math_util.h

#pragma once
 
/*
  Various Useful Math Utilities for nec2++
  
  Copyright (C) 2004-2015  Timothy C.A. Molteno
  tim@molteno.net 
  
  This program is free software; you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation; either version 2 of the License, or
  (at your option) any later version.
  
  This program is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
  
  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*/
 
#include "common.h"
 
 
#include "safe_array.h"
 
typedef safe_array<int32_t>    int_array;
typedef safe_array<nec_float>  real_array;
typedef safe_array<nec_complex> complex_array;
 
typedef safe_matrix<int32_t>    int_matrix;
typedef safe_matrix<nec_float>  real_matrix;
typedef safe_matrix<nec_complex> complex_matrix;
 
typedef Eigen::Matrix<nec_float,3,1>  nec_3vector;
typedef Eigen::Matrix<nec_complex,3,1> nec_c3vector;
 
inline void vector_fill(complex_array& x, int64_t start, int64_t N, const nec_complex& y) {
  x.fill(start, N, y);
}
 
 
inline nec_complex cplx_00() {
  static nec_complex _cplx00(0.0,0.0); return _cplx00;
}
 
inline nec_complex cplx_01() {
  static nec_complex _cplx01(0.0,1.0); return _cplx01;
}
 
inline nec_complex cplx_10() {
  static nec_complex _cplx10(1.0,0.0); return _cplx10;
}
 
inline nec_complex cplx_11() {
  static nec_complex _cplx11(1.0,1.0); return _cplx11;
}
 
 
inline nec_complex cplx_exp(const nec_float& x) {
  return nec_complex(cos(x),sin(x));
}
 
 
inline nec_float pi() {
  static nec_float _pi = 3.1415926536; return _pi;
}
 
inline nec_float two_pi() {
  static nec_float _tmp = 2.0 * pi(); return _tmp;
}
 
inline nec_float four_pi() {
  static nec_float _tmp = 4.0 * pi(); return _tmp;
}
 
inline nec_float pi_two() {
  static nec_float _tmp = pi() / 2.0; return _tmp;
}
 
inline nec_float sqrt_pi() {  // was SP from common.h
  static nec_float _tmp = sqrt(pi()); return _tmp;
}
 
 
inline nec_complex two_pi_j() {
  static nec_complex _tmp(0.0,two_pi()); return _tmp;
}
 
 
 
inline nec_float rad_to_degrees(nec_float in_radians) {
  static nec_float _rad_to_deg = 360.0 / (2 * pi()); // 57.29577951
  return in_radians * _rad_to_deg;
}
 
inline nec_float degrees_to_rad(nec_float in_degrees) {
  static nec_float _deg_to_rad = (2 * pi()) / 360.0;
  return in_degrees * _deg_to_rad;
}
 
inline nec_complex deg_polar(nec_float r, nec_float theta) {
  return std::polar(r, degrees_to_rad(theta));
}
 
 
inline nec_float arg_degrees(nec_complex z) {
  return rad_to_degrees(std::arg(z));
}
 
 
inline nec_float atgn2( nec_float x, nec_float y) {
  if ((0.0 == y) && (0.0 == x))
    return 0.0;
          
  return( std::atan2(y, x) );
}
 
 
inline nec_float db10( nec_float x ) {
  if ( x < 1.0e-20 )
    return( -999.99 );
  
  return( 10.0 * log10(x) );
}
 
inline nec_float from_db10( nec_float x ) {
  if ( x < -99.9 )
    return( 0.0 );
  
  return( std::pow(10,x / 10.0));
}
 
 
inline nec_float db20( nec_float x ) {
  if ( x < 1.0e-20 )
    return( -999.99 );
  
  return( 20.0 * log10(x) );
}
 
 
inline nec_float norm(const nec_float x, const nec_float y) {
  return std::sqrt(x*x + y*y);
}
 
inline nec_float norm2(const nec_float x, const nec_float y, const nec_float z) {
  return (x*x + y*y + z*z);
}
 
inline nec_float norm(const nec_float x, const nec_float y, const nec_float z) {
  return std::sqrt(norm2(x,y,z));
}
 
inline nec_float normL1(const nec_float x, const nec_float y, const nec_float z) {
  return std::fabs(x) + std::fabs(y) + std::fabs(z);
}
 
 
 
 
inline nec_float norm(const nec_3vector& v) {
  return v.norm();
}
 
inline nec_float normL1(const nec_3vector& v) {
  return normL1(v(0), v(1), v(2));
}