首先从我们计½Ž—机人最熟æ?zh¨¨n)‰çš„线性代数开始ã€?/span>

今天先写½W¬ä¸€½‹‡ï¼šå‘量—â€?/span>vector。另外补充一句，每一个具体类或者包的研½I‰™ƒ½æ˜¯ç¤ºä¾‹æ€§è´¨çš„，具体要用åˆîC»€ä¹ˆç±»åž‹çš„¾cÀLˆ–者接口，大家应该自己动手åŽÈ¿»é˜?/span>api docã€?/span>

Vector是一个普通的向量。在mathåŒ?/span>org.apache.commons.math.linear中有RealVectorå’?/span>FieldVector˜q™ä¸¤¿Uå‘量，均是接口¾cÕdž‹ã€‚前者是实数¾cÕdž‹çš„向量，后者是场向量。以实数向量ä¸ÞZ¾‹åQ?/span>RealVectoræœ?/span>AbstractRealVector, ArrayRealVector。具体的¾l“æž„¾cÕd›¾è§ä¸‹åQ?/span>

˜q™ä¸ª¾l“构可能会有些变化，因äØ“åœ?/span>doc中，可以看到ArrayRealVector是ç‘ôæ‰?/span>AbstractRealVector的，è€?/span>2.0的代码中ArrayRealVector˜q˜æ˜¯ç›´æŽ¥å®žçŽ°äº?/span>RealVectoråQŒä¸”包中也没æœ?/span>AbstractRealVector。可见代码的变化å’?/span>doc中的描述也有不同åQŒè™½ç„?/span>doc中说明了AbstractRealVectoræ˜?/span>since 2.0的，而且ArrayRealVector也是since 2.0的。呵呵，一个不一致。其实是update date的不同了ã€?/span>

向量˜q™ä¸ªæ¦‚念是线性代数的基础ã€?/span>RealVector作äؓ基本的接口，已经定义了基本所有的向量操作。比如向量的加减乘除˜qç®—、向量外¿U¯ã€å‘量内¿U¯ã€å‘量范数等½{‰ï¼Œå½“然vector的实现时åŸÞZºŽæ•°ç»„¾cÕdž‹çš„ã€?/span>RealVector的内部实现是double []data;ã€?/span>

需要重点解释的是一个操ä½?/span>map***åQšå°±åƒåŽŸæ¥çš„api解释çš?#8220;The various mapXxx and mapXxxToSelf methods operate on vectors element-wise, i.e. they perform the same operation (adding a scalar, applying a function ...) on each element in turn. The mapXxx versions create a new vector to hold the result and do not change the instance. The mapXxxToSelf versions use the instance itself to store the results, so the instance is changed by these methods. In both cases, the result vector is returned by the methods”ã€?/span>

具体是什么呢åQŸå¾ˆå¤šçš„map***操作å’?/span>map***toself操作ž®±æ˜¯å¯¹å‘量的每一个元素做固定操作的意思。è€?/span>map***是返回新的实例的åQŒè€?/span>map***toself则返回自己。这个从源码可以看出åQŒæ¯”å¦?/span>mapAdd()的实玎ͼš

1public RealVector mapAdd(double d) {
2        double[] out = new double[data.length];
3        for (int i = 0; i < data.length; i++) {
4            out[i] = data[i] + d;
5        }
6        return new ArrayRealVector(out);
7}
8

è€?/span>mapAddToSelf()的实玎ͼš

1public RealVector mapAddToSelf(double d) {
2        for (int i = 0; i < data.length; i++) {
3            data[i] = data[i] + d;
4        }
5        return this;
6}
7

区别昄¡„¶äº†ï¼Œä¸€ä¸ªè¿”å›?/span>new ArrayRealVectoråQŒä¸€ä¸ªè¿”å›?/span>thisã€?/span>

具体见代码：

 1/** *//**
 2 * 
 3 */
 4package algorithm.math;
 5
 6import org.apache.commons.math.linear.ArrayRealVector;
 7import org.apache.commons.math.linear.RealVector;
 8
 9/** *//**
10 * @author Jia Yu
11 * @date 2010-11-18
12 */
13public class VectorTest {
14
15    /** *//**
16     * @param args
17     */
18    public static void main(String[] args) {
19        // TODO Auto-generated method stub
20        vector();
21    }
22
23    private static void vector() {
24        // TODO Auto-generated method stub
25        double[] vec1 = { 1d, 2d, 3d };
26        double[] vec2 = { 4d, 5d, 6d };
27        ArrayRealVector v1 = new ArrayRealVector(vec1);
28        ArrayRealVector v2 = new ArrayRealVector(vec2);
29
30        // output directly
31        System.out.println("v1 is " + v1);
32        // dimension : size of vector
33        System.out.println("size is " + v1.getDimension());
34        // vector add
35        System.out.println("v1 + v2 = " + v1.add(v2));
36        System.out.println("v1 + v2 = " + v1.add(vec2));
37        // vector substract
38        System.out.println("v1 - v2 = " + v1.subtract(v2));
39        // vector element by element multiply
40        System.out.println("v1 * v2 = " + v1.ebeMultiply(v2));
41        // vector element by element divide
42        System.out.println("v1 / v2 = " + v1.ebeDivide(v2));
43        // get index at 1
44        System.out.println("v1[1] = " + v1.getEntry(1));
45        // vector append
46        RealVector t_vec = v1.append(v2);
47        System.out.println("v1 append v2 is " + t_vec);
48        // vector distance
49        System.out.println("distance between v1 and v2 is "
50                + v1.getDistance(v2));
51        System.out.println("L1 distance between v1 and v2 is "
52                + v1.getL1Distance(v2));
53        // vector norm
54        System.out.println("norm of v1 is " + v1.getNorm());
55        // vector dot product
56        System.out.println("dot product of v1 and v2 is " + v1.dotProduct(v2));
57        // vector outer product
58        System.out.println("outer product of v1 and v2 is "
59                + v1.outerProduct(v2));
60        // vector orthogonal projection
61        System.out.println("hogonal projection of v1 and v2 is "
62                + v1.projection(v2));
63        // vector map operations
64        System.out.println("Map the Math.abs(double) function to v1 is "
65                + v1.mapAbs());
66        v1.mapInvToSelf();
67        System.out.println("Map the 1/x function to v1 itself is " + v1);
68        // vector get sub vector
69        System.out.println("sub vector of v1 is " + v1.getSubVector(0, 2));
70    }
71
72}
73

对应的输出：

v1 is {1; 2; 3}
size is 3
v1 + v2 = {5; 7; 9}
v1 + v2 = {5; 7; 9}
v1 - v2 = {-3; -3; -3}
v1 * v2 = {4; 10; 18}
v1 / v2 = {0.25; 0.4; 0.5}
v1[1] = 2.0
v1 append v2 is {1; 2; 3; 4; 5; 6}
distance between v1 and v2 is 5.196152422706632
L1 distance between v1 and v2 is 9.0
norm of v1 is 3.7416573867739413
dot product of v1 and v2 is 32.0
outer product of v1 and v2 is Array2DRowRealMatrix{{4.0,5.0,6.0},{8.0,10.0,12.0},{12.0,15.0,18.0}}
hogonal projection of v1 and v2 is {1.66; 2.08; 2.49}
Map the Math.abs(double) function to v1 is {1; 2; 3}
Map the 1/x function to v1 itself is {1; 0.5; 0.33}
sub vector of v1 is {1; 0.5}

向量是一个基¼‹€æ•°å­¦¾l“æž„åQŒä»¥åŽè¿˜ä¼šå¤§é‡çš„提到ã€?/span>Commons Math库äؓ我们提供了这æ äh–¹ä¾¿çš„向量表示åQŒåœ¨ç”?/span>Java写è“v½E‹åºæ¥ä¹Ÿæ˜¯å¾—心应手ã€?/span>

当然所有的研究要以文档ä¸ÞZ¸»åQŒå‚看文档写代码˜q™æ˜¯å¿…须做到的事情。所以，不要嫌麻烦，赶紧æŠ?/span>api doc攑ֈ°æ¡Œé¢ä¸Šï¼Œå¼€å§?/span>coding吧ã€?/span>

相关资料åQ?/span>

向量定义åQ?/span>http://zh.wikipedia.org/zh/%E7%9F%A2%E9%87%8F

Commons math包：http://commons.apache.org/math/index.html