Merged FieldLUDecomposition and FieldLUDecompositionImpl (see MATH-662).

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1174537 13f79535-47bb-0310-9956-ffa450edef68

src/main/java/org/apache/commons/math/linear/FieldLUDecomposition.java

@@ -17,49 +17,192 @@
 
 package org.apache.commons.math.linear;
 
+import java.lang.reflect.Array;
+
+import org.apache.commons.math.Field;
 import org.apache.commons.math.FieldElement;
+import org.apache.commons.math.exception.DimensionMismatchException;
 
 /**
- * An interface to classes that implement an algorithm to calculate the
+ * Calculates the LUP-decomposition of a square matrix.
- * LU-decomposition of a real matrix.
+ * <p>The LUP-decomposition of a matrix A consists of three matrices
- * <p>The LU-decomposition of matrix A is a set of three matrices: P, L and U
+ * L, U and P that satisfy: PA = LU, L is lower triangular, and U is
- * such that P&times;A = L&times;U. P is a rows permutation matrix that is used
+ * upper triangular and P is a permutation matrix. All matrices are
- * to rearrange the rows of A before so that it can be decomposed. L is a lower
+ * m&times;m.</p>
- * triangular matrix with unit diagonal terms and U is an upper triangular matrix.</p>
+ * <p>Since {@link FieldElement field elements} do not provide an ordering
- * <p>This interface is based on the class with similar name from the
+ * operator, the permutation matrix is computed here only in order to avoid
+ * a zero pivot element, no attempt is done to get the largest pivot
+ * element.</p>
+ * <p>This class is based on the class with similar name from the
  * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p>
  * <ul>
  *   <li>a {@link #getP() getP} method has been added,</li>
- *   <li>the <code>det</code> method has been renamed as {@link #getDeterminant()
+ *   <li>the {@code det} method has been renamed as {@link #getDeterminant()
  *   getDeterminant},</li>
- *   <li>the <code>getDoublePivot</code> method has been removed (but the int based
+ *   <li>the {@code getDoublePivot} method has been removed (but the int based
  *   {@link #getPivot() getPivot} method has been kept),</li>
- *   <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced
+ *   <li>the {@code solve} and {@code isNonSingular} methods have been replaced
- *   by a {@link #getSolver() getSolver} method and the equivalent methods provided by
+ *   by a {@link #getSolver() getSolver} method and the equivalent methods
- *   the returned {@link DecompositionSolver}.</li>
+ *   provided by the returned {@link DecompositionSolver}.</li>
  * </ul>
  *
  * @param <T> the type of the field elements
  * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a>
  * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a>
  * @version $Id$
- * @since 2.0
+ * @since 2.0 (changed to concrete class in 3.0)
  */
-public interface FieldLUDecomposition<T extends FieldElement<T>> {
+public class FieldLUDecomposition<T extends FieldElement<T>> {
+
+    /** Field to which the elements belong. */
+    private final Field<T> field;
+
+    /** Entries of LU decomposition. */
+    private T[][] lu;
+
+    /** Pivot permutation associated with LU decomposition. */
+    private int[] pivot;
+
+    /** Parity of the permutation associated with the LU decomposition. */
+    private boolean even;
+
+    /** Singularity indicator. */
+    private boolean singular;
+
+    /** Cached value of L. */
+    private FieldMatrix<T> cachedL;
+
+    /** Cached value of U. */
+    private FieldMatrix<T> cachedU;
+
+    /** Cached value of P. */
+    private FieldMatrix<T> cachedP;
+
+    /**
+     * Calculates the LU-decomposition of the given matrix.
+     * @param matrix The matrix to decompose.
+     * @throws NonSquareMatrixException if matrix is not square
+     */
+    public FieldLUDecomposition(FieldMatrix<T> matrix) {
+        if (!matrix.isSquare()) {
+            throw new NonSquareMatrixException(matrix.getRowDimension(),
+                                               matrix.getColumnDimension());
+        }
+
+        final int m = matrix.getColumnDimension();
+        field = matrix.getField();
+        lu = matrix.getData();
+        pivot = new int[m];
+        cachedL = null;
+        cachedU = null;
+        cachedP = null;
+
+        // Initialize permutation array and parity
+        for (int row = 0; row < m; row++) {
+            pivot[row] = row;
+        }
+        even     = true;
+        singular = false;
+
+        // Loop over columns
+        for (int col = 0; col < m; col++) {
+
+            T sum = field.getZero();
+
+            // upper
+            for (int row = 0; row < col; row++) {
+                final T[] luRow = lu[row];
+                sum = luRow[col];
+                for (int i = 0; i < row; i++) {
+                    sum = sum.subtract(luRow[i].multiply(lu[i][col]));
+                }
+                luRow[col] = sum;
+            }
+
+            // lower
+            int nonZero = col; // permutation row
+            for (int row = col; row < m; row++) {
+                final T[] luRow = lu[row];
+                sum = luRow[col];
+                for (int i = 0; i < col; i++) {
+                    sum = sum.subtract(luRow[i].multiply(lu[i][col]));
+                }
+                luRow[col] = sum;
+
+                if (lu[nonZero][col].equals(field.getZero())) {
+                    // try to select a better permutation choice
+                    ++nonZero;
+                }
+            }
+
+            // Singularity check
+            if (nonZero >= m) {
+                singular = true;
+                return;
+            }
+
+            // Pivot if necessary
+            if (nonZero != col) {
+                T tmp = field.getZero();
+                for (int i = 0; i < m; i++) {
+                    tmp = lu[nonZero][i];
+                    lu[nonZero][i] = lu[col][i];
+                    lu[col][i] = tmp;
+                }
+                int temp = pivot[nonZero];
+                pivot[nonZero] = pivot[col];
+                pivot[col] = temp;
+                even = !even;
+            }
+
+            // Divide the lower elements by the "winning" diagonal elt.
+            final T luDiag = lu[col][col];
+            for (int row = col + 1; row < m; row++) {
+                final T[] luRow = lu[row];
+                luRow[col] = luRow[col].divide(luDiag);
+            }
+        }
+
+    }
 
     /**
      * Returns the matrix L of the decomposition.
-     * <p>L is an lower-triangular matrix</p>
+     * <p>L is a lower-triangular matrix</p>
      * @return the L matrix (or null if decomposed matrix is singular)
      */
-    FieldMatrix<T> getL();
+    public FieldMatrix<T> getL() {
+        if ((cachedL == null) && !singular) {
+            final int m = pivot.length;
+            cachedL = new Array2DRowFieldMatrix<T>(field, m, m);
+            for (int i = 0; i < m; ++i) {
+                final T[] luI = lu[i];
+                for (int j = 0; j < i; ++j) {
+                    cachedL.setEntry(i, j, luI[j]);
+                }
+                cachedL.setEntry(i, i, field.getOne());
+            }
+        }
+        return cachedL;
+    }
 
     /**
      * Returns the matrix U of the decomposition.
      * <p>U is an upper-triangular matrix</p>
      * @return the U matrix (or null if decomposed matrix is singular)
      */
-    FieldMatrix<T> getU();
+    public FieldMatrix<T> getU() {
+        if ((cachedU == null) && !singular) {
+            final int m = pivot.length;
+            cachedU = new Array2DRowFieldMatrix<T>(field, m, m);
+            for (int i = 0; i < m; ++i) {
+                final T[] luI = lu[i];
+                for (int j = i; j < m; ++j) {
+                    cachedU.setEntry(i, j, luI[j]);
+                }
+            }
+        }
+        return cachedU;
+    }
 
     /**
      * Returns the P rows permutation matrix.
@@ -70,25 +213,240 @@ public interface FieldLUDecomposition<T extends FieldElement<T>> {
      * @return the P rows permutation matrix (or null if decomposed matrix is singular)
      * @see #getPivot()
      */
-    FieldMatrix<T> getP();
+    public FieldMatrix<T> getP() {
+        if ((cachedP == null) && !singular) {
+            final int m = pivot.length;
+            cachedP = new Array2DRowFieldMatrix<T>(field, m, m);
+            for (int i = 0; i < m; ++i) {
+                cachedP.setEntry(i, pivot[i], field.getOne());
+            }
+        }
+        return cachedP;
+    }
 
     /**
      * Returns the pivot permutation vector.
      * @return the pivot permutation vector
      * @see #getP()
      */
-    int[] getPivot();
+    public int[] getPivot() {
+        return pivot.clone();
+    }
 
     /**
-     * Return the determinant of the matrix
+     * Return the determinant of the matrix.
      * @return determinant of the matrix
      */
-    T getDeterminant();
+    public T getDeterminant() {
+        if (singular) {
+            return field.getZero();
+        } else {
+            final int m = pivot.length;
+            T determinant = even ? field.getOne() : field.getZero().subtract(field.getOne());
+            for (int i = 0; i < m; i++) {
+                determinant = determinant.multiply(lu[i][i]);
+            }
+            return determinant;
+        }
+    }
 
     /**
      * Get a solver for finding the A &times; X = B solution in exact linear sense.
      * @return a solver
      */
-    FieldDecompositionSolver<T> getSolver();
+    public FieldDecompositionSolver<T> getSolver() {
+        return new Solver<T>(field, lu, pivot, singular);
+    }
 
+    /** Specialized solver. */
+    private static class Solver<T extends FieldElement<T>> implements FieldDecompositionSolver<T> {
+
+        /** Field to which the elements belong. */
+        private final Field<T> field;
+
+        /** Entries of LU decomposition. */
+        private final T[][] lu;
+
+        /** Pivot permutation associated with LU decomposition. */
+        private final int[] pivot;
+
+        /** Singularity indicator. */
+        private final boolean singular;
+
+        /**
+         * Build a solver from decomposed matrix.
+         * @param field field to which the matrix elements belong
+         * @param lu entries of LU decomposition
+         * @param pivot pivot permutation associated with LU decomposition
+         * @param singular singularity indicator
+         */
+        private Solver(final Field<T> field, final T[][] lu,
+                       final int[] pivot, final boolean singular) {
+            this.field    = field;
+            this.lu       = lu;
+            this.pivot    = pivot;
+            this.singular = singular;
+        }
+
+        /** {@inheritDoc} */
+        public boolean isNonSingular() {
+            return !singular;
+        }
+
+        /** {@inheritDoc} */
+        public FieldVector<T> solve(FieldVector<T> b) {
+            try {
+                return solve((ArrayFieldVector<T>) b);
+            } catch (ClassCastException cce) {
+
+                final int m = pivot.length;
+                if (b.getDimension() != m) {
+                    throw new DimensionMismatchException(b.getDimension(), m);
+                }
+                if (singular) {
+                    throw new SingularMatrixException();
+                }
+
+                @SuppressWarnings("unchecked") // field is of type T
+                final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), m);
+
+                // Apply permutations to b
+                for (int row = 0; row < m; row++) {
+                    bp[row] = b.getEntry(pivot[row]);
+                }
+
+                // Solve LY = b
+                for (int col = 0; col < m; col++) {
+                    final T bpCol = bp[col];
+                    for (int i = col + 1; i < m; i++) {
+                        bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
+                    }
+                }
+
+                // Solve UX = Y
+                for (int col = m - 1; col >= 0; col--) {
+                    bp[col] = bp[col].divide(lu[col][col]);
+                    final T bpCol = bp[col];
+                    for (int i = 0; i < col; i++) {
+                        bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
+                    }
+                }
+
+                return new ArrayFieldVector<T>(field, bp, false);
+
+            }
+        }
+
+        /** Solve the linear equation A &times; X = B.
+         * <p>The A matrix is implicit here. It is </p>
+         * @param b right-hand side of the equation A &times; X = B
+         * @return a vector X such that A &times; X = B
+         * @throws DimensionMismatchException if the matrices dimensions do not match.
+         * @throws SingularMatrixException if the decomposed matrix is singular.
+         */
+        public ArrayFieldVector<T> solve(ArrayFieldVector<T> b) {
+            final int m = pivot.length;
+            if (b.data.length != m) {
+                throw new DimensionMismatchException(b.data.length, m);
+            }
+            if (singular) {
+                throw new SingularMatrixException();
+            }
+
+            @SuppressWarnings("unchecked")
+            // field is of type T
+            final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(),
+                                                   m);
+
+            // Apply permutations to b
+            for (int row = 0; row < m; row++) {
+                bp[row] = b.data[pivot[row]];
+            }
+
+            // Solve LY = b
+            for (int col = 0; col < m; col++) {
+                final T bpCol = bp[col];
+                for (int i = col + 1; i < m; i++) {
+                    bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
+                }
+            }
+
+            // Solve UX = Y
+            for (int col = m - 1; col >= 0; col--) {
+                bp[col] = bp[col].divide(lu[col][col]);
+                final T bpCol = bp[col];
+                for (int i = 0; i < col; i++) {
+                    bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
+                }
+            }
+
+            return new ArrayFieldVector<T>(bp, false);
+        }
+
+        /** {@inheritDoc} */
+        public FieldMatrix<T> solve(FieldMatrix<T> b) {
+            final int m = pivot.length;
+            if (b.getRowDimension() != m) {
+                throw new DimensionMismatchException(b.getRowDimension(), m);
+            }
+            if (singular) {
+                throw new SingularMatrixException();
+            }
+
+            final int nColB = b.getColumnDimension();
+
+            // Apply permutations to b
+            @SuppressWarnings("unchecked") // field is of type T
+            final T[][] bp = (T[][]) Array.newInstance(field.getZero().getClass(), new int[] { m, nColB });
+            for (int row = 0; row < m; row++) {
+                final T[] bpRow = bp[row];
+                final int pRow = pivot[row];
+                for (int col = 0; col < nColB; col++) {
+                    bpRow[col] = b.getEntry(pRow, col);
+                }
+            }
+
+            // Solve LY = b
+            for (int col = 0; col < m; col++) {
+                final T[] bpCol = bp[col];
+                for (int i = col + 1; i < m; i++) {
+                    final T[] bpI = bp[i];
+                    final T luICol = lu[i][col];
+                    for (int j = 0; j < nColB; j++) {
+                        bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));
+                    }
+                }
+            }
+
+            // Solve UX = Y
+            for (int col = m - 1; col >= 0; col--) {
+                final T[] bpCol = bp[col];
+                final T luDiag = lu[col][col];
+                for (int j = 0; j < nColB; j++) {
+                    bpCol[j] = bpCol[j].divide(luDiag);
+                }
+                for (int i = 0; i < col; i++) {
+                    final T[] bpI = bp[i];
+                    final T luICol = lu[i][col];
+                    for (int j = 0; j < nColB; j++) {
+                        bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));
+                    }
+                }
+            }
+
+            return new Array2DRowFieldMatrix<T>(field, bp, false);
+
+        }
+
+        /** {@inheritDoc} */
+        public FieldMatrix<T> getInverse() {
+            final int m = pivot.length;
+            final T one = field.getOne();
+            FieldMatrix<T> identity = new Array2DRowFieldMatrix<T>(field, m, m);
+            for (int i = 0; i < m; ++i) {
+                identity.setEntry(i, i, one);
+            }
+            return solve(identity);
+        }
+    }
 }

src/main/java/org/apache/commons/math/linear/FieldLUDecompositionImpl.java

@@ -1,411 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements.  See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License.  You may obtain a copy of the License at
- *
- *      http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-package org.apache.commons.math.linear;
-
-import java.lang.reflect.Array;
-
-import org.apache.commons.math.Field;
-import org.apache.commons.math.FieldElement;
-import org.apache.commons.math.exception.DimensionMismatchException;
-
-/**
- * Calculates the LUP-decomposition of a square matrix.
- * <p>The LUP-decomposition of a matrix A consists of three matrices
- * L, U and P that satisfy: PA = LU, L is lower triangular, and U is
- * upper triangular and P is a permutation matrix. All matrices are
- * m&times;m.</p>
- * <p>Since {@link FieldElement field elements} do not provide an ordering
- * operator, the permutation matrix is computed here only in order to avoid
- * a zero pivot element, no attempt is done to get the largest pivot element.</p>
- *
- * @param <T> the type of the field elements
- * @version $Id$
- * @since 2.0
- */
-public class FieldLUDecompositionImpl<T extends FieldElement<T>> implements FieldLUDecomposition<T> {
-
-    /** Field to which the elements belong. */
-    private final Field<T> field;
-
-    /** Entries of LU decomposition. */
-    private T lu[][];
-
-    /** Pivot permutation associated with LU decomposition */
-    private int[] pivot;
-
-    /** Parity of the permutation associated with the LU decomposition */
-    private boolean even;
-
-    /** Singularity indicator. */
-    private boolean singular;
-
-    /** Cached value of L. */
-    private FieldMatrix<T> cachedL;
-
-    /** Cached value of U. */
-    private FieldMatrix<T> cachedU;
-
-    /** Cached value of P. */
-    private FieldMatrix<T> cachedP;
-
-    /**
-     * Calculates the LU-decomposition of the given matrix.
-     * @param matrix The matrix to decompose.
-     * @throws NonSquareMatrixException if matrix is not square
-     */
-    public FieldLUDecompositionImpl(FieldMatrix<T> matrix) {
-        if (!matrix.isSquare()) {
-            throw new NonSquareMatrixException(matrix.getRowDimension(),
-                                               matrix.getColumnDimension());
-        }
-
-        final int m = matrix.getColumnDimension();
-        field = matrix.getField();
-        lu = matrix.getData();
-        pivot = new int[m];
-        cachedL = null;
-        cachedU = null;
-        cachedP = null;
-
-        // Initialize permutation array and parity
-        for (int row = 0; row < m; row++) {
-            pivot[row] = row;
-        }
-        even     = true;
-        singular = false;
-
-        // Loop over columns
-        for (int col = 0; col < m; col++) {
-
-            T sum = field.getZero();
-
-            // upper
-            for (int row = 0; row < col; row++) {
-                final T[] luRow = lu[row];
-                sum = luRow[col];
-                for (int i = 0; i < row; i++) {
-                    sum = sum.subtract(luRow[i].multiply(lu[i][col]));
-                }
-                luRow[col] = sum;
-            }
-
-            // lower
-            int nonZero = col; // permutation row
-            for (int row = col; row < m; row++) {
-                final T[] luRow = lu[row];
-                sum = luRow[col];
-                for (int i = 0; i < col; i++) {
-                    sum = sum.subtract(luRow[i].multiply(lu[i][col]));
-                }
-                luRow[col] = sum;
-
-                if (lu[nonZero][col].equals(field.getZero())) {
-                    // try to select a better permutation choice
-                    ++nonZero;
-                }
-            }
-
-            // Singularity check
-            if (nonZero >= m) {
-                singular = true;
-                return;
-            }
-
-            // Pivot if necessary
-            if (nonZero != col) {
-                T tmp = field.getZero();
-                for (int i = 0; i < m; i++) {
-                    tmp = lu[nonZero][i];
-                    lu[nonZero][i] = lu[col][i];
-                    lu[col][i] = tmp;
-                }
-                int temp = pivot[nonZero];
-                pivot[nonZero] = pivot[col];
-                pivot[col] = temp;
-                even = !even;
-            }
-
-            // Divide the lower elements by the "winning" diagonal elt.
-            final T luDiag = lu[col][col];
-            for (int row = col + 1; row < m; row++) {
-                final T[] luRow = lu[row];
-                luRow[col] = luRow[col].divide(luDiag);
-            }
-        }
-
-    }
-
-    /** {@inheritDoc} */
-    public FieldMatrix<T> getL() {
-        if ((cachedL == null) && !singular) {
-            final int m = pivot.length;
-            cachedL = new Array2DRowFieldMatrix<T>(field, m, m);
-            for (int i = 0; i < m; ++i) {
-                final T[] luI = lu[i];
-                for (int j = 0; j < i; ++j) {
-                    cachedL.setEntry(i, j, luI[j]);
-                }
-                cachedL.setEntry(i, i, field.getOne());
-            }
-        }
-        return cachedL;
-    }
-
-    /** {@inheritDoc} */
-    public FieldMatrix<T> getU() {
-        if ((cachedU == null) && !singular) {
-            final int m = pivot.length;
-            cachedU = new Array2DRowFieldMatrix<T>(field, m, m);
-            for (int i = 0; i < m; ++i) {
-                final T[] luI = lu[i];
-                for (int j = i; j < m; ++j) {
-                    cachedU.setEntry(i, j, luI[j]);
-                }
-            }
-        }
-        return cachedU;
-    }
-
-    /** {@inheritDoc} */
-    public FieldMatrix<T> getP() {
-        if ((cachedP == null) && !singular) {
-            final int m = pivot.length;
-            cachedP = new Array2DRowFieldMatrix<T>(field, m, m);
-            for (int i = 0; i < m; ++i) {
-                cachedP.setEntry(i, pivot[i], field.getOne());
-            }
-        }
-        return cachedP;
-    }
-
-    /** {@inheritDoc} */
-    public int[] getPivot() {
-        return pivot.clone();
-    }
-
-    /** {@inheritDoc} */
-    public T getDeterminant() {
-        if (singular) {
-            return field.getZero();
-        } else {
-            final int m = pivot.length;
-            T determinant = even ? field.getOne() : field.getZero().subtract(field.getOne());
-            for (int i = 0; i < m; i++) {
-                determinant = determinant.multiply(lu[i][i]);
-            }
-            return determinant;
-        }
-    }
-
-    /** {@inheritDoc} */
-    public FieldDecompositionSolver<T> getSolver() {
-        return new Solver<T>(field, lu, pivot, singular);
-    }
-
-    /** Specialized solver. */
-    private static class Solver<T extends FieldElement<T>> implements FieldDecompositionSolver<T> {
-
-        /** Field to which the elements belong. */
-        private final Field<T> field;
-
-        /** Entries of LU decomposition. */
-        private final T lu[][];
-
-        /** Pivot permutation associated with LU decomposition. */
-        private final int[] pivot;
-
-        /** Singularity indicator. */
-        private final boolean singular;
-
-        /**
-         * Build a solver from decomposed matrix.
-         * @param field field to which the matrix elements belong
-         * @param lu entries of LU decomposition
-         * @param pivot pivot permutation associated with LU decomposition
-         * @param singular singularity indicator
-         */
-        private Solver(final Field<T> field, final T[][] lu,
-                       final int[] pivot, final boolean singular) {
-            this.field    = field;
-            this.lu       = lu;
-            this.pivot    = pivot;
-            this.singular = singular;
-        }
-
-        /** {@inheritDoc} */
-        public boolean isNonSingular() {
-            return !singular;
-        }
-
-        /** {@inheritDoc} */
-        public FieldVector<T> solve(FieldVector<T> b) {
-            try {
-                return solve((ArrayFieldVector<T>) b);
-            } catch (ClassCastException cce) {
-
-                final int m = pivot.length;
-                if (b.getDimension() != m) {
-                    throw new DimensionMismatchException(b.getDimension(), m);
-                }
-                if (singular) {
-                    throw new SingularMatrixException();
-                }
-
-                @SuppressWarnings("unchecked") // field is of type T
-                final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), m);
-
-                // Apply permutations to b
-                for (int row = 0; row < m; row++) {
-                    bp[row] = b.getEntry(pivot[row]);
-                }
-
-                // Solve LY = b
-                for (int col = 0; col < m; col++) {
-                    final T bpCol = bp[col];
-                    for (int i = col + 1; i < m; i++) {
-                        bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
-                    }
-                }
-
-                // Solve UX = Y
-                for (int col = m - 1; col >= 0; col--) {
-                    bp[col] = bp[col].divide(lu[col][col]);
-                    final T bpCol = bp[col];
-                    for (int i = 0; i < col; i++) {
-                        bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
-                    }
-                }
-
-                return new ArrayFieldVector<T>(field, bp, false);
-
-            }
-        }
-
-        /** Solve the linear equation A &times; X = B.
-         * <p>The A matrix is implicit here. It is </p>
-         * @param b right-hand side of the equation A &times; X = B
-         * @return a vector X such that A &times; X = B
-         * @throws DimensionMismatchException if the matrices dimensions do not match.
-         * @throws SingularMatrixException if the decomposed matrix is singular.
-         */
-        public ArrayFieldVector<T> solve(ArrayFieldVector<T> b) {
-            final int m = pivot.length;
-            if (b.data.length != m) {
-                throw new DimensionMismatchException(b.data.length, m);
-            }
-            if (singular) {
-                throw new SingularMatrixException();
-            }
-
-            @SuppressWarnings("unchecked")
-            // field is of type T
-            final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(),
-                                                   m);
-
-            // Apply permutations to b
-            for (int row = 0; row < m; row++) {
-                bp[row] = b.data[pivot[row]];
-            }
-
-            // Solve LY = b
-            for (int col = 0; col < m; col++) {
-                final T bpCol = bp[col];
-                for (int i = col + 1; i < m; i++) {
-                    bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
-                }
-            }
-
-            // Solve UX = Y
-            for (int col = m - 1; col >= 0; col--) {
-                bp[col] = bp[col].divide(lu[col][col]);
-                final T bpCol = bp[col];
-                for (int i = 0; i < col; i++) {
-                    bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));
-                }
-            }
-
-            return new ArrayFieldVector<T>(bp, false);
-        }
-
-        /** {@inheritDoc} */
-        public FieldMatrix<T> solve(FieldMatrix<T> b) {
-            final int m = pivot.length;
-            if (b.getRowDimension() != m) {
-                throw new DimensionMismatchException(b.getRowDimension(), m);
-            }
-            if (singular) {
-                throw new SingularMatrixException();
-            }
-
-            final int nColB = b.getColumnDimension();
-
-            // Apply permutations to b
-            @SuppressWarnings("unchecked") // field is of type T
-            final T[][] bp = (T[][]) Array.newInstance(field.getZero().getClass(), new int[] { m, nColB });
-            for (int row = 0; row < m; row++) {
-                final T[] bpRow = bp[row];
-                final int pRow = pivot[row];
-                for (int col = 0; col < nColB; col++) {
-                    bpRow[col] = b.getEntry(pRow, col);
-                }
-            }
-
-            // Solve LY = b
-            for (int col = 0; col < m; col++) {
-                final T[] bpCol = bp[col];
-                for (int i = col + 1; i < m; i++) {
-                    final T[] bpI = bp[i];
-                    final T luICol = lu[i][col];
-                    for (int j = 0; j < nColB; j++) {
-                        bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));
-                    }
-                }
-            }
-
-            // Solve UX = Y
-            for (int col = m - 1; col >= 0; col--) {
-                final T[] bpCol = bp[col];
-                final T luDiag = lu[col][col];
-                for (int j = 0; j < nColB; j++) {
-                    bpCol[j] = bpCol[j].divide(luDiag);
-                }
-                for (int i = 0; i < col; i++) {
-                    final T[] bpI = bp[i];
-                    final T luICol = lu[i][col];
-                    for (int j = 0; j < nColB; j++) {
-                        bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));
-                    }
-                }
-            }
-
-            return new Array2DRowFieldMatrix<T>(field, bp, false);
-
-        }
-
-        /** {@inheritDoc} */
-        public FieldMatrix<T> getInverse() {
-            final int m = pivot.length;
-            final T one = field.getOne();
-            FieldMatrix<T> identity = new Array2DRowFieldMatrix<T>(field, m, m);
-            for (int i = 0; i < m; ++i) {
-                identity.setEntry(i, i, one);
-            }
-            return solve(identity);
-        }
-    }
-}

src/main/java/org/apache/commons/math/ode/nonstiff/AdamsNordsieckTransformer.java

@@ -26,7 +26,7 @@ import org.apache.commons.math.linear.Array2DRowFieldMatrix;
 import org.apache.commons.math.linear.Array2DRowRealMatrix;
 import org.apache.commons.math.linear.ArrayFieldVector;
 import org.apache.commons.math.linear.FieldDecompositionSolver;
-import org.apache.commons.math.linear.FieldLUDecompositionImpl;
+import org.apache.commons.math.linear.FieldLUDecomposition;
 import org.apache.commons.math.linear.FieldMatrix;
 import org.apache.commons.math.linear.MatrixUtils;
 import org.apache.commons.math.linear.QRDecomposition;
@@ -154,7 +154,7 @@ public class AdamsNordsieckTransformer {
         // compute exact coefficients
         FieldMatrix<BigFraction> bigP = buildP(nSteps);
         FieldDecompositionSolver<BigFraction> pSolver =
-            new FieldLUDecompositionImpl<BigFraction>(bigP).getSolver();
+            new FieldLUDecomposition<BigFraction>(bigP).getSolver();
 
         BigFraction[] u = new BigFraction[nSteps];
         Arrays.fill(u, BigFraction.ONE);

src/test/java/org/apache/commons/math/linear/BlockFieldMatrixTest.java

@@ -434,8 +434,8 @@ public final class BlockFieldMatrixTest {
     @Test
     public void testTranspose() {
         FieldMatrix<Fraction> m = new BlockFieldMatrix<Fraction>(testData);
-        FieldMatrix<Fraction> mIT = new FieldLUDecompositionImpl<Fraction>(m).getSolver().getInverse().transpose();
+        FieldMatrix<Fraction> mIT = new FieldLUDecomposition<Fraction>(m).getSolver().getInverse().transpose();
-        FieldMatrix<Fraction> mTI = new FieldLUDecompositionImpl<Fraction>(m.transpose()).getSolver().getInverse();
+        FieldMatrix<Fraction> mTI = new FieldLUDecomposition<Fraction>(m.transpose()).getSolver().getInverse();
         TestUtils.assertEquals(mIT, mTI);
         m = new BlockFieldMatrix<Fraction>(testData2);
         FieldMatrix<Fraction> mt = new BlockFieldMatrix<Fraction>(testData2T);
@@ -532,7 +532,7 @@ public final class BlockFieldMatrixTest {
         Assert.assertEquals(2, p.getRowDimension());
         Assert.assertEquals(2, p.getColumnDimension());
         // Invert p
-        FieldMatrix<Fraction> pInverse = new FieldLUDecompositionImpl<Fraction>(p).getSolver().getInverse();
+        FieldMatrix<Fraction> pInverse = new FieldLUDecomposition<Fraction>(p).getSolver().getInverse();
         Assert.assertEquals(2, pInverse.getRowDimension());
         Assert.assertEquals(2, pInverse.getColumnDimension());
 
@@ -547,7 +547,7 @@ public final class BlockFieldMatrixTest {
             new Fraction(1), new Fraction(-2), new Fraction(1)
         };
         Fraction[] solution;
-        solution = new FieldLUDecompositionImpl<Fraction>(coefficients)
+        solution = new FieldLUDecomposition<Fraction>(coefficients)
             .getSolver()
             .solve(new ArrayFieldVector<Fraction>(constants, false)).toArray();
         Assert.assertEquals(new Fraction(2).multiply(solution[0]).

src/test/java/org/apache/commons/math/linear/FieldLUDecompositionTest.java

@@ -24,7 +24,7 @@ import org.apache.commons.math.TestUtils;
 import org.apache.commons.math.fraction.Fraction;
 import org.apache.commons.math.fraction.FractionField;
 
-public class FieldLUDecompositionImplTest {
+public class FieldLUDecompositionTest {
     private Fraction[][] testData = {
             { new Fraction(1), new Fraction(2), new Fraction(3)},
             { new Fraction(2), new Fraction(5), new Fraction(3)},
@@ -58,7 +58,7 @@ public class FieldLUDecompositionImplTest {
     public void testDimensions() {
         FieldMatrix<Fraction> matrix =
             new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData);
-        FieldLUDecomposition<Fraction> LU = new FieldLUDecompositionImpl<Fraction>(matrix);
+        FieldLUDecomposition<Fraction> LU = new FieldLUDecomposition<Fraction>(matrix);
         Assert.assertEquals(testData.length, LU.getL().getRowDimension());
         Assert.assertEquals(testData.length, LU.getL().getColumnDimension());
         Assert.assertEquals(testData.length, LU.getU().getRowDimension());
@@ -73,7 +73,7 @@ public class FieldLUDecompositionImplTest {
     public void testNonSquare() {
         try {
             // we don't use FractionField.getInstance() for testing purposes
-            new FieldLUDecompositionImpl<Fraction>(new Array2DRowFieldMatrix<Fraction>(new Fraction[][] {
+            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix<Fraction>(new Fraction[][] {
                     { Fraction.ZERO, Fraction.ZERO },
                     { Fraction.ZERO, Fraction.ZERO },
                     { Fraction.ZERO, Fraction.ZERO }
@@ -88,14 +88,14 @@ public class FieldLUDecompositionImplTest {
     @Test
     public void testPAEqualLU() {
         FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData);
-        FieldLUDecomposition<Fraction> lu = new FieldLUDecompositionImpl<Fraction>(matrix);
+        FieldLUDecomposition<Fraction> lu = new FieldLUDecomposition<Fraction>(matrix);
         FieldMatrix<Fraction> l = lu.getL();
         FieldMatrix<Fraction> u = lu.getU();
         FieldMatrix<Fraction> p = lu.getP();
         TestUtils.assertEquals(p.multiply(matrix), l.multiply(u));
 
         matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testDataMinus);
-        lu = new FieldLUDecompositionImpl<Fraction>(matrix);
+        lu = new FieldLUDecomposition<Fraction>(matrix);
         l = lu.getL();
         u = lu.getU();
         p = lu.getP();
@@ -105,21 +105,21 @@ public class FieldLUDecompositionImplTest {
         for (int i = 0; i < matrix.getRowDimension(); ++i) {
             matrix.setEntry(i, i, Fraction.ONE);
         }
-        lu = new FieldLUDecompositionImpl<Fraction>(matrix);
+        lu = new FieldLUDecomposition<Fraction>(matrix);
         l = lu.getL();
         u = lu.getU();
         p = lu.getP();
         TestUtils.assertEquals(p.multiply(matrix), l.multiply(u));
 
         matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), singular);
-        lu = new FieldLUDecompositionImpl<Fraction>(matrix);
+        lu = new FieldLUDecomposition<Fraction>(matrix);
         Assert.assertFalse(lu.getSolver().isNonSingular());
         Assert.assertNull(lu.getL());
         Assert.assertNull(lu.getU());
         Assert.assertNull(lu.getP());
 
         matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), bigSingular);
-        lu = new FieldLUDecompositionImpl<Fraction>(matrix);
+        lu = new FieldLUDecomposition<Fraction>(matrix);
         Assert.assertFalse(lu.getSolver().isNonSingular());
         Assert.assertNull(lu.getL());
         Assert.assertNull(lu.getU());
@@ -131,7 +131,7 @@ public class FieldLUDecompositionImplTest {
     @Test
     public void testLLowerTriangular() {
         FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData);
-        FieldMatrix<Fraction> l = new FieldLUDecompositionImpl<Fraction>(matrix).getL();
+        FieldMatrix<Fraction> l = new FieldLUDecomposition<Fraction>(matrix).getL();
         for (int i = 0; i < l.getRowDimension(); i++) {
             Assert.assertEquals(Fraction.ONE, l.getEntry(i, i));
             for (int j = i + 1; j < l.getColumnDimension(); j++) {
@@ -144,7 +144,7 @@ public class FieldLUDecompositionImplTest {
     @Test
     public void testUUpperTriangular() {
         FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData);
-        FieldMatrix<Fraction> u = new FieldLUDecompositionImpl<Fraction>(matrix).getU();
+        FieldMatrix<Fraction> u = new FieldLUDecomposition<Fraction>(matrix).getU();
         for (int i = 0; i < u.getRowDimension(); i++) {
             for (int j = 0; j < i; j++) {
                 Assert.assertEquals(Fraction.ZERO, u.getEntry(i, j));
@@ -156,7 +156,7 @@ public class FieldLUDecompositionImplTest {
     @Test
     public void testPPermutation() {
         FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData);
-        FieldMatrix<Fraction> p   = new FieldLUDecompositionImpl<Fraction>(matrix).getP();
+        FieldMatrix<Fraction> p   = new FieldLUDecomposition<Fraction>(matrix).getP();
 
         FieldMatrix<Fraction> ppT = p.multiply(p.transpose());
         FieldMatrix<Fraction> id  =
@@ -212,11 +212,11 @@ public class FieldLUDecompositionImplTest {
     @Test
     public void testSingular() {
         FieldLUDecomposition<Fraction> lu =
-            new FieldLUDecompositionImpl<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData));
+            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData));
         Assert.assertTrue(lu.getSolver().isNonSingular());
-        lu = new FieldLUDecompositionImpl<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), singular));
+        lu = new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), singular));
         Assert.assertFalse(lu.getSolver().isNonSingular());
-        lu = new FieldLUDecompositionImpl<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), bigSingular));
+        lu = new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), bigSingular));
         Assert.assertFalse(lu.getSolver().isNonSingular());
     }
 
@@ -224,7 +224,7 @@ public class FieldLUDecompositionImplTest {
     @Test
     public void testMatricesValues1() {
        FieldLUDecomposition<Fraction> lu =
-            new FieldLUDecompositionImpl<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData));
+            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData));
         FieldMatrix<Fraction> lRef = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), new Fraction[][] {
                 { new Fraction(1), new Fraction(0), new Fraction(0) },
                 { new Fraction(2), new Fraction(1), new Fraction(0) },
@@ -265,7 +265,7 @@ public class FieldLUDecompositionImplTest {
     @Test
     public void testMatricesValues2() {
        FieldLUDecomposition<Fraction> lu =
-            new FieldLUDecompositionImpl<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), luData));
+            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), luData));
         FieldMatrix<Fraction> lRef = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), new Fraction[][] {
                 { new Fraction(1), new Fraction(0), new Fraction(0) },
                 { new Fraction(3), new Fraction(1), new Fraction(0) },

src/test/java/org/apache/commons/math/linear/FieldLUSolverTest.java

@@ -65,13 +65,13 @@ public class FieldLUSolverTest {
     @Test
     public void testSingular() {
         FieldDecompositionSolver<Fraction> solver;
-        solver = new FieldLUDecompositionImpl<Fraction>(createFractionMatrix(testData))
+        solver = new FieldLUDecomposition<Fraction>(createFractionMatrix(testData))
             .getSolver();
         Assert.assertTrue(solver.isNonSingular());
-        solver = new FieldLUDecompositionImpl<Fraction>(createFractionMatrix(singular))
+        solver = new FieldLUDecomposition<Fraction>(createFractionMatrix(singular))
             .getSolver();
         Assert.assertFalse(solver.isNonSingular());
-        solver = new FieldLUDecompositionImpl<Fraction>(createFractionMatrix(bigSingular))
+        solver = new FieldLUDecomposition<Fraction>(createFractionMatrix(bigSingular))
             .getSolver();
         Assert.assertFalse(solver.isNonSingular());
     }
@@ -80,7 +80,7 @@ public class FieldLUSolverTest {
     @Test
     public void testSolveDimensionErrors() {
         FieldDecompositionSolver<Fraction> solver;
-        solver = new FieldLUDecompositionImpl<Fraction>(createFractionMatrix(testData))
+        solver = new FieldLUDecomposition<Fraction>(createFractionMatrix(testData))
             .getSolver();
         FieldMatrix<Fraction> b = createFractionMatrix(new int[2][2]);
         try {
@@ -101,7 +101,7 @@ public class FieldLUSolverTest {
     @Test
     public void testSolveSingularityErrors() {
         FieldDecompositionSolver solver;
-        solver = new FieldLUDecompositionImpl(createFractionMatrix(singular))
+        solver = new FieldLUDecomposition(createFractionMatrix(singular))
             .getSolver();
         FieldMatrix b = createFractionMatrix(new int[2][2]);
         try {
@@ -122,7 +122,7 @@ public class FieldLUSolverTest {
     @Test
     public void testSolve() {
         FieldDecompositionSolver solver;
-        solver = new FieldLUDecompositionImpl<Fraction>(createFractionMatrix(testData))
+        solver = new FieldLUDecomposition<Fraction>(createFractionMatrix(testData))
             .getSolver();
         FieldMatrix<Fraction> b = createFractionMatrix(new int[][] {
                 { 1, 0 }, { 2, -5 }, { 3, 1 }
@@ -172,6 +172,6 @@ public class FieldLUSolverTest {
     }
 
     private double getDeterminant(final FieldMatrix<Fraction> m) {
-        return new FieldLUDecompositionImpl<Fraction>(m).getDeterminant().doubleValue();
+        return new FieldLUDecomposition<Fraction>(m).getDeterminant().doubleValue();
     }
 }

src/test/java/org/apache/commons/math/linear/FieldMatrixImplTest.java

@@ -297,8 +297,8 @@ public final class FieldMatrixImplTest {
     @Test
     public void testTranspose() {
         FieldMatrix<Fraction> m = new Array2DRowFieldMatrix<Fraction>(testData);
-        FieldMatrix<Fraction> mIT = new FieldLUDecompositionImpl<Fraction>(m).getSolver().getInverse().transpose();
+        FieldMatrix<Fraction> mIT = new FieldLUDecomposition<Fraction>(m).getSolver().getInverse().transpose();
-        FieldMatrix<Fraction> mTI = new FieldLUDecompositionImpl<Fraction>(m.transpose()).getSolver().getInverse();
+        FieldMatrix<Fraction> mTI = new FieldLUDecomposition<Fraction>(m.transpose()).getSolver().getInverse();
         TestUtils.assertEquals(mIT, mTI);
         m = new Array2DRowFieldMatrix<Fraction>(testData2);
         FieldMatrix<Fraction> mt = new Array2DRowFieldMatrix<Fraction>(testData2T);
@@ -395,7 +395,7 @@ public final class FieldMatrixImplTest {
         Assert.assertEquals(2, p.getRowDimension());
         Assert.assertEquals(2, p.getColumnDimension());
         // Invert p
-        FieldMatrix<Fraction> pInverse = new FieldLUDecompositionImpl<Fraction>(p).getSolver().getInverse();
+        FieldMatrix<Fraction> pInverse = new FieldLUDecomposition<Fraction>(p).getSolver().getInverse();
         Assert.assertEquals(2, pInverse.getRowDimension());
         Assert.assertEquals(2, pInverse.getColumnDimension());
 
@@ -410,7 +410,7 @@ public final class FieldMatrixImplTest {
             new Fraction(1), new Fraction(-2), new Fraction(1)
         };
         Fraction[] solution;
-        solution = new FieldLUDecompositionImpl<Fraction>(coefficients)
+        solution = new FieldLUDecomposition<Fraction>(coefficients)
             .getSolver()
             .solve(new ArrayFieldVector<Fraction>(constants, false)).toArray();
         Assert.assertEquals(new Fraction(2).multiply(solution[0]).

src/test/java/org/apache/commons/math/linear/SparseFieldMatrixTest.java

@@ -291,8 +291,8 @@ public class SparseFieldMatrixTest {
     @Test
     public void testTranspose() {
         FieldMatrix<Fraction> m = createSparseMatrix(testData);
-        FieldMatrix<Fraction> mIT = new FieldLUDecompositionImpl<Fraction>(m).getSolver().getInverse().transpose();
+        FieldMatrix<Fraction> mIT = new FieldLUDecomposition<Fraction>(m).getSolver().getInverse().transpose();
-        FieldMatrix<Fraction> mTI = new FieldLUDecompositionImpl<Fraction>(m.transpose()).getSolver().getInverse();
+        FieldMatrix<Fraction> mTI = new FieldLUDecomposition<Fraction>(m.transpose()).getSolver().getInverse();
         assertClose("inverse-transpose", mIT, mTI, normTolerance);
         m = createSparseMatrix(testData2);
         FieldMatrix<Fraction> mt = createSparseMatrix(testData2T);
@@ -387,7 +387,7 @@ public class SparseFieldMatrixTest {
         Assert.assertEquals(2, p.getRowDimension());
         Assert.assertEquals(2, p.getColumnDimension());
         // Invert p
-        FieldMatrix<Fraction> pInverse = new FieldLUDecompositionImpl<Fraction>(p).getSolver().getInverse();
+        FieldMatrix<Fraction> pInverse = new FieldLUDecomposition<Fraction>(p).getSolver().getInverse();
         Assert.assertEquals(2, pInverse.getRowDimension());
         Assert.assertEquals(2, pInverse.getColumnDimension());
 
@@ -397,7 +397,7 @@ public class SparseFieldMatrixTest {
         FieldMatrix<Fraction> coefficients = createSparseMatrix(coefficientsData);
         Fraction[] constants = { new Fraction(1), new Fraction(-2), new Fraction(1) };
         Fraction[] solution;
-        solution = new FieldLUDecompositionImpl<Fraction>(coefficients)
+        solution = new FieldLUDecomposition<Fraction>(coefficients)
             .getSolver()
             .solve(new ArrayFieldVector<Fraction>(constants, false)).toArray();
         Assert.assertEquals((new Fraction(2).multiply((solution[0])).add(new Fraction(3).multiply(solution[1])).subtract(new Fraction(2).multiply(solution[2]))).doubleValue(),