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Posted to commits@commons.apache.org by er...@apache.org on 2011/10/12 00:55:09 UTC
svn commit: r1182134 [1/3] - in /commons/proper/math/trunk/src:
main/java/org/apache/commons/math/analysis/function/
main/java/org/apache/commons/math/analysis/interpolation/
main/java/org/apache/commons/math/analysis/polynomials/
main/java/org/apache/...
Author: erans
Date: Tue Oct 11 22:55:08 2011
New Revision: 1182134
URL: http://svn.apache.org/viewvc?rev=1182134&view=rev
Log:
MATH-689
Moved arrays utilities from "MathUtils" to "MathArrays".
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MathArrays.java (with props)
commons/proper/math/trunk/src/test/java/org/apache/commons/math/util/MathArraysTest.java (with props)
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/function/StepFunction.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolator.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LoessInterpolator.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolator.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/UnivariateRealPeriodicInterpolator.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialFunctionLagrangeForm.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialSplineFunction.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/exception/NonMonotonicSequenceException.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/geometry/euclidean/threed/Vector3D.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/linear/PivotingQRDecomposition.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/BOBYQAOptimizer.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/PowellOptimizer.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/clustering/EuclideanIntegerPoint.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/MillerUpdatingRegression.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/RegressionResults.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MathUtils.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MultidimensionalCounter.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/Precision.java
commons/proper/math/trunk/src/test/java/org/apache/commons/math/exception/NonMonotonicSequenceExceptionTest.java
commons/proper/math/trunk/src/test/java/org/apache/commons/math/util/MathUtilsTest.java
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/function/StepFunction.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/function/StepFunction.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/function/StepFunction.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/function/StepFunction.java Tue Oct 11 22:55:08 2011
@@ -22,7 +22,7 @@ import org.apache.commons.math.analysis.
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NullArgumentException;
import org.apache.commons.math.exception.NoDataException;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* <a href="http://en.wikipedia.org/wiki/Step_function">
@@ -68,10 +68,10 @@ public class StepFunction implements Uni
if (y.length != x.length) {
throw new DimensionMismatchException(y.length, x.length);
}
- MathUtils.checkOrder(x);
+ MathArrays.checkOrder(x);
- abscissa = MathUtils.copyOf(x);
- ordinate = MathUtils.copyOf(y);
+ abscissa = MathArrays.copyOf(x);
+ ordinate = MathArrays.copyOf(y);
}
/** {@inheritDoc} */
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.java Tue Oct 11 22:55:08 2011
@@ -20,7 +20,7 @@ import org.apache.commons.math.analysis.
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NoDataException;
import org.apache.commons.math.exception.OutOfRangeException;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Function that implements the
@@ -114,8 +114,8 @@ public class BicubicSplineInterpolatingF
throw new DimensionMismatchException(xLen, d2FdXdY.length);
}
- MathUtils.checkOrder(x);
- MathUtils.checkOrder(y);
+ MathArrays.checkOrder(x);
+ MathArrays.checkOrder(y);
xval = x.clone();
yval = y.clone();
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolator.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolator.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolator.java Tue Oct 11 22:55:08 2011
@@ -20,7 +20,7 @@ import org.apache.commons.math.analysis.
import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NoDataException;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Generates a bicubic interpolating function.
@@ -43,8 +43,8 @@ public class BicubicSplineInterpolator
throw new DimensionMismatchException(xval.length, fval.length);
}
- MathUtils.checkOrder(xval);
- MathUtils.checkOrder(yval);
+ MathArrays.checkOrder(xval);
+ MathArrays.checkOrder(yval);
final int xLen = xval.length;
final int yLen = yval.length;
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LinearInterpolator.java Tue Oct 11 22:55:08 2011
@@ -21,7 +21,7 @@ import org.apache.commons.math.exception
import org.apache.commons.math.exception.NumberIsTooSmallException;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Implements a linear function for interpolation of real univariate functions.
@@ -53,7 +53,7 @@ public class LinearInterpolator implemen
// Number of intervals. The number of data points is n + 1.
int n = x.length - 1;
- MathUtils.checkOrder(x);
+ MathArrays.checkOrder(x);
// Slope of the lines between the datapoints.
final double m[] = new double[n];
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LoessInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LoessInterpolator.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LoessInterpolator.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/LoessInterpolator.java Tue Oct 11 22:55:08 2011
@@ -28,6 +28,7 @@ import org.apache.commons.math.exception
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;
import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Implements the <a href="http://en.wikipedia.org/wiki/Local_regression">
@@ -216,7 +217,7 @@ public class LoessInterpolator
checkAllFiniteReal(yval);
checkAllFiniteReal(weights);
- MathUtils.checkOrder(xval);
+ MathArrays.checkOrder(xval);
if (n == 1) {
return new double[]{yval[0]};
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.java Tue Oct 11 22:55:08 2011
@@ -18,7 +18,7 @@ package org.apache.commons.math.analysis
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NoDataException;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
import org.apache.commons.math.optimization.general.GaussNewtonOptimizer;
import org.apache.commons.math.optimization.fitting.PolynomialFitter;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
@@ -87,8 +87,8 @@ public class SmoothingPolynomialBicubicS
}
}
- MathUtils.checkOrder(xval);
- MathUtils.checkOrder(yval);
+ MathArrays.checkOrder(xval);
+ MathArrays.checkOrder(yval);
// For each line y[j] (0 <= j < yLen), construct a polynomial, with
// respect to variable x, fitting array fval[][j]
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/SplineInterpolator.java Tue Oct 11 22:55:08 2011
@@ -21,7 +21,7 @@ import org.apache.commons.math.exception
import org.apache.commons.math.exception.NumberIsTooSmallException;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set.
@@ -77,7 +77,7 @@ public class SplineInterpolator implemen
// Number of intervals. The number of data points is n + 1.
int n = x.length - 1;
- MathUtils.checkOrder(x);
+ MathArrays.checkOrder(x);
// Differences between knot points
double h[] = new double[n];
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.java Tue Oct 11 22:55:08 2011
@@ -20,7 +20,7 @@ import org.apache.commons.math.analysis.
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NoDataException;
import org.apache.commons.math.exception.OutOfRangeException;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Function that implements the
@@ -185,9 +185,9 @@ public class TricubicSplineInterpolating
throw new DimensionMismatchException(xLen, d3FdXdYdZ.length);
}
- MathUtils.checkOrder(x);
- MathUtils.checkOrder(y);
- MathUtils.checkOrder(z);
+ MathArrays.checkOrder(x);
+ MathArrays.checkOrder(y);
+ MathArrays.checkOrder(z);
xval = x.clone();
yval = y.clone();
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolator.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolator.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolator.java Tue Oct 11 22:55:08 2011
@@ -18,7 +18,7 @@ package org.apache.commons.math.analysis
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NoDataException;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Generates a tricubic interpolating function.
@@ -42,9 +42,9 @@ public class TricubicSplineInterpolator
throw new DimensionMismatchException(xval.length, fval.length);
}
- MathUtils.checkOrder(xval);
- MathUtils.checkOrder(yval);
- MathUtils.checkOrder(zval);
+ MathArrays.checkOrder(xval);
+ MathArrays.checkOrder(yval);
+ MathArrays.checkOrder(zval);
final int xLen = xval.length;
final int yLen = yval.length;
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/UnivariateRealPeriodicInterpolator.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/UnivariateRealPeriodicInterpolator.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/UnivariateRealPeriodicInterpolator.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/interpolation/UnivariateRealPeriodicInterpolator.java Tue Oct 11 22:55:08 2011
@@ -18,6 +18,7 @@ package org.apache.commons.math.analysis
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
import org.apache.commons.math.exception.NumberIsTooSmallException;
/**
@@ -85,7 +86,7 @@ public class UnivariateRealPeriodicInter
throw new NumberIsTooSmallException(xval.length, extend, true);
}
- MathUtils.checkOrder(xval);
+ MathArrays.checkOrder(xval);
final double offset = xval[0];
final int len = xval.length + extend * 2;
@@ -108,7 +109,7 @@ public class UnivariateRealPeriodicInter
y[index] = yval[i];
}
- MathUtils.sortInPlace(x, y);
+ MathArrays.sortInPlace(x, y);
final UnivariateRealFunction f = interpolator.interpolate(x, y);
return new UnivariateRealFunction() {
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialFunctionLagrangeForm.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialFunctionLagrangeForm.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialFunctionLagrangeForm.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialFunctionLagrangeForm.java Tue Oct 11 22:55:08 2011
@@ -18,7 +18,7 @@ package org.apache.commons.math.analysis
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.util.FastMath;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.NumberIsTooSmallException;
import org.apache.commons.math.exception.util.LocalizedFormats;
@@ -76,7 +76,7 @@ public class PolynomialFunctionLagrangeF
coefficientsComputed = false;
if (!verifyInterpolationArray(x, y, false)) {
- MathUtils.sortInPlace(this.x, this.y);
+ MathArrays.sortInPlace(this.x, this.y);
// Second check in case some abscissa is duplicated.
verifyInterpolationArray(this.x, this.y, true);
}
@@ -179,7 +179,7 @@ public class PolynomialFunctionLagrangeF
System.arraycopy(x, 0, xNew, 0, x.length);
System.arraycopy(y, 0, yNew, 0, y.length);
- MathUtils.sortInPlace(xNew, yNew);
+ MathArrays.sortInPlace(xNew, yNew);
// Second check in case some abscissa is duplicated.
verifyInterpolationArray(xNew, yNew, true);
return evaluateInternal(xNew, yNew, z);
@@ -318,6 +318,6 @@ public class PolynomialFunctionLagrangeF
throw new NumberIsTooSmallException(LocalizedFormats.WRONG_NUMBER_OF_POINTS, 2, x.length, true);
}
- return MathUtils.checkOrder(x, MathUtils.OrderDirection.INCREASING, true, abort);
+ return MathArrays.checkOrder(x, MathArrays.OrderDirection.INCREASING, true, abort);
}
}
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialSplineFunction.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialSplineFunction.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialSplineFunction.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/analysis/polynomials/PolynomialSplineFunction.java Tue Oct 11 22:55:08 2011
@@ -18,7 +18,7 @@ package org.apache.commons.math.analysis
import java.util.Arrays;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.exception.OutOfRangeException;
@@ -109,7 +109,7 @@ public class PolynomialSplineFunction im
if (knots.length - 1 != polynomials.length) {
throw new DimensionMismatchException(polynomials.length, knots.length);
}
- MathUtils.checkOrder(knots);
+ MathArrays.checkOrder(knots);
this.n = knots.length -1;
this.knots = new double[n + 1];
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/exception/NonMonotonicSequenceException.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/exception/NonMonotonicSequenceException.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/exception/NonMonotonicSequenceException.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/exception/NonMonotonicSequenceException.java Tue Oct 11 22:55:08 2011
@@ -16,7 +16,7 @@
*/
package org.apache.commons.math.exception;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
import org.apache.commons.math.exception.util.LocalizedFormats;
/**
@@ -32,7 +32,7 @@ public class NonMonotonicSequenceExcepti
/**
* Direction (positive for increasing, negative for decreasing).
*/
- private final MathUtils.OrderDirection direction;
+ private final MathArrays.OrderDirection direction;
/**
* Whether the sequence must be strictly increasing or decreasing.
*/
@@ -58,7 +58,7 @@ public class NonMonotonicSequenceExcepti
public NonMonotonicSequenceException(Number wrong,
Number previous,
int index) {
- this(wrong, previous, index, MathUtils.OrderDirection.INCREASING, true);
+ this(wrong, previous, index, MathArrays.OrderDirection.INCREASING, true);
}
/**
@@ -75,9 +75,9 @@ public class NonMonotonicSequenceExcepti
public NonMonotonicSequenceException(Number wrong,
Number previous,
int index,
- MathUtils.OrderDirection direction,
+ MathArrays.OrderDirection direction,
boolean strict) {
- super(direction == MathUtils.OrderDirection.INCREASING ?
+ super(direction == MathArrays.OrderDirection.INCREASING ?
(strict ?
LocalizedFormats.NOT_STRICTLY_INCREASING_SEQUENCE :
LocalizedFormats.NOT_INCREASING_SEQUENCE) :
@@ -95,7 +95,7 @@ public class NonMonotonicSequenceExcepti
/**
* @return the order direction.
**/
- public MathUtils.OrderDirection getDirection() {
+ public MathArrays.OrderDirection getDirection() {
return direction;
}
/**
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/geometry/euclidean/threed/Vector3D.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/geometry/euclidean/threed/Vector3D.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/geometry/euclidean/threed/Vector3D.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/geometry/euclidean/threed/Vector3D.java Tue Oct 11 22:55:08 2011
@@ -26,6 +26,7 @@ import org.apache.commons.math.geometry.
import org.apache.commons.math.geometry.Space;
import org.apache.commons.math.util.FastMath;
import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* This class implements vectors in a three-dimensional space.
@@ -132,9 +133,9 @@ public class Vector3D implements Seriali
* @param u2 second base (unscaled) vector
*/
public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2) {
- this.x = MathUtils.linearCombination(a1, u1.x, a2, u2.x);
- this.y = MathUtils.linearCombination(a1, u1.y, a2, u2.y);
- this.z = MathUtils.linearCombination(a1, u1.z, a2, u2.z);
+ this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x);
+ this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y);
+ this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z);
}
/** Linear constructor
@@ -149,9 +150,9 @@ public class Vector3D implements Seriali
*/
public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2,
double a3, Vector3D u3) {
- this.x = MathUtils.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x);
- this.y = MathUtils.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y);
- this.z = MathUtils.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z);
+ this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x);
+ this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y);
+ this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z);
}
/** Linear constructor
@@ -168,9 +169,9 @@ public class Vector3D implements Seriali
*/
public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2,
double a3, Vector3D u3, double a4, Vector3D u4) {
- this.x = MathUtils.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x, a4, u4.x);
- this.y = MathUtils.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y, a4, u4.y);
- this.z = MathUtils.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z, a4, u4.z);
+ this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x, a4, u4.x);
+ this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y, a4, u4.y);
+ this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z, a4, u4.z);
}
/** Get the abscissa of the vector.
@@ -422,11 +423,11 @@ public class Vector3D implements Seriali
* algorithms to preserve accuracy and reduce cancellation effects.
* It should be very accurate even for nearly orthogonal vectors.
* </p>
- * @see MathUtils#linearCombination(double, double, double, double, double, double)
+ * @see MathArrays#linearCombination(double, double, double, double, double, double)
*/
public double dotProduct(final Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
- return MathUtils.linearCombination(x, v3.x, y, v3.y, z, v3.z);
+ return MathArrays.linearCombination(x, v3.x, y, v3.y, z, v3.z);
}
/** Compute the cross-product of the instance with another vector.
@@ -435,9 +436,9 @@ public class Vector3D implements Seriali
*/
public Vector3D crossProduct(final Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
- return new Vector3D(MathUtils.linearCombination(y, v3.z, -z, v3.y),
- MathUtils.linearCombination(z, v3.x, -x, v3.z),
- MathUtils.linearCombination(x, v3.y, -y, v3.x));
+ return new Vector3D(MathArrays.linearCombination(y, v3.z, -z, v3.y),
+ MathArrays.linearCombination(z, v3.x, -x, v3.z),
+ MathArrays.linearCombination(x, v3.y, -y, v3.x));
}
/** {@inheritDoc} */
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/linear/PivotingQRDecomposition.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/linear/PivotingQRDecomposition.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/linear/PivotingQRDecomposition.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/linear/PivotingQRDecomposition.java Tue Oct 11 22:55:08 2011
@@ -16,7 +16,7 @@
package org.apache.commons.math.linear;
import java.util.Arrays;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
import org.apache.commons.math.exception.ConvergenceException;
import org.apache.commons.math.exception.DimensionMismatchException;
import org.apache.commons.math.exception.util.LocalizedFormats;
@@ -55,7 +55,7 @@ public class PivotingQRDecomposition {
}
public int[] getOrder() {
- return MathUtils.copyOf(permutation);
+ return MathArrays.copyOf(permutation);
}
public PivotingQRDecomposition(RealMatrix matrix) throws ConvergenceException {
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/BOBYQAOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/BOBYQAOptimizer.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/BOBYQAOptimizer.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/BOBYQAOptimizer.java Tue Oct 11 22:55:08 2011
@@ -31,7 +31,7 @@ import org.apache.commons.math.linear.Re
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.MultivariateRealOptimizer;
import org.apache.commons.math.optimization.RealPointValuePair;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Powell's BOBYQA algorithm. This implementation is translated and
@@ -157,8 +157,8 @@ public class BOBYQAOptimizer
double[] upperBound,
double initialTrustRegionRadius,
double stoppingTrustRegionRadius) {
- this.lowerBound = lowerBound == null ? null : MathUtils.copyOf(lowerBound);
- this.upperBound = upperBound == null ? null : MathUtils.copyOf(upperBound);
+ this.lowerBound = lowerBound == null ? null : MathArrays.copyOf(lowerBound);
+ this.upperBound = upperBound == null ? null : MathArrays.copyOf(upperBound);
this.numberOfInterpolationPoints = numberOfInterpolationPoints;
this.initialTrustRegionRadius = initialTrustRegionRadius;
this.stoppingTrustRegionRadius = stoppingTrustRegionRadius;
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java Tue Oct 11 22:55:08 2011
@@ -36,7 +36,7 @@ import org.apache.commons.math.optimizat
import org.apache.commons.math.optimization.RealPointValuePair;
import org.apache.commons.math.random.MersenneTwister;
import org.apache.commons.math.random.RandomGenerator;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* <p>An implementation of the active Covariance Matrix Adaptation Evolution Strategy (CMA-ES)
@@ -395,9 +395,9 @@ public class CMAESOptimizer extends
int[] arindex = sortedIndices(fitness);
// Calculate new xmean, this is selection and recombination
RealMatrix xold = xmean; // for speed up of Eq. (2) and (3)
- RealMatrix bestArx = selectColumns(arx, MathUtils.copyOf(arindex, mu));
+ RealMatrix bestArx = selectColumns(arx, MathArrays.copyOf(arindex, mu));
xmean = bestArx.multiply(weights);
- RealMatrix bestArz = selectColumns(arz, MathUtils.copyOf(arindex, mu));
+ RealMatrix bestArz = selectColumns(arz, MathArrays.copyOf(arindex, mu));
RealMatrix zmean = bestArz.multiply(weights);
boolean hsig = updateEvolutionPaths(zmean, xold);
if (diagonalOnly <= 0) {
@@ -711,7 +711,7 @@ public class CMAESOptimizer extends
// prepare vectors, compute negative updating matrix Cneg
int[] arReverseIndex = reverse(arindex);
RealMatrix arzneg
- = selectColumns(arz, MathUtils.copyOf(arReverseIndex, mu));
+ = selectColumns(arz, MathArrays.copyOf(arReverseIndex, mu));
RealMatrix arnorms = sqrt(sumRows(square(arzneg)));
int[] idxnorms = sortedIndices(arnorms.getRow(0));
RealMatrix arnormsSorted = selectColumns(arnorms, idxnorms);
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/PowellOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/PowellOptimizer.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/PowellOptimizer.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/PowellOptimizer.java Tue Oct 11 22:55:08 2011
@@ -18,7 +18,7 @@
package org.apache.commons.math.optimization.direct;
import org.apache.commons.math.util.FastMath;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.MultivariateRealFunction;
import org.apache.commons.math.exception.NumberIsTooSmallException;
@@ -141,7 +141,7 @@ public class PowellOptimizer
double alphaMin = 0;
for (int i = 0; i < n; i++) {
- final double[] d = MathUtils.copyOf(direc[i]);
+ final double[] d = MathArrays.copyOf(direc[i]);
fX2 = fVal;
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/clustering/EuclideanIntegerPoint.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/clustering/EuclideanIntegerPoint.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/clustering/EuclideanIntegerPoint.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/clustering/EuclideanIntegerPoint.java Tue Oct 11 22:55:08 2011
@@ -20,7 +20,7 @@ package org.apache.commons.math.stat.clu
import java.io.Serializable;
import java.util.Collection;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* A simple implementation of {@link Clusterable} for points with integer coordinates.
@@ -54,7 +54,7 @@ public class EuclideanIntegerPoint imple
/** {@inheritDoc} */
public double distanceFrom(final EuclideanIntegerPoint p) {
- return MathUtils.distance(point, p.getPoint());
+ return MathArrays.distance(point, p.getPoint());
}
/** {@inheritDoc} */
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/MillerUpdatingRegression.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/MillerUpdatingRegression.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/MillerUpdatingRegression.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/MillerUpdatingRegression.java Tue Oct 11 22:55:08 2011
@@ -20,6 +20,7 @@ import java.util.Arrays;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;
import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* <p>This class is a concrete implementation of the {@link UpdatingMultipleLinearRegression} interface.</p>
@@ -186,7 +187,7 @@ public class MillerUpdatingRegression im
x.length, nvars);
}
if (!this.hasIntercept) {
- include(MathUtils.copyOf(x, x.length), 1.0, y);
+ include(MathArrays.copyOf(x, x.length), 1.0, y);
} else {
double[] tmp = new double[x.length + 1];
System.arraycopy(x, 0, tmp, 1, x.length);
@@ -918,7 +919,7 @@ public class MillerUpdatingRegression im
* @return int[] with the current order of the regressors
*/
public int[] getOrderOfRegressors(){
- return MathUtils.copyOf(vorder);
+ return MathArrays.copyOf(vorder);
}
/**
Modified: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/RegressionResults.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/RegressionResults.java?rev=1182134&r1=1182133&r2=1182134&view=diff
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/RegressionResults.java (original)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/RegressionResults.java Tue Oct 11 22:55:08 2011
@@ -19,7 +19,7 @@ package org.apache.commons.math.stat.reg
import java.io.Serializable;
import java.util.Arrays;
import org.apache.commons.math.util.FastMath;
-import org.apache.commons.math.util.MathUtils;
+import org.apache.commons.math.util.MathArrays;
/**
* Results of a Multiple Linear Regression model fit.
@@ -98,10 +98,10 @@ public class RegressionResults implement
final boolean containsConstant,
final boolean copyData) {
if (copyData) {
- this.parameters = MathUtils.copyOf(parameters);
+ this.parameters = MathArrays.copyOf(parameters);
this.varCovData = new double[varcov.length][];
for (int i = 0; i < varcov.length; i++) {
- this.varCovData[i] = MathUtils.copyOf(varcov[i]);
+ this.varCovData[i] = MathArrays.copyOf(varcov[i]);
}
} else {
this.parameters = parameters;
@@ -170,7 +170,7 @@ public class RegressionResults implement
if (this.parameters == null) {
return null;
}
- return MathUtils.copyOf(parameters);
+ return MathArrays.copyOf(parameters);
}
/**
Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MathArrays.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MathArrays.java?rev=1182134&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MathArrays.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MathArrays.java Tue Oct 11 22:55:08 2011
@@ -0,0 +1,925 @@
+/*
+ * 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.math.util;
+
+import java.util.List;
+import java.util.ArrayList;
+import java.util.Comparator;
+import java.util.Collections;
+
+import org.apache.commons.math.exception.DimensionMismatchException;
+import org.apache.commons.math.exception.MathInternalError;
+import org.apache.commons.math.exception.NonMonotonicSequenceException;
+import org.apache.commons.math.exception.NullArgumentException;
+
+/**
+ * Arrays utilities.
+ *
+ * @since 3.0
+ * @version $Id$
+ */
+public class MathArrays {
+ /** Factor used for splitting double numbers: n = 2^27 + 1 (i.e. {@value}). */
+ private static final int SPLIT_FACTOR = 0x8000001;
+
+ /**
+ * Private constructor.
+ */
+ private MathArrays() {}
+
+ /**
+ * Calculates the L<sub>1</sub> (sum of abs) distance between two points.
+ *
+ * @param p1 the first point
+ * @param p2 the second point
+ * @return the L<sub>1</sub> distance between the two points
+ */
+ public static double distance1(double[] p1, double[] p2) {
+ double sum = 0;
+ for (int i = 0; i < p1.length; i++) {
+ sum += FastMath.abs(p1[i] - p2[i]);
+ }
+ return sum;
+ }
+
+ /**
+ * Calculates the L<sub>1</sub> (sum of abs) distance between two points.
+ *
+ * @param p1 the first point
+ * @param p2 the second point
+ * @return the L<sub>1</sub> distance between the two points
+ */
+ public static int distance1(int[] p1, int[] p2) {
+ int sum = 0;
+ for (int i = 0; i < p1.length; i++) {
+ sum += FastMath.abs(p1[i] - p2[i]);
+ }
+ return sum;
+ }
+
+ /**
+ * Calculates the L<sub>2</sub> (Euclidean) distance between two points.
+ *
+ * @param p1 the first point
+ * @param p2 the second point
+ * @return the L<sub>2</sub> distance between the two points
+ */
+ public static double distance(double[] p1, double[] p2) {
+ double sum = 0;
+ for (int i = 0; i < p1.length; i++) {
+ final double dp = p1[i] - p2[i];
+ sum += dp * dp;
+ }
+ return FastMath.sqrt(sum);
+ }
+
+ /**
+ * Calculates the L<sub>2</sub> (Euclidean) distance between two points.
+ *
+ * @param p1 the first point
+ * @param p2 the second point
+ * @return the L<sub>2</sub> distance between the two points
+ */
+ public static double distance(int[] p1, int[] p2) {
+ double sum = 0;
+ for (int i = 0; i < p1.length; i++) {
+ final double dp = p1[i] - p2[i];
+ sum += dp * dp;
+ }
+ return FastMath.sqrt(sum);
+ }
+
+ /**
+ * Calculates the L<sub>∞</sub> (max of abs) distance between two points.
+ *
+ * @param p1 the first point
+ * @param p2 the second point
+ * @return the L<sub>∞</sub> distance between the two points
+ */
+ public static double distanceInf(double[] p1, double[] p2) {
+ double max = 0;
+ for (int i = 0; i < p1.length; i++) {
+ max = FastMath.max(max, FastMath.abs(p1[i] - p2[i]));
+ }
+ return max;
+ }
+
+ /**
+ * Calculates the L<sub>∞</sub> (max of abs) distance between two points.
+ *
+ * @param p1 the first point
+ * @param p2 the second point
+ * @return the L<sub>∞</sub> distance between the two points
+ */
+ public static int distanceInf(int[] p1, int[] p2) {
+ int max = 0;
+ for (int i = 0; i < p1.length; i++) {
+ max = FastMath.max(max, FastMath.abs(p1[i] - p2[i]));
+ }
+ return max;
+ }
+
+ /**
+ * Specification of ordering direction.
+ */
+ public static enum OrderDirection {
+ /** Constant for increasing direction. */
+ INCREASING,
+ /** Constant for decreasing direction. */
+ DECREASING
+ }
+
+ /**
+ * Check that an array is monotonically increasing or decreasing.
+ *
+ * @param val Values.
+ * @param dir Ordering direction.
+ * @param strict Whether the order should be strict.
+ * @return {@code true} if sorted, {@code false} otherwise.
+ */
+ public static boolean isMonotonic(Comparable[] val,
+ OrderDirection dir,
+ boolean strict) {
+ Comparable previous = val[0];
+ final int max = val.length;
+ int comp;
+ for (int i = 1; i < max; i++) {
+ switch (dir) {
+ case INCREASING:
+ comp = -val[i].compareTo(previous);
+ if (strict) {
+ if (0 <= comp) {
+ return false;
+ }
+ } else {
+ if ( comp > 0) {
+ return false;
+ }
+ }
+ break;
+ case DECREASING:
+ comp = val[i].compareTo(previous);
+ if (strict) {
+ if (comp >= 0) {
+ return false;
+ }
+ } else {
+ if (comp > 0) {
+ return false;
+ }
+ }
+ break;
+ default:
+ // Should never happen.
+ throw new MathInternalError();
+ }
+
+ previous = val[i];
+ }
+ return true;
+ }
+
+ /**
+ * Check that an array is monotonically increasing or decreasing.
+ *
+ * @param val Values.
+ * @param dir Ordering direction.
+ * @param strict Whether the order should be strict.
+ * @return {@code true} if sorted, {@code false} otherwise.
+ */
+ public static boolean isMonotonic(double[] val,
+ OrderDirection dir,
+ boolean strict) {
+ return checkOrder(val, dir, strict, false);
+ }
+
+ /**
+ * Check that the given array is sorted.
+ *
+ * @param val Values.
+ * @param dir Ordering direction.
+ * @param strict Whether the order should be strict.
+ * @param abort Whether to throw an exception if the check fails.
+ * @return {@code true} if the array is sorted.
+ * @throws NonMonotonicSequenceException if the array is not sorted
+ * and {@code abort} is {@code true}.
+ */
+ public static boolean checkOrder(double[] val, OrderDirection dir,
+ boolean strict, boolean abort) {
+ double previous = val[0];
+ final int max = val.length;
+
+ int index;
+ ITEM:
+ for (index = 1; index < max; index++) {
+ switch (dir) {
+ case INCREASING:
+ if (strict) {
+ if (val[index] <= previous) {
+ break ITEM;
+ }
+ } else {
+ if (val[index] < previous) {
+ break ITEM;
+ }
+ }
+ break;
+ case DECREASING:
+ if (strict) {
+ if (val[index] >= previous) {
+ break ITEM;
+ }
+ } else {
+ if (val[index] > previous) {
+ break ITEM;
+ }
+ }
+ break;
+ default:
+ // Should never happen.
+ throw new MathInternalError();
+ }
+
+ previous = val[index];
+ }
+
+ if (index == max) {
+ // Loop completed.
+ return true;
+ }
+
+ // Loop early exit means wrong ordering.
+ if (abort) {
+ throw new NonMonotonicSequenceException(val[index], previous, index, dir, strict);
+ } else {
+ return false;
+ }
+ }
+
+ /**
+ * Check that the given array is sorted.
+ *
+ * @param val Values.
+ * @param dir Ordering direction.
+ * @param strict Whether the order should be strict.
+ * @throws NonMonotonicSequenceException if the array is not sorted.
+ * @since 2.2
+ */
+ public static void checkOrder(double[] val, OrderDirection dir,
+ boolean strict) {
+ checkOrder(val, dir, strict, true);
+ }
+
+ /**
+ * Check that the given array is sorted in strictly increasing order.
+ *
+ * @param val Values.
+ * @throws NonMonotonicSequenceException if the array is not sorted.
+ * @since 2.2
+ */
+ public static void checkOrder(double[] val) {
+ checkOrder(val, OrderDirection.INCREASING, true);
+ }
+
+ /**
+ * Returns the Cartesian norm (2-norm), handling both overflow and underflow.
+ * Translation of the minpack enorm subroutine.
+ *
+ * The redistribution policy for MINPACK is available
+ * <a href="http://www.netlib.org/minpack/disclaimer">here</a>, for
+ * convenience, it is reproduced below.</p>
+ *
+ * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0">
+ * <tr><td>
+ * Minpack Copyright Notice (1999) University of Chicago.
+ * All rights reserved
+ * </td></tr>
+ * <tr><td>
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * <ol>
+ * <li>Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.</li>
+ * <li>Redistributions in binary form must reproduce the above
+ * copyright notice, this list of conditions and the following
+ * disclaimer in the documentation and/or other materials provided
+ * with the distribution.</li>
+ * <li>The end-user documentation included with the redistribution, if any,
+ * must include the following acknowledgment:
+ * {@code This product includes software developed by the University of
+ * Chicago, as Operator of Argonne National Laboratory.}
+ * Alternately, this acknowledgment may appear in the software itself,
+ * if and wherever such third-party acknowledgments normally appear.</li>
+ * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+ * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+ * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+ * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+ * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+ * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+ * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+ * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+ * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+ * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+ * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+ * BE CORRECTED.</strong></li>
+ * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+ * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+ * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+ * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+ * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+ * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+ * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+ * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li>
+ * <ol></td></tr>
+ * </table>
+ *
+ * @param v Vector of doubles.
+ * @return the 2-norm of the vector.
+ * @since 2.2
+ */
+ public static double safeNorm(double[] v) {
+ double rdwarf = 3.834e-20;
+ double rgiant = 1.304e+19;
+ double s1 = 0;
+ double s2 = 0;
+ double s3 = 0;
+ double x1max = 0;
+ double x3max = 0;
+ double floatn = (double) v.length;
+ double agiant = rgiant / floatn;
+ for (int i = 0; i < v.length; i++) {
+ double xabs = Math.abs(v[i]);
+ if (xabs < rdwarf || xabs > agiant) {
+ if (xabs > rdwarf) {
+ if (xabs > x1max) {
+ double r = x1max / xabs;
+ s1= 1 + s1 * r * r;
+ x1max = xabs;
+ } else {
+ double r = xabs / x1max;
+ s1 += r * r;
+ }
+ } else {
+ if (xabs > x3max) {
+ double r = x3max / xabs;
+ s3= 1 + s3 * r * r;
+ x3max = xabs;
+ } else {
+ if (xabs != 0) {
+ double r = xabs / x3max;
+ s3 += r * r;
+ }
+ }
+ }
+ } else {
+ s2 += xabs * xabs;
+ }
+ }
+ double norm;
+ if (s1 != 0) {
+ norm = x1max * Math.sqrt(s1 + (s2 / x1max) / x1max);
+ } else {
+ if (s2 == 0) {
+ norm = x3max * Math.sqrt(s3);
+ } else {
+ if (s2 >= x3max) {
+ norm = Math.sqrt(s2 * (1 + (x3max / s2) * (x3max * s3)));
+ } else {
+ norm = Math.sqrt(x3max * ((s2 / x3max) + (x3max * s3)));
+ }
+ }
+ }
+ return norm;
+ }
+
+ /**
+ * Sort an array in ascending order in place and perform the same reordering
+ * of entries on other arrays. For example, if
+ * {@code x = [3, 1, 2], y = [1, 2, 3]} and {@code z = [0, 5, 7]}, then
+ * {@code sortInPlace(x, y, z)} will update {@code x} to {@code [1, 2, 3]},
+ * {@code y} to {@code [2, 3, 1]} and {@code z} to {@code [5, 7, 0]}.
+ *
+ * @param x Array to be sorted and used as a pattern for permutation
+ * of the other arrays.
+ * @param yList Set of arrays whose permutations of entries will follow
+ * those performed on {@code x}.
+ * @throws DimensionMismatchException if any {@code y} is not the same
+ * size as {@code x}.
+ * @throws NullArgumentException if {@code x} or any {@code y} is null.
+ * @since 3.0
+ */
+ public static void sortInPlace(double[] x,
+ double[] ... yList) {
+ sortInPlace(x, OrderDirection.INCREASING, yList);
+ }
+
+ /**
+ * Sort an array in place and perform the same reordering of entries on
+ * other arrays. This method works the same as
+ * {@link #sortInPlace(double[], double[] ...)}, but allows the order of
+ * the sort to be provided in the {@code dir} parameter.
+ *
+ * @param x Array to be sorted and used as a pattern for permutation
+ * of the other arrays.
+ * @param dir Order direction.
+ * @param yList Set of arrays whose permutations of entries will follow
+ * those performed on {@code x}.
+ * @throws DimensionMismatchException if any {@code y} is not the same
+ * size as {@code x}.
+ * @throws NullArgumentException if {@code x} or any {@code y} is null
+ * @since 3.0
+ */
+ public static void sortInPlace(double[] x,
+ final OrderDirection dir,
+ double[] ... yList) {
+ if (x == null) {
+ throw new NullArgumentException();
+ }
+
+ final int len = x.length;
+ final List<Pair<Double, double[]>> list
+ = new ArrayList<Pair<Double, double[]>>(len);
+
+ final int yListLen = yList.length;
+ for (int i = 0; i < len; i++) {
+ final double[] yValues = new double[yListLen];
+ for (int j = 0; j < yListLen; j++) {
+ double[] y = yList[j];
+ if (y == null) {
+ throw new NullArgumentException();
+ }
+ if (y.length != len) {
+ throw new DimensionMismatchException(y.length, len);
+ }
+ yValues[j] = y[i];
+ }
+ list.add(new Pair<Double, double[]>(x[i], yValues));
+ }
+
+ final Comparator<Pair<Double, double[]>> comp
+ = new Comparator<Pair<Double, double[]>>() {
+ public int compare(Pair<Double, double[]> o1,
+ Pair<Double, double[]> o2) {
+ int val;
+ switch (dir) {
+ case INCREASING:
+ val = o1.getKey().compareTo(o2.getKey());
+ break;
+ case DECREASING:
+ val = o2.getKey().compareTo(o1.getKey());
+ break;
+ default:
+ // Should never happen.
+ throw new MathInternalError();
+ }
+ return val;
+ }
+ };
+
+ Collections.sort(list, comp);
+
+ for (int i = 0; i < len; i++) {
+ final Pair<Double, double[]> e = list.get(i);
+ x[i] = e.getKey();
+ final double[] yValues = e.getValue();
+ for (int j = 0; j < yListLen; j++) {
+ yList[j][i] = yValues[j];
+ }
+ }
+ }
+
+ /**
+ * Creates a copy of the {@code source} array.
+ *
+ * @param source Array to be copied.
+ * @return the copied array.
+ */
+ public static int[] copyOf(int[] source) {
+ return copyOf(source, source.length);
+ }
+
+ /**
+ * Creates a copy of the {@code source} array.
+ *
+ * @param source Array to be copied.
+ * @return the copied array.
+ */
+ public static double[] copyOf(double[] source) {
+ return copyOf(source, source.length);
+ }
+
+ /**
+ * Creates a copy of the {@code source} array.
+ *
+ * @param source Array to be copied.
+ * @param len Number of entries to copy. If smaller then the source
+ * length, the copy will be truncated, if larger it will padded with
+ * zeroes.
+ * @return the copied array.
+ */
+ public static int[] copyOf(int[] source, int len) {
+ final int[] output = new int[len];
+ System.arraycopy(source, 0, output, 0, FastMath.min(len, source.length));
+ return output;
+ }
+
+ /**
+ * Creates a copy of the {@code source} array.
+ *
+ * @param source Array to be copied.
+ * @param len Number of entries to copy. If smaller then the source
+ * length, the copy will be truncated, if larger it will padded with
+ * zeroes.
+ * @return the copied array.
+ */
+ public static double[] copyOf(double[] source, int len) {
+ final double[] output = new double[len];
+ System.arraycopy(source, 0, output, 0, FastMath.min(len, source.length));
+ return output;
+ }
+
+ /**
+ * Compute a linear combination accurately.
+ * This method computes the sum of the products
+ * <code>a<sub>i</sub> b<sub>i</sub></code> to high accuracy.
+ * It does so by using specific multiplication and addition algorithms to
+ * preserve accuracy and reduce cancellation effects.
+ * <br/>
+ * It is based on the 2005 paper
+ * <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
+ * Accurate Sum and Dot Product</a> by Takeshi Ogita, Siegfried M. Rump,
+ * and Shin'ichi Oishi published in SIAM J. Sci. Comput.
+ *
+ * @param a Factors.
+ * @param b Factors.
+ * @return <code>Σ<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
+ */
+ public static double linearCombination(final double[] a, final double[] b) {
+ final int len = a.length;
+ if (len != b.length) {
+ throw new DimensionMismatchException(len, b.length);
+ }
+
+ final double[] prodHigh = new double[len];
+ double prodLowSum = 0;
+
+ for (int i = 0; i < len; i++) {
+ final double ai = a[i];
+ final double ca = SPLIT_FACTOR * ai;
+ final double aHigh = ca - (ca - ai);
+ final double aLow = ai - aHigh;
+
+ final double bi = b[i];
+ final double cb = SPLIT_FACTOR * bi;
+ final double bHigh = cb - (cb - bi);
+ final double bLow = bi - bHigh;
+ prodHigh[i] = ai * bi;
+ final double prodLow = aLow * bLow - (((prodHigh[i] -
+ aHigh * bHigh) -
+ aLow * bHigh) -
+ aHigh * bLow);
+ prodLowSum += prodLow;
+ }
+
+
+ final double prodHighCur = prodHigh[0];
+ double prodHighNext = prodHigh[1];
+ double sHighPrev = prodHighCur + prodHighNext;
+ double sPrime = sHighPrev - prodHighNext;
+ double sLowSum = (prodHighNext - (sHighPrev - sPrime)) + (prodHighCur - sPrime);
+
+ final int lenMinusOne = len - 1;
+ for (int i = 1; i < lenMinusOne; i++) {
+ prodHighNext = prodHigh[i + 1];
+ final double sHighCur = sHighPrev + prodHighNext;
+ sPrime = sHighCur - prodHighNext;
+ sLowSum += (prodHighNext - (sHighCur - sPrime)) + (sHighPrev - sPrime);
+ sHighPrev = sHighCur;
+ }
+
+ double result = sHighPrev + (prodLowSum + sLowSum);
+
+ if (Double.isNaN(result)) {
+ // either we have split infinite numbers or some coefficients were NaNs,
+ // just rely on the naive implementation and let IEEE754 handle this
+ result = 0;
+ for (int i = 0; i < len; ++i) {
+ result += a[i] * b[i];
+ }
+ }
+
+ return result;
+ }
+
+ /**
+ * Compute a linear combination accurately.
+ * <p>
+ * This method computes a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> to high accuracy. It does
+ * so by using specific multiplication and addition algorithms to
+ * preserve accuracy and reduce cancellation effects. It is based
+ * on the 2005 paper <a
+ * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
+ * Accurate Sum and Dot Product</a> by Takeshi Ogita,
+ * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
+ * </p>
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub>
+ * @see #linearCombination(double, double, double, double, double, double)
+ * @see #linearCombination(double, double, double, double, double, double, double, double)
+ */
+ public static double linearCombination(final double a1, final double b1,
+ final double a2, final double b2) {
+
+ // the code below is split in many additions/subtractions that may
+ // appear redundant. However, they should NOT be simplified, as they
+ // use IEEE754 floating point arithmetic rounding properties.
+ // as an example, the expression "ca1 - (ca1 - a1)" is NOT the same as "a1"
+ // The variable naming conventions are that xyzHigh contains the most significant
+ // bits of xyz and xyzLow contains its least significant bits. So theoretically
+ // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot
+ // be represented in only one double precision number so we preserve two numbers
+ // to hold it as long as we can, combining the high and low order bits together
+ // only at the end, after cancellation may have occurred on high order bits
+
+ // split a1 and b1 as two 26 bits numbers
+ final double ca1 = SPLIT_FACTOR * a1;
+ final double a1High = ca1 - (ca1 - a1);
+ final double a1Low = a1 - a1High;
+ final double cb1 = SPLIT_FACTOR * b1;
+ final double b1High = cb1 - (cb1 - b1);
+ final double b1Low = b1 - b1High;
+
+ // accurate multiplication a1 * b1
+ final double prod1High = a1 * b1;
+ final double prod1Low = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);
+
+ // split a2 and b2 as two 26 bits numbers
+ final double ca2 = SPLIT_FACTOR * a2;
+ final double a2High = ca2 - (ca2 - a2);
+ final double a2Low = a2 - a2High;
+ final double cb2 = SPLIT_FACTOR * b2;
+ final double b2High = cb2 - (cb2 - b2);
+ final double b2Low = b2 - b2High;
+
+ // accurate multiplication a2 * b2
+ final double prod2High = a2 * b2;
+ final double prod2Low = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);
+
+ // accurate addition a1 * b1 + a2 * b2
+ final double s12High = prod1High + prod2High;
+ final double s12Prime = s12High - prod2High;
+ final double s12Low = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);
+
+ // final rounding, s12 may have suffered many cancellations, we try
+ // to recover some bits from the extra words we have saved up to now
+ double result = s12High + (prod1Low + prod2Low + s12Low);
+
+ if (Double.isNaN(result)) {
+ // either we have split infinite numbers or some coefficients were NaNs,
+ // just rely on the naive implementation and let IEEE754 handle this
+ result = a1 * b1 + a2 * b2;
+ }
+
+ return result;
+ }
+
+ /**
+ * Compute a linear combination accurately.
+ * <p>
+ * This method computes a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
+ * to high accuracy. It does so by using specific multiplication and
+ * addition algorithms to preserve accuracy and reduce cancellation effects.
+ * It is based on the 2005 paper <a
+ * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
+ * Accurate Sum and Dot Product</a> by Takeshi Ogita,
+ * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
+ * </p>
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @param a3 first factor of the third term
+ * @param b3 second factor of the third term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
+ * @see #linearCombination(double, double, double, double)
+ * @see #linearCombination(double, double, double, double, double, double, double, double)
+ */
+ public static double linearCombination(final double a1, final double b1,
+ final double a2, final double b2,
+ final double a3, final double b3) {
+
+ // the code below is split in many additions/subtractions that may
+ // appear redundant. However, they should NOT be simplified, as they
+ // do use IEEE754 floating point arithmetic rounding properties.
+ // as an example, the expression "ca1 - (ca1 - a1)" is NOT the same as "a1"
+ // The variables naming conventions are that xyzHigh contains the most significant
+ // bits of xyz and xyzLow contains its least significant bits. So theoretically
+ // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot
+ // be represented in only one double precision number so we preserve two numbers
+ // to hold it as long as we can, combining the high and low order bits together
+ // only at the end, after cancellation may have occurred on high order bits
+
+ // split a1 and b1 as two 26 bits numbers
+ final double ca1 = SPLIT_FACTOR * a1;
+ final double a1High = ca1 - (ca1 - a1);
+ final double a1Low = a1 - a1High;
+ final double cb1 = SPLIT_FACTOR * b1;
+ final double b1High = cb1 - (cb1 - b1);
+ final double b1Low = b1 - b1High;
+
+ // accurate multiplication a1 * b1
+ final double prod1High = a1 * b1;
+ final double prod1Low = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);
+
+ // split a2 and b2 as two 26 bits numbers
+ final double ca2 = SPLIT_FACTOR * a2;
+ final double a2High = ca2 - (ca2 - a2);
+ final double a2Low = a2 - a2High;
+ final double cb2 = SPLIT_FACTOR * b2;
+ final double b2High = cb2 - (cb2 - b2);
+ final double b2Low = b2 - b2High;
+
+ // accurate multiplication a2 * b2
+ final double prod2High = a2 * b2;
+ final double prod2Low = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);
+
+ // split a3 and b3 as two 26 bits numbers
+ final double ca3 = SPLIT_FACTOR * a3;
+ final double a3High = ca3 - (ca3 - a3);
+ final double a3Low = a3 - a3High;
+ final double cb3 = SPLIT_FACTOR * b3;
+ final double b3High = cb3 - (cb3 - b3);
+ final double b3Low = b3 - b3High;
+
+ // accurate multiplication a3 * b3
+ final double prod3High = a3 * b3;
+ final double prod3Low = a3Low * b3Low - (((prod3High - a3High * b3High) - a3Low * b3High) - a3High * b3Low);
+
+ // accurate addition a1 * b1 + a2 * b2
+ final double s12High = prod1High + prod2High;
+ final double s12Prime = s12High - prod2High;
+ final double s12Low = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);
+
+ // accurate addition a1 * b1 + a2 * b2 + a3 * b3
+ final double s123High = s12High + prod3High;
+ final double s123Prime = s123High - prod3High;
+ final double s123Low = (prod3High - (s123High - s123Prime)) + (s12High - s123Prime);
+
+ // final rounding, s123 may have suffered many cancellations, we try
+ // to recover some bits from the extra words we have saved up to now
+ double result = s123High + (prod1Low + prod2Low + prod3Low + s12Low + s123Low);
+
+ if (Double.isNaN(result)) {
+ // either we have split infinite numbers or some coefficients were NaNs,
+ // just rely on the naive implementation and let IEEE754 handle this
+ result = a1 * b1 + a2 * b2 + a3 * b3;
+ }
+
+ return result;
+ }
+
+ /**
+ * Compute a linear combination accurately.
+ * <p>
+ * This method computes a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
+ * a<sub>4</sub>×b<sub>4</sub>
+ * to high accuracy. It does so by using specific multiplication and
+ * addition algorithms to preserve accuracy and reduce cancellation effects.
+ * It is based on the 2005 paper <a
+ * href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.1547">
+ * Accurate Sum and Dot Product</a> by Takeshi Ogita,
+ * Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
+ * </p>
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @param a3 first factor of the third term
+ * @param b3 second factor of the third term
+ * @param a4 first factor of the third term
+ * @param b4 second factor of the third term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
+ * a<sub>4</sub>×b<sub>4</sub>
+ * @see #linearCombination(double, double, double, double)
+ * @see #linearCombination(double, double, double, double, double, double)
+ */
+ public static double linearCombination(final double a1, final double b1,
+ final double a2, final double b2,
+ final double a3, final double b3,
+ final double a4, final double b4) {
+
+ // the code below is split in many additions/subtractions that may
+ // appear redundant. However, they should NOT be simplified, as they
+ // do use IEEE754 floating point arithmetic rounding properties.
+ // as an example, the expression "ca1 - (ca1 - a1)" is NOT the same as "a1"
+ // The variables naming conventions are that xyzHigh contains the most significant
+ // bits of xyz and xyzLow contains its least significant bits. So theoretically
+ // xyz is the sum xyzHigh + xyzLow, but in many cases below, this sum cannot
+ // be represented in only one double precision number so we preserve two numbers
+ // to hold it as long as we can, combining the high and low order bits together
+ // only at the end, after cancellation may have occurred on high order bits
+
+ // split a1 and b1 as two 26 bits numbers
+ final double ca1 = SPLIT_FACTOR * a1;
+ final double a1High = ca1 - (ca1 - a1);
+ final double a1Low = a1 - a1High;
+ final double cb1 = SPLIT_FACTOR * b1;
+ final double b1High = cb1 - (cb1 - b1);
+ final double b1Low = b1 - b1High;
+
+ // accurate multiplication a1 * b1
+ final double prod1High = a1 * b1;
+ final double prod1Low = a1Low * b1Low - (((prod1High - a1High * b1High) - a1Low * b1High) - a1High * b1Low);
+
+ // split a2 and b2 as two 26 bits numbers
+ final double ca2 = SPLIT_FACTOR * a2;
+ final double a2High = ca2 - (ca2 - a2);
+ final double a2Low = a2 - a2High;
+ final double cb2 = SPLIT_FACTOR * b2;
+ final double b2High = cb2 - (cb2 - b2);
+ final double b2Low = b2 - b2High;
+
+ // accurate multiplication a2 * b2
+ final double prod2High = a2 * b2;
+ final double prod2Low = a2Low * b2Low - (((prod2High - a2High * b2High) - a2Low * b2High) - a2High * b2Low);
+
+ // split a3 and b3 as two 26 bits numbers
+ final double ca3 = SPLIT_FACTOR * a3;
+ final double a3High = ca3 - (ca3 - a3);
+ final double a3Low = a3 - a3High;
+ final double cb3 = SPLIT_FACTOR * b3;
+ final double b3High = cb3 - (cb3 - b3);
+ final double b3Low = b3 - b3High;
+
+ // accurate multiplication a3 * b3
+ final double prod3High = a3 * b3;
+ final double prod3Low = a3Low * b3Low - (((prod3High - a3High * b3High) - a3Low * b3High) - a3High * b3Low);
+
+ // split a4 and b4 as two 26 bits numbers
+ final double ca4 = SPLIT_FACTOR * a4;
+ final double a4High = ca4 - (ca4 - a4);
+ final double a4Low = a4 - a4High;
+ final double cb4 = SPLIT_FACTOR * b4;
+ final double b4High = cb4 - (cb4 - b4);
+ final double b4Low = b4 - b4High;
+
+ // accurate multiplication a4 * b4
+ final double prod4High = a4 * b4;
+ final double prod4Low = a4Low * b4Low - (((prod4High - a4High * b4High) - a4Low * b4High) - a4High * b4Low);
+
+ // accurate addition a1 * b1 + a2 * b2
+ final double s12High = prod1High + prod2High;
+ final double s12Prime = s12High - prod2High;
+ final double s12Low = (prod2High - (s12High - s12Prime)) + (prod1High - s12Prime);
+
+ // accurate addition a1 * b1 + a2 * b2 + a3 * b3
+ final double s123High = s12High + prod3High;
+ final double s123Prime = s123High - prod3High;
+ final double s123Low = (prod3High - (s123High - s123Prime)) + (s12High - s123Prime);
+
+ // accurate addition a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4
+ final double s1234High = s123High + prod4High;
+ final double s1234Prime = s1234High - prod4High;
+ final double s1234Low = (prod4High - (s1234High - s1234Prime)) + (s123High - s1234Prime);
+
+ // final rounding, s1234 may have suffered many cancellations, we try
+ // to recover some bits from the extra words we have saved up to now
+ double result = s1234High + (prod1Low + prod2Low + prod3Low + prod4Low + s12Low + s123Low + s1234Low);
+
+ if (Double.isNaN(result)) {
+ // either we have split infinite numbers or some coefficients were NaNs,
+ // just rely on the naive implementation and let IEEE754 handle this
+ result = a1 * b1 + a2 * b2 + a3 * b3 + a4 * b4;
+ }
+
+ return result;
+ }
+}
Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/MathArrays.java
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