220 lines
8.9 KiB
C++
220 lines
8.9 KiB
C++
/*
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* This example demonstrates the use of C++ bindings to call arpack.
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*
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* Use arpack as you would have normally done, but, use [ae]upd instead
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* of *[ae]upd_. The main advantage is that compiler checks the argument types
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* and the correct function is called based on the type (float vs double vs
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* complex). Note: to debug arpack, call debug_c. This is a test program to
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* solve for the 9 eigenvalues of A*x = lambda*x where A is the diagonal
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* matrix with entries 1000, 999, ... , 2, 1 on the diagonal.
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*/
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#include <cmath>
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#include <iostream>
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#include <stdexcept>
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#include <vector>
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#include "arpack.hpp"
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#include "debug_c.hpp" // debug arpack.
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#include "stat_c.hpp" // arpack statistics.
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template <typename Real>
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void diagonal_matrix_vector_product(const Real* x, Real* y) {
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for (int i = 0; i < 1000; ++i) {
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y[i] = static_cast<Real>(i + 1) * x[i];
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}
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}
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template <typename Real>
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void real_symmetric_runner(double const& tol_check, arpack::which const& ritz_option) {
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const a_int N = 1000;
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const a_int nev = 9;
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const a_int ncv = 2 * nev + 1;
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const a_int ldv = N;
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const a_int ldz = N;
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const a_int lworkl = ncv * (ncv + 8);
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const a_int rvec = 1; // need eigenvectors
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const Real tol = 0.000001; // small tol => more stable checks after EV computation.
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const Real sigma = 0.0; // not referenced in this mode
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std::vector<Real> resid(N);
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std::vector<Real> V(ldv * ncv);
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std::vector<Real> z(ldz * nev);
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std::vector<Real> d(nev);
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std::vector<Real> workd(3 * N);
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std::vector<Real> workl(lworkl);
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std::vector<a_int> select(ncv); // since HOWMNY = 'A', only used as workspace here
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a_int iparam[11], ipntr[11];
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iparam[0] = 1; // ishift
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iparam[2] = 10 * N; // on input: maxit; on output: actual iteration
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iparam[3] = 1; // NB, only 1 allowed
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iparam[6] = 1; // mode
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a_int info = 0, ido = 0;
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do {
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arpack::saupd(ido, arpack::bmat::identity, N,
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ritz_option, nev, tol, resid.data(), ncv,
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V.data(), ldv, iparam, ipntr, workd.data(),
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workl.data(), lworkl, info);
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diagonal_matrix_vector_product(&(workd[ipntr[0] - 1]), &(workd[ipntr[1] - 1]));
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} while (ido == 1 || ido == -1);
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// check info and number of ev found by arpack.
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if (info < 0 || iparam[4] < nev) { /*arpack may succeed to compute more EV than expected*/
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std::cout << "ERROR in saupd: iparam[4] " << iparam[4] << ", nev " << nev
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<< ", info " << info << std::endl;
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throw std::domain_error("Error inside ARPACK routines");
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}
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arpack::seupd(rvec, arpack::howmny::ritz_vectors, select.data(), d.data(),
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z.data(), ldz, sigma, arpack::bmat::identity, N,
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ritz_option, nev, tol, resid.data(), ncv,
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V.data(), ldv, iparam, ipntr, workd.data(),
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workl.data(), lworkl, info);
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if (info < 0) throw std::runtime_error("Error in seupd, info " + std::to_string(info));
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for (int i = 0; i < nev; ++i) {
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Real val = d[i];
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Real ref = static_cast<Real>(N - (nev - 1) + i);
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Real eps = std::fabs(val - ref);
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std::cout << val << " - " << ref << " - " << eps << std::endl;
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/*eigen value order: smallest -> biggest*/
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if (eps > tol_check) throw std::domain_error("Correct eigenvalues not computed");
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}
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std::cout << "------" << std::endl;
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}
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template <typename Real>
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void diagonal_matrix_vector_product(const std::complex<Real>* x, std::complex<Real>* y) {
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for (int i = 0; i < 1000; ++i) {
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// Use complex matrix (i, -i) instead of (i, i): this way "largest_magnitude"
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// and "largest_imaginary" options produce different results that can be checked.
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y[i] = x[i] * std::complex<Real>{Real(i + 1), -Real(i + 1)};
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}
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}
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template <typename Real>
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void complex_nonsymmetric_runner(double const& tol_check, arpack::which const& ritz_option) {
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const a_int N = 1000;
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const a_int nev = 9;
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const a_int ncv = 2 * nev + 1;
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const a_int ldv = N;
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const a_int ldz = N;
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const a_int lworkl = ncv * (3 * ncv + 5);
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const a_int rvec = 0; // eigenvectors omitted
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const Real tol = 0.000001; // small tol => more stable checks after EV computation.
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const std::complex<Real> sigma(0.0, 0.0); // not referenced in this mode
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std::vector<std::complex<Real>> resid(N);
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std::vector<std::complex<Real>> V(ldv * ncv);
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std::vector<std::complex<Real>> z(ldz * nev);
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std::vector<std::complex<Real>> d(nev);
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std::vector<std::complex<Real>> workd(3 * N);
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std::vector<std::complex<Real>> workl(lworkl);
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std::vector<std::complex<Real>> workev(2 * ncv);
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std::vector<Real> rwork(ncv);
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std::vector<a_int> select(ncv); // since HOWMNY = 'A', only used as workspace here
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a_int iparam[11], ipntr[14];
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iparam[0] = 1; // ishift
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iparam[2] = 10 * N; // on input: maxit; on output: actual iteration
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iparam[3] = 1; // NB, only 1 allowed
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iparam[6] = 1; // mode
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a_int info = 0, ido = 0;
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do {
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arpack::naupd(ido, arpack::bmat::identity, N,
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ritz_option, nev, tol, resid.data(), ncv,
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V.data(), ldv, iparam, ipntr, workd.data(),
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workl.data(), lworkl, rwork.data(), info);
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diagonal_matrix_vector_product(&(workd[ipntr[0] - 1]), &(workd[ipntr[1] - 1]));
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} while (ido == 1 || ido == -1);
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// check info and number of ev found by arpack.
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if (info < 0 || iparam[4] < nev) { /*arpack may succeed to compute more EV than expected*/
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std::cout << "ERROR in naupd: iparam[4] " << iparam[4] << ", nev " << nev
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<< ", info " << info << std::endl;
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throw std::domain_error("Error inside ARPACK routines");
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}
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arpack::neupd(rvec, arpack::howmny::ritz_vectors, select.data(), d.data(),
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z.data(), ldz, sigma, workev.data(), arpack::bmat::identity, N,
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ritz_option, nev, tol, resid.data(), ncv,
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V.data(), ldv, iparam, ipntr, workd.data(),
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workl.data(), lworkl, rwork.data(), info);
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if (info < 0) throw std::runtime_error("Error in neupd, info " + std::to_string(info));
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if (ritz_option == arpack::which::largest_magnitude) {
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for (int i = 0; i < nev; ++i) {
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Real rval = std::real(d[i]);
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Real rref = static_cast<Real>(N - (nev - 1) + i);
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Real reps = std::fabs(rval - rref);
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Real ival = std::imag(d[i]);
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Real iref = -static_cast<Real>(N - (nev - 1) + i);
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Real ieps = std::fabs(ival - iref);
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std::cout << rval << " " << ival << " - " << rref << " " << iref << " - " << reps << " " << ieps << std::endl;
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if (reps > tol_check || ieps > tol_check) throw std::domain_error("Correct eigenvalues not computed");
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}
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} else if (ritz_option == arpack::which::largest_imaginary) {
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for (int i = 0; i < nev; ++i) {
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Real rval = std::real(d[i]);
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Real rref = static_cast<Real>(nev - i);
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Real reps = std::fabs(rval - rref);
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Real ival = std::imag(d[i]);
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Real iref = -static_cast<Real>(nev - i);
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Real ieps = std::fabs(ival - iref);
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std::cout << rval << " " << ival << " - " << rref << " " << iref << " - " << reps << " " << ieps << std::endl;
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if (reps > tol_check || ieps > tol_check) throw std::domain_error("Correct eigenvalues not computed");
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}
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} else {
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throw std::domain_error("The input Ritz option is not allowed in this test file.");
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}
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std::cout << "------" << std::endl;
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}
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int main() {
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sstats_c();
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// arpack without debug
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real_symmetric_runner<float>(1., arpack::which::largest_magnitude);
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real_symmetric_runner<float>(1., arpack::which::largest_algebraic);
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real_symmetric_runner<double>(1.e-05, arpack::which::largest_magnitude);
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real_symmetric_runner<double>(1.e-05, arpack::which::largest_algebraic);
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a_int nopx_c, nbx_c, nrorth_c, nitref_c, nrstrt_c;
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float tsaupd_c, tsaup2_c, tsaitr_c, tseigt_c, tsgets_c, tsapps_c, tsconv_c;
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float tnaupd_c, tnaup2_c, tnaitr_c, tneigt_c, tngets_c, tnapps_c, tnconv_c;
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float tcaupd_c, tcaup2_c, tcaitr_c, tceigt_c, tcgets_c, tcapps_c, tcconv_c;
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float tmvopx_c, tmvbx_c, tgetv0_c, titref_c, trvec_c;
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stat_c(nopx_c, nbx_c, nrorth_c, nitref_c, nrstrt_c, tsaupd_c, tsaup2_c,
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tsaitr_c, tseigt_c, tsgets_c, tsapps_c, tsconv_c, tnaupd_c, tnaup2_c,
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tnaitr_c, tneigt_c, tngets_c, tnapps_c, tnconv_c, tcaupd_c, tcaup2_c,
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tcaitr_c, tceigt_c, tcgets_c, tcapps_c, tcconv_c, tmvopx_c, tmvbx_c,
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tgetv0_c, titref_c, trvec_c);
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std::cout << "Timers : nopx " << nopx_c << ", tmvopx " << tmvopx_c;
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std::cout << " - nbx " << nbx_c << ", tmvbx " << tmvbx_c << std::endl;
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std::cout << "------" << std::endl;
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// set debug flags
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debug_c(6, -6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
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1);
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// arpack with debug
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complex_nonsymmetric_runner<float>(1., arpack::which::largest_magnitude);
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complex_nonsymmetric_runner<float>(1., arpack::which::largest_imaginary);
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complex_nonsymmetric_runner<double>(1.e-05, arpack::which::largest_magnitude);
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complex_nonsymmetric_runner<double>(1.e-05, arpack::which::largest_imaginary);
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return 0;
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}
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