/// <summary>
/// Constructs a new instance of the <see cref="TVec"/> class using another vector's components.
/// </summary>
/// <param name="first">A vector containing the first vector components to use.</param>
/// <param name="rest">More vector components to add in addition to the components in <paramref name="first"/></param>
public TVec(TVec first, params Term[] rest)
: this(first.terms.Concat(rest ?? System.Linq.Enumerable.Empty <Term>()))
{
/*Contract.Requires(first != null);
* Contract.Requires(Contract.ForAll(rest, term => term != null));
*/
}
/// <summary>
/// Constructs a term representing the inner product of two vectors.
/// </summary>
/// <param name="left">The first vector of the inner product</param>
/// <param name="right">The second vector of the inner product</param>
/// <returns>A term representing the inner product of <paramref name="left"/> and <paramref name="right"/>.</returns>
public static Term InnerProduct(TVec left, TVec right)
{
Guard.NotNull(left, nameof(left));
Guard.NotNull(right, nameof(right));
Guard.MustHold(left.Dimension == right.Dimension, "left and right must be of the same dimension");
var products = from i in Enumerable.Range(0, left.Dimension)
select left.terms[i] * right.terms[i];
return(TermBuilder.Sum(products));
}
/// <summary>
/// Constructs a term representing the inner product of two vectors.
/// </summary>
/// <param name="left">The first vector of the inner product</param>
/// <param name="right">The second vector of the inner product</param>
/// <returns>A term representing the inner product of <paramref name="left"/> and <paramref name="right"/>.</returns>
public static Term InnerProduct(TVec left, TVec right)
{
Contract.Requires(left != null);
Contract.Requires(right != null);
Contract.Requires(left.Dimension == right.Dimension);
Contract.Ensures(Contract.Result <Term>() != null);
var products = from i in System.Linq.Enumerable.Range(0, left.Dimension)
select left.terms[i] * right.terms[i];
return(TermBuilder.Sum(products));
}
/// <summary>
/// Constructs a 3D cross-product vector given two 3D vectors.
/// </summary>
/// <param name="left">The left cross-product term</param>
/// <param name="right">The right cross product term</param>
/// <returns>A vector representing the cross product of <paramref name="left"/> and <paramref name="right"/></returns>
public static TVec CrossProduct(TVec left, TVec right)
{
Guard.NotNull(left, nameof(left));
Guard.NotNull(right, nameof(right));
Guard.MustHold(left.Dimension == 3 && right.Dimension == 3,
"vectors must be three dimensional");
return(new TVec(
left.Y * right.Z - left.Z * right.Y,
left.Z * right.X - left.X * right.Z,
left.X * right.Y - left.Y * right.X
));
}
/// <summary>
/// Constructs a 3D cross-product vector given two 3D vectors.
/// </summary>
/// <param name="left">The left cross-product term</param>
/// <param name="right">The right cross product term</param>
/// <returns>A vector representing the cross product of <paramref name="left"/> and <paramref name="right"/></returns>
public static TVec CrossProduct(TVec left, TVec right)
{
Contract.Requires(left != null);
Contract.Requires(right != null);
Contract.Requires(left.Dimension == 3);
Contract.Requires(right.Dimension == 3);
Contract.Ensures(Contract.Result <TVec>().Dimension == 3);
return(new TVec(
left.Y * right.Z - left.Z * right.Y,
left.Z * right.X - left.X * right.Z,
left.X * right.Y - left.Y * right.X
));
}
/// <summary>
/// Constructs a new instance of the <see cref="TVec"/> class using another vector's components.
/// </summary>
/// <param name="first">A vector containing the first vector components to use.</param>
/// <param name="rest">More vector components to add in addition to the components in <paramref name="first"/></param>
public TVec(TVec first, params Term[] rest)
: this(first.terms.Concat(rest ?? System.Linq.Enumerable.Empty<Term>()))
{
Contract.Requires(first != null);
Contract.Requires(Contract.ForAll(rest, term => term != null));
}
/// <summary>
/// Constructs a 3D cross-product vector given two 3D vectors.
/// </summary>
/// <param name="left">The left cross-product term</param>
/// <param name="right">The right cross product term</param>
/// <returns>A vector representing the cross product of <paramref name="left"/> and <paramref name="right"/></returns>
public static TVec CrossProduct(TVec left, TVec right)
{
Contract.Requires(left != null);
Contract.Requires(right != null);
Contract.Requires(left.Dimension == 3);
Contract.Requires(right.Dimension == 3);
Contract.Ensures(Contract.Result<TVec>().Dimension == 3);
return new TVec(
left.Y * right.Z - left.Z * right.Y,
left.Z * right.X - left.X * right.Z,
left.X * right.Y - left.Y * right.X
);
}
/// <summary>
/// Constructs a term representing the inner product of two vectors.
/// </summary>
/// <param name="left">The first vector of the inner product</param>
/// <param name="right">The second vector of the inner product</param>
/// <returns>A term representing the inner product of <paramref name="left"/> and <paramref name="right"/>.</returns>
public static Term InnerProduct(TVec left, TVec right)
{
Contract.Requires(left != null);
Contract.Requires(right != null);
Contract.Requires(left.Dimension == right.Dimension);
Contract.Ensures(Contract.Result<Term>() != null);
var products = from i in System.Linq.Enumerable.Range(0, left.Dimension)
select left.terms[i] * right.terms[i];
return TermBuilder.Sum(products);
}
/// <summary>
/// Constructs a new instance of the <see cref="TVec"/> class using another vector's components.
/// </summary>
/// <param name="first">A vector containing the first vector components to use.</param>
/// <param name="rest">More vector components to add in addition to the components in <paramref name="first"/></param>
public TVec(TVec first, params Term[] rest)
: this(first.terms.Concat(rest ?? Enumerable.Empty <Term>()))
{
Guard.ItemsNotNull(rest, nameof(rest));
}
public static Term EuclidianDistance(TVec one, TVec two)
{
return(Power(EuclidianDistanceSqr(one, two), 0.5));
}
public static Term EuclidianDistanceSqr(TVec one, TVec two)
{
return((one - two).NormSquared);
}
public static Term BoundedRectangle(TVec arg, TVec leftLower, TVec rightUpper, double steepness)
{
return(BoundedValue(arg.X, leftLower.X, rightUpper.X, steepness) & BoundedValue(arg.Y, leftLower.Y, rightUpper.Y, steepness));
}
public static Term Gaussian(TVec args, TVec mean, double variance)
{
return(Exp(((args - mean).NormSquared) * (-0.5 / variance)));
}
public static Term NormalDistribution(TVec args, TVec mean, double variance)
{
return(Exp(((args - mean).NormSquared) * (-0.5 / variance)) * (1 / Math.Sqrt(2.0 * Math.PI * variance)));
}