如何做一个个人网站,网站该怎么做链接,网站建设的主要技术指什么软件,泰安人才招聘信息网目录 一. CNN卷积神经网络与传统神经网络的不同 1. 模型图 2. 参数分布情况 3. 卷积神经网络和传统神经网络的层次结构 4. 传统神经网络的缺点#xff1a;
二. CNN的基本操作 1. 卷积 2. 池化 三. CNN实现过程 1. 算法流程图 2. 输入层 3. 卷积层 4. 激活层 5. 池化层 6. 全连…目录 一. CNN卷积神经网络与传统神经网络的不同 1. 模型图 2. 参数分布情况 3. 卷积神经网络和传统神经网络的层次结构 4. 传统神经网络的缺点
二. CNN的基本操作 1. 卷积 2. 池化 三. CNN实现过程 1. 算法流程图 2. 输入层 3. 卷积层 4. 激活层 5. 池化层 6. 全连接层
二. CNN卷积神经网络的过程 1. 正向传播过程 2. 反向传播过程算法核心
三. 卷积神经网络代码 1. CnnLayer类 2. Dataset类 3. FullCnn类 4. LayerBuilder类 5. LayerTypeEnum类 6. MathUtils类 7. Size类
四. 运行结果 一. CNN卷积神经网络与传统神经网络的不同 1. 模型图 传统神经网络和卷积神经网络的大致模型如下图所示 传统神经网络 卷积神经网络 2. 参数分布情况 首先我们根据矩阵运算划分——传统神经网络处理过程是一维过程卷积神经网络CNN处理过程是多维的更进一步解释就是传统神经网络的数据输入仅仅是一个向量CNN的数据输入是一张图片这个图片有深度depth、高度height和宽度width。卷积神经网络卷积神经层由多个特征面构成每一个特征面则是由很多个神经元构成卷积核代表参数w。传统神经网络每层由排成一列的神经元构成神经元每个神经元代表矩阵的一个列向量Xi神经元连线代表系数W。每一个像素值都是一个神经元每个神经元代表了一个特征。 3. 卷积神经网络和传统神经网络的层次结构 传统神经网络
输入层的每个神经元代表了一个特征隐藏层特征提取输出层输出层个数代表了分类标签的个数 卷积神经网络
多通道输入多卷积核输出的通道数卷积核的个数。输入层-卷积层-激活层-池化层-全连接层数据输入层对原始数据进行初步处理使卷积神经网络能有更好的效果卷积层提取特征矩阵大小个数都变化卷积核遍历图片上每一个像素点激活层计算结果通过一个激活函数加一个非线性的关系使能逼近任何函数。池化层数据压缩提取主要特征降低网络复杂度不改变矩阵的深度缩小矩阵减少网络的参数矩阵变小个数不变全连接层分类器角色将特征映射到样本标记空间本质是矩阵变换。将特征图拉成一维向量将每个特征点作为一个神经元进行分类任务。把所有局部特征结合变成全局特征用来计算最后每一类的得分。 4. 传统神经网络的缺点 首先将图像展开为向量会丢失空间信息局部相关性被破坏其次参数过多效率低下训练困难同时大量的参数也很快会导致网络过拟合。 相较之下卷积神经网络Convolutional Neural NetworkCNN是一种深度学习的模型它可以有效地处理图像等高维数据。卷积神经网络的主要特点是使用卷积层和池化层来提取图像的局部特征和降低维度从而减少参数数量和计算量。
二. CNN的基本操作 1. 卷积 介绍完卷积神经网络和传统神经网络我们这里继续谈谈基本概念——卷积。 对于一张普通的图片我们人类需要进行识别首先做的事情是不是判断出它有什么特征啊这个是很关键的一步例如下图是汽车的一张图片那么我们是怎么样判断的呢 首先我们是不是看它有轮子它有车灯前挡风玻璃车门把手等等有了这些东西好了那我们就可以判断他是个汽车 回顾我们人类的判断过程最关键的一步就是对于特征的提取而这里所说的卷积就是对于特征提取的一个方法。 我们从卷积的定义开始说起很多人在接触卷积这个概念时, 会感到很奇怪. 我们知道卷积的定义是这样的给定两个函数定义卷积 也就是说给两个函数和我们把它卷积起来成为具体构造如上。它的物理意义大概可以理解为系统某一时刻的输出是由多个输入共同作用叠加的结果。放在图像分析里可以理解为原始像素点(source pixel)所有的原始像素点叠加起来就是原始图了可以称为作用点所有作用点合起来我们称为卷积核Convolution kernel卷积核上所有作用点依次作用于原始像素点后即乘起来线性叠加的输出结果即是最终卷积的输出也是我们想要的结果。 对于图像的卷积处理我们继续来看。每一张照片其实就是一个数字矩阵只不过彩色照片每个像素点不是用0、1表示而是用更广的数字表示这里为了简便就设定为黑白照片像素点是由0、1组合。假设我们现在有一张图片image它对应的像素点是这样的 image 现在我们需要有一个特征提取器也叫卷积核这个东西主要是将上面的图片针对于卷积核的特征提取出来然后构建成为一个新的矩阵这个新的矩阵就有输入图片image的特征。先假定我们有一个卷积核如下图所示 Filter/Kernel 对于它的提取过程——将image中大小和kernel大小相等部分的对应位置相乘即 为了更好的理解这一过程下面有一个GIF动态图片 上述过程结束之后我们得到了一个Feature Map原image图像通过kernel进行特征提取得到的结果这个Feature Map只是其中的一个当然我们可以设置许多的卷积核kernel用于提取原图片不同的特征最终得到许多Feature Map这一部分就是原图片的“核心”用于辨认原图片的什么特征。 从上面的卷积过程我们不难发现每次经过卷积大小都会发生改变那么我们该怎么样保证卷积的结果大小不变呢这里补充一点——零填充就是在原本的图像上增加像素点每个像素点的值都是0。 最后我们可以根据卷积的过程得到的Feature Map的图片大小与原图片的大小和卷积核的大小有关系假设一张图片的大小为卷积核的大小为步长为总共有个卷积核零填充的列数为则可得到输出的Feature Map的大小为 2. 池化 池化过程在一般卷积过程后。池化pooling的本质其实就是采样。Pooling 对于输入的 Feature Map选择某种方式对其进行降维压缩以加快运算速度。采用较多的一种池化过程叫最大池化Max Pooling其具体操作过程如下 最大池化 池化过程类似于卷积过程如上图所示表示的就是对一个 4×4 feature map邻域内的值用一个 2×2 的filter步长为2进行“扫描”选择最大值输出到下一层这叫做 Max Pooling。 还有一种叫平均池化Average Pooling就是从以上取某个区域的最大值改为求这个区域的平均值其具体操作过程如下 平均池化 如上图所示表示的就是对一个 4×4 feature map邻域内的值用一个 2×2 的filter步长为2进行“扫描”选择平均值输出到下一层这叫做 Average Pooling。 三. CNN实现过程 1. 算法流程图 在这里对于传统全连接神经网络模型不详细赘述有兴趣的请参考——文章卷积神经网络一般由以下层实现
数据输入层/ Input layer卷积计算层/ CONV layerReLU激励层 / ReLU layer池化层 / Pooling layer全连接层 / FC layer 对应的模型过程如下图1所示 图1 2. 输入层 这里我们主要是要明白整个CNN模型的输入数据是什么众所周知一张图片就是一个超大的矩阵。输入层主要是n×m×3 RGB图像这不同于人工神经网络人工神经网络的输入是n×1维的矢量。 3. 卷积层 之前我们学习了卷积的概念这里补充一些想法便于理解后文 3.1 为什么选择卷积 有时候可能会问自己为什么要首先使用卷积操作为什么不从一开始就展开输入图像矩阵在这里给出答案如果这样做我们最终会得到大量需要训练的参数而且大多数人都没有能够以最快的方式解决计算成本高昂任务的能力。此外由于卷积神经网络具有的参数会更少因此就可以避免出现过拟合现象。 3.2 多个FeatureMap的卷积 在上文中我提过一张图片的卷积操作那个部分是卷积操作的基础但是假设我们进行到卷积层2的话又该怎么处理多个图片输入的卷积操作呢 答现在有多个featuremap输入我们要对其进行卷积操作之前的卷积操作只是针对于一张图片一个输入现在我们的输入有多个图片我们假设现在需要进行卷积操作的图片为我们的卷积核为那么现在我们的卷积结果为 卷积之后的数量大小和卷积核的数量大小一致。 4. 激活层 这一部分与之前写的BP神经网络激活函数的作用一致于是就不再详谈不过这里还是列出我在后面会用到的激活函数。Sigmoid函数是一个在生物学中常见的S型函数也称为S型生长曲线。在深度学习中由于其单增以及反函数单增等性质Sigmoid函数常被用作神经网络的激活函数将变量映射到[0,1]之间。 Sigmod函数 Sigmod导函数 图像 5. 池化层 详见上文二. 2。 6. 全连接层 我们首先看到上面的图1通过不断地卷积池化可以将一个高维的图片降维成一个低维的图片... 需要补充...
二. CNN卷积神经网络的过程 1. 正向传播过程 所有数学推导都基于如下图2所示 图2 正向传播过程比较简单主要是按照上图2的过程一步一步计算即可。 输入层 假设我们输入的一张L×W×H的图片输入一个矩阵。 卷积层1 首先对于卷积层1随机生成多个卷积核大小与要求一致相关概念参考——二. 1卷积我们得到一个卷积集合 2. 反向传播过程算法核心 补充...
三. 卷积神经网络代码 1. CnnLayer类
package Day_81;/*** One layer, support all four layer types. The code mainly initializes, gets,* and sets variables. Essentially no algorithm is implemented.** author Fan Min minfanphd163.com.*/
public class CnnLayer {/*** The type of the layer.*/LayerTypeEnum type;/*** The number of out map.*/int outMapNum;/*** The map size.*/Size mapSize;/*** The kernel size.*/Size kernelSize;/*** The scale size.*/Size scaleSize;/*** The index of the class (label) attribute.*/int classNum -1;/*** Kernel. Dimensions: [front map][out map][width][height].*/private double[][][][] kernel;/*** Bias. The length is outMapNum.*/private double[] bias;/*** Out maps. Dimensions:* [batchSize][outMapNum][mapSize.width][mapSize.height].*/private double[][][][] outMaps;/*** Errors.*/private double[][][][] errors;/*** For batch processing.*/private static int recordInBatch 0;/************************** The first constructor.** param paraNum* When the type is CONVOLUTION, it is the out map number. when* the type is OUTPUT, it is the class number.* param paraSize* When the type is INPUT, it is the map size; when the type is* CONVOLUTION, it is the kernel size; when the type is SAMPLING,* it is the scale size.************************/public CnnLayer(LayerTypeEnum paraType, int paraNum, Size paraSize) {type paraType;switch (type) {case INPUT:outMapNum 1;mapSize paraSize; // No deep copy.break;case CONVOLUTION:outMapNum paraNum;kernelSize paraSize;break;case SAMPLING:scaleSize paraSize;break;case OUTPUT:classNum paraNum;mapSize new Size(1, 1);outMapNum classNum;break;default:System.out.println(Internal error occurred in AbstractLayer.java constructor.);}// Of switch}// Of the first constructor/************************** Initialize the kernel.** param paraNum* When the type is CONVOLUTION, it is the out map number. when************************/public void initKernel(int paraFrontMapNum) {kernel new double[paraFrontMapNum][outMapNum][][];for (int i 0; i paraFrontMapNum; i) {for (int j 0; j outMapNum; j) {kernel[i][j] MathUtils.randomMatrix(kernelSize.width, kernelSize.height, true);} // Of for j} // Of for i}// Of initKernel/************************** Initialize the output kernel. The code is revised to invoke* initKernel(int).************************/public void initOutputKernel(int paraFrontMapNum, Size paraSize) {kernelSize paraSize;initKernel(paraFrontMapNum);}// Of initOutputKernel/************************** Initialize the bias. No parameter. int frontMapNum is claimed however* not used.************************/public void initBias() {bias MathUtils.randomArray(outMapNum);}// Of initBias/************************** Initialize the errors.** param paraBatchSize* The batch size.************************/public void initErrors(int paraBatchSize) {errors new double[paraBatchSize][outMapNum][mapSize.width][mapSize.height];}// Of initErrors/************************** Initialize out maps.** param paraBatchSize* The batch size.************************/public void initOutMaps(int paraBatchSize) {outMaps new double[paraBatchSize][outMapNum][mapSize.width][mapSize.height];}// Of initOutMaps/************************** Prepare for a new batch.************************/public static void prepareForNewBatch() {recordInBatch 0;}// Of prepareForNewBatch/************************** Prepare for a new record.************************/public static void prepareForNewRecord() {recordInBatch;}// Of prepareForNewRecord/************************** Set one value of outMaps.************************/public void setMapValue(int paraMapNo, int paraX, int paraY, double paraValue) {outMaps[recordInBatch][paraMapNo][paraX][paraY] paraValue;}// Of setMapValue/************************** Set values of the whole map.************************/public void setMapValue(int paraMapNo, double[][] paraOutMatrix) {outMaps[recordInBatch][paraMapNo] paraOutMatrix;}// Of setMapValue/************************** Getter.************************/public Size getMapSize() {return mapSize;}// Of getMapSize/************************** Setter.************************/public void setMapSize(Size paraMapSize) {mapSize paraMapSize;}// Of setMapSize/************************** Getter.************************/public LayerTypeEnum getType() {return type;}// Of getType/************************** Getter.************************/public int getOutMapNum() {return outMapNum;}// Of getOutMapNum/************************** Setter.************************/public void setOutMapNum(int paraOutMapNum) {outMapNum paraOutMapNum;}// Of setOutMapNum/************************** Getter.************************/public Size getKernelSize() {return kernelSize;}// Of getKernelSize/************************** Getter.************************/public Size getScaleSize() {return scaleSize;}// Of getScaleSize/************************** Getter.************************/public double[][] getMap(int paraIndex) {return outMaps[recordInBatch][paraIndex];}// Of getMap/************************** Getter.************************/public double[][] getKernel(int paraFrontMap, int paraOutMap) {return kernel[paraFrontMap][paraOutMap];}// Of getKernel/************************** Setter. Set one error.************************/public void setError(int paraMapNo, int paraMapX, int paraMapY, double paraValue) {errors[recordInBatch][paraMapNo][paraMapX][paraMapY] paraValue;}// Of setError/************************** Setter. Set one error matrix.************************/public void setError(int paraMapNo, double[][] paraMatrix) {errors[recordInBatch][paraMapNo] paraMatrix;}// Of setError/************************** Getter. Get one error matrix.************************/public double[][] getError(int paraMapNo) {return errors[recordInBatch][paraMapNo];}// Of getError/************************** Getter. Get the whole error tensor.************************/public double[][][][] getErrors() {return errors;}// Of getErrors/************************** Setter. Set one kernel.************************/public void setKernel(int paraLastMapNo, int paraMapNo, double[][] paraKernel) {kernel[paraLastMapNo][paraMapNo] paraKernel;}// Of setKernel/************************** Getter.************************/public double getBias(int paraMapNo) {return bias[paraMapNo];}// Of getBias/************************** Setter.************************/public void setBias(int paraMapNo, double paraValue) {bias[paraMapNo] paraValue;}// Of setBias/************************** Getter.************************/public double[][][][] getMaps() {return outMaps;}// Of getMaps/************************** Getter.************************/public double[][] getError(int paraRecordId, int paraMapNo) {return errors[paraRecordId][paraMapNo];}// Of getError/************************** Getter.************************/public double[][] getMap(int paraRecordId, int paraMapNo) {return outMaps[paraRecordId][paraMapNo];}// Of getMap/************************** Getter.************************/public int getClassNum() {return classNum;}// Of getClassNum/************************** Getter. Get the whole kernel tensor.************************/public double[][][][] getKernel() {return kernel;} // Of getKernel
}// Of class CnnLayer2. Dataset类
package Day_81;import java.io.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;/*** Manage the dataset.** author Fan Min minfanphd163.com.*/
public class Dataset {/*** All instances organized by a list.*/private ListInstance instances;/*** The label index.*/private int labelIndex;/*** The max label (label start from 0).*/private double maxLabel -1;/************************** The first constructor.************************/public Dataset() {labelIndex -1;instances new ArrayListInstance();}// Of the first constructor/************************** The second constructor.** param paraFilename* The filename.* param paraSplitSign* Often comma.* param paraLabelIndex* Often the last column.************************/public Dataset(String paraFilename, String paraSplitSign, int paraLabelIndex) {instances new ArrayListInstance();labelIndex paraLabelIndex;File tempFile new File(paraFilename);try {BufferedReader tempReader new BufferedReader(new FileReader(tempFile));String tempLine;while ((tempLine tempReader.readLine()) ! null) {String[] tempDatum tempLine.split(paraSplitSign);if (tempDatum.length 0) {continue;} // Of ifdouble[] tempData new double[tempDatum.length];for (int i 0; i tempDatum.length; i)tempData[i] Double.parseDouble(tempDatum[i]);Instance tempInstance new Instance(tempData);append(tempInstance);} // Of whiletempReader.close();} catch (IOException e) {e.printStackTrace();System.out.println(Unable to load paraFilename);System.exit(0);}//Of try}// Of the second constructor/************************** Append an instance.** param paraInstance* The given record.************************/public void append(Instance paraInstance) {instances.add(paraInstance);}// Of append/************************** Append an instance specified by double values.************************/public void append(double[] paraAttributes, Double paraLabel) {instances.add(new Instance(paraAttributes, paraLabel));}// Of append/************************** Getter.************************/public Instance getInstance(int paraIndex) {return instances.get(paraIndex);}// Of getInstance/************************** Getter.************************/public int size() {return instances.size();}// Of size/************************** Getter.************************/public double[] getAttributes(int paraIndex) {return instances.get(paraIndex).getAttributes();}// Of getAttrs/************************** Getter.************************/public Double getLabel(int paraIndex) {return instances.get(paraIndex).getLabel();}// Of getLabel/************************** Unit test.***********************D:\data*/public static void main(String args[]) {Dataset tempData new Dataset(D:/data/train.format, ,, 784);Instance tempInstance tempData.getInstance(0);System.out.println(The first instance is: tempInstance);}// Of main/************************** An instance.************************/public class Instance {/*** Conditional attributes.*/private double[] attributes;/*** Label.*/private Double label;/************************** The first constructor.************************/private Instance(double[] paraAttrs, Double paraLabel) {attributes paraAttrs;label paraLabel;}//Of the first constructor/************************** The second constructor.************************/public Instance(double[] paraData) {if (labelIndex -1)// No labelattributes paraData;else {label paraData[labelIndex];if (label maxLabel) {// It is a new labelmaxLabel label;} // Of ifif (labelIndex 0) {// The first column is the labelattributes Arrays.copyOfRange(paraData, 1, paraData.length);} else {// The last column is the labelattributes Arrays.copyOfRange(paraData, 0, paraData.length - 1);} // Of if} // Of if}// Of the second constructor/************************** Getter.************************/public double[] getAttributes() {return attributes;}// Of getAttributes/************************** Getter.************************/public Double getLabel() {if (labelIndex -1)return null;return label;}// Of getLabel/************************** toString.************************/public String toString(){return Arrays.toString(attributes) , label;}//Of toString}// Of class Instance
}// Of class Dataset3. FullCnn类
package Day_81;import Day_81.Dataset.Instance;
import Day_81.MathUtils.Operator;import java.util.Arrays;/*** CNN.** author Fan Min minfanphd163.com.*/
public class FullCnn {/*** The value changes.*/private static double ALPHA 0.85;/*** A constant.*/public static double LAMBDA 0;/*** Manage layers.*/private static LayerBuilder layerBuilder;/*** Train using a number of instances simultaneously.*/private int batchSize;/*** Divide the batch size with the given value.*/private Operator divideBatchSize;/*** Multiply alpha with the given value.*/private Operator multiplyAlpha;/*** Multiply lambda and alpha with the given value.*/private Operator multiplyLambda;/************************** The first constructor.*************************/public FullCnn(LayerBuilder paraLayerBuilder, int paraBatchSize) {layerBuilder paraLayerBuilder;batchSize paraBatchSize;setup();initOperators();}// Of the first constructor/************************** Initialize operators using temporary classes.************************/private void initOperators() {divideBatchSize new Operator() {private static final long serialVersionUID 7424011281732651055L;Overridepublic double process(double value) {return value / batchSize;}// Of process};multiplyAlpha new Operator() {private static final long serialVersionUID 5761368499808006552L;Overridepublic double process(double value) {return value * ALPHA;}// Of process};multiplyLambda new Operator() {private static final long serialVersionUID 4499087728362870577L;Overridepublic double process(double value) {return value * (1 - LAMBDA * ALPHA);}// Of process};}// Of initOperators/************************** Setup according to the layer builder.************************/public void setup() {CnnLayer tempInputLayer layerBuilder.getLayer(0);tempInputLayer.initOutMaps(batchSize);for (int i 1; i layerBuilder.getNumLayers(); i) {CnnLayer tempLayer layerBuilder.getLayer(i);CnnLayer tempFrontLayer layerBuilder.getLayer(i - 1);int tempFrontMapNum tempFrontLayer.getOutMapNum();switch (tempLayer.getType()) {case INPUT:// Should not be input. Maybe an error should be thrown out.break;case CONVOLUTION:tempLayer.setMapSize(tempFrontLayer.getMapSize().subtract(tempLayer.getKernelSize(), 1));tempLayer.initKernel(tempFrontMapNum);tempLayer.initBias();tempLayer.initErrors(batchSize);tempLayer.initOutMaps(batchSize);break;case SAMPLING:tempLayer.setOutMapNum(tempFrontMapNum);tempLayer.setMapSize(tempFrontLayer.getMapSize().divide(tempLayer.getScaleSize()));tempLayer.initErrors(batchSize);tempLayer.initOutMaps(batchSize);break;case OUTPUT:tempLayer.initOutputKernel(tempFrontMapNum, tempFrontLayer.getMapSize());tempLayer.initBias();tempLayer.initErrors(batchSize);tempLayer.initOutMaps(batchSize);break;}// Of switch} // Of for i}// Of setup/************************** Forward computing.************************/private void forward(Instance instance) {setInputLayerOutput(instance);for (int l 1; l layerBuilder.getNumLayers(); l) {CnnLayer tempCurrentLayer layerBuilder.getLayer(l);CnnLayer tempLastLayer layerBuilder.getLayer(l - 1);switch (tempCurrentLayer.getType()) {case CONVOLUTION:setConvolutionOutput(tempCurrentLayer, tempLastLayer);break;case SAMPLING:setSampOutput(tempCurrentLayer, tempLastLayer);break;case OUTPUT:setConvolutionOutput(tempCurrentLayer, tempLastLayer);break;default:break;}// Of switch} // Of for l}// Of forward/************************** Set the in layer output. Given a record, copy its values to the input* map.************************/private void setInputLayerOutput(Instance paraRecord) {CnnLayer tempInputLayer layerBuilder.getLayer(0);Size tempMapSize tempInputLayer.getMapSize();double[] tempAttributes paraRecord.getAttributes();if (tempAttributes.length ! tempMapSize.width * tempMapSize.height)throw new RuntimeException(input record does not match the map size.);for (int i 0; i tempMapSize.width; i) {for (int j 0; j tempMapSize.height; j) {tempInputLayer.setMapValue(0, i, j, tempAttributes[tempMapSize.height * i j]);} // Of for j} // Of for i}// Of setInputLayerOutput/************************** Compute the convolution output according to the output of the last layer.** param paraLastLayer* the last layer.* param paraLayer* the current layer.************************/private void setConvolutionOutput(final CnnLayer paraLayer, final CnnLayer paraLastLayer) {// int mapNum paraLayer.getOutMapNum();final int lastMapNum paraLastLayer.getOutMapNum();// Attention: paraLayer.getOutMapNum() may not be right.for (int j 0; j paraLayer.getOutMapNum(); j) {double[][] tempSumMatrix null;for (int i 0; i lastMapNum; i) {double[][] lastMap paraLastLayer.getMap(i);double[][] kernel paraLayer.getKernel(i, j);if (tempSumMatrix null) {// On the first map.tempSumMatrix MathUtils.convnValid(lastMap, kernel);} else {// Sum up convolution mapstempSumMatrix MathUtils.matrixOp(MathUtils.convnValid(lastMap, kernel),tempSumMatrix, null, null, MathUtils.plus);} // Of if} // Of for i// Activation.final double bias paraLayer.getBias(j);tempSumMatrix MathUtils.matrixOp(tempSumMatrix, new Operator() {private static final long serialVersionUID 2469461972825890810L;Overridepublic double process(double value) {return MathUtils.sigmod(value bias);}});paraLayer.setMapValue(j, tempSumMatrix);} // Of for j}// Of setConvolutionOutput/************************** Compute the convolution output according to the output of the last layer.** param paraLastLayer* the last layer.* param paraLayer* the current layer.************************/private void setSampOutput(final CnnLayer paraLayer, final CnnLayer paraLastLayer) {// int tempLastMapNum paraLastLayer.getOutMapNum();// Attention: paraLayer.outMapNum may not be right.for (int i 0; i paraLayer.outMapNum; i) {double[][] lastMap paraLastLayer.getMap(i);Size scaleSize paraLayer.getScaleSize();double[][] sampMatrix MathUtils.scaleMatrix(lastMap, scaleSize);paraLayer.setMapValue(i, sampMatrix);} // Of for i}// Of setSampOutput/************************** Train the cnn.************************/public void train(Dataset paraDataset, int paraRounds) {for (int t 0; t paraRounds; t) {System.out.println(Iteration: t);int tempNumEpochs paraDataset.size() / batchSize;if (paraDataset.size() % batchSize ! 0)tempNumEpochs;// logger.info(第{}次迭代epochsNum: {}, t, epochsNum);double tempNumCorrect 0;int tempCount 0;for (int i 0; i tempNumEpochs; i) {int[] tempRandomPerm MathUtils.randomPerm(paraDataset.size(), batchSize);CnnLayer.prepareForNewBatch();for (int index : tempRandomPerm) {boolean isRight train(paraDataset.getInstance(index));if (isRight)tempNumCorrect;tempCount;CnnLayer.prepareForNewRecord();} // Of for indexupdateParameters();if (i % 50 0) {System.out.print(..);if (i 50 tempNumEpochs)System.out.println();}}double p 1.0 * tempNumCorrect / tempCount;if (t % 10 1 p 0.96) {ALPHA 0.001 ALPHA * 0.9;// logger.info(设置 alpha {}, ALPHA);} // Of iffSystem.out.println(Training precision: p);// logger.info(计算精度 {}/{}{}., right, count, p);} // Of for i}// Of train/************************** Train the cnn with only one record.** param paraRecord* The given record.************************/private boolean train(Instance paraRecord) {forward(paraRecord);boolean result backPropagation(paraRecord);return result;}// Of train/************************** Back-propagation.** param paraRecord* The given record.************************/private boolean backPropagation(Instance paraRecord) {boolean result setOutputLayerErrors(paraRecord);setHiddenLayerErrors();return result;}// Of backPropagation/************************** Update parameters.************************/private void updateParameters() {for (int l 1; l layerBuilder.getNumLayers(); l) {CnnLayer layer layerBuilder.getLayer(l);CnnLayer lastLayer layerBuilder.getLayer(l - 1);switch (layer.getType()) {case CONVOLUTION:case OUTPUT:updateKernels(layer, lastLayer);updateBias(layer, lastLayer);break;default:break;}// Of switch} // Of for l}// Of updateParameters/************************** Update bias.************************/private void updateBias(final CnnLayer paraLayer, CnnLayer paraLastLayer) {final double[][][][] errors paraLayer.getErrors();// int mapNum paraLayer.getOutMapNum();// Attention: getOutMapNum() may not be correct.for (int j 0; j paraLayer.getOutMapNum(); j) {double[][] error MathUtils.sum(errors, j);double deltaBias MathUtils.sum(error) / batchSize;double bias paraLayer.getBias(j) ALPHA * deltaBias;paraLayer.setBias(j, bias);} // Of for j}// Of updateBias/************************** Update kernels.************************/private void updateKernels(final CnnLayer paraLayer, final CnnLayer paraLastLayer) {// int mapNum paraLayer.getOutMapNum();int tempLastMapNum paraLastLayer.getOutMapNum();// Attention: getOutMapNum() may not be rightfor (int j 0; j paraLayer.getOutMapNum(); j) {for (int i 0; i tempLastMapNum; i) {double[][] tempDeltaKernel null;for (int r 0; r batchSize; r) {double[][] error paraLayer.getError(r, j);if (tempDeltaKernel null)tempDeltaKernel MathUtils.convnValid(paraLastLayer.getMap(r, i), error);else {tempDeltaKernel MathUtils.matrixOp(MathUtils.convnValid(paraLastLayer.getMap(r, i), error),tempDeltaKernel, null, null, MathUtils.plus);} // Of if} // Of for rtempDeltaKernel MathUtils.matrixOp(tempDeltaKernel, divideBatchSize);if (!rangeCheck(tempDeltaKernel, -10, 10)) {System.exit(0);} // Of ifdouble[][] kernel paraLayer.getKernel(i, j);tempDeltaKernel MathUtils.matrixOp(kernel, tempDeltaKernel, multiplyLambda,multiplyAlpha, MathUtils.plus);paraLayer.setKernel(i, j, tempDeltaKernel);} // Of for i} // Of for j}// Of updateKernels/************************** Set errors of all hidden layers.************************/private void setHiddenLayerErrors() {// System.out.println(setHiddenLayerErrors);for (int l layerBuilder.getNumLayers() - 2; l 0; l--) {CnnLayer layer layerBuilder.getLayer(l);CnnLayer nextLayer layerBuilder.getLayer(l 1);// System.out.println(layertype layer.getType());switch (layer.getType()) {case SAMPLING:setSamplingErrors(layer, nextLayer);break;case CONVOLUTION:setConvolutionErrors(layer, nextLayer);break;default:break;}// Of switch} // Of for l}// Of setHiddenLayerErrors/************************** Set errors of a sampling layer.************************/private void setSamplingErrors(final CnnLayer paraLayer, final CnnLayer paraNextLayer) {// int mapNum layer.getOutMapNum();int tempNextMapNum paraNextLayer.getOutMapNum();// Attention: getOutMapNum() may not be correctfor (int i 0; i paraLayer.getOutMapNum(); i) {double[][] sum null;for (int j 0; j tempNextMapNum; j) {double[][] nextError paraNextLayer.getError(j);double[][] kernel paraNextLayer.getKernel(i, j);if (sum null) {sum MathUtils.convnFull(nextError, MathUtils.rot180(kernel));} else {sum MathUtils.matrixOp(MathUtils.convnFull(nextError, MathUtils.rot180(kernel)), sum, null,null, MathUtils.plus);} // Of if} // Of for jparaLayer.setError(i, sum);if (!rangeCheck(sum, -2, 2)) {System.out.println(setSampErrors, error out of range.\r\n Arrays.deepToString(sum));} // Of if} // Of for i}// Of setSamplingErrors/************************** Set errors of a sampling layer.************************/private void setConvolutionErrors(final CnnLayer paraLayer, final CnnLayer paraNextLayer) {// System.out.println(setConvErrors);for (int m 0; m paraLayer.getOutMapNum(); m) {Size tempScale paraNextLayer.getScaleSize();double[][] tempNextLayerErrors paraNextLayer.getError(m);double[][] tempMap paraLayer.getMap(m);double[][] tempOutMatrix MathUtils.matrixOp(tempMap, MathUtils.cloneMatrix(tempMap),null, MathUtils.one_value, MathUtils.multiply);tempOutMatrix MathUtils.matrixOp(tempOutMatrix,MathUtils.kronecker(tempNextLayerErrors, tempScale), null, null,MathUtils.multiply);paraLayer.setError(m, tempOutMatrix);// System.out.println(range check nextError);if (!rangeCheck(tempNextLayerErrors, -10, 10)) {System.out.println(setConvErrors, nextError out of range:\r\n Arrays.deepToString(tempNextLayerErrors));System.out.println(the new errors are:\r\n Arrays.deepToString(tempOutMatrix));System.exit(0);} // Of ifif (!rangeCheck(tempOutMatrix, -10, 10)) {System.out.println(setConvErrors, error out of range.);System.exit(0);} // Of if} // Of for m}// Of setConvolutionErrors/************************** Set errors of a sampling layer.************************/private boolean setOutputLayerErrors(Instance paraRecord) {CnnLayer tempOutputLayer layerBuilder.getOutputLayer();int tempMapNum tempOutputLayer.getOutMapNum();double[] tempTarget new double[tempMapNum];double[] tempOutMaps new double[tempMapNum];for (int m 0; m tempMapNum; m) {double[][] outmap tempOutputLayer.getMap(m);tempOutMaps[m] outmap[0][0];} // Of for mint tempLabel paraRecord.getLabel().intValue();tempTarget[tempLabel] 1;// Log.i(record.getLable() outmaps: // Util.fomart(outmaps)// Arrays.toString(target));for (int m 0; m tempMapNum; m) {tempOutputLayer.setError(m, 0, 0,tempOutMaps[m] * (1 - tempOutMaps[m]) * (tempTarget[m] - tempOutMaps[m]));} // Of for mreturn tempLabel MathUtils.getMaxIndex(tempOutMaps);}// Of setOutputLayerErrors/************************** Setup the network.************************/public void setup(int paraBatchSize) {CnnLayer tempInputLayer layerBuilder.getLayer(0);tempInputLayer.initOutMaps(paraBatchSize);for (int i 1; i layerBuilder.getNumLayers(); i) {CnnLayer tempLayer layerBuilder.getLayer(i);CnnLayer tempLastLayer layerBuilder.getLayer(i - 1);int tempLastMapNum tempLastLayer.getOutMapNum();switch (tempLayer.getType()) {case INPUT:break;case CONVOLUTION:tempLayer.setMapSize(tempLastLayer.getMapSize().subtract(tempLayer.getKernelSize(), 1));tempLayer.initKernel(tempLastMapNum);tempLayer.initBias();tempLayer.initErrors(paraBatchSize);tempLayer.initOutMaps(paraBatchSize);break;case SAMPLING:tempLayer.setOutMapNum(tempLastMapNum);tempLayer.setMapSize(tempLastLayer.getMapSize().divide(tempLayer.getScaleSize()));tempLayer.initErrors(paraBatchSize);tempLayer.initOutMaps(paraBatchSize);break;case OUTPUT:tempLayer.initOutputKernel(tempLastMapNum, tempLastLayer.getMapSize());tempLayer.initBias();tempLayer.initErrors(paraBatchSize);tempLayer.initOutMaps(paraBatchSize);break;}// Of switch} // Of for i}// Of setup/************************** Predict for the dataset.************************/public int[] predict(Dataset paraDataset) {System.out.println(Predicting ... );CnnLayer.prepareForNewBatch();int[] resultPredictions new int[paraDataset.size()];double tempCorrect 0.0;Instance tempRecord;for (int i 0; i paraDataset.size(); i) {tempRecord paraDataset.getInstance(i);forward(tempRecord);CnnLayer outputLayer layerBuilder.getOutputLayer();int tempMapNum outputLayer.getOutMapNum();double[] tempOut new double[tempMapNum];for (int m 0; m tempMapNum; m) {double[][] outmap outputLayer.getMap(m);tempOut[m] outmap[0][0];} // Of for mresultPredictions[i] MathUtils.getMaxIndex(tempOut);if (resultPredictions[i] tempRecord.getLabel().intValue()) {tempCorrect;} // Of if} // Of forSystem.out.println(Accuracy: tempCorrect / paraDataset.size());return resultPredictions;}// Of predict/************************** Range check, only for debugging.** param paraMatix* The given matrix.* param paraLowerBound* param paraUpperBound************************/public boolean rangeCheck(double[][] paraMatrix, double paraLowerBound, double paraUpperBound) {for (int i 0; i paraMatrix.length; i) {for (int j 0; j paraMatrix[0].length; j) {if ((paraMatrix[i][j] paraLowerBound) || (paraMatrix[i][j] paraUpperBound)) {System.out.println( paraMatrix[i][j] out of range ( paraLowerBound , paraUpperBound )\r\n);return false;} // Of if} // Of for j} // Of for ireturn true;}// Of rangeCheck/************************** The main entrance.************************/public static void main(String[] args) {LayerBuilder builder new LayerBuilder();// Input layer, the maps are 28*28builder.addLayer(new CnnLayer(LayerTypeEnum.INPUT, -1, new Size(28, 28)));// Convolution output has size 24*24, 24281-5builder.addLayer(new CnnLayer(LayerTypeEnum.CONVOLUTION, 6, new Size(5, 5)));// Sampling output has size 12*12,1224/2builder.addLayer(new CnnLayer(LayerTypeEnum.SAMPLING, -1, new Size(2, 2)));// Convolution output has size 8*8, 8121-5builder.addLayer(new CnnLayer(LayerTypeEnum.CONVOLUTION, 12, new Size(5, 5)));// Sampling output has size4×4,48/2builder.addLayer(new CnnLayer(LayerTypeEnum.SAMPLING, -1, new Size(2, 2)));// output layer, digits 0 - 9.builder.addLayer(new CnnLayer(LayerTypeEnum.OUTPUT, 10, null));// Construct the full CNN.FullCnn tempCnn new FullCnn(builder, 10);Dataset tempTrainingSet new Dataset(d:/data/train.format, ,, 784);// Train the model.tempCnn.train(tempTrainingSet, 10);// tempCnn.predict(tempTrainingSet);}// Of main
}// Of class MfCnn 4. LayerBuilder类
package Day_81;import java.util.ArrayList;
import java.util.List;/*** CnnLayer builder.** author Fan Min minfanphd163.com.*/
public class LayerBuilder {/*** Layers.*/private ListCnnLayer layers;/************************** The first constructor.************************/public LayerBuilder() {layers new ArrayListCnnLayer();}// Of the first constructor/************************** The second constructor.************************/public LayerBuilder(CnnLayer paraLayer) {this();layers.add(paraLayer);}// Of the second constructor/************************** Add a layer.** param paraLayer* The new layer.************************/public void addLayer(CnnLayer paraLayer) {layers.add(paraLayer);}// Of addLayer/************************** Get the specified layer.** param paraIndex* The index of the layer.************************/public CnnLayer getLayer(int paraIndex) throws RuntimeException{if (paraIndex layers.size()) {throw new RuntimeException(CnnLayer paraIndex is out of range: layers.size() .);}//Of ifreturn layers.get(paraIndex);}//Of getLayer/************************** Get the output layer.************************/public CnnLayer getOutputLayer() {return layers.get(layers.size() - 1);}//Of getOutputLayer/************************** Get the number of layers.************************/public int getNumLayers() {return layers.size();}//Of getNumLayers
}// Of class LayerBuilder5. LayerTypeEnum类
package Day_81;/*** Enumerate all layer types.** author Fan Min minfanphd163.com.*/
public enum LayerTypeEnum {INPUT, CONVOLUTION, SAMPLING, OUTPUT;
}//Of enum LayerTypeEnum6. MathUtils类
package Day_81;import java.io.Serializable;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Random;
import java.util.Set;/*** Math operations.** Adopted from cnn-master.*/
public class MathUtils {/*** An interface for different on-demand operators.*/public interface Operator extends Serializable {public double process(double value);}// Of interfact Operator/*** The one-minus-the-value operator.*/public static final Operator one_value new Operator() {private static final long serialVersionUID 3752139491940330714L;Overridepublic double process(double value) {return 1 - value;}// Of process};/*** The sigmoid operator.*/public static final Operator sigmoid new Operator() {private static final long serialVersionUID -1952718905019847589L;Overridepublic double process(double value) {return 1 / (1 Math.pow(Math.E, -value));}// Of process};/*** An interface for operations with two operators.*/interface OperatorOnTwo extends Serializable {public double process(double a, double b);}// Of interface OperatorOnTwo/*** Plus.*/public static final OperatorOnTwo plus new OperatorOnTwo() {private static final long serialVersionUID -6298144029766839945L;Overridepublic double process(double a, double b) {return a b;}// Of process};/*** Multiply.*/public static OperatorOnTwo multiply new OperatorOnTwo() {private static final long serialVersionUID -7053767821858820698L;Overridepublic double process(double a, double b) {return a * b;}// Of process};/*** Minus.*/public static OperatorOnTwo minus new OperatorOnTwo() {private static final long serialVersionUID 7346065545555093912L;Overridepublic double process(double a, double b) {return a - b;}// Of process};/************************** Print a matrix************************/public static void printMatrix(double[][] matrix) {for (int i 0; i matrix.length; i) {String line Arrays.toString(matrix[i]);line line.replaceAll(, , \t);System.out.println(line);} // Of for iSystem.out.println();}// Of printMatrix/************************** Rotate the matrix 180 degrees.************************/public static double[][] rot180(double[][] matrix) {matrix cloneMatrix(matrix);int m matrix.length;int n matrix[0].length;for (int i 0; i m; i) {for (int j 0; j n / 2; j) {double tmp matrix[i][j];matrix[i][j] matrix[i][n - 1 - j];matrix[i][n - 1 - j] tmp;}}for (int j 0; j n; j) {for (int i 0; i m / 2; i) {double tmp matrix[i][j];matrix[i][j] matrix[m - 1 - i][j];matrix[m - 1 - i][j] tmp;}}return matrix;}// Of rot180private static Random myRandom new Random(2);/************************** Generate a random matrix with the given size. Each value takes value in* [-0.005, 0.095].************************/public static double[][] randomMatrix(int x, int y, boolean b) {double[][] matrix new double[x][y];// int tag 1;for (int i 0; i x; i) {for (int j 0; j y; j) {matrix[i][j] (myRandom.nextDouble() - 0.05) / 10;} // Of for j} // Of for ireturn matrix;}// Of randomMatrix/************************** Generate a random array with the given length. Each value takes value in* [-0.005, 0.095].************************/public static double[] randomArray(int len) {double[] data new double[len];for (int i 0; i len; i) {//data[i] myRandom.nextDouble() / 10 - 0.05;data[i] 0;} // Of for ireturn data;}// Of randomArray/************************** Generate a random perm with the batch size.************************/public static int[] randomPerm(int size, int batchSize) {SetInteger set new HashSetInteger();while (set.size() batchSize) {set.add(myRandom.nextInt(size));}int[] randPerm new int[batchSize];int i 0;for (Integer value : set)randPerm[i] value;return randPerm;}// Of randomPerm/************************** Clone a matrix. Do not use it reference directly.************************/public static double[][] cloneMatrix(final double[][] matrix) {final int m matrix.length;int n matrix[0].length;final double[][] outMatrix new double[m][n];for (int i 0; i m; i) {for (int j 0; j n; j) {outMatrix[i][j] matrix[i][j];} // Of for j} // Of for ireturn outMatrix;}// Of cloneMatrix/************************** Matrix operation with the given operator on single operand.************************/public static double[][] matrixOp(final double[][] ma, Operator operator) {final int m ma.length;int n ma[0].length;for (int i 0; i m; i) {for (int j 0; j n; j) {ma[i][j] operator.process(ma[i][j]);} // Of for j} // Of for ireturn ma;}// Of matrixOp/************************** Matrix operation with the given operator on two operands.************************/public static double[][] matrixOp(final double[][] ma, final double[][] mb,final Operator operatorA, final Operator operatorB, OperatorOnTwo operator) {final int m ma.length;int n ma[0].length;if (m ! mb.length || n ! mb[0].length)throw new RuntimeException(ma.length: ma.length mb.length: mb.length);for (int i 0; i m; i) {for (int j 0; j n; j) {double a ma[i][j];if (operatorA ! null)a operatorA.process(a);double b mb[i][j];if (operatorB ! null)b operatorB.process(b);mb[i][j] operator.process(a, b);} // Of for j} // Of for ireturn mb;}// Of matrixOp/************************** Extend the matrix to a bigger one (a number of times).************************/public static double[][] kronecker(final double[][] matrix, final Size scale) {final int m matrix.length;int n matrix[0].length;final double[][] outMatrix new double[m * scale.width][n * scale.height];for (int i 0; i m; i) {for (int j 0; j n; j) {for (int ki i * scale.width; ki (i 1) * scale.width; ki) {for (int kj j * scale.height; kj (j 1) * scale.height; kj) {outMatrix[ki][kj] matrix[i][j];}}}}return outMatrix;}// Of kronecker/************************** Scale the matrix.************************/public static double[][] scaleMatrix(final double[][] matrix, final Size scale) {int m matrix.length;int n matrix[0].length;final int sm m / scale.width;final int sn n / scale.height;final double[][] outMatrix new double[sm][sn];if (sm * scale.width ! m || sn * scale.height ! n)throw new RuntimeException(scale matrix);final int size scale.width * scale.height;for (int i 0; i sm; i) {for (int j 0; j sn; j) {double sum 0.0;for (int si i * scale.width; si (i 1) * scale.width; si) {for (int sj j * scale.height; sj (j 1) * scale.height; sj) {sum matrix[si][sj];} // Of for sj} // Of for sioutMatrix[i][j] sum / size;} // Of for j} // Of for ireturn outMatrix;}// Of scaleMatrix/************************** Convolution full to obtain a bigger size. It is used in back-propagation.************************/public static double[][] convnFull(double[][] matrix, final double[][] kernel) {int m matrix.length;int n matrix[0].length;final int km kernel.length;final int kn kernel[0].length;final double[][] extendMatrix new double[m 2 * (km - 1)][n 2 * (kn - 1)];for (int i 0; i m; i) {for (int j 0; j n; j) {extendMatrix[i km - 1][j kn - 1] matrix[i][j];} // Of for j} // Of for ireturn convnValid(extendMatrix, kernel);}// Of convnFull/************************** Convolution operation, from a given matrix and a kernel, sliding and sum* to obtain the result matrix. It is used in forward.************************/public static double[][] convnValid(final double[][] matrix, double[][] kernel) {// kernel rot180(kernel);int m matrix.length;int n matrix[0].length;final int km kernel.length;final int kn kernel[0].length;int kns n - kn 1;final int kms m - km 1;final double[][] outMatrix new double[kms][kns];for (int i 0; i kms; i) {for (int j 0; j kns; j) {double sum 0.0;for (int ki 0; ki km; ki) {for (int kj 0; kj kn; kj)sum matrix[i ki][j kj] * kernel[ki][kj];}outMatrix[i][j] sum;}}return outMatrix;}// Of convnValid/************************** Convolution on a tensor.************************/public static double[][] convnValid(final double[][][][] matrix, int mapNoX,double[][][][] kernel, int mapNoY) {int m matrix.length;int n matrix[0][mapNoX].length;int h matrix[0][mapNoX][0].length;int km kernel.length;int kn kernel[0][mapNoY].length;int kh kernel[0][mapNoY][0].length;int kms m - km 1;int kns n - kn 1;int khs h - kh 1;if (matrix.length ! kernel.length)throw new RuntimeException(length);final double[][][] outMatrix new double[kms][kns][khs];for (int i 0; i kms; i) {for (int j 0; j kns; j)for (int k 0; k khs; k) {double sum 0.0;for (int ki 0; ki km; ki) {for (int kj 0; kj kn; kj)for (int kk 0; kk kh; kk) {sum matrix[i ki][mapNoX][j kj][k kk]* kernel[ki][mapNoY][kj][kk];}}outMatrix[i][j][k] sum;}}return outMatrix[0];}// Of convnValid/************************** The sigmod operation.************************/public static double sigmod(double x) {return 1 / (1 Math.pow(Math.E, -x));}// Of sigmod/************************** Sum all values of a matrix.************************/public static double sum(double[][] error) {int m error.length;int n error[0].length;double sum 0.0;for (int i 0; i m; i) {for (int j 0; j n; j) {sum error[i][j];}}return sum;}// Of sum/************************** Ad hoc sum.************************/public static double[][] sum(double[][][][] errors, int j) {int m errors[0][j].length;int n errors[0][j][0].length;double[][] result new double[m][n];for (int mi 0; mi m; mi) {for (int nj 0; nj n; nj) {double sum 0;for (int i 0; i errors.length; i)sum errors[i][j][mi][nj];result[mi][nj] sum;}}return result;}// Of sum/************************** Get the index of the maximal value for the final classification.************************/public static int getMaxIndex(double[] out) {double max out[0];int index 0;for (int i 1; i out.length; i)if (out[i] max) {max out[i];index i;}return index;}// Of getMaxIndex
}// Of MathUtils7. Size类
package Day_81;/*** The size of a convolution core.** author Fan Min minfanphd163.com.*/
public class Size {/*** Cannot be changed after initialization.*/public final int width;/*** Cannot be changed after initialization.*/public final int height;/************************** The first constructor.** param paraWidth* The given width.* param paraHeight* The given height.************************/public Size(int paraWidth, int paraHeight) {width paraWidth;height paraHeight;}// Of the first constructor/************************** Divide a scale with another one. For example (4, 12) / (2, 3) (2, 4).** param paraScaleSize* The given scale size.* return The new size.************************/public Size divide(Size paraScaleSize) {int resultWidth width / paraScaleSize.width;int resultHeight height / paraScaleSize.height;if (resultWidth * paraScaleSize.width ! width|| resultHeight * paraScaleSize.height ! height)throw new RuntimeException(Unable to divide this with paraScaleSize);return new Size(resultWidth, resultHeight);}// Of divide/************************** Subtract a scale with another one, and add a value. For example (4, 12) -* (2, 3) 1 (3, 10).** param paraScaleSize* The given scale size.* param paraAppend* The appended size to both dimensions.* return The new size.************************/public Size subtract(Size paraScaleSize, int paraAppend) {int resultWidth width - paraScaleSize.width paraAppend;int resultHeight height - paraScaleSize.height paraAppend;return new Size(resultWidth, resultHeight);}// Of subtract/************************** param The* string showing itself.************************/public String toString() {String resultString ( width , height );return resultString;}// Of toString/************************** Unit test.************************/public static void main(String[] args) {Size tempSize1 new Size(4, 6);Size tempSize2 new Size(2, 2);System.out.println( tempSize1 divide tempSize2 tempSize1.divide(tempSize2));System.out.printf(a);try {System.out.println( tempSize2 divide tempSize1 tempSize2.divide(tempSize1));} catch (Exception ee) {System.out.println(ee);} // Of trySystem.out.println( tempSize1 - tempSize2 1 tempSize1.subtract(tempSize2, 1));}// Of main
}// Of class Size四. 运行结果
