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Posted to commits@mahout.apache.org by gs...@apache.org on 2009/11/23 16:14:38 UTC
svn commit: r883365 [44/47] - in /lucene/mahout/trunk: ./ examples/ matrix/
matrix/src/ matrix/src/main/ matrix/src/main/java/
matrix/src/main/java/org/ matrix/src/main/java/org/apache/
matrix/src/main/java/org/apache/mahout/ matrix/src/main/java/org/a...
Added: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/EigenvalueDecomposition.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/EigenvalueDecomposition.java?rev=883365&view=auto
==============================================================================
--- lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/EigenvalueDecomposition.java (added)
+++ lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/EigenvalueDecomposition.java Mon Nov 23 15:14:26 2009
@@ -0,0 +1,982 @@
+/*
+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.colt.matrix.linalg;
+
+import org.apache.mahout.colt.matrix.DoubleFactory1D;
+import org.apache.mahout.colt.matrix.DoubleFactory2D;
+import org.apache.mahout.colt.matrix.DoubleMatrix1D;
+import org.apache.mahout.colt.matrix.DoubleMatrix2D;
+/**
+Eigenvalues and eigenvectors of a real matrix <tt>A</tt>.
+<P>
+If <tt>A</tt> is symmetric, then <tt>A = V*D*V'</tt> where the eigenvalue matrix <tt>D</tt> is
+diagonal and the eigenvector matrix <tt>V</tt> is orthogonal.
+I.e. <tt>A = V.mult(D.mult(transpose(V)))</tt> and
+<tt>V.mult(transpose(V))</tt> equals the identity matrix.
+
+<P>
+If <tt>A</tt> is not symmetric, then the eigenvalue matrix <tt>D</tt> is block diagonal
+with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
+<tt>lambda + i*mu</tt>, in 2-by-2 blocks, <tt>[lambda, mu; -mu, lambda]</tt>.
+The columns of <tt>V</tt> represent the eigenvectors in the sense that <tt>A*V = V*D</tt>,
+i.e. <tt>A.mult(V) equals V.mult(D)</tt>. The matrix <tt>V</tt> may be badly
+conditioned, or even singular, so the validity of the equation
+<tt>A = V*D*inverse(V)</tt> depends upon <tt>Algebra.cond(V)</tt>.
+**/
+/**
+ * @deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
+ */
+@Deprecated
+public class EigenvalueDecomposition implements java.io.Serializable {
+ static final long serialVersionUID = 1020;
+ /** Row and column dimension (square matrix).
+ @serial matrix dimension.
+ */
+ private int n;
+
+ /** Symmetry flag.
+ @serial internal symmetry flag.
+ */
+ private boolean issymmetric;
+
+ /** Arrays for internal storage of eigenvalues.
+ @serial internal storage of eigenvalues.
+ */
+ private double[] d, e;
+
+ /** Array for internal storage of eigenvectors.
+ @serial internal storage of eigenvectors.
+ */
+ private double[][] V;
+
+ /** Array for internal storage of nonsymmetric Hessenberg form.
+ @serial internal storage of nonsymmetric Hessenberg form.
+ */
+ private double[][] H;
+
+ /** Working storage for nonsymmetric algorithm.
+ @serial working storage for nonsymmetric algorithm.
+ */
+ private double[] ort;
+
+ // Complex scalar division.
+
+ private transient double cdivr, cdivi;
+/**
+Constructs and returns a new eigenvalue decomposition object;
+The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
+Checks for symmetry, then constructs the eigenvalue decomposition.
+@param A A square matrix.
+@return A decomposition object to access <tt>D</tt> and <tt>V</tt>.
+@throws IllegalArgumentException if <tt>A</tt> is not square.
+*/
+public EigenvalueDecomposition(DoubleMatrix2D A) {
+ Property.DEFAULT.checkSquare(A);
+
+ n = A.columns();
+ V = new double[n][n];
+ d = new double[n];
+ e = new double[n];
+
+ issymmetric = Property.DEFAULT.isSymmetric(A);
+
+ if (issymmetric) {
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ V[i][j] = A.getQuick(i,j);
+ }
+ }
+
+ // Tridiagonalize.
+ tred2();
+
+ // Diagonalize.
+ tql2();
+
+ }
+ else {
+ H = new double[n][n];
+ ort = new double[n];
+
+ for (int j = 0; j < n; j++) {
+ for (int i = 0; i < n; i++) {
+ H[i][j] = A.getQuick(i,j);
+ }
+ }
+
+ // Reduce to Hessenberg form.
+ orthes();
+
+ // Reduce Hessenberg to real Schur form.
+ hqr2();
+ }
+}
+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;
+ }
+}
+/**
+Returns the block diagonal eigenvalue matrix, <tt>D</tt>.
+@return <tt>D</tt>
+*/
+public DoubleMatrix2D getD() {
+ double[][] D = new double[n][n];
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ D[i][j] = 0.0;
+ }
+ D[i][i] = d[i];
+ if (e[i] > 0) {
+ D[i][i+1] = e[i];
+ }
+ else if (e[i] < 0) {
+ D[i][i-1] = e[i];
+ }
+ }
+ return DoubleFactory2D.dense.make(D);
+}
+/**
+Returns the imaginary parts of the eigenvalues.
+@return imag(diag(D))
+*/
+public DoubleMatrix1D getImagEigenvalues () {
+ return DoubleFactory1D.dense.make(e);
+}
+/**
+Returns the real parts of the eigenvalues.
+@return real(diag(D))
+*/
+public DoubleMatrix1D getRealEigenvalues () {
+ return DoubleFactory1D.dense.make(d);
+}
+/**
+Returns the eigenvector matrix, <tt>V</tt>
+@return <tt>V</tt>
+*/
+public DoubleMatrix2D getV () {
+ return DoubleFactory2D.dense.make(V);
+}
+/**
+Nonsymmetric reduction from Hessenberg to real Schur form.
+*/
+private void hqr2 () {
+ // 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
+
+ int nn = this.n;
+ int n = nn-1;
+ int low = 0;
+ 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 = 0.0;
+ for (int i = 0; i < nn; i++) {
+ if (i < low | i > high) {
+ d[i] = H[i][i];
+ e[i] = 0.0;
+ }
+ for (int j = Math.max(i-1,0); j < nn; j++) {
+ norm = norm + Math.abs(H[i][j]);
+ }
+ }
+
+ // 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[l-1][l-1]) + Math.abs(H[l][l]);
+ if (s == 0.0) {
+ s = norm;
+ }
+ if (Math.abs(H[l][l-1]) < eps * s) {
+ break;
+ }
+ l--;
+ }
+
+ // Check for convergence
+ // One root found
+
+ if (l == n) {
+ H[n][n] = H[n][n] + exshift;
+ d[n] = H[n][n];
+ e[n] = 0.0;
+ n--;
+ iter = 0;
+
+ // Two roots found
+
+ } else if (l == n-1) {
+ w = H[n][n-1] * H[n-1][n];
+ p = (H[n-1][n-1] - H[n][n]) / 2.0;
+ q = p * p + w;
+ z = Math.sqrt(Math.abs(q));
+ H[n][n] = H[n][n] + exshift;
+ H[n-1][n-1] = H[n-1][n-1] + exshift;
+ x = H[n][n];
+
+ // Real pair
+
+ if (q >= 0) {
+ if (p >= 0) {
+ z = p + z;
+ } else {
+ z = p - z;
+ }
+ d[n-1] = x + z;
+ d[n] = d[n-1];
+ if (z != 0.0) {
+ d[n] = x - w / z;
+ }
+ e[n-1] = 0.0;
+ e[n] = 0.0;
+ x = H[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[n-1][j];
+ H[n-1][j] = q * z + p * H[n][j];
+ H[n][j] = q * H[n][j] - p * z;
+ }
+
+ // Column modification
+
+ for (int i = 0; i <= n; i++) {
+ z = H[i][n-1];
+ H[i][n-1] = q * z + p * H[i][n];
+ H[i][n] = q * H[i][n] - p * z;
+ }
+
+ // Accumulate transformations
+
+ for (int i = low; i <= high; i++) {
+ z = V[i][n-1];
+ V[i][n-1] = q * z + p * V[i][n];
+ V[i][n] = q * V[i][n] - p * z;
+ }
+
+ // Complex pair
+
+ } else {
+ d[n-1] = x + p;
+ d[n] = x + p;
+ e[n-1] = z;
+ e[n] = -z;
+ }
+ n = n - 2;
+ iter = 0;
+
+ // No convergence yet
+
+ } else {
+
+ // Form shift
+
+ x = H[n][n];
+ y = 0.0;
+ w = 0.0;
+ if (l < n) {
+ y = H[n-1][n-1];
+ w = H[n][n-1] * H[n-1][n];
+ }
+
+ // Wilkinson's original ad hoc shift
+
+ if (iter == 10) {
+ exshift += x;
+ for (int i = low; i <= n; i++) {
+ H[i][i] -= x;
+ }
+ s = Math.abs(H[n][n-1]) + Math.abs(H[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[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[m][m];
+ r = x - z;
+ s = y - z;
+ p = (r * s - w) / H[m+1][m] + H[m][m+1];
+ q = H[m+1][m+1] - z - r - s;
+ r = H[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[m][m-1]) * (Math.abs(q) + Math.abs(r)) <
+ eps * (Math.abs(p) * (Math.abs(H[m-1][m-1]) + Math.abs(z) +
+ Math.abs(H[m+1][m+1])))) {
+ break;
+ }
+ m--;
+ }
+
+ for (int i = m+2; i <= n; i++) {
+ H[i][i-2] = 0.0;
+ if (i > m+2) {
+ H[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[k][k-1];
+ q = H[k+1][k-1];
+ r = (notlast ? H[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[k][k-1] = -s * x;
+ } else if (l != m) {
+ H[k][k-1] = -H[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[k][j] + q * H[k+1][j];
+ if (notlast) {
+ p = p + r * H[k+2][j];
+ H[k+2][j] = H[k+2][j] - p * z;
+ }
+ H[k][j] = H[k][j] - p * x;
+ H[k+1][j] = H[k+1][j] - p * y;
+ }
+
+ // Column modification
+
+ for (int i = 0; i <= Math.min(n,k+3); i++) {
+ p = x * H[i][k] + y * H[i][k+1];
+ if (notlast) {
+ p = p + z * H[i][k+2];
+ H[i][k+2] = H[i][k+2] - p * r;
+ }
+ H[i][k] = H[i][k] - p;
+ H[i][k+1] = H[i][k+1] - p * q;
+ }
+
+ // Accumulate transformations
+
+ for (int i = low; i <= high; i++) {
+ p = x * V[i][k] + y * V[i][k+1];
+ if (notlast) {
+ p = p + z * V[i][k+2];
+ V[i][k+2] = V[i][k+2] - p * r;
+ }
+ V[i][k] = V[i][k] - p;
+ V[i][k+1] = V[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[n];
+ q = e[n];
+
+ // Real vector
+
+ if (q == 0) {
+ int l = n;
+ H[n][n] = 1.0;
+ for (int i = n-1; i >= 0; i--) {
+ w = H[i][i] - p;
+ r = 0.0;
+ for (int j = l; j <= n; j++) {
+ r = r + H[i][j] * H[j][n];
+ }
+ if (e[i] < 0.0) {
+ z = w;
+ s = r;
+ } else {
+ l = i;
+ if (e[i] == 0.0) {
+ if (w != 0.0) {
+ H[i][n] = -r / w;
+ } else {
+ H[i][n] = -r / (eps * norm);
+ }
+
+ // Solve real equations
+
+ } else {
+ x = H[i][i+1];
+ y = H[i+1][i];
+ q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
+ t = (x * s - z * r) / q;
+ H[i][n] = t;
+ if (Math.abs(x) > Math.abs(z)) {
+ H[i+1][n] = (-r - w * t) / x;
+ } else {
+ H[i+1][n] = (-s - y * t) / z;
+ }
+ }
+
+ // Overflow control
+
+ t = Math.abs(H[i][n]);
+ if ((eps * t) * t > 1) {
+ for (int j = i; j <= n; j++) {
+ H[j][n] = H[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[n][n-1]) > Math.abs(H[n-1][n])) {
+ H[n-1][n-1] = q / H[n][n-1];
+ H[n-1][n] = -(H[n][n] - p) / H[n][n-1];
+ } else {
+ cdiv(0.0,-H[n-1][n],H[n-1][n-1]-p,q);
+ H[n-1][n-1] = cdivr;
+ H[n-1][n] = cdivi;
+ }
+ H[n][n-1] = 0.0;
+ H[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[i][j] * H[j][n-1];
+ sa = sa + H[i][j] * H[j][n];
+ }
+ w = H[i][i] - p;
+
+ if (e[i] < 0.0) {
+ z = w;
+ r = ra;
+ s = sa;
+ } else {
+ l = i;
+ if (e[i] == 0) {
+ cdiv(-ra,-sa,w,q);
+ H[i][n-1] = cdivr;
+ H[i][n] = cdivi;
+ } else {
+
+ // Solve complex equations
+
+ x = H[i][i+1];
+ y = H[i+1][i];
+ vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
+ vi = (d[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[i][n-1] = cdivr;
+ H[i][n] = cdivi;
+ if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
+ H[i+1][n-1] = (-ra - w * H[i][n-1] + q * H[i][n]) / x;
+ H[i+1][n] = (-sa - w * H[i][n] - q * H[i][n-1]) / x;
+ } else {
+ cdiv(-r-y*H[i][n-1],-s-y*H[i][n],z,q);
+ H[i+1][n-1] = cdivr;
+ H[i+1][n] = cdivi;
+ }
+ }
+
+ // Overflow control
+
+ t = Math.max(Math.abs(H[i][n-1]),Math.abs(H[i][n]));
+ if ((eps * t) * t > 1) {
+ for (int j = i; j <= n; j++) {
+ H[j][n-1] = H[j][n-1] / t;
+ H[j][n] = H[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[i][j] = H[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[i][k] * H[k][j];
+ }
+ V[i][j] = z;
+ }
+ }
+ }
+/**
+Nonsymmetric reduction to Hessenberg form.
+*/
+private void orthes () {
+ // 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 = 0.0;
+ for (int i = m; i <= high; i++) {
+ scale = scale + Math.abs(H[i][m-1]);
+ }
+ if (scale != 0.0) {
+
+ // Compute Householder transformation.
+
+ double h = 0.0;
+ for (int i = high; i >= m; i--) {
+ ort[i] = H[i][m-1]/scale;
+ h += ort[i] * ort[i];
+ }
+ double g = Math.sqrt(h);
+ if (ort[m] > 0) {
+ g = -g;
+ }
+ h = h - ort[m] * g;
+ ort[m] = ort[m] - g;
+
+ // Apply Householder similarity transformation
+ // H = (I-u*u'/h)*H*(I-u*u')/h)
+
+ for (int j = m; j < n; j++) {
+ double f = 0.0;
+ for (int i = high; i >= m; i--) {
+ f += ort[i]*H[i][j];
+ }
+ f = f/h;
+ for (int i = m; i <= high; i++) {
+ H[i][j] -= f*ort[i];
+ }
+ }
+
+ for (int i = 0; i <= high; i++) {
+ double f = 0.0;
+ for (int j = high; j >= m; j--) {
+ f += ort[j]*H[i][j];
+ }
+ f = f/h;
+ for (int j = m; j <= high; j++) {
+ H[i][j] -= f*ort[j];
+ }
+ }
+ ort[m] = scale*ort[m];
+ H[m][m-1] = scale*g;
+ }
+ }
+
+ // Accumulate transformations (Algol's ortran).
+
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < n; j++) {
+ V[i][j] = (i == j ? 1.0 : 0.0);
+ }
+ }
+
+ for (int m = high-1; m >= low+1; m--) {
+ if (H[m][m-1] != 0.0) {
+ for (int i = m+1; i <= high; i++) {
+ ort[i] = H[i][m-1];
+ }
+ for (int j = m; j <= high; j++) {
+ double g = 0.0;
+ for (int i = m; i <= high; i++) {
+ g += ort[i] * V[i][j];
+ }
+ // Double division avoids possible underflow
+ g = (g / ort[m]) / H[m][m-1];
+ for (int i = m; i <= high; i++) {
+ V[i][j] += g * ort[i];
+ }
+ }
+ }
+ }
+ }
+/**
+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>
+*/
+public String toString() {
+ StringBuffer buf = new StringBuffer();
+ String unknown = "Illegal operation or error: ";
+
+ buf.append("---------------------------------------------------------------------\n");
+ buf.append("EigenvalueDecomposition(A) --> D, V, realEigenvalues, imagEigenvalues\n");
+ buf.append("---------------------------------------------------------------------\n");
+
+ buf.append("realEigenvalues = ");
+ try { buf.append(String.valueOf(this.getRealEigenvalues()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\nimagEigenvalues = ");
+ try { buf.append(String.valueOf(this.getImagEigenvalues()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\n\nD = ");
+ try { buf.append(String.valueOf(this.getD()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\n\nV = ");
+ try { buf.append(String.valueOf(this.getV()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ return buf.toString();
+}
+/**
+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.
+
+ for (int i = 1; i < n; i++) {
+ e[i-1] = e[i];
+ }
+ e[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[l]) + Math.abs(e[l]));
+ int m = l;
+ while (m < n) {
+ if (Math.abs(e[m]) <= eps*tst1) {
+ break;
+ }
+ m++;
+ }
+
+ // If m == l, d[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[l];
+ double p = (d[l+1] - g) / (2.0 * e[l]);
+ double r = Algebra.hypot(p,1.0);
+ if (p < 0) {
+ r = -r;
+ }
+ d[l] = e[l] / (p + r);
+ d[l+1] = e[l] * (p + r);
+ double dl1 = d[l+1];
+ double h = g - d[l];
+ for (int i = l+2; i < n; i++) {
+ d[i] -= h;
+ }
+ f = f + h;
+
+ // Implicit QL transformation.
+
+ p = d[m];
+ double c = 1.0;
+ double c2 = c;
+ double c3 = c;
+ double el1 = e[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[i];
+ h = c * p;
+ r = Algebra.hypot(p,e[i]);
+ e[i+1] = s * r;
+ s = e[i] / r;
+ c = p / r;
+ p = c * d[i] - s * g;
+ d[i+1] = h + s * (c * g + s * d[i]);
+
+ // Accumulate transformation.
+
+ for (int k = 0; k < n; k++) {
+ h = V[k][i+1];
+ V[k][i+1] = s * V[k][i] + c * h;
+ V[k][i] = c * V[k][i] - s * h;
+ }
+ }
+ p = -s * s2 * c3 * el1 * e[l] / dl1;
+ e[l] = s * p;
+ d[l] = c * p;
+
+ // Check for convergence.
+
+ } while (Math.abs(e[l]) > eps*tst1);
+ }
+ d[l] = d[l] + f;
+ e[l] = 0.0;
+ }
+
+ // Sort eigenvalues and corresponding vectors.
+
+ for (int i = 0; i < n-1; i++) {
+ int k = i;
+ double p = d[i];
+ for (int j = i+1; j < n; j++) {
+ if (d[j] < p) {
+ k = j;
+ p = d[j];
+ }
+ }
+ if (k != i) {
+ d[k] = d[i];
+ d[i] = p;
+ for (int j = 0; j < n; j++) {
+ p = V[j][i];
+ V[j][i] = V[j][k];
+ V[j][k] = p;
+ }
+ }
+ }
+ }
+/**
+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.
+
+
+ for (int j = 0; j < n; j++) {
+ d[j] = V[n-1][j];
+ }
+
+
+ // Householder reduction to tridiagonal form.
+
+ for (int i = n-1; i > 0; i--) {
+
+ // Scale to avoid under/overflow.
+
+ double scale = 0.0;
+ double h = 0.0;
+ for (int k = 0; k < i; k++) {
+ scale = scale + Math.abs(d[k]);
+ }
+ if (scale == 0.0) {
+ e[i] = d[i-1];
+ for (int j = 0; j < i; j++) {
+ d[j] = V[i-1][j];
+ V[i][j] = 0.0;
+ V[j][i] = 0.0;
+ }
+ } else {
+
+ // Generate Householder vector.
+
+ for (int k = 0; k < i; k++) {
+ d[k] /= scale;
+ h += d[k] * d[k];
+ }
+ double f = d[i-1];
+ double g = Math.sqrt(h);
+ if (f > 0) {
+ g = -g;
+ }
+ e[i] = scale * g;
+ h = h - f * g;
+ d[i-1] = f - g;
+ for (int j = 0; j < i; j++) {
+ e[j] = 0.0;
+ }
+
+ // Apply similarity transformation to remaining columns.
+
+ for (int j = 0; j < i; j++) {
+ f = d[j];
+ V[j][i] = f;
+ g = e[j] + V[j][j] * f;
+ for (int k = j+1; k <= i-1; k++) {
+ g += V[k][j] * d[k];
+ e[k] += V[k][j] * f;
+ }
+ e[j] = g;
+ }
+ f = 0.0;
+ for (int j = 0; j < i; j++) {
+ e[j] /= h;
+ f += e[j] * d[j];
+ }
+ double hh = f / (h + h);
+ for (int j = 0; j < i; j++) {
+ e[j] -= hh * d[j];
+ }
+ for (int j = 0; j < i; j++) {
+ f = d[j];
+ g = e[j];
+ for (int k = j; k <= i-1; k++) {
+ V[k][j] -= (f * e[k] + g * d[k]);
+ }
+ d[j] = V[i-1][j];
+ V[i][j] = 0.0;
+ }
+ }
+ d[i] = h;
+ }
+
+ // Accumulate transformations.
+
+ for (int i = 0; i < n-1; i++) {
+ V[n-1][i] = V[i][i];
+ V[i][i] = 1.0;
+ double h = d[i+1];
+ if (h != 0.0) {
+ for (int k = 0; k <= i; k++) {
+ d[k] = V[k][i+1] / h;
+ }
+ for (int j = 0; j <= i; j++) {
+ double g = 0.0;
+ for (int k = 0; k <= i; k++) {
+ g += V[k][i+1] * V[k][j];
+ }
+ for (int k = 0; k <= i; k++) {
+ V[k][j] -= g * d[k];
+ }
+ }
+ }
+ for (int k = 0; k <= i; k++) {
+ V[k][i+1] = 0.0;
+ }
+ }
+ for (int j = 0; j < n; j++) {
+ d[j] = V[n-1][j];
+ V[n-1][j] = 0.0;
+ }
+ V[n-1][n-1] = 1.0;
+ e[0] = 0.0;
+ }
+}
Propchange: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/EigenvalueDecomposition.java
------------------------------------------------------------------------------
svn:eol-style = native
Added: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecomposition.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecomposition.java?rev=883365&view=auto
==============================================================================
--- lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecomposition.java (added)
+++ lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecomposition.java Mon Nov 23 15:14:26 2009
@@ -0,0 +1,109 @@
+/*
+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.colt.matrix.linalg;
+
+import org.apache.mahout.colt.matrix.DoubleMatrix2D;
+//import org.apache.mahout.colt.matrix.DenseDoubleMatrix1D;
+/**
+For an <tt>m x n</tt> matrix <tt>A</tt> with <tt>m >= n</tt>, the LU decomposition is an <tt>m x n</tt>
+unit lower triangular matrix <tt>L</tt>, an <tt>n x n</tt> upper triangular matrix <tt>U</tt>,
+and a permutation vector <tt>piv</tt> of length <tt>m</tt> so that <tt>A(piv,:) = L*U</tt>;
+If <tt>m < n</tt>, then <tt>L</tt> is <tt>m x m</tt> and <tt>U</tt> is <tt>m x n</tt>.
+<P>
+The LU decomposition with pivoting always exists, even if the matrix is
+singular, so the constructor will never fail. The primary use of the
+LU decomposition is in the solution of square systems of simultaneous
+linear equations. This will fail if <tt>isNonsingular()</tt> returns false.
+*/
+/**
+ * @deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
+ */
+@Deprecated
+public class LUDecomposition implements java.io.Serializable {
+ static final long serialVersionUID = 1020;
+ protected LUDecompositionQuick quick;
+/**
+Constructs and returns a new LU Decomposition object;
+The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
+@param A Rectangular matrix
+@return Structure to access L, U and piv.
+*/
+public LUDecomposition(DoubleMatrix2D A) {
+ quick = new LUDecompositionQuick(0); // zero tolerance for compatibility with Jama
+ quick.decompose(A.copy());
+}
+/**
+Returns the determinant, <tt>det(A)</tt>.
+@exception IllegalArgumentException Matrix must be square
+*/
+public double det() {
+ return quick.det();
+}
+/**
+Returns pivot permutation vector as a one-dimensional double array
+@return (double) piv
+*/
+private double[] getDoublePivot() {
+ return quick.getDoublePivot();
+}
+/**
+Returns the lower triangular factor, <tt>L</tt>.
+@return <tt>L</tt>
+*/
+public DoubleMatrix2D getL() {
+ return quick.getL();
+}
+/**
+Returns a copy of the pivot permutation vector.
+@return piv
+*/
+public int[] getPivot() {
+ return (int[]) quick.getPivot().clone();
+}
+/**
+Returns the upper triangular factor, <tt>U</tt>.
+@return <tt>U</tt>
+*/
+public DoubleMatrix2D getU() {
+ return quick.getU();
+}
+/**
+Returns whether the matrix is nonsingular (has an inverse).
+@return true if <tt>U</tt>, and hence <tt>A</tt>, is nonsingular; false otherwise.
+*/
+public boolean isNonsingular() {
+ return quick.isNonsingular();
+}
+/**
+Solves <tt>A*X = B</tt>.
+@param B A matrix with as many rows as <tt>A</tt> and any number of columns.
+@return <tt>X</tt> so that <tt>L*U*X = B(piv,:)</tt>.
+@exception IllegalArgumentException if </tt>B.rows() != A.rows()</tt>.
+@exception IllegalArgumentException if A is singular, that is, if <tt>!this.isNonsingular()</tt>.
+@exception IllegalArgumentException if <tt>A.rows() < A.columns()</tt>.
+*/
+
+public DoubleMatrix2D solve(DoubleMatrix2D B) {
+ DoubleMatrix2D X = B.copy();
+ quick.solve(X);
+ return X;
+}
+/**
+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>
+*/
+public String toString() {
+ return quick.toString();
+}
+}
Propchange: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecomposition.java
------------------------------------------------------------------------------
svn:eol-style = native
Added: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecompositionQuick.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecompositionQuick.java?rev=883365&view=auto
==============================================================================
--- lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecompositionQuick.java (added)
+++ lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecompositionQuick.java Mon Nov 23 15:14:26 2009
@@ -0,0 +1,675 @@
+/*
+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.colt.matrix.linalg;
+
+import org.apache.mahout.colt.matrix.DoubleMatrix1D;
+import org.apache.mahout.colt.matrix.DoubleMatrix2D;
+/**
+A low level version of {@link LUDecomposition}, avoiding unnecessary memory allocation and copying.
+The input to <tt>decompose</tt> methods is overriden with the result (LU).
+The input to <tt>solve</tt> methods is overriden with the result (X).
+In addition to <tt>LUDecomposition</tt>, this class also includes a faster variant of the decomposition, specialized for tridiagonal (and hence also diagonal) matrices,
+as well as a solver tuned for vectors.
+Its disadvantage is that it is a bit more difficult to use than <tt>LUDecomposition</tt>.
+Thus, you may want to disregard this class and come back later, if a need for speed arises.
+<p>
+An instance of this class remembers the result of its last decomposition.
+Usage pattern is as follows: Create an instance of this class, call a decompose method,
+then retrieve the decompositions, determinant, and/or solve as many equation problems as needed.
+Once another matrix needs to be LU-decomposed, you need not create a new instance of this class.
+Start again by calling a decompose method, then retrieve the decomposition and/or solve your equations, and so on.
+In case a <tt>LU</tt> matrix is already available, call method <tt>setLU</tt> instead of <tt>decompose</tt> and proceed with solving et al.
+<p>
+If a matrix shall not be overriden, use <tt>matrix.copy()</tt> and hand the the copy to methods.
+<p>
+For an <tt>m x n</tt> matrix <tt>A</tt> with <tt>m >= n</tt>, the LU decomposition is an <tt>m x n</tt>
+unit lower triangular matrix <tt>L</tt>, an <tt>n x n</tt> upper triangular matrix <tt>U</tt>,
+and a permutation vector <tt>piv</tt> of length <tt>m</tt> so that <tt>A(piv,:) = L*U</tt>;
+If <tt>m < n</tt>, then <tt>L</tt> is <tt>m x m</tt> and <tt>U</tt> is <tt>m x n</tt>.
+<P>
+The LU decomposition with pivoting always exists, even if the matrix is
+singular, so the decompose methods will never fail. The primary use of the
+LU decomposition is in the solution of square systems of simultaneous
+linear equations.
+Attempting to solve such a system will throw an exception if <tt>isNonsingular()</tt> returns false.
+<p>
+*/
+/**
+ * @deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
+ */
+@Deprecated
+public class LUDecompositionQuick implements java.io.Serializable {
+ static final long serialVersionUID = 1020;
+ /** Array for internal storage of decomposition.
+ @serial internal array storage.
+ */
+ protected DoubleMatrix2D LU;
+
+ /** pivot sign.
+ @serial pivot sign.
+ */
+ protected int pivsign;
+
+ /** Internal storage of pivot vector.
+ @serial pivot vector.
+ */
+ protected int[] piv;
+
+ protected boolean isNonSingular;
+
+ protected Algebra algebra;
+
+ transient protected double[] workDouble;
+ transient protected int[] work1;
+ transient protected int[] work2;
+
+/**
+Constructs and returns a new LU Decomposition object with default tolerance <tt>1.0E-9</tt> for singularity detection.
+*/
+public LUDecompositionQuick() {
+ this(Property.DEFAULT.tolerance());
+}
+/**
+Constructs and returns a new LU Decomposition object which uses the given tolerance for singularity detection;
+*/
+public LUDecompositionQuick(double tolerance) {
+ this.algebra = new Algebra(tolerance);
+}
+/**
+Decomposes matrix <tt>A</tt> into <tt>L</tt> and <tt>U</tt> (in-place).
+Upon return <tt>A</tt> is overridden with the result <tt>LU</tt>, such that <tt>L*U = A</tt>.
+Uses a "left-looking", dot-product, Crout/Doolittle algorithm.
+@param A any matrix.
+*/
+public void decompose(DoubleMatrix2D A) {
+ final int CUT_OFF = 10;
+ // setup
+ LU = A;
+ int m = A.rows();
+ int n = A.columns();
+
+ // setup pivot vector
+ if (this.piv==null || this.piv.length != m) this.piv = new int[m];
+ for (int i = m; --i >= 0; ) piv[i] = i;
+ pivsign = 1;
+
+ if (m*n == 0) {
+ setLU(LU);
+ return; // nothing to do
+ }
+
+ //precompute and cache some views to avoid regenerating them time and again
+ DoubleMatrix1D[] LUrows = new DoubleMatrix1D[m];
+ for (int i = 0; i < m; i++) LUrows[i] = LU.viewRow(i);
+
+ org.apache.mahout.colt.list.IntArrayList nonZeroIndexes = new org.apache.mahout.colt.list.IntArrayList(); // sparsity
+ DoubleMatrix1D LUcolj = LU.viewColumn(0).like(); // blocked column j
+ org.apache.mahout.jet.math.Mult multFunction = org.apache.mahout.jet.math.Mult.mult(0);
+
+ // Outer loop.
+ for (int j = 0; j < n; j++) {
+ // blocking (make copy of j-th column to localize references)
+ LUcolj.assign(LU.viewColumn(j));
+
+ // sparsity detection
+ int maxCardinality = m/CUT_OFF; // == heuristic depending on speedup
+ LUcolj.getNonZeros(nonZeroIndexes,null,maxCardinality);
+ int cardinality = nonZeroIndexes.size();
+ boolean sparse = (cardinality < maxCardinality);
+
+ // Apply previous transformations.
+ for (int i = 0; i < m; i++) {
+ int kmax = Math.min(i,j);
+ double s;
+ if (sparse) {
+ s = LUrows[i].zDotProduct(LUcolj,0,kmax,nonZeroIndexes);
+ }
+ else {
+ s = LUrows[i].zDotProduct(LUcolj,0,kmax);
+ }
+ double before = LUcolj.getQuick(i);
+ double after = before -s;
+ LUcolj.setQuick(i, after); // LUcolj is a copy
+ LU.setQuick(i,j, after); // this is the original
+ if (sparse) {
+ if (before==0 && after!=0) { // nasty bug fixed!
+ int pos = nonZeroIndexes.binarySearch(i);
+ pos = -pos -1;
+ nonZeroIndexes.beforeInsert(pos,i);
+ }
+ if (before!=0 && after==0) {
+ nonZeroIndexes.remove(nonZeroIndexes.binarySearch(i));
+ }
+ }
+ }
+
+ // Find pivot and exchange if necessary.
+ int p = j;
+ if (p < m) {
+ double max = Math.abs(LUcolj.getQuick(p));
+ for (int i = j+1; i < m; i++) {
+ double v = Math.abs(LUcolj.getQuick(i));
+ if (v > max) {
+ p = i;
+ max = v;
+ }
+ }
+ }
+ if (p != j) {
+ LUrows[p].swap(LUrows[j]);
+ int k = piv[p]; piv[p] = piv[j]; piv[j] = k;
+ pivsign = -pivsign;
+ }
+
+ // Compute multipliers.
+ double jj;
+ if (j < m && (jj=LU.getQuick(j,j)) != 0.0) {
+ multFunction.multiplicator = 1 / jj;
+ LU.viewColumn(j).viewPart(j+1,m-(j+1)).assign(multFunction);
+ }
+
+ }
+ setLU(LU);
+}
+/**
+Decomposes the banded and square matrix <tt>A</tt> into <tt>L</tt> and <tt>U</tt> (in-place).
+Upon return <tt>A</tt> is overridden with the result <tt>LU</tt>, such that <tt>L*U = A</tt>.
+Currently supports diagonal and tridiagonal matrices, all other cases fall through to {@link #decompose(DoubleMatrix2D)}.
+@param semiBandwidth == 1 --> A is diagonal, == 2 --> A is tridiagonal.
+@param A any matrix.
+*/
+public void decompose(DoubleMatrix2D A, int semiBandwidth) {
+ if (! algebra.property().isSquare(A) || semiBandwidth<0 || semiBandwidth>2) {
+ decompose(A);
+ return;
+ }
+ // setup
+ LU = A;
+ int m = A.rows();
+ int n = A.columns();
+
+ // setup pivot vector
+ if (this.piv==null || this.piv.length != m) this.piv = new int[m];
+ for (int i = m; --i >= 0; ) piv[i] = i;
+ pivsign = 1;
+
+ if (m*n == 0) {
+ setLU(A);
+ return; // nothing to do
+ }
+
+ //if (semiBandwidth == 1) { // A is diagonal; nothing to do
+ if (semiBandwidth == 2) { // A is tridiagonal
+ // currently no pivoting !
+ if (n>1) A.setQuick(1,0, A.getQuick(1,0) / A.getQuick(0,0));
+
+ for (int i=1; i<n; i++) {
+ double ei = A.getQuick(i,i) - A.getQuick(i,i-1) * A.getQuick(i-1,i);
+ A.setQuick(i,i, ei);
+ if (i<n-1) A.setQuick(i+1,i, A.getQuick(i+1,i) / ei);
+ }
+ }
+ setLU(A);
+}
+/**
+Returns the determinant, <tt>det(A)</tt>.
+@exception IllegalArgumentException if <tt>A.rows() != A.columns()</tt> (Matrix must be square).
+*/
+public double det() {
+ int m = m();
+ int n = n();
+ if (m != n) throw new IllegalArgumentException("Matrix must be square.");
+
+ if (!isNonsingular()) return 0; // avoid rounding errors
+
+ double det = (double) pivsign;
+ for (int j = 0; j < n; j++) {
+ det *= LU.getQuick(j,j);
+ }
+ return det;
+}
+/**
+Returns pivot permutation vector as a one-dimensional double array
+@return (double) piv
+*/
+protected double[] getDoublePivot() {
+ int m = m();
+ double[] vals = new double[m];
+ for (int i = 0; i < m; i++) {
+ vals[i] = (double) piv[i];
+ }
+ return vals;
+}
+/**
+Returns the lower triangular factor, <tt>L</tt>.
+@return <tt>L</tt>
+*/
+public DoubleMatrix2D getL() {
+ return lowerTriangular(LU.copy());
+}
+/**
+Returns a copy of the combined lower and upper triangular factor, <tt>LU</tt>.
+@return <tt>LU</tt>
+*/
+public DoubleMatrix2D getLU() {
+ return LU.copy();
+}
+/**
+Returns the pivot permutation vector (not a copy of it).
+@return piv
+*/
+public int[] getPivot() {
+ return piv;
+}
+/**
+Returns the upper triangular factor, <tt>U</tt>.
+@return <tt>U</tt>
+*/
+public DoubleMatrix2D getU() {
+ return upperTriangular(LU.copy());
+}
+/**
+Returns whether the matrix is nonsingular (has an inverse).
+@return true if <tt>U</tt>, and hence <tt>A</tt>, is nonsingular; false otherwise.
+*/
+public boolean isNonsingular() {
+ return isNonSingular;
+}
+/**
+Returns whether the matrix is nonsingular.
+@return true if <tt>matrix</tt> is nonsingular; false otherwise.
+*/
+protected boolean isNonsingular(DoubleMatrix2D matrix) {
+ int m = matrix.rows();
+ int n = matrix.columns();
+ double epsilon = algebra.property().tolerance(); // consider numerical instability
+ for (int j = Math.min(n,m); --j >= 0;) {
+ //if (matrix.getQuick(j,j) == 0) return false;
+ if (Math.abs(matrix.getQuick(j,j)) <= epsilon) return false;
+ }
+ return true;
+}
+/**
+Modifies the matrix to be a lower triangular matrix.
+<p>
+<b>Examples:</b>
+<table border="0">
+ <tr nowrap>
+ <td valign="top">3 x 5 matrix:<br>
+ 9, 9, 9, 9, 9<br>
+ 9, 9, 9, 9, 9<br>
+ 9, 9, 9, 9, 9 </td>
+ <td align="center">triang.Upper<br>
+ ==></td>
+ <td valign="top">3 x 5 matrix:<br>
+ 9, 9, 9, 9, 9<br>
+ 0, 9, 9, 9, 9<br>
+ 0, 0, 9, 9, 9</td>
+ </tr>
+ <tr nowrap>
+ <td valign="top">5 x 3 matrix:<br>
+ 9, 9, 9<br>
+ 9, 9, 9<br>
+ 9, 9, 9<br>
+ 9, 9, 9<br>
+ 9, 9, 9 </td>
+ <td align="center">triang.Upper<br>
+ ==></td>
+ <td valign="top">5 x 3 matrix:<br>
+ 9, 9, 9<br>
+ 0, 9, 9<br>
+ 0, 0, 9<br>
+ 0, 0, 0<br>
+ 0, 0, 0</td>
+ </tr>
+ <tr nowrap>
+ <td valign="top">3 x 5 matrix:<br>
+ 9, 9, 9, 9, 9<br>
+ 9, 9, 9, 9, 9<br>
+ 9, 9, 9, 9, 9 </td>
+ <td align="center">triang.Lower<br>
+ ==></td>
+ <td valign="top">3 x 5 matrix:<br>
+ 1, 0, 0, 0, 0<br>
+ 9, 1, 0, 0, 0<br>
+ 9, 9, 1, 0, 0</td>
+ </tr>
+ <tr nowrap>
+ <td valign="top">5 x 3 matrix:<br>
+ 9, 9, 9<br>
+ 9, 9, 9<br>
+ 9, 9, 9<br>
+ 9, 9, 9<br>
+ 9, 9, 9 </td>
+ <td align="center">triang.Lower<br>
+ ==></td>
+ <td valign="top">5 x 3 matrix:<br>
+ 1, 0, 0<br>
+ 9, 1, 0<br>
+ 9, 9, 1<br>
+ 9, 9, 9<br>
+ 9, 9, 9</td>
+ </tr>
+</table>
+
+@return <tt>A</tt> (for convenience only).
+@see #triangulateUpper(DoubleMatrix2D)
+*/
+protected DoubleMatrix2D lowerTriangular(DoubleMatrix2D A) {
+ int rows = A.rows();
+ int columns = A.columns();
+ int min = Math.min(rows,columns);
+ for (int r = min; --r >= 0; ) {
+ for (int c = min; --c >= 0; ) {
+ if (r < c) A.setQuick(r,c, 0);
+ else if (r == c) A.setQuick(r,c, 1);
+ }
+ }
+ if (columns>rows) A.viewPart(0,min,rows,columns-min).assign(0);
+
+ return A;
+}
+/**
+ *
+ */
+protected int m() {
+ return LU.rows();
+}
+/**
+ *
+ */
+protected int n() {
+ return LU.columns();
+}
+/**
+Sets the combined lower and upper triangular factor, <tt>LU</tt>.
+The parameter is not checked; make sure it is indeed a proper LU decomposition.
+*/
+public void setLU(DoubleMatrix2D LU) {
+ this.LU = LU;
+ this.isNonSingular = isNonsingular(LU);
+}
+/**
+Solves the system of equations <tt>A*X = B</tt> (in-place).
+Upon return <tt>B</tt> is overridden with the result <tt>X</tt>, such that <tt>L*U*X = B(piv)</tt>.
+@param B A vector with <tt>B.size() == A.rows()</tt>.
+@exception IllegalArgumentException if </tt>B.size() != A.rows()</tt>.
+@exception IllegalArgumentException if A is singular, that is, if <tt>!isNonsingular()</tt>.
+@exception IllegalArgumentException if <tt>A.rows() < A.columns()</tt>.
+*/
+public void solve(DoubleMatrix1D B) {
+ algebra.property().checkRectangular(LU);
+ int m = m();
+ int n = n();
+ if (B.size() != m) throw new IllegalArgumentException("Matrix dimensions must agree.");
+ if (!this.isNonsingular()) throw new IllegalArgumentException("Matrix is singular.");
+
+
+ // right hand side with pivoting
+ // Matrix Xmat = B.getMatrix(piv,0,nx-1);
+ if (this.workDouble == null || this.workDouble.length < m) this.workDouble = new double[m];
+ algebra.permute(B, this.piv, this.workDouble);
+
+ if (m*n == 0) return; // nothing to do
+
+ // Solve L*Y = B(piv,:)
+ for (int k = 0; k < n; k++) {
+ double f = B.getQuick(k);
+ if (f != 0) {
+ for (int i = k+1; i < n; i++) {
+ // B[i] -= B[k]*LU[i][k];
+ double v = LU.getQuick(i,k);
+ if (v != 0) B.setQuick(i, B.getQuick(i) - f*v);
+ }
+ }
+ }
+
+ // Solve U*B = Y;
+ for (int k = n-1; k >= 0; k--) {
+ // B[k] /= LU[k,k]
+ B.setQuick(k, B.getQuick(k) / LU.getQuick(k,k));
+ double f = B.getQuick(k);
+ if (f != 0) {
+ for (int i = 0; i < k; i++) {
+ // B[i] -= B[k]*LU[i][k];
+ double v = LU.getQuick(i,k);
+ if (v != 0) B.setQuick(i, B.getQuick(i) - f*v);
+ }
+ }
+ }
+}
+/**
+Solves the system of equations <tt>A*X = B</tt> (in-place).
+Upon return <tt>B</tt> is overridden with the result <tt>X</tt>, such that <tt>L*U*X = B(piv,:)</tt>.
+@param B A matrix with as many rows as <tt>A</tt> and any number of columns.
+@exception IllegalArgumentException if </tt>B.rows() != A.rows()</tt>.
+@exception IllegalArgumentException if A is singular, that is, if <tt>!isNonsingular()</tt>.
+@exception IllegalArgumentException if <tt>A.rows() < A.columns()</tt>.
+*/
+public void solve(DoubleMatrix2D B) {
+ final int CUT_OFF = 10;
+ algebra.property().checkRectangular(LU);
+ int m = m();
+ int n = n();
+ if (B.rows() != m) throw new IllegalArgumentException("Matrix row dimensions must agree.");
+ if (!this.isNonsingular()) throw new IllegalArgumentException("Matrix is singular.");
+
+
+ // right hand side with pivoting
+ // Matrix Xmat = B.getMatrix(piv,0,nx-1);
+ if (this.work1 == null || this.work1.length < m) this.work1 = new int[m];
+ //if (this.work2 == null || this.work2.length < m) this.work2 = new int[m];
+ algebra.permuteRows(B, this.piv, this.work1);
+
+ if (m*n == 0) return; // nothing to do
+ int nx = B.columns();
+
+ //precompute and cache some views to avoid regenerating them time and again
+ DoubleMatrix1D[] Brows = new DoubleMatrix1D[n];
+ for (int k = 0; k < n; k++) Brows[k] = B.viewRow(k);
+
+ // transformations
+ org.apache.mahout.jet.math.Mult div = org.apache.mahout.jet.math.Mult.div(0);
+ org.apache.mahout.jet.math.PlusMult minusMult = org.apache.mahout.jet.math.PlusMult.minusMult(0);
+
+ org.apache.mahout.colt.list.IntArrayList nonZeroIndexes = new org.apache.mahout.colt.list.IntArrayList(); // sparsity
+ DoubleMatrix1D Browk = org.apache.mahout.colt.matrix.DoubleFactory1D.dense.make(nx); // blocked row k
+
+ // Solve L*Y = B(piv,:)
+ for (int k = 0; k < n; k++) {
+ // blocking (make copy of k-th row to localize references)
+ Browk.assign(Brows[k]);
+
+ // sparsity detection
+ int maxCardinality = nx/CUT_OFF; // == heuristic depending on speedup
+ Browk.getNonZeros(nonZeroIndexes,null,maxCardinality);
+ int cardinality = nonZeroIndexes.size();
+ boolean sparse = (cardinality < maxCardinality);
+
+ for (int i = k+1; i < n; i++) {
+ //for (int j = 0; j < nx; j++) B[i][j] -= B[k][j]*LU[i][k];
+ //for (int j = 0; j < nx; j++) B.set(i,j, B.get(i,j) - B.get(k,j)*LU.get(i,k));
+
+ minusMult.multiplicator = -LU.getQuick(i,k);
+ if (minusMult.multiplicator != 0) {
+ if (sparse) {
+ Brows[i].assign(Browk,minusMult,nonZeroIndexes);
+ }
+ else {
+ Brows[i].assign(Browk,minusMult);
+ }
+ }
+ }
+ }
+
+ // Solve U*B = Y;
+ for (int k = n-1; k >= 0; k--) {
+ // for (int j = 0; j < nx; j++) B[k][j] /= LU[k][k];
+ // for (int j = 0; j < nx; j++) B.set(k,j, B.get(k,j) / LU.get(k,k));
+ div.multiplicator = 1 / LU.getQuick(k,k);
+ Brows[k].assign(div);
+
+ // blocking
+ if (Browk==null) Browk = org.apache.mahout.colt.matrix.DoubleFactory1D.dense.make(B.columns());
+ Browk.assign(Brows[k]);
+
+ // sparsity detection
+ int maxCardinality = nx/CUT_OFF; // == heuristic depending on speedup
+ Browk.getNonZeros(nonZeroIndexes,null,maxCardinality);
+ int cardinality = nonZeroIndexes.size();
+ boolean sparse = (cardinality < maxCardinality);
+
+ //Browk.getNonZeros(nonZeroIndexes,null);
+ //boolean sparse = nonZeroIndexes.size() < nx/10;
+
+ for (int i = 0; i < k; i++) {
+ // for (int j = 0; j < nx; j++) B[i][j] -= B[k][j]*LU[i][k];
+ // for (int j = 0; j < nx; j++) B.set(i,j, B.get(i,j) - B.get(k,j)*LU.get(i,k));
+
+ minusMult.multiplicator = -LU.getQuick(i,k);
+ if (minusMult.multiplicator != 0) {
+ if (sparse) {
+ Brows[i].assign(Browk,minusMult,nonZeroIndexes);
+ }
+ else {
+ Brows[i].assign(Browk,minusMult);
+ }
+ }
+ }
+ }
+}
+/**
+Solves <tt>A*X = B</tt>.
+@param B A matrix with as many rows as <tt>A</tt> and any number of columns.
+@return <tt>X</tt> so that <tt>L*U*X = B(piv,:)</tt>.
+@exception IllegalArgumentException if </tt>B.rows() != A.rows()</tt>.
+@exception IllegalArgumentException if A is singular, that is, if <tt>!this.isNonsingular()</tt>.
+@exception IllegalArgumentException if <tt>A.rows() < A.columns()</tt>.
+*/
+private void solveOld(DoubleMatrix2D B) {
+ algebra.property().checkRectangular(LU);
+ int m = m();
+ int n = n();
+ if (B.rows() != m) throw new IllegalArgumentException("Matrix row dimensions must agree.");
+ if (!this.isNonsingular()) throw new IllegalArgumentException("Matrix is singular.");
+
+ // Copy right hand side with pivoting
+ int nx = B.columns();
+
+ if (this.work1 == null || this.work1.length < m) this.work1 = new int[m];
+ //if (this.work2 == null || this.work2.length < m) this.work2 = new int[m];
+ algebra.permuteRows(B, this.piv, this.work1);
+
+ // Solve L*Y = B(piv,:) --> Y (Y is modified B)
+ for (int k = 0; k < n; k++) {
+ for (int i = k + 1; i < n; i++) {
+ double mult = LU.getQuick(i, k);
+ if (mult != 0) {
+ for (int j = 0; j < nx; j++) {
+ //B[i][j] -= B[k][j]*LU[i,k];
+ B.setQuick(i, j, B.getQuick(i, j) - B.getQuick(k, j) * mult);
+ }
+ }
+ }
+ }
+ // Solve U*X = Y; --> X (X is modified B)
+ for (int k = n - 1; k >= 0; k--) {
+ double mult = 1 / LU.getQuick(k, k);
+ if (mult != 1) {
+ for (int j = 0; j < nx; j++) {
+ //B[k][j] /= LU[k][k];
+ B.setQuick(k, j, B.getQuick(k, j) * mult);
+ }
+ }
+ for (int i = 0; i < k; i++) {
+ mult = LU.getQuick(i, k);
+ if (mult != 0) {
+ for (int j = 0; j < nx; j++) {
+ //B[i][j] -= B[k][j]*LU[i][k];
+ B.setQuick(i, j, B.getQuick(i, j) - B.getQuick(k, j) * mult);
+ }
+ }
+ }
+ }
+}
+/**
+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>
+*/
+public String toString() {
+ StringBuffer buf = new StringBuffer();
+ String unknown = "Illegal operation or error: ";
+
+ buf.append("-----------------------------------------------------------------------------\n");
+ buf.append("LUDecompositionQuick(A) --> isNonSingular(A), det(A), pivot, L, U, inverse(A)\n");
+ buf.append("-----------------------------------------------------------------------------\n");
+
+ buf.append("isNonSingular = ");
+ try { buf.append(String.valueOf(this.isNonsingular()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\ndet = ");
+ try { buf.append(String.valueOf(this.det()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\npivot = ");
+ try { buf.append(String.valueOf(new org.apache.mahout.colt.list.IntArrayList(this.getPivot())));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\n\nL = ");
+ try { buf.append(String.valueOf(this.getL()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\n\nU = ");
+ try { buf.append(String.valueOf(this.getU()));}
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ buf.append("\n\ninverse(A) = ");
+ DoubleMatrix2D identity = org.apache.mahout.colt.matrix.DoubleFactory2D.dense.identity(LU.rows());
+ try { this.solve(identity); buf.append(String.valueOf(identity)); }
+ catch (IllegalArgumentException exc) { buf.append(unknown+exc.getMessage()); }
+
+ return buf.toString();
+}
+/**
+Modifies the matrix to be an upper triangular matrix.
+@return <tt>A</tt> (for convenience only).
+@see #triangulateLower(DoubleMatrix2D)
+*/
+protected DoubleMatrix2D upperTriangular(DoubleMatrix2D A) {
+ int rows = A.rows();
+ int columns = A.columns();
+ int min = Math.min(rows,columns);
+ for (int r = min; --r >= 0; ) {
+ for (int c = min; --c >= 0; ) {
+ if (r > c) A.setQuick(r,c, 0);
+ }
+ }
+ if (columns<rows) A.viewPart(min,0,rows-min,columns).assign(0);
+
+ return A;
+}
+/**
+Returns pivot permutation vector as a one-dimensional double array
+@return (double) piv
+*/
+private double[] xgetDoublePivot() {
+ int m = m();
+ double[] vals = new double[m];
+ for (int i = 0; i < m; i++) {
+ vals[i] = (double) piv[i];
+ }
+ return vals;
+}
+}
Propchange: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecompositionQuick.java
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Added: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/Matrix2DMatrix2DFunction.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/Matrix2DMatrix2DFunction.java?rev=883365&view=auto
==============================================================================
--- lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/Matrix2DMatrix2DFunction.java (added)
+++ lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/Matrix2DMatrix2DFunction.java Mon Nov 23 15:14:26 2009
@@ -0,0 +1,29 @@
+/*
+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.colt.matrix.linalg;
+
+import org.apache.mahout.colt.matrix.DoubleMatrix2D;
+/**
+ * Interface that represents a function object: a function that takes
+ * two arguments and returns a single value.
+ */
+/**
+ * @deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
+ */
+@Deprecated
+public interface Matrix2DMatrix2DFunction {
+/**
+ * Applies a function to two arguments.
+ *
+ * @param x the first argument passed to the function.
+ * @param y the second argument passed to the function.
+ * @return the result of the function.
+ */
+abstract public double apply(DoubleMatrix2D x, DoubleMatrix2D y);
+}
Propchange: lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/Matrix2DMatrix2DFunction.java
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