Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/460#discussion_r11985078
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/optimization/NNLSbyPCG.scala ---
@@ -0,0 +1,183 @@
+/*
+ * 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.optimization
+
+import org.jblas.{DoubleMatrix, SimpleBlas}
+
+import org.apache.spark.annotation.DeveloperApi
+
+
+/**
+ * :: DeveloperApi ::
+ * Object used to solve nonnegative least squares problems using a modified
+ * projected gradient method.
+ */
+@DeveloperApi
+private[mllib] object NNLSbyPCG {
+ class Workspace(val n: Int) {
+ val scratch = new DoubleMatrix(n, 1)
+ val grad = new DoubleMatrix(n, 1)
+ val x = new DoubleMatrix(n, 1)
+ val dir = new DoubleMatrix(n, 1)
+ val lastDir = new DoubleMatrix(n, 1)
+ val res = new DoubleMatrix(n, 1)
+
+ def wipe() {
+ var i: Int = 0
+ while (i < n) {
+ scratch.data(i) = 0.0
+ grad.data(i) = 0.0
+ x.data(i) = 0.0
+ dir.data(i) = 0.0
+ lastDir.data(i) = 0.0
+ res.data(i) = 0.0
+ i = i + 1
+ }
+ }
+ }
+
+ def createWorkspace(n: Int): Workspace = {
+ new Workspace(n)
+ }
+
+ /**
+ * Solve a least squares problem, possibly with nonnegativity
constraints, by a modified
+ * projected gradient method. That is, find x minimising ||Ax - b||_2
given A^T A and A^T b.
+ *
+ * We solve the problem
+ * min_x 1/2 x^T ata x^T - x^T atb
+ * subject to x >= 0 (if nonnegative == true)
+ *
+ * The method used is similar to one described by Polyak (B. T. Polyak,
The conjugate gradient
+ * method in extremal problems, Zh. Vychisl. Mat. Mat. Fiz. 9(4)(1969),
pp. 94-112) for bound-
+ * constrained nonlinear programming. Polyak unconditionally uses a
conjugate gradient
+ * direction, however, while this method only uses a conjugate gradient
direction if the last
+ * iteration did not cause a previously-inactive constraint to become
active.
+ */
+ def solve(ata: DoubleMatrix, atb: DoubleMatrix, nonnegative: Boolean,
+ ws: Workspace): Array[Double] = {
+ ws.wipe()
+
+ val n = atb.rows
+ val scratch = ws.scratch
+
+ // find the optimal unconstrained step
+ def steplen(dir: DoubleMatrix, res: DoubleMatrix): Double = {
+ val top = SimpleBlas.dot(dir, res)
+ SimpleBlas.gemv(1.0, ata, dir, 0.0, scratch)
+ // Push the denominator upward very slightly to avoid infinities and
silliness
+ top / (SimpleBlas.dot(scratch, dir) + 1e-20)
+ }
+
+ // stopping condition
+ def stop(step: Double, ndir: Double, nx: Double): Boolean = {
+ ((step != step) // NaN
+ || (step < 1e-6) // too small or negative
+ || (step > 1e40) // too small; almost certainly numerical problems
+ || (ndir < 1e-12 * nx) // gradient relatively too small
+ || (ndir < 1e-32) // gradient absolutely too small; numerical issues
may lurk
+ )
+ }
+
+ val grad = ws.grad
+ val x = ws.x
+ val dir = ws.dir
+ val lastDir = ws.lastDir
+ val res = ws.res
+ val iterMax = Math.max(400, 20 * n)
+ var lastNorm = 0.0
+ var iterno = 0
+ var lastWall = 0 // Last iteration when we hit a bound constraint.
+ var i = 0
+ while (iterno < iterMax) {
+ // find the residual
+ SimpleBlas.gemv(1.0, ata, x, 0.0, res)
+ SimpleBlas.axpy(-1.0, atb, res)
+ SimpleBlas.copy(res, grad)
+
+ // project the gradient
+ if (nonnegative) {
+ i = 0
+ while (i < n) {
+ if (grad.data(i) > 0.0 && x.data(i) == 0.0) {
+ grad.data(i) = 0.0
+ }
+ i = i + 1
+ }
+ }
+ val ngrad = SimpleBlas.dot(grad, grad)
+
+ SimpleBlas.copy(grad, dir)
+
+ // use a CG direction under certain conditions
+ var step = steplen(grad, res)
+ var ndir = 0.0
+ val nx = SimpleBlas.dot(x, x)
+ if (iterno > lastWall + 1) {
+ val alpha = ngrad / lastNorm
+ SimpleBlas.axpy(alpha, lastDir, dir)
+ val dstep = steplen(dir, res)
+ ndir = SimpleBlas.dot(dir, dir)
+ if (stop(dstep, ndir, nx)) {
+ // reject the CG step if it could lead to premature termination
+ SimpleBlas.copy(grad, dir)
+ ndir = SimpleBlas.dot(dir, dir)
+ } else {
+ step = dstep
+ }
+ } else {
+ ndir = SimpleBlas.dot(dir, dir)
+ }
+
+ // terminate?
+ if (stop(step, ndir, nx)) {
+ return x.data.clone
+ }
+
+ // don't run through the walls
+ if (nonnegative) {
+ i = 0
+ while (i < n) {
+ if (step * dir.data(i) > x.data(i)) {
+ step = Math.min(step, x.data(i) / dir.data(i))
+ }
+ i = i + 1
+ }
+ }
+
+ // take the step
+ i = 0
+ while (i < n) {
+ if (nonnegative) {
+ if (step * dir.data(i) > x.data(i) * (1 - 1e-14)) {
+ x.data(i) = 0
+ lastWall = iterno
+ } else x.data(i) -= step * dir.data(i)
--- End diff --
~~~
} else {
x.data(i) -= step * dir.data(i)
}
~~~
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