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package org.apache.commons.math3.geometry;

import java.text.NumberFormat;

import org.apache.commons.math3.exception.MathArithmeticException;

This interface represents a generic vector in a vectorial space or a point in an affine space.
Type parameters:
<S> – Type of the space.
See Also:
Space
Point
Since:
3.0/** This interface represents a generic vector in a vectorial space or a point in an affine space.
 * @param <S> Type of the space.
 * @see Space
 * @see Point
 * @since 3.0
 */
public interface Vector<S extends Space> extends Point<S> {

    
Get the null vector of the vectorial space or origin point of the affine space.
Returns:
null vector of the vectorial space or origin point of the affine space/** Get the null vector of the vectorial space or origin point of the affine space.
     * @return null vector of the vectorial space or origin point of the affine space
     */
    Vector<S> getZero();

    
Get the L1 norm for the vector.
Returns:
L1 norm for the vector/** Get the L<sub>1</sub> norm for the vector.
     * @return L<sub>1</sub> norm for the vector
     */
    double getNorm1();

    
Get the L2 norm for the vector.
Returns:
Euclidean norm for the vector/** Get the L<sub>2</sub> norm for the vector.
     * @return Euclidean norm for the vector
     */
    double getNorm();

    
Get the square of the norm for the vector.
Returns:
square of the Euclidean norm for the vector/** Get the square of the norm for the vector.
     * @return square of the Euclidean norm for the vector
     */
    double getNormSq();

    
Get the L∞ norm for the vector.
Returns:
L∞ norm for the vector/** Get the L<sub>&infin;</sub> norm for the vector.
     * @return L<sub>&infin;</sub> norm for the vector
     */
    double getNormInf();

    
Add a vector to the instance.
Params:
v – vector to add
Returns:
a new vector/** Add a vector to the instance.
     * @param v vector to add
     * @return a new vector
     */
    Vector<S> add(Vector<S> v);

    
Add a scaled vector to the instance.
Params:
factor – scale factor to apply to v before adding it
v – vector to add
Returns:
a new vector/** Add a scaled vector to the instance.
     * @param factor scale factor to apply to v before adding it
     * @param v vector to add
     * @return a new vector
     */
    Vector<S> add(double factor, Vector<S> v);

    
Subtract a vector from the instance.
Params:
v – vector to subtract
Returns:
a new vector/** Subtract a vector from the instance.
     * @param v vector to subtract
     * @return a new vector
     */
    Vector<S> subtract(Vector<S> v);

    
Subtract a scaled vector from the instance.
Params:
factor – scale factor to apply to v before subtracting it
v – vector to subtract
Returns:
a new vector/** Subtract a scaled vector from the instance.
     * @param factor scale factor to apply to v before subtracting it
     * @param v vector to subtract
     * @return a new vector
     */
    Vector<S> subtract(double factor, Vector<S> v);

    
Get the opposite of the instance.
Returns:
a new vector which is opposite to the instance/** Get the opposite of the instance.
     * @return a new vector which is opposite to the instance
     */
    Vector<S> negate();

    
Get a normalized vector aligned with the instance.
Throws:
MathArithmeticException – if the norm is zero
Returns:
a new normalized vector/** Get a normalized vector aligned with the instance.
     * @return a new normalized vector
     * @exception MathArithmeticException if the norm is zero
     */
    Vector<S> normalize() throws MathArithmeticException;

    
Multiply the instance by a scalar.
Params:
a – scalar
Returns:
a new vector/** Multiply the instance by a scalar.
     * @param a scalar
     * @return a new vector
     */
    Vector<S> scalarMultiply(double a);

    
Returns true if any coordinate of this vector is infinite and none are NaN;
false otherwise
Returns:
 true if any coordinate of this vector is infinite and none are NaN;
false otherwise/**
     * Returns true if any coordinate of this vector is infinite and none are NaN;
     * false otherwise
     * @return  true if any coordinate of this vector is infinite and none are NaN;
     * false otherwise
     */
    boolean isInfinite();

    
Compute the distance between the instance and another vector according to the L1 norm.
Calling this method is equivalent to calling:
q.subtract(p).getNorm1() except that no intermediate
vector is built
Params:
v – second vector
Returns:
the distance between the instance and p according to the L1 norm/** Compute the distance between the instance and another vector according to the L<sub>1</sub> norm.
     * <p>Calling this method is equivalent to calling:
     * <code>q.subtract(p).getNorm1()</code> except that no intermediate
     * vector is built</p>
     * @param v second vector
     * @return the distance between the instance and p according to the L<sub>1</sub> norm
     */
    double distance1(Vector<S> v);

    
Compute the distance between the instance and another vector according to the L2 norm.
Calling this method is equivalent to calling:
q.subtract(p).getNorm() except that no intermediate
vector is built
Params:
v – second vector
Returns:
the distance between the instance and p according to the L2 norm/** Compute the distance between the instance and another vector according to the L<sub>2</sub> norm.
     * <p>Calling this method is equivalent to calling:
     * <code>q.subtract(p).getNorm()</code> except that no intermediate
     * vector is built</p>
     * @param v second vector
     * @return the distance between the instance and p according to the L<sub>2</sub> norm
     */
    double distance(Vector<S> v);

    
Compute the distance between the instance and another vector according to the L∞ norm.
Calling this method is equivalent to calling:
q.subtract(p).getNormInf() except that no intermediate
vector is built
Params:
v – second vector
Returns:
the distance between the instance and p according to the L∞ norm/** Compute the distance between the instance and another vector according to the L<sub>&infin;</sub> norm.
     * <p>Calling this method is equivalent to calling:
     * <code>q.subtract(p).getNormInf()</code> except that no intermediate
     * vector is built</p>
     * @param v second vector
     * @return the distance between the instance and p according to the L<sub>&infin;</sub> norm
     */
    double distanceInf(Vector<S> v);

    
Compute the square of the distance between the instance and another vector.
Calling this method is equivalent to calling:
q.subtract(p).getNormSq() except that no intermediate
vector is built
Params:
v – second vector
Returns:
the square of the distance between the instance and p/** Compute the square of the distance between the instance and another vector.
     * <p>Calling this method is equivalent to calling:
     * <code>q.subtract(p).getNormSq()</code> except that no intermediate
     * vector is built</p>
     * @param v second vector
     * @return the square of the distance between the instance and p
     */
    double distanceSq(Vector<S> v);

    
Compute the dot-product of the instance and another vector.
Params:
v – second vector
Returns:
the dot product this.v/** Compute the dot-product of the instance and another vector.
     * @param v second vector
     * @return the dot product this.v
     */
    double dotProduct(Vector<S> v);

    
Get a string representation of this vector.
Params:
format – the custom format for components
Returns:
a string representation of this vector/** Get a string representation of this vector.
     * @param format the custom format for components
     * @return a string representation of this vector
     */
    String toString(final NumberFormat format);

}