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From gsing...@apache.org
Subject 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...
Date Mon, 23 Nov 2009 15:14:38 GMT
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
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--- 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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