optimize computeYtY and updateBlock

mllib/src/main/scala/org/apache/spark/mllib/recommendation/ALS.scala

@@ -210,21 +210,47 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
    */
   def computeYtY(factors: RDD[(Int, Array[Array[Double]])]) = {
     if (implicitPrefs) {
-      Option(
-        factors.flatMapValues { case factorArray =>
-          factorArray.view.map { vector =>
-            val x = new DoubleMatrix(vector)
-            x.mmul(x.transpose())
-          }
-        }.reduceByKeyLocally((a, b) => a.addi(b))
-         .values
-         .reduce((a, b) => a.addi(b))
-      )
+      val n = rank * (rank + 1) / 2
+      val LYtY = factors.values.aggregate(new DoubleMatrix(n))( seqOp = (L, Y) => {
+        Y.foreach(y => dspr(1.0, new DoubleMatrix(y), L))
+        L
+      }, combOp = (L1, L2) => {
+        L1.addi(L2)
+      })
+      val YtY = new DoubleMatrix(rank, rank)
+      fillFullMatrix(LYtY, YtY)
+      Option(YtY)
     } else {
       None
     }
   }
 
+  /**
+   * Adding x * x.t to a matrix, the same as BLAS's DSPR.
+   *
+   * @param x a vector of length n
+   * @param L the lower triangular part of the matrix packed in an array (row major)
+   */
+  private def dspr(alpha: Double, x: DoubleMatrix, L: DoubleMatrix) = {
+    val n = x.length
+    var i = 0
+    var j = 0
+    var idx = 0
+    var axi = 0.0
+    val xd = x.data
+    val Ld = L.data
+    while (i < n) {
+      axi = alpha * xd(i)
+      j = 0
+      while (j <= i) {
+        Ld(idx) += axi * xd(j)
+        j += 1
+        idx += 1
+      }
+      i += 1
+    }
+  }
+
   /**
    * Flatten out blocked user or product factors into an RDD of (id, factor vector) pairs
    */
@@ -376,18 +402,21 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
     for (productBlock <- 0 until numBlocks) {
       for (p <- 0 until blockFactors(productBlock).length) {
         val x = new DoubleMatrix(blockFactors(productBlock)(p))
-        fillXtX(x, tempXtX)
+        tempXtX.fill(0.0)
+        dspr(1.0, x, tempXtX)
         val (us, rs) = inLinkBlock.ratingsForBlock(productBlock)(p)
         for (i <- 0 until us.length) {
           implicitPrefs match {
             case false =>
               userXtX(us(i)).addi(tempXtX)
+              // dspr(1.0, x, userXtX(us(i)))
               SimpleBlas.axpy(rs(i), x, userXy(us(i)))
             case true =>
               // Extension to the original paper to handle rs(i) < 0. confidence is a function
               // of |rs(i)| instead so that it is never negative:
               val confidence = 1 + alpha * abs(rs(i))
-              userXtX(us(i)).addi(tempXtX.mul(confidence - 1))
+              SimpleBlas.axpy(confidence - 1.0, tempXtX, userXtX(us(i)))
+              // dspr(confidence - 1.0, x, userXtX(us(i)))
               // For rs(i) < 0, the corresponding entry in P is 0 now, not 1 -- negative rs(i)
               // means we try to reconstruct 0. We add terms only where P = 1, so, term below
               // is now only added for rs(i) > 0:
@@ -400,38 +429,19 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
     }
 
     // Solve the least-squares problem for each user and return the new feature vectors
-    userXtX.zipWithIndex.map{ case (triangularXtX, index) =>
+    userXtX.zip(userXy).map { case (triangularXtX, rhs) =>
       // Compute the full XtX matrix from the lower-triangular part we got above
       fillFullMatrix(triangularXtX, fullXtX)
       // Add regularization
       (0 until rank).foreach(i => fullXtX.data(i*rank + i) += lambda)
       // Solve the resulting matrix, which is symmetric and positive-definite
       implicitPrefs match {
-        case false => Solve.solvePositive(fullXtX, userXy(index)).data
-        case true => Solve.solvePositive(fullXtX.add(YtY.value.get), userXy(index)).data
+        case false => Solve.solvePositive(fullXtX, rhs).data
+        case true => Solve.solvePositive(fullXtX.addi(YtY.value.get), rhs).data
       }
     }
   }
 
-  /**
-   * Set xtxDest to the lower-triangular part of x transpose * x. For efficiency in summing
-   * these matrices, we store xtxDest as only rank * (rank+1) / 2 values, namely the values
-   * at (0,0), (1,0), (1,1), (2,0), (2,1), (2,2), etc in that order.
-   */
-  private def fillXtX(x: DoubleMatrix, xtxDest: DoubleMatrix) {
-    var i = 0
-    var pos = 0
-    while (i < x.length) {
-      var j = 0
-      while (j <= i) {
-        xtxDest.data(pos) = x.data(i) * x.data(j)
-        pos += 1
-        j += 1
-      }
-      i += 1
-    }
-  }
-
   /**
    * Given a triangular matrix in the order of fillXtX above, compute the full symmetric square
    * matrix that it represents, storing it into destMatrix.
@@ -455,7 +465,7 @@ class ALS private (var numBlocks: Int, var rank: Int, var iterations: Int, var l
 
 
 /**
- * Top-level methods for calling Alternating Least Squares (ALS) matrix factorizaton.
+ * Top-level methods for calling Alternating Least Squares (ALS) matrix factorization.
  */
 object ALS {
   /**