Example Sparse Matrices - Revision history

Peter at 15:56, 10 February 2023

2023-02-10T15:56:54Z

Peter at 15:25, 7 July 2021

2021-07-07T15:25:22Z

Peter: /* Sparse Matrix Example */

2020-11-05T04:58:44Z

Sparse Matrix Example

Peter at 04:16, 14 March 2019

2019-03-14T04:16:06Z

Peter: Created page with " Support for sparse matrices has recently been added to EJML. It supports many but not all of the standard operations that are supported for dense matrics. The code below show..."

2017-09-18T15:23:20Z

Created page with " Support for sparse matrices has recently been added to EJML. It supports many but not all of the standard operations that are supported for dense matrics. The code below show..."

New page

Support for sparse matrices has recently been added to EJML. It supports many but not all of the standard operations that are supported for dense matrics. The code below shows the basics of working with a sparse matrix. In some situations the speed improvement of using a sparse matrix can be substantial. Do note that if your system isn't sparse enough or if its structure isn't advantageous it could run even slower using sparse operations!

<center>
{| class="wikitable"
! Type !! Execution Time (ms)
|-
| Dense || 12660
|-
| Sparse || 1642
|}
</center>

== Sparse Matrix Example ==

<syntaxhighlight lang="java">
/**
* Example showing how to construct and solve a linear system using sparse matrices
*
* @author Peter Abeles
*/
public class ExampleSparseMatrix {

public static int ROWS = 100000;
public static int COLS = 1000;
public static int XCOLS = 1;

public static void main(String[] args) {
Random rand = new Random(234);

// easy to work with sparse format, but hard to do computations with
DMatrixSparseTriplet work = new DMatrixSparseTriplet(5,4,5);
work.addItem(0,1,1.2);
work.addItem(3,0,3);
work.addItem(1,1,22.21234);
work.addItem(2,3,6);

// convert into a format that's easier to perform math with
DMatrixSparseCSC Z = ConvertDMatrixStruct.convert(work,(DMatrixSparseCSC)null);

// print the matrix to standard out in two different formats
Z.print();
System.out.println();
Z.printNonZero();
System.out.println();

// Create a large matrix that is 5% filled
DMatrixSparseCSC A = RandomMatrices_DSCC.rectangle(ROWS,COLS,(int)(ROWS*COLS*0.05),rand);
// large vector that is 70% filled
DMatrixSparseCSC x = RandomMatrices_DSCC.rectangle(COLS,XCOLS,(int)(XCOLS*COLS*0.7),rand);

System.out.println("Done generating random matrices");
// storage for the initial solution
DMatrixSparseCSC y = new DMatrixSparseCSC(ROWS,XCOLS,0);
DMatrixSparseCSC z = new DMatrixSparseCSC(ROWS,XCOLS,0);

// To demonstration how to perform sparse math let's multiply:
// y=A*x
// Optional storage is set to null so that it will declare it internally
long before = System.currentTimeMillis();
IGrowArray workA = new IGrowArray(A.numRows);
DGrowArray workB = new DGrowArray(A.numRows);
for (int i = 0; i < 100; i++) {
CommonOps_DSCC.mult(A,x,y,workA,workB);
CommonOps_DSCC.add(1.5,y,0.75,y,z,workA,workB);
}
long after = System.currentTimeMillis();

System.out.println("norm = "+ NormOps_DSCC.fastNormF(y)+" sparse time = "+(after-before)+" ms");

DMatrixRMaj Ad = ConvertDMatrixStruct.convert(A,(DMatrixRMaj)null);
DMatrixRMaj xd = ConvertDMatrixStruct.convert(x,(DMatrixRMaj)null);
DMatrixRMaj yd = new DMatrixRMaj(y.numRows,y.numCols);
DMatrixRMaj zd = new DMatrixRMaj(y.numRows,y.numCols);

before = System.currentTimeMillis();
for (int i = 0; i < 100; i++) {
CommonOps_DDRM.mult(Ad, xd, yd);
CommonOps_DDRM.add(1.5,yd,0.75, yd, zd);
}
after = System.currentTimeMillis();
System.out.println("norm = "+ NormOps_DDRM.fastNormF(yd)+" dense time = "+(after-before)+" ms");

}
}
</syntaxhighlight>

@@ Line 35: / Line 35: @@
          //       If you don't it will be forced to thrash memory as it grows its internal data structures.
          //       Failure to heed this advice will make construction of large matrices 4x slower and use 2x more memory
-         DMatrixSparseTriplet work = new DMatrixSparseTriplet(5, 4, 5);
+         var work = new DMatrixSparseTriplet(5, 4, 5);
          work.addItem(0, 1, 1.2);
          work.addItem(3, 0, 3);
@@ Line 57: / Line 57: @@
          System.out.println("Done generating random matrices");
          // storage for the initial solution
-         DMatrixSparseCSC y = new DMatrixSparseCSC(ROWS, XCOLS, 0);
+         var y = new DMatrixSparseCSC(ROWS, XCOLS, 0);
-         DMatrixSparseCSC z = new DMatrixSparseCSC(ROWS, XCOLS, 0);
+         var z = new DMatrixSparseCSC(ROWS, XCOLS, 0);
          // To demonstration how to perform sparse math let's multiply:
@@ Line 64: / Line 64: @@
          // Optional storage is set to null so that it will declare it internally
          long before = System.currentTimeMillis();
-         IGrowArray workA = new IGrowArray(A.numRows);
+         var workA = new IGrowArray(A.numRows);
-         DGrowArray workB = new DGrowArray(A.numRows);
+         var workB = new DGrowArray(A.numRows);
          for (int i = 0; i < 100; i++) {
              CommonOps_DSCC.mult(A, x, y, workA, workB);
@@ Line 76: / Line 76: @@
          DMatrixRMaj Ad = DConvertMatrixStruct.convert(A, (DMatrixRMaj)null);
          DMatrixRMaj xd = DConvertMatrixStruct.convert(x, (DMatrixRMaj)null);
-         DMatrixRMaj yd = new DMatrixRMaj(y.numRows, y.numCols);
+         var yd = new DMatrixRMaj(y.numRows, y.numCols);
-         DMatrixRMaj zd = new DMatrixRMaj(y.numRows, y.numCols);
+         var zd = new DMatrixRMaj(y.numRows, y.numCols);
          before = System.currentTimeMillis();

@@ Line 11: / Line 11: @@
 |}
 </center>
 == Sparse Matrix Example ==
@@ Line 21: / Line 24: @@
   */
 public class ExampleSparseMatrix {
      public static int ROWS = 100000;
      public static int COLS = 1000;
      public static int XCOLS = 1;
-     public static void main(String[] args) {
+     public static void main( String[] args ) {
          Random rand = new Random(234);
@@ Line 34: / Line 35: @@
          //       If you don't it will be forced to thrash memory as it grows its internal data structures.
          //       Failure to heed this advice will make construction of large matrices 4x slower and use 2x more memory
-         DMatrixSparseTriplet work = new DMatrixSparseTriplet(5,4,5);
+         DMatrixSparseTriplet work = new DMatrixSparseTriplet(5, 4, 5);
-         work.addItem(0,1,1.2);
+         work.addItem(0, 1, 1.2);
-         work.addItem(3,0,3);
+         work.addItem(3, 0, 3);
-         work.addItem(1,1,22.21234);
+         work.addItem(1, 1, 22.21234);
-         work.addItem(2,3,6);
+         work.addItem(2, 3, 6);
          // convert into a format that's easier to perform math with
-         DMatrixSparseCSC Z = DConvertMatrixStruct.convert(work,(DMatrixSparseCSC)null);
+         DMatrixSparseCSC Z = DConvertMatrixStruct.convert(work, (DMatrixSparseCSC)null);
          // print the matrix to standard out in two different formats
@@ Line 50: / Line 51: @@
          // Create a large matrix that is 5% filled
-         DMatrixSparseCSC A = RandomMatrices_DSCC.rectangle(ROWS,COLS,(int)(ROWS*COLS*0.05),rand);
+         DMatrixSparseCSC A = RandomMatrices_DSCC.rectangle(ROWS, COLS, (int)(ROWS*COLS*0.05), rand);
          //          large vector that is 70% filled
-         DMatrixSparseCSC x = RandomMatrices_DSCC.rectangle(COLS,XCOLS,(int)(XCOLS*COLS*0.7),rand);
+         DMatrixSparseCSC x = RandomMatrices_DSCC.rectangle(COLS, XCOLS, (int)(XCOLS*COLS*0.7), rand);
          System.out.println("Done generating random matrices");
          // storage for the initial solution
-         DMatrixSparseCSC y = new DMatrixSparseCSC(ROWS,XCOLS,0);
+         DMatrixSparseCSC y = new DMatrixSparseCSC(ROWS, XCOLS, 0);
-         DMatrixSparseCSC z = new DMatrixSparseCSC(ROWS,XCOLS,0);
+         DMatrixSparseCSC z = new DMatrixSparseCSC(ROWS, XCOLS, 0);
          // To demonstration how to perform sparse math let's multiply:
@@ Line 66: / Line 67: @@
          DGrowArray workB = new DGrowArray(A.numRows);
          for (int i = 0; i < 100; i++) {
-             CommonOps_DSCC.mult(A,x,y,workA,workB);
+             CommonOps_DSCC.mult(A, x, y, workA, workB);
-             CommonOps_DSCC.add(1.5,y,0.75,y,z,workA,workB);
+             CommonOps_DSCC.add(1.5, y, 0.75, y, z, workA, workB);
+         }
          long after = System.currentTimeMillis();
-         System.out.println("norm = "+ NormOps_DSCC.fastNormF(y)+"  sparse time = "+(after-before)+" ms");
+         System.out.println("norm = " + NormOps_DSCC.fastNormF(y) + "  sparse time = " + (after - before) + " ms");
-         DMatrixRMaj Ad = DConvertMatrixStruct.convert(A,(DMatrixRMaj)null);
+         DMatrixRMaj Ad = DConvertMatrixStruct.convert(A, (DMatrixRMaj)null);
-         DMatrixRMaj xd = DConvertMatrixStruct.convert(x,(DMatrixRMaj)null);
+         DMatrixRMaj xd = DConvertMatrixStruct.convert(x, (DMatrixRMaj)null);
-         DMatrixRMaj yd = new DMatrixRMaj(y.numRows,y.numCols);
+         DMatrixRMaj yd = new DMatrixRMaj(y.numRows, y.numCols);
-         DMatrixRMaj zd = new DMatrixRMaj(y.numRows,y.numCols);
+         DMatrixRMaj zd = new DMatrixRMaj(y.numRows, y.numCols);
          before = System.currentTimeMillis();
          for (int i = 0; i < 100; i++) {
              CommonOps_DDRM.mult(Ad, xd, yd);
-             CommonOps_DDRM.add(1.5,yd,0.75, yd, zd);
+             CommonOps_DDRM.add(1.5, yd, 0.75, yd, zd);
+         }
          after = System.currentTimeMillis();
-         System.out.println("norm = "+ NormOps_DDRM.fastNormF(yd)+"  dense time  = "+(after-before)+" ms");
+         System.out.println("norm = " + NormOps_DDRM.fastNormF(yd) + "  dense time  = " + (after - before) + " ms");
+     }
+}
 </syntaxhighlight>