Github user vrilleup commented on a diff in the pull request: https://github.com/apache/spark/pull/964#discussion_r13896261 --- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/EigenValueDecomposition.scala --- @@ -0,0 +1,150 @@ +/* + * 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 + +import breeze.linalg.{DenseMatrix => BDM, DenseVector => BDV} +import com.github.fommil.netlib.ARPACK +import org.netlib.util.{intW, doubleW} + +import org.apache.spark.annotation.Experimental + +/** + * :: Experimental :: + * Represents eigenvalue decomposition factors. + */ +@Experimental +case class EigenValueDecomposition[VType](s: Vector, V: VType) + +@Experimental +object EigenValueDecomposition { + /** + * Compute the leading k eigenvalues and eigenvectors on a symmetric square matrix using ARPACK. + * The caller needs to ensure that the input matrix is real symmetric. This function requires + * memory for `n*(4*k+4)` doubles. + * + * @param mul a function that multiplies the symmetric matrix with a DenseVector. + * @param n dimension of the square matrix (maximum Int.MaxValue). + * @param k number of leading eigenvalues required. + * @param tol tolerance of the eigs computation. + * @return a dense vector of eigenvalues in descending order and a dense matrix of eigenvectors + * (columns of the matrix). The number of computed eigenvalues might be smaller than k. + */ + private[mllib] def symmetricEigs(mul: DenseVector => DenseVector, n: Int, k: Int, tol: Double) + : (BDV[Double], BDM[Double]) = { + // TODO: remove this function and use eigs in breeze when switching breeze version + require(n > k, s"Number of required eigenvalues $k must be smaller than matrix dimension $n") + + val arpack = ARPACK.getInstance() + + // tolerance used in stopping criterion + val tolW = new doubleW(tol) + // number of desired eigenvalues, 0 < nev < n + val nev = new intW(k) + // nev Lanczos vectors are generated are generated in the first iteration + // ncv-nev Lanczos vectors are generated are generated in each subsequent iteration + // ncv must be smaller than n + val ncv = scala.math.min(2 * k, n) + + // "I" for standard eigenvalue problem, "G" for generalized eigenvalue problem + val bmat = "I" + // "LM" : compute the NEV largest (in magnitude) eigenvalues + val which = "LM" + + var iparam = new Array[Int](11) + // use exact shift in each iteration + iparam(0) = 1 + // maximum number of Arnoldi update iterations, or the actual number of iterations on output + iparam(2) = 300 + // Mode 1: A*x = lambda*x, A symmetric + iparam(6) = 1 + + var ido = new intW(0) + var info = new intW(0) + var resid:Array[Double] = new Array[Double](n) + var v = new Array[Double](n * ncv) + var workd = new Array[Double](n * 3) + var workl = new Array[Double](ncv * (ncv + 8)) + var ipntr = new Array[Int](11) + + // call ARPACK's reverse communication, first iteration with ido = 0 + arpack.dsaupd(ido, bmat, n, which, nev.`val`, tolW, resid, ncv, v, n, iparam, ipntr, workd, + workl, workl.length, info) + + val w = BDV(workd) + + // ido = 99 : done flag in reverse communication + while (ido.`val` != 99) { + if (ido.`val` != -1 && ido.`val` != 1) { + throw new IllegalStateException("ARPACK returns ido = " + ido.`val` + + " This flag is not compatible with Mode 1: A*x = lambda*x, A symmetric.") + } + // multiply working vector with the matrix + val inputOffset = ipntr(0) - 1 + val outputOffset = ipntr(1) - 1 + val x = w(inputOffset until inputOffset + n) + val y = w(outputOffset until outputOffset + n) + y := BDV(mul(Vectors.fromBreeze(x).asInstanceOf[DenseVector]).toArray) + // call ARPACK's reverse communication + arpack.dsaupd(ido, bmat, n, which, nev.`val`, tolW, resid, ncv, v, n, iparam, ipntr, + workd, workl, workl.length, info) + } + + if (info.`val` != 0) { + info.`val` match { + case 1 => throw new IllegalStateException("ARPACK returns non-zero info = " + info.`val` + + " Maximum number of iterations taken. (Refer ARPACK user guide for details)") + case 2 => throw new IllegalStateException("ARPACK returns non-zero info = " + info.`val` + + " No shifts could be applied. Try to increase NCV. " + + "(Refer ARPACK user guide for details)") + case _ => throw new IllegalStateException("ARPACK returns non-zero info = " + info.`val` + + " Please refer ARPACK user guide for error message.") + } + } + + val d = new Array[Double](nev.`val`) + val select = new Array[Boolean](ncv) + // copy the Ritz vectors + val z = java.util.Arrays.copyOfRange(v, 0, nev.`val` * n) + + // call ARPACK's post-processing for eigenvectors + arpack.dseupd(true, "A", select, d, z, n, 0.0, bmat, n, which, nev, tol, resid, ncv, v, n, + iparam, ipntr, workd, workl, workl.length, info) + + // number of computed eigenvalues, might be smaller than k + val computed = iparam(4) + + val eigenPairs = java.util.Arrays.copyOfRange(d, 0, computed).zipWithIndex.map{ + r => (r._1, java.util.Arrays.copyOfRange(z, r._2 * n, r._2 * n + n)) + } + + // sort the eigen-pairs in descending order + val sortedEigenPairs = eigenPairs.sortBy(-1 * _._1) --- End diff -- replace multiplication with negation
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