mahout-commits mailing list archives

Site index · List index
Message view « Date » · « Thread »
Top « Date » · « Thread »
From sro...@apache.org
Subject svn commit: r883974 [17/20] - in /lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix: ./ bench/ doublealgo/ impl/ linalg/ objectalgo/
Date Wed, 25 Nov 2009 03:41:31 GMT
Modified: 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=883974&r1=883973&r2=883974&view=diff
==============================================================================
--- lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/EigenvalueDecomposition.java (original)
+++ lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/EigenvalueDecomposition.java Wed Nov 25 03:41:28 2009
@@ -34,40 +34,40 @@
  */
 @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;
+  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.
@@ -77,634 +77,634 @@
 @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();
-	}
+  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;
-	}
+  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);
+  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);
+  return DoubleFactory1D.dense.make(e);
 }
 /** 
 Returns the real parts of the eigenvalues.
 @return     real(diag(D))
 */
 public DoubleMatrix1D getRealEigenvalues () {
-	return DoubleFactory1D.dense.make(d);
+  return DoubleFactory1D.dense.make(d);
 }
 /** 
 Returns the eigenvector matrix, <tt>V</tt>
 @return     <tt>V</tt>
 */
 public DoubleMatrix2D getV () {
-	return DoubleFactory2D.dense.make(V);
+  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;
-		 }
-	  }
+    //  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];
-			   }
-			}
-		 }
-	  }
+    //  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.
@@ -716,150 +716,150 @@
 </pre>
 */
 public String toString() {
-	StringBuffer buf = new StringBuffer();
-	String unknown = "Illegal operation or error: ";
+  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();
+  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;
-			}
-		 }
-	  }
+  //  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.
@@ -870,113 +870,113 @@
    //  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;
+    
+    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;
    }   
 }

Modified: 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=883974&r1=883973&r2=883974&view=diff
==============================================================================
--- lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecomposition.java (original)
+++ lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecomposition.java Wed Nov 25 03:41:28 2009
@@ -26,59 +26,59 @@
  */
 @Deprecated
 public class LUDecomposition implements java.io.Serializable {
-	static final long serialVersionUID = 1020;
-	protected LUDecompositionQuick quick;
+  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());
+  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();
+  return quick.det();
 }
 /** 
 Returns pivot permutation vector as a one-dimensional double array
 @return     (double) piv
 */
 private double[] getDoublePivot() {
-	return quick.getDoublePivot();
+  return quick.getDoublePivot();
 }
 /** 
 Returns the lower triangular factor, <tt>L</tt>.
 @return     <tt>L</tt>
 */
 public DoubleMatrix2D getL() {
-	return quick.getL();
+  return quick.getL();
 }
 /** 
 Returns a copy of the pivot permutation vector.
 @return     piv
 */
 public int[] getPivot() {
-	return (int[]) quick.getPivot().clone();
+  return (int[]) quick.getPivot().clone();
 }
 /** 
 Returns the upper triangular factor, <tt>U</tt>.
 @return     <tt>U</tt>
 */
 public DoubleMatrix2D getU() {
-	return quick.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();
+  return quick.isNonsingular();
 }
 /** 
 Solves <tt>A*X = B</tt>.
@@ -90,9 +90,9 @@
 */
 
 public DoubleMatrix2D solve(DoubleMatrix2D B) {
-	DoubleMatrix2D X = B.copy();
-	quick.solve(X);
-	return X;
+  DoubleMatrix2D X = B.copy();
+  quick.solve(X);
+  return X;
 }
 /**
 Returns a String with (propertyName, propertyValue) pairs.
@@ -104,6 +104,6 @@
 </pre>
 */
 public String toString() {
-	return quick.toString();
+  return quick.toString();
 }
 }

Modified: 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=883974&r1=883973&r2=883974&view=diff
==============================================================================
--- lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecompositionQuick.java (original)
+++ lucene/mahout/trunk/matrix/src/main/java/org/apache/mahout/matrix/matrix/linalg/LUDecompositionQuick.java Wed Nov 25 03:41:28 2009
@@ -45,137 +45,137 @@
  */
 @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;
+  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());
+  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);
+  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.matrix.list.IntArrayList nonZeroIndexes = new org.apache.mahout.matrix.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);
+  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.matrix.list.IntArrayList nonZeroIndexes = new org.apache.mahout.matrix.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).
@@ -183,117 +183,117 @@
 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);
+  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;
+  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;
+  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());
+  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();
+  return LU.copy();
 }
 /** 
 Returns the pivot permutation vector (not a copy of it).
 @return     piv
 */
 public int[] getPivot() {
-	return piv;
+  return piv;
 }
 /** 
 Returns the upper triangular factor, <tt>U</tt>.
 @return     <tt>U</tt>
 */
 public DoubleMatrix2D getU() {
-	return upperTriangular(LU.copy());
+  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;
+  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;
+  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.
@@ -301,60 +301,60 @@
 <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>
+  <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>
+  <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>
+  <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>
+  <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>
 
@@ -362,38 +362,38 @@
 @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);
+  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;
+  return A;
 }
 /**
  *
  */
 protected int m() {
-	return LU.rows();
+  return LU.rows();
 }
 /**
  *
  */
 protected int n() {
-	return LU.columns();
+  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);
+  this.LU = LU;
+  this.isNonSingular = isNonsingular(LU);
 }
 /** 
 Solves the system of equations <tt>A*X = B</tt> (in-place).
@@ -404,45 +404,45 @@
 @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);
-			}
-		}
-	}
+  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).
@@ -453,96 +453,96 @@
 @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.matrix.list.IntArrayList nonZeroIndexes = new org.apache.mahout.matrix.list.IntArrayList(); // sparsity
-	DoubleMatrix1D Browk = org.apache.mahout.matrix.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.matrix.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);
-				}
-			}			
-		}
-	}
+  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.matrix.list.IntArrayList nonZeroIndexes = new org.apache.mahout.matrix.list.IntArrayList(); // sparsity
+  DoubleMatrix1D Browk = org.apache.mahout.matrix.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.matrix.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>.
@@ -553,50 +553,50 @@
 @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);
-				}
-			}
-		}
-	}
+  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.
@@ -608,39 +608,39 @@
 </pre>
 */
 public String toString() {
-	StringBuffer buf = new StringBuffer();
-	String unknown = "Illegal operation or error: ";
+  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.matrix.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.matrix.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();
+  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.matrix.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.matrix.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.
@@ -648,28 +648,28 @@
 @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);
+  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;
+  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;
+  int m = m();
+  double[] vals = new double[m];
+  for (int i = 0; i < m; i++) {
+    vals[i] = (double) piv[i];
+  }
+  return vals;
 }
 }



Mime
View raw message