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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 (double) vector spaces. No direct access to the coefficients of the underlying matrix is provided. The motivation for such an interface is well stated by Barrett et al. (1994):
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 · x
(and perhaps z = AT · 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.
- Barret et al. (1994)
-
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,
Templates for the Solution of Linear Systems: Building Blocks for
Iterative Methods, SIAM
Since: 3.0
/**
* 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.
*
* 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 · x
* (and perhaps z = A<sup>T</sup> · 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></dt>
* <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
* </dd>
* </dl>
*
* @since 3.0
*/
public abstract class RealLinearOperator {
Returns the dimension of the codomain of this operator.
Returns: the number of rows of the underlying matrix
/**
* 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.
Returns: the number of columns of the underlying matrix
/**
* 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 this by the vector x. Params: - x – the vector to operate on
Throws: - DimensionMismatchException – if the column dimension does not match the size of
x
Returns: the product of this instance with x
/**
* 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 this operator by the vector x (optional operation). The default implementation throws an UnsupportedOperationException. Users overriding this method must also override isTransposable(). Params: - x – the vector to operate on
Throws: - DimensionMismatchException – if the row dimension does not match the size of
x - UnsupportedOperationException – if this operation is not supported by
this operator
Returns: the product of the transpose of this instance with x
/**
* 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 true if this operator supports operateTranspose(RealVector). If true is returned, operateTranspose(RealVector) should not throw UnsupportedOperationException. The default implementation returns false. Returns: false
/**
* 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;
}
}