#define RCSID "$Id: Arpack.c,v 1.29 2006/02/26 00:42:54 geuzaine Exp $"
/*
* Copyright (C) 1997-2006 P. Dular, C. Geuzaine
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
* USA.
*
* Please report all bugs and problems to <getdp@geuz.org>.
*
* Contributor(s):
* Alexandru Mustatea
* Andre Nicolet
*/
#include "GetDP.h"
#include "DofData.h"
#include "CurrentData.h"
#include "Numeric.h"
#include "EigenPar.h"
#if !defined(HAVE_ARPACK) || !defined(HAVE_BLAS_LAPACK)
void EigenSolve (struct DofData * DofData_P, int NumEigenvalues,
double shift_r, double shift_i){
Msg(GERROR, "EigenSolve not available without BLAS, LAPACK and ARPACK");
}
#else
#include "Arpack_F.h"
/* This routine uses Arpack to solve Generalized Complex Non-Hermitian
eigenvalue problems. We don't use the "Generalized" Arpack mode
(bmat=='G') since it requires M to be Hermitian. Instead, we use
the regular mode (bmat='I') and apply the shift "by hand", which
allows us to use arbitrary matrices K and M. */
static void Arpack2GetDP(int N, complex_16 *in, gVector *out){
int i, j;
double re, im;
for(i = 0; i < N; i++){
re = in[i].re;
im = in[i].im;
j = i * gCOMPLEX_INCREMENT;
LinAlg_SetComplexInVector(re, im, out, j, j+1);
}
}
static void Arpack2GetDPSplit(int N, complex_16 *in, gVector *out1, gVector *out2){
int i, j;
double re, im;
for(i = 0; i < N/2; i++){
j = i * gCOMPLEX_INCREMENT;
re = in[i].re;
im = in[i].im;
LinAlg_SetComplexInVector(re, im, out1, j, j+1);
re = in[N/2+i].re;
im = in[N/2+i].im;
LinAlg_SetComplexInVector(re, im, out2, j, j+1);
}
}
static void GetDP2Arpack(gVector *in, complex_16 *out){
int i, N;
double re, im;
LinAlg_GetVectorSize(in, &N);
for(i = 0; i < N; i += gCOMPLEX_INCREMENT){
LinAlg_GetComplexInVector(&re, &im, in, i, i+1);
out[i/gCOMPLEX_INCREMENT].re = re;
out[i/gCOMPLEX_INCREMENT].im = im;
}
}
static void GetDP2ArpackMerge(gVector *in1, gVector *in2, complex_16 *out){
int i, N;
double re, im;
LinAlg_GetVectorSize(in1, &N);
for(i = 0; i < N; i += gCOMPLEX_INCREMENT){
LinAlg_GetComplexInVector(&re, &im, in1, i, i+1);
out[i/gCOMPLEX_INCREMENT].re = re;
out[i/gCOMPLEX_INCREMENT].im = im;
LinAlg_GetComplexInVector(&re, &im, in2, i, i+1);
out[N/gCOMPLEX_INCREMENT + i/gCOMPLEX_INCREMENT].re = re;
out[N/gCOMPLEX_INCREMENT + i/gCOMPLEX_INCREMENT].im = im;
}
}
void EigenSolve (struct DofData * DofData_P, int NumEigenvalues,
double shift_r, double shift_i){
struct EigenPar eigenpar;
struct Solution Solution_S;
gVector v1, v2, w1, w2, x, y;
int n, j, k, l, newsol, quad_evp = 0;
double tmp, d1, d2, abs, arg;
complex_16 f, omega, omega2;
gMatrix *K = &DofData_P->M1; /* matrix associated with terms with no Dt nor DtDt */
gMatrix *L = &DofData_P->M2; /* matrix associated with Dt terms */
gMatrix *M = &DofData_P->M3; /* matrix associated with DtDt terms */
gMatrix D; /* temp matrix for quadratic eigenvalue problem */
/* Arpack parameters: see below for explanation */
int ido, nev, ncv, ldv, iparam[11], ipntr[14], lworkl, info, ldz;
char bmat, *which, howmny;
double tol, *rwork;
unsigned int rvec, *select;
complex_16 *resid, *v, *workd, *workl, *d, *z, sigma, *workev;
GetDP_Begin("EigenSolve");
/* Bail out if we are not in harmonic regime: it's much easier this
way (since, for real, non-symmetric matrices we would get complex
eigenvectors we could not easily store) */
if(Current.NbrHar != 2)
Msg(GERROR, "EigenSolve requires system defined with \"Type Complex\"");
/* Sanity checks */
if(!DofData_P->Flag_Init[1] || !DofData_P->Flag_Init[3])
Msg(GERROR, "No System available for EigenSolve: check 'DtDt' and 'GenerateSeparate'");
/* Check if we have a "quadratic" evp (- w^2 M x + i w L x + K x = 0) */
if(DofData_P->Flag_Init[2])
quad_evp = 1;
/* Get eigenproblem parameters */
EigenPar("eigen.par", &eigenpar);
n = DofData_P->NbrDof / gCOMPLEX_INCREMENT; /* size of the system */
if(quad_evp)
n *= 2;
ido = 0;
/* Reverse communication flag. IDO must be zero on the first
call to znaupd. IDO will be set internally to
indicate the type of operation to be performed. Control is
then given back to the calling routine which has the
responsibility to carry out the requested operation and call
znaupd with the result. The operand is given in
WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)).
-------------------------------------------------------------
IDO = 0: first call to the reverse communication interface
IDO = -1: compute Y = OP * X where
IPNTR(1) is the pointer into WORKD for X,
IPNTR(2) is the pointer into WORKD for Y.
This is for the initialization phase to force the
starting vector into the range of OP.
IDO = 1: compute Y = OP * X where
IPNTR(1) is the pointer into WORKD for X,
IPNTR(2) is the pointer into WORKD for Y.
In mode 3, the vector B * X is already
available in WORKD(ipntr(3)). It does not
need to be recomputed in forming OP * X.
IDO = 2: compute Y = M * X where
IPNTR(1) is the pointer into WORKD for X,
IPNTR(2) is the pointer into WORKD for Y.
IDO = 3: compute and return the shifts in the first
NP locations of WORKL.
IDO = 99: done
-------------------------------------------------------------
After the initialization phase, when the routine is used in
the "shift-and-invert" mode, the vector M * X is already
available and does not need to be recomputed in forming OP*X. */
bmat = 'I';
/* BMAT specifies the type of the matrix B that defines the
semi-inner product for the operator OP.
BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x
BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x */
which = "LM";
/* Which eigenvalues we want:
SM = smallest magnitude ( magnitude = absolute value )
LM = largest magnitude
SR = smallest real part
LR = largest real part
SI = smallest imaginary part
LI = largest imaginary part */
nev = NumEigenvalues;
/* Number of eigenvalues of OP to be computed. 0 < NEV < N-1.
Therefore, you'll be able to compute AT MOST n-2 eigenvalues! */
/* sanity check */
if(nev >= n-1){
Msg(WARNING, "NumEigenvalues too large (%d < %d): setting to %d", nev, n-1, n-2);
nev = n-2;
}
tol = eigenpar.prec; /* 1.e-4; */
/* Stopping criteria: the relative accuracy of the Ritz value
is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I))
where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex.
DEFAULT = dlamch('EPS') (machine precision as computed
by the LAPACK auxiliary subroutine dlamch). */
resid = (complex_16*)Malloc(n * sizeof(complex_16));
/* On INPUT:
If INFO .EQ. 0, a random initial residual vector is used.
If INFO .NE. 0, RESID contains the initial residual vector,
possibly from a previous run.
On OUTPUT:
RESID contains the final residual vector. */
ncv = eigenpar.size; /* Rule of thumb: NumEigenvalues * 2; */
/* Number of columns of the matrix V. NCV must satisfy the two
inequalities 1 <= NCV-NEV and NCV <= N.
This will indicate how many Arnoldi vectors are generated
at each iteration. After the startup phase in which NEV
Arnoldi vectors are generated, the algorithm generates
approximately NCV-NEV Arnoldi vectors at each subsequent update
iteration. Most of the cost in generating each Arnoldi vector is
in the matrix-vector operation OP*x. */
/* sanity checks */
if(ncv <= nev){
Msg(WARNING, "Krylov space size too small (%d <= %d), setting to %d", ncv, nev, nev*2);
ncv = nev * 2;
}
if(ncv > n){
Msg(WARNING, "Krylov space size too large (%d > %d), setting to %d", ncv, n, n);
ncv = n;
}
v = (complex_16*)Malloc(n * ncv * sizeof(complex_16));
/* At the end of calculations, here will be stored the Arnoldi basis
vectors */
ldv = n;
/* Leading dimension of "v". In our case, the number of lines of
"v". */
iparam[0] = 1;
iparam[1] = 0;
iparam[2] = 10000;
iparam[3] = 1;
iparam[4] = 0;
iparam[5] = 0;
iparam[6] = 1;
iparam[7] = 0;
iparam[8] = 0;
iparam[9] = 0;
iparam[10] = 0;
/* IPARAM(1) = ISHIFT: method for selecting the implicit shifts.
The shifts selected at each iteration are used to filter out
the components of the unwanted eigenvector.
-------------------------------------------------------------
ISHIFT = 0: the shifts are to be provided by the user via
reverse communication. The NCV eigenvalues of
the Hessenberg matrix H are returned in the part
of WORKL array corresponding to RITZ.
ISHIFT = 1: exact shifts with respect to the current
Hessenberg matrix H. This is equivalent to
restarting the iteration from the beginning
after updating the starting vector with a linear
combination of Ritz vectors associated with the
"wanted" eigenvalues.
ISHIFT = 2: other choice of internal shift to be defined.
-------------------------------------------------------------
IPARAM(2) = No longer referenced
IPARAM(3) = MXITER
On INPUT: maximum number of Arnoldi update iterations allowed.
On OUTPUT: actual number of Arnoldi update iterations taken.
IPARAM(4) = NB: blocksize to be used in the recurrence.
The code currently works only for NB = 1.
IPARAM(5) = NCONV: number of "converged" Ritz values.
This represents the number of Ritz values that satisfy
the convergence criterion.
IPARAM(6) = IUPD
No longer referenced. Implicit restarting is ALWAYS used.
IPARAM(7) = MODE
On INPUT determines what type of eigenproblem is being solved.
Must be 1,2,3; See under \Description of znaupd for the
four modes available.
IPARAM(8) = NP
When ido = 3 and the user provides shifts through reverse
communication (IPARAM(1)=0), _naupd returns NP, the number
of shifts the user is to provide. 0 < NP < NCV-NEV.
IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO,
OUTPUT: NUMOP = total number of OP*x operations,
NUMOPB = total number of B*x operations if BMAT='G',
NUMREO = total number of steps of re-orthogonalization. */
ipntr[0] = 0;
/* Pointer to mark the starting locations in the WORKD and WORKL
arrays for matrices/vectors used by the Arnoldi iteration.
-------------------------------------------------------------
IPNTR(1): pointer to the current operand vector X in WORKD.
IPNTR(2): pointer to the current result vector Y in WORKD.
IPNTR(3): pointer to the vector B * X in WORKD when used in
the shift-and-invert mode.
IPNTR(4): pointer to the next available location in WORKL
that is untouched by the program.
IPNTR(5): pointer to the NCV by NCV upper Hessenberg
matrix H in WORKL.
IPNTR(6): pointer to the ritz value array RITZ
IPNTR(7): pointer to the (projected) ritz vector array Q
IPNTR(8): pointer to the error BOUNDS array in WORKL.
IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below.
Note: IPNTR(9:13) is only referenced by zneupd. See Remark 2 below.
IPNTR(9): pointer to the NCV RITZ values of the
original system.
IPNTR(10): Not Used
IPNTR(11): pointer to the NCV corresponding error bounds.
IPNTR(12): pointer to the NCV by NCV upper triangular
Schur matrix for H.
IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors
of the upper Hessenberg matrix H. Only referenced by
zneupd if RVEC = .TRUE. See Remark 2 below. */
workd = (complex_16*)Malloc(3 * n * sizeof(complex_16));
/* Distributed array to be used in the basic Arnoldi iteration
for reverse communication. The user should not use WORKD
as temporary workspace during the iteration !!!!!!!!!!
See Data Distribution Note below. */
lworkl = 3*ncv*ncv + 5*ncv;
/* Dimension of the "workl" vector (see below). On must have:
lworkl >= 3*ncv*ncv + 5*ncv */
workl = (complex_16*)Malloc(lworkl * sizeof(complex_16));
/* Private (replicated) array on each PE or array allocated on
the front end. See Data Distribution Note below. */
rwork = (double*)Malloc(ncv * sizeof(double));
/* Used as workspace */
info = 0;
/* If INFO .EQ. 0, a randomly initial residual vector is used.
If INFO .NE. 0, RESID contains the initial residual vector,
possibly from a previous run.
Error flag on output.
= 0: Normal exit.
= 1: Maximum number of iterations taken.
All possible eigenvalues of OP has been found. IPARAM(5)
returns the number of wanted converged Ritz values.
= 2: No longer an informational error. Deprecated starting
with release 2 of ARPACK.
= 3: No shifts could be applied during a cycle of the
Implicitly restarted Arnoldi iteration. One possibility
is to increase the size of NCV relative to NEV.
See remark 4 below.
= -1: N must be positive.
= -2: NEV must be positive.
= -3: NCV-NEV >= 1 and less than or equal to N.
= -4: The maximum number of Arnoldi update iteration
must be greater than zero.
= -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI'
= -6: BMAT must be one of 'I' or 'G'.
= -7: Length of private work array is not sufficient.
= -8: Error return from LAPACK eigenvalue calculation;
= -9: Starting vector is zero.
= -10: IPARAM(7) must be 1,2,3.
= -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible.
= -12: IPARAM(1) must be equal to 0 or 1.
= -9999: Could not build an Arnoldi factorization.
User input error highly likely. Please
check actual array dimensions and layout.
IPARAM(5) returns the size of the current Arnoldi
factorization. */
rvec = 1; /* .true. */
/* If we want Ritz vectors to be computed as well. */
howmny = 'A';
/* What do we want: Ritz or Schur vectors? For Schur, choose: howmny
= 'P' */
select = (unsigned int*)Malloc(ncv * sizeof(unsigned int));
/* Internal workspace */
d = (complex_16*)Malloc(nev * sizeof(complex_16));
/* Vector containing the "nev" eigenvalues computed.
VERY IMPORTANT: on line 69 of zneupd.f they say it should be nev+1;
this is wrong, for see line 283 where it is declared as d(nev) */
z = (complex_16*)Malloc(n * nev * sizeof(complex_16));
/* On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of
Z represents approximate eigenvectors (Ritz vectors) corresponding
to the NCONV=IPARAM(5) Ritz values for eigensystem
A*z = lambda*B*z.
If RVEC = .FALSE. or HOWMNY = 'P', then Z is NOT REFERENCED.
NOTE: If if RVEC = .TRUE. and a Schur basis is not required,
the array Z may be set equal to first NEV+1 columns of the Arnoldi
basis array V computed by ZNAUPD. In this case the Arnoldi basis
will be destroyed and overwritten with the eigenvector basis. */
ldz = n;
/* Leading dimension of "z". In our case, the number of lines of "z". */
sigma.re = 0.;
sigma.im = 0.;
/* The shift. Not used in this case: we deal with the shift "by
hand". */
workev = (complex_16*)Malloc(2 * ncv * sizeof(complex_16));
/* Workspace */
if(bmat != 'I' || iparam[6] != 1)
Msg(GERROR, "General and/or shift-invert mode should not be used");
/* Create temp vectors and matrices and apply shift. Warning: with
PETSc, the shifting can be very slow if the masks are very
different, for example if we are in real arithmetic and have one
real matrix and one complex "simulated-real" matrix */
if(!quad_evp){
LinAlg_CreateVector(&v1, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
LinAlg_CreateVector(&v2, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
/* K = K - shift * M */
LinAlg_AddMatrixProdMatrixDouble(K, M, -shift_r, K) ;
}
else{
/* This is an explanation of our approach to a quadratic
eigenvalue problem i.e. - w^2 M x + i w L x + K x = 0. This
system is equivalent to (y = i w x) and (i w M y + i w L x + K
x = 0), or, in matrix form:
| L M | |x| |-K 0 | |x|
| I 0 | |y| iw = | 0 I | |y| , or
|x| |x|
A |y| iw = B |y|.
To apply Arpack with a shift 's' (but not in shift inverted
mode to avoid the Hermitian constraint!), we build the
following operator: (B- sA)^-1 A. To do this, the following
computation is performed: (x,y) is transformed to
(Solve(D,Lx+sMx+My),Solve(D,-Kx+sMy)) where Solve(D,v) means
the solution of the Dx=v linear system and where
D=-(s^2M+sL+K). Note that if the number of degrees of freedom
is N, the matrix computations are still performed on NxN
matrices but the Arpack vector is of size n=2*N. Only the x
part of the (x,y) eigenvectors are retained as physical
solutions. */
LinAlg_CreateVector(&x, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
LinAlg_CreateVector(&y, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
LinAlg_CreateVector(&v1, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
LinAlg_CreateVector(&w1, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
LinAlg_CreateVector(&w2, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
LinAlg_CreateMatrix(&D, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrDof, DofData_P->NbrPart,
DofData_P->Part, NULL);
/* D = -(shift^2 * M + shift * L + K) */
LinAlg_CopyMatrix(M, &D);
LinAlg_AddMatrixProdMatrixDouble(L, &D, shift_r, &D);
LinAlg_AddMatrixProdMatrixDouble(K, &D, shift_r, &D);
LinAlg_ProdMatrixDouble(&D, -1., &D);
}
/* Keep calling znaupd again and again until ido == 99 */
k = 0;
do {
znaupd_(&ido, &bmat, &n, which, &nev, &tol, resid, &ncv, v, &ldv, iparam,
ipntr, workd, workl, &lworkl, rwork, &info);
if(ido == 1 || ido == -1){
Msg(INFO, "Arpack iteration %d", k+1);
if(!quad_evp){
Arpack2GetDP(n, &workd[ipntr[0]-1], &v1);
LinAlg_ProdMatrixVector(M, &v1, &v2);
if(!k)
LinAlg_Solve(K, &v2, &DofData_P->Solver, &v1);
else
LinAlg_SolveAgain(K, &v2, &DofData_P->Solver, &v1);
GetDP2Arpack(&v1, &workd[ipntr[1]-1]);
}
else{
Arpack2GetDPSplit(n, &workd[ipntr[0]-1], &x, &y);
LinAlg_ProdMatrixVector(M, &y, &w2);
LinAlg_ProdMatrixVector(L, &x, &v1);
LinAlg_AddVectorVector(&v1, &w2, &v1);
LinAlg_ProdMatrixVector(M, &x, &w1);
LinAlg_AddVectorProdVectorDouble(&v1, &w1, shift_r, &v1);
if(!k)
LinAlg_Solve(&D, &v1, &DofData_P->Solver, &w1);
else
LinAlg_SolveAgain(&D, &v1, &DofData_P->Solver, &w1);
LinAlg_ProdMatrixVector(K, &x, &v1);
LinAlg_ProdVectorDouble(&v1, -1., &v1);
LinAlg_AddVectorProdVectorDouble(&v1, &w2, shift_r, &v1);
LinAlg_SolveAgain(&D, &v1, &DofData_P->Solver, &w2);
GetDP2ArpackMerge(&w1, &w2, &workd[ipntr[1]-1]);
}
k++;
}
else if(ido == 99){
/* We're done! */
break;
}
else{
Msg(INFO, "Arpack code = %d (ignored)", info);
}
} while (1);
Msg(BIGINFO, "Arpack required %d iterations", k);
/* Testing for errors */
if(info == 0){
/* OK */
}
else if(info == 1){
Msg(WARNING, "Maxmimum number of iteration reached in EigenSolve");
}
else if(info == 2){
Msg(WARNING, "No shifts could be applied during a cycle of the");
Msg(WARNING, "Implicitly restarted Arnoldi iteration. One possibility");
Msg(WARNING, "is to increase the size of NCV relative to NEV.");
}
else if(info < 0){
Msg(GERROR, "Arpack code = %d", info);
}
else{
Msg(WARNING, "Arpack code = %d (unknown)", info);
}
/* Call to zneupd for post-processing */
zneupd_(&rvec, &howmny, select, d, z, &ldz, &sigma, workev, &bmat, &n, which,
&nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl,
rwork, &info);
/* Test for errors */
if(info != 0)
Msg(GERROR, "Arpack code = %d (eigenvector post-processing)", info);
/* Compute the unshifted eigenvalues and print them, and store the
associated eigenvectors */
newsol = 0;
for (k = 0; k < nev; k++){
/* Unshift the eigenvalues */
tmp = SQU(d[k].re) + SQU(d[k].im);
d[k].re = shift_r + d[k].re/tmp;
d[k].im = shift_i - d[k].im/tmp;
if(!quad_evp){
/* Eigenvalue = omega^2 */
omega2.re = d[k].re;
omega2.im = d[k].im;
abs = sqrt(SQU(omega2.re) + SQU(omega2.im));
arg = atan2(omega2.im, omega2.re);
omega.re = sqrt(abs) * cos(0.5*arg);
omega.im = sqrt(abs) * sin(0.5*arg);
f.re = omega.re / TWO_PI;
f.im = omega.im / TWO_PI;
}
else{
/* Eigenvalue = i*omega */
omega.re = d[k].im;
omega.im = -d[k].re;
omega2.re = SQU(omega.re) - SQU(omega.im);
omega2.im = 2. * omega.re * omega.im;
f.re = omega.re / TWO_PI;
f.im = omega.im / TWO_PI;
}
Msg(BIGINFO, "Eigenvalue %03d: w^2 = %.12e %s %.12e * i",
k+1, omega2.re, (omega2.im > 0) ? "+" : "-", (omega2.im > 0) ? omega2.im : -omega2.im);
Msg(BIGINFO, " w = %.12e %s %.12e * i",
omega.re, (omega.im > 0) ? "+" : "-", (omega.im > 0) ? omega.im : -omega.im);
Msg(BIGINFO, " f = %.12e %s %.12e * i",
f.re, (f.im > 0) ? "+" : "-", (f.im > 0) ? f.im : -f.im);
if(newsol) {
/* Create new solution */
LinAlg_CreateVector(&Solution_S.x, &DofData_P->Solver, DofData_P->NbrDof,
DofData_P->NbrPart, DofData_P->Part);
List_Add(DofData_P->Solutions, &Solution_S);
DofData_P->CurrentSolution = (struct Solution*)
List_Pointer(DofData_P->Solutions, List_Nbr(DofData_P->Solutions)-1);
}
newsol = 1;
DofData_P->CurrentSolution->Time = omega.re;
DofData_P->CurrentSolution->TimeImag = omega.im;
DofData_P->CurrentSolution->TimeStep = (int)Current.TimeStep;
DofData_P->CurrentSolution->TimeFunctionValues = NULL;
DofData_P->CurrentSolution->SolutionExist = 1;
for(l = 0; l < DofData_P->NbrDof; l+=gCOMPLEX_INCREMENT){
j = l / gCOMPLEX_INCREMENT;
LinAlg_SetComplexInVector(z[k*n+j].re, z[k*n+j].im,
&DofData_P->CurrentSolution->x, l, l+1);
}
/* Arpack returns eigenvectors normalized in L-2 norm. Renormalize
them in L-infty norm so that the absolute value of the largest
element is 1 */
tmp = 0.;
for(l = 0; l < DofData_P->NbrDof; l+=gCOMPLEX_INCREMENT){
LinAlg_GetComplexInVector(&d1, &d2,
&DofData_P->CurrentSolution->x, l, l+1);
abs = sqrt(SQU(d1) + SQU(d2));
if(abs > tmp) tmp = abs;
}
if(tmp > 1.e-16)
LinAlg_ProdVectorDouble(&DofData_P->CurrentSolution->x, 1./tmp,
&DofData_P->CurrentSolution->x);
/* Increment the global timestep counter so that a future
GenerateSystem knows which solutions exist */
Current.TimeStep += 1.;
/* Update the current value of Time and TimeImag so that
$EigenvalueReal and $EigenvalueImag are up-to-date */
Current.Time = omega.re;
Current.TimeImag = omega.im;
}
/* Deallocate */
if(!quad_evp){
LinAlg_DestroyVector(&v1);
LinAlg_DestroyVector(&v2);
}
else{
LinAlg_DestroyVector(&x);
LinAlg_DestroyVector(&y);
LinAlg_DestroyVector(&v1);
LinAlg_DestroyVector(&w1);
LinAlg_DestroyVector(&w2);
LinAlg_DestroyMatrix(&D);
}
Free(resid);
Free(v);
Free(workd);
Free(workl);
Free(rwork);
Free(select);
Free(d);
Free(z);
Free(workev);
GetDP_End;
}
#endif
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