diff --git a/flink-ml-parent/flink-ml-lib/src/main/java/org/apache/flink/ml/common/linalg/BLAS.java b/flink-ml-parent/flink-ml-lib/src/main/java/org/apache/flink/ml/common/linalg/BLAS.java
index f5d9e8497e8e6..b1d0ba64cb77e 100644
--- a/flink-ml-parent/flink-ml-lib/src/main/java/org/apache/flink/ml/common/linalg/BLAS.java
+++ b/flink-ml-parent/flink-ml-lib/src/main/java/org/apache/flink/ml/common/linalg/BLAS.java
@@ -19,18 +19,51 @@
 
 package org.apache.flink.ml.common.linalg;
 
+import org.apache.flink.util.Preconditions;
+
 /**
  * A utility class that provides BLAS routines over matrices and vectors.
  */
 public class BLAS {
+
+	// For level-1 routines, we use Java implementation.
 	private static final com.github.fommil.netlib.BLAS NATIVE_BLAS = com.github.fommil.netlib.BLAS.getInstance();
+
+	// For level-2 and level-3 routines, we use the native BLAS.
+	// The NATIVE_BLAS instance tries to load BLAS implementations in the order:
+	//   1) optimized system libraries such as Intel MKL,
+	//   2) self-contained native builds using the reference Fortran from netlib.org,
+	//   3) F2J implementation.
+	// If to use optimized system libraries, it is important to turn of their multi-thread support.
+	// Otherwise, it will conflict with Flink's executor and leads to performance loss.
 	private static final com.github.fommil.netlib.BLAS F2J_BLAS = com.github.fommil.netlib.F2jBLAS.getInstance();
 
+	/**
+	 * \sum_i |x_i| .
+	 */
+	public static double asum(int n, double[] x, int offset) {
+		return F2J_BLAS.dasum(n, x, offset, 1);
+	}
+
+	/**
+	 * \sum_i |x_i| .
+	 */
+	public static double asum(DenseVector x) {
+		return asum(x.data.length, x.data, 0);
+	}
+
+	/**
+	 * \sum_i |x_i| .
+	 */
+	public static double asum(SparseVector x) {
+		return asum(x.values.length, x.values, 0);
+	}
+
 	/**
 	 * y += a * x .
 	 */
 	public static void axpy(double a, double[] x, double[] y) {
-		assert x.length == y.length : "Array dimension mismatched.";
+		Preconditions.checkArgument(x.length == y.length, "Array dimension mismatched.");
 		F2J_BLAS.daxpy(x.length, a, x, 1, y, 1);
 	}
 
@@ -38,7 +71,7 @@ public static void axpy(double a, double[] x, double[] y) {
 	 * y += a * x .
 	 */
 	public static void axpy(double a, DenseVector x, DenseVector y) {
-		assert x.data.length == y.data.length : "Vector dimension mismatched.";
+		Preconditions.checkArgument(x.data.length == y.data.length, "Vector dimension mismatched.");
 		F2J_BLAS.daxpy(x.data.length, a, x.data, 1, y.data, 1);
 	}
 
@@ -55,24 +88,34 @@ public static void axpy(double a, SparseVector x, DenseVector y) {
 	 * y += a * x .
 	 */
 	public static void axpy(double a, DenseMatrix x, DenseMatrix y) {
-		assert x.m == y.m && x.n == y.n : "Matrix dimension mismatched.";
+		Preconditions.checkArgument(x.m == y.m && x.n == y.n, "Matrix dimension mismatched.");
 		F2J_BLAS.daxpy(x.data.length, a, x.data, 1, y.data, 1);
 	}
 
+	/**
+	 * y[yOffset:yOffset+n] += a * x[xOffset:xOffset+n] .
+	 */
+	public static void axpy(int n, double a, double[] x, int xOffset, double[] y, int yOffset) {
+		F2J_BLAS.daxpy(n, a, x, xOffset, 1, y, yOffset, 1);
+	}
+
 	/**
 	 * x \cdot y .
 	 */
 	public static double dot(double[] x, double[] y) {
-		assert x.length == y.length : "Array dimension mismatched.";
-		return F2J_BLAS.ddot(x.length, x, 1, y, 1);
+		Preconditions.checkArgument(x.length == y.length, "Array dimension mismatched.");
+		double s = 0.;
+		for (int i = 0; i < x.length; i++) {
+			s += x[i] * y[i];
+		}
+		return s;
 	}
 
 	/**
 	 * x \cdot y .
 	 */
 	public static double dot(DenseVector x, DenseVector y) {
-		assert x.data.length == y.data.length : "Vector dimension mismatched.";
-		return F2J_BLAS.ddot(x.data.length, x.data, 1, y.data, 1);
+		return dot(x.getData(), y.getData());
 	}
 
 	/**
@@ -109,14 +152,18 @@ public static void scal(double a, DenseMatrix x) {
 	public static void gemm(double alpha, DenseMatrix matA, boolean transA, DenseMatrix matB, boolean transB,
 							double beta, DenseMatrix matC) {
 		if (transA) {
-			assert matA.numCols() == matC.numRows() : "The columns of A does not match the rows of C";
+			Preconditions.checkArgument(matA.numCols() == matC.numRows(),
+				"The columns of A does not match the rows of C");
 		} else {
-			assert matA.numRows() == matC.numRows() : "The rows of A does not match the rows of C";
+			Preconditions.checkArgument(matA.numRows() == matC.numRows(),
+				"The rows of A does not match the rows of C");
 		}
 		if (transB) {
-			assert matB.numRows() == matC.numCols() : "The rows of B does not match the columns of C";
+			Preconditions.checkArgument(matB.numRows() == matC.numCols(),
+				"The rows of B does not match the columns of C");
 		} else {
-			assert matB.numCols() == matC.numCols() : "The columns of B does not match the columns of C";
+			Preconditions.checkArgument(matB.numCols() == matC.numCols(),
+				"The columns of B does not match the columns of C");
 		}
 
 		final int m = matC.numRows();
@@ -131,19 +178,56 @@ public static void gemm(double alpha, DenseMatrix matA, boolean transA, DenseMat
 	}
 
 	/**
-	 * y := alpha * A * x + beta * y .
+	 * Check the compatibility of matrix and vector sizes in <code>gemv</code>.
 	 */
-	public static void gemv(double alpha, DenseMatrix matA, boolean transA,
-							DenseVector x, double beta, DenseVector y) {
+	private static void gemvDimensionCheck(DenseMatrix matA, boolean transA, Vector x, Vector y) {
 		if (transA) {
-			assert (matA.numCols() == y.size() && matA.numRows() == x.size()) : "Matrix and vector size mismatched.";
+			Preconditions.checkArgument(matA.numCols() == y.size() && matA.numRows() == x.size(),
+				"Matrix and vector size mismatched.");
 		} else {
-			assert (matA.numRows() == y.size() && matA.numCols() == x.size()) : "Matrix and vector size mismatched.";
+			Preconditions.checkArgument(matA.numRows() == y.size() && matA.numCols() == x.size(),
+				"Matrix and vector size mismatched.");
 		}
+	}
+
+	/**
+	 * y := alpha * A * x + beta * y .
+	 */
+	public static void gemv(double alpha, DenseMatrix matA, boolean transA,
+							DenseVector x, double beta, DenseVector y) {
+		gemvDimensionCheck(matA, transA, x, y);
 		final int m = matA.numRows();
 		final int n = matA.numCols();
 		final int lda = matA.numRows();
 		final String ta = transA ? "T" : "N";
 		NATIVE_BLAS.dgemv(ta, m, n, alpha, matA.getData(), lda, x.getData(), 1, beta, y.getData(), 1);
 	}
+
+	/**
+	 * y := alpha * A * x + beta * y .
+	 */
+	public static void gemv(double alpha, DenseMatrix matA, boolean transA,
+							SparseVector x, double beta, DenseVector y) {
+		gemvDimensionCheck(matA, transA, x, y);
+		final int m = matA.numRows();
+		final int n = matA.numCols();
+		if (transA) {
+			int start = 0;
+			for (int i = 0; i < n; i++) {
+				double s = 0.;
+				for (int j = 0; j < x.indices.length; j++) {
+					s += x.values[j] * matA.data[start + x.indices[j]];
+				}
+				y.data[i] = beta * y.data[i] + alpha * s;
+				start += m;
+			}
+		} else {
+			scal(beta, y);
+			for (int i = 0; i < x.indices.length; i++) {
+				int index = x.indices[i];
+				double value = alpha * x.values[i];
+				F2J_BLAS.daxpy(m, value, matA.data, index * m, 1, y.data, 0, 1);
+			}
+		}
+	}
 }
diff --git a/flink-ml-parent/flink-ml-lib/src/test/java/org/apache/flink/ml/common/linalg/BLASTest.java b/flink-ml-parent/flink-ml-lib/src/test/java/org/apache/flink/ml/common/linalg/BLASTest.java
new file mode 100644
index 0000000000000..c30b0dfaee57b
--- /dev/null
+++ b/flink-ml-parent/flink-ml-lib/src/test/java/org/apache/flink/ml/common/linalg/BLASTest.java
@@ -0,0 +1,188 @@
+/*
+ * 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.flink.ml.common.linalg;
+
+import org.junit.Assert;
+import org.junit.Rule;
+import org.junit.Test;
+import org.junit.rules.ExpectedException;
+
+/**
+ * The test cases for {@link BLAS}.
+ */
+public class BLASTest {
+	private static final double TOL = 1.0e-8;
+	private DenseMatrix mat = new DenseMatrix(2, 3, new double[]{1, 4, 2, 5, 3, 6});
+	private DenseVector dv1 = new DenseVector(new double[]{1, 2});
+	private DenseVector dv2 = new DenseVector(new double[]{1, 2, 3});
+	private SparseVector spv1 = new SparseVector(2, new int[]{0, 1}, new double[]{1, 2});
+	private SparseVector spv2 = new SparseVector(3, new int[]{0, 2}, new double[]{1, 3});
+
+	@Rule
+	public ExpectedException thrown = ExpectedException.none();
+
+	@Test
+	public void testAsum() throws Exception {
+		Assert.assertEquals(BLAS.asum(dv1), 3.0, TOL);
+		Assert.assertEquals(BLAS.asum(spv1), 3.0, TOL);
+	}
+
+	@Test
+	public void testScal() throws Exception {
+		DenseVector v1 = dv1.clone();
+		BLAS.scal(0.5, v1);
+		Assert.assertArrayEquals(v1.getData(), new double[]{0.5, 1.0}, TOL);
+
+		SparseVector v2 = spv1.clone();
+		BLAS.scal(0.5, v2);
+		Assert.assertArrayEquals(v2.getIndices(), spv1.getIndices());
+		Assert.assertArrayEquals(v2.getValues(), new double[]{0.5, 1.0}, TOL);
+	}
+
+	@Test
+	public void testDot() throws Exception {
+		DenseVector v = DenseVector.ones(2);
+		Assert.assertEquals(BLAS.dot(dv1, v), 3.0, TOL);
+	}
+
+	@Test
+	public void testAxpy() throws Exception {
+		DenseVector v = DenseVector.ones(2);
+		BLAS.axpy(1.0, dv1, v);
+		Assert.assertArrayEquals(v.getData(), new double[]{2, 3}, TOL);
+		BLAS.axpy(1.0, spv1, v);
+		Assert.assertArrayEquals(v.getData(), new double[]{3, 5}, TOL);
+		BLAS.axpy(1, 1.0, new double[]{1}, 0, v.getData(), 1);
+		Assert.assertArrayEquals(v.getData(), new double[]{3, 6}, TOL);
+	}
+
+	private DenseMatrix simpleMM(DenseMatrix m1, DenseMatrix m2) {
+		DenseMatrix mm = new DenseMatrix(m1.numRows(), m2.numCols());
+		for (int i = 0; i < m1.numRows(); i++) {
+			for (int j = 0; j < m2.numCols(); j++) {
+				double s = 0.;
+				for (int k = 0; k < m1.numCols(); k++) {
+					s += m1.get(i, k) * m2.get(k, j);
+				}
+				mm.set(i, j, s);
+			}
+		}
+		return mm;
+	}
+
+	@Test
+	public void testGemm() throws Exception {
+		DenseMatrix m32 = DenseMatrix.rand(3, 2);
+		DenseMatrix m24 = DenseMatrix.rand(2, 4);
+		DenseMatrix m34 = DenseMatrix.rand(3, 4);
+		DenseMatrix m42 = DenseMatrix.rand(4, 2);
+		DenseMatrix m43 = DenseMatrix.rand(4, 3);
+
+		DenseMatrix a34 = DenseMatrix.zeros(3, 4);
+		BLAS.gemm(1.0, m32, false, m24, false, 0., a34);
+		Assert.assertArrayEquals(a34.getData(), simpleMM(m32, m24).getData(), TOL);
+
+		BLAS.gemm(1.0, m32, false, m42, true, 0., a34);
+		Assert.assertArrayEquals(a34.getData(), simpleMM(m32, m42.transpose()).getData(), TOL);
+
+		DenseMatrix a24 = DenseMatrix.zeros(2, 4);
+		BLAS.gemm(1.0, m32, true, m34, false, 0., a24);
+		Assert.assertArrayEquals(a24.getData(), simpleMM(m32.transpose(), m34).getData(), TOL);
+
+		BLAS.gemm(1.0, m32, true, m43, true, 0., a24);
+		Assert.assertArrayEquals(a24.getData(), simpleMM(m32.transpose(), m43.transpose()).getData(), TOL);
+	}
+
+	@Test
+	public void testGemmSizeCheck() throws Exception {
+		thrown.expect(IllegalArgumentException.class);
+		DenseMatrix m32 = DenseMatrix.rand(3, 2);
+		DenseMatrix m42 = DenseMatrix.rand(4, 2);
+		DenseMatrix a34 = DenseMatrix.zeros(3, 4);
+		BLAS.gemm(1.0, m32, false, m42, false, 0., a34);
+	}
+
+	@Test
+	public void testGemmTransposeSizeCheck() throws Exception {
+		thrown.expect(IllegalArgumentException.class);
+		DenseMatrix m32 = DenseMatrix.rand(3, 2);
+		DenseMatrix m42 = DenseMatrix.rand(4, 2);
+		DenseMatrix a34 = DenseMatrix.zeros(3, 4);
+		BLAS.gemm(1.0, m32, true, m42, true, 0., a34);
+	}
+
+	@Test
+	public void testGemvDense() throws Exception {
+		DenseVector y1 = DenseVector.ones(2);
+		BLAS.gemv(2.0, mat, false, dv2, 0., y1);
+		Assert.assertArrayEquals(new double[]{28, 64}, y1.data, TOL);
+
+		DenseVector y2 = DenseVector.ones(2);
+		BLAS.gemv(2.0, mat, false, dv2, 1., y2);
+		Assert.assertArrayEquals(new double[]{29, 65}, y2.data, TOL);
+	}
+
+	@Test
+	public void testGemvDenseTranspose() throws Exception {
+		DenseVector y1 = DenseVector.ones(3);
+		BLAS.gemv(1.0, mat, true, dv1, 0., y1);
+		Assert.assertArrayEquals(new double[]{9, 12, 15}, y1.data, TOL);
+
+		DenseVector y2 = DenseVector.ones(3);
+		BLAS.gemv(1.0, mat, true, dv1, 1., y2);
+		Assert.assertArrayEquals(new double[]{10, 13, 16}, y2.data, TOL);
+	}
+
+	@Test
+	public void testGemvSparse() throws Exception {
+		DenseVector y1 = DenseVector.ones(2);
+		BLAS.gemv(2.0, mat, false, spv2, 0., y1);
+		Assert.assertArrayEquals(new double[]{20, 44}, y1.data, TOL);
+
+		DenseVector y2 = DenseVector.ones(2);
+		BLAS.gemv(2.0, mat, false, spv2, 1., y2);
+		Assert.assertArrayEquals(new double[]{21, 45}, y2.data, TOL);
+	}
+
+	@Test
+	public void testGemvSparseTranspose() throws Exception {
+		DenseVector y1 = DenseVector.ones(3);
+		BLAS.gemv(2.0, mat, true, spv1, 0., y1);
+		Assert.assertArrayEquals(new double[]{18, 24, 30}, y1.data, TOL);
+
+		DenseVector y2 = DenseVector.ones(3);
+		BLAS.gemv(2.0, mat, true, spv1, 1., y2);
+		Assert.assertArrayEquals(new double[]{19, 25, 31}, y2.data, TOL);
+	}
+
+	@Test
+	public void testGemvSizeCheck() throws Exception {
+		thrown.expect(IllegalArgumentException.class);
+		DenseVector y = DenseVector.ones(2);
+		BLAS.gemv(2.0, mat, false, dv1, 0., y);
+	}
+
+	@Test
+	public void testGemvTransposeSizeCheck() throws Exception {
+		thrown.expect(IllegalArgumentException.class);
+		DenseVector y = DenseVector.ones(2);
+		BLAS.gemv(2.0, mat, true, dv1, 0., y);
+	}
+}