Github user brkyvz commented on a diff in the pull request:
https://github.com/apache/spark/pull/2451#discussion_r17765187
--- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/BLAS.scala ---
@@ -197,4 +201,452 @@ private[mllib] object BLAS extends Serializable {
throw new IllegalArgumentException(s"scal doesn't support vector
type ${x.getClass}.")
}
}
+
+ // For level-3 routines, we use the native BLAS.
+ private def nativeBLAS: NetlibBLAS = {
+ if (_nativeBLAS == null) {
+ _nativeBLAS = NativeBLAS
+ }
+ _nativeBLAS
+ }
+
+ /**
+ * C := alpha * A * B + beta * C
+ * @param transA whether to use the transpose of matrix A (true), or A
itself (false).
+ * @param transB whether to use the transpose of matrix B (true), or B
itself (false).
+ * @param alpha a scalar to scale the multiplication A * B.
+ * @param A the matrix A that will be left multiplied to B. Size of m x
k.
+ * @param B the matrix B that will be left multiplied by A. Size of k x
n.
+ * @param beta a scalar that can be used to scale matrix C.
+ * @param C the resulting matrix C. Size of m x n.
+ */
+ def gemm(
+ transA: Boolean,
+ transB: Boolean,
+ alpha: Double,
+ A: Matrix,
+ B: Matrix,
+ beta: Double,
+ C: DenseMatrix): Unit = {
+ if (alpha == 0.0) {
+ logDebug("gemm: alpha is equal to 0. Returning C.")
+ } else {
+ A match {
+ case sparse: SparseMatrix =>
+ B match {
+ case dB: DenseMatrix => gemm(transA, transB, alpha, sparse,
dB, beta, C)
+ case sB: SparseMatrix =>
+ throw new IllegalArgumentException(s"gemm doesn't support
sparse-sparse matrix " +
+ s"multiplication")
+ case _ =>
+ throw new IllegalArgumentException(s"gemm doesn't support
matrix type ${B.getClass}.")
+ }
+ case dense: DenseMatrix =>
+ B match {
+ case dB: DenseMatrix => gemm(transA, transB, alpha, dense, dB,
beta, C)
+ case sB: SparseMatrix => gemm(transA, transB, alpha, dense,
sB, beta, C)
+ case _ =>
+ throw new IllegalArgumentException(s"gemm doesn't support
matrix type ${B.getClass}.")
+ }
+ case _ =>
+ throw new IllegalArgumentException(s"gemm doesn't support matrix
type ${A.getClass}.")
+ }
+ }
+ }
+
+ /**
+ * C := alpha * A * B + beta * C
+ *
+ * @param alpha a scalar to scale the multiplication A * B.
+ * @param A the matrix A that will be left multiplied to B. Size of m x
k.
+ * @param B the matrix B that will be left multiplied by A. Size of k x
n.
+ * @param beta a scalar that can be used to scale matrix C.
+ * @param C the resulting matrix C. Size of m x n.
+ */
+ def gemm(
+ alpha: Double,
+ A: Matrix,
+ B: Matrix,
+ beta: Double,
+ C: DenseMatrix): Unit = {
+ gemm(false, false, alpha, A, B, beta, C)
+ }
+
+ /**
+ * C := alpha * A * B + beta * C
+ * For `DenseMatrix` A.
+ */
+ private def gemm(
+ transA: Boolean,
+ transB: Boolean,
+ alpha: Double,
+ A: DenseMatrix,
+ B: DenseMatrix,
+ beta: Double,
+ C: DenseMatrix): Unit = {
+ val mA: Int = if (!transA) A.numRows else A.numCols
+ val nB: Int = if (!transB) B.numCols else B.numRows
+ val kA: Int = if (!transA) A.numCols else A.numRows
+ val kB: Int = if (!transB) B.numRows else B.numCols
+ val tAstr = if (!transA) "N" else "T"
+ val tBstr = if (!transB) "N" else "T"
+
+ require(kA == kB, s"The columns of A don't match the rows of B. A:
$kA, B: $kB")
+ require(mA == C.numRows, s"The rows of C don't match the rows of A. C:
${C.numRows}, A: $mA")
+ require(nB == C.numCols,
+ s"The columns of C don't match the columns of B. C: ${C.numCols}, A:
$nB")
+
+ nativeBLAS.dgemm(tAstr, tBstr, mA, nB, kA, alpha, A.values, A.numRows,
B.values, B.numRows,
+ beta, C.values, C.numRows)
+ }
+
+ /**
+ * C := alpha * A * B + beta * C
+ * For `SparseMatrix` A.
+ */
+ private def gemm(
+ transA: Boolean,
+ transB: Boolean,
+ alpha: Double,
+ A: SparseMatrix,
+ B: DenseMatrix,
+ beta: Double,
+ C: DenseMatrix): Unit = {
+ val mA: Int = if (!transA) A.numRows else A.numCols
+ val nB: Int = if (!transB) B.numCols else B.numRows
+ val kA: Int = if (!transA) A.numCols else A.numRows
+ val kB: Int = if (!transB) B.numRows else B.numCols
+
+ require(kA == kB, s"The columns of A don't match the rows of B. A:
$kA, B: $kB")
+ require(mA == C.numRows, s"The rows of C don't match the rows of A. C:
${C.numRows}, A: $mA")
+ require(nB == C.numCols,
+ s"The columns of C don't match the columns of B. C: ${C.numCols}, A:
$nB")
+
+ val Avals = A.values
+ val Arows = if (!transA) A.rowIndices else A.colPtrs
+ val Acols = if (!transA) A.colPtrs else A.rowIndices
+
+ // Slicing is easy in this case. This is the optimal multiplication
setting for sparse matrices
+ if (transA){
+ var colCounterForB = 0
+ if (!transB) { // Expensive to put the check inside the loop
+ while (colCounterForB < nB) {
+ var rowCounterForA = 0
+ val Cstart = colCounterForB * mA
+ val Bstart = colCounterForB * kA
+ while (rowCounterForA < mA) {
+ var i = Arows(rowCounterForA)
+ val indEnd = Arows(rowCounterForA + 1)
+ var sum = 0.0
+ while (i < indEnd) {
+ sum += Avals(i) * B.values(Bstart + Acols(i))
+ i += 1
+ }
+ val Cindex = Cstart + rowCounterForA
+ C.values(Cindex) = beta * C.values(Cindex) + sum * alpha
+ rowCounterForA += 1
+ }
+ colCounterForB += 1
+ }
+ } else {
+ while (colCounterForB < nB) {
+ var rowCounter = 0
+ val Cstart = colCounterForB * mA
+ while (rowCounter < mA) {
+ var i = Arows(rowCounter)
+ val indEnd = Arows(rowCounter + 1)
+ var sum = 0.0
+ while (i < indEnd) {
+ sum += Avals(i) * B(colCounterForB, Acols(i))
+ i += 1
+ }
+ val Cindex = Cstart + rowCounter
+ C.values(Cindex) = beta * C.values(Cindex) + sum * alpha
+ rowCounter += 1
+ }
+ colCounterForB += 1
+ }
+ }
+ } else {
+ // Scale matrix first if `beta` is not equal to 0.0
--- End diff --
The matrix multiplication algorithms are different. If A is transposed, the
multiplication is very easy. A is in CSC format, therefore when you multiply
something with A', we get the column indices for free. Then it is your high
school matrix multiplication, but just using non-zero elements. Notice here
that we update the values of C only once, therefore you can scale it inside the
loop.
When A is not transposed, then you multiply the columns of A with the
corresponding rows of B and add it to C. Every multiplication of the column of
A and the row of B has the size C. Then it turns out you update the values of C
multiple times inside the loop. Therefore if you wanted to have an initial
scaling of C, you have to put it before the loop.
---
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