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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.spark.mllib.linalg.distributed
import breeze.linalg.{DenseMatrix => BDM}
import org.apache.spark.annotation.Since
import org.apache.spark.mllib.linalg._
import org.apache.spark.mllib.linalg.SingularValueDecomposition
import org.apache.spark.rdd.RDD
/**
* Represents a row of [[org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix]].
*/
@Since("1.0.0")
case class IndexedRow(index: Long, vector: Vector)
/**
* Represents a row-oriented [[org.apache.spark.mllib.linalg.distributed.DistributedMatrix]] with
* indexed rows.
*
* @param rows indexed rows of this matrix
* @param nRows number of rows. A non-positive value means unknown, and then the number of rows will
* be determined by the max row index plus one.
* @param nCols number of columns. A non-positive value means unknown, and then the number of
* columns will be determined by the size of the first row.
*/
@Since("1.0.0")
class IndexedRowMatrix @Since("1.0.0") (
@Since("1.0.0") val rows: RDD[IndexedRow],
private var nRows: Long,
private var nCols: Int) extends DistributedMatrix {
/** Alternative constructor leaving matrix dimensions to be determined automatically. */
@Since("1.0.0")
def this(rows: RDD[IndexedRow]) = this(rows, 0L, 0)
@Since("1.0.0")
override def numCols(): Long = {
if (nCols <= 0) {
// Calling `first` will throw an exception if `rows` is empty.
nCols = rows.first().vector.size
}
nCols
}
@Since("1.0.0")
override def numRows(): Long = {
if (nRows <= 0L) {
// Reduce will throw an exception if `rows` is empty.
nRows = rows.map(_.index).reduce(math.max) + 1L
}
nRows
}
/**
* Compute all cosine similarities between columns of this matrix using the brute-force
* approach of computing normalized dot products.
*
* @return An n x n sparse upper-triangular matrix of cosine similarities between
* columns of this matrix.
*/
@Since("1.6.0")
def columnSimilarities(): CoordinateMatrix = {
toRowMatrix().columnSimilarities()
}
/**
* Drops row indices and converts this matrix to a
* [[org.apache.spark.mllib.linalg.distributed.RowMatrix]].
*/
@Since("1.0.0")
def toRowMatrix(): RowMatrix = {
new RowMatrix(rows.map(_.vector), 0L, nCols)
}
/** Converts to BlockMatrix. Creates blocks of [[SparseMatrix]] with size 1024 x 1024. */
@Since("1.3.0")
def toBlockMatrix(): BlockMatrix = {
toBlockMatrix(1024, 1024)
}
/**
* Converts to BlockMatrix. Creates blocks of [[SparseMatrix]].
* @param rowsPerBlock The number of rows of each block. The blocks at the bottom edge may have
* a smaller value. Must be an integer value greater than 0.
* @param colsPerBlock The number of columns of each block. The blocks at the right edge may have
* a smaller value. Must be an integer value greater than 0.
* @return a [[BlockMatrix]]
*/
@Since("1.3.0")
def toBlockMatrix(rowsPerBlock: Int, colsPerBlock: Int): BlockMatrix = {
// TODO: This implementation may be optimized
toCoordinateMatrix().toBlockMatrix(rowsPerBlock, colsPerBlock)
}
/**
* Converts this matrix to a
* [[org.apache.spark.mllib.linalg.distributed.CoordinateMatrix]].
*/
@Since("1.3.0")
def toCoordinateMatrix(): CoordinateMatrix = {
val entries = rows.flatMap { row =>
val rowIndex = row.index
row.vector match {
case SparseVector(size, indices, values) =>
Iterator.tabulate(indices.length)(i => MatrixEntry(rowIndex, indices(i), values(i)))
case DenseVector(values) =>
Iterator.tabulate(values.length)(i => MatrixEntry(rowIndex, i, values(i)))
}
}
new CoordinateMatrix(entries, numRows(), numCols())
}
/**
* Computes the singular value decomposition of this IndexedRowMatrix.
* Denote this matrix by A (m x n), this will compute matrices U, S, V such that A = U * S * V'.
*
* The cost and implementation of this method is identical to that in
* [[org.apache.spark.mllib.linalg.distributed.RowMatrix]]
* With the addition of indices.
*
* At most k largest non-zero singular values and associated vectors are returned.
* If there are k such values, then the dimensions of the return will be:
*
* U is an [[org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix]] of size m x k that
* satisfies U'U = eye(k),
* s is a Vector of size k, holding the singular values in descending order,
* and V is a local Matrix of size n x k that satisfies V'V = eye(k).
*
* @param k number of singular values to keep. We might return less than k if there are
* numerically zero singular values. See rCond.
* @param computeU whether to compute U
* @param rCond the reciprocal condition number. All singular values smaller than rCond * sigma(0)
* are treated as zero, where sigma(0) is the largest singular value.
* @return SingularValueDecomposition(U, s, V)
*/
@Since("1.0.0")
def computeSVD(
k: Int,
computeU: Boolean = false,
rCond: Double = 1e-9): SingularValueDecomposition[IndexedRowMatrix, Matrix] = {
val n = numCols().toInt
require(k > 0 && k <= n, s"Requested k singular values but got k=$k and numCols=$n.")
val indices = rows.map(_.index)
val svd = toRowMatrix().computeSVD(k, computeU, rCond)
val U = if (computeU) {
val indexedRows = indices.zip(svd.U.rows).map { case (i, v) =>
IndexedRow(i, v)
}
new IndexedRowMatrix(indexedRows, nRows, svd.U.numCols().toInt)
} else {
null
}
SingularValueDecomposition(U, svd.s, svd.V)
}
/**
* Multiply this matrix by a local matrix on the right.
*
* @param B a local matrix whose number of rows must match the number of columns of this matrix
* @return an IndexedRowMatrix representing the product, which preserves partitioning
*/
@Since("1.0.0")
def multiply(B: Matrix): IndexedRowMatrix = {
val mat = toRowMatrix().multiply(B)
val indexedRows = rows.map(_.index).zip(mat.rows).map { case (i, v) =>
IndexedRow(i, v)
}
new IndexedRowMatrix(indexedRows, nRows, B.numCols)
}
/**
* Computes the Gramian matrix `A^T A`. Note that this cannot be
* computed on matrices with more than 65535 columns.
*/
@Since("1.0.0")
def computeGramianMatrix(): Matrix = {
toRowMatrix().computeGramianMatrix()
}
private[mllib] override def toBreeze(): BDM[Double] = {
val m = numRows().toInt
val n = numCols().toInt
val mat = BDM.zeros[Double](m, n)
rows.collect().foreach { case IndexedRow(rowIndex, vector) =>
val i = rowIndex.toInt
vector.foreachActive { case (j, v) =>
mat(i, j) = v
}
}
mat
}
}
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