complex<typename boost::units::subtract_typeof_helper<X,Y>::type>
operator-(const complex<X>& x,const complex<Y>& y)
{
typedef typename boost::units::subtract_typeof_helper<X,Y>::type type;
return complex<type>(x.real()-y.real(),x.imag()-y.imag());
}
void EMLTracker::integrate(complex<double> in)
{
localReplica.tick();
// First bring the signal level of the input to the same as the
// local replicas
in *= baseGain;
complex<double> carrier = localReplica.getCarrier();
complex<double> code = localReplica.getCode() ? plusOne : minusOne;
// mix in the carrier local replica
complex<double> m0 = in * conj(carrier);
// and sum them up.. (yea, the conj of the codes should be a NoOp)
code = conj(code);
early.process(m0, code);
prompt.process(m0, code);
late.process(m0, code);
// Update our sums for normalizing things...
complex<double> lr = conj(carrier) * code;
inSumSq += in.real()*in.real() + in.imag()*in.imag();
lrSumSq += lr.real()*lr.real() + lr.imag()*lr.imag();
}
complex<typename add_typeof_helper<X,Y>::type>
operator+(const complex<X>& x,const complex<Y>& y)
{
typedef typename boost::units::add_typeof_helper<X,Y>::type type;
return complex<type>(x.real()+y.real(),x.imag()+y.imag());
}
complex<typename unary_minus_typeof_helper<X>::type>
operator-(const complex<X>& x)
{
typedef typename unary_minus_typeof_helper<X>::type type;
return complex<type>(-x.real(),-x.imag());
}
complex complex::operator *(complex x)
{
complex y;
y.Re=Re*x.take_Re()-Im*x.take_Im();
y.Im=Re*x.take_Im()+Im*x.take_Re();
return y;
}
/** Implement Exponential Integral function, E1(z), based on formulaes in
*Abramowitz and Stegun (A&S)
* In fact this implementation returns exp(z)*E1(z) where z is a complex number
*
* @param z :: input
* @return exp(z)*E1(z)
*/
complex<double> exponentialIntegral(const complex<double> &z) {
double z_abs = abs(z);
if (z_abs == 0.0) {
// Basically function is infinite in along the real axis for this case
return complex<double>(std::numeric_limits<double>::max(), 0.0);
} else if (z_abs < 10.0) // 10.0 is a guess based on formula 5.1.55 (no idea
// how good it really is)
{
// use formula 5.1.11 in A&S. rewrite last term in 5.1.11 as
// x*sum_n=0 (-1)^n x^n / (n+1)*(n+1)! and then calculate the
// terms in the sum recursively
complex<double> z1(1.0, 0.0);
complex<double> z2(1.0, 0.0);
for (int i = 1; i <= 100; i++) // is max of 100 here best?
{
z2 = -static_cast<double>(i) * (z2 * z) / ((i + 1.0) * (i + 1.0));
z1 += z2;
if (abs(z2) < 1.0E-10 * abs(z1))
break; // i.e. if break loop if little change to term added
}
return exp(z) * (-log(z) - M_EULER + z * z1);
} else {
// use formula 5.1.22 in A&S. See discussion page 231
complex<double> z1(0.0, 0.0);
for (int i = 20; i >= 1; i--) // not sure if 20 is always sensible?
z1 = static_cast<double>(i) / (1.0 + static_cast<double>(i) / (z + z1));
complex<double> retVal = 1.0 / (z + z1);
if (z.real() <= 0.0 && z.imag() == 0.0)
retVal -= exp(z) * complex<double>(0.0, 1.0) * M_PI; // see formula 5.1.7
return retVal;
}
}
complex<double> cos(complex<double> x) {
double cosh(double x);
double cos(double x);
double r = cosh(x.imag())*cos(x.real());
double i = sinh(x.imag())*sin(x.real());
return(complex<double>(r,i));
}
complex<Float> Comms::GlobalSum(complex<Float> z)
{
if (!initialized) { Initialize(); }
#ifdef USE_MPI
Float sendbuf[2];
Float recvbuf[2];
sendbuf[0] = z.real();
sendbuf[1] = z.imag();
MPI_Barrier(MPI_COMM_WORLD);
#ifdef USE_SINGLE
MPI_Reduce( sendbuf, recvbuf, 2, MPI_FLOAT, MPI_SUM, 0, MPI_COMM_WORLD );
#endif
#ifdef USE_DOUBLE
MPI_Reduce( sendbuf, recvbuf, 2, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD );
#endif
#ifdef USE_LONG_DOUBLE
MPI_Reduce( sendbuf, recvbuf, 2, MPI_LONG_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD );
#endif
return complex<Float>(recvbuf[0], recvbuf[1]);
#else
return z;
#endif
}
void write_mandel(std::string name, int x, int y)
{
GIF_image gif(x, y);
for(int i=0; i<256;i++)
{
gif.setColor(i, i, i, (char)255);
}
for (int i = 0; i < y; i++)
{
for (int j = 0; j < x; j++)
{
complex<double> c(c1.real()+j*(c2-c1).real()/X, c1.imag()+i*(c2-c1).imag()/Y);
complex<double> z = 0;
int iter = 0;
while (abs(z) < 2 && iter < MAX_ITER)
{
z = z*z+c;
iter++;
}
gif.setPixel(j, i, ((MAX_ITER-iter)*255)/40);
}
}
gif.writeToFile(name.c_str());
}
complex<typename unary_plus_typeof_helper<X>::type>
operator+(const complex<X>& x)
{
typedef typename unary_plus_typeof_helper<X>::type type;
return complex<type>(x.real(),x.imag());
}
complex operator- (const complex& c1, const complex& c2)
{
double res_re = c1.get_re() - c2.get_re();
double res_im = c1.get_im() - c2.get_im();
complex res{res_re, res_im};
return res;
}
complex<Y>
pow(const complex<Y>& x,const Y& y)
{
std::complex<Y> tmp(x.real(),x.imag());
tmp = std::pow(tmp,y);
return complex<Y>(tmp.real(),tmp.imag());
}
static type value(const complex<quantity<Unit,Y> >& x)
{
const complex<value_type> tmp =
root<static_rational<N,D> >(complex<Y>(x.real().value(),
x.imag().value()));
return type(quantity_type::from_value(tmp.real()),
quantity_type::from_value(tmp.imag()));
}
complex<double> complexAdd(complex<double> x1, complex<double> x2)
{
int x1_real = int(x1.real());
int x2_real = int(x2.real());
int x1_imag = int(x1.imag());
int x2_imag = int(x2.imag());
int r1 = int(bitset<16>(x1_real+x2_real).to_ulong());
int r2 = int(bitset<16>(x1_imag+x2_imag).to_ulong());
return complex<double>(double(r1), double(r2));
}
QTextStream& operator<<(QTextStream& ts, KCValue value)
{
ts << value.type();
switch (value.type()) {
case KCValue::Empty: break;
case KCValue::Boolean:
ts << ": ";
if (value.asBoolean()) ts << "TRUE";
else ts << "FALSE"; break;
case KCValue::Integer:
ts << ": " << value.asInteger(); break;
case KCValue::Float:
ts << ": " << (double) numToDouble(value.asFloat()); break;
case KCValue::Complex: {
const complex<KCNumber> complex(value.asComplex());
ts << ": " << (double) numToDouble(complex.real());
if (complex.imag() >= 0.0)
ts << '+';
ts << (double) numToDouble(complex.imag()) << 'i';
break;
}
case KCValue::String:
ts << ": " << value.asString(); break;
case KCValue::Array: {
ts << ": {" << value.asString();
const int cols = value.columns();
const int rows = value.rows();
for (int row = 0; row < rows; ++row) {
for (int col = 0; col < cols; ++col) {
ts << value.element(col, row);
if (col < cols - 1)
ts << ';';
}
if (row < rows - 1)
ts << '|';
}
ts << '}';
break;
}
case KCValue::Error:
ts << '(' << value.errorMessage() << ')'; break;
default: break;
}
return ts;
}
std::string fmtvalue(std::true_type, const complex<T>& x)
{
std::string restr = as_string(fmt<'g', number_width, number_precision>(x.real()));
if (restr.size() > number_width)
restr = as_string(fmt<'g', number_width, number_precision_short>(x.real()));
std::string imstr = as_string(fmt<'g', -1, number_precision>(std::abs(x.imag())));
if (imstr.size() > number_width)
imstr = as_string(fmt<'g', -1, number_precision_short>(std::abs(x.imag())));
return restr + (x.imag() < T(0) ? "-" : "+") + padleft(number_width, imstr + "j");
}
/* Complex root forward deflation.
*/
static int complexdeflation( const register int n, double a[], const complex<double> z )
{
register int i;
double r, u;
r = -2.0 * z.real();
u = z.real() * z.real() + z.imag() * z.imag();
a[ 1 ] -= r * a[ 0 ];
for( i = 2; i < n - 1; i++ )
a[ i ] = a[ i ] - r * a[ i - 1 ] - u * a[ i - 2 ];
return n - 2;
}
complex<long double> sum_to_all(complex<long double> in) {
complex<long double> out = in;
#ifdef HAVE_MPI
if (MPI_LONG_DOUBLE == MPI_DATATYPE_NULL) {
complex<double> dout;
dout = sum_to_all(complex<double>(double(in.real()), double(in.imag())));
out = complex<long double>(dout.real(), dout.imag());
}
else
MPI_Allreduce(&in,&out,2,MPI_LONG_DOUBLE,MPI_SUM,mycomm);
#endif
return out;
}
void transmissioncom::sendToTransmissionSolver(complex value)
{
uint8_t data[sizeof(double)*2];
double realPart=value.Re();
double imagineryPart=value.Im();
memcpy(&data,&realPart,sizeof(double));
memcpy(&data[sizeof(double)],&imagineryPart,sizeof(double));
OBJECT *hdr = OBJECTHDR(this);
Message *msg=new Message(hdr->name,this->connectedBus,gl_globalclock,(uint8_t*)data,sizeof(double)*2);
msg->setDelayThroughComm(false);
myinterface->send(msg);
}
complex<double> complexMultiply(complex<double> x1, complex<double> x2)
{
int x1_real = int(x1.real());
int x2_real = int(x2.real());
int x1_imag = int(x1.imag());
int x2_imag = int(x2.imag());
int r1 = int(bitset<16>(x1_real*x2_real).to_ulong());
int r2 = int(bitset<16>(x1_imag*x2_imag).to_ulong());
int r3 = int(bitset<16>(x1_real*x2_imag).to_ulong());
int r4 = int(bitset<16>(x1_imag*x2_real).to_ulong());
int m_real = int(bitset<16>(r1-r2).to_ulong());
int m_imag = int(bitset<16>(r3+r4).to_ulong());
return complex<double>(double(m_real), double(m_imag));
}
void Biquad::setZeroPolePairs(const complex<double> &zero, const complex<double> &pole)
{
double b0 = 1;
double b1 = -2 * zero.real();
double zeroMag = abs(zero);
double b2 = zeroMag * zeroMag;
double a1 = -2 * pole.real();
double poleMag = abs(pole);
double a2 = poleMag * poleMag;
setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
}
void put(index_type i, complex<T> val)
{
assert(this->format_ != no_user_format);
if (this->format_ == array_format)
this->u_.data_[i] = val;
else if (this->format_ == interleaved_format)
{
this->u_.split_.real_[2*i+0] = val.real();
this->u_.split_.real_[2*i+1] = val.imag();
}
else // if (format_ == split_format)
{
this->u_.split_.real_[i] = val.real();
this->u_.split_.imag_[i] = val.imag();
}
}
double microturbine::determine_frequency(complex power_out){
//double Kx = 3 * Rinternal / 3.14159;
//used linear approximation which does better job than textbook equation...
//assumes power in W
double f = power_out.Mag() * 1.5 + 55000;\
f = f/60;
return f;
}
bool linesIntersection
(complex<T> p1,complex<T> p2,complex<T> p3,
complex<T> p4,complex<double>& p)
{
if(fabs(dcross(p1-p2,p3-p4))<EPS)return false;
double t=dcross(p3-p1,p3-p4)/dcross(p2-p1,p3-p4);
p.x()=1.0*p1.x()+1.0*(p2.x()-p1.x())*t;
p.y()=1.0*p1.y()+1.0*(p2.y()-p1.y())*t;
return true;
}
complex operator/ (const complex& c1, const complex& c2)
{
double abs2c2 = c2.abs2();
double res_re = (c1.get_re()*c2.get_re() + c1.get_im()*c2.get_im())/abs2c2;
double res_im = (c1.get_im()*c2.get_re() - c1.get_re()*c2.get_im())/abs2c2;
complex res{res_re, res_im};
return res;
}
float EnergyToBeat::transform_bwd (complex beat)
{
m_mutex.lock();
float pos_mean = m_pos_mean;
float pos_variance = m_pos_variance;
m_mutex.unlock();
float pos = max(0.0f, pos_mean + sqrtf(pos_variance) * beat.real());
return powf(pos, 3);
}
void ElectronicStructure::rot(complex<double> Hij,double dt,int i,int j){
/***********************************************************************
Action of operator: exp(iL_ij*dt) = exp(-(i/hbar)*dt*(H_ij*c_j*d/dc_i + H_ji*c_i*d/dc_j)):
exp(iL_ij*dt) = A * B * A, where
A = exp(iL_ij^-), phi = (dt/2) * Im(H_ij)/hbar
B = exp(iL_ij^+), phi = dt * -Re(H_ij)/hbar
composite rotation in plane i,j due to Hamiltonian matrix elements H_ij
note Hamiltonian is Hermitian: H_ij^* = H_ji
***********************************************************************/
double phi1 = 0.5*dt*Hij.imag()/hbar;
double phi2 = -dt*Hij.real()/hbar;
rot1(phi1,i,j);
rot2(phi2,i,j);
rot1(phi1,i,j);
}
double julia(complex c)
{
complex seed(-0.8, 0.156);
double i = 0, n = 200;;
do
{
c = c * c + seed;
} while (++i < n && c.abs() < 5);
return i / (n + 1);
}
int cmp1(complex<double> a,complex<double> b)
{
if(a.real()==b.real())
return a.imag()<=b.imag();
else
return a.real()<b.real();
}
/* https://github.com/AE9RB/fftbench/blob/master/cxlr.hpp
* Nice trick from AE9RB (David Turnbull) to get compiler to produce simpler
* fma (fused multiply-accumulate) instead of worrying about NaN handling
*/
inline complex<float>
operator*(const complex<float>& v1, const complex<float>& v2) {
return complex<float> {
v1.real() * v2.real() - v1.imag() * v2.imag(),
v1.real() * v2.imag() + v1.imag() * v2.real()
};
}