Github user brkyvz commented on a diff in the pull request:
https://github.com/apache/spark/pull/2294#discussion_r17746583
--- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/BLAS.scala ---
@@ -197,4 +201,368 @@ 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 specify whether to use matrix A, or the transpose of
matrix A. Should be "N" or
+ * "n" to use A, and "T" or "t" to use the transpose of A.
+ * @param transB specify whether to use matrix B, or the transpose of
matrix B. Should be "N" or
+ * "n" to use B, and "T" or "t" to use the transpose of B.
+ * @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: DenseMatrix,
+ beta: Double,
+ C: DenseMatrix): Unit = {
+ if (alpha == 0.0) {
+ logWarning("gemm: alpha is equal to 0. Returning C.")
+ } else {
+ A match {
+ case sparse: SparseMatrix =>
+ gemm(transA, transB, alpha, sparse, B, beta, C)
+ case dense: DenseMatrix =>
+ gemm(transA, transB, alpha, dense, B, beta, C)
+ 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: DenseMatrix,
+ 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
+ if (beta != 0.0){
+ nativeBLAS.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
+ // B, and added to C.
+ var colCounterForB = 0 // the column to be updated in C
+ if (!transB) { // Expensive to put the check inside the loop
+ while (colCounterForB < nB) {
+ var colCounterForA = 0 // The column of A to multiply with the
row of B
+ while (colCounterForA < kA){
+ var i = Acols(colCounterForA)
+ val indEnd = Acols(colCounterForA + 1)
+ val Bval = B(colCounterForA, colCounterForB)
+ val Cstart = colCounterForB * mA
+ while (i < indEnd){
+ C.values(Cstart + Arows(i)) += Avals(i) * Bval * alpha
+ i += 1
+ }
+ colCounterForA += 1
+ }
+ colCounterForB += 1
+ }
+ } else {
+ while (colCounterForB < nB) {
+ var colCounterForA = 0 // The column of A to multiply with the
row of B
+ while (colCounterForA < kA){
+ var i = Acols(colCounterForA)
+ val indEnd = Acols(colCounterForA + 1)
+ val Bval = B(colCounterForB, colCounterForA)
+ val Cstart = colCounterForB * mA
+ while (i < indEnd){
+ C.values(Cstart + Arows(i)) += Avals(i) * Bval * alpha
+ i += 1
+ }
+ colCounterForA += 1
+ }
+ colCounterForB += 1
+ }
+ }
+ }
+ }
+
+ /**
+ * y := alpha * A * x + beta * y
+ * @param trans specify whether to use matrix A, or the transpose of
matrix A. Should be "N" or
+ * "n" to use A, and "T" or "t" to use the transpose of A.
+ * @param alpha a scalar to scale the multiplication A * x.
+ * @param A the matrix A that will be left multiplied to x. Size of m x
n.
+ * @param x the vector x that will be left multiplied by A. Size of n x
1.
+ * @param beta a scalar that can be used to scale vector y.
+ * @param y the resulting vector y. Size of m x 1.
+ */
+ def gemv(
+ trans: Boolean,
+ alpha: Double,
+ A: Matrix,
+ x: DenseVector,
+ beta: Double,
+ y: DenseVector): Unit = {
+
+ val mA: Int = if (!trans) A.numRows else A.numCols
+ val nx: Int = x.size
+ val nA: Int = if (!trans) A.numCols else A.numRows
+
+ require(nA == nx, s"The columns of A don't match the number of
elements of x. A: $nA, x: $nx")
+ require(mA == y.size,
+ s"The rows of A don't match the number of elements of y. A: $mA,
y:${y.size}}")
+ if (alpha == 0.0) {
+ logWarning("gemv: alpha is equal to 0. Returning y.")
+ } else {
+ A match {
+ case sparse: SparseMatrix =>
+ gemv(trans, alpha, sparse, x, beta, y)
+ case dense: DenseMatrix =>
+ gemv(trans, alpha, dense, x, beta, y)
+ case _ =>
+ throw new IllegalArgumentException(s"gemv doesn't support matrix
type ${A.getClass}.")
+ }
+ }
+ }
+
+ /**
+ * y := alpha * A * x + beta * y
+ *
+ * @param alpha a scalar to scale the multiplication A * x.
+ * @param A the matrix A that will be left multiplied to x. Size of m x
n.
+ * @param x the vector x that will be left multiplied by A. Size of n x
1.
+ * @param beta a scalar that can be used to scale vector y.
+ * @param y the resulting vector y. Size of m x 1.
+ */
+ def gemv(
+ alpha: Double,
+ A: Matrix,
+ x: DenseVector,
+ beta: Double,
+ y: DenseVector): Unit = {
+ gemv(false, alpha, A, x, beta, y)
+ }
+
+ /**
+ * y := alpha * A * x
+ *
+ * @param trans specify whether to use matrix A, or the transpose of
matrix A. Should be "N" or
+ * "n" to use A, and "T" or "t" to use the transpose of A.
+ * @param alpha a scalar to scale the multiplication A * x.
+ * @param A the matrix A that will be left multiplied to x. Size of m x
n.
+ * @param x the vector x that will be left multiplied by A. Size of n x
1.
+ *
+ * @return `DenseVector` y, the result of the matrix-vector
multiplication. Size of m x 1.
+ */
+ def gemv(
+ trans: Boolean,
+ alpha: Double,
+ A: Matrix,
+ x: DenseVector): DenseVector = {
+ val m = if(!trans) A.numRows else A.numCols
+
+ val y: DenseVector = new DenseVector(Array.fill(m)(0.0))
+ gemv(trans, alpha, A, x, 0.0, y)
+
+ y
+ }
+
+ /**
+ * y := alpha * A * x
+ *
+ * @param alpha a scalar to scale the multiplication A * x.
+ * @param A the matrix A that will be left multiplied to x. Size of m x
n.
+ * @param x the vector x that will be left multiplied by A. Size of n x
1.
+ *
+ * @return `DenseVector` y, the result of the matrix-vector
multiplication. Size of m x 1.
+ */
+ def gemv(
+ alpha: Double,
+ A: Matrix,
+ x: DenseVector): DenseVector = {
+ gemv(false, alpha, A, x)
+ }
+
+
+ /**
+ * y := alpha * A * x + beta * y
+ * For `DenseMatrix` A.
+ */
+ private def gemv(
+ trans: Boolean,
+ alpha: Double,
+ A: DenseMatrix,
+ x: DenseVector,
+ beta: Double,
+ y: DenseVector): Unit = {
+ val tStrA = if (!trans) "N" else "T"
+ nativeBLAS.dgemv(tStrA, A.numRows, A.numCols, alpha, A.values,
A.numRows, x.values, 1, beta,
--- End diff --
nativeBLAS was faster across the board. Here are the results (in ms):
m | n | f2j | native
---|----|-----|--------
1000 | 500 | 0.7 | 0.1
1000 | 1000 | 2.3 | 0.7
1000 | 5000 | 7.7 | 3.6
5000 | 500 | 3.8 | 2.4
5000 | 1000 | 7.7 | 4.0
5000 | 5000 | 38.4 | 17.4
10000 | 500 | 6.5 | 4.5
10000 | 1000 | 13.0 | 8.9
10000 | 5000 | 75.4 | 36.7
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