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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.geometry;
import org.apache.commons.math3.exception.MathArithmeticException;
import java.text.NumberFormat;
/**
* 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.
*
* @return null vector of the vectorial space or origin point of the affine space
*/
Vector<S> getZero();
/**
* Get the L<sub>1</sub> norm for the vector.
*
* @return L<sub>1</sub> norm for the vector
*/
double getNorm1();
/**
* 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.
*
* @return square of the Euclidean norm for the vector
*/
double getNormSq();
/**
* Get the L<sub>∞</sub> norm for the vector.
*
* @return L<sub>∞</sub> norm for the vector
*/
double getNormInf();
/**
* 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.
*
* @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.
*
* @param v vector to subtract
* @return a new vector
*/
Vector<S> subtract(Vector<S> v);
/**
* 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.
*
* @return a new vector which is opposite to the instance
*/
Vector<S> negate();
/**
* 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.
*
* @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
*
* @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 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
*
* @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 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
*
* @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<sub>∞</sub> norm.
*
* <p>Calling this method is equivalent to calling: <code>q.subtract(p).getNormInf()</code>
* except that no intermediate vector is built
*
* @param v second vector
* @return the distance between the instance and p according to the L<sub>∞</sub> norm
*/
double distanceInf(Vector<S> v);
/**
* 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
*
* @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.
*
* @param v second vector
* @return the dot product this.v
*/
double dotProduct(Vector<S> v);
/**
* 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);
}
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