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change upper triangular
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@liamkuan
liamkuan committed May 1, 2019
1 parent de2c765 commit cac2168
Showing 1 changed file with 65 additions and 52 deletions.
117 changes: 65 additions & 52 deletions lib/src/command/matrix.dart
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Original file line number Diff line number Diff line change
Expand Up @@ -18,7 +18,7 @@ class MatrixUtil {
buffer.write("\n\n");
}
var result = buffer.toString();
result = result.substring(0,result.length - 2);
result = result.substring(0, result.length - 2);
return result;
}

Expand All @@ -39,8 +39,9 @@ class MatrixUtil {
/// 矩阵相乘
static List<List<num>> m2mRide(List<List<num>> list1, List<List<num>> list2) {
if (list1[0].length != list2.length) {
throw FormatException(SettingData.language == 'zh' ? "相乘矩阵的行列数不符合要求" :
"The rows and columns of the multiplication matrix do not meet the requirements");
throw FormatException(SettingData.language == 'zh'
? "相乘矩阵的行列数不符合要求"
: "The rows and columns of the multiplication matrix do not meet the requirements");
}
List<List<num>> newl = [];
num sum = 0.0;
Expand All @@ -61,7 +62,9 @@ class MatrixUtil {
static List<List<num>> m2mMinus(
List<List<num>> list1, List<List<num>> list2) {
if (list1.length != list2.length || list1[0].length != list2[0].length) {
throw FormatException(SettingData.language == 'zh' ? "相减矩阵的行列数不符合要求" : "The number of rows and columns in the subtraction matrix does not meet the requirements");
throw FormatException(SettingData.language == 'zh'
? "相减矩阵的行列数不符合要求"
: "The number of rows and columns in the subtraction matrix does not meet the requirements");
}
List<List<num>> newl = [];
for (int i = 0; i < list1.length; i++) {
Expand All @@ -76,7 +79,9 @@ class MatrixUtil {
/// 矩阵相加
static List<List<num>> m2mPlus(List<List<num>> list1, List<List<num>> list2) {
if (list1.length != list2.length || list1[0].length != list2[0].length) {
throw FormatException(SettingData.language == 'zh' ? "相加矩阵的行列数不符合要求" : "The number of rows and columns in the additive matrix does not meet the requirement");
throw FormatException(SettingData.language == 'zh'
? "相加矩阵的行列数不符合要求"
: "The number of rows and columns in the additive matrix does not meet the requirement");
}
List<List<num>> newl = [];
for (int i = 0; i < list1.length; i++) {
Expand Down Expand Up @@ -109,7 +114,9 @@ class MatrixUtil {
/// 矩阵除以一个浮点数
static List<List<num>> m2dDivide(List<List<num>> list1, num d) {
if (d == 0.0) {
throw FormatException(SettingData.language == 'zh' ? "除数不能为零" : "The divisor cannot be zero");
throw FormatException(SettingData.language == 'zh'
? "除数不能为零"
: "The divisor cannot be zero");
}
List<List<num>> newl = [];
for (int i = 0; i < list1.length; i++) {
Expand Down Expand Up @@ -155,7 +162,10 @@ class MatrixUtil {

/// 获取给定行列式的值
static num getDetValue(List<List<num>> list) {
if (!isSquare(list)) throw FormatException(SettingData.language == 'zh' ? '只有方阵才能求行列式的值' : "Only a square matrix can evaluate a determinant");
if (!isSquare(list))
throw FormatException(SettingData.language == 'zh'
? '只有方阵才能求行列式的值'
: "Only a square matrix can evaluate a determinant");
if (list.length == 2) {
return list[0][0] * list[1][1] - list[0][1] * list[1][0];
}
Expand All @@ -177,7 +187,10 @@ class MatrixUtil {

/// 获取矩阵的逆阵
static List<List<num>> getAdjoint(List<List<num>> list) {
if (!isSquare(list)) throw FormatException(SettingData.language == 'zh' ? '只有方阵才可逆' : "Only the square matrix is invertible");
if (!isSquare(list))
throw FormatException(SettingData.language == 'zh'
? '只有方阵才可逆'
: "Only the square matrix is invertible");
List<List<num>> newdata = [];
//1阶方阵返回倒数
if (list.length == 1) {
Expand All @@ -186,7 +199,10 @@ class MatrixUtil {
return newdata;
}
num A = getDetValue(list);
if (A == 0.0) throw FormatException(SettingData.language == 'zh' ? '行列式的值为零的矩阵不能求逆' : "A matrix whose determinant is zero cannot be inversed");
if (A == 0.0)
throw FormatException(SettingData.language == 'zh'
? '行列式的值为零的矩阵不能求逆'
: "A matrix whose determinant is zero cannot be inversed");

//2阶方阵直接求逆
if (list.length == 2) {
Expand Down Expand Up @@ -217,9 +233,13 @@ class MatrixUtil {
/// 获取给定方阵中 （h,v）位置的代数余子式
static List<List<num>> getConfactor(List<List<num>> list, int h, int v) {
if (!(h < list.length)) {
throw FormatException(SettingData.language == 'zh' ? 'h: $h 索引值越界 H: ${list.length}' : "h: $h The index value is out of bounds H: ${list.length}");
throw FormatException(SettingData.language == 'zh'
? 'h: $h 索引值越界 H: ${list.length}'
: "h: $h The index value is out of bounds H: ${list.length}");
} else if (!(v < list[0].length)) {
throw FormatException(SettingData.language == 'zh' ? 'v: $v 索引值越界 V: ${list[0].length}' : "v: $v The index value is out of bounds V: ${list[0].length}");
throw FormatException(SettingData.language == 'zh'
? 'v: $v 索引值越界 V: ${list[0].length}'
: "v: $v The index value is out of bounds V: ${list[0].length}");
}
List<List<num>> newlist = [];
for (int i = 0; i < list.length; i++) {
Expand Down Expand Up @@ -247,23 +267,23 @@ class MatrixUtil {
return newlist;
}

/// 获取传入矩阵的上三角矩阵
/// 获取传入矩阵的上三角矩阵(列选主元法)
static List<List<num>> upperTriangular(List<List<num>> list) {
//(n-1)!*2n (n-1)!n
var newlist = copyMatrix(list); //拷贝出一个新矩阵
var newlist = copyMatrix(list); //深拷贝出一个新矩阵
var divisor = new List(list.length); //用于记录对角线下的每一行的倍数
for (int i = 0; i < newlist.length; i++) {
if (newlist[i][i] == 0) {
//如果该对角线上的元素为零，将最近的不为零的一行换上来
var temp;
for (int k = i + 1; k < newlist.length; k++) {
if (newlist[k][i] != 0) {
temp = newlist[k];
newlist[k] = newlist[i];
newlist[i] = temp;
}
num max = newlist[i][i]; //记录第i列的最大值
var temp;
for (int k = i + 1; k < newlist.length; k++) {
if (newlist[k][i] > max) {
max = newlist[k][i];
temp = newlist[k];
newlist[k] = newlist[i];
newlist[i] = temp;
}
}
if(max == 0) throw FormatException(SettingData.language == "zh" ?
"第 $i 列全为零！" : "The $i column of the matrix is all zero");
for (int k = i + 1; k < newlist.length; k++) {
if (newlist[k][i] == 0) {
continue;
Expand Down Expand Up @@ -292,7 +312,9 @@ class MatrixUtil {
static List<num> _listMinus(List<num> list1, List<num> list2) {
List<num> newlist = [];
if (list1.length != list2.length) {
throw FormatException(SettingData.language == 'zh' ? '相减数组的长度不相等' : "The length of the subtraction array is not equal");
throw FormatException(SettingData.language == 'zh'
? '相减数组的长度不相等'
: "The length of the subtraction array is not equal");
}
for (int i = 0; i < list1.length; i++) {
newlist.add(list1[i] - list2[i]);
Expand All @@ -318,10 +340,12 @@ class MatrixUtil {
}
return newresult;
}

///求绝对值
static num _abs(num d) {
return d > 0 ? d : -d;
}

///初始化一个m行n列的矩阵
static List<List<num>> initMatrix(int m, int n) {
List<List<num>> matrix = [];
Expand All @@ -330,10 +354,13 @@ class MatrixUtil {
}
return matrix;
}

///将一般矩阵转化为上海森柏格矩阵
static List<List<num>> getHessenberg(List<List<num>> matrix) {
if(!isSquare(matrix)){
throw FormatException(SettingData.language == 'zh' ? '只有方阵才能转化为上海森柏格矩阵' : "Only the square matrix can be transformed into Shanghai senberg matrix");
if (!isSquare(matrix)) {
throw FormatException(SettingData.language == 'zh'
? '只有方阵才能转化为上海森柏格矩阵'
: "Only the square matrix can be transformed into Shanghai senberg matrix");
}
int n = matrix.length;
var result = initMatrix(n, n);
Expand Down Expand Up @@ -387,40 +414,27 @@ class MatrixUtil {
return result;
}

static List<List<num>> eigenValue(List<List<num>> matrix, int loopNu, int erro) {
if(!isSquare(matrix)) {
throw FormatException(SettingData.language == 'zh' ? '方阵才能求特征值' : "Square matrix to find the eigenvalues");
static List<List<num>> eigenValue(
List<List<num>> matrix, int loopNu, int erro) {
if (!isSquare(matrix)) {
throw FormatException(SettingData.language == 'zh'
? '方阵才能求特征值'
: "Square matrix to find the eigenvalues");
}
int n = matrix.length;
List<List<num>> result = initMatrix(n, 2);
int i;
int j;
int k;
int t;
int m;
int i, j, k, t, m;
List<List<num>> A = initMatrix(n, n);
num newerro = pow(0.1, erro);
num b;
num c;
num d;
num g;
num xy;
num p;
num q;
num r;
num x;
num s;
num e;
num f;
num z;
num y;
num b, c, d, g, p, q, x, y, z, s, e, f, r, xy;
int loop1 = loopNu;
A = getHessenberg(matrix); // 将方阵matrix转化成Hessenberg矩阵A
m = n;
while (m != 0) {
t = m - 1;
while (t > 0) {
if (_abs(A[t][t - 1]) > newerro * (_abs(A[t - 1][t - 1]) + _abs(A[t][t]))) {
if (_abs(A[t][t - 1]) >
newerro * (_abs(A[t - 1][t - 1]) + _abs(A[t][t]))) {
t -= 1;
} else {
break;
Expand All @@ -433,7 +447,8 @@ class MatrixUtil {
loop1 = loopNu;
} else if (t == m - 2) {
b = -(A[m - 1][m - 1] + A[m - 2][m - 2]);
c = A[m - 1][m - 1] * A[m - 2][m - 2] - A[m - 1][m - 2] * A[m - 2][m - 1];
c = A[m - 1][m - 1] * A[m - 2][m - 2] -
A[m - 1][m - 2] * A[m - 2][m - 1];
d = b * b - 4 * c;
y = pow(_abs(d), 0.5);
if (d > 0) {
Expand Down Expand Up @@ -547,5 +562,3 @@ class MatrixUtil {
return result;
}
}


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