[从头学数学] 第207节 风险与决策

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下进入了[九转金丹]之第七转的修炼。
这次要研究的是[风险与决策]。

正剧开始：

星历2016年05月09日 10:58:13, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起研究[风险与决策]。

<span style="font-size:18px;">0.30 , 0.50 , 0.20 , *12.00 , 8.00 , 3.00 , 5.00 , 6.00 , 3.00 , -4.00 , -1.00 , 2.00 , =5.30 , 5.20 , 2.80 , if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();var m1 = [[12,5,-4],[8,6,-1],[3,3,2]];var m2 = [[0.3, 0.5, 0.2]];m1 = matrix.transposition(m1);var m3 = matrix.multiple(m2, m1);matrix.print(m2);hint('*');matrix.print(m1);hint('=');matrix.print(m3);}</span>

<span style="font-size:18px;">0.01 , 0.25 , 0.74 , *3800.00 , 62000.00 , 60000.00 , 3800.00 , 2000.00 , 10000.00 , 3800.00 , 2000.00 , 0.00 , =3800.00 , 2600.00 , 3100.00 , if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();var m1 = [[3800, 62000, 60000], [3800, 2000, 10000],[3800, 2000, 0]];var m2 = [[0.01, 0.25, 0.74]];var m3 = matrix.multiple(m2, m1);matrix.print(m2);hint('*');matrix.print(m1);hint('=');matrix.print(m3);}</span>

<span style="font-size:18px;">0.60 , 0.40 , *-8.00 , -2.00 , 0.00 , 0.00 , -3.00 , -4.00 , =-4.80 , -2.40 , -1.60 , if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();//损失函数，单位：万元var m1 = [[-8, -2, 0], [0, -3, -4]];var m2 = [[0.6, 0.4]];var m3 = matrix.multiple(m2, m1);matrix.print(m2);hint('*');matrix.print(m1);hint('=');matrix.print(m3);}</span>

<span style="font-size:18px;">//进货17台收益最大0.05 , 0.10 , 0.20 , 0.40 , 0.20 , 0.05 , *3000.00 , 2200.00 , 1400.00 , 600.00 , -200.00 , -1000.00 , 3000.00 , 3200.00 , 2400.00 , 1600.00 , 800.00 , 0.00 , 3000.00 , 3200.00 , 3400.00 , 2600.00 , 1800.00 , 1000.00 , 3000.00 , 3200.00 , 3400.00 , 3600.00 , 2800.00 , 2000.00 , 3000.00 , 3200.00 , 3400.00 , 3600.00 , 3800.00 , 3000.00 , 3000.00 , 3200.00 , 3400.00 , 3600.00 , 3800.00 , 4000.00 , =3000.00 , 3150.00 , 3200.00 , 3050.00 , 2500.00 , 1750.00 , if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();//收益函数，单位：元var m1 = [], vector1 = [];//6种销售量for (var i = 15; i <= 20; i++) { //销售量vector1 = [];for (var j = 15; j <= 20; j++) { //进货量vector1.push(1000*Math.min(i, j)-800*j);}m1.push(vector1);}var m2 = [[0.05, 0.10, 0.20, 0.40, 0.20, 0.05]];var m3 = matrix.multiple(m2, m1);matrix.print(m2);hint('*');matrix.print(m1);hint('=');matrix.print(m3);}</span>

<span style="font-size:18px;">//进货100本书收益最大0.20 , 0.40 , 0.30 , 0.10 , *100.00 , 0.00 , -100.00 , -200.00 , 100.00 , 200.00 , 100.00 , 0.00 , 100.00 , 200.00 , 300.00 , 200.00 , 100.00 , 200.00 , 300.00 , 400.00 , =100.00 , 160.00 , 140.00 , 60.00 ,if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();//收益函数，单位：元var m1 = [], vector1 = [];//4种销售量for (var i = 50; i <= 200; i+=50) { //一个月内销售量vector1 = [];for (var j = 50; j <= 200; j+=50) { //进货量vector1.push(6*Math.min(i, j)-4*j + 2*(j-Math.min(i,j)));}m1.push(vector1);}var m2 = [[0.2, 0.4, 0.3, 0.1]];var m3 = matrix.multiple(m2, m1);matrix.print(m2);hint('*');matrix.print(m1);hint('=');matrix.print(m3);}</span>

<span style="font-size:18px;">0.90 , 0.10 , *1300.00 , 1500.00 , 1300.00 , 100.00 , =1300.00 , 1360.00 , if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();//收益函数，单位：元var m1 = [[1300, 1300],[1500, 100]];var m2 = [[0.9,0.1]];m1 = matrix.transposition(m1);var m3 = matrix.multiple(m2, m1);matrix.print(m2);hint('*');matrix.print(m1);hint('=');matrix.print(m3);}</span>

<span style="font-size:18px;">9.050,9.002,9.000,9.000,9.000,9.000,9.000,9.000,9.000,9.000,9.0009.200,8.920,8.822,8.788,8.776,8.771,8.770,8.770,8.769,8.769,8.769if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();//马尔可夫转移概率矩阵//第一种选择var m1 = [[0.95, 0.05],[0.9, 0.1]];var m2 = [[1, 0]];var m3 = matrix.multiple(m2, m1);var profitA = [];var tmp = 0;tmp = matrix.multiple(m3, [[10], [-9]]);profitA.push(tmp[0][0].toFixed(3));for (var i = 0; i < 10; i++) {m3 = matrix.multiple(m3, m1);tmp = matrix.multiple(m3, [[10], [-9]]);profitA.push(tmp[0][0].toFixed(3));}hint(profitA);//第二种选择m1 = [[0.95, 0.05], [0.6, 0.4]];m2 = [[1, 0]];m3 = matrix.multiple(m2, m1);var profitB = [];tmp = 0;tmp = matrix.multiple(m3, [[10], [-6]]);profitB.push(tmp[0][0].toFixed(3));for (var i = 0; i < 10; i++) {m3 = matrix.multiple(m3, m1);tmp = matrix.multiple(m3, [[10], [-6]]);profitB.push(tmp[0][0].toFixed(3));}hint(profitB);}</span>

<span style="font-size:18px;">1.000 , 0.000 , *0.950 , 0.050 , 0.600 , 0.400 , =0.950 , 0.050 , *0.950 , 0.050 , 0.600 , 0.400 , =0.932 , 0.068 , *0.950 , 0.050 , 0.600 , 0.400 , =0.926 , 0.074 , *0.950 , 0.050 , 0.600 , 0.400 , =0.924 , 0.076 , *0.950 , 0.050 , 0.600 , 0.400 , =0.923 , 0.077 , if (1) {var analyze = new DataAnalyze();var matrix = new Matrix();//马尔可夫转移概率矩阵var m1 = [[0.95, 0.05],[0.6, 0.4]];var m2 = [[1, 0]];var m3 = matrix.multiple(m2, m1);matrix.print(m2);hint('*');matrix.print(m1);hint('=');matrix.print(m3);for (var i = 0; i < 4; i++) {m2 = m3;hint('*');matrix.print(m1);hint('=');m3 = matrix.multiple(m2, m1);matrix.print(m3);}}</span>

<span style="font-size:18px;">/*** @usage   矩阵类* @author  mw* @date    2016年03月24日  星期四  14:51:45 * @param* @return**/function Matrix() {this.delta = function(matrix) {var size = matrix.length;if (!matrix[0].length) {return 0;}else {if (matrix[0].length != size) {return 0;}if (size < 1) {return 0;}else if (size == 1) {return matrix[0][0];}else {var d = 0;var subMatrix = [];for (var i = 0; i < size; i++) {subMatrix = this.subSet(matrix, i, 0);d += Math.pow(-1, i)*matrix[i][0]*this.delta(subMatrix);}return d;}}}this.subSet = function(matrix, row, col) {var size = matrix.length;if (!matrix[0].length) {return [];}else {if (matrix[0].length != size) {return [];}var newMatrix = new Array();var rowArray= new Array();for (var i = 0; i < size; i++) {if (i == row) {continue;}else {rowArray = [];for (var j = 0; j < size; j++) {if (j == col) {continue;}else {rowArray.push(matrix[i][j]);}}newMatrix.push(rowArray)}}return newMatrix;}}this.identityMatrix = function(rank) {var newMatrix = new Array();var rowArray= new Array();for (var i = 0; i < rank; i++) {rowArray = [];for (var j = 0; j < rank; j++) {if (j == i) {rowArray.push(1);}else {rowArray.push(0);}}newMatrix.push(rowArray);}return newMatrix;}//建立row*col空矩阵this.zeroMatrix = function(row, col) {var newMatrix = new Array();var rowArray= new Array();for (var i = 0; i < row; i++) {rowArray = [];for (var j = 0; j < col; j++) {rowArray.push(0);}newMatrix.push(rowArray);}return newMatrix;}//把从1-n的n个数按顺序放到矩阵中this.sequenceMatrix = function(rank) {var newMatrix = new Array();var rowArray= new Array();var count = 0;for (var i = 0; i < rank; i++) {rowArray = [];for (var j = 0; j < rank; j++) {count++;rowArray.push(count);}newMatrix.push(rowArray);}return newMatrix;}this.print = function(matrix) {var size = matrix.length;if (!matrix[0].length) {return [];}else {var rSize = matrix[0].length;var s = '';for (var i = 0; i < size; i++) {s = '';for (var j = 0; j < rSize; j++) {s += matrix[i][j].toFixed(3) + ' , ';}document.write(s+'<br/>');}}}this.deepCopy = function(matrix) {var size = matrix.length;if (!matrix[0].length) {return this.zeroMatrix(1, 1);}else {var rSize = matrix[0].length;var newMatrix = new Array();var rowArray= new Array();for (var i = 0; i < size; i++) {rowArray = [];for (var j = 0; j < rSize; j++) {rowArray.push(matrix[i][j]);}newMatrix.push(rowArray);}return newMatrix;}}/*** @usage   矩阵的转置* @author  mw* @date    2016年05月09日  星期一  08:21:34 * @param* @return**/this.transposition = function(matrix) {var row = matrix.length;var col = matrix[0].length;if (row > 0 && col > 0) {var transMatrix = this.zeroMatrix(col, row);for (var i = 0; i < row; i++) {for (var j = 0; j < col; j++) {transMatrix[j][i] = matrix[i][j];}}return transMatrix;}return this.zeroMatrix(1, 1);}/*** @usage   矩阵的乘法* @author  mw* @date    2016年05月02日  星期一  10:44:46 * @param* @return**/this.multiple = function(matrix1, matrix2) {var row1 = matrix1.length;var col1 = matrix1[0].length;var row2 = matrix2.length;var col2 = matrix2[0].length;var A = [row1, col1, row2, col2];if (col1 != row2) {return this.zeroMatrix(1, 1);}var mulResult = this.zeroMatrix(row1, col2);for (var i = 0; i < row1; i++) {for (var j = 0; j < col2; j++) {for (var k = 0; k < row2; k++) {mulResult[i][j] += matrix1[i][k]*matrix2[k][j];}}}return mulResult;}this.add = function(matrix1, matrix2) {var row1 = matrix1.length;var col1 = matrix1[0].length;var row2 = matrix2.length;var col2 = matrix2[0].length;if (row1 != row2 || col1 != col2) {return this.zeroMatrix(1, 1);}var addResult = this.zeroMatrix(row1, col1);for (var i = 0; i < row1; i++) {for (var j = 0; j < col1; j++) {addResult[i][j] = matrix1[i][j]+matrix2[i][j];}}return addResult;}//二阶矩阵的逆this.invOfRank2 = function(matrix) {var d = this.delta(matrix);if (d != 0) {return [[matrix[1][1]/d, -matrix[0][1]/d], [-matrix[1][0]/d, matrix[0][0]/d]];}else {return this.zeroMatrix(1, 1);}}//二阶矩阵的特征值this.eigenvalue = function(matrix) {var a = matrix[0][0];var b = matrix[0][1];var c = matrix[1][0];var d = matrix[1][1];var judge = (a+d)*(a+d)-4*(a*d-b*c);if ( judge >= 0) {var lambda_1 = 0.5*((a+d)-Math.sqrt(judge));var lambda_2 = 0.5*((a+d)+Math.sqrt(judge));}//特征向量有很多组，这里随便取一组//特征值放在第一行，然后是每个特征值对应的一个特征向量if (b != 0) {return [[lambda_1, lambda_2], [1, (lambda_1-a)/b], [b/(lambda_2-a), 1]];}else if (c != 0) {return [[lambda_1, lambda_2], [1, c/(lambda_1-d)], [(lambda_2-d)/c, 1]];}return this.zeroMatrix(1, 1);}}</span>

本节到此结束，欲知后事如何，请看下回分解。