------------------------------------% */
/* | Reordered the eigenvalues and eigenvectors | */
/* | computed by _steqr so that the "converged" | */
/* | eigenvalues appear in the first NCONV | */
/* | positions of workl(ihd), and the associated | */
/* | eigenvectors appear in the first NCONV | */
/* | columns. | */
/* %---------------------------------------------% */
leftptr = 1;
rghtptr = *ncv;
if (*ncv == 1) {
goto L30;
}
L20:
if (select[leftptr]) {
/* %-------------------------------------------% */
/* | Search, from the left, for the first Ritz | */
/* | value that has not converged. | */
/* %-------------------------------------------% */
++leftptr;
} else if (! select[rghtptr]) {
/* %----------------------------------------------% */
/* | Search, from the right, the first Ritz value | */
/* | that has converged. | */
/* %----------------------------------------------% */
--rghtptr;
} else {
/* %----------------------------------------------% */
/* | Swap the Ritz value on the left that has not | */
/* | converged with the Ritz value on the right | */
/* | that has converged. Swap the associated | */
/* | eigenvector of the tridiagonal matrix H as | */
/* | well. | */
/* %----------------------------------------------% */
temp = workl[ihd + leftptr - 1];
workl[ihd + leftptr - 1] = workl[ihd + rghtptr - 1];
workl[ihd + rghtptr - 1] = temp;
dcopy_(ncv, &workl[iq + *ncv * (leftptr - 1)], &c__1, &workl[
iw], &c__1);
dcopy_(ncv, &workl[iq + *ncv * (rghtptr - 1)], &c__1, &workl[
iq + *ncv * (leftptr - 1)], &c__1);
dcopy_(ncv, &workl[iw], &c__1, &workl[iq + *ncv * (rghtptr -
1)], &c__1);
++leftptr;
--rghtptr;
}
if (leftptr < rghtptr) {
goto L20;
}
L30:
;
}
if (msglvl > 2) {
dvout_(&debug_1.logfil, ncv, &workl[ihd], &debug_1.ndigit, "_seu"
"pd: The eigenvalues of H--reordered", (ftnlen)39);
}
/* %----------------------------------------% */
/* | Load the converged Ritz values into D. | */
/* %----------------------------------------% */
dcopy_(&nconv, &workl[ihd], &c__1, &d__[1], &c__1);
} else {
/* %-----------------------------------------------------% */
/* | Ritz vectors not required. Load Ritz values into D. | */
/* %-----------------------------------------------------% */
dcopy_(&nconv, &workl[ritz], &c__1, &d__[1], &c__1);
dcopy_(ncv, &workl[ritz], &c__1, &workl[ihd], &c__1);
}
/* %------------------------------------------------------------------% */
/* | Transform the Ritz values and possibly vectors and corresponding | */
/* | Ritz estimates of OP to those of A*x=lambda*B*x. The Ritz values | */
/* | (and corresponding data) are returned in ascending order. | */
/* %------------------------------------------------------------------% */
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
/* %---------------------------------------------------------% */
/* | Ascending sort of wanted Ritz values, vectors and error | */
/* | bounds. Not necessary if only Ritz values are desired. | */
/* %---------------------------------------------------------% */
if (*rvec) {
dsesrt_("LA", rvec, &nconv, &d__[1], ncv, &workl[iq], &ldq, (
ftnlen)2);
} else {
dcopy_(ncv, &workl[bounds], &c__1, &workl[ihb], &c__1);
}
} else {
/* %-------------------------------------------------------------% */
/* | * Make a copy of all the Ritz values. | */
/* | * Transform the Ritz values back to the original system. | */
/* | For TYPE = 'SHIFTI' the transformation is | */
/* | lambda = 1/theta + sigma | */
/* | For TYPE = 'BUCKLE' the transformation is | */
/* | lambda = sigma * theta / ( theta - 1 ) | */
/* | For TYPE = 'CAYLEY' the transformation is | */
/* | lambda = sigma * (theta + 1) / (theta - 1 ) | */
/* | where the theta are the Ritz values returned by dsaupd . | */
/* | NOTES: | */
/* | *The Ritz vectors are not affected by the transformation. | */
/* | They are only reordered. | */
/* %-------------------------------------------------------------% */
dcopy_(ncv, &workl[ihd], &c__1, &workl[iw], &c__1);
if (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
workl[ihd + k - 1] = 1. / workl[ihd + k - 1] + *sigma;
/* L40: */
}
} else if (s_cmp(type__, "BUCKLE", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
workl[ihd + k - 1] = *sigma * workl[ihd + k - 1] / (workl[ihd
+ k - 1] - 1.);
/* L50: */
}
} else if (s_cmp(type__, "CAYLEY", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
workl[ihd + k - 1] = *sigma * (workl[ihd + k - 1] + 1.) / (
workl[ihd + k - 1] - 1.);
/* L60: */
}
}
/* %-------------------------------------------------------------% */
/* | * Store the wanted NCONV lambda values into D. | */
/* | * Sort the NCONV wanted lambda in WORKL(IHD:IHD+NCONV-1) | */
/* | into ascending order and apply sort to the NCONV theta | */
/* | values in the transformed system. We will need this to | */
/* | compute Ritz estimates in the original system. | */
/* | * Finally sort the lambda`s into ascending order and apply | */
/* | to Ritz vectors if wanted. Else just sort lambda`s into | */
/* | ascending order. | */
/* | NOTES: | */
/* | *workl(iw:iw+ncv-1) contain the theta ordered so that they | */
/* | match the ordering of the lambda. We`ll use them again for | */
/* | Ritz vector purification. | */
/* %-------------------------------------------------------------% */
dcopy_(&nconv, &workl[ihd], &c__1, &d__[1], &c__1);
dsortr_("LA", &c_true, &nconv, &workl[ihd], &workl[iw], (ftnlen)2);
if (*rvec) {
dsesrt_("LA", rvec, &nconv, &d__[1], ncv, &workl[iq], &ldq, (
ftnlen)2);
} else {
dcopy_(ncv, &workl[bounds], &c__1, &workl[ihb], &c__1);
d__1 = bnorm2 / rnorm;
dscal_(ncv, &d__1, &workl[ihb], &c__1);
dsortr_("LA", &c_true, &nconv, &d__[1], &workl[ihb], (ftnlen)2);
}
}
/* %------------------------------------------------% */
/* | Compute the Ritz vectors. Transform the wanted | */
/* | eigenvectors of the symmetric tridiagonal H by | */
/* | the Lanczos basis matrix V. | */
/* %------------------------------------------------% */
if (*rvec && *(unsigned char *)howmny == 'A') {
/* %----------------------------------------------------------% */
/* | Compute the QR factorization of the matrix representing | */
/* | the wanted invariant subspace located in the first NCONV | */
/* | columns of workl(iq,ldq). | */
/* %----------------------------------------------------------% */
dgeqr2_(ncv, &nconv, &workl[iq], &ldq, &workl[iw + *ncv], &workl[ihb],
&ierr);
/* %--------------------------------------------------------% */
/* | * Postmultiply V by Q. | */
/* | * Copy the first NCONV columns of VQ into Z. | */
/* | The N by NCONV matrix Z is now a matrix representation | */
/* | of the approximate invariant subspace associated with | */
/* | the Ritz values in workl(ihd). | */
/* %--------------------------------------------------------% */
dorm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[iq], &ldq, &
workl[iw + *ncv], &v[v_offset], ldv, &workd[*n + 1], &ierr, (
ftnlen)5, (ftnlen)11);
dlacpy_("All", n, &nconv, &v[v_offset], ldv, &z__[z_offset], ldz, (
ftnlen)3);
/* %-----------------------------------------------------% */
/* | In order to compute the Ritz estimates for the Ritz | */
/* | values in both systems, need the last row of the | */
/* | eigenvector matrix. Remember, it`s in factored form | */
/* %-----------------------------------------------------% */
i__1 = *ncv - 1;
for (j = 1; j <= i__1; ++j) {
workl[ihb + j - 1] = 0.;
/* L65: */
}
workl[ihb + *ncv - 1] = 1.;
dorm2r_("Left", "Transpose", ncv, &c__1, &nconv, &workl[iq], &ldq, &
workl[iw + *ncv], &workl[ihb], ncv, &temp, &ierr, (ftnlen)4, (
ftnlen)9);
} else if (*rvec && *(unsigned char *)howmny == 'S') {
/* Not yet implemented. See remark 2 above. */
}
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0 && *rvec) {
i__1 = *ncv;
for (j = 1; j <= i__1; ++j) {
workl[ihb + j - 1] = rnorm * (d__1 = workl[ihb + j - 1], abs(d__1)
);
/* L70: */
}
} else if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) != 0 && *rvec) {
/* %-------------------------------------------------% */
/* | * Determine Ritz estimates of the theta. | */
/* | If RVEC = .true. then compute Ritz estimates | */
/* | of the theta. | */
/* | If RVEC = .false. then copy Ritz estimates | */
/* | as computed by dsaupd . | */
/* | * Determine Ritz estimates of the lambda. | */
/* %-------------------------------------------------% */
dscal_(ncv, &bnorm2, &workl[ihb], &c__1);
if (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
/* Computing 2nd power */
d__2 = workl[iw + k - 1];
workl[ihb + k - 1] = (d__1 = workl[ihb + k - 1], abs(d__1)) /
(d__2 * d__2);
/* L80: */
}
} else if (s_cmp(type__, "BUCKLE", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
/* Computing 2nd power */
d__2 = workl[iw + k - 1] - 1.;
workl[ihb + k - 1] = *sigma * (d__1 = workl[ihb + k - 1], abs(
d__1)) / (d__2 * d__2);
/* L90: */
}
} else if (s_cmp(type__, "CAYLEY", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
workl[ihb + k - 1] = (d__1 = workl[ihb + k - 1] / workl[iw +
k - 1] * (workl[iw + k - 1] - 1.), abs(d__1));
/* L100: */
}
}
}
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) != 0 && msglvl > 1) {
dvout_(&debug_1.logfil, &nconv, &d__[1], &debug_1.ndigit, "_seupd: U"
"ntransformed converged Ritz values", (ftnlen)43);
dvout_(&debug_1.logfil, &nconv, &workl[ihb], &debug_1.ndigit, "_seup"
"d: Ritz estimates of the untransformed Ritz values", (ftnlen)
55);
} else if (msglvl > 1) {
dvout_(&debug_1.logfil, &nconv, &d__[1], &debug_1.ndigit, "_seupd: C"
"onverged Ritz values", (ftnlen)29);
dvout_(&debug_1.logfil, &nconv, &workl[ihb], &debug_1.ndigit, "_seup"
"d: Associated Ritz estimates", (ftnlen)33);
}
/* %-------------------------------------------------% */
/* | Ritz vector purification step. Formally perform | */
/* | one of inverse subspace iteration. Only used | */
/* | for MODE = 3,4,5. See reference 7 | */
/* %-------------------------------------------------% */
if (*rvec && (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0 || s_cmp(
type__, "CAYLEY", (ftnlen)6, (ftnlen)6) == 0)) {
i__1 = nconv - 1;
for (k = 0; k <= i__1; ++k) {
workl[iw + k] = workl[iq + k * ldq + *ncv - 1] / workl[iw + k];
/* L110: */
}
} else if (*rvec && s_cmp(type__, "BUCKLE", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = nconv - 1;
for (k = 0; k <= i__1; ++k) {
workl[iw + k] = workl[iq + k * ldq + *ncv - 1] / (workl[iw + k] -
1.);
/* L120: */
}
}
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) != 0) {
dger_(n, &nconv, &c_b110, &resid[1], &c__1, &workl[iw], &c__1, &z__[
z_offset], ldz);
}
L9000:
return 0;
/* %---------------% */
/* | End of dseupd | */
/* %---------------% */
} /* dseupd_ */
/* ----------------------------------------------------------------------- */
/* Subroutine */ int zneupd_(logical *rvec, char *howmny, logical *select,
doublecomplex *d__, doublecomplex *z__, integer *ldz, doublecomplex *
sigma, doublecomplex *workev, char *bmat, integer *n, char *which,
integer *nev, doublereal *tol, doublecomplex *resid, integer *ncv,
doublecomplex *v, integer *ldv, integer *iparam, integer *ipntr,
doublecomplex *workd, doublecomplex *workl, integer *lworkl,
doublereal *rwork, integer *info, ftnlen howmny_len, ftnlen bmat_len,
ftnlen which_len)
{
/* System generated locals */
integer v_dim1, v_offset, z_dim1, z_offset, i__1, i__2;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2;
/* Builtin functions */
double pow_dd(doublereal *, doublereal *);
integer s_cmp(char *, char *, ftnlen, ftnlen);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double d_imag(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
static integer j, k, ih, jj, iq, np;
static doublecomplex vl[1];
static integer wr, ibd, ldh, ldq;
static doublereal sep;
static integer irz, mode;
static doublereal eps23;
static integer ierr;
static doublecomplex temp;
static integer iwev;
static char type__[6];
static integer ritz, iheig, ihbds;
static doublereal conds;
static logical reord;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
static integer nconv;
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static doublereal rtemp;
static doublecomplex rnorm;
extern /* Subroutine */ int zgeru_(integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zcopy_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *), ivout_(integer *, integer
*, integer *, integer *, char *, ftnlen), ztrmm_(char *, char *,
char *, char *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, ftnlen,
ftnlen, ftnlen, ftnlen), zmout_(integer *, integer *, integer *,
doublecomplex *, integer *, integer *, char *, ftnlen), zvout_(
integer *, integer *, doublecomplex *, integer *, char *, ftnlen);
extern doublereal dlapy2_(doublereal *, doublereal *);
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *), dlamch_(
char *, ftnlen);
extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, ftnlen,
ftnlen);
static integer bounds, invsub, iuptri, msglvl, outncv, numcnv, ishift;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, ftnlen),
zlahqr_(logical *, logical *, integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, integer *), zngets_(integer *, char *
, integer *, integer *, doublecomplex *, doublecomplex *, ftnlen),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *, ftnlen), ztrsen_(
char *, char *, logical *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, integer *, integer *,
ftnlen, ftnlen), ztrevc_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, integer *, doublecomplex *,
doublereal *, integer *, ftnlen, ftnlen), zdscal_(integer *,
doublereal *, doublecomplex *, integer *);
/* %----------------------------------------------------% */
/* | 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 | */
/* %--------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* %------------------------% */
/* | Set default parameters | */
/* %------------------------% */
/* Parameter adjustments */
--workd;
--resid;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--d__;
--rwork;
--workev;
--select;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--iparam;
--ipntr;
--workl;
/* Function Body */
msglvl = debug_1.mceupd;
mode = iparam[7];
nconv = iparam[5];
*info = 0;
/* %---------------------------------% */
/* | Get machine dependent constant. | */
/* %---------------------------------% */
eps23 = dlamch_("Epsilon-Machine", (ftnlen)15);
eps23 = pow_dd(&eps23, &c_b5);
/* %-------------------------------% */
/* | Quick return | */
/* | Check for incompatible input | */
/* %-------------------------------% */
ierr = 0;
if (nconv <= 0) {
ierr = -14;
} else if (*n <= 0) {
ierr = -1;
} else if (*nev <= 0) {
ierr = -2;
} else if (*ncv <= *nev || *ncv > *n) {
ierr = -3;
} else if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which,
"SM", (ftnlen)2, (ftnlen)2) != 0 && s_cmp(which, "LR", (ftnlen)2,
(ftnlen)2) != 0 && s_cmp(which, "SR", (ftnlen)2, (ftnlen)2) != 0
&& s_cmp(which, "LI", (ftnlen)2, (ftnlen)2) != 0 && s_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 << 2)) {
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) {
s_copy(type__, "REGULR", (ftnlen)6, (ftnlen)6);
} else if (mode == 3) {
s_copy(type__, "SHIFTI", (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, WORKEV, 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+ncv) := ritz values | */
/* | workl(ncv*ncv+ncv+1:ncv*ncv+2*ncv) := error bounds | */
/* %--------------------------------------------------------% */
/* %-----------------------------------------------------------% */
/* | The following is used and set by ZNEUPD. | */
/* | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := The untransformed | */
/* | Ritz values. | */
/* | workl(ncv*ncv+3*ncv+1:ncv*ncv+4*ncv) := The untransformed | */
/* | error bounds of | */
/* | the Ritz values | */
/* | workl(ncv*ncv+4*ncv+1:2*ncv*ncv+4*ncv) := Holds the upper | */
/* | triangular matrix | */
/* | for H. | */
/* | workl(2*ncv*ncv+4*ncv+1: 3*ncv*ncv+4*ncv) := Holds the | */
/* | associated matrix | */
/* | representation of | */
/* | the invariant | */
/* | subspace for H. | */
/* | GRAND total of NCV * ( 3 * NCV + 4 ) locations. | */
/* %-----------------------------------------------------------% */
ih = ipntr[5];
ritz = ipntr[6];
iq = ipntr[7];
bounds = ipntr[8];
ldh = *ncv;
ldq = *ncv;
iheig = bounds + ldh;
ihbds = iheig + ldh;
iuptri = ihbds + ldh;
invsub = iuptri + ldh * *ncv;
ipntr[9] = iheig;
ipntr[11] = ihbds;
ipntr[12] = iuptri;
ipntr[13] = invsub;
wr = 1;
iwev = wr + *ncv;
/* %-----------------------------------------% */
/* | irz points to the Ritz values computed | */
/* | by _neigh before exiting _naup2. | */
/* | ibd points to the Ritz estimates | */
/* | computed by _neigh before exiting | */
/* | _naup2. | */
/* %-----------------------------------------% */
irz = ipntr[14] + *ncv * *ncv;
ibd = irz + *ncv;
/* %------------------------------------% */
/* | RNORM is B-norm of the RESID(1:N). | */
/* %------------------------------------% */
i__1 = ih + 2;
rnorm.r = workl[i__1].r, rnorm.i = workl[i__1].i;
i__1 = ih + 2;
workl[i__1].r = 0., workl[i__1].i = 0.;
if (msglvl > 2) {
zvout_(&debug_1.logfil, ncv, &workl[irz], &debug_1.ndigit, "_neupd: "
"Ritz values passed in from _NAUPD.", (ftnlen)42);
zvout_(&debug_1.logfil, ncv, &workl[ibd], &debug_1.ndigit, "_neupd: "
"Ritz estimates passed in from _NAUPD.", (ftnlen)45);
}
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) {
i__2 = bounds + j - 1;
workl[i__2].r = (doublereal) j, workl[i__2].i = 0.;
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(ibd) | */
/* | accordingly. | */
/* %-------------------------------------% */
np = *ncv - *nev;
ishift = 0;
zngets_(&ishift, which, nev, &np, &workl[irz], &workl[bounds], (
ftnlen)2);
if (msglvl > 2) {
zvout_(&debug_1.logfil, ncv, &workl[irz], &debug_1.ndigit, "_neu"
"pd: Ritz values after calling _NGETS.", (ftnlen)41);
zvout_(&debug_1.logfil, ncv, &workl[bounds], &debug_1.ndigit,
"_neupd: Ritz value indices after calling _NGETS.", (
ftnlen)48);
}
/* %-----------------------------------------------------% */
/* | 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 */
i__2 = irz + *ncv - j;
d__3 = workl[i__2].r;
d__4 = d_imag(&workl[irz + *ncv - j]);
d__1 = eps23, d__2 = dlapy2_(&d__3, &d__4);
rtemp = max(d__1,d__2);
i__2 = bounds + *ncv - j;
jj = (integer) workl[i__2].r;
i__2 = ibd + jj - 1;
d__1 = workl[i__2].r;
d__2 = d_imag(&workl[ibd + jj - 1]);
if (numcnv < nconv && dlapy2_(&d__1, &d__2) <= *tol * rtemp) {
select[jj] = TRUE_;
++numcnv;
if (jj > *nev) {
reord = TRUE_;
}
}
/* L11: */
}
/* %-----------------------------------------------------------% */
/* | Check the count (numcnv) of converged Ritz values with | */
/* | the number (nconv) reported by dnaupd. If these two | */
/* | are different then there has probably been an error | */
/* | caused by incorrect passing of the dnaupd data. | */
/* %-----------------------------------------------------------% */
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, &numcnv, &debug_1.ndigit, "_neupd"
": Number of specified eigenvalues", (ftnlen)39);
ivout_(&debug_1.logfil, &c__1, &nconv, &debug_1.ndigit, "_neupd:"
" Number of \"converged\" eigenvalues", (ftnlen)41);
}
if (numcnv != nconv) {
*info = -15;
goto L9000;
}
/* %-------------------------------------------------------% */
/* | Call LAPACK routine zlahqr to compute the Schur form | */
/* | of the upper Hessenberg matrix returned by ZNAUPD. | */
/* | Make a copy of the upper Hessenberg matrix. | */
/* | Initialize the Schur vector matrix Q to the identity. | */
/* %-------------------------------------------------------% */
i__1 = ldh * *ncv;
zcopy_(&i__1, &workl[ih], &c__1, &workl[iuptri], &c__1);
zlaset_("All", ncv, ncv, &c_b2, &c_b1, &workl[invsub], &ldq, (ftnlen)
3);
zlahqr_(&c_true, &c_true, ncv, &c__1, ncv, &workl[iuptri], &ldh, &
workl[iheig], &c__1, ncv, &workl[invsub], &ldq, &ierr);
zcopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &c__1);
if (ierr != 0) {
*info = -8;
goto L9000;
}
if (msglvl > 1) {
zvout_(&debug_1.logfil, ncv, &workl[iheig], &debug_1.ndigit,
"_neupd: Eigenvalues of H", (ftnlen)24);
zvout_(&debug_1.logfil, ncv, &workl[ihbds], &debug_1.ndigit,
"_neupd: Last row of the Schur vector matrix", (ftnlen)43)
;
if (msglvl > 3) {
zmout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldh, &
debug_1.ndigit, "_neupd: The upper triangular matrix "
, (ftnlen)36);
}
}
if (reord) {
/* %-----------------------------------------------% */
/* | Reorder the computed upper triangular matrix. | */
/* %-----------------------------------------------% */
ztrsen_("None", "V", &select[1], ncv, &workl[iuptri], &ldh, &
workl[invsub], &ldq, &workl[iheig], &nconv, &conds, &sep,
&workev[1], ncv, &ierr, (ftnlen)4, (ftnlen)1);
if (ierr == 1) {
*info = 1;
goto L9000;
}
if (msglvl > 2) {
zvout_(&debug_1.logfil, ncv, &workl[iheig], &debug_1.ndigit,
"_neupd: Eigenvalues of H--reordered", (ftnlen)35);
if (msglvl > 3) {
zmout_(&debug_1.logfil, ncv, ncv, &workl[iuptri], &ldq, &
debug_1.ndigit, "_neupd: Triangular matrix after"
" re-ordering", (ftnlen)43);
}
}
}
/* %---------------------------------------------% */
/* | Copy the last row of the Schur basis matrix | */
/* | to workl(ihbds). This vector will be used | */
/* | to compute the Ritz estimates of converged | */
/* | Ritz values. | */
/* %---------------------------------------------% */
zcopy_(ncv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds], &c__1);
/* %--------------------------------------------% */
/* | Place the computed eigenvalues of H into D | */
/* | if a spectral transformation was not used. | */
/* %--------------------------------------------% */
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
zcopy_(&nconv, &workl[iheig], &c__1, &d__[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). | */
/* %----------------------------------------------------------% */
zgeqr2_(ncv, &nconv, &workl[invsub], &ldq, &workev[1], &workev[*ncv +
1], &ierr);
/* %--------------------------------------------------------% */
/* | * Postmultiply V by Q using zunm2r. | */
/* | * 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(iheig). The first NCONV | */
/* | columns of V are now approximate Schur vectors | */
/* | associated with the upper triangular matrix of order | */
/* | NCONV in workl(iuptri). | */
/* %--------------------------------------------------------% */
zunm2r_("Right", "Notranspose", n, ncv, &nconv, &workl[invsub], &ldq,
&workev[1], &v[v_offset], ldv, &workd[*n + 1], &ierr, (ftnlen)
5, (ftnlen)11);
zlacpy_("All", n, &nconv, &v[v_offset], ldv, &z__[z_offset], ldz, (
ftnlen)3);
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 | */
/* | triangular form of workl(iuptri,ldq). | */
/* | Note that since Q is orthogonal, R is a diagonal | */
/* | matrix consisting of plus or minus ones. | */
/* %---------------------------------------------------% */
i__2 = invsub + (j - 1) * ldq + j - 1;
if (workl[i__2].r < 0.) {
z__1.r = -1., z__1.i = -0.;
zscal_(&nconv, &z__1, &workl[iuptri + j - 1], &ldq);
z__1.r = -1., z__1.i = -0.;
zscal_(&nconv, &z__1, &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: */
}
ztrevc_("Right", "Select", &select[1], ncv, &workl[iuptri], &ldq,
vl, &c__1, &workl[invsub], &ldq, ncv, &outncv, &workev[1],
&rwork[1], &ierr, (ftnlen)5, (ftnlen)6);
if (ierr != 0) {
*info = -9;
goto L9000;
}
/* %------------------------------------------------% */
/* | Scale the returning eigenvectors so that their | */
/* | Euclidean norms are all one. LAPACK subroutine | */
/* | ztrevc returns each eigenvector normalized so | */
/* | that the element of largest magnitude has | */
/* | magnitude 1. | */
/* %------------------------------------------------% */
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
rtemp = dznrm2_(ncv, &workl[invsub + (j - 1) * ldq], &c__1);
rtemp = 1. / rtemp;
zdscal_(ncv, &rtemp, &workl[invsub + (j - 1) * ldq], &c__1);
/* %------------------------------------------% */
/* | Ritz estimates can be obtained by taking | */
/* | the inner product of the last row of the | */
/* | Schur basis of H with eigenvectors of T. | */
/* | Note that the eigenvector matrix of T is | */
/* | upper triangular, thus the length of the | */
/* | inner product can be set to j. | */
/* %------------------------------------------% */
i__2 = j;
zdotc_(&z__1, &j, &workl[ihbds], &c__1, &workl[invsub + (j -
1) * ldq], &c__1);
workev[i__2].r = z__1.r, workev[i__2].i = z__1.i;
/* L40: */
}
if (msglvl > 2) {
zcopy_(&nconv, &workl[invsub + *ncv - 1], &ldq, &workl[ihbds],
&c__1);
zvout_(&debug_1.logfil, &nconv, &workl[ihbds], &
debug_1.ndigit, "_neupd: Last row of the eigenvector"
" matrix for T", (ftnlen)48);
if (msglvl > 3) {
zmout_(&debug_1.logfil, ncv, ncv, &workl[invsub], &ldq, &
debug_1.ndigit, "_neupd: The eigenvector matrix "
"for T", (ftnlen)36);
}
}
/* %---------------------------------------% */
/* | Copy Ritz estimates into workl(ihbds) | */
/* %---------------------------------------% */
zcopy_(&nconv, &workev[1], &c__1, &workl[ihbds], &c__1);
/* %----------------------------------------------% */
/* | The eigenvector matrix Q of T is triangular. | */
/* | Form Z*Q. | */
/* %----------------------------------------------% */
ztrmm_("Right", "Upper", "No transpose", "Non-unit", n, &nconv, &
c_b1, &workl[invsub], &ldq, &z__[z_offset], ldz, (ftnlen)
5, (ftnlen)5, (ftnlen)12, (ftnlen)8);
}
} else {
/* %--------------------------------------------------% */
/* | An approximate invariant subspace is not needed. | */
/* | Place the Ritz values computed ZNAUPD into D. | */
/* %--------------------------------------------------% */
zcopy_(&nconv, &workl[ritz], &c__1, &d__[1], &c__1);
zcopy_(&nconv, &workl[ritz], &c__1, &workl[iheig], &c__1);
zcopy_(&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 (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) == 0) {
if (*rvec) {
zscal_(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 (*rvec) {
zscal_(ncv, &rnorm, &workl[ihbds], &c__1);
}
i__1 = *ncv;
for (k = 1; k <= i__1; ++k) {
i__2 = iheig + k - 1;
temp.r = workl[i__2].r, temp.i = workl[i__2].i;
i__2 = ihbds + k - 1;
z_div(&z__2, &workl[ihbds + k - 1], &temp);
z_div(&z__1, &z__2, &temp);
workl[i__2].r = z__1.r, workl[i__2].i = z__1.i;
/* L50: */
}
}
/* %-----------------------------------------------------------% */
/* | * Transform the Ritz values back to the original system. | */
/* | For TYPE = 'SHIFTI' the transformation is | */
/* | lambda = 1/theta + sigma | */
/* | NOTES: | */
/* | *The Ritz vectors are not affected by the transformation. | */
/* %-----------------------------------------------------------% */
if (s_cmp(type__, "SHIFTI", (ftnlen)6, (ftnlen)6) == 0) {
i__1 = nconv;
for (k = 1; k <= i__1; ++k) {
i__2 = k;
z_div(&z__2, &c_b1, &workl[iheig + k - 1]);
z__1.r = z__2.r + sigma->r, z__1.i = z__2.i + sigma->i;
d__[i__2].r = z__1.r, d__[i__2].i = z__1.i;
/* L60: */
}
}
if (s_cmp(type__, "REGULR", (ftnlen)6, (ftnlen)6) != 0 && msglvl > 1) {
zvout_(&debug_1.logfil, &nconv, &d__[1], &debug_1.ndigit, "_neupd: U"
"ntransformed Ritz values.", (ftnlen)34);
zvout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Ritz estimates of the untransformed Ritz values.", (
ftnlen)56);
} else if (msglvl > 1) {
zvout_(&debug_1.logfil, &nconv, &d__[1], &debug_1.ndigit, "_neupd: C"
"onverged Ritz values.", (ftnlen)30);
zvout_(&debug_1.logfil, &nconv, &workl[ihbds], &debug_1.ndigit, "_ne"
"upd: Associated Ritz estimates.", (ftnlen)34);
}
/* %-------------------------------------------------% */
/* | Eigenvector Purification step. Formally perform | */
/* | one of inverse subspace iteration. Only used | */
/* | for MODE = 3. See reference 3. | */
/* %-------------------------------------------------% */
if (*rvec && *(unsigned char *)howmny == 'A' && s_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. | */
/* %------------------------------------------------% */
i__1 = nconv;
for (j = 1; j <= i__1; ++j) {
i__2 = iheig + j - 1;
if (workl[i__2].r != 0. || workl[i__2].i != 0.) {
i__2 = j;
z_div(&z__1, &workl[invsub + (j - 1) * ldq + *ncv - 1], &
workl[iheig + j - 1]);
workev[i__2].r = z__1.r, workev[i__2].i = z__1.i;
}
/* L100: */
}
/* %---------------------------------------% */
/* | Perform a rank one update to Z and | */
/* | purify all the Ritz vectors together. | */
/* %---------------------------------------% */
zgeru_(n, &nconv, &c_b1, &resid[1], &c__1, &workev[1], &c__1, &z__[
z_offset], ldz);
}
L9000:
return 0;
/* %---------------% */
/* | End of zneupd| */
/* %---------------% */
} /* zneupd_ */
/* Subroutine */ int snapps_(integer *n, integer *kev, integer *np, real *
shiftr, real *shifti, real *v, integer *ldv, real *h__, integer *ldh,
real *resid, real *q, integer *ldq, real *workl, real *workd)
{
/* Initialized data */
static 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;
real r__1, r__2;
/* Local variables */
static real c__, f, g;
static integer i__, j;
static real r__, s, t, u[3], t0, t1, h11, h12, h21, h22, h32;
static integer jj, ir, nr;
static real tau, ulp, tst1;
static integer iend;
static real unfl, ovfl;
static logical cconj;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
slarf_(char *, integer *, integer *, real *, integer *, real *,
real *, integer *, real *, ftnlen), sgemv_(char *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *, ftnlen), scopy_(integer *, real *, integer *,
real *, integer *), saxpy_(integer *, real *, real *, integer *,
real *, integer *), ivout_(integer *, integer *, integer *,
integer *, char *, ftnlen), smout_(integer *, integer *, integer *
, real *, integer *, integer *, char *, ftnlen), svout_(integer *,
integer *, real *, integer *, char *, ftnlen);
extern doublereal slapy2_(real *, real *);
extern /* Subroutine */ int slabad_(real *, real *);
extern doublereal slamch_(char *, ftnlen);
static real sigmai;
extern /* Subroutine */ int second_(real *);
static real sigmar;
static integer istart, kplusp, msglvl;
static real smlnum;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen), slarfg_(integer *, real *,
real *, integer *, real *), slaset_(char *, integer *, integer *,
real *, real *, real *, integer *, ftnlen), slartg_(real *, real *
, real *, real *, real *);
extern doublereal slanhs_(char *, integer *, real *, integer *, real *,
ftnlen);
/* %----------------------------------------------------% */
/* | 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 & 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 slahqr | */
/* %-----------------------------------------------% */
unfl = slamch_("safe minimum", (ftnlen)12);
ovfl = 1.f / unfl;
slabad_(&unfl, &ovfl);
ulp = slamch_("precision", (ftnlen)9);
smlnum = unfl * (*n / ulp);
first = FALSE_;
}
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
second_(&t0);
msglvl = debug_1.mnapps;
kplusp = *kev + *np;
/* %--------------------------------------------% */
/* | Initialize Q to the identity to accumulate | */
/* | the rotations and reflections | */
/* %--------------------------------------------% */
slaset_("All", &kplusp, &kplusp, &c_b5, &c_b6, &q[q_offset], ldq, (ftnlen)
3);
/* %----------------------------------------------% */
/* | 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) {
ivout_(&debug_1.logfil, &c__1, &jj, &debug_1.ndigit, "_napps: sh"
"ift number.", (ftnlen)21);
svout_(&debug_1.logfil, &c__1, &sigmar, &debug_1.ndigit, "_napps"
": The real part of the shift ", (ftnlen)35);
svout_(&debug_1.logfil, &c__1, &sigmai, &debug_1.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 && dabs(sigmai) > 0.f) {
/* %------------------------------------% */
/* | Start of a complex conjugate pair. | */
/* %------------------------------------% */
cconj = TRUE_;
} else if (jj == *np && dabs(sigmai) > 0.f) {
/* %----------------------------------------------% */
/* | 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 slahqr | */
/* %----------------------------------------% */
tst1 = (r__1 = h__[i__ + i__ * h_dim1], dabs(r__1)) + (r__2 = h__[
i__ + 1 + (i__ + 1) * h_dim1], dabs(r__2));
if (tst1 == 0.f) {
i__3 = kplusp - jj + 1;
tst1 = slanhs_("1", &i__3, &h__[h_offset], ldh, &workl[1], (
ftnlen)1);
}
/* Computing MAX */
r__2 = ulp * tst1;
if ((r__1 = h__[i__ + 1 + i__ * h_dim1], dabs(r__1)) <= dmax(r__2,
smlnum)) {
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, &i__, &debug_1.ndigit,
"_napps: matrix splitting at row/column no.", (
ftnlen)42);
ivout_(&debug_1.logfil, &c__1, &jj, &debug_1.ndigit,
"_napps: matrix splitting with shift number.", (
ftnlen)43);
svout_(&debug_1.logfil, &c__1, &h__[i__ + 1 + i__ *
h_dim1], &debug_1.ndigit, "_napps: off diagonal "
"element.", (ftnlen)29);
}
iend = i__;
h__[i__ + 1 + i__ * h_dim1] = 0.f;
goto L40;
}
/* L30: */
}
iend = kplusp;
L40:
if (msglvl > 2) {
ivout_(&debug_1.logfil, &c__1, &istart, &debug_1.ndigit, "_napps"
": Start of current block ", (ftnlen)31);
ivout_(&debug_1.logfil, &c__1, &iend, &debug_1.ndigit, "_napps: "
"End of current block ", (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 && dabs(sigmai) > 0.f) {
goto L100;
}
h11 = h__[istart + istart * h_dim1];
h21 = h__[istart + 1 + istart * h_dim1];
if (dabs(sigmai) <= 0.f) {
/* %---------------------------------------------% */
/* | 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 | */
/* %-----------------------------------------------------% */
slartg_(&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.f) {
r__ = -r__;
c__ = -c__;
s = -s;
}
h__[i__ + (i__ - 1) * h_dim1] = r__;
h__[i__ + 1 + (i__ - 1) * h_dim1] = 0.f;
}
/* %---------------------------------------------% */
/* | 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 = i__ + 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 = slapy2_(&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' ). | */
/* %-----------------------------------------------------% */
slarfg_(&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.f;
if (i__ < iend - 1) {
h__[i__ + 2 + (i__ - 1) * h_dim1] = 0.f;
}
}
u[0] = 1.f;
/* %--------------------------------------% */
/* | Apply the reflector to the left of H | */
/* %--------------------------------------% */
i__3 = kplusp - i__ + 1;
slarf_("Left", &nr, &i__3, u, &c__1, &tau, &h__[i__ + i__ *
h_dim1], ldh, &workl[1], (ftnlen)4);
/* %---------------------------------------% */
/* | Apply the reflector to the right of H | */
/* %---------------------------------------% */
/* Computing MIN */
i__3 = i__ + 3;
ir = min(i__3,iend);
slarf_("Right", &ir, &nr, u, &c__1, &tau, &h__[i__ * h_dim1 +
1], ldh, &workl[1], (ftnlen)5);
/* %-----------------------------------------------------% */
/* | Accumulate the reflector in the matrix Q; Q <- Q*G | */
/* %-----------------------------------------------------% */
slarf_("Right", &kplusp, &nr, u, &c__1, &tau, &q[i__ * q_dim1
+ 1], ldq, &workl[1], (ftnlen)5);
/* %----------------------------% */
/* | 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.f) {
i__2 = kplusp - j + 1;
sscal_(&i__2, &c_b43, &h__[j + 1 + j * h_dim1], ldh);
/* Computing MIN */
i__3 = j + 2;
i__2 = min(i__3,kplusp);
sscal_(&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);
sscal_(&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 slahqr | */
/* %--------------------------------------------% */
tst1 = (r__1 = h__[i__ + i__ * h_dim1], dabs(r__1)) + (r__2 = h__[i__
+ 1 + (i__ + 1) * h_dim1], dabs(r__2));
if (tst1 == 0.f) {
tst1 = slanhs_("1", kev, &h__[h_offset], ldh, &workl[1], (ftnlen)
1);
}
/* Computing MAX */
r__1 = ulp * tst1;
if (h__[i__ + 1 + i__ * h_dim1] <= dmax(r__1,smlnum)) {
h__[i__ + 1 + i__ * h_dim1] = 0.f;
}
/* 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.f) {
sgemv_("N", n, &kplusp, &c_b6, &v[v_offset], ldv, &q[(*kev + 1) *
q_dim1 + 1], &c__1, &c_b5, &workd[*n + 1], &c__1, (ftnlen)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;
sgemv_("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, (ftnlen)1);
scopy_(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). | */
/* %-------------------------------------------------% */
slacpy_("A", n, kev, &v[(kplusp - *kev + 1) * v_dim1 + 1], ldv, &v[
v_offset], ldv, (ftnlen)1);
/* %--------------------------------------------------------------% */
/* | Copy the (kev+1)-st column of (V*Q) in the appropriate place | */
/* %--------------------------------------------------------------% */
if (h__[*kev + 1 + *kev * h_dim1] > 0.f) {
scopy_(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} | */
/* %-------------------------------------% */
sscal_(n, &q[kplusp + *kev * q_dim1], &resid[1], &c__1);
if (h__[*kev + 1 + *kev * h_dim1] > 0.f) {
saxpy_(n, &h__[*kev + 1 + *kev * h_dim1], &v[(*kev + 1) * v_dim1 + 1],
&c__1, &resid[1], &c__1);
}
if (msglvl > 1) {
svout_(&debug_1.logfil, &c__1, &q[kplusp + *kev * q_dim1], &
debug_1.ndigit, "_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}", (
ftnlen)40);
svout_(&debug_1.logfil, &c__1, &h__[*kev + 1 + *kev * h_dim1], &
debug_1.ndigit, "_napps: betak = e_{kev+1}^T*H*e_{kev}", (
ftnlen)37);
ivout_(&debug_1.logfil, &c__1, kev, &debug_1.ndigit, "_napps: Order "
"of the final Hessenberg matrix ", (ftnlen)45);
if (msglvl > 2) {
smout_(&debug_1.logfil, kev, kev, &h__[h_offset], ldh, &
debug_1.ndigit, "_napps: updated Hessenberg matrix H for"
" next iteration", (ftnlen)54);
}
}
L9000:
second_(&t1);
timing_1.tnapps += t1 - t0;
return 0;
/* %---------------% */
/* | End of snapps | */
/* %---------------% */
} /* snapps_ */
/* Subroutine */ int dsgets_(integer *ishift, char *which, integer *kev,
integer *np, doublereal *ritz, doublereal *bounds, doublereal *shifts,
ftnlen which_len)
{
/* System generated locals */
integer i__1;
/* Local variables */
static real t0, t1;
static integer kevd2;
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *), dcopy_(integer *, doublereal *, integer
*, doublereal *, integer *), dvout_(integer *, integer *,
doublereal *, integer *, char *, ftnlen), ivout_(integer *,
integer *, integer *, integer *, char *, ftnlen), arscnd_(real *);
static integer msglvl;
extern /* Subroutine */ int dsortr_(char *, logical *, integer *,
doublereal *, doublereal *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 | */
/* %----------------------% */
/* %---------------------% */
/* | Intrinsic Functions | */
/* %---------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
/* Parameter adjustments */
--shifts;
--bounds;
--ritz;
/* Function Body */
arscnd_(&t0);
msglvl = debug_1.msgets;
if (s_cmp(which, "BE", (ftnlen)2, (ftnlen)2) == 0) {
/* %-----------------------------------------------------% */
/* | Both ends of the spectrum are requested. | */
/* | Sort the eigenvalues into algebraically increasing | */
/* | order first then swap high end of the spectrum next | */
/* | to low end in appropriate locations. | */
/* | NOTE: when np < floor(kev/2) be careful not to swap | */
/* | overlapping locations. | */
/* %-----------------------------------------------------% */
i__1 = *kev + *np;
dsortr_("LA", &c_true, &i__1, &ritz[1], &bounds[1], (ftnlen)2);
kevd2 = *kev / 2;
if (*kev > 1) {
i__1 = min(kevd2,*np);
dswap_(&i__1, &ritz[1], &c__1, &ritz[max(kevd2,*np) + 1], &c__1);
i__1 = min(kevd2,*np);
dswap_(&i__1, &bounds[1], &c__1, &bounds[max(kevd2,*np) + 1], &
c__1);
}
} else {
/* %----------------------------------------------------% */
/* | LM, SM, LA, SA case. | */
/* | Sort the eigenvalues of H into the desired order | */
/* | and apply the resulting order to BOUNDS. | */
/* | The eigenvalues are sorted so that the wanted part | */
/* | are always in the last KEV locations. | */
/* %----------------------------------------------------% */
i__1 = *kev + *np;
dsortr_(which, &c_true, &i__1, &ritz[1], &bounds[1], (ftnlen)2);
}
if (*ishift == 1 && *np > 0) {
/* %-------------------------------------------------------% */
/* | Sort the unwanted Ritz values used as shifts so that | */
/* | the ones with largest Ritz estimates are first. | */
/* | This will tend to minimize the effects of the | */
/* | forward instability of the iteration when the shifts | */
/* | are applied in subroutine dsapps. | */
/* %-------------------------------------------------------% */
dsortr_("SM", &c_true, np, &bounds[1], &ritz[1], (ftnlen)2);
dcopy_(np, &ritz[1], &c__1, &shifts[1], &c__1);
}
arscnd_(&t1);
timing_1.tsgets += t1 - t0;
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, kev, &debug_1.ndigit, "_sgets: KEV is",
(ftnlen)14);
ivout_(&debug_1.logfil, &c__1, np, &debug_1.ndigit, "_sgets: NP is", (
ftnlen)13);
i__1 = *kev + *np;
dvout_(&debug_1.logfil, &i__1, &ritz[1], &debug_1.ndigit, "_sgets: E"
"igenvalues of current H matrix", (ftnlen)39);
i__1 = *kev + *np;
dvout_(&debug_1.logfil, &i__1, &bounds[1], &debug_1.ndigit, "_sgets:"
" Associated Ritz estimates", (ftnlen)33);
}
return 0;
/* %---------------% */
/* | End of dsgets | */
/* %---------------% */
} /* dsgets_ */
/* Subroutine */ int sngets_(integer *ishift, char *which, integer *kev,
integer *np, real *ritzr, real *ritzi, real *bounds, real *shiftr,
real *shifti, ftnlen which_len)
{
/* System generated locals */
integer i__1;
/* Local variables */
static real t0, t1;
extern /* Subroutine */ int ivout_(integer *, integer *, integer *,
integer *, char *, ftnlen), svout_(integer *, integer *, real *,
integer *, char *, ftnlen), arscnd_(real *);
static integer msglvl;
extern /* Subroutine */ int ssortc_(char *, logical *, integer *, real *,
real *, real *, ftnlen);
/* %----------------------------------------------------% */
/* | 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 | */
/* %----------------------% */
/* %----------------------% */
/* | Intrinsics Functions | */
/* %----------------------% */
/* %-----------------------% */
/* | Executable Statements | */
/* %-----------------------% */
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
/* Parameter adjustments */
--bounds;
--ritzi;
--ritzr;
--shiftr;
--shifti;
/* Function Body */
arscnd_(&t0);
msglvl = debug_1.mngets;
/* %----------------------------------------------------% */
/* | LM, SM, LR, SR, LI, SI case. | */
/* | Sort the eigenvalues of H into the desired order | */
/* | and apply the resulting order to BOUNDS. | */
/* | The eigenvalues are sorted so that the wanted part | */
/* | are always in the last KEV locations. | */
/* | We first do a pre-processing sort in order to keep | */
/* | complex conjugate pairs together | */
/* %----------------------------------------------------% */
if (s_cmp(which, "LM", (ftnlen)2, (ftnlen)2) == 0) {
i__1 = *kev + *np;
ssortc_("LR", &c_true, &i__1, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
} else if (s_cmp(which, "SM", (ftnlen)2, (ftnlen)2) == 0) {
i__1 = *kev + *np;
ssortc_("SR", &c_true, &i__1, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
} else if (s_cmp(which, "LR", (ftnlen)2, (ftnlen)2) == 0) {
i__1 = *kev + *np;
ssortc_("LM", &c_true, &i__1, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
} else if (s_cmp(which, "SR", (ftnlen)2, (ftnlen)2) == 0) {
i__1 = *kev + *np;
ssortc_("SM", &c_true, &i__1, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
} else if (s_cmp(which, "LI", (ftnlen)2, (ftnlen)2) == 0) {
i__1 = *kev + *np;
ssortc_("LM", &c_true, &i__1, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
} else if (s_cmp(which, "SI", (ftnlen)2, (ftnlen)2) == 0) {
i__1 = *kev + *np;
ssortc_("SM", &c_true, &i__1, &ritzr[1], &ritzi[1], &bounds[1], (
ftnlen)2);
}
i__1 = *kev + *np;
ssortc_(which, &c_true, &i__1, &ritzr[1], &ritzi[1], &bounds[1], (ftnlen)
2);
/* %-------------------------------------------------------% */
/* | Increase KEV by one if the ( ritzr(np),ritzi(np) ) | */
/* | = ( ritzr(np+1),-ritzi(np+1) ) and ritz(np) .ne. zero | */
/* | Accordingly decrease NP by one. In other words keep | */
/* | complex conjugate pairs together. | */
/* %-------------------------------------------------------% */
if (ritzr[*np + 1] - ritzr[*np] == 0.f && ritzi[*np + 1] + ritzi[*np] ==
0.f) {
--(*np);
++(*kev);
}
if (*ishift == 1) {
/* %-------------------------------------------------------% */
/* | Sort the unwanted Ritz values used as shifts so that | */
/* | the ones with largest Ritz estimates are first | */
/* | This will tend to minimize the effects of the | */
/* | forward instability of the iteration when they shifts | */
/* | are applied in subroutine snapps. | */
/* | Be careful and use 'SR' since we want to sort BOUNDS! | */
/* %-------------------------------------------------------% */
ssortc_("SR", &c_true, np, &bounds[1], &ritzr[1], &ritzi[1], (ftnlen)
2);
}
arscnd_(&t1);
timing_1.tngets += t1 - t0;
if (msglvl > 0) {
ivout_(&debug_1.logfil, &c__1, kev, &debug_1.ndigit, "_ngets: KEV is",
(ftnlen)14);
ivout_(&debug_1.logfil, &c__1, np, &debug_1.ndigit, "_ngets: NP is", (
ftnlen)13);
i__1 = *kev + *np;
svout_(&debug_1.logfil, &i__1, &ritzr[1], &debug_1.ndigit, "_ngets: "
"Eigenvalues of current H matrix -- real part", (ftnlen)52);
i__1 = *kev + *np;
svout_(&debug_1.logfil, &i__1, &ritzi[1], &debug_1.ndigit, "_ngets: "
"Eigenvalues of current H matrix -- imag part", (ftnlen)52);
i__1 = *kev + *np;
svout_(&debug_1.logfil, &i__1, &bounds[1], &debug_1.ndigit, "_ngets:"
" Ritz estimates of the current KEV+NP Ritz values", (ftnlen)
56);
}
return 0;
/* %---------------% */
/* | End of sngets | */
/* %---------------% */
} /* sngets_ */
