Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/88#discussion_r10772728
--- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/SVD.scala ---
@@ -38,20 +39,113 @@ class SVD {
this
}
- /**
+ /**
+ * Singular values smaller than this value
+ * relative to the largest singular value are considered zero
+ */
+ def setReciprocalConditionNumber(smallS: Double): SVD = {
+ this.rCond = smallS
+ this
+ }
+
+ /**
+ * Should U be computed?
+ */
+ def setComputeU(compU: Boolean): SVD = {
+ this.computeU = compU
+ this
+ }
+
+ /**
* Compute SVD using the current set parameters
*/
- def compute(matrix: SparseMatrix) : MatrixSVD = {
- SVD.sparseSVD(matrix, k)
+ def compute(matrix: TallSkinnyDenseMatrix) : TallSkinnyMatrixSVD = {
+ denseSVD(matrix)
}
-}
+ /**
+ * Compute SVD using the current set parameters
+ * Returns (U, S, V) such that A = USV^T
+ * U is a row-by-row dense matrix
+ * S is a simple double array of singular values
+ * V is a 2d array matrix
+ * See denseSVD for more documentation
+ */
+ def compute(matrix: RDD[Array[Double]]) :
+ (RDD[Array[Double]], Array[Double], Array[Array[Double]]) = {
+ denseSVD(matrix)
+ }
+
+ /**
+ * Compute SVD with default parameter for computeU = true.
+ * See full paramter definition of sparseSVD for more description.
+ *
+ * @param matrix sparse matrix to factorize
+ * @return Three sparse matrices: U, S, V such that A = USV^T
+ */
+ def compute(matrix: SparseMatrix): MatrixSVD = {
+ sparseSVD(matrix)
+ }
/**
- * Top-level methods for calling Singular Value Decomposition
- * NOTE: All matrices are in 0-indexed sparse format RDD[((int, int),
value)]
+ * 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
--- End diff --
sigma is an array.
---
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