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Posted to commits@mahout.apache.org by gs...@apache.org on 2009/12/18 00:22:41 UTC
svn commit: r891983 [42/47] - in /lucene/mahout/trunk: ./ core/
core/src/main/java/org/apache/mahout/cf/taste/hadoop/item/
core/src/main/java/org/apache/mahout/clustering/
core/src/main/java/org/apache/mahout/clustering/canopy/
core/src/main/java/org/a...
Added: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Blas.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Blas.java?rev=891983&view=auto
==============================================================================
--- lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Blas.java (added)
+++ lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Blas.java Thu Dec 17 23:22:16 2009
@@ -0,0 +1,244 @@
+/*
+Copyright � 1999 CERN - European Organization for Nuclear Research.
+Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
+is hereby granted without fee, provided that the above copyright notice appear in all copies and
+that both that copyright notice and this permission notice appear in supporting documentation.
+CERN makes no representations about the suitability of this software for any purpose.
+It is provided "as is" without expressed or implied warranty.
+*/
+package org.apache.mahout.math.matrix.linalg;
+
+import org.apache.mahout.math.matrix.DoubleMatrix1D;
+import org.apache.mahout.math.matrix.DoubleMatrix2D;
+
+/** @deprecated until unit tests are in place. Until this time, this class/interface is unsupported. */
+@Deprecated
+public interface Blas {
+
+ /**
+ * Assigns the result of a function to each cell; <tt>x[row,col] = function(x[row,col])</tt>.
+ *
+ * @param A the matrix to modify.
+ * @param function a function object taking as argument the current cell's value.
+ * @see org.apache.mahout.math.jet.math.Functions
+ */
+ void assign(DoubleMatrix2D A, org.apache.mahout.math.function.DoubleFunction function);
+
+ /**
+ * Assigns the result of a function to each cell; <tt>x[row,col] = function(x[row,col],y[row,col])</tt>.
+ *
+ * @param x the matrix to modify.
+ * @param y the secondary matrix to operate on.
+ * @param function a function object taking as first argument the current cell's value of <tt>this</tt>, and as second
+ * argument the current cell's value of <tt>y</tt>,
+ * @return <tt>this</tt> (for convenience only).
+ * @throws IllegalArgumentException if <tt>x.columns() != y.columns() || x.rows() != y.rows()</tt>
+ * @see org.apache.mahout.math.jet.math.Functions
+ */
+ void assign(DoubleMatrix2D x, DoubleMatrix2D y, org.apache.mahout.math.function.DoubleDoubleFunction function);
+
+ /**
+ * Returns the sum of absolute values; <tt>|x[0]| + |x[1]| + ... </tt>. In fact equivalent to
+ * <tt>x.aggregate(Functions.plus, org.apache.mahout.math.jet.math.Functions.abs)</tt>.
+ *
+ * @param x the first vector.
+ */
+ double dasum(DoubleMatrix1D x);
+
+ /**
+ * Combined vector scaling; <tt>y = y + alpha*x</tt>. In fact equivalent to <tt>y.assign(x,org.apache.mahout.math.jet.math.Functions.plusMult(alpha))</tt>.
+ *
+ * @param alpha a scale factor.
+ * @param x the first source vector.
+ * @param y the second source vector, this is also the vector where results are stored.
+ * @throws IllegalArgumentException <tt>x.size() != y.size()</tt>..
+ */
+ void daxpy(double alpha, DoubleMatrix1D x, DoubleMatrix1D y);
+
+ /**
+ * Combined matrix scaling; <tt>B = B + alpha*A</tt>. In fact equivalent to <tt>B.assign(A,org.apache.mahout.math.jet.math.Functions.plusMult(alpha))</tt>.
+ *
+ * @param alpha a scale factor.
+ * @param A the first source matrix.
+ * @param B the second source matrix, this is also the matrix where results are stored.
+ * @throws IllegalArgumentException if <tt>A.columns() != B.columns() || A.rows() != B.rows()</tt>.
+ */
+ void daxpy(double alpha, DoubleMatrix2D A, DoubleMatrix2D B);
+
+ /**
+ * Vector assignment (copying); <tt>y = x</tt>. In fact equivalent to <tt>y.assign(x)</tt>.
+ *
+ * @param x the source vector.
+ * @param y the destination vector.
+ * @throws IllegalArgumentException <tt>x.size() != y.size()</tt>.
+ */
+ void dcopy(DoubleMatrix1D x, DoubleMatrix1D y);
+
+ /**
+ * Matrix assignment (copying); <tt>B = A</tt>. In fact equivalent to <tt>B.assign(A)</tt>.
+ *
+ * @param A the source matrix.
+ * @param B the destination matrix.
+ * @throws IllegalArgumentException if <tt>A.columns() != B.columns() || A.rows() != B.rows()</tt>.
+ */
+ void dcopy(DoubleMatrix2D A, DoubleMatrix2D B);
+
+ /**
+ * Returns the dot product of two vectors x and y, which is <tt>Sum(x[i]*y[i])</tt>. In fact equivalent to
+ * <tt>x.zDotProduct(y)</tt>.
+ *
+ * @param x the first vector.
+ * @param y the second vector.
+ * @return the sum of products.
+ * @throws IllegalArgumentException if <tt>x.size() != y.size()</tt>.
+ */
+ double ddot(DoubleMatrix1D x, DoubleMatrix1D y);
+
+ /**
+ * Generalized linear algebraic matrix-matrix multiply; <tt>C = alpha*A*B + beta*C</tt>. In fact equivalent to
+ * <tt>A.zMult(B,C,alpha,beta,transposeA,transposeB)</tt>. Note: Matrix shape conformance is checked <i>after</i>
+ * potential transpositions.
+ *
+ * @param transposeA set this flag to indicate that the multiplication shall be performed on A'.
+ * @param transposeB set this flag to indicate that the multiplication shall be performed on B'.
+ * @param alpha a scale factor.
+ * @param A the first source matrix.
+ * @param B the second source matrix.
+ * @param beta a scale factor.
+ * @param C the third source matrix, this is also the matrix where results are stored.
+ * @throws IllegalArgumentException if <tt>B.rows() != A.columns()</tt>.
+ * @throws IllegalArgumentException if <tt>C.rows() != A.rows() || C.columns() != B.columns()</tt>.
+ * @throws IllegalArgumentException if <tt>A == C || B == C</tt>.
+ */
+ void dgemm(boolean transposeA, boolean transposeB, double alpha, DoubleMatrix2D A, DoubleMatrix2D B, double beta,
+ DoubleMatrix2D C);
+
+ /**
+ * Generalized linear algebraic matrix-vector multiply; <tt>y = alpha*A*x + beta*y</tt>. In fact equivalent to
+ * <tt>A.zMult(x,y,alpha,beta,transposeA)</tt>. Note: Matrix shape conformance is checked <i>after</i> potential
+ * transpositions.
+ *
+ * @param transposeA set this flag to indicate that the multiplication shall be performed on A'.
+ * @param alpha a scale factor.
+ * @param A the source matrix.
+ * @param x the first source vector.
+ * @param beta a scale factor.
+ * @param y the second source vector, this is also the vector where results are stored.
+ * @throws IllegalArgumentException <tt>A.columns() != x.size() || A.rows() != y.size())</tt>..
+ */
+ void dgemv(boolean transposeA, double alpha, DoubleMatrix2D A, DoubleMatrix1D x, double beta, DoubleMatrix1D y);
+
+ /**
+ * Performs a rank 1 update; <tt>A = A + alpha*x*y'</tt>. Example:
+ * <pre>
+ * A = { {6,5}, {7,6} }, x = {1,2}, y = {3,4}, alpha = 1 -->
+ * A = { {9,9}, {13,14} }
+ * </pre>
+ *
+ * @param alpha a scalar.
+ * @param x an m element vector.
+ * @param y an n element vector.
+ * @param A an m by n matrix.
+ */
+ void dger(double alpha, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix2D A);
+
+ /**
+ * Return the 2-norm; <tt>sqrt(x[0]^2 + x[1]^2 + ...)</tt>. In fact equivalent to
+ * <tt>Math.sqrt(Algebra.DEFAULT.norm2(x))</tt>.
+ *
+ * @param x the vector.
+ */
+ double dnrm2(DoubleMatrix1D x);
+
+ /**
+ * Applies a givens plane rotation to (x,y); <tt>x = c*x + s*y; y = c*y - s*x</tt>.
+ *
+ * @param x the first vector.
+ * @param y the second vector.
+ * @param c the cosine of the angle of rotation.
+ * @param s the sine of the angle of rotation.
+ */
+ void drot(DoubleMatrix1D x, DoubleMatrix1D y, double c, double s);
+
+ /**
+ * Constructs a Givens plane rotation for <tt>(a,b)</tt>. Taken from the LINPACK translation from FORTRAN to Java,
+ * interface slightly modified. In the LINPACK listing DROTG is attributed to Jack Dongarra
+ *
+ * @param a rotational elimination parameter a.
+ * @param b rotational elimination parameter b.
+ * @param rotvec Must be at least of length 4. On output contains the values <tt>{a,b,c,s}</tt>.
+ */
+ void drotg(double a, double b, double[] rotvec);
+
+ /**
+ * Vector scaling; <tt>x = alpha*x</tt>. In fact equivalent to <tt>x.assign(Functions.mult(alpha))</tt>.
+ *
+ * @param alpha a scale factor.
+ * @param x the first vector.
+ */
+ void dscal(double alpha, DoubleMatrix1D x);
+
+ /**
+ * Matrix scaling; <tt>A = alpha*A</tt>. In fact equivalent to <tt>A.assign(Functions.mult(alpha))</tt>.
+ *
+ * @param alpha a scale factor.
+ * @param A the matrix.
+ */
+ void dscal(double alpha, DoubleMatrix2D A);
+
+ /**
+ * Swaps the elements of two vectors; <tt>y <==> x</tt>. In fact equivalent to <tt>y.swap(x)</tt>.
+ *
+ * @param x the first vector.
+ * @param y the second vector.
+ * @throws IllegalArgumentException <tt>x.size() != y.size()</tt>.
+ */
+ void dswap(DoubleMatrix1D x, DoubleMatrix1D y);
+
+ /**
+ * Swaps the elements of two matrices; <tt>B <==> A</tt>.
+ *
+ * @param x the first matrix.
+ * @param y the second matrix.
+ * @throws IllegalArgumentException if <tt>A.columns() != B.columns() || A.rows() != B.rows()</tt>.
+ */
+ void dswap(DoubleMatrix2D x, DoubleMatrix2D y);
+
+ /**
+ * Symmetric matrix-vector multiplication; <tt>y = alpha*A*x + beta*y</tt>. Where alpha and beta are scalars, x and y
+ * are n element vectors and A is an n by n symmetric matrix. A can be in upper or lower triangular format.
+ *
+ * @param isUpperTriangular is A upper triangular or lower triangular part to be used?
+ * @param alpha scaling factor.
+ * @param A the source matrix.
+ * @param x the first source vector.
+ * @param beta scaling factor.
+ * @param y the second vector holding source and destination.
+ */
+ void dsymv(boolean isUpperTriangular, double alpha, DoubleMatrix2D A, DoubleMatrix1D x, double beta,
+ DoubleMatrix1D y);
+
+ /**
+ * Triangular matrix-vector multiplication; <tt>x = A*x</tt> or <tt>x = A'*x</tt>. Where x is an n element vector and
+ * A is an n by n unit, or non-unit, upper or lower triangular matrix.
+ *
+ * @param isUpperTriangular is A upper triangular or lower triangular?
+ * @param transposeA set this flag to indicate that the multiplication shall be performed on A'.
+ * @param isUnitTriangular true --> A is assumed to be unit triangular; false --> A is not assumed to be unit
+ * triangular
+ * @param A the source matrix.
+ * @param x the vector holding source and destination.
+ */
+ void dtrmv(boolean isUpperTriangular, boolean transposeA, boolean isUnitTriangular, DoubleMatrix2D A,
+ DoubleMatrix1D x);
+
+ /**
+ * Returns the index of largest absolute value; <tt>i such that |x[i]| == max(|x[0]|,|x[1]|,...).</tt>.
+ *
+ * @param x the vector to search through.
+ * @return the index of largest absolute value (-1 if x is empty).
+ */
+ int idamax(DoubleMatrix1D x);
+
+
+}
Propchange: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Blas.java
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svn:eol-style = native
Added: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/CholeskyDecomposition.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/CholeskyDecomposition.java?rev=891983&view=auto
==============================================================================
--- lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/CholeskyDecomposition.java (added)
+++ lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/CholeskyDecomposition.java Thu Dec 17 23:22:16 2009
@@ -0,0 +1,228 @@
+/*
+Copyright � 1999 CERN - European Organization for Nuclear Research.
+Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
+is hereby granted without fee, provided that the above copyright notice appear in all copies and
+that both that copyright notice and this permission notice appear in supporting documentation.
+CERN makes no representations about the suitability of this software for any purpose.
+It is provided "as is" without expressed or implied warranty.
+*/
+package org.apache.mahout.math.matrix.linalg;
+
+import org.apache.mahout.math.jet.math.Functions;
+import org.apache.mahout.math.matrix.DoubleFactory2D;
+import org.apache.mahout.math.matrix.DoubleMatrix1D;
+import org.apache.mahout.math.matrix.DoubleMatrix2D;
+
+/** @deprecated until unit tests are in place. Until this time, this class/interface is unsupported. */
+@Deprecated
+public class CholeskyDecomposition implements java.io.Serializable {
+
+ /** Array for internal storage of decomposition. */
+ //private double[][] L;
+ private final DoubleMatrix2D L;
+
+ /** Row and column dimension (square matrix). */
+ private final int n;
+
+ /** Symmetric and positive definite flag. */
+ private boolean isSymmetricPositiveDefinite;
+
+ /**
+ * Constructs and returns a new Cholesky decomposition object for a symmetric and positive definite matrix; The
+ * decomposed matrices can be retrieved via instance methods of the returned decomposition object.
+ *
+ * @param A Square, symmetric matrix.
+ * @return Structure to access <tt>L</tt> and <tt>isSymmetricPositiveDefinite</tt> flag.
+ * @throws IllegalArgumentException if <tt>A</tt> is not square.
+ */
+ public CholeskyDecomposition(DoubleMatrix2D A) {
+ Property.DEFAULT.checkSquare(A);
+ // Initialize.
+ //double[][] A = Arg.getArray();
+
+ n = A.rows();
+ //L = new double[n][n];
+ L = A.like(n, n);
+ isSymmetricPositiveDefinite = (A.columns() == n);
+
+ //precompute and cache some views to avoid regenerating them time and again
+ DoubleMatrix1D[] Lrows = new DoubleMatrix1D[n];
+ for (int j = 0; j < n; j++) {
+ Lrows[j] = L.viewRow(j);
+ }
+
+ // Main loop.
+ for (int j = 0; j < n; j++) {
+ //double[] Lrowj = L[j];
+ //DoubleMatrix1D Lrowj = L.viewRow(j);
+ double d = 0.0;
+ for (int k = 0; k < j; k++) {
+ //double[] Lrowk = L[k];
+ double s = Lrows[k].zDotProduct(Lrows[j], 0, k);
+ /*
+ DoubleMatrix1D Lrowk = L.viewRow(k);
+ double s = 0.0;
+ for (int i = 0; i < k; i++) {
+ s += Lrowk.getQuick(i)*Lrowj.getQuick(i);
+ }
+ */
+ s = (A.getQuick(j, k) - s) / L.getQuick(k, k);
+ Lrows[j].setQuick(k, s);
+ d += s * s;
+ isSymmetricPositiveDefinite = isSymmetricPositiveDefinite && (A.getQuick(k, j) == A.getQuick(j, k));
+ }
+ d = A.getQuick(j, j) - d;
+ isSymmetricPositiveDefinite = isSymmetricPositiveDefinite && (d > 0.0);
+ L.setQuick(j, j, Math.sqrt(Math.max(d, 0.0)));
+
+ for (int k = j + 1; k < n; k++) {
+ L.setQuick(j, k, 0.0);
+ }
+ }
+ }
+
+ /**
+ * Returns the triangular factor, <tt>L</tt>.
+ *
+ * @return <tt>L</tt>
+ */
+ public DoubleMatrix2D getL() {
+ return L;
+ }
+
+ /**
+ * Returns whether the matrix <tt>A</tt> is symmetric and positive definite.
+ *
+ * @return true if <tt>A</tt> is symmetric and positive definite; false otherwise
+ */
+ public boolean isSymmetricPositiveDefinite() {
+ return isSymmetricPositiveDefinite;
+ }
+
+ /**
+ * Solves <tt>A*X = B</tt>; returns <tt>X</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*L'*X = B</tt>.
+ * @throws IllegalArgumentException if <tt>B.rows() != A.rows()</tt>.
+ * @throws IllegalArgumentException if <tt>!isSymmetricPositiveDefinite()</tt>.
+ */
+ public DoubleMatrix2D solve(DoubleMatrix2D B) {
+ // Copy right hand side.
+ DoubleMatrix2D X = B.copy();
+ int nx = B.columns();
+
+ // fix by MG Ferreira <mg...@webmail.co.za>
+ // old code is in method xxxSolveBuggy()
+ for (int c = 0; c < nx; c++) {
+ // Solve L*Y = B;
+ for (int i = 0; i < n; i++) {
+ double sum = B.getQuick(i, c);
+ for (int k = i - 1; k >= 0; k--) {
+ sum -= L.getQuick(i, k) * X.getQuick(k, c);
+ }
+ X.setQuick(i, c, sum / L.getQuick(i, i));
+ }
+
+ // Solve L'*X = Y;
+ for (int i = n - 1; i >= 0; i--) {
+ double sum = X.getQuick(i, c);
+ for (int k = i + 1; k < n; k++) {
+ sum -= L.getQuick(k, i) * X.getQuick(k, c);
+ }
+ X.setQuick(i, c, sum / L.getQuick(i, i));
+ }
+ }
+
+ return X;
+ }
+
+ /**
+ * Solves <tt>A*X = B</tt>; returns <tt>X</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*L'*X = B</tt>.
+ * @throws IllegalArgumentException if <tt>B.rows() != A.rows()</tt>.
+ * @throws IllegalArgumentException if <tt>!isSymmetricPositiveDefinite()</tt>.
+ */
+ private DoubleMatrix2D XXXsolveBuggy(DoubleMatrix2D B) {
+ if (B.rows() != n) {
+ throw new IllegalArgumentException("Matrix row dimensions must agree.");
+ }
+ if (!isSymmetricPositiveDefinite) {
+ throw new IllegalArgumentException("Matrix is not symmetric positive definite.");
+ }
+
+ // Copy right hand side.
+ DoubleMatrix2D X = B.copy();
+ //int nx = B.columns();
+
+ // precompute and cache some views to avoid regenerating them time and again
+ DoubleMatrix1D[] Xrows = new DoubleMatrix1D[n];
+ for (int k = 0; k < n; k++) {
+ Xrows[k] = X.viewRow(k);
+ }
+
+ // Solve L*Y = B;
+ for (int k = 0; k < n; k++) {
+ for (int i = k + 1; i < n; i++) {
+ // X[i,j] -= X[k,j]*L[i,k]
+ Xrows[i].assign(Xrows[k], Functions.minusMult(L.getQuick(i, k)));
+ }
+ Xrows[k].assign(Functions.div(L.getQuick(k, k)));
+ }
+
+ // Solve L'*X = Y;
+ for (int k = n - 1; k >= 0; k--) {
+ Xrows[k].assign(Functions.div(L.getQuick(k, k)));
+ for (int i = 0; i < k; i++) {
+ // X[i,j] -= X[k,j]*L[k,i]
+ Xrows[i].assign(Xrows[k], Functions.minusMult(L.getQuick(k, i)));
+ }
+ }
+ 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() {
+ StringBuilder buf = new StringBuilder();
+
+ buf.append("--------------------------------------------------------------------------\n");
+ buf.append("CholeskyDecomposition(A) --> isSymmetricPositiveDefinite(A), L, inverse(A)\n");
+ buf.append("--------------------------------------------------------------------------\n");
+
+ buf.append("isSymmetricPositiveDefinite = ");
+ String unknown = "Illegal operation or error: ";
+ try {
+ buf.append(String.valueOf(this.isSymmetricPositiveDefinite()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\n\nL = ");
+ try {
+ buf.append(String.valueOf(this.getL()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\n\ninverse(A) = ");
+ try {
+ buf.append(String.valueOf(this.solve(DoubleFactory2D.dense.identity(L.rows()))));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ return buf.toString();
+ }
+}
Propchange: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/CholeskyDecomposition.java
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Added: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Diagonal.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Diagonal.java?rev=891983&view=auto
==============================================================================
--- lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Diagonal.java (added)
+++ lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Diagonal.java Thu Dec 17 23:22:16 2009
@@ -0,0 +1,35 @@
+/*
+Copyright � 1999 CERN - European Organization for Nuclear Research.
+Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
+is hereby granted without fee, provided that the above copyright notice appear in all copies and
+that both that copyright notice and this permission notice appear in supporting documentation.
+CERN makes no representations about the suitability of this software for any purpose.
+It is provided "as is" without expressed or implied warranty.
+*/
+package org.apache.mahout.math.matrix.linalg;
+
+import org.apache.mahout.math.matrix.DoubleMatrix2D;
+
+/** For diagonal matrices we can often do better. */
+class Diagonal {
+
+ private Diagonal() {
+ }
+
+ /**
+ * Modifies A to hold its inverse.
+ *
+ * @return isNonSingular.
+ * @throws IllegalArgumentException if <tt>x.size() != y.size()</tt>.
+ */
+ public static boolean inverse(DoubleMatrix2D A) {
+ Property.DEFAULT.checkSquare(A);
+ boolean isNonSingular = true;
+ for (int i = A.rows(); --i >= 0;) {
+ double v = A.getQuick(i, i);
+ isNonSingular &= (v != 0);
+ A.setQuick(i, i, 1 / v);
+ }
+ return isNonSingular;
+ }
+}
Propchange: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Diagonal.java
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Added: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/EigenvalueDecomposition.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/EigenvalueDecomposition.java?rev=891983&view=auto
==============================================================================
--- lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/EigenvalueDecomposition.java (added)
+++ lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/EigenvalueDecomposition.java Thu Dec 17 23:22:16 2009
@@ -0,0 +1,969 @@
+/*
+Copyright � 1999 CERN - European Organization for Nuclear Research.
+Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
+is hereby granted without fee, provided that the above copyright notice appear in all copies and
+that both that copyright notice and this permission notice appear in supporting documentation.
+CERN makes no representations about the suitability of this software for any purpose.
+It is provided "as is" without expressed or implied warranty.
+*/
+package org.apache.mahout.math.matrix.linalg;
+
+import org.apache.mahout.math.matrix.DoubleFactory1D;
+import org.apache.mahout.math.matrix.DoubleFactory2D;
+import org.apache.mahout.math.matrix.DoubleMatrix1D;
+import org.apache.mahout.math.matrix.DoubleMatrix2D;
+
+/** @deprecated until unit tests are in place. Until this time, this class/interface is unsupported. */
+@Deprecated
+public class EigenvalueDecomposition implements java.io.Serializable {
+
+ /** Row and column dimension (square matrix). */
+ private final int n;
+
+ /** Arrays for internal storage of eigenvalues. */
+ private final double[] d, e;
+
+ /** Array for internal storage of eigenvectors. */
+ private final double[][] V;
+
+ /** Array for internal storage of nonsymmetric Hessenberg form. */
+ private double[][] H;
+
+ /** 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];
+
+ boolean 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);
+
+ // 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 += Math.abs(H[i][j]);
+ }
+ }
+
+ // Outer loop over eigenvalue index
+
+ int iter = 0;
+ double y;
+ double x;
+ double w;
+ double z = 0;
+ double s = 0;
+ double r = 0;
+ double q = 0;
+ double p = 0;
+ double exshift = 0.0;
+ 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] += 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] += exshift;
+ 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 /= r;
+ 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 -= 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 += 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 /= s;
+ q /= s;
+ 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 /= x;
+ q /= x;
+ 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 += s;
+ x = p / s;
+ y = q / s;
+ z = r / s;
+ q /= p;
+ r /= p;
+
+ // Row modification
+
+ for (int j = k; j < nn; j++) {
+ p = H[k][j] + q * H[k + 1][j];
+ if (notlast) {
+ p += r * H[k + 2][j];
+ H[k + 2][j] -= p * z;
+ }
+ H[k][j] -= p * x;
+ 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 += z * H[i][k + 2];
+ H[i][k + 2] -= p * r;
+ }
+ H[i][k] -= p;
+ 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 += z * V[i][k + 2];
+ V[i][k + 2] -= p * r;
+ }
+ V[i][k] -= p;
+ 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
+
+ double t;
+ 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 += 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] /= 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 = 0.0;
+ double sa = 0.0;
+ for (int j = l; j <= n; j++) {
+ ra += H[i][j] * H[j][n - 1];
+ 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];
+ double vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
+ double 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] /= t;
+ H[j][n] /= t;
+ }
+ }
+ }
+ }
+ }
+ }
+
+ // Vectors of isolated roots
+
+ for (int i = 0; i < nn; i++) {
+ if (i < low || i > high) {
+ System.arraycopy(H[i], i, V[i], i, nn - i);
+ }
+ }
+
+ // 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 += 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 += 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 -= ort[m] * g;
+ 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 /= 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 /= 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() {
+ StringBuilder buf = new StringBuilder();
+
+ buf.append("---------------------------------------------------------------------\n");
+ buf.append("EigenvalueDecomposition(A) --> D, V, realEigenvalues, imagEigenvalues\n");
+ buf.append("---------------------------------------------------------------------\n");
+
+ buf.append("realEigenvalues = ");
+ String unknown = "Illegal operation or error: ";
+ try {
+ buf.append(String.valueOf(this.getRealEigenvalues()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\nimagEigenvalues = ");
+ try {
+ buf.append(String.valueOf(this.getImagEigenvalues()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\n\nD = ");
+ try {
+ buf.append(String.valueOf(this.getD()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\n\nV = ");
+ try {
+ buf.append(String.valueOf(this.getV()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ return buf.toString();
+ }
+
+ /** 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.
+
+ System.arraycopy(e, 1, e, 0, n - 1);
+ 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 += 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 += 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] += 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.
+
+
+ System.arraycopy(V[n - 1], 0, d, 0, n);
+
+
+ // Householder reduction to tridiagonal form.
+
+ for (int i = n - 1; i > 0; i--) {
+
+ // Scale to avoid under/overflow.
+
+ double scale = 0.0;
+ for (int k = 0; k < i; k++) {
+ scale += Math.abs(d[k]);
+ }
+ double h = 0.0;
+ 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 -= 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/math/src/main/java/org/apache/mahout/math/matrix/linalg/EigenvalueDecomposition.java
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svn:eol-style = native
Added: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecomposition.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecomposition.java?rev=891983&view=auto
==============================================================================
--- lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecomposition.java (added)
+++ lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecomposition.java Thu Dec 17 23:22:16 2009
@@ -0,0 +1,123 @@
+/*
+Copyright � 1999 CERN - European Organization for Nuclear Research.
+Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
+is hereby granted without fee, provided that the above copyright notice appear in all copies and
+that both that copyright notice and this permission notice appear in supporting documentation.
+CERN makes no representations about the suitability of this software for any purpose.
+It is provided "as is" without expressed or implied warranty.
+*/
+package org.apache.mahout.math.matrix.linalg;
+
+import org.apache.mahout.math.matrix.DoubleMatrix2D;
+
+/**
+ * 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 until unit tests are in place. Until this time, this class/interface is unsupported. */
+@Deprecated
+public class LUDecomposition implements java.io.Serializable {
+
+ private final 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>.
+ *
+ * @throws 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 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>.
+ * @throws IllegalArgumentException if </tt>B.rows() != A.rows()</tt>.
+ * @throws IllegalArgumentException if A is singular, that is, if <tt>!this.isNonsingular()</tt>.
+ * @throws 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/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecomposition.java
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svn:eol-style = native
Added: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecompositionQuick.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecompositionQuick.java?rev=891983&view=auto
==============================================================================
--- lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecompositionQuick.java (added)
+++ lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecompositionQuick.java Thu Dec 17 23:22:16 2009
@@ -0,0 +1,694 @@
+/*
+Copyright 1999 CERN - European Organization for Nuclear Research.
+Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
+is hereby granted without fee, provided that the above copyright notice appear in all copies and
+that both that copyright notice and this permission notice appear in supporting documentation.
+CERN makes no representations about the suitability of this software for any purpose.
+It is provided "as is" without expressed or implied warranty.
+*/
+package org.apache.mahout.math.matrix.linalg;
+
+import org.apache.mahout.math.jet.math.Mult;
+import org.apache.mahout.math.jet.math.PlusMult;
+import org.apache.mahout.math.list.IntArrayList;
+import org.apache.mahout.math.matrix.DoubleMatrix1D;
+import org.apache.mahout.math.matrix.DoubleMatrix2D;
+
+/** @deprecated until unit tests are in place. Until this time, this class/interface is unsupported. */
+@Deprecated
+public class LUDecompositionQuick implements java.io.Serializable {
+
+ /** Array for internal storage of decomposition. */
+ private DoubleMatrix2D LU;
+
+ /** pivot sign. */
+ private int pivsign;
+
+ /** Internal storage of pivot vector. */
+ private int[] piv;
+
+ private boolean isNonSingular;
+
+ private final Algebra algebra;
+
+ private transient double[] workDouble;
+ private transient int[] work1;
+ protected transient 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) {
+ // 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);
+ }
+
+ IntArrayList nonZeroIndexes =
+ new IntArrayList(); // sparsity
+ DoubleMatrix1D LUcolj = LU.viewColumn(0).like(); // blocked column j
+ Mult multFunction = org.apache.mahout.math.jet.math.Mult.mult(0);
+
+ // Outer loop.
+ int CUT_OFF = 10;
+ 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.setMultiplicator(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>.
+ *
+ * @throws 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).
+ */
+ 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>.
+ * @throws IllegalArgumentException if </tt>B.size() != A.rows()</tt>.
+ * @throws IllegalArgumentException if A is singular, that is, if <tt>!isNonsingular()</tt>.
+ * @throws 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.
+ * @throws IllegalArgumentException if </tt>B.rows() != A.rows()</tt>.
+ * @throws IllegalArgumentException if A is singular, that is, if <tt>!isNonsingular()</tt>.
+ * @throws IllegalArgumentException if <tt>A.rows() < A.columns()</tt>.
+ */
+ public void solve(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.");
+ }
+
+
+ // 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
+ Mult div = org.apache.mahout.math.jet.math.Mult.div(0);
+ PlusMult minusMult = org.apache.mahout.math.jet.math.PlusMult.minusMult(0);
+
+ IntArrayList nonZeroIndexes =
+ new IntArrayList(); // sparsity
+ DoubleMatrix1D Browk = org.apache.mahout.math.matrix.DoubleFactory1D.dense.make(nx); // blocked row k
+
+ // Solve L*Y = B(piv,:)
+ int CUT_OFF = 10;
+ 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.setMultiplicator(-LU.getQuick(i, k));
+ if (minusMult.getMultiplicator() != 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.setMultiplicator(1 / LU.getQuick(k, k));
+ Brows[k].assign(div);
+
+ // blocking
+ if (Browk == null) {
+ Browk = org.apache.mahout.math.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.setMultiplicator(-LU.getQuick(i, k));
+ if (minusMult.getMultiplicator() != 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>.
+ * @throws IllegalArgumentException if </tt>B.rows() != A.rows()</tt>.
+ * @throws IllegalArgumentException if A is singular, that is, if <tt>!this.isNonsingular()</tt>.
+ * @throws 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() {
+ StringBuilder buf = new StringBuilder();
+
+ buf.append("-----------------------------------------------------------------------------\n");
+ buf.append("LUDecompositionQuick(A) --> isNonSingular(A), det(A), pivot, L, U, inverse(A)\n");
+ buf.append("-----------------------------------------------------------------------------\n");
+
+ buf.append("isNonSingular = ");
+ String unknown = "Illegal operation or error: ";
+ try {
+ buf.append(String.valueOf(this.isNonsingular()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\ndet = ");
+ try {
+ buf.append(String.valueOf(this.det()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\npivot = ");
+ try {
+ buf.append(String.valueOf(new IntArrayList(this.getPivot())));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\n\nL = ");
+ try {
+ buf.append(String.valueOf(this.getL()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\n\nU = ");
+ try {
+ buf.append(String.valueOf(this.getU()));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ buf.append("\n\ninverse(A) = ");
+ DoubleMatrix2D identity = org.apache.mahout.math.matrix.DoubleFactory2D.dense.identity(LU.rows());
+ try {
+ this.solve(identity);
+ buf.append(String.valueOf(identity));
+ }
+ catch (IllegalArgumentException exc) {
+ buf.append(unknown).append(exc.getMessage());
+ }
+
+ return buf.toString();
+ }
+
+ /**
+ * Modifies the matrix to be an upper triangular matrix.
+ *
+ * @return <tt>A</tt> (for convenience only).
+ */
+ 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;
+ }
+
+}
Propchange: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/LUDecompositionQuick.java
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Added: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Matrix2DMatrix2DFunction.java
URL: http://svn.apache.org/viewvc/lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Matrix2DMatrix2DFunction.java?rev=891983&view=auto
==============================================================================
--- lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Matrix2DMatrix2DFunction.java (added)
+++ lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Matrix2DMatrix2DFunction.java Thu Dec 17 23:22:16 2009
@@ -0,0 +1,25 @@
+/*
+Copyright 1999 CERN - European Organization for Nuclear Research.
+Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose
+is hereby granted without fee, provided that the above copyright notice appear in all copies and
+that both that copyright notice and this permission notice appear in supporting documentation.
+CERN makes no representations about the suitability of this software for any purpose.
+It is provided "as is" without expressed or implied warranty.
+*/
+package org.apache.mahout.math.matrix.linalg;
+
+import org.apache.mahout.math.matrix.DoubleMatrix2D;
+
+/** @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.
+ */
+ double apply(DoubleMatrix2D x, DoubleMatrix2D y);
+}
Propchange: lucene/mahout/trunk/math/src/main/java/org/apache/mahout/math/matrix/linalg/Matrix2DMatrix2DFunction.java
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