Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/88#discussion_r10773006
--- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/SVD.scala ---
@@ -73,19 +170,110 @@ object SVD {
* U is m x k and satisfies U'U = eye(k)
* V is n x k and satisfies V'V = eye(k)
*
- * All input and output is expected in sparse matrix format, 0-indexed
- * as tuples of the form ((i,j),value) all in RDDs using the
- * SparseMatrix class
+ * 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 sparse matrix to factorize
+ * @param matrix dense matrix to factorize
* @param k Recover k singular values and vectors
- * @return Three sparse matrices: U, S, V such that A = USV^T
+ * @return Three matrices: U, S, V such that A = USV^T
*/
- def sparseSVD(
- matrix: SparseMatrix,
- k: Int)
- : MatrixSVD =
- {
+ private def denseSVD(matrix: RDD[Array[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 values k=$k n=$n")
+ }
+
+ // Compute A^T A
+ val fullata = matrix.mapPartitions { iter =>
+ val miniata = Array.ofDim[Double](n, n)
+ while(iter.hasNext) {
+ val row = iter.next
+ var i = 0
+ while(i < n) {
+ var j = 0
+ while(j < n) {
+ miniata(i)(j) += row(i) * row(j)
+ j += 1
+ }
+ i += 1
+ }
+ }
+ List(miniata).iterator
+ }.fold(Array.ofDim[Double](n, n)) { (a, b) =>
+ var i = 0
+ while(i < n) {
+ var j = 0
+ while(j < n) {
+ a(i)(j) += b(i)(j)
+ j += 1
+ }
+ i += 1
+ }
+ a
+ }
+
+ // Construct jblas A^T A locally
+ val ata = new DoubleMatrix(fullata)
+
+ // Since A^T A is small, we can compute its SVD directly
+ val svd = Singular.sparseSVD(ata)
+ val V = svd(0)
+ val sigmas = MatrixFunctions.sqrt(svd(1)).toArray.filter(x => x /
svd(1).get(0) > rCond)
+
+ val sk = Math.min(k, sigmas.size)
+ val sigma = sigmas.take(sk)
+
+ // prepare V for returning
+ val retV = Array.tabulate(n, sk)((i, j) => V.get(i, j))
+
+ if (computeU) {
+ // Compute U as U = A V S^-1
+ // Compute VS^-1
+ val vsinv = new DoubleMatrix(Array.tabulate(n, sk)((i, j) =>
V.get(i, j) / sigma(j)))
+ val retU = matrix.map { x =>
+ val v = new DoubleMatrix(Array(x))
+ v.mmul(vsinv).data
+ }
+ (retU, sigma, retV)
+ } else {
+ (null, sigma, retV)
+ }
+ }
+
+ /**
+ * Singular Value Decomposition for Tall and Skinny sparse 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.
--- End diff --
n^2 -> `O(n^2)`
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