/*
* Copyright (c) 2009-2015, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* Licensed 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.ejml.ops;
import org.ejml.alg.dense.decompose.chol.CholeskyDecompositionInner_CD64;
import org.ejml.alg.dense.mult.CVectorVectorMult;
import org.ejml.data.CD1Matrix64F;
import org.ejml.data.CDenseMatrix64F;
import org.ejml.data.Complex64F;
import org.ejml.data.ComplexMatrix64F;
/**
*
* Functions for computing the features of complex matrices
*
*
* @author Peter Abeles
*/
public class CMatrixFeatures {
/**
* Checks to see if any element in the matrix is NaN.
*
* @param m A matrix. Not modified.
* @return True if any element in the matrix is NaN.
*/
public static boolean hasNaN( CD1Matrix64F m )
{
int length = m.getDataLength();
for( int i = 0; i < length; i++ ) {
if( Double.isNaN(m.data[i]))
return true;
}
return false;
}
/**
* Checks to see if any element in the matrix is NaN of Infinite.
*
* @param m A matrix. Not modified.
* @return True if any element in the matrix is NaN of Infinite.
*/
public static boolean hasUncountable( CD1Matrix64F m )
{
int length = m.getDataLength();
for( int i = 0; i < length; i++ ) {
double a = m.data[i];
if( Double.isNaN(a) || Double.isInfinite(a))
return true;
}
return false;
}
/**
*
* Checks to see if each element in the two matrices are equal:
* aij == bij
*
*
*
* NOTE: If any of the elements are NaN then false is returned. If two corresponding
* elements are both positive or negative infinity then they are equal.
*
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @return true if identical and false otherwise.
*/
public static boolean isEquals( CD1Matrix64F a, CD1Matrix64F b ) {
if( a.numRows != b.numRows || a.numCols != b.numCols ) {
return false;
}
final int length = a.getDataLength();
for( int i = 0; i < length; i++ ) {
if( !(a.data[i] == b.data[i]) ) {
return false;
}
}
return true;
}
/**
*
* Checks to see if each element in the two matrices are within tolerance of
* each other: tol ≥ |aij - bij|.
*
*
*
* NOTE: If any of the elements are not countable then false is returned.
* NOTE: If a tolerance of zero is passed in this is equivalent to calling
* {@link #isEquals(org.ejml.data.CD1Matrix64F, org.ejml.data.CD1Matrix64F)}
*
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @param tol How close to being identical each element needs to be.
* @return true if equals and false otherwise.
*/
public static boolean isEquals( CD1Matrix64F a , CD1Matrix64F b , double tol )
{
if( a.numRows != b.numRows || a.numCols != b.numCols ) {
return false;
}
if( tol == 0.0 )
return isEquals(a,b);
final int length = a.getDataLength();
for( int i = 0; i < length; i++ ) {
if( !(tol >= Math.abs(a.data[i] - b.data[i])) ) {
return false;
}
}
return true;
}
/**
*
* Checks to see if each corresponding element in the two matrices are
* within tolerance of each other or have the some symbolic meaning. This
* can handle NaN and Infinite numbers.
*
*
*
* If both elements are countable then the following equality test is used:
* |aij - bij| ≤ tol.
* Otherwise both numbers must both be Double.NaN, Double.POSITIVE_INFINITY, or
* Double.NEGATIVE_INFINITY to be identical.
*
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @param tol Tolerance for equality.
* @return true if identical and false otherwise.
*/
public static boolean isIdentical( CD1Matrix64F a, CD1Matrix64F b , double tol ) {
if( a.numRows != b.numRows || a.numCols != b.numCols ) {
return false;
}
if( tol < 0 )
throw new IllegalArgumentException("Tolerance must be greater than or equal to zero.");
final int length = a.getDataLength();
for( int i = 0; i < length; i++ ) {
double valA = a.data[i];
double valB = b.data[i];
// if either is negative or positive infinity the result will be positive infinity
// if either is NaN the result will be NaN
double diff = Math.abs(valA-valB);
// diff = NaN == false
// diff = infinity == false
if( tol >= diff )
continue;
if( Double.isNaN(valA) ) {
return Double.isNaN(valB);
} else if( Double.isInfinite(valA) ) {
return valA == valB;
} else {
return false;
}
}
return true;
}
/**
* Checks to see if the provided matrix is within tolerance to an identity matrix.
*
* @param mat Matrix being examined. Not modified.
* @param tol Tolerance.
* @return True if it is within tolerance to an identify matrix.
*/
public static boolean isIdentity( ComplexMatrix64F mat , double tol ) {
// see if the result is an identity matrix
Complex64F c = new Complex64F();
for (int i = 0; i < mat.getNumRows(); i++) {
for (int j = 0; j < mat.getNumCols(); j++) {
mat.get(i, j, c);
if (i == j) {
if (!(Math.abs(c.real - 1) <= tol))
return false;
if (!(Math.abs(c.imaginary) <= tol))
return false;
} else {
if (!(Math.abs(c.real) <= tol))
return false;
if (!(Math.abs(c.imaginary) <= tol))
return false;
}
}
}
return true;
}
/**
* Hermitian matrix is a square matrix with complex entries that is equal to its own conjugate transpose.
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static boolean isHermitian( CDenseMatrix64F Q , double tol ) {
if( Q.numCols != Q.numRows )
return false;
Complex64F a = new Complex64F();
Complex64F b = new Complex64F();
for( int i = 0; i < Q.numCols; i++ ) {
for( int j = i+1; j < Q.numCols; j++ ) {
Q.get(i,j,a);
Q.get(j,i,b);
if( Math.abs(a.real-b.real)>tol)
return false;
if( Math.abs(a.imaginary+b.imaginary)>tol)
return false;
}
}
return true;
}
/**
*
* Unitary matrices have the following properties:
* Q*QH = I
*
*
* This is the complex equivalent of orthogonal matrix.
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static boolean isUnitary( CDenseMatrix64F Q , double tol ) {
if( Q.numRows < Q.numCols ) {
throw new IllegalArgumentException("The number of rows must be more than or equal to the number of columns");
}
Complex64F prod = new Complex64F();
CDenseMatrix64F u[] = CCommonOps.columnsToVector(Q, null);
for( int i = 0; i < u.length; i++ ) {
CDenseMatrix64F a = u[i];
CVectorVectorMult.innerProdH(a, a, prod);
if( Math.abs(prod.real-1) > tol)
return false;
if( Math.abs(prod.imaginary) > tol)
return false;
for( int j = i+1; j < u.length; j++ ) {
CVectorVectorMult.innerProdH(a, u[j], prod);
if( !(prod.getMagnitude2() <= tol*tol))
return false;
}
}
return true;
}
/**
*
* Checks to see if the matrix is positive definite.
*
*
* xT A x > 0
* for all x where x is a non-zero vector and A is a hermitian matrix.
*
*
* @param A square hermitian matrix. Not modified.
*
* @return True if it is positive definite and false if it is not.
*/
public static boolean isPositiveDefinite( CDenseMatrix64F A ) {
if( A.numCols != A.numRows)
return false;
CholeskyDecompositionInner_CD64 chol = new CholeskyDecompositionInner_CD64(true);
if( chol.inputModified() )
A = A.copy();
return chol.decompose(A);
}
}
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