spark | scala | 线性代数库Breeze学习
spark | scala | 线性代数库Breeze学习
最近在学习spark，对线性代数库Breeze做了学习，介绍下常用的函数
前提，使用Breeze库，必须导入相关的包
import breeze.linalg._
import breeze.numerics._最基础的操作：矩阵，向量，数组的转换
1、DenseMatrix.zerosDouble
全为零的n*m的矩阵，Double类型
2、DenseVector.zerosDouble
全为零的n个数组成的向量，Double类型
3、DenseVector.onesDouble
全为1的n个数组成的向量，Double类型
4、DenseVector.fill(n){5.0}
产生向量，长度为n，用5.0来填充
5、DenseVector.range(start,stop,step) DenseVector.rangeD(start,stop,step)
产生序列向量 6、DenseVector.linspace(start,stop,numvals)
产生向量，有numvals个数的向量
7、DenseMatrix.eyeDouble
产生n*n的矩阵，对角为1，Double类型
8、diag(DenseVector(1.0,2.0,3.0))
产生主对角元素为1.0,2.0,3.0的矩阵
9、DenseMatrix((1.0,2.0),(3.0,4.0))
产生矩阵
10、DenseVector(1,2,3,4)
产生向量
11、DenseVector(1,2,3,4).t
向量转置
12、DenseVector.tabulate(3){i => 2*i}
scala> DenseVector.tabulate(3){i => 2*i}res33: breeze.linalg.DenseVector[Int] = DenseVector(0, 2, 4)
结果为:0,2,4
13、DenseMatrix.tabulate(3,2){case(i,j) => i+j}
scala> DenseMatrix.tabulate(3,2){case(i,j) => i+j}
res34: breeze.linalg.DenseMatrix[Int] =
0 1
1 2
2 3行列数相加
14、new DenseVector(Array(1,2,3,4)) 从数组创建向量
scala> new DenseVector(Array(1,2,3,4))
res35: breeze.linalg.DenseVector[Int] = DenseVector(1, 2, 3, 4)15、new DenseMatrix(2,3,Array(11,12,13,21,22,23)) 从数组创建矩阵
scala> new DenseMatrix(2,3,Array(11,12,13,21,22,23))
res36: breeze.linalg.DenseMatrix[Int] =
11 13 22
12 21 2316、DenseVector.rand(4) 得到0到1的随机向量，长度为4
scala> DenseVector.rand(4)
res37: breeze.linalg.DenseVector[Double] = DenseVector(0.9838289972536518, 0.798555117073358, 0.30308183931925403, 0.7958095551517774)17、DenseMatrix.rand(2,3) 得到0到1的随机矩阵
scala> DenseMatrix.rand(2,3)
res38: breeze.linalg.DenseMatrix[Double] =
0.3891370890132193 0.06732600444704517 0.2136759825764527
0.587145241786718 0.8670050354290917 0.5494899108312414Breeze元素访问
1、指定位置
scala> val a = DenseVector(1,2,3,4,5)
a: breeze.linalg.DenseVector[Int] = DenseVector(1, 2, 3, 4, 5)
scala> a(2)
res44: Int = 32、向量子集
scala> a(1 to 2)
res40: breeze.linalg.DenseVector[Int] = DenseVector(2, 3)
scala> a(1 until 2)
res41: breeze.linalg.DenseVector[Int] = DenseVector(2)
scala> a.slice(1,2)
res42: breeze.linalg.DenseVector[Int] = DenseVector(2)3、按照指定步长取子集
scala> a(3 to 1 by -1)
res45: breeze.linalg.DenseVector[Int] = DenseVector(4, 3, 2)4、指定开始位置至结尾
scala> a(2 to -1 )
res48: breeze.linalg.DenseVector[Int] = DenseVector(3, 4, 5)5、最后一个元素
scala> a(2 to -1 )
res48: breeze.linalg.DenseVector[Int] = DenseVector(3, 4, 5)6、矩阵指定列
scala> val a = DenseMatrix((1,2,3,4,5),(3,4,5,6,7),(5,6,7,8,9))
a: breeze.linalg.DenseMatrix[Int] =
1 2 3 4 5
3 4 5 6 7
5 6 7 8 9
scala> a(::,2)
res1: breeze.linalg.DenseVector[Int] = DenseVector(3, 5, 7)Breeze元素操作
1、a.reshape(3,2) 调整矩阵形状
scala> val a = DenseMatrix((2,3),(3,4),(6,7))
a: breeze.linalg.DenseMatrix[Int] =
2 3
3 4
6 7
scala> val a = DenseMatrix((2,3),(3,4),(6,7))
a: breeze.linalg.DenseMatrix[Int] =
2 3
3 4
6 72、a.toDenseVector 矩阵转成向量
scala> val a = DenseMatrix((2,3),(3,4),(6,7))
a: breeze.linalg.DenseMatrix[Int] =
2 3
3 4
6 7
scala> a.toDenseVector
res3: breeze.linalg.DenseVector[Int] = DenseVector(2, 3, 6, 3, 4, 7)3、lowerTriangular 下三角矩阵
scala> val b = DenseMatrix((1,2,3,4,5,6),(2,3,4,5,6,7),(3,4,5,6,7,8))
b: breeze.linalg.DenseMatrix[Int] =
1 2 3 4 5 6
2 3 4 5 6 7
3 4 5 6 7 8
scala> lowerTriangular(b)
res7: breeze.linalg.DenseMatrix[Int] =
1 0 0
2 3 0
3 4 54、upperTriangular 上三角矩阵
scala> upperTriangular(b)
res8: breeze.linalg.DenseMatrix[Int] =
1 2 3
0 3 4
0 0 55、b.copy 复制矩阵
scala> b.copy
res9: breeze.linalg.DenseMatrix[Int] =
1 2 3 4 5 6
2 3 4 5 6 7
3 4 5 6 7 86、diag(a) 取对角线元素
scala> val c = DenseMatrix((1,2,3),(2,3,4),(3,4,5))
c: breeze.linalg.DenseMatrix[Int] =
1 2 3
2 3 4
3 4 5
scala> diag(c)
res12: breeze.linalg.DenseVector[Int] = DenseVector(1, 3, 5)7、c(1 to 4 ) := 5.0 子集赋值，将c中的第2个数到第五个数赋值为5.0
scala> val d = DenseVector(1,2,3,4,5,6,7,8,8)
d: breeze.linalg.DenseVector[Int] = DenseVector(1, 2, 3, 4, 5, 6, 7, 8, 8)
scala> d(1 to 4) := 5
res18: breeze.linalg.DenseVector[Int] = DenseVector(5, 5, 5, 5)
scala> d
res21: breeze.linalg.DenseVector[Int] = DenseVector(1, 5, 5, 5, 5, 6, 7, 8, 8)8、d(1 to 4) := DenseVector(1,2,3) 子集赋向量
scala> d(1 to 4):=DenseVector(1,2,3,4)
res26: breeze.linalg.DenseVector[Int] = DenseVector(1, 2, 3, 4)
scala> d
res27: breeze.linalg.DenseVector[Int] = DenseVector(1, 1, 2, 3, 4, 6, 7, 8, 8)9、a(1 to 3,1 to 3) :=5 矩阵赋值
scala> b(1 to 2,1 to 3):= 6
res30: breeze.linalg.DenseMatrix[Int] =
6 6 6
6 6 6
scala> b
res31: breeze.linalg.DenseMatrix[Int] =
1 2 3 4 5 6
2 6 6 6 6 7
3 6 6 6 7 810、a(::,2) := 5 矩阵列赋值
scala> b(::,2) := 7
res32: breeze.linalg.DenseVector[Int] = DenseVector(7, 7, 7)
scala> b
res33: breeze.linalg.DenseMatrix[Int] =
1 2 7 4 5 6
2 6 7 6 6 7
3 6 7 6 7 811、DenseMatrix.vertcat(a,b) 垂直合并
12、DenseMatrix.horzcat(d,e) 水平合并
13、DenseVector.vertvat(a,b) 向量连接
数值计算
求和函数
布尔函数
线性代数
一些很基础的函数，很实用。