VectorUtil

The VectorUtil class is used to work with vectors.

To import this class use:

import ru.biosoft.physicell.biofvm.VectorUtil

All members of the VectorUtil class are presented below.

Members of the VectorUtil class
Class member	Description
static double[] newDiff(double[] vector1, double[] vector2)	vector1 is a three-dimensional vector. vector2 is a three-dimensional vector. Returns a three-dimensional vector that is the coordinate difference of the vectors vector1 and vector2. Example of usage.
static double norm(double[] vector)	vector - a three-dimensional vector. Returns the L2-norm of a vector. Example of usage.
static double norm_squared(double[] vector)	vector - a three-dimensional vector. Returns the square L2-norm of vector. Example of usage.
static double[] newNormalize(double[] vector)	vector - a three-dimensional vector. Returns the normalized vector. Example of usage.
static void normalize(double[] vector)	vector - a three-dimensional vector. Normalizes vector. Example of usage.
static double dist(double[] vector1, double[] vector2)	vector1 is a three-dimensional vector. vector2 is a three-dimensional vector. Returns the distance between vectors vector1 and vector2. Example of usage.
static double[] newProd(double[] vector, double const)	vector - a three-dimensional vector. const - number. Returns a three-dimensional vector res_vector of the following form: res_vector[i] = const*vector[i], where i is each coordinate of the vectors res_vector and vector. Example of usage.
static double[] axpy(double[] vector1, double const, double[] vector2)	vector1 is a three-dimensional vector. const - number. vector2 is a three-dimensional vector. Returns a three-dimensional vector of the following form: vector[i] = vector1[i] + const*vector2[i], где i - каждая координата векторов vector, vector1 и vector2. Example of usage.
static void zero(double[] vector)	vector - a three-dimensional vector. Zeroes all vector coordinates. Example of usage.

Vector Operations Help

Coordinate vector difference

The coordinate difference of vectors is a vector subtraction operation in which the corresponding components (coordinates) of the vectors are subtracted.

Example

// Given
Vector3D a = new Vector3D(5, 3, 7);
Vector3D b = new Vector3D(1, 2, 4);

// Component-wise difference
Vector3D difference = a.subtract(b); // Result: (4, 1, 3)

L2-norm of a vector

The L2 norm of a vector (Euclidean norm) is a standard way of measuring the length of a vector. It is calculated as the square root of the sum of the squares of all vector components.

For a vector v = (v₁, v₂, ..., v_n) in n-dimensional space:

\[\|v\|_2 = \sqrt{v_1^2 + v_2^2 + \cdots + v_n^2}\]

Vector normalization

Vector normalization is the transformation of a vector into a unit-length vector (with L2-norm equal to 1) preserving its direction.

The normalized version of the vector v = (v₁, v₂, ..., v_n) is a vector v`, each coordinate of which is less than the corresponding coordinate of the vector v in the L2 norm of that vector:

\[{v'}_i = \frac{v_i}{\sqrt{v_1^2 + v_2^2 + \cdots + v_n^2}}, \quad \text{where } i = 1, 2, \ldots, n.\]

Расстояние между векторами

В двумерной системе координат расстояние (d) между векторами A(x₁, y₁) и B(x₂, y₂) вычисляется следующим образом:

\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

В трехмерной системе координат расстояние (d) между векторами A(x₁, y₁, z₁) и B(x₂, y₂, z₂) вычисляется следующим образом:

\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\]