spark训练rm推荐模型cholesky分解异常分析

最近隔壁的小伙伴跑模型出现了类似以下的错误，当然最主要的错误在下面的红色标识出来

问题的来源定位在 spark 源码中的位置

  private def checkReturnValue(info: intW, method: String): Unit = {
    info.`val` match {
      case code if code < 0 =>
        throw new IllegalStateException(s"LAPACK.$method returned $code; arg ${-code} is illegal")
      case code if code > 0 =>
        throw new SingularMatrixException (
          s"LAPACK.$method returned $code because A is not positive definite. Is A derived from " +
          "a singular matrix (e.g. collinear column values)?")
      case _ => // do nothing
    }
  }

运行时代码的环境还是 spark1.6.上面代码解析都是在 2.1.1 中进行的，相关接口基本上差异不是太大，核心代码如下

def train[ID: ClassTag]( // scalastyle:ignore
      ratings: RDD[Rating[ID]],
      rank: Int = 10,
      numUserBlocks: Int = 10,
      numItemBlocks: Int = 10,
      maxIter: Int = 10,
      regParam: Double = 0.1,
      implicitPrefs: Boolean = false,
      alpha: Double = 1.0,
      nonnegative: Boolean = false,
      intermediateRDDStorageLevel: StorageLevel = StorageLevel.MEMORY_AND_DISK,
      finalRDDStorageLevel: StorageLevel = StorageLevel.MEMORY_AND_DISK,
      checkpointInterval: Int = 10,
      seed: Long = 0L)(
      implicit ord: Ordering[ID]): (RDD[(ID, Array[Float])], RDD[(ID, Array[Float])]) = {
    require(!ratings.isEmpty(), s"No ratings available from $ratings")
    require(intermediateRDDStorageLevel != StorageLevel.NONE,
      "ALS is not designed to run without persisting intermediate RDDs.")
    val sc = ratings.sparkContext
    val userPart = new ALSPartitioner(numUserBlocks)
    val itemPart = new ALSPartitioner(numItemBlocks)
    val userLocalIndexEncoder = new LocalIndexEncoder(userPart.numPartitions)
    val itemLocalIndexEncoder = new LocalIndexEncoder(itemPart.numPartitions)
    val solver = if (nonnegative) new NNLSSolver else new CholeskySolver
    val blockRatings = partitionRatings(ratings, userPart, itemPart)
      .persist(intermediateRDDStorageLevel)
    val (userInBlocks, userOutBlocks) =
      makeBlocks("user", blockRatings, userPart, itemPart, intermediateRDDStorageLevel)
    // materialize blockRatings and user blocks
    userOutBlocks.count()
    val swappedBlockRatings = blockRatings.map {
      case ((userBlockId, itemBlockId), RatingBlock(userIds, itemIds, localRatings)) =>
        ((itemBlockId, userBlockId), RatingBlock(itemIds, userIds, localRatings))
    }
    val (itemInBlocks, itemOutBlocks) =
      makeBlocks("item", swappedBlockRatings, itemPart, userPart, intermediateRDDStorageLevel)
    // materialize item blocks
    itemOutBlocks.count()
    val seedGen = new XORShiftRandom(seed)
    var userFactors = initialize(userInBlocks, rank, seedGen.nextLong())
    var itemFactors = initialize(itemInBlocks, rank, seedGen.nextLong())
    var previousCheckpointFile: Option[String] = None
    val shouldCheckpoint: Int => Boolean = (iter) =>
      sc.checkpointDir.isDefined && checkpointInterval != -1 && (iter % checkpointInterval == 0)
    val deletePreviousCheckpointFile: () => Unit = () =>
      previousCheckpointFile.foreach { file =>
        try {
          val checkpointFile = new Path(file)
          checkpointFile.getFileSystem(sc.hadoopConfiguration).delete(checkpointFile, true)
        } catch {
          case e: IOException =>
            logWarning(s"Cannot delete checkpoint file $file:", e)
        }
      }
    if (implicitPrefs) {
      for (iter <- 1 to maxIter) {
        userFactors.setName(s"userFactors-$iter").persist(intermediateRDDStorageLevel)
        val previousItemFactors = itemFactors
        itemFactors = computeFactors(userFactors, userOutBlocks, itemInBlocks, rank, regParam,
          userLocalIndexEncoder, implicitPrefs, alpha, solver)
        previousItemFactors.unpersist()
        itemFactors.setName(s"itemFactors-$iter").persist(intermediateRDDStorageLevel)
        // TODO: Generalize PeriodicGraphCheckpointer and use it here.
        val deps = itemFactors.dependencies
        if (shouldCheckpoint(iter)) {
          itemFactors.checkpoint() // itemFactors gets materialized in computeFactors
        }
        val previousUserFactors = userFactors
        userFactors = computeFactors(itemFactors, itemOutBlocks, userInBlocks, rank, regParam,
          itemLocalIndexEncoder, implicitPrefs, alpha, solver)
        if (shouldCheckpoint(iter)) {
          ALS.cleanShuffleDependencies(sc, deps)
          deletePreviousCheckpointFile()
          previousCheckpointFile = itemFactors.getCheckpointFile
        }
        previousUserFactors.unpersist()
      }
    } else {
      for (iter <- 0 until maxIter) { itemFactors = computeFactors(userFactors, userOutBlocks, itemInBlocks, rank, regParam, userLocalIndexEncoder, solver = solver) if (shouldCheckpoint(iter)) { val deps = itemFactors.dependencies itemFactors.checkpoint() itemFactors.count() // checkpoint item factors and cut lineage ALS.cleanShuffleDependencies(sc, deps) deletePreviousCheckpointFile() previousCheckpointFile = itemFactors.getCheckpointFile } userFactors = computeFactors(itemFactors, itemOutBlocks, userInBlocks, rank, regParam, itemLocalIndexEncoder, solver = solver) } } val userIdAndFactors = userInBlocks .mapValues(_.srcIds) .join(userFactors) .mapPartitions({ items =>
        items.flatMap { case (_, (ids, factors)) =>
          ids.view.zip(factors)
        }
      // Preserve the partitioning because IDs are consistent with the partitioners in userInBlocks
      // and userFactors.
      }, preservesPartitioning = true)
      .setName("userFactors")
      .persist(finalRDDStorageLevel)
    val itemIdAndFactors = itemInBlocks
      .mapValues(_.srcIds)
      .join(itemFactors)
      .mapPartitions({ items =>
        items.flatMap { case (_, (ids, factors)) =>
          ids.view.zip(factors)
        }
      }, preservesPartitioning = true)
      .setName("itemFactors")
      .persist(finalRDDStorageLevel)
    if (finalRDDStorageLevel != StorageLevel.NONE) {
      userIdAndFactors.count()
      itemFactors.unpersist()
      itemIdAndFactors.count()
      userInBlocks.unpersist()
      userOutBlocks.unpersist()
      itemInBlocks.unpersist()
      itemOutBlocks.unpersist()
      blockRatings.unpersist()
    }
    (userIdAndFactors, itemIdAndFactors)
  }

关于上述代码的解析可以推荐一个博客写的非常好，对博主阅读源码找问题时提供了很大的帮助，als 源码解析，在这里最主要在

val previousItemFactors = itemFactors itemFactors = computeFactors(userFactors, userOutBlocks, itemInBlocks, rank, regParam, userLocalIndexEncoder, implicitPrefs, alpha, solver)

  private def computeFactors[ID](
      srcFactorBlocks: RDD[(Int, FactorBlock)],
      srcOutBlocks: RDD[(Int, OutBlock)],
      dstInBlocks: RDD[(Int, InBlock[ID])],
      rank: Int,
      regParam: Double,
      srcEncoder: LocalIndexEncoder,
      implicitPrefs: Boolean = false,
      alpha: Double = 1.0,
      solver: LeastSquaresNESolver): RDD[(Int, FactorBlock)] = {
    val numSrcBlocks = srcFactorBlocks.partitions.length
    //涉及隐式与显式，默认都是显式
    val YtY = if (implicitPrefs) Some(computeYtY(srcFactorBlocks, rank)) else None
    val srcOut = srcOutBlocks.join(srcFactorBlocks).flatMap {
      case (srcBlockId, (srcOutBlock, srcFactors)) =>
        srcOutBlock.view.zipWithIndex.map { case (activeIndices, dstBlockId) =>
          (dstBlockId, (srcBlockId, activeIndices.map(idx => srcFactors(idx))))
        }
    }
    val merged = srcOut.groupByKey(new ALSPartitioner(dstInBlocks.partitions.length))
    dstInBlocks.join(merged).mapValues {
      case (InBlock(dstIds, srcPtrs, srcEncodedIndices, ratings), srcFactors) =>
        val sortedSrcFactors = new Array[FactorBlock](numSrcBlocks)
        srcFactors.foreach { case (srcBlockId, factors) =>
          sortedSrcFactors(srcBlockId) = factors
        }
        val dstFactors = new Array[Array[Float]](dstIds.length)
        var j = 0
        val ls = new NormalEquation(rank)
        //以计算商品的特征矩阵为例，这个就是遍历每一个商品
        while (j < dstIds.length) {
          ls.reset()
          if (implicitPrefs) {
            ls.merge(YtY.get)
          }
          var i = srcPtrs(j)
          var numExplicits = 0
          //此处遍历每一个商品相关联的用户
          while (i < srcPtrs(j + 1)) {
            //加密计算索引
            val encoded = srcEncodedIndices(i)
            //根据索引计算得到分区 ID
            val blockId = srcEncoder.blockId(encoded)
            val localIndex = srcEncoder.localIndex(encoded)
            val srcFactor = sortedSrcFactors(blockId)(localIndex)
            val rating = ratings(i)
            if (implicitPrefs) {
              // Extension to the original paper to handle rating < 0. confidence is a function
              // of |rating| instead so that it is never negative. c1 is confidence - 1.
              val c1 = alpha * math.abs(rating)
              // For rating <= 0, the corresponding preference is 0. So the second argument of add // is only there for rating > 0.
              if (rating > 0.0) {
                numExplicits += 1
              }
              ls.add(srcFactor, if (rating > 0.0) 1.0 + c1 else 0.0, c1)
            } else {
              ls.add(srcFactor, rating)
              numExplicits += 1
            }
            i += 1
          }
          // Weight lambda by the number of explicit ratings based on the ALS-WR paper.
          //此处执行 wls 求解，使用的是 cholesky 分解方法
          dstFactors(j) = solver.solve(ls, numExplicits * regParam)
          j += 1
        }
        dstFactors
    }
  }

下面贴出 cholesky 代码

 private[recommendation] class CholeskySolver extends LeastSquaresNESolver {

    /**
     * Solves a least squares problem with L2 regularization:
     *
     *   min norm(A x - b)^2^ + lambda * norm(x)^2^
     *
     * @param ne a [[NormalEquation]] instance that contains AtA, Atb, and n (number of instances)
     * @param lambda regularization constant
     * @return the solution x
     */
    override def solve(ne: NormalEquation, lambda: Double): Array[Float] = {
      val k = ne.k
      // Add scaled lambda to the diagonals of AtA.
      var i = 0
      var j = 2
      while (i < ne.triK) {
        ne.ata(i) += lambda
        i += j
        j += 1
      }
      //分解方法使用的是 lapack 打包的方法，spark 这边这是负责封装 api
      CholeskyDecomposition.solve(ne.ata, ne.atb)
      val x = new Array[Float](k)
      i = 0
      while (i < k) {
        x(i) = ne.atb(i).toFloat
        i += 1
      }
      ne.reset()
      x
    }
  }

choklesky 计算的原理可以参考这个文章：cholesky 分解

该线性回归问题时，对左边 ata 矩阵进行 cholesky 分解出现错误，原因在于矩阵的对称矩阵中的数据太小，cholesky 分解的前提是矩阵要是正定矩阵，如果不满足条件就会出现分解异常中断程序，因此在评分的构造时建议将评分数据最小值适当定义，建议从 1 开始定义数据
ps：从网上查到的资料显示如果存在多列数据方差为 0，及时数据不是很小也会出现上面描述的情况，出现这个现象就是矩阵 A 并不是列满秩