001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math3.geometry;
018    
019    import java.io.Serializable;
020    import java.text.NumberFormat;
021    
022    import org.apache.commons.math3.exception.MathArithmeticException;
023    
024    /** This interface represents a generic vector in a vectorial space or a point in an affine space.
025     * @param <S> Type of the space.
026     * @version $Id: Vector.java 1416643 2012-12-03 19:37:14Z tn $
027     * @see Space
028     * @see Vector
029     * @since 3.0
030     */
031    public interface Vector<S extends Space> extends Serializable {
032    
033        /** Get the space to which the vector belongs.
034         * @return containing space
035         */
036        Space getSpace();
037    
038        /** Get the null vector of the vectorial space or origin point of the affine space.
039         * @return null vector of the vectorial space or origin point of the affine space
040         */
041        Vector<S> getZero();
042    
043        /** Get the L<sub>1</sub> norm for the vector.
044         * @return L<sub>1</sub> norm for the vector
045         */
046        double getNorm1();
047    
048        /** Get the L<sub>2</sub> norm for the vector.
049         * @return Euclidean norm for the vector
050         */
051        double getNorm();
052    
053        /** Get the square of the norm for the vector.
054         * @return square of the Euclidean norm for the vector
055         */
056        double getNormSq();
057    
058        /** Get the L<sub>&infin;</sub> norm for the vector.
059         * @return L<sub>&infin;</sub> norm for the vector
060         */
061        double getNormInf();
062    
063        /** Add a vector to the instance.
064         * @param v vector to add
065         * @return a new vector
066         */
067        Vector<S> add(Vector<S> v);
068    
069        /** Add a scaled vector to the instance.
070         * @param factor scale factor to apply to v before adding it
071         * @param v vector to add
072         * @return a new vector
073         */
074        Vector<S> add(double factor, Vector<S> v);
075    
076        /** Subtract a vector from the instance.
077         * @param v vector to subtract
078         * @return a new vector
079         */
080        Vector<S> subtract(Vector<S> v);
081    
082        /** Subtract a scaled vector from the instance.
083         * @param factor scale factor to apply to v before subtracting it
084         * @param v vector to subtract
085         * @return a new vector
086         */
087        Vector<S> subtract(double factor, Vector<S> v);
088    
089        /** Get the opposite of the instance.
090         * @return a new vector which is opposite to the instance
091         */
092        Vector<S> negate();
093    
094        /** Get a normalized vector aligned with the instance.
095         * @return a new normalized vector
096         * @exception MathArithmeticException if the norm is zero
097         */
098        Vector<S> normalize() throws MathArithmeticException;
099    
100        /** Multiply the instance by a scalar.
101         * @param a scalar
102         * @return a new vector
103         */
104        Vector<S> scalarMultiply(double a);
105    
106        /**
107         * Returns true if any coordinate of this vector is NaN; false otherwise
108         * @return  true if any coordinate of this vector is NaN; false otherwise
109         */
110        boolean isNaN();
111    
112        /**
113         * Returns true if any coordinate of this vector is infinite and none are NaN;
114         * false otherwise
115         * @return  true if any coordinate of this vector is infinite and none are NaN;
116         * false otherwise
117         */
118        boolean isInfinite();
119    
120        /** Compute the distance between the instance and another vector according to the L<sub>1</sub> norm.
121         * <p>Calling this method is equivalent to calling:
122         * <code>q.subtract(p).getNorm1()</code> except that no intermediate
123         * vector is built</p>
124         * @param v second vector
125         * @return the distance between the instance and p according to the L<sub>1</sub> norm
126         */
127        double distance1(Vector<S> v);
128    
129        /** Compute the distance between the instance and another vector according to the L<sub>2</sub> norm.
130         * <p>Calling this method is equivalent to calling:
131         * <code>q.subtract(p).getNorm()</code> except that no intermediate
132         * vector is built</p>
133         * @param v second vector
134         * @return the distance between the instance and p according to the L<sub>2</sub> norm
135         */
136        double distance(Vector<S> v);
137    
138        /** Compute the distance between the instance and another vector according to the L<sub>&infin;</sub> norm.
139         * <p>Calling this method is equivalent to calling:
140         * <code>q.subtract(p).getNormInf()</code> except that no intermediate
141         * vector is built</p>
142         * @param v second vector
143         * @return the distance between the instance and p according to the L<sub>&infin;</sub> norm
144         */
145        double distanceInf(Vector<S> v);
146    
147        /** Compute the square of the distance between the instance and another vector.
148         * <p>Calling this method is equivalent to calling:
149         * <code>q.subtract(p).getNormSq()</code> except that no intermediate
150         * vector is built</p>
151         * @param v second vector
152         * @return the square of the distance between the instance and p
153         */
154        double distanceSq(Vector<S> v);
155    
156        /** Compute the dot-product of the instance and another vector.
157         * @param v second vector
158         * @return the dot product this.v
159         */
160        double dotProduct(Vector<S> v);
161    
162        /** Get a string representation of this vector.
163         * @param format the custom format for components
164         * @return a string representation of this vector
165         */
166        String toString(final NumberFormat format);
167    
168    }