http://git-wip-us.apache.org/repos/asf/mahout/blob/99a5358f/math/src/main/java/org/apache/mahout/math/SingularValueDecomposition.java
----------------------------------------------------------------------
diff --git
a/math/src/main/java/org/apache/mahout/math/SingularValueDecomposition.java
b/math/src/main/java/org/apache/mahout/math/SingularValueDecomposition.java
deleted file mode 100644
index 2abff10..0000000
--- a/math/src/main/java/org/apache/mahout/math/SingularValueDecomposition.java
+++ /dev/null
@@ -1,669 +0,0 @@
-/*
- * 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.
- *
- * Copyright 1999 CERN - European Organization for Nuclear Research.
- * Permission to use, copy, modify, distribute and sell this software and its
documentation for any purpose
- * is hereby granted without fee, provided that the above copyright notice
appear in all copies and
- * that both that copyright notice and this permission notice appear in
supporting documentation.
- * CERN makes no representations about the suitability of this software for
any purpose.
- * It is provided "as is" without expressed or implied warranty.
- */
-package org.apache.mahout.math;
-
-public class SingularValueDecomposition implements java.io.Serializable {
-
- /** Arrays for internal storage of U and V. */
- private final double[][] u;
- private final double[][] v;
-
- /** Array for internal storage of singular values. */
- private final double[] s;
-
- /** Row and column dimensions. */
- private final int m;
- private final int n;
-
- /**To handle the case where numRows() < numCols() and to use the fact that
SVD(A')=VSU'=> SVD(A')'=SVD(A)**/
- private boolean transpositionNeeded;
-
- /**
- * Constructs and returns a new singular value decomposition object; The
- * decomposed matrices can be retrieved via instance methods of the returned
- * decomposition object.
- *
- * @param arg
- * A rectangular matrix.
- */
- public SingularValueDecomposition(Matrix arg) {
- if (arg.numRows() < arg.numCols()) {
- transpositionNeeded = true;
- }
-
- // Derived from LINPACK code.
- // Initialize.
- double[][] a;
- if (transpositionNeeded) {
- //use the transpose Matrix
- m = arg.numCols();
- n = arg.numRows();
- a = new double[m][n];
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- a[i][j] = arg.get(j, i);
- }
- }
- } else {
- m = arg.numRows();
- n = arg.numCols();
- a = new double[m][n];
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < n; j++) {
- a[i][j] = arg.get(i, j);
- }
- }
- }
-
-
- int nu = Math.min(m, n);
- s = new double[Math.min(m + 1, n)];
- u = new double[m][nu];
- v = new double[n][n];
- double[] e = new double[n];
- double[] work = new double[m];
- boolean wantu = true;
- boolean wantv = true;
-
- // Reduce A to bidiagonal form, storing the diagonal elements
- // in s and the super-diagonal elements in e.
-
- int nct = Math.min(m - 1, n);
- int nrt = Math.max(0, Math.min(n - 2, m));
- for (int k = 0; k < Math.max(nct, nrt); k++) {
- if (k < nct) {
-
- // Compute the transformation for the k-th column and
- // place the k-th diagonal in s[k].
- // Compute 2-norm of k-th column without under/overflow.
- s[k] = 0;
- for (int i = k; i < m; i++) {
- s[k] = Algebra.hypot(s[k], a[i][k]);
- }
- if (s[k] != 0.0) {
- if (a[k][k] < 0.0) {
- s[k] = -s[k];
- }
- for (int i = k; i < m; i++) {
- a[i][k] /= s[k];
- }
- a[k][k] += 1.0;
- }
- s[k] = -s[k];
- }
- for (int j = k + 1; j < n; j++) {
- if (k < nct && s[k] != 0.0) {
-
- // Apply the transformation.
-
- double t = 0;
- for (int i = k; i < m; i++) {
- t += a[i][k] * a[i][j];
- }
- t = -t / a[k][k];
- for (int i = k; i < m; i++) {
- a[i][j] += t * a[i][k];
- }
- }
-
- // Place the k-th row of A into e for the
- // subsequent calculation of the row transformation.
-
- e[j] = a[k][j];
- }
- if (wantu && k < nct) {
-
- // Place the transformation in U for subsequent back
- // multiplication.
-
- for (int i = k; i < m; i++) {
- u[i][k] = a[i][k];
- }
- }
- if (k < nrt) {
-
- // Compute the k-th row transformation and place the
- // k-th super-diagonal in e[k].
- // Compute 2-norm without under/overflow.
- e[k] = 0;
- for (int i = k + 1; i < n; i++) {
- e[k] = Algebra.hypot(e[k], e[i]);
- }
- if (e[k] != 0.0) {
- if (e[k + 1] < 0.0) {
- e[k] = -e[k];
- }
- for (int i = k + 1; i < n; i++) {
- e[i] /= e[k];
- }
- e[k + 1] += 1.0;
- }
- e[k] = -e[k];
- if (k + 1 < m && e[k] != 0.0) {
-
- // Apply the transformation.
-
- for (int i = k + 1; i < m; i++) {
- work[i] = 0.0;
- }
- for (int j = k + 1; j < n; j++) {
- for (int i = k + 1; i < m; i++) {
- work[i] += e[j] * a[i][j];
- }
- }
- for (int j = k + 1; j < n; j++) {
- double t = -e[j] / e[k + 1];
- for (int i = k + 1; i < m; i++) {
- a[i][j] += t * work[i];
- }
- }
- }
- if (wantv) {
-
- // Place the transformation in V for subsequent
- // back multiplication.
-
- for (int i = k + 1; i < n; i++) {
- v[i][k] = e[i];
- }
- }
- }
- }
-
- // Set up the final bidiagonal matrix or order p.
-
- int p = Math.min(n, m + 1);
- if (nct < n) {
- s[nct] = a[nct][nct];
- }
- if (m < p) {
- s[p - 1] = 0.0;
- }
- if (nrt + 1 < p) {
- e[nrt] = a[nrt][p - 1];
- }
- e[p - 1] = 0.0;
-
- // If required, generate U.
-
- if (wantu) {
- for (int j = nct; j < nu; j++) {
- for (int i = 0; i < m; i++) {
- u[i][j] = 0.0;
- }
- u[j][j] = 1.0;
- }
- for (int k = nct - 1; k >= 0; k--) {
- if (s[k] != 0.0) {
- for (int j = k + 1; j < nu; j++) {
- double t = 0;
- for (int i = k; i < m; i++) {
- t += u[i][k] * u[i][j];
- }
- t = -t / u[k][k];
- for (int i = k; i < m; i++) {
- u[i][j] += t * u[i][k];
- }
- }
- for (int i = k; i < m; i++) {
- u[i][k] = -u[i][k];
- }
- u[k][k] = 1.0 + u[k][k];
- for (int i = 0; i < k - 1; i++) {
- u[i][k] = 0.0;
- }
- } else {
- for (int i = 0; i < m; i++) {
- u[i][k] = 0.0;
- }
- u[k][k] = 1.0;
- }
- }
- }
-
- // If required, generate V.
-
- if (wantv) {
- for (int k = n - 1; k >= 0; k--) {
- if (k < nrt && e[k] != 0.0) {
- for (int j = k + 1; j < nu; j++) {
- double t = 0;
- for (int i = k + 1; i < n; i++) {
- t += v[i][k] * v[i][j];
- }
- t = -t / v[k + 1][k];
- for (int i = k + 1; i < n; i++) {
- v[i][j] += t * v[i][k];
- }
- }
- }
- for (int i = 0; i < n; i++) {
- v[i][k] = 0.0;
- }
- v[k][k] = 1.0;
- }
- }
-
- // Main iteration loop for the singular values.
-
- int pp = p - 1;
- int iter = 0;
- double eps = Math.pow(2.0, -52.0);
- double tiny = Math.pow(2.0,-966.0);
- while (p > 0) {
- int k;
-
- // Here is where a test for too many iterations would go.
-
- // This section of the program inspects for
- // negligible elements in the s and e arrays. On
- // completion the variables kase and k are set as follows.
-
- // kase = 1 if s(p) and e[k-1] are negligible and k<p
- // kase = 2 if s(k) is negligible and k<p
- // kase = 3 if e[k-1] is negligible, k<p, and
- // s(k), ..., s(p) are not negligible (qr step).
- // kase = 4 if e(p-1) is negligible (convergence).
-
- for (k = p - 2; k >= -1; k--) {
- if (k == -1) {
- break;
- }
- if (Math.abs(e[k]) <= tiny +eps * (Math.abs(s[k]) + Math.abs(s[k +
1]))) {
- e[k] = 0.0;
- break;
- }
- }
- int kase;
- if (k == p - 2) {
- kase = 4;
- } else {
- int ks;
- for (ks = p - 1; ks >= k; ks--) {
- if (ks == k) {
- break;
- }
- double t =
- (ks != p ? Math.abs(e[ks]) : 0.) +
- (ks != k + 1 ? Math.abs(e[ks-1]) : 0.);
- if (Math.abs(s[ks]) <= tiny + eps * t) {
- s[ks] = 0.0;
- break;
- }
- }
- if (ks == k) {
- kase = 3;
- } else if (ks == p - 1) {
- kase = 1;
- } else {
- kase = 2;
- k = ks;
- }
- }
- k++;
-
- // Perform the task indicated by kase.
-
- switch (kase) {
-
- // Deflate negligible s(p).
-
- case 1: {
- double f = e[p - 2];
- e[p - 2] = 0.0;
- for (int j = p - 2; j >= k; j--) {
- double t = Algebra.hypot(s[j], f);
- double cs = s[j] / t;
- double sn = f / t;
- s[j] = t;
- if (j != k) {
- f = -sn * e[j - 1];
- e[j - 1] = cs * e[j - 1];
- }
- if (wantv) {
- for (int i = 0; i < n; i++) {
- t = cs * v[i][j] + sn * v[i][p - 1];
- v[i][p - 1] = -sn * v[i][j] + cs * v[i][p - 1];
- v[i][j] = t;
- }
- }
- }
- }
- break;
-
- // Split at negligible s(k).
-
- case 2: {
- double f = e[k - 1];
- e[k - 1] = 0.0;
- for (int j = k; j < p; j++) {
- double t = Algebra.hypot(s[j], f);
- double cs = s[j] / t;
- double sn = f / t;
- s[j] = t;
- f = -sn * e[j];
- e[j] = cs * e[j];
- if (wantu) {
- for (int i = 0; i < m; i++) {
- t = cs * u[i][j] + sn * u[i][k - 1];
- u[i][k - 1] = -sn * u[i][j] + cs * u[i][k - 1];
- u[i][j] = t;
- }
- }
- }
- }
- break;
-
- // Perform one qr step.
-
- case 3: {
-
- // Calculate the shift.
-
- double scale = Math.max(Math.max(Math.max(Math.max(
- Math.abs(s[p - 1]), Math.abs(s[p - 2])), Math.abs(e[p - 2])),
- Math.abs(s[k])), Math.abs(e[k]));
- double sp = s[p - 1] / scale;
- double spm1 = s[p - 2] / scale;
- double epm1 = e[p - 2] / scale;
- double sk = s[k] / scale;
- double ek = e[k] / scale;
- double b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0;
- double c = sp * epm1 * sp * epm1;
- double shift = 0.0;
- if (b != 0.0 || c != 0.0) {
- shift = Math.sqrt(b * b + c);
- if (b < 0.0) {
- shift = -shift;
- }
- shift = c / (b + shift);
- }
- double f = (sk + sp) * (sk - sp) + shift;
- double g = sk * ek;
-
- // Chase zeros.
-
- for (int j = k; j < p - 1; j++) {
- double t = Algebra.hypot(f, g);
- double cs = f / t;
- double sn = g / t;
- if (j != k) {
- e[j - 1] = t;
- }
- f = cs * s[j] + sn * e[j];
- e[j] = cs * e[j] - sn * s[j];
- g = sn * s[j + 1];
- s[j + 1] = cs * s[j + 1];
- if (wantv) {
- for (int i = 0; i < n; i++) {
- t = cs * v[i][j] + sn * v[i][j + 1];
- v[i][j + 1] = -sn * v[i][j] + cs * v[i][j + 1];
- v[i][j] = t;
- }
- }
- t = Algebra.hypot(f, g);
- cs = f / t;
- sn = g / t;
- s[j] = t;
- f = cs * e[j] + sn * s[j + 1];
- s[j + 1] = -sn * e[j] + cs * s[j + 1];
- g = sn * e[j + 1];
- e[j + 1] = cs * e[j + 1];
- if (wantu && j < m - 1) {
- for (int i = 0; i < m; i++) {
- t = cs * u[i][j] + sn * u[i][j + 1];
- u[i][j + 1] = -sn * u[i][j] + cs * u[i][j + 1];
- u[i][j] = t;
- }
- }
- }
- e[p - 2] = f;
- iter = iter + 1;
- }
- break;
-
- // Convergence.
-
- case 4: {
-
- // Make the singular values positive.
-
- if (s[k] <= 0.0) {
- s[k] = s[k] < 0.0 ? -s[k] : 0.0;
- if (wantv) {
- for (int i = 0; i <= pp; i++) {
- v[i][k] = -v[i][k];
- }
- }
- }
-
- // Order the singular values.
-
- while (k < pp) {
- if (s[k] >= s[k + 1]) {
- break;
- }
- double t = s[k];
- s[k] = s[k + 1];
- s[k + 1] = t;
- if (wantv && k < n - 1) {
- for (int i = 0; i < n; i++) {
- t = v[i][k + 1];
- v[i][k + 1] = v[i][k];
- v[i][k] = t;
- }
- }
- if (wantu && k < m - 1) {
- for (int i = 0; i < m; i++) {
- t = u[i][k + 1];
- u[i][k + 1] = u[i][k];
- u[i][k] = t;
- }
- }
- k++;
- }
- iter = 0;
- p--;
- }
- break;
- default:
- throw new IllegalStateException();
- }
- }
- }
-
- /**
- * Returns the two norm condition number, which is <tt>max(S) / min(S)</tt>.
- */
- public double cond() {
- return s[0] / s[Math.min(m, n) - 1];
- }
-
- /**
- * @return the diagonal matrix of singular values.
- */
- public Matrix getS() {
- double[][] s = new double[n][n];
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < n; j++) {
- s[i][j] = 0.0;
- }
- s[i][i] = this.s[i];
- }
-
- return new DenseMatrix(s);
- }
-
- /**
- * Returns the diagonal of <tt>S</tt>, which is a one-dimensional array of
- * singular values
- *
- * @return diagonal of <tt>S</tt>.
- */
- public double[] getSingularValues() {
- return s;
- }
-
- /**
- * Returns the left singular vectors <tt>U</tt>.
- *
- * @return <tt>U</tt>
- */
- public Matrix getU() {
- if (transpositionNeeded) { //case numRows() < numCols()
- return new DenseMatrix(v);
- } else {
- int numCols = Math.min(m + 1, n);
- Matrix r = new DenseMatrix(m, numCols);
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < numCols; j++) {
- r.set(i, j, u[i][j]);
- }
- }
-
- return r;
- }
- }
-
- /**
- * Returns the right singular vectors <tt>V</tt>.
- *
- * @return <tt>V</tt>
- */
- public Matrix getV() {
- if (transpositionNeeded) { //case numRows() < numCols()
- int numCols = Math.min(m + 1, n);
- Matrix r = new DenseMatrix(m, numCols);
- for (int i = 0; i < m; i++) {
- for (int j = 0; j < numCols; j++) {
- r.set(i, j, u[i][j]);
- }
- }
-
- return r;
- } else {
- return new DenseMatrix(v);
- }
- }
-
- /** Returns the two norm, which is <tt>max(S)</tt>. */
- public double norm2() {
- return s[0];
- }
-
- /**
- * Returns the effective numerical matrix rank, which is the number of
- * nonnegligible singular values.
- */
- public int rank() {
- double eps = Math.pow(2.0, -52.0);
- double tol = Math.max(m, n) * s[0] * eps;
- int r = 0;
- for (double value : s) {
- if (value > tol) {
- r++;
- }
- }
- return r;
- }
-
- /**
- * @param minSingularValue
- * minSingularValue - value below which singular values are ignored (a 0 or
negative
- * value implies all singular value will be used)
- * @return Returns the n à n covariance matrix.
- * The covariance matrix is V Ã J Ã Vt where J is the diagonal matrix of
the inverse
- * of the squares of the singular values.
- */
- Matrix getCovariance(double minSingularValue) {
- Matrix j = new DenseMatrix(s.length,s.length);
- Matrix vMat = new DenseMatrix(this.v);
- for (int i = 0; i < s.length; i++) {
- j.set(i, i, s[i] >= minSingularValue ? 1 / (s[i] * s[i]) : 0.0);
- }
- return vMat.times(j).times(vMat.transpose());
- }
-
- /**
- * Returns a String with (propertyName, propertyValue) pairs. Useful for
- * debugging or to quickly get the rough picture. For example,
- *
- * <pre>
- * rank : 3
- * trace : 0
- * </pre>
- */
- @Override
- public String toString() {
- StringBuilder buf = new StringBuilder();
-
buf.append("---------------------------------------------------------------------\n");
- buf.append("SingularValueDecomposition(A) --> cond(A), rank(A), norm2(A),
U, S, V\n");
-
buf.append("---------------------------------------------------------------------\n");
-
- buf.append("cond = ");
- String unknown = "Illegal operation or error: ";
- try {
- buf.append(String.valueOf(this.cond()));
- } catch (IllegalArgumentException exc) {
- buf.append(unknown).append(exc.getMessage());
- }
-
- buf.append("\nrank = ");
- try {
- buf.append(String.valueOf(this.rank()));
- } catch (IllegalArgumentException exc) {
- buf.append(unknown).append(exc.getMessage());
- }
-
- buf.append("\nnorm2 = ");
- try {
- buf.append(String.valueOf(this.norm2()));
- } catch (IllegalArgumentException exc) {
- buf.append(unknown).append(exc.getMessage());
- }
-
- buf.append("\n\nU = ");
- try {
- buf.append(String.valueOf(this.getU()));
- } catch (IllegalArgumentException exc) {
- buf.append(unknown).append(exc.getMessage());
- }
-
- buf.append("\n\nS = ");
- try {
- buf.append(String.valueOf(this.getS()));
- } catch (IllegalArgumentException exc) {
- buf.append(unknown).append(exc.getMessage());
- }
-
- buf.append("\n\nV = ");
- try {
- buf.append(String.valueOf(this.getV()));
- } catch (IllegalArgumentException exc) {
- buf.append(unknown).append(exc.getMessage());
- }
-
- return buf.toString();
- }
-}
