Github user rxin commented on a diff in the pull request:
https://github.com/apache/spark/pull/88#discussion_r10739162
--- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/SVD.scala ---
@@ -142,17 +172,189 @@ object SVD {
val vsirdd = sc.makeRDD(Array.tabulate(V.rows, sigma.length)
{ (i,j) => ((i, j), V.get(i,j) / sigma(j)) }.flatten)
- // Multiply A by VS^-1
- val aCols = data.map(entry => (entry.j, (entry.i, entry.mval)))
- val bRows = vsirdd.map(entry => (entry._1._1, (entry._1._2, entry._2)))
- val retUdata = aCols.join(bRows).map( {case (key, ( (rowInd, rowVal),
(colInd, colVal)))
- => ((rowInd, colInd), rowVal*colVal)}).reduceByKey(_ + _)
- .map{ case ((row, col), mval) => MatrixEntry(row, col, mval)}
- val retU = SparseMatrix(retUdata, m, sigma.length)
-
- MatrixSVD(retU, retS, retV)
+ if (computeU) {
+ // Multiply A by VS^-1
+ val aCols = data.map(entry => (entry.j, (entry.i, entry.mval)))
+ val bRows = vsirdd.map(entry => (entry._1._1, (entry._1._2,
entry._2)))
+ val retUdata = aCols.join(bRows).map {
+ case (key, ( (rowInd, rowVal), (colInd, colVal)) ) =>
+ ((rowInd, colInd), rowVal * colVal)
+ }.reduceByKey(_ + _).map{ case ((row, col), mval) =>
MatrixEntry(row, col, mval)}
+
+ val retU = SparseMatrix(retUdata, m, sigma.length)
+ MatrixSVD(retU, retS, retV)
+ } else {
+ MatrixSVD(null, retS, retV)
+ }
+ }
+
+/**
+ * Singular Value Decomposition for Tall and Skinny matrices.
+ * Given an m x n matrix A, this will compute matrices U, S, V such that
+ * A = U * S * V'
+ *
+ * There is no restriction on m, but we require n^2 doubles to fit in
memory.
+ * Further, n should be less than m.
+ *
+ * The decomposition is computed by first computing A'A = V S^2 V',
+ * computing svd locally on that (since n x n is small),
+ * from which we recover S and V.
+ * Then we compute U via easy matrix multiplication
+ * as U = A * V * S^-1
+ *
+ * Only the k largest singular values and associated vectors are found.
+ * If there are k such values, then the dimensions of the return will be:
+ *
+ * S is k x k and diagonal, holding the singular values on diagonal
+ * U is m x k and satisfies U'U = eye(k)
+ * V is n x k and satisfies V'V = eye(k)
+ *
+ * @param matrix dense matrix to factorize
+ * @param k Recover k singular values and vectors
+ * @param computeU gives the option of skipping the U computation
+ * @param rcond smallest singular value considered nonzero
+ * @return Three dense matrices: U, S, V such that A = USV^T
+ */
+ private def denseSVD(matrix: TallSkinnyDenseMatrix, k: Int,
+ computeU: Boolean, rcond: Double): TallSkinnyMatrixSVD = {
+ val rows = matrix.rows
+ val m = matrix.m
+ val n = matrix.n
+ val sc = matrix.rows.sparkContext
+
+ if (m < n || m <= 0 || n <= 0) {
+ throw new IllegalArgumentException("Expecting a tall and skinny
matrix m=" + m + " n=" + n)
+ }
+
+ if (k < 1 || k > n) {
+ throw new IllegalArgumentException("Request up to n singular values
n=" + n + " k=" + k)
+ }
+
+ val rowIndices = matrix.rows.map(_.i)
+
+ // compute SVD
+ val (u, sigma, v) = denseSVD(matrix.rows.map(_.data), k, computeU,
rcond)
+
+ if(computeU) {
+ // prep u for returning
+ val retU = TallSkinnyDenseMatrix(u.zip(rowIndices).map{
+ case (row, i) => MatrixRow(i, row) }, m, k)
+
+ TallSkinnyMatrixSVD(retU, sigma, v)
+ } else {
+ TallSkinnyMatrixSVD(null, sigma, v)
+ }
+ }
+
+/**
+ * Singular Value Decomposition for Tall and Skinny matrices.
+ * Given an m x n matrix A, this will compute matrices U, S, V such that
+ * A = U * S * V'
+ *
+ * There is no restriction on m, but we require n^2 doubles to fit in
memory.
+ * Further, n should be less than m.
+ *
+ * The decomposition is computed by first computing A'A = V S^2 V',
+ * computing svd locally on that (since n x n is small),
+ * from which we recover S and V.
+ * Then we compute U via easy matrix multiplication
+ * as U = A * V * S^-1
+ *
+ * Only the k largest singular values and associated vectors are found.
+ * If there are k such values, then the dimensions of the return will be:
+ *
+ * S is k x k and diagonal, holding the singular values on diagonal
+ * U is m x k and satisfies U'U = eye(k)
+ * V is n x k and satisfies V'V = eye(k)
+ *
+ * The return values are as lean as possible: an RDD of rows for U,
+ * a simple array for sigma, and a dense 2d matrix array for V
+ *
+ * @param matrix dense matrix to factorize
+ * @param k Recover k singular values and vectors
+ * @return Three matrices: U, S, V such that A = USV^T
+ */
+ private def denseSVD(matrix: RDD[Array[Double]], k: Int,
+ computeU: Boolean, rcond: Double) :
+ (RDD[Array[Double]], Array[Double], Array[Array[Double]])
= {
+ val n = matrix.first.size
+
+ if (k < 1 || k > n) {
+ throw new IllegalArgumentException(
+ "Request up to n singular valuesi k=" + k + " n= " + n)
+ }
+
+ // Compute A^T A
+ val fullata = matrix.mapPartitions{
--- End diff --
add a space after mapParititons, put iter on the same line, and only indent
the body using two spaces
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