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|
/* arpack/dsaitr.f -- translated by f2c (version 20090411).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Common Block Declarations */
/*Extern struct { */
/* integer logfil, ndigit, mgetv0, msaupd, msaup2, msaitr, mseigt, msapps, */
/* msgets, mseupd, mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, */
/* mneupd, mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd; */
/*} debug_; */
/*#define debug_1 debug_ */
/*Extern struct { */
/* integer nopx, nbx, nrorth, nitref, nrstrt; */
/* real tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv, tnaupd, */
/* tnaup2, tnaitr, tneigh, tngets, tnapps, tnconv, tcaupd, tcaup2, */
/* tcaitr, tceigh, tcgets, tcapps, tcconv, tmvopx, tmvbx, tgetv0, */
/* titref, trvec; */
/*} timing_; */
/*#define timing_1 timing_ */
/* Table of constant values */
static logical c_false = FALSE_;
static integer c__1 = 1;
static doublereal c_b18 = 1.;
static doublereal c_b43 = 0.;
static doublereal c_b51 = -1.;
/* ----------------------------------------------------------------------- */
/* \BeginDoc */
/* \Name: dsaitr */
/* \Description: */
/* Reverse communication interface for applying NP additional steps to */
/* a K step symmetric Arnoldi factorization. */
/* Input: OP*V_{k} - V_{k}*H = r_{k}*e_{k}^T */
/* with (V_{k}^T)*B*V_{k} = I, (V_{k}^T)*B*r_{k} = 0. */
/* Output: OP*V_{k+p} - V_{k+p}*H = r_{k+p}*e_{k+p}^T */
/* with (V_{k+p}^T)*B*V_{k+p} = I, (V_{k+p}^T)*B*r_{k+p} = 0. */
/* where OP and B are as in dsaupd. The B-norm of r_{k+p} is also */
/* computed and returned. */
/* \Usage: */
/* call dsaitr */
/* ( IDO, BMAT, N, K, NP, MODE, RESID, RNORM, V, LDV, H, LDH, */
/* IPNTR, WORKD, INFO ) */
/* \Arguments */
/* IDO Integer. (INPUT/OUTPUT) */
/* Reverse communication flag. */
/* ------------------------------------------------------------- */
/* IDO = 0: first call to the reverse communication interface */
/* IDO = -1: compute Y = OP * X where */
/* IPNTR(1) is the pointer into WORK for X, */
/* IPNTR(2) is the pointer into WORK for Y. */
/* This is for the restart phase to force the new */
/* starting vector into the range of OP. */
/* IDO = 1: compute Y = OP * X where */
/* IPNTR(1) is the pointer into WORK for X, */
/* IPNTR(2) is the pointer into WORK for Y, */
/* IPNTR(3) is the pointer into WORK for B * X. */
/* IDO = 2: compute Y = B * X where */
/* IPNTR(1) is the pointer into WORK for X, */
/* IPNTR(2) is the pointer into WORK for Y. */
/* IDO = 99: done */
/* ------------------------------------------------------------- */
/* When the routine is used in the "shift-and-invert" mode, the */
/* vector B * Q is already available and does not need to be */
/* recomputed in forming OP * Q. */
/* BMAT Character*1. (INPUT) */
/* BMAT specifies the type of matrix B that defines the */
/* semi-inner product for the operator OP. See dsaupd. */
/* B = 'I' -> standard eigenvalue problem A*x = lambda*x */
/* B = 'G' -> generalized eigenvalue problem A*x = lambda*M*x */
/* N Integer. (INPUT) */
/* Dimension of the eigenproblem. */
/* K Integer. (INPUT) */
/* Current order of H and the number of columns of V. */
/* NP Integer. (INPUT) */
/* Number of additional Arnoldi steps to take. */
/* MODE Integer. (INPUT) */
/* Signifies which form for "OP". If MODE=2 then */
/* a reduction in the number of B matrix vector multiplies */
/* is possible since the B-norm of OP*x is equivalent to */
/* the inv(B)-norm of A*x. */
/* RESID Double precision array of length N. (INPUT/OUTPUT) */
/* On INPUT: RESID contains the residual vector r_{k}. */
/* On OUTPUT: RESID contains the residual vector r_{k+p}. */
/* RNORM Double precision scalar. (INPUT/OUTPUT) */
/* On INPUT the B-norm of r_{k}. */
/* On OUTPUT the B-norm of the updated residual r_{k+p}. */
/* V Double precision N by K+NP array. (INPUT/OUTPUT) */
/* On INPUT: V contains the Arnoldi vectors in the first K */
/* columns. */
/* On OUTPUT: V contains the new NP Arnoldi vectors in the next */
/* NP columns. The first K columns are unchanged. */
/* LDV Integer. (INPUT) */
/* Leading dimension of V exactly as declared in the calling */
/* program. */
/* H Double precision (K+NP) by 2 array. (INPUT/OUTPUT) */
/* H is used to store the generated symmetric tridiagonal matrix */
/* with the subdiagonal in the first column starting at H(2,1) */
/* and the main diagonal in the second column. */
/* LDH Integer. (INPUT) */
/* Leading dimension of H exactly as declared in the calling */
/* program. */
/* IPNTR Integer array of length 3. (OUTPUT) */
/* Pointer to mark the starting locations in the WORK for */
/* vectors used by the Arnoldi iteration. */
/* ------------------------------------------------------------- */
/* IPNTR(1): pointer to the current operand vector X. */
/* IPNTR(2): pointer to the current result vector Y. */
/* IPNTR(3): pointer to the vector B * X when used in the */
/* shift-and-invert mode. X is the current operand. */
/* ------------------------------------------------------------- */
/* WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION) */
/* Distributed array to be used in the basic Arnoldi iteration */
/* for reverse communication. The calling program should not */
/* use WORKD as temporary workspace during the iteration !!!!!! */
/* On INPUT, WORKD(1:N) = B*RESID where RESID is associated */
/* with the K step Arnoldi factorization. Used to save some */
/* computation at the first step. */
/* On OUTPUT, WORKD(1:N) = B*RESID where RESID is associated */
/* with the K+NP step Arnoldi factorization. */
/* INFO Integer. (OUTPUT) */
/* = 0: Normal exit. */
/* > 0: Size of an invariant subspace of OP is found that is */
/* less than K + NP. */
/* \EndDoc */
/* ----------------------------------------------------------------------- */
/* \BeginLib */
/* \Local variables: */
/* xxxxxx real */
/* \Routines called: */
/* dgetv0 ARPACK routine to generate the initial vector. */
/* ivout ARPACK utility routine that prints integers. */
/* dmout ARPACK utility routine that prints matrices. */
/* dlamch LAPACK routine that determines machine constants. */
/* dlascl LAPACK routine for careful scaling of a matrix. */
/* dgemv Level 2 BLAS routine for matrix vector multiplication. */
/* daxpy Level 1 BLAS that computes a vector triad. */
/* dscal Level 1 BLAS that scales a vector. */
/* dcopy Level 1 BLAS that copies one vector to another . */
/* ddot Level 1 BLAS that computes the scalar product of two vectors. */
/* dnrm2 Level 1 BLAS that computes the norm of a vector. */
/* \Author */
/* Danny Sorensen Phuong Vu */
/* Richard Lehoucq CRPC / Rice University */
/* Dept. of Computational & Houston, Texas */
/* Applied Mathematics */
/* Rice University */
/* Houston, Texas */
/* \Revision history: */
/* xx/xx/93: Version ' 2.4' */
/* \SCCS Information: @(#) */
/* FILE: saitr.F SID: 2.6 DATE OF SID: 8/28/96 RELEASE: 2 */
/* \Remarks */
/* The algorithm implemented is: */
/* restart = .false. */
/* Given V_{k} = [v_{1}, ..., v_{k}], r_{k}; */
/* r_{k} contains the initial residual vector even for k = 0; */
/* Also assume that rnorm = || B*r_{k} || and B*r_{k} are already */
/* computed by the calling program. */
/* betaj = rnorm ; p_{k+1} = B*r_{k} ; */
/* For j = k+1, ..., k+np Do */
/* 1) if ( betaj < tol ) stop or restart depending on j. */
/* if ( restart ) generate a new starting vector. */
/* 2) v_{j} = r(j-1)/betaj; V_{j} = [V_{j-1}, v_{j}]; */
/* p_{j} = p_{j}/betaj */
/* 3) r_{j} = OP*v_{j} where OP is defined as in dsaupd */
/* For shift-invert mode p_{j} = B*v_{j} is already available. */
/* wnorm = || OP*v_{j} || */
/* 4) Compute the j-th step residual vector. */
/* w_{j} = V_{j}^T * B * OP * v_{j} */
/* r_{j} = OP*v_{j} - V_{j} * w_{j} */
/* alphaj <- j-th component of w_{j} */
/* rnorm = || r_{j} || */
/* betaj+1 = rnorm */
/* If (rnorm > 0.717*wnorm) accept step and go back to 1) */
/* 5) Re-orthogonalization step: */
/* s = V_{j}'*B*r_{j} */
/* r_{j} = r_{j} - V_{j}*s; rnorm1 = || r_{j} || */
/* alphaj = alphaj + s_{j}; */
/* 6) Iterative refinement step: */
/* If (rnorm1 > 0.717*rnorm) then */
/* rnorm = rnorm1 */
/* accept step and go back to 1) */
/* Else */
/* rnorm = rnorm1 */
/* If this is the first time in step 6), go to 5) */
/* Else r_{j} lies in the span of V_{j} numerically. */
/* Set r_{j} = 0 and rnorm = 0; go to 1) */
/* EndIf */
/* End Do */
/* \EndLib */
/* ----------------------------------------------------------------------- */
/*< >*/
/* Subroutine */ int dsaitr_(integer *ido, char *bmat, integer *n, integer *k,
integer *np, integer *mode, doublereal *resid, doublereal *rnorm,
doublereal *v, integer *ldv, doublereal *h__, integer *ldh, integer *
ipntr, doublereal *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;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
static integer j;
/* static real t0, t1, t2, t3, t4, t5; */
integer jj;
static integer ipj, irj, ivj;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static integer ierr, iter, itry;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
doublereal temp1;
static logical orth1, orth2, step3, step4;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dgemv_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, ftnlen);
integer infol;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
/* doublereal xtemp[2]; */
static doublereal wnorm;
extern /* Subroutine */ int dgetv0_(integer *, char *, integer *, logical
*, integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, ftnlen);
static doublereal rnorm1;
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *, ftnlen), second_(real *);
static doublereal safmin;
static logical rstart;
/* static integer msglvl; */
/* %----------------------------------------------------% */
/* | Include files for debugging and timing information | */
/* %----------------------------------------------------% */
/*< include 'debug.h' >*/
/*< include 'stat.h' >*/
/* \SCCS Information: @(#) */
/* FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 */
/* %---------------------------------% */
/* | See debug.doc for documentation | */
/* %---------------------------------% */
/*< >*/
/*< character bmat*1 >*/
/* %------------------% */
/* | Scalar Arguments | */
/* %------------------% */
/* %--------------------------------% */
/* | See stat.doc for documentation | */
/* %--------------------------------% */
/* \SCCS Information: @(#) */
/* FILE: stat.h SID: 2.2 DATE OF SID: 11/16/95 RELEASE: 2 */
/*< save t0, t1, t2, t3, t4, t5 >*/
/*< integer nopx, nbx, nrorth, nitref, nrstrt >*/
/*< >*/
/*< >*/
/*< integer ido, info, k, ldh, ldv, n, mode, np >*/
/*< >*/
/* %-----------------% */
/* | Array Arguments | */
/* %-----------------% */
/*< integer ipntr(3) >*/
/*< >*/
/* %------------% */
/* | Parameters | */
/* %------------% */
/*< >*/
/*< parameter (one = 1.0D+0, zero = 0.0D+0) >*/
/* %---------------% */
/* | Local Scalars | */
/* %---------------% */
/*< logical first, orth1, orth2, rstart, step3, step4 >*/
/*< >*/
/*< >*/
/*< >*/
/* %-----------------------% */
/* | Local Array Arguments | */
/* %-----------------------% */
/*< >*/
/* %----------------------% */
/* | External Subroutines | */
/* %----------------------% */
/*< >*/
/* %--------------------% */
/* | External Functions | */
/* %--------------------% */
/*< >*/
/*< external ddot, dnrm2, dlamch >*/
/* %-----------------% */
/* | Data statements | */
/* %-----------------% */
/*< data first / .true. / >*/
/* 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) then >*/
if (first) {
/*< first = .false. >*/
first = FALSE_;
/* %--------------------------------% */
/* | safmin = safe minimum is such | */
/* | that 1/sfmin does not overflow | */
/* %--------------------------------% */
/*< safmin = dlamch('safmin') >*/
safmin = dlamch_("safmin", (ftnlen)6);
/*< end if >*/
}
/*< if (ido .eq. 0) then >*/
if (*ido == 0) {
/* %-------------------------------% */
/* | Initialize timing statistics | */
/* | & message level for debugging | */
/* %-------------------------------% */
/*< call second (t0) >*/
/* second_(&t0); */
/*< msglvl = msaitr >*/
/* msglvl = debug_1.msaitr; */
/* %------------------------------% */
/* | Initial call to this routine | */
/* %------------------------------% */
/*< info = 0 >*/
*info = 0;
/*< step3 = .false. >*/
step3 = FALSE_;
/*< step4 = .false. >*/
step4 = FALSE_;
/*< rstart = .false. >*/
rstart = FALSE_;
/*< orth1 = .false. >*/
orth1 = FALSE_;
/*< orth2 = .false. >*/
orth2 = FALSE_;
/* %--------------------------------% */
/* | Pointer to the current step of | */
/* | the factorization to build | */
/* %--------------------------------% */
/*< j = k + 1 >*/
j = *k + 1;
/* %------------------------------------------% */
/* | Pointers used for reverse communication | */
/* | when using WORKD. | */
/* %------------------------------------------% */
/*< ipj = 1 >*/
ipj = 1;
/*< irj = ipj + n >*/
irj = ipj + *n;
/*< ivj = irj + n >*/
ivj = irj + *n;
/*< end if >*/
}
/* %-------------------------------------------------% */
/* | When in reverse communication mode one of: | */
/* | STEP3, STEP4, ORTH1, ORTH2, RSTART | */
/* | will be .true. | */
/* | STEP3: return from computing OP*v_{j}. | */
/* | STEP4: return from computing B-norm of OP*v_{j} | */
/* | ORTH1: return from computing B-norm of r_{j+1} | */
/* | ORTH2: return from computing B-norm of | */
/* | correction to the residual vector. | */
/* | RSTART: return from OP computations needed by | */
/* | dgetv0. | */
/* %-------------------------------------------------% */
/*< if (step3) go to 50 >*/
if (step3) {
goto L50;
}
/*< if (step4) go to 60 >*/
if (step4) {
goto L60;
}
/*< if (orth1) go to 70 >*/
if (orth1) {
goto L70;
}
/*< if (orth2) go to 90 >*/
if (orth2) {
goto L90;
}
/*< if (rstart) go to 30 >*/
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) | */
/* %--------------------------------------------------------------% */
/*< 1000 continue >*/
L1000:
/* if (msglvl .gt. 2) then */
/* call ivout (logfil, 1, j, ndigit, */
/* & '_saitr: generating Arnoldi vector no.') */
/* call dvout (logfil, 1, rnorm, ndigit, */
/* & '_saitr: B-norm of the current residual =') */
/* end if */
/* %---------------------------------------------------------% */
/* | Check for exact zero. Equivalent to determining whether | */
/* | a j-step Arnoldi factorization is present. | */
/* %---------------------------------------------------------% */
/*< if (rnorm .gt. zero) go to 40 >*/
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 .gt. 0) then */
/* call ivout (logfil, 1, j, ndigit, */
/* & '_saitr: ****** restart at step ******') */
/* end if */
/* %---------------------------------------------% */
/* | ITRY is the loop variable that controls the | */
/* | maximum amount of times that a restart is | */
/* | attempted. NRSTRT is used by stat.h | */
/* %---------------------------------------------% */
/*< nrstrt = nrstrt + 1 >*/
/* ++timing_1.nrstrt; */
/*< itry = 1 >*/
itry = 1;
/*< 20 continue >*/
L20:
/*< rstart = .true. >*/
rstart = TRUE_;
/*< ido = 0 >*/
*ido = 0;
/*< 30 continue >*/
L30:
/* %--------------------------------------% */
/* | If in reverse communication mode and | */
/* | RSTART = .true. flow returns here. | */
/* %--------------------------------------% */
/*< >*/
dgetv0_(ido, bmat, &itry, &c_false, n, &j, &v[v_offset], ldv, &resid[1],
rnorm, &ipntr[1], &workd[1], &ierr, (ftnlen)1);
/*< if (ido .ne. 99) go to 9000 >*/
if (*ido != 99) {
goto L9000;
}
/*< if (ierr .lt. 0) then >*/
if (ierr < 0) {
/*< itry = itry + 1 >*/
++itry;
/*< if (itry .le. 3) go to 20 >*/
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 >*/
*info = j - 1;
/*< call second (t1) >*/
/* second_(&t1); */
/*< tsaitr = tsaitr + (t1 - t0) >*/
/* timing_1.tsaitr += t1 - t0; */
/*< ido = 99 >*/
*ido = 99;
/*< go to 9000 >*/
goto L9000;
/*< end if >*/
}
/*< 40 continue >*/
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. | */
/* %---------------------------------------------------------% */
/*< call dcopy (n, resid, 1, v(1,j), 1) >*/
dcopy_(n, &resid[1], &c__1, &v[j * v_dim1 + 1], &c__1);
/*< if (rnorm .ge. safmin) then >*/
if (*rnorm >= safmin) {
/*< temp1 = one / rnorm >*/
temp1 = 1. / *rnorm;
/*< call dscal (n, temp1, v(1,j), 1) >*/
dscal_(n, &temp1, &v[j * v_dim1 + 1], &c__1);
/*< call dscal (n, temp1, workd(ipj), 1) >*/
dscal_(n, &temp1, &workd[ipj], &c__1);
/*< else >*/
} else {
/* %-----------------------------------------% */
/* | To scale both v_{j} and p_{j} carefully | */
/* | use LAPACK routine SLASCL | */
/* %-----------------------------------------% */
/*< >*/
dlascl_("General", &i__, &i__, rnorm, &c_b18, n, &c__1, &v[j * v_dim1
+ 1], n, &infol, (ftnlen)7);
/*< >*/
dlascl_("General", &i__, &i__, rnorm, &c_b18, n, &c__1, &workd[ipj],
n, &infol, (ftnlen)7);
/*< end if >*/
}
/* %------------------------------------------------------% */
/* | 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. >*/
step3 = TRUE_;
/*< nopx = nopx + 1 >*/
/* ++timing_1.nopx; */
/*< call second (t2) >*/
/* second_(&t2); */
/*< call dcopy (n, v(1,j), 1, workd(ivj), 1) >*/
dcopy_(n, &v[j * v_dim1 + 1], &c__1, &workd[ivj], &c__1);
/*< ipntr(1) = ivj >*/
ipntr[1] = ivj;
/*< ipntr(2) = irj >*/
ipntr[2] = irj;
/*< ipntr(3) = ipj >*/
ipntr[3] = ipj;
/*< ido = 1 >*/
*ido = 1;
/* %-----------------------------------% */
/* | Exit in order to compute OP*v_{j} | */
/* %-----------------------------------% */
/*< go to 9000 >*/
goto L9000;
/*< 50 continue >*/
L50:
/* %-----------------------------------% */
/* | Back from reverse communication; | */
/* | WORKD(IRJ:IRJ+N-1) := OP*v_{j}. | */
/* %-----------------------------------% */
/*< call second (t3) >*/
/* second_(&t3); */
/*< tmvopx = tmvopx + (t3 - t2) >*/
/* timing_1.tmvopx += t3 - t2; */
/*< step3 = .false. >*/
step3 = FALSE_;
/* %------------------------------------------% */
/* | Put another copy of OP*v_{j} into RESID. | */
/* %------------------------------------------% */
/*< call dcopy (n, workd(irj), 1, resid, 1) >*/
dcopy_(n, &workd[irj], &c__1, &resid[1], &c__1);
/* %-------------------------------------------% */
/* | STEP 4: Finish extending the symmetric | */
/* | Arnoldi to length j. If MODE = 2 | */
/* | then B*OP = B*inv(B)*A = A and | */
/* | we don't need to compute B*OP. | */
/* | NOTE: If MODE = 2 WORKD(IVJ:IVJ+N-1) is | */
/* | assumed to have A*v_{j}. | */
/* %-------------------------------------------% */
/*< if (mode .eq. 2) go to 65 >*/
if (*mode == 2) {
goto L65;
}
/*< call second (t2) >*/
/* second_(&t2); */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< nbx = nbx + 1 >*/
/* ++timing_1.nbx; */
/*< step4 = .true. >*/
step4 = TRUE_;
/*< ipntr(1) = irj >*/
ipntr[1] = irj;
/*< ipntr(2) = ipj >*/
ipntr[2] = ipj;
/*< ido = 2 >*/
*ido = 2;
/* %-------------------------------------% */
/* | Exit in order to compute B*OP*v_{j} | */
/* %-------------------------------------% */
/*< go to 9000 >*/
goto L9000;
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< call dcopy(n, resid, 1 , workd(ipj), 1) >*/
dcopy_(n, &resid[1], &c__1, &workd[ipj], &c__1);
/*< end if >*/
}
/*< 60 continue >*/
L60:
/* %-----------------------------------% */
/* | Back from reverse communication; | */
/* | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j}. | */
/* %-----------------------------------% */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< call second (t3) >*/
/* second_(&t3); */
/*< tmvbx = tmvbx + (t3 - t2) >*/
/* timing_1.tmvbx += t3 - t2; */
/*< end if >*/
}
/*< step4 = .false. >*/
step4 = FALSE_;
/* %-------------------------------------% */
/* | The following is needed for STEP 5. | */
/* | Compute the B-norm of OP*v_{j}. | */
/* %-------------------------------------% */
/*< 65 continue >*/
L65:
/*< if (mode .eq. 2) then >*/
if (*mode == 2) {
/* %----------------------------------% */
/* | Note that the B-norm of OP*v_{j} | */
/* | is the inv(B)-norm of A*v_{j}. | */
/* %----------------------------------% */
/*< wnorm = ddot (n, resid, 1, workd(ivj), 1) >*/
wnorm = ddot_(n, &resid[1], &c__1, &workd[ivj], &c__1);
/*< wnorm = sqrt(abs(wnorm)) >*/
wnorm = sqrt((abs(wnorm)));
/*< else if (bmat .eq. 'G') then >*/
} else if (*(unsigned char *)bmat == 'G') {
/*< wnorm = ddot (n, resid, 1, workd(ipj), 1) >*/
wnorm = ddot_(n, &resid[1], &c__1, &workd[ipj], &c__1);
/*< wnorm = sqrt(abs(wnorm)) >*/
wnorm = sqrt((abs(wnorm)));
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< wnorm = dnrm2(n, resid, 1) >*/
wnorm = dnrm2_(n, &resid[1], &c__1);
/*< end if >*/
}
/* %-----------------------------------------% */
/* | 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}. | */
/* %------------------------------------------% */
/*< if (mode .ne. 2 ) then >*/
if (*mode != 2) {
/*< >*/
dgemv_("T", n, &j, &c_b18, &v[v_offset], ldv, &workd[ipj], &c__1, &
c_b43, &workd[irj], &c__1, (ftnlen)1);
/*< else if (mode .eq. 2) then >*/
} else if (*mode == 2) {
/*< >*/
dgemv_("T", n, &j, &c_b18, &v[v_offset], ldv, &workd[ivj], &c__1, &
c_b43, &workd[irj], &c__1, (ftnlen)1);
/*< end if >*/
}
/* %--------------------------------------% */
/* | Orthgonalize r_{j} against V_{j}. | */
/* | RESID contains OP*v_{j}. See STEP 3. | */
/* %--------------------------------------% */
/*< >*/
dgemv_("N", n, &j, &c_b51, &v[v_offset], ldv, &workd[irj], &c__1, &c_b18,
&resid[1], &c__1, (ftnlen)1);
/* %--------------------------------------% */
/* | Extend H to have j rows and columns. | */
/* %--------------------------------------% */
/*< h(j,2) = workd(irj + j - 1) >*/
h__[j + (h_dim1 << 1)] = workd[irj + j - 1];
/*< if (j .eq. 1 .or. rstart) then >*/
if (j == 1 || rstart) {
/*< h(j,1) = zero >*/
h__[j + h_dim1] = 0.;
/*< else >*/
} else {
/*< h(j,1) = rnorm >*/
h__[j + h_dim1] = *rnorm;
/*< end if >*/
}
/*< call second (t4) >*/
/* second_(&t4); */
/*< orth1 = .true. >*/
orth1 = TRUE_;
/*< iter = 0 >*/
iter = 0;
/*< call second (t2) >*/
/* second_(&t2); */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< nbx = nbx + 1 >*/
/* ++timing_1.nbx; */
/*< call dcopy (n, resid, 1, workd(irj), 1) >*/
dcopy_(n, &resid[1], &c__1, &workd[irj], &c__1);
/*< ipntr(1) = irj >*/
ipntr[1] = irj;
/*< ipntr(2) = ipj >*/
ipntr[2] = ipj;
/*< ido = 2 >*/
*ido = 2;
/* %----------------------------------% */
/* | Exit in order to compute B*r_{j} | */
/* %----------------------------------% */
/*< go to 9000 >*/
goto L9000;
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< call dcopy (n, resid, 1, workd(ipj), 1) >*/
dcopy_(n, &resid[1], &c__1, &workd[ipj], &c__1);
/*< end if >*/
}
/*< 70 continue >*/
L70:
/* %---------------------------------------------------% */
/* | Back from reverse communication if ORTH1 = .true. | */
/* | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | */
/* %---------------------------------------------------% */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< call second (t3) >*/
/* second_(&t3); */
/*< tmvbx = tmvbx + (t3 - t2) >*/
/* timing_1.tmvbx += t3 - t2; */
/*< end if >*/
}
/*< orth1 = .false. >*/
orth1 = FALSE_;
/* %------------------------------% */
/* | Compute the B-norm of r_{j}. | */
/* %------------------------------% */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< rnorm = ddot (n, resid, 1, workd(ipj), 1) >*/
*rnorm = ddot_(n, &resid[1], &c__1, &workd[ipj], &c__1);
/*< rnorm = sqrt(abs(rnorm)) >*/
*rnorm = sqrt((abs(*rnorm)));
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< rnorm = dnrm2(n, resid, 1) >*/
*rnorm = dnrm2_(n, &resid[1], &c__1);
/*< end if >*/
}
/* %-----------------------------------------------------------% */
/* | 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} || | */
/* %-----------------------------------------------------------% */
/*< if (rnorm .gt. 0.717*wnorm) go to 100 >*/
if (*rnorm > wnorm * (float).717) {
goto L100;
}
/*< nrorth = nrorth + 1 >*/
/* ++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} | */
/* %---------------------------------------------------% */
/*< 80 continue >*/
L80:
/*< if (msglvl .gt. 2) then >*/
/* if (msglvl > 2) { */
/*< xtemp(1) = wnorm >*/
/* xtemp[0] = wnorm; */
/*< xtemp(2) = rnorm >*/
/* xtemp[1] = *rnorm; */
/* call dvout (logfil, 2, xtemp, ndigit, */
/* & '_saitr: re-orthonalization ; wnorm and rnorm are') */
/*< end if >*/
/* } */
/* %----------------------------------------------------% */
/* | Compute V_{j}^T * B * r_{j}. | */
/* | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | */
/* %----------------------------------------------------% */
/*< >*/
dgemv_("T", n, &j, &c_b18, &v[v_offset], ldv, &workd[ipj], &c__1, &c_b43,
&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, but only | */
/* | H(j,j) is updated. | */
/* %----------------------------------------------% */
/*< >*/
dgemv_("N", n, &j, &c_b51, &v[v_offset], ldv, &workd[irj], &c__1, &c_b18,
&resid[1], &c__1, (ftnlen)1);
/*< if (j .eq. 1 .or. rstart) h(j,1) = zero >*/
if (j == 1 || rstart) {
h__[j + h_dim1] = 0.;
}
/*< h(j,2) = h(j,2) + workd(irj + j - 1) >*/
h__[j + (h_dim1 << 1)] += workd[irj + j - 1];
/*< orth2 = .true. >*/
orth2 = TRUE_;
/*< call second (t2) >*/
/* second_(&t2); */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< nbx = nbx + 1 >*/
/* ++timing_1.nbx; */
/*< call dcopy (n, resid, 1, workd(irj), 1) >*/
dcopy_(n, &resid[1], &c__1, &workd[irj], &c__1);
/*< ipntr(1) = irj >*/
ipntr[1] = irj;
/*< ipntr(2) = ipj >*/
ipntr[2] = ipj;
/*< ido = 2 >*/
*ido = 2;
/* %-----------------------------------% */
/* | Exit in order to compute B*r_{j}. | */
/* | r_{j} is the corrected residual. | */
/* %-----------------------------------% */
/*< go to 9000 >*/
goto L9000;
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< call dcopy (n, resid, 1, workd(ipj), 1) >*/
dcopy_(n, &resid[1], &c__1, &workd[ipj], &c__1);
/*< end if >*/
}
/*< 90 continue >*/
L90:
/* %---------------------------------------------------% */
/* | Back from reverse communication if ORTH2 = .true. | */
/* %---------------------------------------------------% */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< call second (t3) >*/
/* second_(&t3); */
/*< tmvbx = tmvbx + (t3 - t2) >*/
/* timing_1.tmvbx += t3 - t2; */
/*< end if >*/
}
/* %-----------------------------------------------------% */
/* | Compute the B-norm of the corrected residual r_{j}. | */
/* %-----------------------------------------------------% */
/*< if (bmat .eq. 'G') then >*/
if (*(unsigned char *)bmat == 'G') {
/*< rnorm1 = ddot (n, resid, 1, workd(ipj), 1) >*/
rnorm1 = ddot_(n, &resid[1], &c__1, &workd[ipj], &c__1);
/*< rnorm1 = sqrt(abs(rnorm1)) >*/
rnorm1 = sqrt((abs(rnorm1)));
/*< else if (bmat .eq. 'I') then >*/
} else if (*(unsigned char *)bmat == 'I') {
/*< rnorm1 = dnrm2(n, resid, 1) >*/
rnorm1 = dnrm2_(n, &resid[1], &c__1);
/*< end if >*/
}
/* if (msglvl .gt. 0 .and. iter .gt. 0) then */
/* call ivout (logfil, 1, j, ndigit, */
/* & '_saitr: Iterative refinement for Arnoldi residual') */
/* if (msglvl .gt. 2) then */
/* xtemp(1) = rnorm */
/* xtemp(2) = rnorm1 */
/* call dvout (logfil, 2, xtemp, ndigit, */
/* & '_saitr: iterative refinement ; rnorm and rnorm1 are') */
/* end if */
/* end if */
/* %-----------------------------------------% */
/* | Determine if we need to perform another | */
/* | step of re-orthogonalization. | */
/* %-----------------------------------------% */
/*< if (rnorm1 .gt. 0.717*rnorm) then >*/
if (rnorm1 > *rnorm * (float).717) {
/* %--------------------------------% */
/* | No need for further refinement | */
/* %--------------------------------% */
/*< rnorm = rnorm1 >*/
*rnorm = rnorm1;
/*< else >*/
} else {
/* %-------------------------------------------% */
/* | Another step of iterative refinement step | */
/* | is required. NITREF is used by stat.h | */
/* %-------------------------------------------% */
/*< nitref = nitref + 1 >*/
/* ++timing_1.nitref; */
/*< rnorm = rnorm1 >*/
*rnorm = rnorm1;
/*< iter = iter + 1 >*/
++iter;
/*< if (iter .le. 1) go to 80 >*/
if (iter <= 1) {
goto L80;
}
/* %-------------------------------------------------% */
/* | Otherwise RESID is numerically in the span of V | */
/* %-------------------------------------------------% */
/*< do 95 jj = 1, n >*/
i__1 = *n;
for (jj = 1; jj <= i__1; ++jj) {
/*< resid(jj) = zero >*/
resid[jj] = 0.;
/*< 95 continue >*/
/* L95: */
}
/*< rnorm = zero >*/
*rnorm = 0.;
/*< end if >*/
}
/* %----------------------------------------------% */
/* | Branch here directly if iterative refinement | */
/* | wasn't necessary or after at most NITER_REF | */
/* | steps of iterative refinement. | */
/* %----------------------------------------------% */
/*< 100 continue >*/
L100:
/*< rstart = .false. >*/
rstart = FALSE_;
/*< orth2 = .false. >*/
orth2 = FALSE_;
/*< call second (t5) >*/
/* second_(&t5); */
/*< titref = titref + (t5 - t4) >*/
/* timing_1.titref += t5 - t4; */
/* %----------------------------------------------------------% */
/* | Make sure the last off-diagonal element is non negative | */
/* | If not perform a similarity transformation on H(1:j,1:j) | */
/* | and scale v(:,j) by -1. | */
/* %----------------------------------------------------------% */
/*< if (h(j,1) .lt. zero) then >*/
if (h__[j + h_dim1] < 0.) {
/*< h(j,1) = -h(j,1) >*/
h__[j + h_dim1] = -h__[j + h_dim1];
/*< if ( j .lt. k+np) then >*/
if (j < *k + *np) {
/*< call dscal(n, -one, v(1,j+1), 1) >*/
dscal_(n, &c_b51, &v[(j + 1) * v_dim1 + 1], &c__1);
/*< else >*/
} else {
/*< call dscal(n, -one, resid, 1) >*/
dscal_(n, &c_b51, &resid[1], &c__1);
/*< end if >*/
}
/*< end if >*/
}
/* %------------------------------------% */
/* | STEP 6: Update j = j+1; Continue | */
/* %------------------------------------% */
/*< j = j + 1 >*/
++j;
/*< if (j .gt. k+np) then >*/
if (j > *k + *np) {
/*< call second (t1) >*/
/* second_(&t1); */
/*< tsaitr = tsaitr + (t1 - t0) >*/
/* timing_1.tsaitr += t1 - t0; */
/*< ido = 99 >*/
*ido = 99;
/* if (msglvl .gt. 1) then */
/* call dvout (logfil, k+np, h(1,2), ndigit, */
/* & '_saitr: main diagonal of matrix H of step K+NP.') */
/* if (k+np .gt. 1) then */
/* call dvout (logfil, k+np-1, h(2,1), ndigit, */
/* & '_saitr: sub diagonal of matrix H of step K+NP.') */
/* end if */
/* end if */
/*< go to 9000 >*/
goto L9000;
/*< end if >*/
}
/* %--------------------------------------------------------% */
/* | Loop back to extend the factorization by another step. | */
/* %--------------------------------------------------------% */
/*< go to 1000 >*/
goto L1000;
/* %---------------------------------------------------------------% */
/* | | */
/* | E N D O F M A I N I T E R A T I O N L O O P | */
/* | | */
/* %---------------------------------------------------------------% */
/*< 9000 continue >*/
L9000:
/*< return >*/
return 0;
/* %---------------% */
/* | End of dsaitr | */
/* %---------------% */
/*< end >*/
} /* dsaitr_ */
#ifdef __cplusplus
}
#endif
|
