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/* MIT License
*
* Copyright (c) 2016--2017 Felix Lenders
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
#include "trlib.h"
#include "trlib_private.h"
#include "_c99compat.h"
trlib_int_t trlib_eigen_inverse(
trlib_int_t n, trlib_flt_t *diag, trlib_flt_t *offdiag,
trlib_flt_t lam_init, trlib_int_t itmax, trlib_flt_t tol_abs,
trlib_flt_t *ones, trlib_flt_t *diag_fac, trlib_flt_t *offdiag_fac,
trlib_flt_t *eig, trlib_int_t verbose, trlib_int_t unicode, char *prefix, FILE *fout,
trlib_int_t *timing, trlib_flt_t *lam_pert, trlib_flt_t *pert, trlib_int_t *iter_inv) {
// Local variables
#if TRLIB_MEASURE_TIME
struct timespec verystart, start, end;
TRLIB_TIC(verystart)
#endif
trlib_int_t info_fac = 0; // status variable for factorization
trlib_flt_t invnorm = 0.0; // 1/norm of eig before normalization
trlib_flt_t minuslam = - lam_init; // negative of current estimation of eigenvalue
trlib_int_t inc = 1; trlib_int_t nm = n-1;
trlib_int_t seeds[TRLIB_EIR_N_STARTVEC];
trlib_flt_t residuals[TRLIB_EIR_N_STARTVEC];
trlib_int_t jj = 0;
trlib_int_t kk = 0;
trlib_int_t seedpivot = 0;
*iter_inv = 0; // iteration counter
*pert = 0.0; // perturbation factor to update lam until factorization is possible
*iter_inv = 0;
*pert = 0.0;
info_fac = 0;
invnorm = 0.0;
minuslam = - lam_init;
// obtain factorization of T - lam*I, perturb until possible
// iter_inv is misused in this loop as flag if we can find a suitable lambda to start with
*iter_inv = TRLIB_EIR_FAIL_FACTOR;
while (*pert <= 1.0/TRLIB_EPS) {
// set diag_fac to diag - lam
TRLIB_DCOPY(&n, diag, &inc, diag_fac, &inc) // diag_fac <-- diag
TRLIB_DAXPY(&n, &minuslam, ones, &inc, diag_fac, &inc) // diag_fac <-- diag_fac - lam
TRLIB_DCOPY(&nm, offdiag, &inc, offdiag_fac, &inc) // offdiag_fac <-- offdiag
TRLIB_DPTTRF(&n, diag_fac, offdiag_fac, &info_fac); // compute factorization
if (info_fac == 0) { *iter_inv = 0; break; }
if (*pert == 0.0) {
*pert = TRLIB_EPS_POW_4 * fmax(1.0, -lam_init);
}
else {
*pert = 10.0*(*pert);
}
minuslam = *pert - lam_init;
}
*lam_pert = -minuslam;
if ( *iter_inv == TRLIB_EIR_FAIL_FACTOR ) { TRLIB_PRINTLN_2("Failure on factorizing in inverse correction!") TRLIB_RETURN(TRLIB_EIR_FAIL_FACTOR) }
// try with TRLIB_EIR_N_STARTVEC different start vectors and hope that it converges for one
seeds[0] = time(NULL);
for(jj = 1; jj < TRLIB_EIR_N_STARTVEC; ++jj ) { seeds[jj] = rand(); }
for(jj = 0; jj < TRLIB_EIR_N_STARTVEC; ++jj ) {
*iter_inv = 0;
srand((unsigned) seeds[jj]);
for(kk = 0; kk < n; ++kk ) { eig[kk] = ((trlib_flt_t)rand()/(trlib_flt_t)RAND_MAX); }
TRLIB_DNRM2(invnorm, &n, eig, &inc) invnorm = 1.0/invnorm;
TRLIB_DSCAL(&n, &invnorm, eig, &inc) // normalize eig
// perform inverse iteration
while (1) {
*iter_inv += 1;
if ( *iter_inv > itmax ) { break; }
// solve (T - lam*I)*eig_new = eig_old
TRLIB_DPTTRS(&n, &inc, diag_fac, offdiag_fac, eig, &n, &info_fac)
if( info_fac != 0 ) { TRLIB_PRINTLN_2("Failure on solving inverse correction!") TRLIB_RETURN(TRLIB_EIR_FAIL_LINSOLVE) }
// normalize eig
TRLIB_DNRM2(invnorm, &n, eig, &inc) invnorm = 1.0/invnorm;
TRLIB_DSCAL(&n, &invnorm, eig, &inc)
residuals[jj] = fabs(invnorm - *pert);
// check for convergence
if (residuals[jj] <= tol_abs ) { TRLIB_RETURN(TRLIB_EIR_CONV) }
}
}
// no convergence with any of the starting values.
// take the seed with least residual and redo computation
for(jj = 0; jj < TRLIB_EIR_N_STARTVEC; ++jj) { if (residuals[jj] < residuals[seedpivot]) { seedpivot = jj; } }
*iter_inv = 0;
srand((unsigned) seeds[seedpivot]);
for(kk = 0; kk < n; ++kk ) { eig[kk] = ((trlib_flt_t)rand()/(trlib_flt_t)RAND_MAX); }
TRLIB_DNRM2(invnorm, &n, eig, &inc) invnorm = 1.0/invnorm;
TRLIB_DSCAL(&n, &invnorm, eig, &inc) // normalize eig
// perform inverse iteration
while (1) {
*iter_inv += 1;
if ( *iter_inv > itmax ) { break; }
// solve (T - lam*I)*eig_new = eig_old
TRLIB_DPTTRS(&n, &inc, diag_fac, offdiag_fac, eig, &n, &info_fac)
if( info_fac != 0 ) { TRLIB_PRINTLN_2("Failure on solving inverse correction!") TRLIB_RETURN(TRLIB_EIR_FAIL_LINSOLVE) }
// normalize eig
TRLIB_DNRM2(invnorm, &n, eig, &inc) invnorm = 1.0/invnorm;
TRLIB_DSCAL(&n, &invnorm, eig, &inc)
residuals[seedpivot] = fabs(invnorm - *pert);
// check for convergence
if (residuals[seedpivot] <= tol_abs ) { TRLIB_RETURN(TRLIB_EIR_CONV) }
}
TRLIB_RETURN(TRLIB_EIR_ITMAX)
}
trlib_int_t trlib_eigen_timing_size() {
#if TRLIB_MEASURE_TIME
return 1 + TRLIB_SIZE_TIMING_LINALG;
#endif
return 0;
}
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