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From a.@apache.org
Subject [13/13] ignite git commit: IGNITE-4572 Machine Learning: Develop distributed algebra support for dense and sparse data sets.
Date Fri, 14 Apr 2017 15:51:12 GMT
IGNITE-4572 Machine Learning: Develop distributed algebra support for dense and sparse data sets.


Project: http://git-wip-us.apache.org/repos/asf/ignite/repo
Commit: http://git-wip-us.apache.org/repos/asf/ignite/commit/acd21fb8
Tree: http://git-wip-us.apache.org/repos/asf/ignite/tree/acd21fb8
Diff: http://git-wip-us.apache.org/repos/asf/ignite/diff/acd21fb8

Branch: refs/heads/master
Commit: acd21fb8b0d1c7f274d50d30da292c96ede7515c
Parents: 1f867c6
Author: Yury Babak <ybabak@gridgain.com>
Authored: Fri Apr 14 18:50:30 2017 +0300
Committer: Anton Vinogradov <av@apache.org>
Committed: Fri Apr 14 18:50:30 2017 +0300

----------------------------------------------------------------------
 examples/pom-standalone-lgpl.xml                |    6 +
 examples/pom-standalone.xml                     |    6 +
 examples/pom.xml                                |    6 +
 .../CholeskyDecompositionExample.java           |   80 ++
 .../EigenDecompositionExample.java              |   69 ++
 .../decompositions/LUDecompositionExample.java  |   83 ++
 .../SingularValueDecompositionExample.java      |   70 ++
 .../java8/math/decompositions/package-info.java |   22 +
 .../java8/math/matrix/CacheMatrixExample.java   |   91 ++
 .../java8/math/matrix/ExampleMatrixStorage.java |  162 +++
 .../math/matrix/MatrixCustomStorageExample.java |  141 +++
 .../java8/math/matrix/MatrixExample.java        |   79 ++
 .../java8/math/matrix/MatrixExampleUtil.java    |   52 +
 .../java8/math/matrix/OffHeapMatrixExample.java |   84 ++
 .../matrix/SparseDistributedMatrixExample.java  |   65 +
 .../java8/math/matrix/SparseMatrixExample.java  |   84 ++
 .../java8/math/matrix/package-info.java         |   22 +
 .../examples/java8/math/package-info.java       |   22 +
 .../java8/math/tracer/TracerExample.java        |   63 +
 .../java8/math/tracer/package-info.java         |   22 +
 .../java8/math/vector/CacheVectorExample.java   |  102 ++
 .../java8/math/vector/ExampleVectorStorage.java |  126 ++
 .../java8/math/vector/OffHeapVectorExample.java |   78 ++
 .../java8/math/vector/SparseVectorExample.java  |   80 ++
 .../math/vector/VectorCustomStorageExample.java |  124 ++
 .../java8/math/vector/VectorExample.java        |   75 ++
 .../java8/math/vector/package-info.java         |   22 +
 modules/math/README.txt                         |   15 +
 modules/math/licenses/apache-2.0.txt            |  202 ++++
 modules/math/licenses/mit.txt                   |    7 +
 modules/math/pom.xml                            |  109 ++
 .../java/org/apache/ignite/math/Algebra.java    |  571 +++++++++
 .../java/org/apache/ignite/math/Constants.java  |   42 +
 .../org/apache/ignite/math/Destroyable.java     |   30 +
 .../apache/ignite/math/IdentityValueMapper.java |   53 +
 .../java/org/apache/ignite/math/KeyMapper.java  |   33 +
 .../java/org/apache/ignite/math/Matrix.java     |  518 ++++++++
 .../org/apache/ignite/math/MatrixKeyMapper.java |   30 +
 .../org/apache/ignite/math/MatrixStorage.java   |   58 +
 .../org/apache/ignite/math/MetaAttributes.java  |   76 ++
 .../java/org/apache/ignite/math/MurmurHash.java |  246 ++++
 .../apache/ignite/math/StorageConstants.java    |   49 +
 .../apache/ignite/math/StorageOpsMetrics.java   |   49 +
 .../java/org/apache/ignite/math/Tracer.java     |  456 +++++++
 .../org/apache/ignite/math/ValueMapper.java     |   27 +
 .../java/org/apache/ignite/math/Vector.java     |  498 ++++++++
 .../org/apache/ignite/math/VectorKeyMapper.java |   29 +
 .../org/apache/ignite/math/VectorStorage.java   |   53 +
 .../decompositions/CholeskyDecomposition.java   |  306 +++++
 .../decompositions/DecompositionSupport.java    |  105 ++
 .../math/decompositions/EigenDecomposition.java |  923 +++++++++++++++
 .../math/decompositions/LUDecomposition.java    |  366 ++++++
 .../math/decompositions/QRDecomposition.java    |  186 +++
 .../SingularValueDecomposition.java             |  620 ++++++++++
 .../math/decompositions/package-info.java       |   22 +
 .../math/exceptions/CardinalityException.java   |   38 +
 .../math/exceptions/ColumnIndexException.java   |   35 +
 .../ignite/math/exceptions/IndexException.java  |   35 +
 .../NonPositiveDefiniteMatrixException.java     |   20 +
 .../exceptions/NonSymmetricMatrixException.java |   18 +
 .../math/exceptions/RowIndexException.java      |   35 +
 .../exceptions/SingularMatrixException.java     |   30 +
 .../exceptions/UnknownProviderException.java    |   35 +
 .../UnsupportedOperationException.java          |   44 +
 .../ignite/math/exceptions/package-info.java    |   22 +
 .../apache/ignite/math/functions/Functions.java |  136 +++
 .../ignite/math/functions/IgniteBiConsumer.java |   12 +
 .../ignite/math/functions/IgniteBiFunction.java |   29 +
 .../ignite/math/functions/IgniteConsumer.java   |   29 +
 .../math/functions/IgniteDoubleFunction.java    |   29 +
 .../ignite/math/functions/IgniteFunction.java   |   30 +
 .../math/functions/IntDoubleToVoidFunction.java |   25 +
 .../functions/IntIntDoubleToVoidFunction.java   |   28 +
 .../math/functions/IntIntToDoubleFunction.java  |   24 +
 .../ignite/math/functions/package-info.java     |   22 +
 .../apache/ignite/math/impls/CacheUtils.java    |  356 ++++++
 .../math/impls/matrix/AbstractMatrix.java       |  880 ++++++++++++++
 .../ignite/math/impls/matrix/CacheMatrix.java   |  158 +++
 .../impls/matrix/DenseLocalOffHeapMatrix.java   |   90 ++
 .../impls/matrix/DenseLocalOnHeapMatrix.java    |   86 ++
 .../math/impls/matrix/DiagonalMatrix.java       |  101 ++
 .../math/impls/matrix/FunctionMatrix.java       |   95 ++
 .../ignite/math/impls/matrix/MatrixView.java    |   84 ++
 .../math/impls/matrix/PivotedMatrixView.java    |  243 ++++
 .../ignite/math/impls/matrix/RandomMatrix.java  |   97 ++
 .../impls/matrix/SparseDistributedMatrix.java   |  155 +++
 .../impls/matrix/SparseLocalOnHeapMatrix.java   |   72 ++
 .../math/impls/matrix/TransposedMatrixView.java |   84 ++
 .../ignite/math/impls/matrix/package-info.java  |   22 +
 .../apache/ignite/math/impls/package-info.java  |   22 +
 .../storage/matrix/ArrayMatrixStorage.java      |  161 +++
 .../storage/matrix/CacheMatrixStorage.java      |  180 +++
 .../matrix/DenseOffHeapMatrixStorage.java       |  197 ++++
 .../storage/matrix/DiagonalMatrixStorage.java   |  136 +++
 .../storage/matrix/FunctionMatrixStorage.java   |  175 +++
 .../storage/matrix/MatrixDelegateStorage.java   |  205 ++++
 .../storage/matrix/PivotedMatrixStorage.java    |  256 ++++
 .../storage/matrix/RandomMatrixStorage.java     |  176 +++
 .../matrix/SparseDistributedMatrixStorage.java  |  283 +++++
 .../matrix/SparseLocalOnHeapMatrixStorage.java  |  226 ++++
 .../math/impls/storage/matrix/package-info.java |   22 +
 .../storage/vector/ArrayVectorStorage.java      |  135 +++
 .../storage/vector/CacheVectorStorage.java      |  175 +++
 .../storage/vector/ConstantVectorStorage.java   |  133 +++
 .../storage/vector/DelegateVectorStorage.java   |  157 +++
 .../vector/DenseLocalOffHeapVectorStorage.java  |  172 +++
 .../storage/vector/FunctionVectorStorage.java   |  141 +++
 .../storage/vector/MatrixVectorStorage.java     |  185 +++
 .../storage/vector/PivotedVectorStorage.java    |  175 +++
 .../storage/vector/RandomVectorStorage.java     |  152 +++
 .../SingleElementVectorDelegateStorage.java     |  145 +++
 .../vector/SingleElementVectorStorage.java      |  143 +++
 .../vector/SparseLocalOffHeapVectorStorage.java |  148 +++
 .../vector/SparseLocalOnHeapVectorStorage.java  |  152 +++
 .../math/impls/storage/vector/package-info.java |   22 +
 .../impls/vector/AbstractReadOnlyVector.java    |  108 ++
 .../math/impls/vector/AbstractVector.java       |  903 ++++++++++++++
 .../ignite/math/impls/vector/CacheVector.java   |  140 +++
 .../math/impls/vector/ConstantVector.java       |   84 ++
 .../math/impls/vector/DelegatingVector.java     |  391 ++++++
 .../impls/vector/DenseLocalOffHeapVector.java   |   89 ++
 .../impls/vector/DenseLocalOnHeapVector.java    |  104 ++
 .../math/impls/vector/FunctionVector.java       |  112 ++
 .../math/impls/vector/MatrixVectorView.java     |  139 +++
 .../math/impls/vector/PivotedVectorView.java    |  163 +++
 .../ignite/math/impls/vector/RandomVector.java  |  128 ++
 .../math/impls/vector/SingleElementVector.java  |  102 ++
 .../impls/vector/SingleElementVectorView.java   |   97 ++
 .../impls/vector/SparseLocalOffHeapVector.java  |   47 +
 .../math/impls/vector/SparseLocalVector.java    |   71 ++
 .../ignite/math/impls/vector/VectorView.java    |   85 ++
 .../ignite/math/impls/vector/package-info.java  |   22 +
 .../org/apache/ignite/math/package-info.java    |   22 +
 .../apache/ignite/math/d3-matrix-template.html  |  128 ++
 .../apache/ignite/math/d3-vector-template.html  |  111 ++
 .../org/apache/ignite/math/ExternalizeTest.java |   66 ++
 .../math/MathImplDistributedTestSuite.java      |   39 +
 .../ignite/math/MathImplLocalTestSuite.java     |  123 ++
 .../ignite/math/MathImplMainTestSuite.java      |   33 +
 .../java/org/apache/ignite/math/TracerTest.java |  195 +++
 .../ignite/math/benchmark/MathBenchmark.java    |  205 ++++
 .../math/benchmark/MathBenchmarkSelfTest.java   |  100 ++
 .../ignite/math/benchmark/ResultsWriter.java    |  127 ++
 .../math/benchmark/VectorBenchmarkTest.java     |  138 +++
 .../ignite/math/benchmark/package-info.java     |   18 +
 .../CholeskyDecompositionTest.java              |  158 +++
 .../decompositions/EigenDecompositionTest.java  |  193 +++
 .../decompositions/LUDecompositionTest.java     |  250 ++++
 .../decompositions/QRDecompositionTest.java     |  139 +++
 .../SingularValueDecompositionTest.java         |  120 ++
 .../ignite/math/impls/MathTestConstants.java    |   88 ++
 .../math/impls/matrix/CacheMatrixTest.java      |  369 ++++++
 .../DenseLocalOffHeapMatrixConstructorTest.java |   65 +
 .../DenseLocalOnHeapMatrixConstructorTest.java  |   71 ++
 .../math/impls/matrix/DiagonalMatrixTest.java   |  209 ++++
 .../matrix/FunctionMatrixConstructorTest.java   |  113 ++
 .../math/impls/matrix/MatrixAttributeTest.java  |  156 +++
 .../matrix/MatrixImplementationFixtures.java    |  381 ++++++
 .../impls/matrix/MatrixImplementationsTest.java | 1113 ++++++++++++++++++
 .../impls/matrix/MatrixKeyMapperForTests.java   |   69 ++
 .../impls/matrix/MatrixViewConstructorTest.java |  114 ++
 .../PivotedMatrixViewConstructorTest.java       |  128 ++
 .../matrix/RandomMatrixConstructorTest.java     |   71 ++
 .../matrix/SparseDistributedMatrixTest.java     |  265 +++++
 .../SparseLocalOnHeapMatrixConstructorTest.java |   53 +
 .../impls/matrix/TransposedMatrixViewTest.java  |   87 ++
 .../storage/matrix/MatrixArrayStorageTest.java  |   63 +
 .../storage/matrix/MatrixBaseStorageTest.java   |   89 ++
 .../matrix/MatrixOffHeapStorageTest.java        |   39 +
 .../storage/matrix/MatrixStorageFixtures.java   |  141 +++
 .../matrix/MatrixStorageImplementationTest.java |   73 ++
 .../SparseDistributedMatrixStorageTest.java     |  126 ++
 .../RandomAccessSparseVectorStorageTest.java    |   60 +
 .../SparseLocalOffHeapVectorStorageTest.java    |   78 ++
 .../storage/vector/VectorArrayStorageTest.java  |   58 +
 .../storage/vector/VectorBaseStorageTest.java   |   69 ++
 .../vector/VectorOffheapStorageTest.java        |   73 ++
 .../math/impls/vector/AbstractVectorTest.java   |  543 +++++++++
 .../math/impls/vector/CacheVectorTest.java      |  417 +++++++
 .../vector/ConstantVectorConstructorTest.java   |   52 +
 .../vector/DelegatingVectorConstructorTest.java |   62 +
 .../DenseLocalOffHeapVectorConstructorTest.java |   59 +
 .../DenseLocalOnHeapVectorConstructorTest.java  |  163 +++
 .../vector/FunctionVectorConstructorTest.java   |  121 ++
 .../math/impls/vector/MatrixVectorViewTest.java |  209 ++++
 .../PivotedVectorViewConstructorTest.java       |  211 ++++
 .../vector/RandomVectorConstructorTest.java     |  145 +++
 .../SingleElementVectorConstructorTest.java     |  159 +++
 .../SingleElementVectorViewConstructorTest.java |  137 +++
 .../SparseLocalVectorConstructorTest.java       |   54 +
 .../math/impls/vector/VectorAttributesTest.java |  217 ++++
 .../math/impls/vector/VectorFoldMapTest.java    |  122 ++
 .../vector/VectorImplementationsFixtures.java   |  655 +++++++++++
 .../impls/vector/VectorImplementationsTest.java |  860 ++++++++++++++
 .../math/impls/vector/VectorIterableTest.java   |  376 ++++++
 .../math/impls/vector/VectorNormTest.java       |  247 ++++
 .../math/impls/vector/VectorToMatrixTest.java   |  291 +++++
 .../math/impls/vector/VectorViewTest.java       |  162 +++
 pom.xml                                         |    7 +
 199 files changed, 29228 insertions(+)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/pom-standalone-lgpl.xml
----------------------------------------------------------------------
diff --git a/examples/pom-standalone-lgpl.xml b/examples/pom-standalone-lgpl.xml
index d9e630b..f9d8a2c 100644
--- a/examples/pom-standalone-lgpl.xml
+++ b/examples/pom-standalone-lgpl.xml
@@ -73,6 +73,12 @@
 
         <dependency>
             <groupId>org.apache.ignite</groupId>
+            <artifactId>ignite-math</artifactId>
+            <version>to_be_replaced_by_ignite_version</version>
+        </dependency>
+
+        <dependency>
+            <groupId>org.apache.ignite</groupId>
             <artifactId>ignite-spring-data</artifactId>
             <version>to_be_replaced_by_ignite_version</version>
         </dependency>

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/pom-standalone.xml
----------------------------------------------------------------------
diff --git a/examples/pom-standalone.xml b/examples/pom-standalone.xml
index fe559f8..f48b74f 100644
--- a/examples/pom-standalone.xml
+++ b/examples/pom-standalone.xml
@@ -78,6 +78,12 @@
         </dependency>
 
         <dependency>
+            <groupId>org.apache.ignite</groupId>
+            <artifactId>ignite-math</artifactId>
+            <version>to_be_replaced_by_ignite_version</version>
+        </dependency>
+
+        <dependency>
             <groupId>com.google.code.simple-spring-memcached</groupId>
             <artifactId>spymemcached</artifactId>
             <version>2.7.3</version>

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/pom.xml
----------------------------------------------------------------------
diff --git a/examples/pom.xml b/examples/pom.xml
index cdb72ca..bed361b 100644
--- a/examples/pom.xml
+++ b/examples/pom.xml
@@ -107,6 +107,12 @@
         </dependency>
 
         <dependency>
+            <groupId>org.apache.ignite</groupId>
+            <artifactId>ignite-math</artifactId>
+            <version>${project.version}</version>
+        </dependency>
+
+        <dependency>
             <groupId>org.gridgain</groupId>
             <artifactId>ignite-shmem</artifactId>
             <version>1.0.0</version>

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/CholeskyDecompositionExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/CholeskyDecompositionExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/CholeskyDecompositionExample.java
new file mode 100644
index 0000000..9a68e28
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/CholeskyDecompositionExample.java
@@ -0,0 +1,80 @@
+/*
+ * 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.ignite.examples.java8.math.decompositions;
+
+import org.apache.ignite.math.Matrix;
+import org.apache.ignite.math.Tracer;
+import org.apache.ignite.math.decompositions.CholeskyDecomposition;
+import org.apache.ignite.math.impls.matrix.DenseLocalOnHeapMatrix;
+
+/**
+ * Example of using {@link CholeskyDecomposition}.
+ */
+public class CholeskyDecompositionExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println(">>> Cholesky decomposition example started.");
+        // Let's compute a Cholesky decomposition of Hermitian matrix m:
+        // m = l l^{*}, where
+        // l is a lower triangular matrix
+        // l^{*} is its conjugate transpose
+
+        DenseLocalOnHeapMatrix m = new DenseLocalOnHeapMatrix(new double[][] {
+            {2.0d, -1.0d, 0.0d},
+            {-1.0d, 2.0d, -1.0d},
+            {0.0d, -1.0d, 2.0d}
+        });
+        System.out.println("\n>>> Matrix m for decomposition: ");
+        Tracer.showAscii(m);
+
+        // This decomposition is useful when dealing with systems of linear equations of the form
+        // m x = b where m is a Hermitian matrix.
+        // For such systems Cholesky decomposition provides
+        // more effective method of solving compared to LU decomposition.
+        // Suppose we want to solve system
+        // m x = b for various bs. Then after we computed Cholesky decomposition, we can feed various bs
+        // as a matrix of the form
+        // (b1, b2, ..., bm)
+        // to the method Cholesky::solve which returns solutions in the form
+        // (sol1, sol2, ..., solm)
+        CholeskyDecomposition dec = new CholeskyDecomposition(m);
+        System.out.println("\n>>> Made decomposition m = l * l^{*}.");
+        System.out.println(">>> Matrix l is ");
+        Tracer.showAscii(dec.getL());
+        System.out.println(">>> Matrix l^{*} is ");
+        Tracer.showAscii(dec.getLT());
+
+        Matrix bs = new DenseLocalOnHeapMatrix(new double[][] {
+            {4.0, -6.0, 7.0},
+            {1.0, 1.0, 1.0}
+        }).transpose();
+        System.out.println("\n>>> Solving systems of linear equations of the form m x = b for various bs represented by columns of matrix");
+        Tracer.showAscii(bs);
+        Matrix sol = dec.solve(bs);
+
+        System.out.println("\n>>> List of solutions: ");
+        for (int i = 0; i < sol.columnSize(); i++)
+            Tracer.showAscii(sol.viewColumn(i));
+
+        System.out.println("\n>>> Cholesky decomposition example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/EigenDecompositionExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/EigenDecompositionExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/EigenDecompositionExample.java
new file mode 100644
index 0000000..e11d642
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/EigenDecompositionExample.java
@@ -0,0 +1,69 @@
+/*
+ * 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.ignite.examples.java8.math.decompositions;
+
+import org.apache.ignite.math.Tracer;
+import org.apache.ignite.math.decompositions.EigenDecomposition;
+import org.apache.ignite.math.functions.Functions;
+import org.apache.ignite.math.impls.matrix.DenseLocalOnHeapMatrix;
+
+/**
+ * Example of using {@link EigenDecomposition}.
+ */
+public class EigenDecompositionExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println(">>> Eigen decomposition example started.");
+
+        // Let's compute EigenDecomposition for some square (n x n) matrix m with real eigenvalues:
+        // m = v d v^{-1}, where d is diagonal matrix having eigenvalues of m on diagonal
+        // and v is matrix where i-th column is eigenvector for i-th eigenvalue (i from 0 to n - 1)
+        DenseLocalOnHeapMatrix m = new DenseLocalOnHeapMatrix(new double[][] {
+            {1.0d, 0.0d, 0.0d, 0.0d},
+            {0.0d, 1.0d, 0.0d, 0.0d},
+            {0.0d, 0.0d, 2.0d, 0.0d},
+            {1.0d, 1.0d, 0.0d, 2.0d}
+        });
+        System.out.println("\n>>> Matrix m for decomposition: ");
+        Tracer.showAscii(m);
+
+        EigenDecomposition dec = new EigenDecomposition(m);
+        System.out.println("\n>>> Made decomposition.");
+        System.out.println(">>> Matrix getV is ");
+        Tracer.showAscii(dec.getV());
+        System.out.println(">>> Matrix getD is ");
+        Tracer.showAscii(dec.getD());
+
+        // From this decomposition we, for example, can easily compute determinant of matrix m
+        // det (m) = det (v d v^{-1}) =
+        // det(v) det (d) det(v^{-1}) =
+        // det(v) det(v)^{-1} det(d) =
+        // det (d) =
+        // product of diagonal elements of d =
+        // product of eigenvalues
+        double det = dec.getRealEigenValues().foldMap(Functions.MULT, Functions.IDENTITY, 1.0);
+        System.out.println("\n>>> Determinant is " + det);
+
+        System.out.println("\n>>> Eigen decomposition example completed.");
+    }
+
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/LUDecompositionExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/LUDecompositionExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/LUDecompositionExample.java
new file mode 100644
index 0000000..bf005ec
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/LUDecompositionExample.java
@@ -0,0 +1,83 @@
+/*
+ * 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.ignite.examples.java8.math.decompositions;
+
+import org.apache.ignite.math.Matrix;
+import org.apache.ignite.math.Tracer;
+import org.apache.ignite.math.decompositions.LUDecomposition;
+import org.apache.ignite.math.impls.matrix.DenseLocalOnHeapMatrix;
+
+/**
+ * Example of using {@link LUDecomposition}.
+ */
+public class LUDecompositionExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println(">>> LU decomposition example started.");
+        // Let's compute a LU decomposition for some (n x n) matrix m:
+        // m = p l u, where
+        // p is an (n x n) is a row-permutation matrix
+        // l is a (n x n) lower triangular matrix
+        // u is a (n x n) upper triangular matrix
+
+        DenseLocalOnHeapMatrix m = new DenseLocalOnHeapMatrix(new double[][] {
+            {1.0d, 1.0d, -1.0d},
+            {1.0d, -2.0d, 3.0d},
+            {2.0d, 3.0d, 1.0d}
+        });
+        System.out.println("\n>>> Matrix m for decomposition: ");
+        Tracer.showAscii(m);
+
+        // This decomposition is useful when dealing with systems of linear equations.
+        // (see https://en.wikipedia.org/wiki/LU_decomposition)
+        // suppose we want to solve system
+        // m x = b for various bs. Then after we computed LU decomposition, we can feed various bs
+        // as a matrix of the form
+        // (b1, b2, ..., bm)
+        // to the method LUDecomposition::solve which returns solutions in the form
+        // (sol1, sol2, ..., solm)
+
+        LUDecomposition dec = new LUDecomposition(m);
+        System.out.println("\n>>> Made decomposition.");
+        System.out.println(">>> Matrix getL is ");
+        Tracer.showAscii(dec.getL());
+        System.out.println(">>> Matrix getU is ");
+        Tracer.showAscii(dec.getU());
+        System.out.println(">>> Matrix getP is ");
+        Tracer.showAscii(dec.getP());
+
+        Matrix bs = new DenseLocalOnHeapMatrix(new double[][] {
+            {4.0, -6.0, 7.0},
+            {1.0, 1.0, 1.0}
+        });
+        System.out.println("\n>>> Matrix to solve: ");
+        Tracer.showAscii(bs);
+
+        Matrix sol = dec.solve(bs.transpose());
+
+        System.out.println("\n>>> List of solutions: ");
+        for (int i = 0; i < sol.columnSize(); i++)
+            Tracer.showAscii(sol.viewColumn(i));
+
+        System.out.println("\n>>> LU decomposition example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/SingularValueDecompositionExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/SingularValueDecompositionExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/SingularValueDecompositionExample.java
new file mode 100644
index 0000000..1b2998f
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/SingularValueDecompositionExample.java
@@ -0,0 +1,70 @@
+/*
+ * 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.ignite.examples.java8.math.decompositions;
+
+import org.apache.ignite.math.Tracer;
+import org.apache.ignite.math.decompositions.SingularValueDecomposition;
+import org.apache.ignite.math.impls.matrix.DenseLocalOnHeapMatrix;
+
+/**
+ * Example of using {@link SingularValueDecomposition}.
+ */
+public class SingularValueDecompositionExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println(">>> Singular value decomposition (SVD) example started.");
+
+        // Let's compute a SVD of (l x k) matrix m. This decomposition can be thought as extension of EigenDecomposition to
+        // rectangular matrices. The factorization we get is following:
+        // m = u * s * v^{*}, where
+        // u is a real or complex unitary matrix
+        // s is a rectangular diagonal matrix with non-negative real numbers on diagonal (this numbers are singular values of m)
+        // v is a real or complex unitary matrix
+        // If m is real then u and v are also real.
+        // Complex case is not supported for the moment.
+        DenseLocalOnHeapMatrix m = new DenseLocalOnHeapMatrix(new double[][] {
+            {1.0d, 0.0d, 0.0d, 0.0d, 2.0d},
+            {0.0d, 0.0d, 3.0d, 0.0d, 0.0d},
+            {0.0d, 0.0d, 0.0d, 0.0d, 0.0d},
+            {0.0d, 2.0d, 0.0d, 0.0d, 0.0d}
+        });
+        System.out.println("\n>>> Matrix m for decomposition: ");
+        Tracer.showAscii(m);
+
+        SingularValueDecomposition dec = new SingularValueDecomposition(m);
+        System.out.println("\n>>> Made decomposition m = u * s * v^{*}.");
+        System.out.println(">>> Matrix u is ");
+        Tracer.showAscii(dec.getU());
+        System.out.println(">>> Matrix s is ");
+        Tracer.showAscii(dec.getS());
+        System.out.println(">>> Matrix v is ");
+        Tracer.showAscii(dec.getV());
+
+        // This decomposition can in particular help with solving problem of finding x minimizing 2-norm of m x such
+        // that 2-norm of x is 1. It appears that it is the right singular vector corresponding to minimal singular
+        // value, which is always last.
+        System.out.println("\n>>> Vector x minimizing 2-norm of m x such that 2 norm of x is 1: ");
+        Tracer.showAscii(dec.getV().viewColumn(dec.getSingularValues().length - 1));
+
+        System.out.println("\n>>> Singular value decomposition (SVD) example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/package-info.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/package-info.java
new file mode 100644
index 0000000..cd02b21
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/decompositions/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * 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 description. -->
+ * Core algebra decomposition examples.
+ */
+package org.apache.ignite.examples.java8.math.decompositions;

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/CacheMatrixExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/CacheMatrixExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/CacheMatrixExample.java
new file mode 100644
index 0000000..44f97d2
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/CacheMatrixExample.java
@@ -0,0 +1,91 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import org.apache.ignite.Ignite;
+import org.apache.ignite.IgniteCache;
+import org.apache.ignite.Ignition;
+import org.apache.ignite.configuration.CacheConfiguration;
+import org.apache.ignite.math.IdentityValueMapper;
+import org.apache.ignite.math.MatrixKeyMapper;
+import org.apache.ignite.math.ValueMapper;
+import org.apache.ignite.math.functions.Functions;
+import org.apache.ignite.math.impls.matrix.CacheMatrix;
+
+/** */
+public class CacheMatrixExample {
+    /** */ private static final String CACHE_NAME = CacheMatrixExample.class.getSimpleName();
+    /** */ private static final int ROWS = 3;
+    /** */ private static final int COLS = 3;
+
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        try (Ignite ignite = Ignition.start("examples/config/example-ignite.xml")) {
+            System.out.println();
+            System.out.println(">>> CacheMatrix example started.");
+
+            CacheConfiguration<Integer, Double> cfg = new CacheConfiguration<>();
+
+            cfg.setName(CACHE_NAME);
+
+            try (IgniteCache<Integer, Double> cache = ignite.getOrCreateCache(cfg)) {
+                double[][] testValues = {{1.0, 0.0, 0.0}, {1.0, 1.0, 0.0}, {1.0, 1.0, 1.0}};
+
+                ValueMapper valMapper = new IdentityValueMapper();
+
+                // Map matrix element indices to cache keys.
+                MatrixKeyMapper<Integer> keyMapper = new MatrixKeyMapper<Integer>() {
+                    @Override public Integer apply(int x, int y) {
+                        return x * COLS + y;
+                    }
+
+                    @Override public boolean isValid(Integer integer) {
+                        return integer >= 0 && integer < COLS * ROWS;
+                    }
+                };
+
+                // Create cache matrix.
+                CacheMatrix<Integer, Double> cacheMatrix = new CacheMatrix<>(ROWS, COLS, cache, keyMapper, valMapper);
+
+                cacheMatrix.assign(testValues);
+
+                // Find all positive elements.
+                Integer nonZeroes = cacheMatrix.foldMap((o, aDouble) -> {
+                    if (aDouble > 0)
+                        return o + 1;
+                    return o;
+                }, Functions.IDENTITY, 0);
+
+                assert nonZeroes.equals(6);
+
+                System.out.println(">>>");
+                System.out.println(">>> Finished executing Ignite \"CacheMatrix\" example.");
+                System.out.println(">>> Lower triangular matrix 3x3 have only 6 positive elements.");
+                System.out.println(">>>");
+            }
+            finally {
+                // Distributed cache could be removed from cluster only by #destroyCache() call.
+                ignite.destroyCache(CACHE_NAME);
+            }
+        }
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/ExampleMatrixStorage.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/ExampleMatrixStorage.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/ExampleMatrixStorage.java
new file mode 100644
index 0000000..260f62d
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/ExampleMatrixStorage.java
@@ -0,0 +1,162 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import java.io.IOException;
+import java.io.ObjectInput;
+import java.io.ObjectOutput;
+import java.util.Arrays;
+
+import org.apache.ignite.math.MatrixStorage;
+
+/**
+ * Example matrix storage, modeled after {@link org.apache.ignite.math.impls.storage.matrix.ArrayMatrixStorage}.
+ */
+class ExampleMatrixStorage implements MatrixStorage {
+    /** Backing data array. */
+    private double[][] data;
+    /** Amount of rows in a matrix storage. */
+    private int rows;
+    /** Amount of columns in a matrix storage. */
+    private int cols;
+
+    /**
+     *
+     */
+    public ExampleMatrixStorage() {
+        // No-op.
+    }
+
+    /**
+     * @param rows Amount of rows in a matrix storage.
+     * @param cols Amount of columns in a matrix storage.
+     */
+    ExampleMatrixStorage(int rows, int cols) {
+        assert rows > 0;
+        assert cols > 0;
+
+        this.data = new double[rows][cols];
+        this.rows = rows;
+        this.cols = cols;
+    }
+
+    /**
+     * @param data Backing data array.
+     */
+    ExampleMatrixStorage(double[][] data) {
+        assert data != null;
+        assert data[0] != null;
+
+        this.data = data;
+        this.rows = data.length;
+        this.cols = data[0].length;
+
+        assert rows > 0;
+        assert cols > 0;
+    }
+
+    /** {@inheritDoc} */
+    @Override public double get(int x, int y) {
+        return data[x][y];
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isSequentialAccess() {
+        return false;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isDense() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isRandomAccess() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isDistributed() {
+        return false;
+    }
+
+    /** {@inheritDoc} */
+    @Override public void set(int x, int y, double v) {
+        data[x][y] = v;
+    }
+
+    /** {@inheritDoc} */
+    @Override public int columnSize() {
+        return cols;
+    }
+
+    /** {@inheritDoc} */
+    @Override public int rowSize() {
+        return rows;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isArrayBased() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    @Override public double[][] data() {
+        return data;
+    }
+
+    /** {@inheritDoc */
+    @Override public void writeExternal(ObjectOutput out) throws IOException {
+        out.writeInt(rows);
+        out.writeInt(cols);
+
+        out.writeObject(data);
+    }
+
+    /** {@inheritDoc */
+    @Override public void readExternal(ObjectInput in) throws IOException, ClassNotFoundException {
+        rows = in.readInt();
+        cols = in.readInt();
+
+        data = (double[][])in.readObject();
+    }
+
+    /** {@inheritDoc} */
+    @Override public int hashCode() {
+        int res = 1;
+
+        res += res * 37 + rows;
+        res += res * 37 + cols;
+        res += res * 37 + Arrays.deepHashCode(data);
+
+        return res;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean equals(Object o) {
+        if (this == o)
+            return true;
+
+        if (o == null || getClass() != o.getClass())
+            return false;
+
+        ExampleMatrixStorage that = (ExampleMatrixStorage)o;
+
+        return Arrays.deepEquals(data, that.data);
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixCustomStorageExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixCustomStorageExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixCustomStorageExample.java
new file mode 100644
index 0000000..637b2b4
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixCustomStorageExample.java
@@ -0,0 +1,141 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import org.apache.ignite.math.Matrix;
+import org.apache.ignite.math.MatrixStorage;
+import org.apache.ignite.math.Vector;
+import org.apache.ignite.math.impls.matrix.AbstractMatrix;
+import org.apache.ignite.math.impls.vector.DenseLocalOnHeapVector;
+
+/**
+ * This example shows how to use {@link Matrix} API based on custom {@link MatrixStorage}.
+ */
+public final class MatrixCustomStorageExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println();
+        System.out.println(">>> Matrix API usage example started.");
+
+        System.out.println("\n>>> Creating a matrix to be transposed.");
+        double[][] data = new double[][] {{1, 2, 3}, {4, 5, 6}};
+        Matrix m = new MatrixCustomStorage(data);
+        Matrix transposed = m.transpose();
+
+        System.out.println(">>> Matrix: ");
+        MatrixExampleUtil.print(m);
+        System.out.println(">>> Transposed matrix: ");
+        MatrixExampleUtil.print(transposed);
+
+        MatrixExampleUtil.verifyTransposition(m, transposed);
+
+        System.out.println("\n>>> Creating matrices to be multiplied.");
+        double[][] data1 = new double[][] {{1, 2}, {3, 4}};
+        double[][] data2 = new double[][] {{5, 6}, {7, 8}};
+
+        Matrix m1 = new MatrixCustomStorage(data1);
+        Matrix m2 = new MatrixCustomStorage(data2);
+        Matrix mult = m1.times(m2);
+
+        System.out.println(">>> First matrix: ");
+        MatrixExampleUtil.print(m1);
+        System.out.println(">>> Second matrix: ");
+        MatrixExampleUtil.print(m2);
+        System.out.println(">>> Matrix product: ");
+        MatrixExampleUtil.print(mult);
+
+        System.out.println("\n>>> Calculating matrices determinants.");
+        double det1 = m1.determinant();
+        double det2 = m2.determinant();
+        double detMult = mult.determinant();
+        boolean detMultIsAsExp = Math.abs(detMult - det1 * det2) < 0.0001d;
+
+        System.out.println(">>> First matrix determinant: [" + det1 + "].");
+        System.out.println(">>> Second matrix determinant: [" + det2 + "].");
+        System.out.println(">>> Matrix product determinant: [" + detMult
+            + "], equals product of two other matrices determinants: [" + detMultIsAsExp + "].");
+
+        assert detMultIsAsExp : "Determinant of product matrix [" + detMult
+            + "] should be equal to product of determinants [" + (det1 * det2) + "].";
+
+        System.out.println("\n>>> Matrix API usage example completed.");
+    }
+
+    /**
+     * Example of vector with custom storage, modeled after
+     * {@link org.apache.ignite.math.impls.matrix.DenseLocalOnHeapMatrix}.
+     */
+    static class MatrixCustomStorage extends AbstractMatrix {
+        /**
+         *
+         */
+        public MatrixCustomStorage() {
+            // No-op.
+        }
+
+        /**
+         * @param rows Amount of rows in a matrix.
+         * @param cols Amount of columns in a matrix.
+         */
+        MatrixCustomStorage(int rows, int cols) {
+            assert rows > 0;
+            assert cols > 0;
+
+            setStorage(new ExampleMatrixStorage(rows, cols));
+        }
+
+        /**
+         * @param mtx Source matrix.
+         */
+        MatrixCustomStorage(double[][] mtx) {
+            assert mtx != null;
+
+            setStorage(new ExampleMatrixStorage(mtx));
+        }
+
+        /**
+         * @param orig original matrix to be copied.
+         */
+        private MatrixCustomStorage(MatrixCustomStorage orig) {
+            assert orig != null;
+
+            setStorage(new ExampleMatrixStorage(orig.rowSize(), orig.columnSize()));
+
+            assign(orig);
+        }
+
+        /** {@inheritDoc} */
+        @Override public Matrix copy() {
+            return new MatrixCustomStorage(this);
+        }
+
+        /** {@inheritDoc} */
+        @Override public Matrix like(int rows, int cols) {
+            return new MatrixCustomStorage(rows, cols);
+        }
+
+        /** {@inheritDoc} */
+        @Override public Vector likeVector(int crd) {
+            return new DenseLocalOnHeapVector(crd);
+        }
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExample.java
new file mode 100644
index 0000000..58cedab
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExample.java
@@ -0,0 +1,79 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import org.apache.ignite.math.Matrix;
+import org.apache.ignite.math.impls.matrix.DenseLocalOnHeapMatrix;
+
+/**
+ * This example shows how to use {@link Matrix} API.
+ */
+public final class MatrixExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println();
+        System.out.println(">>> Basic Matrix API usage example started.");
+
+        System.out.println("\n>>> Creating a matrix to be transposed.");
+        double[][] data = new double[][] {{1, 2, 3}, {4, 5, 6}};
+        Matrix m = new DenseLocalOnHeapMatrix(data);
+        Matrix transposed = m.transpose();
+
+        System.out.println(">>> Matrix: ");
+        MatrixExampleUtil.print(m);
+        System.out.println(">>> Transposed matrix: ");
+        MatrixExampleUtil.print(transposed);
+
+        MatrixExampleUtil.verifyTransposition(m, transposed);
+
+        System.out.println("\n>>> Creating matrices to be multiplied.");
+        double[][] data1 = new double[][] {{1, 2}, {3, 4}};
+        double[][] data2 = new double[][] {{5, 6}, {7, 8}};
+
+        Matrix m1 = new DenseLocalOnHeapMatrix(data1);
+        Matrix m2 = new DenseLocalOnHeapMatrix(data2);
+        Matrix mult = m1.times(m2);
+
+        System.out.println(">>> First matrix: ");
+        MatrixExampleUtil.print(m1);
+        System.out.println(">>> Second matrix: ");
+        MatrixExampleUtil.print(m2);
+        System.out.println(">>> Matrix product: ");
+        MatrixExampleUtil.print(mult);
+
+        System.out.println("\n>>> Calculating matrices determinants.");
+        double det1 = m1.determinant();
+        double det2 = m2.determinant();
+        double detMult = mult.determinant();
+        boolean detMultIsAsExp = Math.abs(detMult - det1 * det2) < 0.0001d;
+
+        System.out.println(">>> First matrix determinant: [" + det1 + "].");
+        System.out.println(">>> Second matrix determinant: [" + det2 + "].");
+        System.out.println(">>> Matrix product determinant: [" + detMult
+            + "], equals product of two other matrices determinants: [" + detMultIsAsExp + "].");
+
+        assert detMultIsAsExp : "Determinant of product matrix [" + detMult
+            + "] should be equal to product of determinants [" + (det1 * det2) + "].";
+
+        System.out.println("\n>>> Basic Matrix API usage example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExampleUtil.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExampleUtil.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExampleUtil.java
new file mode 100644
index 0000000..f3b4a62
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/MatrixExampleUtil.java
@@ -0,0 +1,52 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import org.apache.ignite.math.Matrix;
+import org.apache.ignite.math.Tracer;
+
+/**
+ * Utility functions for {@link Matrix} API examples.
+ */
+class MatrixExampleUtil {
+    /**
+     * Verifies matrix transposition.
+     *
+     * @param m Original matrix.
+     * @param transposed Transposed matrix.
+     */
+    static void verifyTransposition(Matrix m, Matrix transposed) {
+        for (int row = 0; row < m.rowSize(); row++)
+            for (int col = 0; col < m.columnSize(); col++) {
+                double val = m.get(row, col);
+                double valTransposed = transposed.get(col, row);
+
+                assert val == valTransposed : "Values not equal at (" + row + "," + col
+                    + "), original: " + val + " transposed: " + valTransposed;
+            }
+    }
+
+    /**
+     * Prints matrix values to console.
+     *
+     * @param m Matrix to print.
+     */
+    static void print(Matrix m) {
+        Tracer.showAscii(m);
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/OffHeapMatrixExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/OffHeapMatrixExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/OffHeapMatrixExample.java
new file mode 100644
index 0000000..bf99da1
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/OffHeapMatrixExample.java
@@ -0,0 +1,84 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import org.apache.ignite.math.Matrix;
+import org.apache.ignite.math.impls.matrix.DenseLocalOffHeapMatrix;
+
+/**
+ * This example shows how to use off-heap {@link Matrix} API.
+ */
+public final class OffHeapMatrixExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println();
+        System.out.println(">>> Off-heap matrix API usage example started.");
+
+        System.out.println("\n>>> Creating a matrix to be transposed.");
+        double[][] data = new double[][] {{1, 2, 3}, {4, 5, 6}};
+        Matrix m = new DenseLocalOffHeapMatrix(data.length, data[0].length);
+        m.assign(data);
+        Matrix transposed = m.transpose();
+
+        System.out.println(">>> Matrix: ");
+        MatrixExampleUtil.print(m);
+        System.out.println(">>> Transposed matrix: ");
+        MatrixExampleUtil.print(transposed);
+
+        MatrixExampleUtil.verifyTransposition(m, transposed);
+
+        System.out.println("\n>>> Creating matrices to be multiplied.");
+        double[][] data1 = new double[][] {{1, 2}, {3, 4}};
+        double[][] data2 = new double[][] {{5, 6}, {7, 8}};
+
+        Matrix m1 = new DenseLocalOffHeapMatrix(data1.length, data1[0].length);
+        Matrix m2 = new DenseLocalOffHeapMatrix(data2.length, data2[0].length);
+
+        m1.assign(data1);
+        m2.assign(data2);
+
+        Matrix mult = m1.times(m2);
+
+        System.out.println(">>> First matrix: ");
+        MatrixExampleUtil.print(m1);
+        System.out.println(">>> Second matrix: ");
+        MatrixExampleUtil.print(m2);
+        System.out.println(">>> Matrix product: ");
+        MatrixExampleUtil.print(mult);
+
+        System.out.println("\n>>> Calculating matrices determinants.");
+        double det1 = m1.determinant();
+        double det2 = m2.determinant();
+        double detMult = mult.determinant();
+        boolean detMultIsAsExp = Math.abs(detMult - det1 * det2) < 0.0001d;
+
+        System.out.println(">>> First matrix determinant: [" + det1 + "].");
+        System.out.println(">>> Second matrix determinant: [" + det2 + "].");
+        System.out.println(">>> Matrix product determinant: [" + detMult
+            + "], equals product of two other matrices determinants: [" + detMultIsAsExp + "].");
+
+        assert detMultIsAsExp : "Determinant of product matrix [" + detMult
+            + "] should be equal to product of determinants [" + (det1 * det2) + "].";
+
+        System.out.println("\n>>> Off-heap matrix API usage example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseDistributedMatrixExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseDistributedMatrixExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseDistributedMatrixExample.java
new file mode 100644
index 0000000..7e71eb0
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseDistributedMatrixExample.java
@@ -0,0 +1,65 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import org.apache.ignite.Ignite;
+import org.apache.ignite.Ignition;
+import org.apache.ignite.math.StorageConstants;
+import org.apache.ignite.math.impls.matrix.SparseDistributedMatrix;
+import org.apache.ignite.thread.IgniteThread;
+
+/**
+ * This example shows how to use {@link SparseDistributedMatrix} API.
+ */
+public class SparseDistributedMatrixExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) throws InterruptedException {
+        System.out.println();
+        System.out.println(">>> Sparse distributed matrix API usage example started.");
+        // Start ignite grid.
+        try (Ignite ignite = Ignition.start("examples/config/example-ignite.xml")) {
+            System.out.println(">>> Ignite grid started.");
+            // Create IgniteThread, we must work with SparseDistributedMatrix inside IgniteThread
+            // because we create ignite cache internally.
+            IgniteThread igniteThread = new IgniteThread(ignite.configuration().getIgniteInstanceName(), SparseDistributedMatrixExample.class.getSimpleName(), () -> {
+
+                double[][] testValues = {{1.0, 0.0, 0.0}, {0.0, 1.0, 0.0}, {0.0, 0.0, 1.0}};
+
+                System.out.println(">>> Create new SparseDistributedMatrix inside IgniteThread.");
+                // Create SparseDistributedMatrix, new cache will be created automagically.
+                SparseDistributedMatrix distributedMatrix = new SparseDistributedMatrix(testValues.length, testValues[0].length,
+                    StorageConstants.ROW_STORAGE_MODE, StorageConstants.RANDOM_ACCESS_MODE);
+
+                distributedMatrix.assign(testValues);
+
+                assert distributedMatrix.sum() == 3.0;
+
+                System.out.println(">>> Destroy SparseDistributedMatrix after using.");
+                // Destroy internal cache.
+                distributedMatrix.destroy();
+            });
+
+            igniteThread.start();
+
+            igniteThread.join();
+        }
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseMatrixExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseMatrixExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseMatrixExample.java
new file mode 100644
index 0000000..ba4e72b
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/SparseMatrixExample.java
@@ -0,0 +1,84 @@
+/*
+ * 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.ignite.examples.java8.math.matrix;
+
+import org.apache.ignite.math.Matrix;
+import org.apache.ignite.math.impls.matrix.SparseLocalOnHeapMatrix;
+
+/**
+ * This example shows how to use sparse {@link Matrix} API.
+ */
+public final class SparseMatrixExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println();
+        System.out.println(">>> Sparse matrix API usage example started.");
+
+        System.out.println("\n>>> Creating a matrix to be transposed.");
+        double[][] data = new double[][] {{1, 2, 3}, {4, 5, 6}};
+        Matrix m = new SparseLocalOnHeapMatrix(data.length, data[0].length);
+        m.assign(data);
+        Matrix transposed = m.transpose();
+
+        System.out.println(">>> Matrix: ");
+        MatrixExampleUtil.print(m);
+        System.out.println(">>> Transposed matrix: ");
+        MatrixExampleUtil.print(transposed);
+
+        MatrixExampleUtil.verifyTransposition(m, transposed);
+
+        System.out.println("\n>>> Creating matrices to be multiplied.");
+        double[][] data1 = new double[][] {{1, 2}, {3, 4}};
+        double[][] data2 = new double[][] {{5, 6}, {7, 8}};
+
+        Matrix m1 = new SparseLocalOnHeapMatrix(data1.length, data1[0].length);
+        Matrix m2 = new SparseLocalOnHeapMatrix(data2.length, data2[0].length);
+
+        m1.assign(data1);
+        m2.assign(data2);
+
+        Matrix mult = m1.times(m2);
+
+        System.out.println(">>> First matrix: ");
+        MatrixExampleUtil.print(m1);
+        System.out.println(">>> Second matrix: ");
+        MatrixExampleUtil.print(m2);
+        System.out.println(">>> Matrix product: ");
+        MatrixExampleUtil.print(mult);
+
+        System.out.println("\n>>> Calculating matrices determinants.");
+        double det1 = m1.determinant();
+        double det2 = m2.determinant();
+        double detMult = mult.determinant();
+        boolean detMultIsAsExp = Math.abs(detMult - det1 * det2) < 0.0001d;
+
+        System.out.println(">>> First matrix determinant: [" + det1 + "].");
+        System.out.println(">>> Second matrix determinant: [" + det2 + "].");
+        System.out.println(">>> Matrix product determinant: [" + detMult
+            + "], equals product of two other matrices determinants: [" + detMultIsAsExp + "].");
+
+        assert detMultIsAsExp : "Determinant of product matrix [" + detMult
+            + "] should be equal to product of determinants [" + (det1 * det2) + "].";
+
+        System.out.println("\n>>> Sparse matrix API usage example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/package-info.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/package-info.java
new file mode 100644
index 0000000..9154518
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/matrix/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * 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 description. -->
+ * Core algebra matrix examples.
+ */
+package org.apache.ignite.examples.java8.math.matrix;

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/package-info.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/package-info.java
new file mode 100644
index 0000000..90dae33
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * 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 description. -->
+ * Core algebra examples.
+ */
+package org.apache.ignite.examples.java8.math;

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/TracerExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/TracerExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/TracerExample.java
new file mode 100644
index 0000000..f6e1baa
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/TracerExample.java
@@ -0,0 +1,63 @@
+/*
+ * 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.ignite.examples.java8.math.tracer;
+
+import java.awt.Color;
+import java.io.IOException;
+import org.apache.ignite.math.Tracer;
+import org.apache.ignite.math.impls.matrix.DenseLocalOnHeapMatrix;
+
+/**
+ * Example of using {@link Tracer} utility API.
+ */
+public class TracerExample {
+    /**
+     * Double to color mapper example.
+     */
+    private static final Tracer.ColorMapper COLOR_MAPPER = d -> {
+        if (d <= 0.33)
+            return Color.RED;
+        else if (d <= 0.66)
+            return Color.GREEN;
+        else
+            return Color.BLUE;
+    };
+
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) throws IOException {
+        System.out.println(">>> Tracer utility example started.");
+
+        // Tracer is a simple utility class that allows pretty-printing of matrices/vectors
+        DenseLocalOnHeapMatrix m = new DenseLocalOnHeapMatrix(new double[][] {
+            {1.12345, 2.12345},
+            {3.12345, 4.12345}
+        });
+
+        System.out.println("\n>>> Tracer output to console in ASCII.");
+        Tracer.showAscii(m, "%.3g");
+
+        System.out.println("\n>>> Tracer output to browser in HTML.");
+        Tracer.showHtml(m, COLOR_MAPPER);
+
+        System.out.println("\n>>> Tracer utility example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/package-info.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/package-info.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/package-info.java
new file mode 100644
index 0000000..5a08504
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/tracer/package-info.java
@@ -0,0 +1,22 @@
+/*
+ * 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 description. -->
+ * Core algebra tracer example.
+ */
+package org.apache.ignite.examples.java8.math.tracer;

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/CacheVectorExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/CacheVectorExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/CacheVectorExample.java
new file mode 100644
index 0000000..dd0fcb3
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/CacheVectorExample.java
@@ -0,0 +1,102 @@
+/*
+ * 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.ignite.examples.java8.math.vector;
+
+import org.apache.ignite.Ignite;
+import org.apache.ignite.IgniteCache;
+import org.apache.ignite.Ignition;
+import org.apache.ignite.configuration.CacheConfiguration;
+import org.apache.ignite.math.IdentityValueMapper;
+import org.apache.ignite.math.ValueMapper;
+import org.apache.ignite.math.VectorKeyMapper;
+import org.apache.ignite.math.impls.vector.CacheVector;
+
+/**
+ * This example shows how to use {@link CacheVector} API.
+ */
+public class CacheVectorExample {
+    /** */ private static final String CACHE_NAME = CacheVectorExample.class.getSimpleName();
+    /** */ private static final int CARDINALITY = 10;
+
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        try (Ignite ignite = Ignition.start("examples/config/example-ignite.xml")) {
+            System.out.println();
+            System.out.println(">>> CacheVector example started.");
+
+            CacheConfiguration<Integer, Double> cfg = new CacheConfiguration<>();
+
+            cfg.setName(CACHE_NAME);
+
+            try (IgniteCache<Integer, Double> cache = ignite.getOrCreateCache(cfg)) {
+                double[] testValues1 = {1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
+                double[] testValues2 = {0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
+
+                ValueMapper valMapper = new IdentityValueMapper();
+
+                // Map vector element index to cache keys.
+                VectorKeyMapper<Integer> keyMapper1 = new VectorKeyMapper<Integer>() {
+                    @Override public Integer apply(int i) {
+                        return i;
+                    }
+
+                    @Override public boolean isValid(Integer integer) {
+                        return integer >= 0 && CARDINALITY > integer;
+                    }
+                };
+
+                // Map vector element index to cache keys with shift.
+                VectorKeyMapper<Integer> keyMapper2 = new VectorKeyMapper<Integer>() {
+                    @Override public Integer apply(int i) {
+                        return i + CARDINALITY;
+                    }
+
+                    @Override public boolean isValid(Integer integer) {
+                        return integer >= 0 && CARDINALITY > integer;
+                    }
+                };
+
+                // Create two cache vectors over one cache.
+                CacheVector cacheVector1 = new CacheVector(CARDINALITY, cache, keyMapper1, valMapper);
+                System.out.println(">>> First cache vector created.");
+
+                CacheVector cacheVector2 = new CacheVector(CARDINALITY, cache, keyMapper2, valMapper);
+                System.out.println(">>> Second cache vector created.");
+
+                cacheVector1.assign(testValues1);
+                cacheVector2.assign(testValues2);
+
+                // Dot product for orthogonal vectors is 0.0.
+                assert cacheVector1.dot(cacheVector2) == 0.0;
+
+                System.out.println(">>>");
+                System.out.println(">>> Finished executing Ignite \"CacheVector\" example.");
+                System.out.println(">>> Dot product is 0.0 for orthogonal vectors.");
+                System.out.println(">>>");
+            }
+            finally {
+                // Distributed cache could be removed from cluster only by #destroyCache() call.
+                ignite.destroyCache(CACHE_NAME);
+            }
+        }
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/ExampleVectorStorage.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/ExampleVectorStorage.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/ExampleVectorStorage.java
new file mode 100644
index 0000000..3b88e0a
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/ExampleVectorStorage.java
@@ -0,0 +1,126 @@
+/*
+ * 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.ignite.examples.java8.math.vector;
+
+import java.io.IOException;
+import java.io.ObjectInput;
+import java.io.ObjectOutput;
+import java.util.Arrays;
+
+import org.apache.ignite.math.VectorStorage;
+
+/**
+ * Example vector storage, modeled after {@link org.apache.ignite.math.impls.storage.vector.ArrayVectorStorage}.
+ */
+class ExampleVectorStorage implements VectorStorage {
+    /** */
+    private double[] data;
+
+    /**
+     * IMPL NOTE required by Externalizable
+     */
+    public ExampleVectorStorage() {
+        // No-op.
+    }
+
+    /**
+     * @param data backing data array.
+     */
+    ExampleVectorStorage(double[] data) {
+        assert data != null;
+
+        this.data = data;
+    }
+
+    /** {@inheritDoc} */
+    @Override public int size() {
+        return data == null ? 0 : data.length;
+    }
+
+    /** {@inheritDoc} */
+    @Override public double get(int i) {
+        return data[i];
+    }
+
+    /** {@inheritDoc} */
+    @Override public void set(int i, double v) {
+        data[i] = v;
+    }
+
+    /** {@inheritDoc}} */
+    @Override public boolean isArrayBased() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    @Override public double[] data() {
+        return data;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isSequentialAccess() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isDense() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isRandomAccess() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean isDistributed() {
+        return false;
+    }
+
+    /** {@inheritDoc} */
+    @Override public void writeExternal(ObjectOutput out) throws IOException {
+        out.writeObject(data);
+    }
+
+    /** {@inheritDoc} */
+    @Override public void readExternal(ObjectInput in) throws IOException, ClassNotFoundException {
+        data = (double[])in.readObject();
+    }
+
+    /** {@inheritDoc} */
+    @Override public int hashCode() {
+        int res = 1;
+
+        res = res * 37 + Arrays.hashCode(data);
+
+        return res;
+    }
+
+    /** {@inheritDoc} */
+    @Override public boolean equals(Object obj) {
+        if (this == obj)
+            return true;
+
+        if (obj == null || getClass() != obj.getClass())
+            return false;
+
+        ExampleVectorStorage that = (ExampleVectorStorage)obj;
+
+        return Arrays.equals(data, (that.data));
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/OffHeapVectorExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/OffHeapVectorExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/OffHeapVectorExample.java
new file mode 100644
index 0000000..7184245
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/OffHeapVectorExample.java
@@ -0,0 +1,78 @@
+/*
+ * 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.ignite.examples.java8.math.vector;
+
+import java.util.Arrays;
+import org.apache.ignite.math.Vector;
+import org.apache.ignite.math.impls.vector.DenseLocalOffHeapVector;
+
+/**
+ * This example shows how to use off-heap {@link Vector} API.
+ */
+public final class OffHeapVectorExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println();
+        System.out.println(">>> Off-heap vector API usage example started.");
+
+        System.out.println("\n>>> Creating perpendicular off-heap vectors.");
+        double[] data1 = new double[] {1, 0, 3, 0, 5, 0};
+        double[] data2 = new double[] {0, 2, 0, 4, 0, 6};
+
+        Vector v1 = new DenseLocalOffHeapVector(data1.length);
+        Vector v2 = new DenseLocalOffHeapVector(data2.length);
+
+        v1.assign(data1);
+        v2.assign(data2);
+
+        System.out.println(">>> First vector: " + Arrays.toString(data1));
+        System.out.println(">>> Second vector: " + Arrays.toString(data2));
+
+        double dotProduct = v1.dot(v2);
+        boolean dotProductIsAsExp = dotProduct == 0;
+
+        System.out.println("\n>>> Dot product of vectors: [" + dotProduct
+            + "], it is 0 as expected: [" + dotProductIsAsExp + "].");
+
+        assert dotProductIsAsExp : "Expect dot product of perpendicular vectors to be 0.";
+
+        Vector hypotenuse = v1.plus(v2);
+
+        System.out.println("\n>>> Hypotenuse (sum of vectors): " + Arrays.toString(hypotenuse.getStorage().data()));
+
+        double lenSquared1 = v1.getLengthSquared();
+        double lenSquared2 = v2.getLengthSquared();
+        double lenSquaredHypotenuse = hypotenuse.getLengthSquared();
+
+        boolean lenSquaredHypotenuseIsAsExp = lenSquaredHypotenuse == lenSquared1 + lenSquared2;
+
+        System.out.println(">>> Squared length of first vector: [" + lenSquared1 + "].");
+        System.out.println(">>> Squared length of second vector: [" + lenSquared2 + "].");
+        System.out.println(">>> Squared length of hypotenuse: [" + lenSquaredHypotenuse
+            + "], equals sum of squared lengths of two original vectors as expected: ["
+            + lenSquaredHypotenuseIsAsExp + "].");
+
+        assert lenSquaredHypotenuseIsAsExp : "Expect squared length of hypotenuse to be as per Pythagorean theorem.";
+
+        System.out.println("\n>>> Off-heap vector API usage example completed.");
+    }
+}

http://git-wip-us.apache.org/repos/asf/ignite/blob/acd21fb8/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/SparseVectorExample.java
----------------------------------------------------------------------
diff --git a/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/SparseVectorExample.java b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/SparseVectorExample.java
new file mode 100644
index 0000000..79e0567
--- /dev/null
+++ b/examples/src/main/java8/org/apache/ignite/examples/java8/math/vector/SparseVectorExample.java
@@ -0,0 +1,80 @@
+/*
+ * 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.ignite.examples.java8.math.vector;
+
+import java.util.Arrays;
+import org.apache.ignite.math.Vector;
+import org.apache.ignite.math.impls.vector.SparseLocalVector;
+
+import static org.apache.ignite.math.StorageConstants.RANDOM_ACCESS_MODE;
+
+/**
+ * This example shows how to use sparse {@link Vector} API.
+ */
+public final class SparseVectorExample {
+    /**
+     * Executes example.
+     *
+     * @param args Command line arguments, none required.
+     */
+    public static void main(String[] args) {
+        System.out.println();
+        System.out.println(">>> Sparse vector API usage example started.");
+
+        System.out.println("\n>>> Creating perpendicular sparse vectors.");
+        double[] data1 = new double[] {1, 0, 3, 0, 5, 0};
+        double[] data2 = new double[] {0, 2, 0, 4, 0, 6};
+
+        Vector v1 = new SparseLocalVector(data1.length, RANDOM_ACCESS_MODE);
+        Vector v2 = new SparseLocalVector(data2.length, RANDOM_ACCESS_MODE);
+
+        v1.assign(data1);
+        v2.assign(data2);
+
+        System.out.println(">>> First vector: " + Arrays.toString(data1));
+        System.out.println(">>> Second vector: " + Arrays.toString(data2));
+
+        double dotProduct = v1.dot(v2);
+        boolean dotProductIsAsExp = dotProduct == 0;
+
+        System.out.println("\n>>> Dot product of vectors: [" + dotProduct
+            + "], it is 0 as expected: [" + dotProductIsAsExp + "].");
+
+        assert dotProductIsAsExp : "Expect dot product of perpendicular vectors to be 0.";
+
+        Vector hypotenuse = v1.plus(v2);
+
+        System.out.println("\n>>> Hypotenuse (sum of vectors): " + Arrays.toString(hypotenuse.getStorage().data()));
+
+        double lenSquared1 = v1.getLengthSquared();
+        double lenSquared2 = v2.getLengthSquared();
+        double lenSquaredHypotenuse = hypotenuse.getLengthSquared();
+
+        boolean lenSquaredHypotenuseIsAsExp = lenSquaredHypotenuse == lenSquared1 + lenSquared2;
+
+        System.out.println(">>> Squared length of first vector: [" + lenSquared1 + "].");
+        System.out.println(">>> Squared length of second vector: [" + lenSquared2 + "].");
+        System.out.println(">>> Squared length of hypotenuse: [" + lenSquaredHypotenuse
+            + "], equals sum of squared lengths of two original vectors as expected: ["
+            + lenSquaredHypotenuseIsAsExp + "].");
+
+        assert lenSquaredHypotenuseIsAsExp : "Expect squared length of hypotenuse to be as per Pythagorean theorem.";
+
+        System.out.println("\n>>> Sparse vector API usage example completed.");
+    }
+}


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