Breeze库API总结(Spark线性代数库)

Myth丶恋晨 2022-05-28 10:36 90阅读 0赞

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。在使用Breeze库时，需要导入相关包：

Import breeze.linalg.\_

Import breeze.numeric.\_

Breeze创建函数:

<table> 
 <tbody> 
 <tr> 
 <td style="vertical-align:top;"> 操作名称 </td> 
 <td style="vertical-align:top;"> Breeze函数 </td> 
 <td style="vertical-align:top;"> 输出结果 </td> 
 <td style="vertical-align:top;"> 对应Numpy函数 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 全0矩阵 </td> 
 <td style="vertical-align:top;"> DenseMatrix.zeros[Double](2,3) </td> 
 <td style="vertical-align:top;"> 0.0 0.0 0.0 0.0 0.0 0.0 </td> 
 <td style="vertical-align:top;"> zeros((2,3)) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 全0向量 </td> 
 <td style="vertical-align:top;"> DenseVector.zeros[Double](3) </td> 
 <td style="vertical-align:top;"> DenseVector(0.0,0.0,0.0) </td> 
 <td style="vertical-align:top;"> zeros(3) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 全1向量 </td> 
 <td style="vertical-align:top;"> DenseVector.ones[Double](3) </td> 
 <td style="vertical-align:top;"> DenseVector(1.0,1.0,1.0) </td> 
 <td style="vertical-align:top;"> ones(3) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 按数值填充向量 </td> 
 <td style="vertical-align:top;"> DenseVector.fill(3){1.0} </td> 
 <td style="vertical-align:top;"> DenseVector(1.0,1.0,1.0) </td> 
 <td style="vertical-align:top;"> ones(3)*1.0 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 生成随机向量 </td> 
 <td style="vertical-align:top;"> DenseVector.range(start,end,step), Vector.rangeD(start,end,step) </td> 
 <td style="vertical-align:top;"> DenseVector(1,3,5,7,9) </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 线性等分向量（用于产生Start, end之间的N点行矢量） </td> 
 <td style="vertical-align:top;"> DenseVector.linspace(start,end,numvals) </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 单位矩阵 </td> 
 <td style="vertical-align:top;"> DenseMatr.eye[Double](3) </td> 
 <td style="vertical-align:top;"> 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 </td> 
 <td style="vertical-align:top;"> eye(3) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 对角矩阵 </td> 
 <td style="vertical-align:top;"> Diag(DenseVector(1.0,2.0,3.0)) </td> 
 <td style="vertical-align:top;"> 1.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 3.0 </td> 
 <td style="vertical-align:top;"> diag((1.0,2.0,3.0)) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 按照行创建矩阵 </td> 
 <td style="vertical-align:top;"> DenseMatrix((1.0,2.0),(3.0,4.0)) </td> 
 <td style="vertical-align:top;"> 1.0 2.0 3.0 4.0 </td> 
 <td style="vertical-align:top;"> array([[1.0,2.0],[3.0,4.0]]) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 按照行创建向量 </td> 
 <td style="vertical-align:top;"> DenseVector(1,2,3,4) </td> 
 <td style="vertical-align:top;"> [1 2 3 4] </td> 
 <td style="vertical-align:top;"> array([1,2,3,4]) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 向量转置 </td> 
 <td style="vertical-align:top;"> DenseVector(1,2,3,4).t </td> 
 <td style="vertical-align:top;"> [1 2 3 4]T </td> 
 <td style="vertical-align:top;"> array([1 2 3 4]).reshape(-1,1) </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 从函数创建向量 </td> 
 <td style="vertical-align:top;"> DenseVector.tabulate(3){i =&gt; i*2} </td> 
 <td style="vertical-align:top;"> [0 1 4] </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 从函数创建矩阵 </td> 
 <td style="vertical-align:top;"> DenseMatrix.tabulate(3,2){case(i,j) =&gt; i+j} </td> 
 <td style="vertical-align:top;"> 0 1 1 2 2 3 </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 从数组创建向量 </td> 
 <td style="vertical-align:top;"> new DenseVector(array(1, 2, 3,4)) </td> 
 <td style="vertical-align:top;"> [1 2 3 4] </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 从数组创建矩阵 </td> 
 <td style="vertical-align:top;"> new DenseMatrix(2,3,array(11,12,13,21.22,23)) </td> 
 <td style="vertical-align:top;"> 11 12 13 21 22 23 </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 0到1的随机向量 </td> 
 <td style="vertical-align:top;"> DenseVector.rand(4) </td> 
 <td style="vertical-align:top;"> [0.0222 0.2231 0.5356 0.6902] </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> 0到1的随机矩阵 </td> 
 <td style="vertical-align:top;"> DenseMatrix.rand(2,3) </td> 
 <td style="vertical-align:top;"> 0.2122 0.3033 0.8675 0.6628 0.0023 0.9987 </td> 
 <td style="vertical-align:top;"> &nbsp; </td> 
 </tr> 
 </tbody> 
</table>

Breeze元素访问

Breeze元素操作

Breeze数值计算函数

Breeze求和函数

Breeze布尔函数

Breeze线性代数函数

Breeze取整函数

BLAS向量-向量运算

<table> 
 <tbody> 
 <tr> 
 <td style="vertical-align:top;"> SROTG </td> 
 <td style="vertical-align:top;"> Givens旋转设置 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SROTMG </td> 
 <td style="vertical-align:top;"> 改进Givens旋转设置 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SROT </td> 
 <td style="vertical-align:top;"> Givens旋转 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SROTM </td> 
 <td style="vertical-align:top;"> 改进Givens旋转 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSWAP </td> 
 <td style="vertical-align:top;"> 交换x和y </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSCAL </td> 
 <td style="vertical-align:top;"> 常数a乘以向量x() </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SCOPY </td> 
 <td style="vertical-align:top;"> 把x复制到y </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SAXPY </td> 
 <td style="vertical-align:top;"> 向量y+常数a乘以向量x（y = a*x + y） </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SDOT </td> 
 <td style="vertical-align:top;"> 点积 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SDSDOT </td> 
 <td style="vertical-align:top;"> 扩展精度累积的点积 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SNRM2 </td> 
 <td style="vertical-align:top;"> 欧氏范数 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SCNRM2 </td> 
 <td style="vertical-align:top;"> 欧氏范数 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SASUM </td> 
 <td style="vertical-align:top;"> 绝对值之和 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> ISAMAX </td> 
 <td style="vertical-align:top;"> 最大值位置 </td> 
 </tr> 
 </tbody> 
</table>

BLAS矩阵-向量运算

<table> 
 <tbody> 
 <tr> 
 <td style="vertical-align:top;"> SGEMV </td> 
 <td style="vertical-align:top;"> 矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SGBMV </td> 
 <td style="vertical-align:top;"> 带状矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSYMV </td> 
 <td style="vertical-align:top;"> 对称矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSBMV </td> 
 <td style="vertical-align:top;"> 对称带状矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSPMV </td> 
 <td style="vertical-align:top;"> 对称填充矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STRMV </td> 
 <td style="vertical-align:top;"> 三角矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STBMV </td> 
 <td style="vertical-align:top;"> 三角带状矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STPMV </td> 
 <td style="vertical-align:top;"> 三角填充矩阵向量乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STRSV </td> 
 <td style="vertical-align:top;"> 求解三角矩阵 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STBSV </td> 
 <td style="vertical-align:top;"> 求解三角带状矩阵 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STPSV </td> 
 <td style="vertical-align:top;"> 求解三角填充矩阵 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SGER </td> 
 <td style="vertical-align:top;"> A := alpha*x*y’&nbsp;+ A </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSYR </td> 
 <td style="vertical-align:top;"> A := alpha*x*x’&nbsp;+ A </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSPR </td> 
 <td style="vertical-align:top;"> A := alpha*x*x’&nbsp;+ A </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSYR2 </td> 
 <td style="vertical-align:top;"> A := alpha*x*y’&nbsp;+ alpha*y*x’&nbsp;+ A </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSPR2 </td> 
 <td style="vertical-align:top;"> A := alpha*x*y’&nbsp;+ alpha*y*x’&nbsp;+ A </td> 
 </tr> 
 </tbody> 
</table>

BLAS矩阵-矩阵运算

<table> 
 <tbody> 
 <tr> 
 <td style="vertical-align:top;"> SGEMM </td> 
 <td style="vertical-align:top;"> 矩阵乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSYMM </td> 
 <td style="vertical-align:top;"> 对称矩阵乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSYPK </td> 
 <td style="vertical-align:top;"> 对称矩阵的秩-k修正 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> SSYR2K </td> 
 <td style="vertical-align:top;"> 对称矩阵的秩-2k修正 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STRMM </td> 
 <td style="vertical-align:top;"> 三角矩阵乘法 </td> 
 </tr> 
 <tr> 
 <td style="vertical-align:top;"> STRSM </td> 
 <td style="vertical-align:top;"> 多重右端的三角线性方程组求解 </td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td>BLAS向量-向量运算</td> 
 <td>&nbsp;</td> 
 </tr> 
 <tr> 
 <td>SROTG</td> 
 <td>Givens旋转设置</td> 
 </tr> 
 <tr> 
 <td>SROTMG</td> 
 <td>改进Givens旋转设置</td> 
 </tr> 
 <tr> 
 <td>SROT</td> 
 <td>Givens旋转</td> 
 </tr> 
 <tr> 
 <td>SROTM</td> 
 <td>改进Givens旋转</td> 
 </tr> 
 <tr> 
 <td>SSWAP</td> 
 <td>交换x和y</td> 
 </tr> 
 <tr> 
 <td>SSCAL</td> 
 <td>常数a乘以向量x()</td> 
 </tr> 
 <tr> 
 <td>SCOPY</td> 
 <td>把x复制到y</td> 
 </tr> 
 <tr> 
 <td>SAXPY</td> 
 <td>向量y+常数a乘以向量x（y&nbsp;=&nbsp;a*x&nbsp;+&nbsp;y）</td> 
 </tr> 
 <tr> 
 <td>SDOT</td> 
 <td>点积</td> 
 </tr> 
 <tr> 
 <td>SDSDOT</td> 
 <td>扩展精度累积的点积</td> 
 </tr> 
 <tr> 
 <td>SNRM2</td> 
 <td>欧氏范数</td> 
 </tr> 
 <tr> 
 <td>SCNRM2</td> 
 <td>欧氏范数</td> 
 </tr> 
 <tr> 
 <td>SASUM</td> 
 <td>绝对值之和</td> 
 </tr> 
 <tr> 
 <td>ISAMAX</td> 
 <td>最大值位置</td> 
 </tr> 
 <tr> 
 <td>&nbsp;</td> 
 <td>&nbsp;</td> 
 </tr> 
 <tr> 
 <td>BLAS矩阵-向量运算</td> 
 <td>&nbsp;</td> 
 </tr> 
 <tr> 
 <td>SGEMV</td> 
 <td>矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>SGBMV</td> 
 <td>带状矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>SSYMV</td> 
 <td>对称矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>SSBMV</td> 
 <td>对称带状矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>SSPMV</td> 
 <td>对称填充矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>STRMV</td> 
 <td>三角矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>STBMV</td> 
 <td>三角带状矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>STPMV</td> 
 <td>三角填充矩阵向量乘法</td> 
 </tr> 
 <tr> 
 <td>STRSV</td> 
 <td>求解三角矩阵</td> 
 </tr> 
 <tr> 
 <td>STBSV</td> 
 <td>求解三角带状矩阵</td> 
 </tr> 
 <tr> 
 <td>STPSV</td> 
 <td>求解三角填充矩阵</td> 
 </tr> 
 <tr> 
 <td>SGER</td> 
 <td>A&nbsp;:=&nbsp;alpha*x*y’&nbsp;+&nbsp;A</td> 
 </tr> 
 <tr> 
 <td>SSYR</td> 
 <td>A&nbsp;:=&nbsp;alpha*x*x’&nbsp;+&nbsp;A</td> 
 </tr> 
 <tr> 
 <td>SSPR</td> 
 <td>A&nbsp;:=&nbsp;alpha*x*x’&nbsp;+&nbsp;A</td> 
 </tr> 
 <tr> 
 <td>SSYR2</td> 
 <td>A&nbsp;:=&nbsp;alpha*x*y’&nbsp;+&nbsp;alpha*y*x’&nbsp;+&nbsp;A</td> 
 </tr> 
 <tr> 
 <td>SSPR2</td> 
 <td>A&nbsp;:=&nbsp;alpha*x*y’&nbsp;+&nbsp;alpha*y*x’&nbsp;+&nbsp;A</td> 
 </tr> 
 <tr> 
 <td>&nbsp;</td> 
 <td>&nbsp;</td> 
 </tr> 
 <tr> 
 <td>BLAS矩阵-矩阵运算</td> 
 <td>&nbsp;</td> 
 </tr> 
 <tr> 
 <td>SGEMM</td> 
 <td>矩阵乘法</td> 
 </tr> 
 <tr> 
 <td>SSYMM</td> 
 <td>对称矩阵乘法</td> 
 </tr> 
 <tr> 
 <td>SSYPK</td> 
 <td>对称矩阵的秩-k修正</td> 
 </tr> 
 <tr> 
 <td>SSYR2K</td> 
 <td>对称矩阵的秩-2k修正</td> 
 </tr> 
 <tr> 
 <td>STRMM</td> 
 <td>三角矩阵乘法</td> 
 </tr> 
 <tr> 
 <td>STRSM</td> 
 <td>多重右端的三角线性方程组求解</td> 
 </tr> 
 </tbody> 
</table>

# 向量与向量 #

*  加：**+**    减：**-   点乘：  :\*   点除：:/    向量乘法: \*  向量除法: /**

# 矩阵与矩阵 #

*  加：+    减：-   **点乘：  :\*   点除：:/        矩阵乘法: \*  矩阵除法: /**

# 矩阵或向量与数值 #

*  加：**+ **  减：**-  **  乘：**\*  **  除：**/  **

# 矩阵和向量 #

*  加：+    减：-  ** 点乘：  :\*   点除：:/        矩阵乘法: \*  矩阵除法: /**
 *  **Matrix(\*, ::)+Vector 逐行**
 *  **Matrix(::, \*)+Vector 逐列**