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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