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Posted to commits@mahout.apache.org by td...@apache.org on 2012/05/04 00:36:50 UTC
svn commit: r1333667 - in /mahout/trunk/math/src:
main/java/org/apache/mahout/math/decomposer/lanczos/
main/java/org/apache/mahout/math/matrix/linalg/
main/java/org/apache/mahout/math/solver/
test/java/org/apache/mahout/math/decomposer/lanczos/ test/ja...
Author: tdunning
Date: Thu May 3 22:36:49 2012
New Revision: 1333667
URL: http://svn.apache.org/viewvc?rev=1333667&view=rev
Log:
MAHOUT-1005 - Added new implementation of EigenDecomposition based on JAMA code. Deleted old EigenvalueDecomposition from Colt.
Added:
mahout/trunk/math/src/main/java/org/apache/mahout/math/solver/EigenDecomposition.java
mahout/trunk/math/src/test/java/org/apache/mahout/math/solver/EigenDecompositionTest.java
Removed:
mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/EigenvalueDecomposition.java
Modified:
mahout/trunk/math/src/main/java/org/apache/mahout/math/decomposer/lanczos/LanczosSolver.java
mahout/trunk/math/src/test/java/org/apache/mahout/math/decomposer/lanczos/TestLanczosSolver.java
Modified: mahout/trunk/math/src/main/java/org/apache/mahout/math/decomposer/lanczos/LanczosSolver.java
URL: http://svn.apache.org/viewvc/mahout/trunk/math/src/main/java/org/apache/mahout/math/decomposer/lanczos/LanczosSolver.java?rev=1333667&r1=1333666&r2=1333667&view=diff
==============================================================================
--- mahout/trunk/math/src/main/java/org/apache/mahout/math/decomposer/lanczos/LanczosSolver.java (original)
+++ mahout/trunk/math/src/main/java/org/apache/mahout/math/decomposer/lanczos/LanczosSolver.java Thu May 3 22:36:49 2012
@@ -23,9 +23,7 @@ import org.apache.mahout.math.Vector;
import org.apache.mahout.math.VectorIterable;
import org.apache.mahout.math.function.DoubleFunction;
import org.apache.mahout.math.function.PlusMult;
-import org.apache.mahout.math.matrix.DoubleMatrix1D;
-import org.apache.mahout.math.matrix.DoubleMatrix2D;
-import org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition;
+import org.apache.mahout.math.solver.EigenDecomposition;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
@@ -50,7 +48,7 @@ import java.util.Map;
* problems into floating point <em>underflow</em> (ie, very small singular values will become invisible, as they
* will appear to be zero and the algorithm will terminate).
* </p>
- * <p>This implementation uses {@link org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition} to do the
+ * <p>This implementation uses {@link EigenDecomposition} to do the
* eigenvalue extraction from the small (desiredRank x desiredRank) tridiagonal matrix. Numerical stability is
* achieved via brute-force: re-orthogonalization against all previous eigenvectors is computed after every pass.
* This can be made smarter if (when!) this proves to be a major bottleneck. Of course, this step can be parallelized
@@ -140,16 +138,16 @@ public class LanczosSolver {
log.info("Lanczos iteration complete - now to diagonalize the tri-diagonal auxiliary matrix.");
// at this point, have tridiag all filled out, and basis is all filled out, and orthonormalized
- EigenvalueDecomposition decomp = new EigenvalueDecomposition(triDiag);
+ EigenDecomposition decomp = new EigenDecomposition(triDiag);
- DoubleMatrix2D eigenVects = decomp.getV();
- DoubleMatrix1D eigenVals = decomp.getRealEigenvalues();
+ Matrix eigenVects = decomp.getV();
+ Vector eigenVals = decomp.getRealEigenvalues();
endTime(TimingSection.TRIDIAG_DECOMP);
startTime(TimingSection.FINAL_EIGEN_CREATE);
for (int row = 0; row < i; row++) {
Vector realEigen = null;
// the eigenvectors live as columns of V, in reverse order. Weird but true.
- DoubleMatrix1D ejCol = eigenVects.viewColumn(i - row - 1);
+ Vector ejCol = eigenVects.viewColumn(i - row - 1);
int size = Math.min(ejCol.size(), state.getBasisSize());
for (int j = 0; j < size; j++) {
double d = ejCol.get(j);
Added: mahout/trunk/math/src/main/java/org/apache/mahout/math/solver/EigenDecomposition.java
URL: http://svn.apache.org/viewvc/mahout/trunk/math/src/main/java/org/apache/mahout/math/solver/EigenDecomposition.java?rev=1333667&view=auto
==============================================================================
--- mahout/trunk/math/src/main/java/org/apache/mahout/math/solver/EigenDecomposition.java (added)
+++ mahout/trunk/math/src/main/java/org/apache/mahout/math/solver/EigenDecomposition.java Thu May 3 22:36:49 2012
@@ -0,0 +1,895 @@
+/*
+ * 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.
+ */
+
+/**
+ * Adapted from the public domain Jama code.
+ */
+
+package org.apache.mahout.math.solver;
+
+
+import org.apache.mahout.math.DenseMatrix;
+import org.apache.mahout.math.DenseVector;
+import org.apache.mahout.math.Matrix;
+import org.apache.mahout.math.Vector;
+import org.apache.mahout.math.function.Functions;
+
+/**
+ * Eigenvalues and eigenvectors of a real matrix.
+ * <p/>
+ * If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector
+ * matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose())
+ * equals the identity matrix.
+ * <p/>
+ * If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues
+ * in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu,
+ * lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e.
+ * A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the
+ * validity of the equation A = V*D*inverse(V) depends upon V.cond().
+ */
+
+public class EigenDecomposition {
+ /**
+ * Row and column dimension (square matrix).
+ */
+ private int n;
+
+ /**
+ * Arrays for internal storage of eigenvalues.
+ */
+ private Vector d, e;
+
+ /**
+ * Array for internal storage of eigenvectors.
+ */
+ private Matrix v;
+
+ public EigenDecomposition(Matrix x) {
+ this(x, isSymmetric(x));
+ }
+
+ public EigenDecomposition(Matrix x, boolean isSymmetric) {
+ n = x.columnSize();
+ d = new DenseVector(n);
+ e = new DenseVector(n);
+ v = new DenseMatrix(n, n);
+
+ if (isSymmetric) {
+ v.assign(x);
+
+ // Tridiagonalize.
+ tred2();
+
+ // Diagonalize.
+ tql2();
+
+ } else {
+ // Reduce to Hessenberg form.
+ // Reduce Hessenberg to real Schur form.
+ hqr2(orthes(x));
+ }
+ }
+
+ /**
+ * Return the eigenvector matrix
+ *
+ * @return V
+ */
+ public Matrix getV() {
+ return v.like().assign(v);
+ }
+
+ /**
+ * Return the real parts of the eigenvalues
+ */
+ public Vector getRealEigenvalues() {
+ return d;
+ }
+
+ /**
+ * Return the imaginary parts of the eigenvalues
+ */
+ public Vector getImagEigenvalues() {
+ return e;
+ }
+
+ /**
+ * Return the block diagonal eigenvalue matrix
+ *
+ * @return D
+ */
+ public Matrix getD() {
+ Matrix X = new DenseMatrix(n, n);
+ X.assign(0);
+ X.viewDiagonal().assign(d);
+ for (int i = 0; i < n; i++) {
+ final double v = e.getQuick(i);
+ if (v > 0) {
+ X.setQuick(i, i + 1, v);
+ } else if (v < 0) {
+ X.setQuick(i, i - 1, v);
+ }
+ }
+ return X;
+ }
+
+ // Symmetric Householder reduction to tridiagonal form.
+ private void tred2() {
+ // This is derived from the Algol procedures tred2 by
+ // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
+ // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutine in EISPACK.
+
+ d.assign(v.viewColumn(n - 1));
+
+ // Householder reduction to tridiagonal form.
+
+ for (int i = n - 1; i > 0; i--) {
+
+ // Scale to avoid under/overflow.
+
+ double scale = d.norm(1);
+ double h = 0.0;
+
+
+ if (scale == 0.0) {
+ e.setQuick(i, d.getQuick(i - 1));
+ for (int j = 0; j < i; j++) {
+ d.setQuick(j, v.getQuick(i - 1, j));
+ v.setQuick(i, j, 0.0);
+ v.setQuick(j, i, 0.0);
+ }
+ } else {
+
+ // Generate Householder vector.
+
+ for (int k = 0; k < i; k++) {
+ d.setQuick(k, d.getQuick(k) / scale);
+ h += d.getQuick(k) * d.getQuick(k);
+ }
+ double f = d.getQuick(i - 1);
+ double g = Math.sqrt(h);
+ if (f > 0) {
+ g = -g;
+ }
+ e.setQuick(i, scale * g);
+ h = h - f * g;
+ d.setQuick(i - 1, f - g);
+ for (int j = 0; j < i; j++) {
+ e.setQuick(j, 0.0);
+ }
+
+ // Apply similarity transformation to remaining columns.
+
+ for (int j = 0; j < i; j++) {
+ f = d.getQuick(j);
+ v.setQuick(j, i, f);
+ g = e.getQuick(j) + v.getQuick(j, j) * f;
+ for (int k = j + 1; k <= i - 1; k++) {
+ g += v.getQuick(k, j) * d.getQuick(k);
+ e.setQuick(k, e.getQuick(k) + v.getQuick(k, j) * f);
+ }
+ e.setQuick(j, g);
+ }
+ f = 0.0;
+ for (int j = 0; j < i; j++) {
+ e.setQuick(j, e.getQuick(j) / h);
+ f += e.getQuick(j) * d.getQuick(j);
+ }
+ double hh = f / (h + h);
+ for (int j = 0; j < i; j++) {
+ e.setQuick(j, e.getQuick(j) - hh * d.getQuick(j));
+ }
+ for (int j = 0; j < i; j++) {
+ f = d.getQuick(j);
+ g = e.getQuick(j);
+ for (int k = j; k <= i - 1; k++) {
+ v.setQuick(k, j, v.getQuick(k, j) - (f * e.getQuick(k) + g * d.getQuick(k)));
+ }
+ d.setQuick(j, v.getQuick(i - 1, j));
+ v.setQuick(i, j, 0.0);
+ }
+ }
+ d.setQuick(i, h);
+ }
+
+ // Accumulate transformations.
+
+ for (int i = 0; i < n - 1; i++) {
+ v.setQuick(n - 1, i, v.getQuick(i, i));
+ v.setQuick(i, i, 1.0);
+ double h = d.getQuick(i + 1);
+ if (h != 0.0) {
+ for (int k = 0; k <= i; k++) {
+ d.setQuick(k, v.getQuick(k, i + 1) / h);
+ }
+ for (int j = 0; j <= i; j++) {
+ double g = 0.0;
+ for (int k = 0; k <= i; k++) {
+ g += v.getQuick(k, i + 1) * v.getQuick(k, j);
+ }
+ for (int k = 0; k <= i; k++) {
+ v.setQuick(k, j, v.getQuick(k, j) - g * d.getQuick(k));
+ }
+ }
+ }
+ for (int k = 0; k <= i; k++) {
+ v.setQuick(k, i + 1, 0.0);
+ }
+ }
+ d.assign(v.viewRow(n - 1));
+ v.viewRow(n - 1).assign(0);
+ v.setQuick(n - 1, n - 1, 1.0);
+ e.setQuick(0, 0.0);
+ }
+
+ // Symmetric tridiagonal QL algorithm.
+ private void tql2() {
+
+ // This is derived from the Algol procedures tql2, by
+ // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
+ // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutine in EISPACK.
+
+ e.viewPart(0, n - 1).assign(e.viewPart(1, n - 1));
+ e.setQuick(n - 1, 0.0);
+
+ double f = 0.0;
+ double tst1 = 0.0;
+ double eps = Math.pow(2.0, -52.0);
+ for (int l = 0; l < n; l++) {
+
+ // Find small subdiagonal element
+
+ tst1 = Math.max(tst1, Math.abs(d.getQuick(l)) + Math.abs(e.getQuick(l)));
+ int m = l;
+ while (m < n) {
+ if (Math.abs(e.getQuick(m)) <= eps * tst1) {
+ break;
+ }
+ m++;
+ }
+
+ // If m == l, d.getQuick(l) is an eigenvalue,
+ // otherwise, iterate.
+
+ if (m > l) {
+ int iter = 0;
+ do {
+ iter = iter + 1; // (Could check iteration count here.)
+
+ // Compute implicit shift
+
+ double g = d.getQuick(l);
+ double p = (d.getQuick(l + 1) - g) / (2.0 * e.getQuick(l));
+ double r = Math.hypot(p, 1.0);
+ if (p < 0) {
+ r = -r;
+ }
+ d.setQuick(l, e.getQuick(l) / (p + r));
+ d.setQuick(l + 1, e.getQuick(l) * (p + r));
+ double dl1 = d.getQuick(l + 1);
+ double h = g - d.getQuick(l);
+ for (int i = l + 2; i < n; i++) {
+ d.setQuick(i, d.getQuick(i) - h);
+ }
+ f = f + h;
+
+ // Implicit QL transformation.
+
+ p = d.getQuick(m);
+ double c = 1.0;
+ double c2 = c;
+ double c3 = c;
+ double el1 = e.getQuick(l + 1);
+ double s = 0.0;
+ double s2 = 0.0;
+ for (int i = m - 1; i >= l; i--) {
+ c3 = c2;
+ c2 = c;
+ s2 = s;
+ g = c * e.getQuick(i);
+ h = c * p;
+ r = Math.hypot(p, e.getQuick(i));
+ e.setQuick(i + 1, s * r);
+ s = e.getQuick(i) / r;
+ c = p / r;
+ p = c * d.getQuick(i) - s * g;
+ d.setQuick(i + 1, h + s * (c * g + s * d.getQuick(i)));
+
+ // Accumulate transformation.
+
+ for (int k = 0; k < n; k++) {
+ h = v.getQuick(k, i + 1);
+ v.setQuick(k, i + 1, s * v.getQuick(k, i) + c * h);
+ v.setQuick(k, i, c * v.getQuick(k, i) - s * h);
+ }
+ }
+ p = -s * s2 * c3 * el1 * e.getQuick(l) / dl1;
+ e.setQuick(l, s * p);
+ d.setQuick(l, c * p);
+
+ // Check for convergence.
+
+ } while (Math.abs(e.getQuick(l)) > eps * tst1);
+ }
+ d.setQuick(l, d.getQuick(l) + f);
+ e.setQuick(l, 0.0);
+ }
+
+ // Sort eigenvalues and corresponding vectors.
+
+ for (int i = 0; i < n - 1; i++) {
+ int k = i;
+ double p = d.getQuick(i);
+ for (int j = i + 1; j < n; j++) {
+ if (d.getQuick(j) < p) {
+ k = j;
+ p = d.getQuick(j);
+ }
+ }
+ if (k != i) {
+ d.setQuick(k, d.getQuick(i));
+ d.setQuick(i, p);
+ for (int j = 0; j < n; j++) {
+ p = v.getQuick(j, i);
+ v.setQuick(j, i, v.getQuick(j, k));
+ v.setQuick(j, k, p);
+ }
+ }
+ }
+ }
+
+ // Nonsymmetric reduction to Hessenberg form.
+ private Matrix orthes(Matrix x) {
+ // Working storage for nonsymmetric algorithm.
+ Vector ort = new DenseVector(n);
+ Matrix H = new DenseMatrix(n, n).assign(x);
+
+ // This is derived from the Algol procedures orthes and ortran,
+ // by Martin and Wilkinson, Handbook for Auto. Comp.,
+ // Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutines in EISPACK.
+
+ int low = 0;
+ int high = n - 1;
+
+ for (int m = low + 1; m <= high - 1; m++) {
+
+ // Scale column.
+
+ double scale = H.viewColumn(m - 1).viewPart(m, high - m + 1).norm(1);
+
+ if (scale != 0.0) {
+ // Compute Householder transformation.
+
+ ort.viewPart(m, high - m + 1).assign(H.viewColumn(m - 1).viewPart(m, high - m + 1), Functions.plusMult(1 / scale));
+ double h = ort.viewPart(m, high - m + 1).getLengthSquared();
+
+ double g = Math.sqrt(h);
+ if (ort.getQuick(m) > 0) {
+ g = -g;
+ }
+ h = h - ort.getQuick(m) * g;
+ ort.setQuick(m, ort.getQuick(m) - g);
+
+ // Apply Householder similarity transformation
+ // H = (I-u*u'/h)*H*(I-u*u')/h)
+
+ Vector ortPiece = ort.viewPart(m, high - m + 1);
+ for (int j = m; j < n; j++) {
+ double f = ortPiece.dot(H.viewColumn(j).viewPart(m, high - m + 1)) / h;
+ H.viewColumn(j).viewPart(m, high - m + 1).assign(ortPiece, Functions.plusMult(-f));
+ }
+
+ for (int i = 0; i <= high; i++) {
+ double f = ortPiece.dot(H.viewRow(i).viewPart(m, high - m + 1)) / h;
+ H.viewRow(i).viewPart(m, high - m + 1).assign(ortPiece, Functions.plusMult(-f));
+ }
+ ort.setQuick(m, scale * ort.getQuick(m));
+ H.setQuick(m, m - 1, scale * g);
+ }
+ }
+
+ // Accumulate transformations (Algol's ortran).
+
+ v.assign(0);
+ v.viewDiagonal().assign(1);
+
+ for (int m = high - 1; m >= low + 1; m--) {
+ if (H.getQuick(m, m - 1) != 0.0) {
+ ort.viewPart(m + 1, high - m).assign(H.viewColumn(m - 1).viewPart(m + 1, high - m));
+ for (int j = m; j <= high; j++) {
+ double g = ort.viewPart(m, high - m + 1).dot(v.viewColumn(j).viewPart(m, high - m + 1));
+ // Double division avoids possible underflow
+ g = (g / ort.getQuick(m)) / H.getQuick(m, m - 1);
+ v.viewColumn(j).viewPart(m, high - m + 1).assign(ort.viewPart(m, high - m + 1), Functions.plusMult(g));
+ }
+ }
+ }
+ return H;
+ }
+
+
+ // Complex scalar division.
+ private transient double cdivr, cdivi;
+
+ private void cdiv(double xr, double xi, double yr, double yi) {
+ double r, d;
+ if (Math.abs(yr) > Math.abs(yi)) {
+ r = yi / yr;
+ d = yr + r * yi;
+ cdivr = (xr + r * xi) / d;
+ cdivi = (xi - r * xr) / d;
+ } else {
+ r = yr / yi;
+ d = yi + r * yr;
+ cdivr = (r * xr + xi) / d;
+ cdivi = (r * xi - xr) / d;
+ }
+ }
+
+
+ // Nonsymmetric reduction from Hessenberg to real Schur form.
+
+ private void hqr2(Matrix h) {
+
+ // This is derived from the Algol procedure hqr2,
+ // by Martin and Wilkinson, Handbook for Auto. Comp.,
+ // Vol.ii-Linear Algebra, and the corresponding
+ // Fortran subroutine in EISPACK.
+
+ // Initialize
+
+ final int nn = this.n;
+ int n = nn - 1;
+ final int low = 0;
+ final int high = nn - 1;
+ double eps = Math.pow(2.0, -52.0);
+ double exshift = 0.0;
+ double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
+
+ // Store roots isolated by balanc and compute matrix norm
+
+ double norm = h.aggregate(Functions.PLUS, Functions.ABS);
+
+ // Outer loop over eigenvalue index
+
+ int iter = 0;
+ while (n >= low) {
+
+ // Look for single small sub-diagonal element
+
+ int l = n;
+ while (l > low) {
+ s = Math.abs(h.getQuick(l - 1, l - 1)) + Math.abs(h.getQuick(l, l));
+ if (s == 0.0) {
+ s = norm;
+ }
+ if (Math.abs(h.getQuick(l, l - 1)) < eps * s) {
+ break;
+ }
+ l--;
+ }
+
+ // Check for convergence
+
+ if (l == n) {
+ // One root found
+ h.setQuick(n, n, h.getQuick(n, n) + exshift);
+ d.setQuick(n, h.getQuick(n, n));
+ e.setQuick(n, 0.0);
+ n--;
+ iter = 0;
+
+
+ } else if (l == n - 1) {
+ // Two roots found
+ w = h.getQuick(n, n - 1) * h.getQuick(n - 1, n);
+ p = (h.getQuick(n - 1, n - 1) - h.getQuick(n, n)) / 2.0;
+ q = p * p + w;
+ z = Math.sqrt(Math.abs(q));
+ h.setQuick(n, n, h.getQuick(n, n) + exshift);
+ h.setQuick(n - 1, n - 1, h.getQuick(n - 1, n - 1) + exshift);
+ x = h.getQuick(n, n);
+
+ // Real pair
+ if (q >= 0) {
+ if (p >= 0) {
+ z = p + z;
+ } else {
+ z = p - z;
+ }
+ d.setQuick(n - 1, x + z);
+ d.setQuick(n, d.getQuick(n - 1));
+ if (z != 0.0) {
+ d.setQuick(n, x - w / z);
+ }
+ e.setQuick(n - 1, 0.0);
+ e.setQuick(n, 0.0);
+ x = h.getQuick(n, n - 1);
+ s = Math.abs(x) + Math.abs(z);
+ p = x / s;
+ q = z / s;
+ r = Math.sqrt(p * p + q * q);
+ p = p / r;
+ q = q / r;
+
+ // Row modification
+
+ for (int j = n - 1; j < nn; j++) {
+ z = h.getQuick(n - 1, j);
+ h.setQuick(n - 1, j, q * z + p * h.getQuick(n, j));
+ h.setQuick(n, j, q * h.getQuick(n, j) - p * z);
+ }
+
+ // Column modification
+
+ for (int i = 0; i <= n; i++) {
+ z = h.getQuick(i, n - 1);
+ h.setQuick(i, n - 1, q * z + p * h.getQuick(i, n));
+ h.setQuick(i, n, q * h.getQuick(i, n) - p * z);
+ }
+
+ // Accumulate transformations
+
+ for (int i = low; i <= high; i++) {
+ z = v.getQuick(i, n - 1);
+ v.setQuick(i, n - 1, q * z + p * v.getQuick(i, n));
+ v.setQuick(i, n, q * v.getQuick(i, n) - p * z);
+ }
+
+ // Complex pair
+
+ } else {
+ d.setQuick(n - 1, x + p);
+ d.setQuick(n, x + p);
+ e.setQuick(n - 1, z);
+ e.setQuick(n, -z);
+ }
+ n = n - 2;
+ iter = 0;
+
+ // No convergence yet
+
+ } else {
+
+ // Form shift
+
+ x = h.getQuick(n, n);
+ y = 0.0;
+ w = 0.0;
+ if (l < n) {
+ y = h.getQuick(n - 1, n - 1);
+ w = h.getQuick(n, n - 1) * h.getQuick(n - 1, n);
+ }
+
+ // Wilkinson's original ad hoc shift
+
+ if (iter == 10) {
+ exshift += x;
+ for (int i = low; i <= n; i++) {
+ h.setQuick(i, i, x);
+ }
+ s = Math.abs(h.getQuick(n, n - 1)) + Math.abs(h.getQuick(n - 1, n - 2));
+ x = y = 0.75 * s;
+ w = -0.4375 * s * s;
+ }
+
+ // MATLAB's new ad hoc shift
+
+ if (iter == 30) {
+ s = (y - x) / 2.0;
+ s = s * s + w;
+ if (s > 0) {
+ s = Math.sqrt(s);
+ if (y < x) {
+ s = -s;
+ }
+ s = x - w / ((y - x) / 2.0 + s);
+ for (int i = low; i <= n; i++) {
+ h.setQuick(i, i, h.getQuick(i, i) - s);
+ }
+ exshift += s;
+ x = y = w = 0.964;
+ }
+ }
+
+ iter = iter + 1; // (Could check iteration count here.)
+
+ // Look for two consecutive small sub-diagonal elements
+
+ int m = n - 2;
+ while (m >= l) {
+ z = h.getQuick(m, m);
+ r = x - z;
+ s = y - z;
+ p = (r * s - w) / h.getQuick(m + 1, m) + h.getQuick(m, m + 1);
+ q = h.getQuick(m + 1, m + 1) - z - r - s;
+ r = h.getQuick(m + 2, m + 1);
+ s = Math.abs(p) + Math.abs(q) + Math.abs(r);
+ p = p / s;
+ q = q / s;
+ r = r / s;
+ if (m == l) {
+ break;
+ }
+ if (Math.abs(h.getQuick(m, m - 1)) * (Math.abs(q) + Math.abs(r)) <
+ eps * (Math.abs(p) * (Math.abs(h.getQuick(m - 1, m - 1)) + Math.abs(z) +
+ Math.abs(h.getQuick(m + 1, m + 1))))) {
+ break;
+ }
+ m--;
+ }
+
+ for (int i = m + 2; i <= n; i++) {
+ h.setQuick(i, i - 2, 0.0);
+ if (i > m + 2) {
+ h.setQuick(i, i - 3, 0.0);
+ }
+ }
+
+ // Double QR step involving rows l:n and columns m:n
+
+ for (int k = m; k <= n - 1; k++) {
+ boolean notlast = (k != n - 1);
+ if (k != m) {
+ p = h.getQuick(k, k - 1);
+ q = h.getQuick(k + 1, k - 1);
+ r = (notlast ? h.getQuick(k + 2, k - 1) : 0.0);
+ x = Math.abs(p) + Math.abs(q) + Math.abs(r);
+ if (x != 0.0) {
+ p = p / x;
+ q = q / x;
+ r = r / x;
+ }
+ }
+ if (x == 0.0) {
+ break;
+ }
+ s = Math.sqrt(p * p + q * q + r * r);
+ if (p < 0) {
+ s = -s;
+ }
+ if (s != 0) {
+ if (k != m) {
+ h.setQuick(k, k - 1, -s * x);
+ } else if (l != m) {
+ h.setQuick(k, k - 1, -h.getQuick(k, k - 1));
+ }
+ p = p + s;
+ x = p / s;
+ y = q / s;
+ z = r / s;
+ q = q / p;
+ r = r / p;
+
+ // Row modification
+
+ for (int j = k; j < nn; j++) {
+ p = h.getQuick(k, j) + q * h.getQuick(k + 1, j);
+ if (notlast) {
+ p = p + r * h.getQuick(k + 2, j);
+ h.setQuick(k + 2, j, h.getQuick(k + 2, j) - p * z);
+ }
+ h.setQuick(k, j, h.getQuick(k, j) - p * x);
+ h.setQuick(k + 1, j, h.getQuick(k + 1, j) - p * y);
+ }
+
+ // Column modification
+
+ for (int i = 0; i <= Math.min(n, k + 3); i++) {
+ p = x * h.getQuick(i, k) + y * h.getQuick(i, k + 1);
+ if (notlast) {
+ p = p + z * h.getQuick(i, k + 2);
+ h.setQuick(i, k + 2, h.getQuick(i, k + 2) - p * r);
+ }
+ h.setQuick(i, k, h.getQuick(i, k) - p);
+ h.setQuick(i, k + 1, h.getQuick(i, k + 1) - p * q);
+ }
+
+ // Accumulate transformations
+
+ for (int i = low; i <= high; i++) {
+ p = x * v.getQuick(i, k) + y * v.getQuick(i, k + 1);
+ if (notlast) {
+ p = p + z * v.getQuick(i, k + 2);
+ v.setQuick(i, k + 2, v.getQuick(i, k + 2) - p * r);
+ }
+ v.setQuick(i, k, v.getQuick(i, k) - p);
+ v.setQuick(i, k + 1, v.getQuick(i, k + 1) - p * q);
+ }
+ } // (s != 0)
+ } // k loop
+ } // check convergence
+ } // while (n >= low)
+
+ // Backsubstitute to find vectors of upper triangular form
+
+ if (norm == 0.0) {
+ return;
+ }
+
+ for (n = nn - 1; n >= 0; n--) {
+ p = d.getQuick(n);
+ q = e.getQuick(n);
+
+ // Real vector
+
+ if (q == 0) {
+ int l = n;
+ h.setQuick(n, n, 1.0);
+ for (int i = n - 1; i >= 0; i--) {
+ w = h.getQuick(i, i) - p;
+ r = 0.0;
+ for (int j = l; j <= n; j++) {
+ r = r + h.getQuick(i, j) * h.getQuick(j, n);
+ }
+ if (e.getQuick(i) < 0.0) {
+ z = w;
+ s = r;
+ } else {
+ l = i;
+ if (e.getQuick(i) == 0.0) {
+ if (w != 0.0) {
+ h.setQuick(i, n, -r / w);
+ } else {
+ h.setQuick(i, n, -r / (eps * norm));
+ }
+
+ // Solve real equations
+
+ } else {
+ x = h.getQuick(i, i + 1);
+ y = h.getQuick(i + 1, i);
+ q = (d.getQuick(i) - p) * (d.getQuick(i) - p) + e.getQuick(i) * e.getQuick(i);
+ t = (x * s - z * r) / q;
+ h.setQuick(i, n, t);
+ if (Math.abs(x) > Math.abs(z)) {
+ h.setQuick(i + 1, n, (-r - w * t) / x);
+ } else {
+ h.setQuick(i + 1, n, (-s - y * t) / z);
+ }
+ }
+
+ // Overflow control
+
+ t = Math.abs(h.getQuick(i, n));
+ if ((eps * t) * t > 1) {
+ for (int j = i; j <= n; j++) {
+ h.setQuick(j, n, h.getQuick(j, n) / t);
+ }
+ }
+ }
+ }
+
+ // Complex vector
+
+ } else if (q < 0) {
+ int l = n - 1;
+
+ // Last vector component imaginary so matrix is triangular
+
+ if (Math.abs(h.getQuick(n, n - 1)) > Math.abs(h.getQuick(n - 1, n))) {
+ h.setQuick(n - 1, n - 1, q / h.getQuick(n, n - 1));
+ h.setQuick(n - 1, n, -(h.getQuick(n, n) - p) / h.getQuick(n, n - 1));
+ } else {
+ cdiv(0.0, -h.getQuick(n - 1, n), h.getQuick(n - 1, n - 1) - p, q);
+ h.setQuick(n - 1, n - 1, cdivr);
+ h.setQuick(n - 1, n, cdivi);
+ }
+ h.setQuick(n, n - 1, 0.0);
+ h.setQuick(n, n, 1.0);
+ for (int i = n - 2; i >= 0; i--) {
+ double ra, sa, vr, vi;
+ ra = 0.0;
+ sa = 0.0;
+ for (int j = l; j <= n; j++) {
+ ra = ra + h.getQuick(i, j) * h.getQuick(j, n - 1);
+ sa = sa + h.getQuick(i, j) * h.getQuick(j, n);
+ }
+ w = h.getQuick(i, i) - p;
+
+ if (e.getQuick(i) < 0.0) {
+ z = w;
+ r = ra;
+ s = sa;
+ } else {
+ l = i;
+ if (e.getQuick(i) == 0) {
+ cdiv(-ra, -sa, w, q);
+ h.setQuick(i, n - 1, cdivr);
+ h.setQuick(i, n, cdivi);
+ } else {
+
+ // Solve complex equations
+
+ x = h.getQuick(i, i + 1);
+ y = h.getQuick(i + 1, i);
+ vr = (d.getQuick(i) - p) * (d.getQuick(i) - p) + e.getQuick(i) * e.getQuick(i) - q * q;
+ vi = (d.getQuick(i) - p) * 2.0 * q;
+ if (vr == 0.0 & vi == 0.0) {
+ vr = eps * norm * (Math.abs(w) + Math.abs(q) +
+ Math.abs(x) + Math.abs(y) + Math.abs(z));
+ }
+ cdiv(x * r - z * ra + q * sa, x * s - z * sa - q * ra, vr, vi);
+ h.setQuick(i, n - 1, cdivr);
+ h.setQuick(i, n, cdivi);
+ if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
+ h.setQuick(i + 1, n - 1, (-ra - w * h.getQuick(i, n - 1) + q * h.getQuick(i, n)) / x);
+ h.setQuick(i + 1, n, (-sa - w * h.getQuick(i, n) - q * h.getQuick(i, n - 1)) / x);
+ } else {
+ cdiv(-r - y * h.getQuick(i, n - 1), -s - y * h.getQuick(i, n), z, q);
+ h.setQuick(i + 1, n - 1, cdivr);
+ h.setQuick(i + 1, n, cdivi);
+ }
+ }
+
+ // Overflow control
+
+ t = Math.max(Math.abs(h.getQuick(i, n - 1)), Math.abs(h.getQuick(i, n)));
+ if ((eps * t) * t > 1) {
+ for (int j = i; j <= n; j++) {
+ h.setQuick(j, n - 1, h.getQuick(j, n - 1) / t);
+ h.setQuick(j, n, h.getQuick(j, n) / t);
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // Vectors of isolated roots
+
+ for (int i = 0; i < nn; i++) {
+ if (i < low | i > high) {
+ for (int j = i; j < nn; j++) {
+ v.setQuick(i, j, h.getQuick(i, j));
+ }
+ }
+ }
+
+ // Back transformation to get eigenvectors of original matrix
+
+ for (int j = nn - 1; j >= low; j--) {
+ for (int i = low; i <= high; i++) {
+ z = 0.0;
+ for (int k = low; k <= Math.min(j, high); k++) {
+ z = z + v.getQuick(i, k) * h.getQuick(k, j);
+ }
+ v.setQuick(i, j, z);
+ }
+ }
+ }
+
+
+
+ private static boolean isSymmetric(Matrix a) {
+ /*
+ Symmetry flag.
+ */
+ int n = a.columnSize();
+
+ boolean isSymmetric = true;
+ for (int j = 0; (j < n) & isSymmetric; j++) {
+ for (int i = 0; (i < n) & isSymmetric; i++) {
+ isSymmetric = (a.getQuick(i, j) == a.getQuick(j, i));
+ }
+ }
+ return isSymmetric;
+ }
+}
Modified: mahout/trunk/math/src/test/java/org/apache/mahout/math/decomposer/lanczos/TestLanczosSolver.java
URL: http://svn.apache.org/viewvc/mahout/trunk/math/src/test/java/org/apache/mahout/math/decomposer/lanczos/TestLanczosSolver.java?rev=1333667&r1=1333666&r2=1333667&view=diff
==============================================================================
--- mahout/trunk/math/src/test/java/org/apache/mahout/math/decomposer/lanczos/TestLanczosSolver.java (original)
+++ mahout/trunk/math/src/test/java/org/apache/mahout/math/decomposer/lanczos/TestLanczosSolver.java Thu May 3 22:36:49 2012
@@ -21,8 +21,7 @@ import org.apache.mahout.math.DenseVecto
import org.apache.mahout.math.Matrix;
import org.apache.mahout.math.Vector;
import org.apache.mahout.math.decomposer.SolverTest;
-import org.apache.mahout.math.matrix.DoubleMatrix1D;
-import org.apache.mahout.math.matrix.linalg.EigenvalueDecomposition;
+import org.apache.mahout.math.solver.EigenDecomposition;
import org.junit.Test;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
@@ -45,8 +44,8 @@ public final class TestLanczosSolver ext
// set initial vector?
solver.solve(state, desiredRank, true);
- EigenvalueDecomposition decomposition = new EigenvalueDecomposition(m);
- DoubleMatrix1D eigenvalues = decomposition.getRealEigenvalues();
+ EigenDecomposition decomposition = new EigenDecomposition(m);
+ Vector eigenvalues = decomposition.getRealEigenvalues();
float fractionOfEigensExpectedGood = 0.6f;
for(int i = 0; i < fractionOfEigensExpectedGood * desiredRank; i++) {
@@ -55,7 +54,7 @@ public final class TestLanczosSolver ext
log.info("{} : L = {}, E = {}", new Object[] {i, s, e});
assertTrue("Singular value differs from eigenvalue", Math.abs((s-e)/e) < ERROR_TOLERANCE);
Vector v = state.getRightSingularVector(i);
- Vector v2 = decomposition.getV().viewColumn(eigenvalues.size() - i - 1).toVector();
+ Vector v2 = decomposition.getV().viewColumn(eigenvalues.size() - i - 1);
double error = 1 - Math.abs(v.dot(v2)/(v.norm(2) * v2.norm(2)));
log.info("error: {}", error);
assertTrue(i + ": 1 - cosAngle = " + error, error < ERROR_TOLERANCE);
Added: mahout/trunk/math/src/test/java/org/apache/mahout/math/solver/EigenDecompositionTest.java
URL: http://svn.apache.org/viewvc/mahout/trunk/math/src/test/java/org/apache/mahout/math/solver/EigenDecompositionTest.java?rev=1333667&view=auto
==============================================================================
--- mahout/trunk/math/src/test/java/org/apache/mahout/math/solver/EigenDecompositionTest.java (added)
+++ mahout/trunk/math/src/test/java/org/apache/mahout/math/solver/EigenDecompositionTest.java Thu May 3 22:36:49 2012
@@ -0,0 +1,105 @@
+/*
+ * 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.mahout.math.solver;
+
+import org.apache.mahout.common.RandomUtils;
+import org.apache.mahout.math.DenseMatrix;
+import org.apache.mahout.math.Matrix;
+import org.apache.mahout.math.MatrixSlice;
+import org.apache.mahout.math.Vector;
+import org.apache.mahout.math.function.DoubleFunction;
+import org.apache.mahout.math.function.Functions;
+import org.junit.Test;
+
+import java.util.Random;
+
+import static org.junit.Assert.assertEquals;
+
+public class EigenDecompositionTest {
+ @Test
+ public void testDeficientRank() {
+ Matrix a = new DenseMatrix(10, 3).assign(new DoubleFunction() {
+ Random gen = RandomUtils.getRandom();
+
+ @Override
+ public double apply(double arg1) {
+ return gen.nextGaussian();
+ }
+ });
+
+ a = a.transpose().times(a);
+
+ EigenDecomposition eig = new EigenDecomposition(a);
+ Matrix d = eig.getD();
+ Matrix v = eig.getV();
+ check("EigenvalueDecomposition (rank deficient)...", a.times(v), v.times(d));
+
+ assertEquals(0, eig.getImagEigenvalues().norm(1), 1e-10);
+ assertEquals(3, eig.getRealEigenvalues().norm(0), 1e-10);
+ }
+
+ @Test
+ public void testEigen() {
+ double[] evals =
+ {0., 1., 0., 0.,
+ 1., 0., 2.e-7, 0.,
+ 0., -2.e-7, 0., 1.,
+ 0., 0., 1., 0.};
+ int i = 0;
+ Matrix a = new DenseMatrix(4, 4);
+ for (MatrixSlice row : a) {
+ for (Vector.Element element : row.vector()) {
+ element.set(evals[i++]);
+ }
+ }
+ EigenDecomposition eig = new EigenDecomposition(a);
+ Matrix d = eig.getD();
+ Matrix v = eig.getV();
+ check("EigenvalueDecomposition (nonsymmetric)...", a.times(v), v.times(d));
+ }
+
+ @Test
+ public void testSequential() {
+ int validld = 3;
+ Matrix A = new DenseMatrix(validld, validld);
+ double[] columnwise = {1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.};
+ int i = 0;
+ for (MatrixSlice row : A) {
+ for (Vector.Element element : row.vector()) {
+ element.set(columnwise[i++]);
+ }
+ }
+
+ EigenDecomposition Eig = new EigenDecomposition(A);
+ Matrix D = Eig.getD();
+ Matrix V = Eig.getV();
+ check("EigenvalueDecomposition (nonsymmetric)...", A.times(V), V.times(D));
+
+ A = A.transpose().times(A);
+ Eig = new EigenDecomposition(A);
+ D = Eig.getD();
+ V = Eig.getV();
+ check("EigenvalueDecomposition (symmetric)...", A.times(V), V.times(D));
+
+ }
+
+ private void check(String msg, Matrix a, Matrix b) {
+ assertEquals(msg, 0, a.minus(b).aggregate(Functions.PLUS, Functions.ABS), 1e-10);
+ }
+
+}