/* ----------------------------------------------------------------------- */
/* 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 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_ */