std::vector<double> tb_lt_invert_Cpp_impl(double t, const std::vector<double>& lambda1,
const std::vector<double>& lambda2, const std::vector<double>& lambda3,
const int Ap1, const int Bp1, const int Cp1, const int direction,
const int nblocks, const double tol, int& Lmax,
ParallelizationScheme& scheme) {
// auto start = std::chrono::steady_clock::now();
const double double_PI = 3.141592653589793238463, AA = 20.0;
const int matsize = Ap1*Bp1*Cp1;
std::vector<mytype::ComplexVector> ig;
std::vector<double> res(matsize), yvec(matsize);
for (int i=0; i<matsize; ++i) {
yvec[i] = lambda1[i] + lambda2[i] + lambda3[i];
}
/////////////////////////////////////////////////////////////
// The following code computes the inverse Laplace transform
// Algorithm from Abate and Whitt using a Riemann sum
// Levin tranform is used to accelerate the convergence
/////////////////////////////////////////////////////////////
ig.resize(Lmax);
scheme.for_each( boost::make_counting_iterator(0), boost::make_counting_iterator(Lmax),
[&](int w) {
mytype::ComplexNumber s(AA/(2*t),double_PI*(w+1)/t);
ig[w].resize(matsize);
tb_lt_Cpp(s,lambda1,lambda2,lambda3,Ap1,Bp1,Cp1,direction,yvec,ig[w]);
});
mytype::ComplexNumber s(AA/(2*t),0.0);
mytype::ComplexVector psum0(matsize);
tb_lt_Cpp(s,lambda1,lambda2,lambda3,Ap1,Bp1,Cp1,direction,yvec,psum0);
std::for_each(boost::make_counting_iterator(0), boost::make_counting_iterator(matsize),
[&](int i) {
Levin levin(tol); // A struct for Levin transform
double term = 1e16, sdiff = 1e16;
int k = 1;
double psum = real(psum0[i])/(2*t);
double sk,sk1;
while ((std::abs(sdiff) > 1e-16)||(std::abs(term)>1e-3)) {
double sgn = (k%2 == 0) ? 1.0 : -1.0;
term = sgn*real(ig[k-1][i])/t;
psum += term;
double omega = k*term;
sk = levin.next(psum,omega,1.0);
if (k>1) sdiff = sk - sk1;
k++;
sk1 = sk;
if (k > Lmax) {
ig.resize(Lmax+nblocks);
scheme.for_each( boost::make_counting_iterator(0), boost::make_counting_iterator(nblocks),
[&](int w) {
mytype::ComplexNumber s(AA/(2*t),double_PI*(w+Lmax+1)/t);
ig[w+Lmax].resize(matsize);
tb_lt_Cpp(s,lambda1,lambda2,lambda3,Ap1,Bp1,Cp1,direction,yvec,ig[w+Lmax]);
});
Lmax += nblocks;
}
}
res[i] = sk1*exp(AA/2);
});
// Rcpp::Rcout << "Lmax: " << Lmax;
// auto end = std::chrono::steady_clock::now();
//
// using TimingUnits = std::chrono::microseconds;
// Rcpp::Rcout << "Time: " << std::chrono::duration_cast<TimingUnits>(end - start).count() << std::endl;
return(std::move(res));
}
/**
* Maximum entropy estimate by autocorrelation method. Implements
* Yule-Walker method.
*
* @param r
* Vector of correlation coefficients.
* @param n
* Number of lags used by MEM algorithm.
* @param nfft
* Size of fft for display.
* @param spect
* REAL*4 array of length FFT_SIZE in which the spectrum is returned.
* @param errmsg
* ERROR_MESSAGE CHARACTER*130 variable containing error message if an
* an error occurs, ' ' otherwise.
* @param errmsg_s
* Length of \p errmsg
* @param aux
* REAL*4 scratch array of length FFT_SIZE.
*
* @author David Harris
*
* @date December 28, 1984 Last Modified
*
*/
void
mem(float *r,
int n,
int nfft,
float *spect,
char *errmsg,
int errmsg_s,
float *aux) {
int i;
float scale;
float *a, *reflct;
float *A;
float *const Aux = &aux[0] - 1;
float *const R = &r[0] - 1;
float *const Spect = &spect[0] - 1;
UNUSED(errmsg_s);
if((a = (float *)malloc(n*sizeof(float))) == NULL){
strcpy(errmsg, "error allocating memory--mem\n");
return;
}
if((reflct = (float *)malloc(n*sizeof(float))) == NULL){
strcpy(errmsg, "error allocating memory--mem\n");
free(a);
return;
}
A = a-1;
/*
if( n > 100 ){
fstrncpy( errmsg, errmsg_s-1, "MEM *** Maximum order (100) exceeded ***"
, 40 );
return;
}
*/
/* Zero arrays
* */
zero( spect, nfft );
zero( aux, nfft );
/* Invoke Levinson's recursion to compute prediction filter
* */
levin( r, a, reflct, n );
/* Compute transfer function of prediction filter
* */
for( i = 1; i <= n; i++ )
Spect[i] = A[i];
fft( spect, aux, nfft, -1 );
/* Spectral estimate is reciprocal of filter's power spectrum
*
* Scale factor is equal to prediction error
* */
scale = 0.;
for( i = 1; i <= n; i++ )
scale = scale + R[i]*A[i];
for( i = 1; i <= nfft; i++ )
Spect[i] = scale/(powi(Spect[i],2) + powi(Aux[i],2));
/* Bye
* */
free(a); free(reflct);
return;
} /* end of function */