RingMatrix


1   package JSci.maths.matrices;
2   
3   import JSci.GlobalSettings;
4   import JSci.maths.groups.AbelianGroup;
5   import JSci.maths.algebras.*;
6   import JSci.maths.fields.*;
7   
8   /**
9   * The RingMatrix class provides an object for encapsulating matrices over an arbitrary ring.
10  * @version 1.1
11  * @author Mark Hale
12  */
13  public class RingMatrix extends Matrix {
14          /**
15          * Array containing the elements of the matrix.
16          */
17          protected Ring.Member matrix[][];
18          /**
19          * Constructs a matrix.
20          */
21          protected RingMatrix(final int rows, final int cols) {
22                  super(rows,cols);
23          }
24          /**
25          * Constructs a matrix by wrapping an array.
26          * @param array an assigned value
27          */
28          public RingMatrix(final Ring.Member array[][]) {
29                  this(array.length,array[0].length);
30                  matrix=array;
31          }
32          /**
33          * Compares two matrices for equality.
34          * @param m a matrix
35          */
36          public boolean equals(Object   m) {
37                  if(m!=null && (m instanceof RingMatrix) &&
38                  numRows==((RingMatrix)m).rows() && numCols==((RingMatrix)m).columns()) {
39                          final RingMatrix rm=(RingMatrix)m;
40                          for(int j,i=0;i<numRows;i++) {
41                                  for(j=0;j<numCols;j++) {
42                                          if(!matrix[i][j].equals(rm.getElement(i,j)))
43                                                  return false;
44                                  }
45                          }
46                          return true;
47                  } else
48                          return false;
49          }
50          /**
51          * Returns a string representing this matrix.
52          */
53          public String   toString() {
54                  final StringBuffer   buf=new StringBuffer  (5*numRows*numCols);
55                  for(int j,i=0;i<numRows;i++) {
56                          for(j=0;j<numCols;j++) {
57                                  buf.append(matrix[i][j].toString());
58                                  buf.append(' ');
59                          }
60                          buf.append('\n');
61                  }
62                  return buf.toString();
63          }
64          /**
65          * Returns an element of the matrix.
66          * @param i row index of the element
67          * @param j column index of the element
68          * @exception MatrixDimensionException If attempting to access an invalid element.
69          */
70          public Ring.Member getElement(final int i, final int j) {
71                  if(i>=0 && i<numRows && j>=0 && j<numCols)
72                          return matrix[i][j];
73                  else
74                          throw new MatrixDimensionException(getInvalidElementMsg(i,j));
75          }
76          /**
77          * Sets the value of an element of the matrix.
78          * @param i row index of the element
79          * @param j column index of the element
80          * @param r a ring element
81          * @exception MatrixDimensionException If attempting to access an invalid element.
82          */
83          public void setElement(final int i, final int j, final Ring.Member r) {
84                  if(i>=0 && i<numRows && j>=0 && j<numCols)
85                          matrix[i][j]=r;
86                  else
87                          throw new MatrixDimensionException(getInvalidElementMsg(i,j));
88          }
89      public Object   getSet() {
90          throw new RuntimeException  ("Not yet implemented: please file bug report");
91      }
92  
93  //============
94  // OPERATIONS
95  //============
96  
97          /**
98          * Returns the negative of this matrix.
99          */
100         public AbelianGroup.Member negate() {
101                 final Ring.Member array[][]=new Ring.Member[numRows][numCols];
102                 for(int j,i=0;i<numRows;i++) {
103                         array[i][0]=(Ring.Member) matrix[i][0].negate();
104                         for(j=1;j<numCols;j++)
105                                 array[i][j]=(Ring.Member) matrix[i][j].negate();
106                 }
107                 return new RingMatrix(array);
108         }
109 
110 // ADDITION
111 
112         /**
113         * Returns the addition of this matrix and another.
114         */
115         public final AbelianGroup.Member add(final AbelianGroup.Member m) {
116                 if(m instanceof RingMatrix)
117                         return add((RingMatrix)m);
118                 else
119                         throw new IllegalArgumentException  ("Member class not recognised by this method.");
120         }
121         /**
122         * Returns the addition of this matrix and another.
123         * @param m a matrix
124         * @exception MatrixDimensionException If the matrices are different sizes.
125         */
126         public RingMatrix add(final RingMatrix m) {
127                 if(numRows==m.numRows && numCols==m.numCols) {
128                         final Ring.Member array[][]=new Ring.Member[numRows][numCols];
129                         for(int j,i=0;i<numRows;i++) {
130                                 array[i][0]=(Ring.Member) matrix[i][0].add(m.getElement(i,0));
131                                 for(j=1;j<numCols;j++)
132                                         array[i][j]=(Ring.Member) matrix[i][j].add(m.getElement(i,j));
133                         }
134                         return new RingMatrix(array);
135                 } else
136                         throw new MatrixDimensionException("Matrices are different sizes.");
137         }
138 
139 // SUBTRACTION
140 
141         /**
142         * Returns the subtraction of this matrix and another.
143         */
144         public final AbelianGroup.Member subtract(final AbelianGroup.Member m) {
145                 if(m instanceof RingMatrix)
146                         return subtract((RingMatrix)m);
147                 else
148                         throw new IllegalArgumentException  ("Member class not recognised by this method.");
149         }
150         /**
151         * Returns the subtraction of this matrix and another.
152         * @param m a matrix
153         * @exception MatrixDimensionException If the matrices are different sizes.
154         */
155         public RingMatrix subtract(final RingMatrix m) {
156                 if(numRows==m.numRows && numCols==m.numCols) {
157                         final Ring.Member array[][]=new Ring.Member[numRows][numCols];
158                         for(int j,i=0;i<numRows;i++) {
159                                 array[i][0]=(Ring.Member) matrix[i][0].subtract(m.getElement(i,0));
160                                 for(j=1;j<numCols;j++)
161                                         array[i][j]=(Ring.Member) matrix[i][j].subtract(m.getElement(i,j));
162                         }
163                         return new RingMatrix(array);
164                 } else
165                         throw new MatrixDimensionException("Matrices are different sizes.");
166         }
167 
168 // SCALAR MULTIPLICATION
169 
170         /**
171         * Returns the multiplication of this matrix by a scalar.
172         * @param r a ring element.
173         */
174         public Module.Member scalarMultiply(Ring.Member r) {
175                 final Ring.Member array[][]=new Ring.Member[numRows][numCols];
176                 for(int j,i=0;i<numRows;i++) {
177                         array[i][0]=r.multiply(matrix[i][0]);
178                         for(j=1;j<numCols;j++)
179                                 array[i][j]=r.multiply(matrix[i][j]);
180                 }
181                 return new RingMatrix(array);
182         }
183 
184 // SCALAR DIVISON
185 
186         /**
187         * Returns the division of this matrix by a scalar.
188         * @param x a field element.
189         */
190         public VectorSpace.Member scalarDivide(Field.Member x) {
191                 final Ring.Member array[][]=new Ring.Member[numRows][numCols];
192                 for(int j,i=0;i<numRows;i++) {
193                         array[i][0]=((Field.Member)matrix[i][0]).divide(x);
194                         for(j=1;j<numCols;j++)
195                                 array[i][j]=((Field.Member)matrix[i][j]).divide(x);
196                 }
197                 return new RingMatrix(array);
198         }
199 
200 // MATRIX MULTIPLICATION
201 
202         /**
203         * Returns the multiplication of this matrix and another.
204         */
205         public final Ring.Member multiply(final Ring.Member m) {
206                 if(m instanceof RingMatrix)
207                         return multiply((RingMatrix)m);
208                 else
209                         throw new IllegalArgumentException  ("Member class not recognised by this method.");
210         }
211         /**
212         * Returns the multiplication of this matrix and another.
213         * @param m a matrix
214         * @exception MatrixDimensionException If the matrices are incompatible.
215         */
216         public RingMatrix multiply(final RingMatrix m) {
217                 if(numCols==m.numRows) {
218                         int n,k;
219                         final Ring.Member array[][]=new Ring.Member[numRows][m.numCols];
220                         for(int j=0;j<numRows;j++) {
221                                 for(k=0;k<m.numCols;k++) {
222                                         AbelianGroup.Member g=matrix[j][0].multiply(m.getElement(0,k));
223                                         for(n=1;n<numCols;n++)
224                                                 g=g.add(matrix[j][n].multiply(m.getElement(n,k)));
225                                         array[j][k]=(Ring.Member) g;
226                                 }
227                         }
228                         return new RingMatrix(array);
229                 } else
230                         throw new MatrixDimensionException("Incompatible matrices.");
231         }
232 
233 // DIRECT SUM
234 
235         /**
236         * Returns the direct sum of this matrix and another.
237         */
238         public RingMatrix directSum(final RingMatrix m) {
239                 final Ring.Member array[][]=new Ring.Member[numRows+m.numRows][numCols+m.numCols];
240                 for(int j,i=0;i<numRows;i++) {
241                         for(j=0;j<numCols;j++)
242                                 array[i][j]=matrix[i][j];
243                 }
244                 for(int j,i=0;i<m.numRows;i++) {
245                         for(j=0;j<m.numCols;j++)
246                                 array[i+numRows][j+numCols]=m.getElement(i,j);
247                 }
248                 return new RingMatrix(array);
249         }
250 
251 // TENSOR PRODUCT
252 
253         /**
254         * Returns the tensor product of this matrix and another.
255         */
256         public RingMatrix tensor(final RingMatrix m) {
257                 final Ring.Member array[][]=new Ring.Member[numRows*m.numRows][numCols*m.numCols];
258                 for(int i=0;i<numRows;i++) {
259                         for(int j=0;j<numCols;j++) {
260                                 for(int k=0;k<m.numRows;j++) {
261                                         for(int l=0;l<m.numCols;l++)
262                                                 array[i*m.numRows+k][j*m.numCols+l]=matrix[i][j].multiply(m.getElement(k,l));
263                                 }
264                         }
265                 }
266                 return new RingMatrix(array);
267         }
268 
269 // TRANSPOSE
270 
271         /**
272         * Returns the transpose of this matrix.
273         * @return a matrix
274         */
275         public Matrix transpose() {
276                 final Ring.Member array[][]=new Ring.Member[numCols][numRows];
277                 for(int j,i=0;i<numRows;i++) {
278                         array[0][i]=matrix[i][0];
279                         for(j=1;j<numCols;j++)
280                                 array[j][i]=matrix[i][j];
281                 }
282                 return new RingMatrix(array);
283         }
284 }
285 
286
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