C++ std::atan方法代碼示例

double DirectionCanvas::translateMouseCoords(double trans_x, double trans_y)
{
	// We now have 4 squares. One four every corner.
	// With a cross in the middle.
	// For every square we calculate a different tangent
	// therefore we have to add of substract a number of degrees
	double result = 0;
	if (trans_x >= 0 && trans_y >= 0) {
		// Right down
		double arc_tan = trans_y / trans_x;
		result = 90 + (atan(arc_tan)) * (180/M_PI);
	} else if (trans_x <= 0 && trans_y >= 0) {
		// Left down
		trans_x = trans_x * -1;
		double arc_tan = trans_y / trans_x;
		result = 270 - (atan(arc_tan)) * (180/M_PI);
	} else if (trans_x >= 0 && trans_y <= 0) {
		// Right up
		trans_y = trans_y * -1;
		double arc_tan = trans_y / trans_x;
		result = 90 - (atan(arc_tan)) * (180/M_PI);
	} else if (trans_x <= 0 && trans_y <= 0) {
		// Left up
		trans_x = trans_x * -1;
		trans_y = trans_y * -1;
		double arc_tan = trans_y / trans_x;
		result = 270 + (atan(arc_tan)) * (180/M_PI);
	}
	return result;
}

TEST_F(AgradFwdAtan,FvarFvarDouble) {
  using stan::agrad::fvar;
  using std::atan;

  fvar<fvar<double> > x;
  x.val_.val_ = 1.5;
  x.val_.d_ = 2.0;

  fvar<fvar<double> > a = atan(x);

  EXPECT_FLOAT_EQ(atan(1.5), a.val_.val_);
  EXPECT_FLOAT_EQ(2.0 / (1.0 + 1.5 * 1.5), a.val_.d_);
  EXPECT_FLOAT_EQ(0, a.d_.val_);
  EXPECT_FLOAT_EQ(0, a.d_.d_);

  fvar<fvar<double> > y;
  y.val_.val_ = 1.5;
  y.d_.val_ = 2.0;

  a = atan(y);
  EXPECT_FLOAT_EQ(atan(1.5), a.val_.val_);
  EXPECT_FLOAT_EQ(0, a.val_.d_);
  EXPECT_FLOAT_EQ(2.0 / (1.0 + 1.5 * 1.5), a.d_.val_);
  EXPECT_FLOAT_EQ(0, a.d_.d_);
}

//! Compute Prandtl-Meyer function.
double computePrandtlMeyerFunction( double machNumber, double ratioOfSpecificHeats )
{
    // Declare local variables.
    // Declare Mach number squared.
    double machNumberSquared_ = pow( machNumber, 2.0 );

    // Return value of Prandtl-Meyer function.
    return sqrt ( ( ratioOfSpecificHeats + 1.0 ) / ( ratioOfSpecificHeats - 1.0 ) )
            * atan ( sqrt ( ( ratioOfSpecificHeats - 1.0 ) / ( ratioOfSpecificHeats + 1.0 )
                            * ( machNumberSquared_ - 1.0 ) ) )
            - atan( sqrt ( machNumberSquared_ - 1.0 ) );
}

int main () {
  typedef const double c_dbl;
  typedef const double * c_p_dbl;
  typedef const double * const c_p_c_dbl;
  typedef double * p_dbl;
  typedef double & r_dbl;

  cout << fixed << setprecision(3);

  double my_double = 123.456789;    // Set 1
  cout << "Set1: " << my_double;    // 123.457


  r_dbl r_my_dbl = my_double;       // Set 2  (ref. to my_double)
  r_my_dbl = 987.654321;            // 987.654
  cout << "\nSet2: " << my_double;

  p_dbl p_my_dbl = &my_double;     // Set 3 (pointer to my_double)
  my_double = 1.012345;            // 1.012
  cout << "\nSet3: " << *p_my_dbl;
  
  c_dbl pi = atan(1.0) * 4.0;     // Set 4
  //r_dbl r_pi = pi;              // error because pi is const
  //cout << r_pi;

  c_p_dbl c_p_pi = &pi;           // Set 5  (ptr. to a const double)
  c_p_pi = &my_double;            // adds const modifier
  cout << "\nSet5: " << *c_p_pi;  // 1.012


  c_p_c_dbl cpc_pi = &pi;        // Set 6 (const ptr to const double)
  //cpc_pi = &my_double;         // error, can't change what const ptr points to
  cout << "\nSet6: "<< *cpc_pi << endl;    // 3.142           
}

void app::benchmark::task_func()
{
  using std::atan;

  mcal::irq::disable_all();
  port_type::set_pin_high();

  y = atan(x);

  port_type::set_pin_low();
  mcal::irq::enable_all();

  // atan(4/10) = approx. 0.3805063771123649
  const bool value_is_ok =    (y > (numeric_type(38) / 100))
                           && (y < (numeric_type(39) / 100));

  if(value_is_ok)
  {
    // The benchmark is OK.
    // Perform one nop and leave.

    mcal::cpu::nop();
  }
  else
  {
    // The benchmark result is not OK!
    // Remain in a blocking loop and crash the system.

    for(;;) { mcal::cpu::nop(); }
  }
}

 typename stan::return_type<T_y, T_loc, T_scale>::type 
 ccdf_log_function(const T_y& y, const T_loc& mu, const T_scale& sigma,
                  const T3&, const T4&, const T5&) {
   using std::atan;
   using stan::math::pi;
   using std::log;
   return log(0.5 - atan((y - mu) / sigma) / pi());
 }

  Solution() {
    phip = 0.0;
    using std::atan;
    using std::cos;
    using std::sin;

    phi[X] = atan(-( a[X]/x0[X] )/( omega[X]/omega_prime[X] - omega_prime[X]/omega[X] ));
    phi[Y] = atan(-( a[Y]/x0[Y] )/( omega[Y]/omega_prime[Y] - omega_prime[Y]/omega[Y] ));
    phi[Z] = atan(-( a[Z]/x0[Z] )/( omega[Z]/omega_prime[Z] - omega_prime[Z]/omega[Z] ));

    A[X] = x0[X] / cos(phi[X]);
    A[Y] = x0[Y] / cos(phi[Y]);
    A[Z] = x0[Z] / cos(phi[Z]);

    B[X] = (omega[X]/omega_prime[X]) * sin(phi[X]);
    B[Y] = (omega[Y]/omega_prime[Y]) * sin(phi[Y]);
    B[Z] = (omega[Z]/omega_prime[Z]) * sin(phi[Z]);
  }

void complex_number_examples()
{
    Complex z1{0, 1};
    std::cout << std::setprecision(std::numeric_limits<typename Complex::value_type>::digits10);
    std::cout << std::scientific << std::fixed;
    std::cout << "Print a complex number: " << z1 << std::endl;
    std::cout << "Square it             : " << z1*z1 << std::endl;
    std::cout << "Real part             : " << z1.real() << " = " << real(z1) << std::endl;
    std::cout << "Imaginary part        : " << z1.imag() << " = " << imag(z1) << std::endl;
    using std::abs;
    std::cout << "Absolute value        : " << abs(z1) << std::endl;
    std::cout << "Argument              : " << arg(z1) << std::endl;
    std::cout << "Norm                  : " << norm(z1) << std::endl;
    std::cout << "Complex conjugate     : " << conj(z1) << std::endl;
    std::cout << "Projection onto Riemann sphere: " <<  proj(z1) << std::endl;
    typename Complex::value_type r = 1;
    typename Complex::value_type theta = 0.8;
    using std::polar;
    std::cout << "Polar coordinates (phase = 0)    : " << polar(r) << std::endl;
    std::cout << "Polar coordinates (phase !=0)    : " << polar(r, theta) << std::endl;

    std::cout << "\nElementary special functions:\n";
    using std::exp;
    std::cout << "exp(z1) = " << exp(z1) << std::endl;
    using std::log;
    std::cout << "log(z1) = " << log(z1) << std::endl;
    using std::log10;
    std::cout << "log10(z1) = " << log10(z1) << std::endl;
    using std::pow;
    std::cout << "pow(z1, z1) = " << pow(z1, z1) << std::endl;
    using std::sqrt;
    std::cout << "Take its square root  : " << sqrt(z1) << std::endl;
    using std::sin;
    std::cout << "sin(z1) = " << sin(z1) << std::endl;
    using std::cos;
    std::cout << "cos(z1) = " << cos(z1) << std::endl;
    using std::tan;
    std::cout << "tan(z1) = " << tan(z1) << std::endl;
    using std::asin;
    std::cout << "asin(z1) = " << asin(z1) << std::endl;
    using std::acos;
    std::cout << "acos(z1) = " << acos(z1) << std::endl;
    using std::atan;
    std::cout << "atan(z1) = " << atan(z1) << std::endl;
    using std::sinh;
    std::cout << "sinh(z1) = " << sinh(z1) << std::endl;
    using std::cosh;
    std::cout << "cosh(z1) = " << cosh(z1) << std::endl;
    using std::tanh;
    std::cout << "tanh(z1) = " << tanh(z1) << std::endl;
    using std::asinh;
    std::cout << "asinh(z1) = " << asinh(z1) << std::endl;
    using std::acosh;
    std::cout << "acosh(z1) = " << acosh(z1) << std::endl;
    using std::atanh;
    std::cout << "atanh(z1) = " << atanh(z1) << std::endl;
}

inline double cdf_hcauchy(double x, double sigma, bool& throw_warning) {
#ifdef IEEE_754
  if (ISNAN(x) || ISNAN(sigma))
    return x+sigma;
#endif
  if (sigma <= 0.0) {
    throw_warning = true;
    return NAN;
  }
  if (x < 0.0)
    return 0.0;
  return 2.0/M_PI * atan(x/sigma);
}

//! Compute shock deflection angle.
double computeShockDeflectionAngle( double shockAngle, double machNumber,
                                    double ratioOfSpecificHeats )
{
    // Declare local variables.
    double tangentOfDeflectionAngle_;

    // Calculate tangent of deflection angle.
    tangentOfDeflectionAngle_ = 2.0 * ( pow( machNumber * sin( shockAngle ), 2.0 ) - 1.0 )
            / ( tan( shockAngle ) * ( pow( machNumber, 2.0 )
                                      * ( ratioOfSpecificHeats
                                          + cos( 2.0 * shockAngle ) ) + 2.0 ) );

    // Return deflection angle.
    return atan( tangentOfDeflectionAngle_ );
}

int vectester (Vector zerovec)
{
  using std::abs;
  using std::acos;
  using std::asin;
  using std::atan;
  using std::floor;
  using std::pow;
  using std::sin;
  using std::sqrt;
  using std::tan;

  typedef typename Vector::value_type Scalar;

  Vector random_vec = zerovec;

  Vector error_vec = zerovec;

  std::srand(12345); // Fixed seed for reproduceability of failures

  // Avoid divide by zero errors or acos(x>1) NaNs later
  for (unsigned int i=0; i != random_vec.size(); ++i)
    random_vec.raw_at(i) = .25 + (static_cast<Scalar>(std::rand())/RAND_MAX/2);

  int returnval = 0;

  one_test(2*random_vec - random_vec - random_vec);

  one_test(3*random_vec - random_vec*3);

  one_test((random_vec + random_vec)/2 - random_vec);

  one_test(sqrt(random_vec) * sqrt(random_vec) - random_vec);
  one_test(random_vec*random_vec - pow(random_vec,2));
  one_test(sqrt(random_vec) - pow(random_vec,Scalar(.5)));

  one_test(random_vec - sin(asin(random_vec)));
  one_test(random_vec - tan(atan(random_vec)));

  one_test(floor(random_vec / 2));
  one_test(abs(random_vec) - random_vec);

  return returnval;
}

 static inline real Datan(real x, real y) {
   using std::atan;
   real d = x - y, xy = x * y;
   return d ? (2 * xy > -1 ? atan( d / (1 + xy) ) : atan(x) - atan(y)) / d :
     1 / (1 + xy);
 }

    typename return_type<T_y,T_loc,T_scale>::type
    cauchy_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
        
      // Size checks
      if ( !( stan::length(y) && stan::length(mu) && stan::length(sigma) ) ) return 1.0;
        
      static const char* function = "stan::prob::cauchy_cdf(%1%)";
      
      using stan::math::check_positive;
      using stan::math::check_finite;
      using stan::math::check_not_nan;
      using stan::math::check_consistent_sizes;
      using boost::math::tools::promote_args;
      using stan::math::value_of;

      double P(1.0);
        
      if(!check_not_nan(function, y, "Random variable", &P))
        return P;
        
      if(!check_finite(function, mu, "Location parameter", &P))
        return P;
        
      if(!check_finite(function, sigma, "Scale parameter", &P))
        return P;
        
      if(!check_positive(function, sigma, "Scale parameter", &P))
        return P;

      if (!(check_consistent_sizes(function, y, mu, sigma,
                                   "Random variable", "Location parameter", "Scale Parameter",
                                   &P)))
        return P;
        
      // Wrap arguments in vectors
      VectorView<const T_y> y_vec(y);
      VectorView<const T_loc> mu_vec(mu);
      VectorView<const T_scale> sigma_vec(sigma);
      size_t N = max_size(y, mu, sigma);
        
      agrad::OperandsAndPartials<T_y, T_loc, T_scale> operands_and_partials(y, mu, sigma);
        
      std::fill(operands_and_partials.all_partials,
                operands_and_partials.all_partials + operands_and_partials.nvaris, 0.0);
        
      // Explicit return for extreme values
      // The gradients are technically ill-defined, but treated as zero
      for (size_t i = 0; i < stan::length(y); i++) {
        if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity()) 
          return operands_and_partials.to_var(0.0);
      }
        
      // Compute CDF and its gradients
      using std::atan;
      using stan::math::pi;

      // Compute vectorized CDF and gradient
      for (size_t n = 0; n < N; n++) {
            
        // Explicit results for extreme values
        // The gradients are technically ill-defined, but treated as zero
        if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
          continue;
        }
            
        // Pull out values
        const double y_dbl = value_of(y_vec[n]);
        const double mu_dbl = value_of(mu_vec[n]);
        const double sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
            
        const double z = (y_dbl - mu_dbl) * sigma_inv_dbl;
          
        // Compute
        const double Pn = atan(z) / pi() + 0.5;
            
        P *= Pn;
            
        if (!is_constant_struct<T_y>::value)
          operands_and_partials.d_x1[n] 
            += sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
            
        if (!is_constant_struct<T_loc>::value)
          operands_and_partials.d_x2[n] 
            += - sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
            
        if (!is_constant_struct<T_scale>::value)
          operands_and_partials.d_x3[n] 
            += - z * sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
            
      }
        
      if (!is_constant_struct<T_y>::value) {
        for(size_t n = 0; n < stan::length(y); ++n) operands_and_partials.d_x1[n] *= P;
      }
        
      if (!is_constant_struct<T_loc>::value) {
        for(size_t n = 0; n < stan::length(mu); ++n) operands_and_partials.d_x2[n] *= P;
      }
        
      if (!is_constant_struct<T_scale>::value) {
//.........這裏部分代碼省略.........

void deriv_eq1(T *ans, T &x, double *h, int &size){
    for (int i=0; i<size; i++){
        ans[i] = ( atan(x+h[i])-atan(x) )/h[i];
    }
}

int vectester (Vector zerovec)
{
  using std::abs;
  using std::acos;
  using std::asin;
  using std::atan;
  using std::ceil;
  using std::cos;
  using std::cosh;
  using std::exp;
  using std::fabs;
  using std::floor;
  using std::log;
  using std::log10;
  using std::pow;
  using std::sin;
  using std::sinh;
  using std::sqrt;
  using std::tan;
  using std::tanh;

  typedef typename ValueType<Vector>::type DualScalar;
  typedef typename DualScalar::value_type Scalar;

  Vector random_vec = zerovec;

  typename DerivativeType<Vector>::type error_vec = 0;

  std::srand(12345); // Fixed seed for reproduceability of failures

  // Avoid divide by zero errors later
  for (unsigned int i=0; i != N; ++i)
    {
      random_vec.raw_at(i) = .25 + (static_cast<Scalar>(std::rand())/RAND_MAX);
      random_vec.raw_at(i).derivatives() = 1;
    }

  // Scalar pi = acos(Scalar(-1));

  int returnval = 0;

  // Running non-derivatives tests with DualNumbers sometimes catches
  // problems too

  one_test(2*random_vec - random_vec - random_vec);

  one_test(3*random_vec - random_vec*3);

  one_test((random_vec + random_vec)/2 - random_vec);

  // We had a problem in user code with the mixing of long double and
  // DualNumber<double, DynamicSparseNumberArray>

  one_test(2.L*random_vec - random_vec - 1.f*random_vec);

  // pow() is still having problems with sparse vectors?  Disabling it
  // for now.

  one_test(sqrt(random_vec) * sqrt(random_vec) - random_vec);
//  one_test(random_vec*random_vec - pow(random_vec,2));
//  one_test(sqrt(random_vec) - pow(random_vec,Scalar(.5)));

  // functions which map zero to non-zero are not defined for sparse
  // vectors.  This includes exp(), log(), cos(), cosh(),
  // pow(scalar,sparse), scalar/sparse, sparse +/- scalar...

  // one_test(log(exp(random_vec)) - random_vec);
  // one_test(exp(log(random_vec)) - random_vec);
  // one_test(exp(random_vec) - pow(exp(Scalar(1)), random_vec));

  // one_test(tan(random_vec) - sin(random_vec)/cos(random_vec));
  one_test(random_vec - sin(asin(random_vec)));
  // one_test(random_vec - cos(acos(random_vec)));
  one_test(random_vec - tan(atan(random_vec)));
  // one_test(1 - pow(sin(random_vec), 2) - pow(cos(random_vec), 2));
  // one_test(cos(random_vec) - sin(random_vec + pi/2));

  // one_test(tanh(random_vec) - sinh(random_vec)/cosh(random_vec));
  // one_test(1 + pow(sinh(random_vec), 2) - pow(cosh(random_vec), 2));

  // one_test(log10(random_vec) - log(random_vec)/log(Scalar(10)));

  one_test(floor(random_vec / 2));
  // one_test(ceil(random_vec / 2 - 1));

  one_test(abs(random_vec) - random_vec);
  // one_test(fabs(random_vec-.75) - abs(random_vec-.75));

  // And now for derivatives tests

  // one_test(derivatives(pow(sin(random_vec-2),2)) -
  //          2*sin(random_vec)*cos(random_vec));

  // one_test(derivatives(cos(2*random_vec)) + 2*sin(2*random_vec));
  // one_test(derivatives(tan(.5*random_vec)) - .5/pow(cos(.5*random_vec),2));

  // one_test(derivatives(sqrt(random_vec+1)) - 1/sqrt(random_vec+1)/2);

  // one_test(derivatives((random_vec-1)*(random_vec-1)) - 2*(random_vec-1));

//.........這裏部分代碼省略.........