computeSVD()函数中使用的Mapper和Reducer是什么？

computeSVD()函数是Spark MLlib中的一个函数，用于计算奇异值分解（SVD）。在此函数中，使用了两个Mapper和两个Reducer。其中第一个Mapper将原始数据转换为IndexedRowMatrix格式，第一个Reducer将IndexedRowMatrix拆分为子矩阵，第二个Mapper不做任何转换，最终的Reducer计算奇异值分解并返回结果。

具体代码如下：

//将原始数据转换为IndexedRowMatrix格式 JavaRDD<Vector> rows = sc.parallelize(data); JavaRDD<IndexedRow> indexedRows = rows.zipWithIndex().map( new Function<Tuple2<Vector, Long>, IndexedRow>() { public IndexedRow call(Tuple2<Vector, Long> t) { return new IndexedRow(t._2(), t._1()); } } ); IndexedRowMatrix matrix = new IndexedRowMatrix(indexedRows.rdd());

//拆分子矩阵 int rank = 2; int k = 5; SingularValueDecomposition<RowMatrix, Matrix> svd = matrix.toRowMatrix().computeSVD(rank, true, 1.0E-9d); Matrix U = svd.U(); Vector s = Vectors.dense(Arrays.copyOfRange(svd.s().toArray(), 0, rank)); Matrix V = svd.V(); Matrix Vsub = V.transpose().multiply(new DenseMatrix(k, rank, new double[rank*k]));

//计算奇异值分解并返回结果 JavaRDD<Vector> projected = matrix.rows().map(new Function<IndexedRow, Vector>() { public Vector call(IndexedRow row) { Vector result = new DenseVector(Vsub.numCols()); Vsub.multiply(row.vector(), result); return result; } });

return new RowMatrix(projected.rdd()).multiply( new DenseMatrix(rank, rank, Vsub.transpose().toArray()) ).multiply(new DenseMatrix(rank, s.size(), Matrices.diag(s.toArray()).toArray())).multiply( new DenseMatrix(k, rank, U.transpose().toArray()) );