Spark MLlib底层的向量、矩阵运算使用了Breeze库,Breeze库提供了Vector/Matrix的实现以及相应计算的接口(Linalg)。但是在MLlib里面同时也提供了Vector和Linalg等的实现。
使用需导入:
import breeze.linalg._
import breeze.numerics._
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Breeze创建函数
val m1 = DenseMatrix.zeros[Double](2,3)
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DenseMatrix[Double] =
0.0 0.0 0.0
0.0 0.0 0.0
val v1 = DenseVector.zeros[Double](3)
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DenseVector(0.0, 0.0, 0.0)
val v2 = DenseVector.ones[Double](3)
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DenseVector(1.0, 1.0, 1.0)
val v3 = DenseVector.fill(3){5.0}
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DenseVector(5.0, 5.0, 5.0)
val v4 = DenseVector.range(1,10,2)
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DenseVector(1, 3, 5, 7, 9)
val m2 = DenseMatrix.eye[Double](3)
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DenseMatrix[Double] =
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
val v6 = diag(DenseVector(1.0,2.0,3.0))
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DenseMatrix[Double] =
1.0 0.0 0.0
0.0 2.0 0.0
0.0 0.0 3.0
val v8 = DenseVector(1,2,3,4)
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DenseVector(1, 2, 3, 4)
val v9 = DenseVector(1,2,3,4).t
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Transpose(DenseVector(1, 2, 3, 4))
val v10 = DenseVector.tabulate(3){i => 2*i}
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DenseVector(0, 2, 4)
val m4 = DenseMatrix.tabulate(3, 2){case (i, j) => i+j}
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DenseMatrix[Int] =
0 1
1 2
2 3
val v11 = new DenseVector(Array(1, 2, 3, 4))
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DenseVector(1, 2, 3, 4)
val m5 = new DenseMatrix(2, 3, Array(11, 12, 13, 21, 22, 23))
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DenseMatrix[Int] =
11 13 22
12 21 23
val v12 = DenseVector.rand(4)
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DenseVector(0.7517657487447951, 0.8171495400874123, 0.8923542318540489, 0.174311259949119)
val m6 = DenseMatrix.rand(2, 3)
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DenseMatrix[Double] =
0.5349430131148125 0.8822136832272578 0.7946323804433382
0.41097756311601086 0.3181490074596882 0.34195102205697414
Breeze元素访问
val a = DenseVector(1,2,3,4,5,6,7,8,9,10)
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DenseVector(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
a(1 to 4)
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DenseVector(2, 3, 4, 5)
a(5 to 0 by -1)
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DenseVector(6, 5, 4, 3, 2, 1)
a(1 to -1)
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DenseVector(2, 3, 4, 5, 6, 7, 8, 9, 10)
a( -1 )
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Int = 10
val m = DenseMatrix((1.0,2.0,3.0), (3.0,4.0,5.0))
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DenseMatrix[Double] =
1.0 2.0 3.0
3.0 4.0 5.0
m(0,1)
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Double = 2.0
m(::,1)
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DenseVector(2.0, 4.0)
Breeze元素操作
val m = DenseMatrix((1.0,2.0,3.0), (3.0,4.0,5.0))
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DenseMatrix[Double] =
1.0 2.0 3.0
3.0 4.0 5.0
m.reshape(3, 2) //从列开始计数
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DenseMatrix[Double] =
1.0 4.0
3.0 3.0
2.0 5.0
m.toDenseVector
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DenseVector(1.0, 3.0, 2.0, 4.0, 3.0, 5.0)
val m = DenseMatrix((1.0,2.0,3.0), (4.0,5.0,6.0) , (7.0,8.0,9.0))
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DenseMatrix[Double] =
1.0 2.0 3.0
4.0 5.0 6.0
7.0 8.0 9.0
lowerTriangular(m)
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DenseMatrix[Double] =
1.0 0.0 0.0
4.0 5.0 0.0
7.0 8.0 9.0
upperTriangular(m)
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DenseMatrix[Double] =
1.0 2.0 3.0
0.0 5.0 6.0
0.0 0.0 9.0
m.copy
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linalg.DenseMatrix[Double] =
1.0 2.0 3.0
4.0 5.0 6.0
7.0 8.0 9.0
diag(m)
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DenseVector(1.0, 5.0, 9.0)
m(::, 2) := 5.0
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DenseVector(5.0, 5.0, 5.0)
m
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DenseMatrix[Double] =
1.0 2.0 5.0
4.0 5.0 5.0
7.0 8.0 5.0
m(1 to 2,1 to 2) := 5.0
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DenseMatrix[Double] =
5.0 5.0
5.0 5.0
val a = DenseVector(1,2,3,4,5,6,7,8,9,10)
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DenseVector(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
a(1 to 4) := 5
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DenseVector(5, 5, 5, 5)
a(1 to 4) := DenseVector(1,2,3,4)
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DenseVector(1, 2, 3, 4)
val a1 = DenseMatrix((1.0,2.0,3.0), (4.0,5.0,6.0))
val a2 = DenseMatrix((1.0,1.0,1.0), (2.0,2.0,2.0))
DenseMatrix.vertcat(a1,a2)
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DenseMatrix[Double] =
1.0 2.0 3.0
4.0 5.0 6.0
1.0 1.0 1.0
2.0 2.0 2.0
DenseMatrix.horzcat(a1,a2)
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DenseMatrix[Double] =
1.0 2.0 3.0 1.0 1.0 1.0
4.0 5.0 6.0 2.0 2.0 2.0
val b1 = DenseVector(1,2,3,4)
val b2 = DenseVector(1,1,1,1)
DenseVector.vertcat(b1,b2)
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DenseVector(1, 2, 3, 4, 1, 1, 1, 1)
Breeze数值计算函数
val a = DenseMatrix((1.0,2.0,3.0), (4.0,5.0,6.0))
val b = DenseMatrix((1.0,1.0,1.0), (2.0,2.0,2.0))
a + b
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DenseMatrix[Double] =
2.0 3.0 4.0
6.0 7.0 8.0
a :* b
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DenseMatrix[Double] =
1.0 2.0 3.0
8.0 10.0 12.0
a :/ b
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DenseMatrix[Double] =
1.0 2.0 3.0
2.0 2.5 3.0
a :< b
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DenseMatrix[Boolean] =
false false false
false false false
a :== b
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DenseMatrix[Boolean] =
true false false
false false false
a :+= 1.0
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DenseMatrix[Double] =
2.0 3.0 4.0
5.0 6.0 7.0
a :*= 2.0
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DenseMatrix[Double] =
4.0 6.0 8.0
10.0 12.0 14.0
max(a)
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Double = 14.0
argmax(a)
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(Int, Int) = (1,2)
DenseVector(1, 2, 3, 4) dot DenseVector(1, 1, 1, 1)//点积
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Int = 10
Breeze求和函数
val a = DenseMatrix((1.0,2.0,3.0), (4.0,5.0,6.0) , (7.0,8.0,9.0))
sum(a)
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Double = 45.0
sum(a, Axis._0)//每列求和
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DenseMatrix[Double] = 12.0 15.0 18.0
sum(a, Axis._1)//按行求和
trace(a) //对角线求和 15
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accumulate(DenseVector(1, 2, 3, 4)) //累计和 1+2 、1+2+3
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DenseVector(1, 3, 6, 10)
Breeze布尔函数
val a = DenseVector(true, false, true)
val b = DenseVector(false, true, true)
a :& b
a :| b
!a
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DenseVector(false, false, true)
val a = DenseVector(1.0, 0.0, -2.0)
any(a) //任一元素非0,true
all(a) //所有元素非0,false
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Breeze线性代数函数
a b //线性求解
a.t //转置
det(a) //求特征值
inv(a) //求逆
pinv(a) //求伪逆
norm(a) //求范数
eigSym(a)//特征值和特征向量
val (er, ei, _) = eig(a) (实部与虚部分开) //特征值
eig(a)._3//特征向量
val svd.SVD(u,s,v) = svd(a)//奇异值分解
rank(a)//求矩阵的秩
a.length//矩阵长度
a.rows//矩阵行数
a.cols//矩阵列数
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DenseMatrix((1.0,2.0,3.0), (4.0,5.0,6.0) , (7.0,8.0,9.0))
DenseMatrix((1.0,1.0,1.0), (1.0,1.0,1.0) , (1.0,1.0,1.0))
a b
a.t
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DenseMatrix[Double] =
1.0 4.0 7.0
2.0 5.0 8.0
3.0 6.0 9.0
Breeze取整函数
round(a)//四舍五入
ceil(a)
floor(a)
signum(a)//符号函数
abs(a)
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val a = DenseVector(1.2, 0.6, -2.3)
signum(a)
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DenseVector(1.0, 1.0, -1.0)
Breeze其它函数
Breeze三角函数包括:
sin, sinh, asin, asinh
cos, cosh, acos, acosh
tan, tanh, atan, atanh
atan2
sinc(x) ,即sin(x)/x
sincpi(x) ,即 sinc(x * Pi)
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Breeze对数和指数函数
Breeze对数和指数函数包括:
log, exp log10
log1p, expm1
sqrt, sbrt
pow
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BLAS介绍(一个线性代数库)
BLAS按照功能被分为三个级别:
Level 1:矢量-矢量运算,比如点积(ddot),加法和数乘 (daxpy), 绝对值的和(dasum),等等;
Level 2:矩阵-矢量运算,最重要的函数是一般的矩阵向量乘法(dgemv);
Level 3:矩阵-矩阵运算,最重要的函数是一般的矩阵乘法 (dgemm);
每一种函数操作都区分不同数据类型(单精度、双精度、复数)