// sv-2.cc
// 		A ZOOM PhysicsVectors tutorial example
//
// 		Tutorial example 2 for the SpaceVector class:
//
// 		Vector properties and arithmetic
//
// * Linear arithmetic
// * Dot and cross products
// * Vector properties

// Key lines are indicated by 				    // <-------------

	// Get the SpaceVector class

#include "ZMutility/ZMenvironment.h"
#include "ZMutility/FixedTypes.h"
#include "PhysicsVectors/SpaceVector.h"
ZM_USING_NAMESPACE( zmpv )
USING( std::cout )
USING( std::endl )

	// This example will use iostream output, so get that --
	// in a portable way.

#include "ZMutility/iostream"
using std::cout;
using std::endl;

int main() {

	// (See tutorial example sv-1 for how to construct and access
	//  SpaceVectors.)

  SpaceVector v1 (2, 4, -7);
  cout << "v1 =" << v1 << endl;
  SpaceVector v2 (3, 90, DEGREES, .1, RADIANS);
	// This is the first example of supplying an angle in DEGREES
  cout << "v2 =" << v2 << endl;

  SpaceVector v3, v4; 	// = (0,0,0)


// ***** Linear arithmetic

	// Here is how to add, subtract, multiply by scalars, and so forth.
	//-----------------------------------------------------------------

   	// Simple addition and subtraction
  v3 = v1 + v2;						    // <-------------
  cout << "v3 = v1 + v2 =" << v3 << endl;

	// Multiplication -- from either side
  v2 = 4*v3 - v1*2;					    // <-------------
  cout << "Now v2 =" << v2 << endl;

	// Division by a scalar
  v1 = v3 / 2.5;					    // <-------------
		// But NOT v1 = 2.5 / v3 !!
  cout << "v3 / 2.5 =" << v1 << endl;

	// Modify and assign operators

  v1 *= 3;						    // <-------------
  cout << "Now v1 =" << v1 << endl;

// ***** Dot and cross products

	// Here is how to take a dot product v1.dot(v2)
	//---------------------------------------------

  Float8 a;
  Float8 b;

	// Dot product is a method, not overloaded * operator

  a = v1.dot(v2);					     // <-------------
  b = v2.dot(v1);	// These will be exactly equal

  cout << "v1.dot(v2) = " << a << " v2.dot(v1) = " << b << endl;

	// Here is how to take a cross product v1.cross(v2)
	//-------------------------------------------------

	// Cross product is a method, not overloaded * or ^ operator.

  v3 = v1.cross(v2);					    // <-------------
  v4 = v2.cross(v1);	// These will be negative of one another

  cout << "v1.cross(v2) = " << v3 << "\n";
  cout << "v2.cross(v1) = " << v4 << endl;


// ***** Vector Properties

	// Here is how to find the magnitude of a vector
	//----------------------------------------------

  v1.set ( 3, 4, 12 );  // The magnitude of this sample should be 13

  Float8 m = v1.mag();					    // <-------------
  cout << "Magnitude of " << v1 << " is " << m << endl;

  	// If you can use the square of the magnitude, that is quicker:

  cout << "Squared magnitude of " << v1 << " is " << v1.mag2() << endl; // <---

  	// The spherical r component happens to be equivalent to mag():

	// Here is how to find relativistic beta and gamma
	//------------------------------------------------

  v2.set ( .04, -.03, .12 );  // Representing a velocity of v2 * speed of light

  Float8 beta = v2.beta();    				    // <-------------
  Float8 gamma = v2.gamma();  // = 1/sqrt(1-beta**2)	    // <-------------
  cout << "For velocity " << v2 << " beta = " << beta <<
		" gamma = " << gamma << endl;

	// beta will match v2.mag() but will throw a WARNING if v2.mag() > 1.
	// gamma will throw a ERROR if v2.mag() >= 1.

  return 0;

} /* end of main */