[SPARK-4717][MLlib] Optimize BLAS library to avoid de-reference multiple times in loop

Have a local reference to `values` and `indices` array in the `Vector` object
so JVM can locate the value with one operation call. See `SPARK-4581`
for similar optimization, and the bytecode analysis.

Author: DB Tsai <dbtsai@alpinenow.com>

Closes #3577 from dbtsai/blasopt and squashes the following commits:

62d38c4 [DB Tsai] formating
0316cef [DB Tsai] first commit

mllib/src/main/scala/org/apache/spark/mllib/linalg/BLAS.scala

@@ -72,17 +72,21 @@ private[spark] object BLAS extends Serializable with Logging {
    * y += a * x
    */
   private def axpy(a: Double, x: SparseVector, y: DenseVector): Unit = {
-    val nnz = x.indices.size
+    val xValues = x.values
+    val xIndices = x.indices
+    val yValues = y.values
+    val nnz = xIndices.size
+
     if (a == 1.0) {
       var k = 0
       while (k < nnz) {
-        y.values(x.indices(k)) += x.values(k)
+        yValues(xIndices(k)) += xValues(k)
         k += 1
       }
     } else {
       var k = 0
       while (k < nnz) {
-        y.values(x.indices(k)) += a * x.values(k)
+        yValues(xIndices(k)) += a * xValues(k)
         k += 1
       }
     }
@@ -119,11 +123,15 @@ private[spark] object BLAS extends Serializable with Logging {
    * dot(x, y)
    */
   private def dot(x: SparseVector, y: DenseVector): Double = {
-    val nnz = x.indices.size
+    val xValues = x.values
+    val xIndices = x.indices
+    val yValues = y.values
+    val nnz = xIndices.size
+
     var sum = 0.0
     var k = 0
     while (k < nnz) {
-      sum += x.values(k) * y.values(x.indices(k))
+      sum += xValues(k) * yValues(xIndices(k))
       k += 1
     }
     sum
@@ -133,19 +141,24 @@ private[spark] object BLAS extends Serializable with Logging {
    * dot(x, y)
    */
   private def dot(x: SparseVector, y: SparseVector): Double = {
+    val xValues = x.values
+    val xIndices = x.indices
+    val yValues = y.values
+    val yIndices = y.indices
+    val nnzx = xIndices.size
+    val nnzy = yIndices.size
+
     var kx = 0
-    val nnzx = x.indices.size
     var ky = 0
-    val nnzy = y.indices.size
     var sum = 0.0
     // y catching x
     while (kx < nnzx && ky < nnzy) {
-      val ix = x.indices(kx)
-      while (ky < nnzy && y.indices(ky) < ix) {
+      val ix = xIndices(kx)
+      while (ky < nnzy && yIndices(ky) < ix) {
         ky += 1
       }
-      if (ky < nnzy && y.indices(ky) == ix) {
-        sum += x.values(kx) * y.values(ky)
+      if (ky < nnzy && yIndices(ky) == ix) {
+        sum += xValues(kx) * yValues(ky)
         ky += 1
       }
       kx += 1
@@ -163,21 +176,25 @@ private[spark] object BLAS extends Serializable with Logging {
       case dy: DenseVector =>
         x match {
           case sx: SparseVector =>
+            val sxIndices = sx.indices
+            val sxValues = sx.values
+            val dyValues = dy.values
+            val nnz = sxIndices.size
+
             var i = 0
             var k = 0
-            val nnz = sx.indices.size
             while (k < nnz) {
-              val j = sx.indices(k)
+              val j = sxIndices(k)
               while (i < j) {
-                dy.values(i) = 0.0
+                dyValues(i) = 0.0
                 i += 1
               }
-              dy.values(i) = sx.values(k)
+              dyValues(i) = sxValues(k)
               i += 1
               k += 1
             }
             while (i < n) {
-              dy.values(i) = 0.0
+              dyValues(i) = 0.0
               i += 1
             }
           case dx: DenseVector =>
@@ -311,6 +328,8 @@ private[spark] object BLAS extends Serializable with Logging {
       s"The columns of C don't match the columns of B. C: ${C.numCols}, A: $nB")
 
     val Avals = A.values
+    val Bvals = B.values
+    val Cvals = C.values
     val Arows = if (!transA) A.rowIndices else A.colPtrs
     val Acols = if (!transA) A.colPtrs else A.rowIndices
 
@@ -327,11 +346,11 @@ private[spark] object BLAS extends Serializable with Logging {
             val indEnd = Arows(rowCounterForA + 1)
             var sum = 0.0
             while (i < indEnd) {
-              sum += Avals(i) * B.values(Bstart + Acols(i))
+              sum += Avals(i) * Bvals(Bstart + Acols(i))
               i += 1
             }
             val Cindex = Cstart + rowCounterForA
-            C.values(Cindex) = beta * C.values(Cindex) + sum * alpha
+            Cvals(Cindex) = beta * Cvals(Cindex) + sum * alpha
             rowCounterForA += 1
           }
           colCounterForB += 1
@@ -349,7 +368,7 @@ private[spark] object BLAS extends Serializable with Logging {
               i += 1
             }
             val Cindex = Cstart + rowCounter
-            C.values(Cindex) = beta * C.values(Cindex) + sum * alpha
+            Cvals(Cindex) = beta * Cvals(Cindex) + sum * alpha
             rowCounter += 1
           }
           colCounterForB += 1
@@ -357,7 +376,7 @@ private[spark] object BLAS extends Serializable with Logging {
       }
     } else {
       // Scale matrix first if `beta` is not equal to 0.0
-      if (beta != 0.0){
+      if (beta != 0.0) {
         f2jBLAS.dscal(C.values.length, beta, C.values, 1)
       }
       // Perform matrix multiplication and add to C. The rows of A are multiplied by the columns of
@@ -371,9 +390,9 @@ private[spark] object BLAS extends Serializable with Logging {
           while (colCounterForA < kA) {
             var i = Acols(colCounterForA)
             val indEnd = Acols(colCounterForA + 1)
-            val Bval = B.values(Bstart + colCounterForA) * alpha
-            while (i < indEnd){
-              C.values(Cstart + Arows(i)) += Avals(i) * Bval
+            val Bval = Bvals(Bstart + colCounterForA) * alpha
+            while (i < indEnd) {
+              Cvals(Cstart + Arows(i)) += Avals(i) * Bval
               i += 1
             }
             colCounterForA += 1
@@ -384,12 +403,12 @@ private[spark] object BLAS extends Serializable with Logging {
         while (colCounterForB < nB) {
           var colCounterForA = 0 // The column of A to multiply with the row of B
           val Cstart = colCounterForB * mA
-          while (colCounterForA < kA){
+          while (colCounterForA < kA) {
             var i = Acols(colCounterForA)
             val indEnd = Acols(colCounterForA + 1)
             val Bval = B(colCounterForB, colCounterForA) * alpha
-            while (i < indEnd){
-              C.values(Cstart + Arows(i)) += Avals(i) * Bval
+            while (i < indEnd) {
+              Cvals(Cstart + Arows(i)) += Avals(i) * Bval
               i += 1
             }
             colCounterForA += 1
@@ -484,41 +503,43 @@ private[spark] object BLAS extends Serializable with Logging {
       beta: Double,
       y: DenseVector): Unit =  {
 
-    val mA: Int = if(!trans) A.numRows else A.numCols
-    val nA: Int = if(!trans) A.numCols else A.numRows
+    val xValues = x.values
+    val yValues = y.values
+
+    val mA: Int = if (!trans) A.numRows else A.numCols
+    val nA: Int = if (!trans) A.numCols else A.numRows
 
     val Avals = A.values
     val Arows = if (!trans) A.rowIndices else A.colPtrs
     val Acols = if (!trans) A.colPtrs else A.rowIndices
-
     // Slicing is easy in this case. This is the optimal multiplication setting for sparse matrices
-    if (trans){
+    if (trans) {
       var rowCounter = 0
-      while (rowCounter < mA){
+      while (rowCounter < mA) {
         var i = Arows(rowCounter)
         val indEnd = Arows(rowCounter + 1)
         var sum = 0.0
-        while(i < indEnd){
-          sum += Avals(i) * x.values(Acols(i))
+        while (i < indEnd) {
+          sum += Avals(i) * xValues(Acols(i))
           i += 1
         }
-        y.values(rowCounter) =  beta * y.values(rowCounter) + sum * alpha
+        yValues(rowCounter) = beta * yValues(rowCounter) + sum * alpha
         rowCounter += 1
       }
     } else {
       // Scale vector first if `beta` is not equal to 0.0
-      if (beta != 0.0){
+      if (beta != 0.0) {
         scal(beta, y)
       }
       // Perform matrix-vector multiplication and add to y
       var colCounterForA = 0
-      while (colCounterForA < nA){
+      while (colCounterForA < nA) {
         var i = Acols(colCounterForA)
         val indEnd = Acols(colCounterForA + 1)
-        val xVal = x.values(colCounterForA) * alpha
-        while (i < indEnd){
+        val xVal = xValues(colCounterForA) * alpha
+        while (i < indEnd) {
           val rowIndex = Arows(i)
-          y.values(rowIndex) += Avals(i) * xVal
+          yValues(rowIndex) += Avals(i) * xVal
           i += 1
         }
         colCounterForA += 1