Overhaul of lyapunov exponents
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@ -48,3 +48,6 @@ limitations under the License.
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#define FIX_ENSTROPHY 1
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#define FIX_ENERGY 2
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#define LYAPUNOV_TRIGGER_TIME 1
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#define LYAPUNOV_TRIGGER_SIZE 2
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726
src/lyapunov.c
726
src/lyapunov.c
@ -32,110 +32,113 @@ int lyapunov(
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int N2,
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double final_time,
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double lyapunov_reset,
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unsigned int lyapunov_trigger,
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double nu,
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double D_epsilon,
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double delta,
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double L,
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double adaptive_tolerance,
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double adaptive_factor,
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double max_delta,
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unsigned int adaptive_norm,
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unsigned int adaptive_cost,
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_Complex double* u0,
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_Complex double* g,
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bool irreversible,
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bool keep_en_cst,
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double target_en,
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unsigned int algorithm,
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unsigned int algorithm_lyapunov,
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double starting_time,
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unsigned int nthreads
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){
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double* lyapunov;
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double* lyapunov_avg;
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double* Du_prod;
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double* Du;
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double* flow;
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_Complex double* u;
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_Complex double* prevu;
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_Complex double* tmp1;
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_Complex double* tmp2;
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_Complex double* tmp3;
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double time;
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fft_vect fftu1;
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fft_vect fftu2;
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fft_vect fftu3;
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fft_vect fftu4;
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fft_vect fft1;
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fft_vect ifft;
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double* tmp1;
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double* tmp2;
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double* tmp3;
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_Complex double* tmp4;
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_Complex double* tmp5;
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_Complex double* tmp6;
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_Complex double* tmp7;
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_Complex double* tmp8;
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_Complex double* tmp9;
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double* tmp10;
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double time;
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fft_vect fft1;
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fft_vect fft2;
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fft_vect ifft;
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_Complex double* tmp10;
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double* tmp11;
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int i,j;
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// period
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// period (only useful with LYAPUNOV_TRIGGER_TIME, but compute it anyways: it won't take much time...)
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// add 0.1 to ensure proper rounding
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uint64_t n=(uint64_t)((starting_time-fmod(starting_time, lyapunov_reset))/lyapunov_reset+0.1);
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lyapunov_init_tmps(&lyapunov, &lyapunov_avg, &Du_prod, &Du, &u, &prevu, &tmp1, &tmp2, &tmp3, &tmp4, &tmp5, &tmp6, &tmp7, &tmp8, &tmp9, &tmp10, &fft1, &fft2, &ifft, K1, K2, N1, N2, nthreads, algorithm);
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lyapunov_init_tmps(&lyapunov, &lyapunov_avg, &flow, &u, &tmp1, &tmp2, &tmp3, &tmp4, &tmp5, &tmp6, &tmp7, &tmp8, &tmp9, &tmp10, &tmp11, &fftu1, &fftu2, &fftu3, &fftu4, &fft1, &ifft, K1, K2, N1, N2, nthreads, algorithm, algorithm_lyapunov);
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// copy initial condition
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copy_u(u, u0, K1, K2);
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// initialize Du_prod
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int i,j;
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for(i=0;i<MATSIZE;i++){
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for(j=0;j<MATSIZE;j++){
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Du_prod[i*MATSIZE+j]=0.;
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// initialize flow with identity matrix
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for (i=0;i<MATSIZE;i++){
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for (j=0;j<MATSIZE;j++){
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if(i!=j){
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flow[i*MATSIZE+j]=0.;
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} else {
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flow[i*MATSIZE+j]=1.;
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}
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}
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}
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for(i=0;i<MATSIZE;i++){
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Du_prod[i*MATSIZE+i]=1.;
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}
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// store step (useful for adaptive step methods
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double prev_step=delta;
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// store step (useful for adaptive step methods)
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double step=delta;
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double next_step=step;
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// init average
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for (i=0; i<MATSIZE; i++){
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lyapunov_avg[i]=0;
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}
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// save times at which Lyapunov exponents are computed
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double prevtime=starting_time;
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// iterate
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time=starting_time;
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while(final_time<0 || time<final_time){
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// copy before step
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copy_u(prevu, u, K1, K2);
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prev_step=step;
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ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, L, g, time, starting_time, fft1, fft2, ifft, &tmp1, &tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, irreversible, keep_en_cst, target_en);
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// compute Jacobian
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// do not touch tmp1, it might be used in the next step
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ns_D_step(Du, prevu, u, K1, K2, N1, N2, nu, D_epsilon, prev_step, algorithm, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, L, g, time, fft1, fft2, ifft, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8, tmp9, irreversible, keep_en_cst, target_en);
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// multiply Jacobian
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// switch to column major order, so transpose Du
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cblas_dgemm(CblasColMajor, CblasNoTrans, CblasTrans, MATSIZE, MATSIZE, MATSIZE, 1., Du_prod, MATSIZE, Du, MATSIZE, 0., tmp10, MATSIZE);
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// copy back to Du_prod
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double* move=tmp10;
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tmp10=Du_prod;
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Du_prod=move;
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// compute u first
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// if using an adaptive step, the step for the tangent flow is set by this computation of u
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// use fftu1 as a tmp fft vector (it hasn't been used yet this step)
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ns_step(algorithm, u, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_cost, L, g, time, starting_time, fft1, fftu1, ifft, &tmp4, &tmp5, tmp6, tmp7, tmp8, tmp9, tmp10, irreversible, keep_en_cst, target_en);
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// compute tangent flow
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lyapunov_D_step(flow, u, K1, K2, N1, N2, nu, step, algorithm_lyapunov, L, g, fftu1, fftu2, fftu3, fftu4, fft1, ifft, tmp1, tmp2, tmp3, tmp4, irreversible);
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// increment time
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time+=step;
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// reset Jacobian
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if(time>(n+1)*lyapunov_reset){
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double norm=0;
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if(lyapunov_trigger==LYAPUNOV_TRIGGER_SIZE){
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// size of flow (for reset)
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for(i=0;i<MATSIZE;i++){
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for(j=0;j<MATSIZE;j++){
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norm+=fabs(flow[i*MATSIZE+j]);
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if(norm>lyapunov_reset){
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break;
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}
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}
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if(norm>lyapunov_reset){
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break;
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}
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}
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}
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// QR decomposition
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if((lyapunov_trigger==LYAPUNOV_TRIGGER_TIME && time>(n+1)*lyapunov_reset) || (lyapunov_trigger==LYAPUNOV_TRIGGER_SIZE && norm>lyapunov_reset)){
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n++;
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// QR decomposition
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// do not touch tmp1, it might be used in the next step
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LAPACKE_dgerqf(LAPACK_COL_MAJOR, MATSIZE, MATSIZE, Du_prod, MATSIZE, tmp10);
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// extract eigenvalues (diagonal elements of Du_prod)
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LAPACKE_dgeqrf(LAPACK_COL_MAJOR, MATSIZE, MATSIZE, flow, MATSIZE, tmp11);
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// extract diagonal elements of R (represented as diagonal elements of flow
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for(i=0; i<MATSIZE; i++){
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lyapunov[i]=log(fabs(Du_prod[i*MATSIZE+i]))/(time-prevtime);
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lyapunov[i]=log(fabs(flow[i*MATSIZE+i]))/(time-prevtime);
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}
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// sort lyapunov exponents
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@ -155,23 +158,24 @@ int lyapunov(
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}
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printf("\n");
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fprintf(stderr,"% .15e",time);
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// print largest and smallest lyapunov exponent
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// print largest and smallest lyapunov exponent to stderr
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if(MATSIZE>0){
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fprintf(stderr," % .15e % .15e\n", lyapunov[0], lyapunov[MATSIZE-1]);
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}
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// set Du_prod to Q:
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LAPACKE_dorgrq(LAPACK_COL_MAJOR, MATSIZE, MATSIZE, MATSIZE, Du_prod, MATSIZE, tmp10);
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// set flow to Q:
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LAPACKE_dorgqr(LAPACK_COL_MAJOR, MATSIZE, MATSIZE, MATSIZE, flow, MATSIZE, tmp11);
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// reset prevtime
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prevtime=time;
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}
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}
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lyapunov_free_tmps(lyapunov, lyapunov_avg, Du_prod, Du, u, prevu, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8, tmp9, tmp10, fft1, fft2, ifft, algorithm);
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lyapunov_free_tmps(lyapunov, lyapunov_avg, flow, u, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8, tmp9, tmp10, tmp11, fftu1, fftu2, fftu3, fftu4, fft1, ifft, algorithm, algorithm_lyapunov);
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return(0);
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}
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// comparison function for qsort
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int compare_double(const void* x, const void* y) {
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if (*(const double*)x<*(const double*)y) {
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@ -183,87 +187,64 @@ int compare_double(const void* x, const void* y) {
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}
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}
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// Jacobian of u_n -> u_{n+1}
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int ns_D_step(
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double* out,
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_Complex double* un,
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_Complex double* un_next,
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// compute tangent flow
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int lyapunov_D_step(
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double* flow,
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_Complex double* u,
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int K1,
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int K2,
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int N1,
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int N2,
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double nu,
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double epsilon,
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double delta,
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unsigned int algorithm,
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double adaptive_tolerance,
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double adaptive_factor,
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double max_delta,
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unsigned int adaptive_norm,
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double L,
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_Complex double* g,
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double time,
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fft_vect fftu1,
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fft_vect fftu2,
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fft_vect fftu3,
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fft_vect fftu4,
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fft_vect fft1,
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fft_vect fft2,
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fft_vect ifft,
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_Complex double* tmp1,
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_Complex double* tmp2,
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_Complex double* tmp3,
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double* tmp1,
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double* tmp2,
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double* tmp3,
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_Complex double* tmp4,
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_Complex double* tmp5,
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_Complex double* tmp6,
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_Complex double* tmp7,
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_Complex double* tmp8,
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bool irreversible,
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bool keep_en_cst,
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double target_en
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bool irreversible
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){
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int lx,ly;
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int i;
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double step, next_step;
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double alpha;
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// compute fft of u for future use
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lyapunov_fft_u_T(u,K1,K2,N1,N2,fftu1,fftu2,fftu3,fftu4);
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// compute T
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lyapunov_T(N1,N2,fftu1,fftu2,fftu3,fftu4,ifft);
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// save to vect
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for(lx=-K1;lx<=K1;lx++){
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for(ly=-K2;ly<=K2;ly++){
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tmp4[klookup_sym(lx,ly,K2)]=ifft.fft[klookup(lx,ly,N1,N2)];
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}
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}
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//compute alpha
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if (irreversible) {
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alpha=nu;
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} else {
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alpha=compute_alpha(u,K1,K2,g,L);
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}
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// loop over columns
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for(lx=0;lx<=K1;lx++){
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for(ly=(lx>0 ? -K2 : 1);ly<=K2;ly++){
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// derivative in the real direction
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// finite difference vector
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for (i=0;i<USIZE;i++){
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if(i==klookup_sym(lx,ly,K2)){
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tmp1[i]=un[i]+epsilon;
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}else{
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tmp1[i]=un[i];
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}
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}
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// compute step
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// reinitialize step
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step=delta;
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next_step=delta;
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ns_step(algorithm, tmp1, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, L, g, time, time, fft1, fft2, ifft, &tmp2, &tmp3, tmp4, tmp5, tmp6, tmp7, tmp8, irreversible, keep_en_cst, target_en);
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// derivative
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for (i=0;i<USIZE;i++){
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// use row major order
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out[2*klookup_sym(lx,ly,K2)*MATSIZE+2*i]=(__real__ (tmp1[i]-un_next[i]))/epsilon;
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out[2*klookup_sym(lx,ly,K2)*MATSIZE+2*i+1]=(__imag__ (tmp1[i]-un_next[i]))/epsilon;
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}
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// derivative in the imaginary direction
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// finite difference vector
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for (i=0;i<USIZE;i++){
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if(i==klookup_sym(lx,ly,K2)){
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tmp1[i]=un[i]+epsilon*I;
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}else{
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tmp1[i]=un[i];
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}
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}
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// compute step
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// reinitialize step
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step=delta;
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next_step=delta;
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ns_step(algorithm, tmp1, K1, K2, N1, N2, nu, &step, &next_step, adaptive_tolerance, adaptive_factor, max_delta, adaptive_norm, L, g, time, time, fft1, fft2, ifft, &tmp2, &tmp3, tmp4, tmp5, tmp6, tmp7, tmp8, irreversible, keep_en_cst, target_en);
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// compute derivative
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for (i=0;i<USIZE;i++){
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// use row major order
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out[(2*klookup_sym(lx,ly,K2)+1)*MATSIZE+2*i]=(__real__ (tmp1[i]-un_next[i]))/epsilon;
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out[(2*klookup_sym(lx,ly,K2)+1)*MATSIZE+2*i+1]=(__imag__ (tmp1[i]-un_next[i]))/epsilon;
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// do not use adaptive step algorithms for the tangent flow: it must be locked to the same times as u
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if(algorithm==ALGORITHM_RK2){
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lyapunov_D_step_rk2(flow+2*klookup_sym(lx,ly,K2)*MATSIZE, u, K1, K2, N1, N2, alpha, delta, L, g, tmp4, fftu1, fftu2, fftu3, fftu4, fft1, ifft, tmp1, tmp2, irreversible);
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} else if (algorithm==ALGORITHM_RK4) {
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lyapunov_D_step_rk4(flow+2*klookup_sym(lx,ly,K2)*MATSIZE, u, K1, K2, N1, N2, alpha, delta, L, g, tmp4, fftu1, fftu2, fftu3, fftu4, fft1, ifft, tmp1, tmp2, tmp3, irreversible);
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} else {
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fprintf(stderr,"bug: unknown algorithm for tangent flow: %u, contact ian.jauslin@rutgers.edu\n",algorithm);
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}
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}
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}
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@ -271,80 +252,501 @@ int ns_D_step(
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return(0);
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}
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// RK 4 algorithm
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int lyapunov_D_step_rk4(
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double* flow,
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_Complex double* u,
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int K1,
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int K2,
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int N1,
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int N2,
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double nu,
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double delta,
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double L,
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_Complex double* g,
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_Complex double* T,
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fft_vect fftu1,
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fft_vect fftu2,
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fft_vect fftu3,
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fft_vect fftu4,
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fft_vect fft1,
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fft_vect ifft,
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double* tmp1,
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double* tmp2,
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double* tmp3,
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bool irreversible
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){
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int i;
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// k1
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lyapunov_D_rhs(tmp1, flow, u, K1, K2, N1, N2, nu, L, g, T, fftu1, fftu2, fftu3, fftu4, fft1, ifft, irreversible);
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// add to output
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for(i=0;i<MATSIZE;i++){
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tmp3[i]=flow[i]+delta/6*tmp1[i];
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}
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// d+h*k1/2
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for(i=0;i<MATSIZE;i++){
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tmp2[i]=flow[i]+delta/2*tmp1[i];
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}
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// k2
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lyapunov_D_rhs(tmp1, tmp2, u, K1, K2, N1, N2, nu, L, g, T, fftu1, fftu2, fftu3, fftu4, fft1, ifft, irreversible);
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// add to output
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for(i=0;i<MATSIZE;i++){
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tmp3[i]+=delta/3*tmp1[i];
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}
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// d+h*k2/2
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for(i=0;i<MATSIZE;i++){
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tmp2[i]=flow[i]+delta/2*tmp1[i];
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}
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// k3
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lyapunov_D_rhs(tmp1, tmp2, u, K1, K2, N1, N2, nu, L, g, T, fftu1, fftu2, fftu3, fftu4, fft1, ifft, irreversible);
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// add to output
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for(i=0;i<MATSIZE;i++){
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tmp3[i]+=delta/3*tmp1[i];
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}
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// d+h*k3
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for(i=0;i<MATSIZE;i++){
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tmp2[i]=flow[i]+delta*tmp1[i];
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}
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// k4
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lyapunov_D_rhs(tmp1, tmp2, u, K1, K2, N1, N2, nu, L, g, T, fftu1, fftu2, fftu3, fftu4, fft1, ifft, irreversible);
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// add to output
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for(i=0;i<MATSIZE;i++){
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flow[i]=tmp3[i]+delta/6*tmp1[i];
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}
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return(0);
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}
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// RK 2 algorithm
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int lyapunov_D_step_rk2(
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double* flow,
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_Complex double* u,
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int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
double nu,
|
||||
double delta,
|
||||
double L,
|
||||
_Complex double* g,
|
||||
_Complex double* T,
|
||||
fft_vect fftu1,
|
||||
fft_vect fftu2,
|
||||
fft_vect fftu3,
|
||||
fft_vect fftu4,
|
||||
fft_vect fft1,
|
||||
fft_vect ifft,
|
||||
double* tmp1,
|
||||
double* tmp2,
|
||||
bool irreversible
|
||||
){
|
||||
int i;
|
||||
|
||||
// k1
|
||||
lyapunov_D_rhs(tmp1, flow, u, K1, K2, N1, N2, nu, L, g, T, fftu1, fftu2, fftu3, fftu4, fft1, ifft, irreversible);
|
||||
|
||||
// u+h*k1/2
|
||||
for(i=0;i<MATSIZE;i++){
|
||||
tmp2[i]=flow[i]+delta/2*tmp1[i];
|
||||
}
|
||||
// k2
|
||||
lyapunov_D_rhs(tmp1, tmp2, u, K1, K2, N1, N2, nu, L, g, T, fftu1, fftu2, fftu3, fftu4, fft1, ifft, irreversible);
|
||||
// add to output
|
||||
for(i=0;i<MATSIZE;i++){
|
||||
flow[i]+=delta*tmp1[i];
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
// Right side of equation for tangent flow
|
||||
int lyapunov_D_rhs(
|
||||
double* out,
|
||||
double* flow,
|
||||
_Complex double* u,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
double alpha,
|
||||
double L,
|
||||
_Complex double* g,
|
||||
_Complex double* T,
|
||||
fft_vect fftu1,
|
||||
fft_vect fftu2,
|
||||
fft_vect fftu3,
|
||||
fft_vect fftu4,
|
||||
fft_vect fft1,
|
||||
fft_vect ifft,
|
||||
bool irreversible
|
||||
){
|
||||
int kx,ky;
|
||||
int i;
|
||||
|
||||
// compute DT
|
||||
lyapunov_D_T(flow,K1,K2,N1,N2,fftu1,fftu2,fftu3,fftu4,fft1,ifft);
|
||||
|
||||
for(i=0; i<K1*(2*K2+1)+K2; i++){
|
||||
out[i]=0;
|
||||
}
|
||||
for(kx=0;kx<=K1;kx++){
|
||||
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
|
||||
// real part
|
||||
out[2*klookup_sym(kx,ky,K2)]=-4*M_PI*M_PI/L/L*alpha*(kx*kx+ky*ky)*flow[2*klookup_sym(kx,ky,K2)]+4*M_PI*M_PI/L/L/sqrt(kx*kx+ky*ky)*__real__ ifft.fft[klookup(kx,ky,N1,N2)];
|
||||
// imaginary part
|
||||
out[2*klookup_sym(kx,ky,K2)+1]=-4*M_PI*M_PI/L/L*alpha*(kx*kx+ky*ky)*flow[2*klookup_sym(kx,ky,K2)+1]+4*M_PI*M_PI/L/L/sqrt(kx*kx+ky*ky)*__imag__ ifft.fft[klookup(kx,ky,N1,N2)];
|
||||
}
|
||||
}
|
||||
|
||||
if(!irreversible){
|
||||
double Dalpha=lyapunov_D_alpha(flow,u,K1,K2,N1,N2,alpha,L,g,T,ifft.fft);
|
||||
for(kx=0;kx<=K1;kx++){
|
||||
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
|
||||
// real part
|
||||
out[2*klookup_sym(kx,ky,K2)]+=4*M_PI*M_PI/L/L*(kx*kx+ky*ky)*Dalpha*__real__ u[klookup_sym(kx,ky,K2)];
|
||||
// imaginary part
|
||||
out[2*klookup_sym(kx,ky,K2)+1]+=4*M_PI*M_PI/L/L*(kx*kx+ky*ky)*Dalpha*__imag__ u[klookup_sym(kx,ky,K2)];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
// Compute T from the already computed fourier transforms of u
|
||||
int lyapunov_T(
|
||||
int N1,
|
||||
int N2,
|
||||
fft_vect fftu1,
|
||||
fft_vect fftu2,
|
||||
fft_vect fftu3,
|
||||
fft_vect fftu4,
|
||||
fft_vect ifft
|
||||
){
|
||||
int i;
|
||||
|
||||
for(i=0;i<N1*N2;i++){
|
||||
ifft.fft[i]=fftu1.fft[i]*fftu3.fft[i]-fftu2.fft[i]*fftu4.fft[i];
|
||||
}
|
||||
// inverse fft
|
||||
fftw_execute(ifft.fft_plan);
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
// compute derivative of T
|
||||
int lyapunov_D_T(
|
||||
double* flow,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
fft_vect fftu1,
|
||||
fft_vect fftu2,
|
||||
fft_vect fftu3,
|
||||
fft_vect fftu4,
|
||||
fft_vect fft1,
|
||||
fft_vect ifft
|
||||
){
|
||||
int i;
|
||||
int kx,ky;
|
||||
|
||||
// F(px/|p|*u)*F(qy*|q|*delta)
|
||||
// init to 0
|
||||
for(i=0; i<N1*N2; i++){
|
||||
fft1.fft[i]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
fft1.fft[klookup(kx,ky,N1,N2)]=ky*sqrt(kx*kx+ky*ky)*lyapunov_delta_getval_sym(flow, kx,ky,K2)/N2;
|
||||
}
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(fft1.fft_plan);
|
||||
// write to ifft
|
||||
for(i=0;i<N1*N2;i++){
|
||||
ifft.fft[i]=fftu1.fft[i]*fft1.fft[i];
|
||||
}
|
||||
|
||||
// F(px/|p|*delta)*F(qy*|q|*p)
|
||||
// init to 0
|
||||
for(i=0; i<N1*N2; i++){
|
||||
fft1.fft[i]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
fft1.fft[klookup(kx,ky,N1,N2)]=kx/sqrt(kx*kx+ky*ky)*lyapunov_delta_getval_sym(flow, kx,ky,K2)/N1;
|
||||
}
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(fft1.fft_plan);
|
||||
// write to ifft
|
||||
for(i=0;i<N1*N2;i++){
|
||||
ifft.fft[i]=fftu2.fft[i]*fft1.fft[i];
|
||||
}
|
||||
|
||||
// F(py/|p|*u)*F(qx*|q|*delta)
|
||||
// init to 0
|
||||
for(i=0; i<N1*N2; i++){
|
||||
fft1.fft[i]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
fft1.fft[klookup(kx,ky,N1,N2)]=kx*sqrt(kx*kx+ky*ky)*lyapunov_delta_getval_sym(flow, kx,ky,K2)/N2;
|
||||
}
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(fft1.fft_plan);
|
||||
// write to ifft
|
||||
for(i=0;i<N1*N2;i++){
|
||||
ifft.fft[i]=ifft.fft[i]-fftu3.fft[i]*fft1.fft[i];
|
||||
}
|
||||
|
||||
// F(py/|p|*delta)*F(qx*|q|*u)
|
||||
// init to 0
|
||||
for(i=0; i<N1*N2; i++){
|
||||
fft1.fft[i]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
fft1.fft[klookup(kx,ky,N1,N2)]=ky/sqrt(kx*kx+ky*ky)*lyapunov_delta_getval_sym(flow, kx,ky,K2)/N1;
|
||||
}
|
||||
}
|
||||
}
|
||||
// fft
|
||||
fftw_execute(fft1.fft_plan);
|
||||
// write to ifft
|
||||
for(i=0;i<N1*N2;i++){
|
||||
ifft.fft[i]=ifft.fft[i]-fftu4.fft[i]*fft1.fft[i];
|
||||
}
|
||||
|
||||
// inverse fft
|
||||
fftw_execute(ifft.fft_plan);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
double lyapunov_D_alpha(
|
||||
double* flow,
|
||||
_Complex double* u,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
double alpha,
|
||||
double L,
|
||||
_Complex double* g,
|
||||
_Complex double* T,
|
||||
_Complex double* DT
|
||||
){
|
||||
int kx,ky;
|
||||
|
||||
_Complex double num=0.;
|
||||
_Complex double denom=0.;
|
||||
|
||||
for(kx=0;kx<=K1;kx++){
|
||||
for(ky=(kx>0 ? -K2 : 1);ky<=K2;ky++){
|
||||
num+=L*L/4/M_PI/M_PI*(kx*kx+ky*ky)*(flow[2*klookup_sym(kx,ky,K2)]*(__real__ g[klookup_sym(kx,ky,K2)])+flow[2*klookup_sym(kx,ky,K2)+1]*(__imag__ g[klookup_sym(kx,ky,K2)]))//
|
||||
+sqrt(kx*kx+ky*ky)*(flow[2*klookup_sym(kx,ky,K2)]*(__real__ T[klookup_sym(kx,ky,K2)])+flow[2*klookup_sym(kx,ky,K2)+1]*(__imag__ T[klookup_sym(kx,ky,K2)])//
|
||||
// recall that DT is ifft.fft, so is of size N1xN2
|
||||
+__real__(conj(u[klookup_sym(kx,ky,K2)])*DT[klookup(kx,ky,N1,N2)]))//
|
||||
-2*alpha*(kx*kx+ky*ky)*(kx*kx+ky*ky)*(flow[2*klookup_sym(kx,ky,K2)]*(__real__ u[klookup_sym(kx,ky,K2)])+flow[2*klookup_sym(kx,ky,K2)+1]*(__imag__ u[klookup_sym(kx,ky,K2)]));
|
||||
denom+=(kx*kx+ky*ky)*(kx*kx+ky*ky)*__real__(u[klookup_sym(kx,ky,K2)]*conj(u[klookup_sym(kx,ky,K2)]));
|
||||
}
|
||||
}
|
||||
|
||||
return num/denom;
|
||||
}
|
||||
|
||||
// get delta_{kx,ky} from a vector delta in which only the values for kx>=0 are stored, as separate real part and imaginary part
|
||||
_Complex double lyapunov_delta_getval_sym(
|
||||
double* delta,
|
||||
int kx,
|
||||
int ky,
|
||||
int K2
|
||||
){
|
||||
if(kx>0 || (kx==0 && ky>0)){
|
||||
return delta[2*klookup_sym(kx,ky,K2)]+delta[2*klookup_sym(kx,ky,K2)+1]*_Complex_I;
|
||||
}
|
||||
else if(kx==0 && ky==0){
|
||||
return 0;
|
||||
} else {
|
||||
return delta[2*klookup_sym(-kx,-ky,K2)]-delta[2*klookup_sym(-kx,-ky,K2)+1]*_Complex_I;
|
||||
}
|
||||
}
|
||||
|
||||
// compute ffts of u for future use in DT
|
||||
int lyapunov_fft_u_T(
|
||||
_Complex double* u,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
fft_vect fftu1,
|
||||
fft_vect fftu2,
|
||||
fft_vect fftu3,
|
||||
fft_vect fftu4
|
||||
){
|
||||
int kx,ky;
|
||||
int i;
|
||||
|
||||
// F(px/|p|*u)*F(qy*|q|*u)
|
||||
// init to 0
|
||||
for(i=0; i<N1*N2; i++){
|
||||
fftu1.fft[i]=0;
|
||||
fftu2.fft[i]=0;
|
||||
fftu3.fft[i]=0;
|
||||
fftu4.fft[i]=0;
|
||||
}
|
||||
// fill modes
|
||||
for(kx=-K1;kx<=K1;kx++){
|
||||
for(ky=-K2;ky<=K2;ky++){
|
||||
if(kx!=0 || ky!=0){
|
||||
fftu1.fft[klookup(kx,ky,N1,N2)]=kx/sqrt(kx*kx+ky*ky)*getval_sym(u, kx,ky,K2)/N1;
|
||||
fftu2.fft[klookup(kx,ky,N1,N2)]=ky*sqrt(kx*kx+ky*ky)*getval_sym(u, kx,ky,K2)/N2;
|
||||
fftu3.fft[klookup(kx,ky,N1,N2)]=ky/sqrt(kx*kx+ky*ky)*getval_sym(u, kx,ky,K2)/N1;
|
||||
fftu4.fft[klookup(kx,ky,N1,N2)]=kx*sqrt(kx*kx+ky*ky)*getval_sym(u, kx,ky,K2)/N2;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// fft
|
||||
fftw_execute(fftu1.fft_plan);
|
||||
fftw_execute(fftu2.fft_plan);
|
||||
fftw_execute(fftu3.fft_plan);
|
||||
fftw_execute(fftu4.fft_plan);
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
int lyapunov_init_tmps(
|
||||
double ** lyapunov,
|
||||
double ** lyapunov_avg,
|
||||
double ** Du_prod,
|
||||
double ** Du,
|
||||
double ** flow,
|
||||
_Complex double ** u,
|
||||
_Complex double ** prevu,
|
||||
_Complex double ** tmp1,
|
||||
_Complex double ** tmp2,
|
||||
_Complex double ** tmp3,
|
||||
double ** tmp1,
|
||||
double ** tmp2,
|
||||
double ** tmp3,
|
||||
_Complex double ** tmp4,
|
||||
_Complex double ** tmp5,
|
||||
_Complex double ** tmp6,
|
||||
_Complex double ** tmp7,
|
||||
_Complex double ** tmp8,
|
||||
_Complex double ** tmp9,
|
||||
double ** tmp10,
|
||||
_Complex double ** tmp10,
|
||||
double ** tmp11,
|
||||
fft_vect* fftu1,
|
||||
fft_vect* fftu2,
|
||||
fft_vect* fftu3,
|
||||
fft_vect* fftu4,
|
||||
fft_vect* fft1,
|
||||
fft_vect* fft2,
|
||||
fft_vect* ifft,
|
||||
int K1,
|
||||
int K2,
|
||||
int N1,
|
||||
int N2,
|
||||
unsigned int nthreads,
|
||||
unsigned int algorithm
|
||||
unsigned int algorithm,
|
||||
unsigned int algorithm_lyapunov
|
||||
){
|
||||
ns_init_tmps(u, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8, tmp9, fft1, fft2, ifft, K1, K2, N1, N2, nthreads, algorithm);
|
||||
// velocity field
|
||||
*u=calloc(USIZE,sizeof(_Complex double));
|
||||
|
||||
// allocate tmp vectors for computation
|
||||
if(algorithm_lyapunov==ALGORITHM_RK2){
|
||||
*tmp1=calloc(MATSIZE,sizeof(double));
|
||||
*tmp2=calloc(MATSIZE,sizeof(double));
|
||||
} else if (algorithm_lyapunov==ALGORITHM_RK4){
|
||||
*tmp1=calloc(MATSIZE,sizeof(double));
|
||||
*tmp2=calloc(MATSIZE,sizeof(double));
|
||||
*tmp3=calloc(MATSIZE,sizeof(double));
|
||||
} else {
|
||||
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm_lyapunov);
|
||||
};
|
||||
*tmp11=calloc(MATSIZE*MATSIZE,sizeof(double));
|
||||
|
||||
ns_init_tmps(u, tmp4, tmp5, tmp6, tmp7, tmp8, tmp9, tmp10, fft1, fftu1, ifft, K1, K2, N1, N2, nthreads, algorithm);
|
||||
|
||||
// prepare vectors for fft
|
||||
fftu2->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
|
||||
fftu2->fft_plan=fftw_plan_dft_2d(N1,N2, fftu2->fft, fftu2->fft, FFTW_FORWARD, FFTW_MEASURE);
|
||||
fftu3->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
|
||||
fftu3->fft_plan=fftw_plan_dft_2d(N1,N2, fftu3->fft, fftu3->fft, FFTW_FORWARD, FFTW_MEASURE);
|
||||
fftu4->fft=fftw_malloc(sizeof(fftw_complex)*N1*N2);
|
||||
fftu4->fft_plan=fftw_plan_dft_2d(N1,N2, fftu4->fft, fftu4->fft, FFTW_FORWARD, FFTW_MEASURE);
|
||||
|
||||
*lyapunov=calloc(MATSIZE,sizeof(double));
|
||||
*lyapunov_avg=calloc(MATSIZE,sizeof(double));
|
||||
*Du_prod=calloc(MATSIZE*MATSIZE,sizeof(double));
|
||||
*Du=calloc(MATSIZE*MATSIZE,sizeof(double));
|
||||
*prevu=calloc(USIZE,sizeof(_Complex double));
|
||||
*tmp1=calloc(USIZE,sizeof(_Complex double));
|
||||
*tmp2=calloc(USIZE,sizeof(_Complex double));
|
||||
*tmp10=calloc(MATSIZE*MATSIZE,sizeof(double));
|
||||
*flow=calloc(MATSIZE*MATSIZE,sizeof(double));
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
// release vectors
|
||||
int lyapunov_free_tmps(
|
||||
double* lyapunov,
|
||||
double* lyapunov_avg,
|
||||
double* Du_prod,
|
||||
double* Du,
|
||||
_Complex double* u,
|
||||
_Complex double* prevu,
|
||||
_Complex double* tmp1,
|
||||
_Complex double* tmp2,
|
||||
_Complex double* tmp3,
|
||||
_Complex double* tmp4,
|
||||
_Complex double* tmp5,
|
||||
_Complex double* tmp6,
|
||||
_Complex double* tmp7,
|
||||
_Complex double* tmp8,
|
||||
_Complex double* tmp9,
|
||||
double* tmp10,
|
||||
double * lyapunov,
|
||||
double * lyapunov_avg,
|
||||
double * flow,
|
||||
_Complex double * u,
|
||||
double * tmp1,
|
||||
double * tmp2,
|
||||
double * tmp3,
|
||||
_Complex double * tmp4,
|
||||
_Complex double * tmp5,
|
||||
_Complex double * tmp6,
|
||||
_Complex double * tmp7,
|
||||
_Complex double * tmp8,
|
||||
_Complex double * tmp9,
|
||||
_Complex double * tmp10,
|
||||
double * tmp11,
|
||||
fft_vect fftu1,
|
||||
fft_vect fftu2,
|
||||
fft_vect fftu3,
|
||||
fft_vect fftu4,
|
||||
fft_vect fft1,
|
||||
fft_vect fft2,
|
||||
fft_vect ifft,
|
||||
unsigned int algorithm
|
||||
unsigned int algorithm,
|
||||
unsigned int algorithm_lyapunov
|
||||
){
|
||||
free(tmp10);
|
||||
free(tmp2);
|
||||
free(tmp1);
|
||||
free(prevu);
|
||||
free(Du);
|
||||
free(Du_prod);
|
||||
free(lyapunov_avg);
|
||||
free(flow);
|
||||
free(lyapunov);
|
||||
ns_free_tmps(u, tmp3, tmp4, tmp5, tmp6, tmp7, tmp8, tmp9, fft1, fft2, ifft, algorithm);
|
||||
free(lyapunov_avg);
|
||||
|
||||
fftw_destroy_plan(fftu2.fft_plan);
|
||||
fftw_destroy_plan(fftu3.fft_plan);
|
||||
fftw_destroy_plan(fftu4.fft_plan);
|
||||
fftw_free(fftu2.fft);
|
||||
fftw_free(fftu3.fft);
|
||||
fftw_free(fftu4.fft);
|
||||
|
||||
ns_free_tmps(u, tmp4, tmp5, tmp6, tmp7, tmp8, tmp9, tmp10, fft1, fftu1, ifft, algorithm);
|
||||
|
||||
free(tmp11);
|
||||
if(algorithm_lyapunov==ALGORITHM_RK2){
|
||||
free(tmp1);
|
||||
free(tmp2);
|
||||
} else if (algorithm_lyapunov==ALGORITHM_RK4){
|
||||
free(tmp1);
|
||||
free(tmp2);
|
||||
free(tmp3);
|
||||
} else {
|
||||
fprintf(stderr,"bug: unknown algorithm: %u, contact ian.jauslin@rutgers,edu\n",algorithm_lyapunov);
|
||||
};
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
@ -20,18 +20,41 @@ limitations under the License.
|
||||
#include "navier-stokes.h"
|
||||
|
||||
// compute Lyapunov exponents
|
||||
int lyapunov( int K1, int K2, int N1, int N2, double final_time, double lyapunov_reset, double nu, double D_epsilon, double delta, double L, double adaptive_tolerance, double adaptive_factor, double max_delta, unsigned int adaptive_norm, _Complex double* u0, _Complex double* g, bool irreversible, bool keep_en_cst, double target_en, unsigned int algorithm, double starting_time, unsigned int nthreads);
|
||||
int lyapunov( int K1, int K2, int N1, int N2, double final_time, double lyapunov_reset, unsigned int lyapunov_trigger, double nu, double delta, double L, double adaptive_tolerance, double adaptive_factor, double max_delta, unsigned int adaptive_norm, _Complex double* u0, _Complex double* g, bool irreversible, bool keep_en_cst, double target_en, unsigned int algorithm, unsigned int algorithm_lyapunov, double starting_time, unsigned int nthreads);
|
||||
|
||||
// comparison function for qsort
|
||||
int compare_double(const void* x, const void* y);
|
||||
|
||||
// Jacobian of step
|
||||
int ns_D_step( double* out, _Complex double* un, _Complex double* un_next, int K1, int K2, int N1, int N2, double nu, double epsilon, double delta, unsigned int algorithm, double adaptive_tolerance, double adaptive_factor, double max_delta, unsigned int adaptive_norm, double L, _Complex double* g, double time, fft_vect fft1, fft_vect fft2, fft_vect ifft, _Complex double* tmp1, _Complex double* tmp2, _Complex double* tmp3, _Complex double* tmp4, _Complex double* tmp5, _Complex double* tmp6, _Complex double* tmp7, _Complex double* tmp8, bool irreversible, bool keep_en_cst, double target_en);
|
||||
// compute tangent flow
|
||||
int lyapunov_D_step( double* flow, _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, unsigned int algorithm, double L, _Complex double* g, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4, fft_vect fft1, fft_vect ifft, double* tmp1, double* tmp2, double* tmp3, _Complex double* tmp4, bool irreversible);
|
||||
|
||||
// RK 4 algorithm
|
||||
int lyapunov_D_step_rk4( double* flow, _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, _Complex double* T, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4, fft_vect fft1, fft_vect ifft, double* tmp1, double* tmp2, double* tmp3, bool irreversible);
|
||||
|
||||
// RK 2 algorithm
|
||||
int lyapunov_D_step_rk2( double* flow, _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, _Complex double* T, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4, fft_vect fft1, fft_vect ifft, double* tmp1, double* tmp2, bool irreversible);
|
||||
|
||||
// Right side of equation for tangent flow
|
||||
int lyapunov_D_rhs( double* out, double* flow, _Complex double* u, int K1, int K2, int N1, int N2, double alpha, double L, _Complex double* g, _Complex double* T, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4, fft_vect fft1, fft_vect ifft, bool irreversible);
|
||||
|
||||
// Compute T from the already computed fourier transforms of u
|
||||
int lyapunov_T( int N1, int N2, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4, fft_vect ifft);
|
||||
|
||||
// compute derivative of T
|
||||
int lyapunov_D_T( double* flow, int K1, int K2, int N1, int N2, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4, fft_vect fft1, fft_vect ifft);
|
||||
|
||||
double lyapunov_D_alpha( double* flow, _Complex double* u, int K1, int K2, int N1, int N2, double alpha, double L, _Complex double* g, _Complex double* T, _Complex double* DT);
|
||||
|
||||
// get delta_{kx,ky} from a vector delta in which only the values for kx>=0 are stored, as separate real part and imaginary part
|
||||
_Complex double lyapunov_delta_getval_sym( double* delta, int kx, int ky, int K2);
|
||||
|
||||
// compute ffts of u for future use in DT
|
||||
int lyapunov_fft_u_T( _Complex double* u, int K1, int K2, int N1, int N2, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4);
|
||||
|
||||
int lyapunov_init_tmps( double ** lyapunov, double ** lyapunov_avg, double ** flow, _Complex double ** u, double ** tmp1, double ** tmp2, double ** tmp3, _Complex double ** tmp4, _Complex double ** tmp5, _Complex double ** tmp6, _Complex double ** tmp7, _Complex double ** tmp8, _Complex double ** tmp9, _Complex double ** tmp10, double ** tmp11, fft_vect* fftu1, fft_vect* fftu2, fft_vect* fftu3, fft_vect* fftu4, fft_vect* fft1, fft_vect* ifft, int K1, int K2, int N1, int N2, unsigned int nthreads, unsigned int algorithm, unsigned int algorithm_lyapunov);
|
||||
|
||||
// init vectors
|
||||
int lyapunov_init_tmps(double** lyapunov, double** lyapunov_avg, double ** Du_prod, double ** Du, _Complex double ** u, _Complex double ** prevu, _Complex double ** tmp1, _Complex double ** tmp2, _Complex double ** tmp3, _Complex double ** tmp4, _Complex double ** tmp5, _Complex double ** tmp6, _Complex double ** tmp7, _Complex double ** tmp8, _Complex double ** tmp9, double** tmp10, fft_vect* fft1, fft_vect* fft2, fft_vect* ifft, int K1, int K2, int N1, int N2, unsigned int nthreads, unsigned int algorithm);
|
||||
// release vectors
|
||||
int lyapunov_free_tmps(double* lyapunov, double* lyapunov_avg, double* Du_prod, double* Du, _Complex double* u, _Complex double* prevu, _Complex double* tmp1, _Complex double* tmp2, _Complex double* tmp3, _Complex double* tmp4, _Complex double* tmp5, _Complex double* tmp6, _Complex double* tmp7, _Complex double* tmp8, _Complex double* tmp9, double* tmp10, fft_vect fft1, fft_vect fft2, fft_vect ifft, unsigned int algorithm);
|
||||
int lyapunov_free_tmps( double * lyapunov, double * lyapunov_avg, double * flow, _Complex double * u, double * tmp1, double * tmp2, double * tmp3, _Complex double * tmp4, _Complex double * tmp5, _Complex double * tmp6, _Complex double * tmp7, _Complex double * tmp8, _Complex double * tmp9, _Complex double * tmp10, double * tmp11, fft_vect fftu1, fft_vect fftu2, fft_vect fftu3, fft_vect fftu4, fft_vect fft1, fft_vect ifft, unsigned int algorithm, unsigned int algorithm_lyapunov);
|
||||
|
||||
#endif
|
||||
|
||||
|
||||
61
src/main.c
61
src/main.c
@ -56,10 +56,12 @@ typedef struct nstrophy_parameters {
|
||||
unsigned int driving;
|
||||
unsigned int init;
|
||||
unsigned int algorithm;
|
||||
unsigned int algorithm_lyapunov;
|
||||
bool keep_en_cst;
|
||||
FILE* initfile;
|
||||
FILE* drivingfile;
|
||||
double lyapunov_reset;
|
||||
unsigned int lyapunov_trigger;
|
||||
double D_epsilon;
|
||||
bool print_alpha;
|
||||
} nstrophy_parameters;
|
||||
@ -296,7 +298,7 @@ int main (
|
||||
quiet(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.final_time, parameters.nu, parameters.delta, parameters.L, parameters.adaptive_tolerance, parameters.adaptive_factor, parameters.max_delta, parameters.adaptive_cost, parameters.starting_time, u0, g, parameters.irreversible, parameters.keep_en_cst, parameters.init_enstrophy, parameters.algorithm, nthreads, savefile);
|
||||
}
|
||||
else if(command==COMMAND_LYAPUNOV){
|
||||
lyapunov(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.final_time, parameters.lyapunov_reset, parameters.nu, parameters.D_epsilon, parameters.delta, parameters.L, parameters.adaptive_tolerance, parameters.adaptive_factor, parameters.max_delta, parameters.adaptive_cost, u0, g, parameters.irreversible, parameters.keep_en_cst, parameters.init_enstrophy, parameters.algorithm, parameters.starting_time, nthreads);
|
||||
lyapunov(parameters.K1, parameters.K2, parameters.N1, parameters.N2, parameters.final_time, parameters.lyapunov_reset, parameters.lyapunov_trigger, parameters.nu, parameters.delta, parameters.L, parameters.adaptive_tolerance, parameters.adaptive_factor, parameters.max_delta, parameters.adaptive_cost, u0, g, parameters.irreversible, parameters.keep_en_cst, parameters.init_enstrophy, parameters.algorithm, parameters.algorithm_lyapunov, parameters.starting_time, nthreads);
|
||||
}
|
||||
else if(command==0){
|
||||
fprintf(stderr, "error: no command specified\n");
|
||||
@ -576,6 +578,9 @@ int set_default_params(
|
||||
parameters->initfile=NULL;
|
||||
parameters->algorithm=ALGORITHM_RK4;
|
||||
parameters->keep_en_cst=false;
|
||||
parameters->algorithm_lyapunov=ALGORITHM_RK4;
|
||||
// default lyapunov_reset will be print_time (set later) for now set target to 0 to indicate it hasn't been set explicitly
|
||||
parameters->lyapunov_trigger=0;
|
||||
|
||||
parameters->print_alpha=false;
|
||||
|
||||
@ -648,6 +653,12 @@ int read_params(
|
||||
parameters->N2=smallest_pow2(3*(parameters->K2));
|
||||
}
|
||||
|
||||
// if lyapunov_reset or lyapunov_maxu are not set explicitly
|
||||
if(parameters->lyapunov_trigger==0){
|
||||
parameters->lyapunov_trigger=LYAPUNOV_TRIGGER_TIME;
|
||||
parameters->lyapunov_reset=parameters->print_freq;
|
||||
}
|
||||
|
||||
return(0);
|
||||
}
|
||||
|
||||
@ -841,13 +852,6 @@ int set_parameter(
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"lyapunov_reset")==0){
|
||||
ret=sscanf(rhs,"%lf",&(parameters->lyapunov_reset));
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'lyapunov_reset' should be a double\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"D_epsilon")==0){
|
||||
ret=sscanf(rhs,"%lf",&(parameters->D_epsilon));
|
||||
if(ret!=1){
|
||||
@ -940,6 +944,47 @@ int set_parameter(
|
||||
}
|
||||
parameters->print_alpha=(tmp==1);
|
||||
}
|
||||
else if (strcmp(lhs,"lyapunov_reset")==0){
|
||||
if(parameters->lyapunov_trigger==LYAPUNOV_TRIGGER_SIZE){
|
||||
fprintf(stderr, "error: cannot use 'lyapunov_reset' and 'lyapunov_maxu' in the same run:\n 'lyapunov_reset' is to be used to renormalize the tangent flow at fixed times, 'lyapunov_maxu' is to be used to renormalize the tangent flow when the matrix exceeds a certain size.");
|
||||
return(-1);
|
||||
}
|
||||
parameters->lyapunov_trigger=LYAPUNOV_TRIGGER_TIME;
|
||||
ret=sscanf(rhs,"%lf",&(parameters->lyapunov_reset));
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'lyapunov_reset' should be a double\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else if (strcmp(lhs,"lyapunov_maxu")==0){
|
||||
if(parameters->lyapunov_trigger==LYAPUNOV_TRIGGER_TIME){
|
||||
fprintf(stderr, "error: cannot use 'lyapunov_maxu' and 'lyapunov_reset' in the same run:\n 'lyapunov_reset' is to be used to renormalize the tangent flow at fixed times, 'lyapunov_maxu' is to be used to renormalize the tangent flow when the matrix exceeds a certain size.");
|
||||
return(-1);
|
||||
}
|
||||
parameters->lyapunov_trigger=LYAPUNOV_TRIGGER_SIZE;
|
||||
ret=sscanf(rhs,"%lf",&(parameters->lyapunov_reset));
|
||||
if(ret!=1){
|
||||
fprintf(stderr, "error: parameter 'lyapunov_maxu' should be a double\n got '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
// algorithm for tangent flow (for lyapunov)
|
||||
else if (strcmp(lhs,"algorithm_lyapunov")==0){
|
||||
if (strcmp(rhs,"RK4")==0){
|
||||
parameters->algorithm_lyapunov=ALGORITHM_RK4;
|
||||
}
|
||||
else if (strcmp(rhs,"RK2")==0){
|
||||
parameters->algorithm_lyapunov=ALGORITHM_RK2;
|
||||
}
|
||||
else if (strcmp(rhs,"RKF45")==0 || strcmp(rhs,"RKDP45")==0 || strcmp(rhs,"RKBS32")==0){
|
||||
fprintf(stderr, "error: cannot use an adaptove step algorithm for the tangent flow (Lyapunov exponents); must be one of 'RK4' or 'RK2', got:'%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
else{
|
||||
fprintf(stderr, "error: unrecognized algorithm '%s'\n",rhs);
|
||||
return(-1);
|
||||
}
|
||||
}
|
||||
else{
|
||||
fprintf(stderr, "error: unrecognized parameter '%s'\n",lhs);
|
||||
return(-1);
|
||||
|
||||
@ -82,7 +82,7 @@ int uk(
|
||||
// add 0.1 to ensure proper rounding
|
||||
uint64_t n=(uint64_t)((starting_time-fmod(starting_time, print_freq))/print_freq+0.1);
|
||||
|
||||
// store step (useful for adaptive step methods
|
||||
// store step (useful for adaptive step methods)
|
||||
double step=delta;
|
||||
double next_step=step;
|
||||
|
||||
@ -524,6 +524,7 @@ int ns_step(
|
||||
return (0);
|
||||
}
|
||||
|
||||
// TODO: do not need to use klookup in any of the rk routines
|
||||
// RK 4 algorithm
|
||||
int ns_step_rk4(
|
||||
_Complex double* u,
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user