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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math3.linear;
+
+import org.apache.commons.math3.exception.DimensionMismatchException;
+
+/**
+ * This class defines a linear operator operating on real ({@code double}) vector spaces. No direct
+ * access to the coefficients of the underlying matrix is provided.
+ *
+ * <p>The motivation for such an interface is well stated by <a href="#BARR1994">Barrett et al.
+ * (1994)</a>:
+ *
+ * <blockquote>
+ *
+ * We restrict ourselves to iterative methods, which work by repeatedly improving an approximate
+ * solution until it is accurate enough. These methods access the coefficient matrix A of the linear
+ * system only via the matrix-vector product y = A &middot; x (and perhaps z = A<sup>T</sup>
+ * &middot; x). Thus the user need only supply a subroutine for computing y (and perhaps z) given x,
+ * which permits full exploitation of the sparsity or other special structure of A.
+ *
+ * </blockquote>
+ *
+ * <br>
+ *
+ * <dl>
+ *   <dt><a name="BARR1994">Barret et al. (1994)</a>
+ *   <dd>R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra, V. Eijkhout, R.
+ *       Pozo, C. Romine and H. Van der Vorst, <em>Templates for the Solution of Linear Systems:
+ *       Building Blocks for Iterative Methods</em>, SIAM
+ * </dl>
+ *
+ * @since 3.0
+ */
+public abstract class RealLinearOperator {
+    /**
+     * Returns the dimension of the codomain of this operator.
+     *
+     * @return the number of rows of the underlying matrix
+     */
+    public abstract int getRowDimension();
+
+    /**
+     * Returns the dimension of the domain of this operator.
+     *
+     * @return the number of columns of the underlying matrix
+     */
+    public abstract int getColumnDimension();
+
+    /**
+     * Returns the result of multiplying {@code this} by the vector {@code x}.
+     *
+     * @param x the vector to operate on
+     * @return the product of {@code this} instance with {@code x}
+     * @throws DimensionMismatchException if the column dimension does not match the size of {@code
+     *     x}
+     */
+    public abstract RealVector operate(final RealVector x) throws DimensionMismatchException;
+
+    /**
+     * Returns the result of multiplying the transpose of {@code this} operator by the vector {@code
+     * x} (optional operation). The default implementation throws an {@link
+     * UnsupportedOperationException}. Users overriding this method must also override {@link
+     * #isTransposable()}.
+     *
+     * @param x the vector to operate on
+     * @return the product of the transpose of {@code this} instance with {@code x}
+     * @throws org.apache.commons.math3.exception.DimensionMismatchException if the row dimension
+     *     does not match the size of {@code x}
+     * @throws UnsupportedOperationException if this operation is not supported by {@code this}
+     *     operator
+     */
+    public RealVector operateTranspose(final RealVector x)
+            throws DimensionMismatchException, UnsupportedOperationException {
+        throw new UnsupportedOperationException();
+    }
+
+    /**
+     * Returns {@code true} if this operator supports {@link #operateTranspose(RealVector)}. If
+     * {@code true} is returned, {@link #operateTranspose(RealVector)} should not throw {@code
+     * UnsupportedOperationException}. The default implementation returns {@code false}.
+     *
+     * @return {@code false}
+     */
+    public boolean isTransposable() {
+        return false;
+    }
+}