Package org.hipparchus.util

Class MathArrays

java.lang.Object

org.hipparchus.util.MathArrays

public class MathArrays
extends Object

Arrays utilities.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static interface	MathArrays.Function	Real-valued function that operates on an array or a part of it.
static class	MathArrays.OrderDirection	Specification of ordering direction.
static class	MathArrays.Position	Specification for indicating that some operation applies before or after a given index.

Method Summary

Modifier and Type	Method	Description
static <T extends FieldElement<T>> T[]	buildArray(Field<T> field, int length)	Build an array of elements.
static <T extends FieldElement<T>> T[][]	buildArray(Field<T> field, int rows, int columns)	Build a double dimension array of elements.
static <T extends FieldElement<T>> T[][][]	buildArray(Field<T> field, int l1, int l2, int l3)	Build a triple dimension array of elements.
static void	checkEqualLength(double[] a, double[] b)	Check that both arrays have the same length.
static boolean	checkEqualLength(double[] a, double[] b, boolean abort)	Check that both arrays have the same length.
static void	checkEqualLength(int[] a, int[] b)	Check that both arrays have the same length.
static boolean	checkEqualLength(int[] a, int[] b, boolean abort)	Check that both arrays have the same length.
static <T extends CalculusFieldElement<T>> void	checkEqualLength(T[] a, T[] b)	Check that both arrays have the same length.
static <T extends CalculusFieldElement<T>> boolean	checkEqualLength(T[] a, T[] b, boolean abort)	Check that both arrays have the same length.
static void	checkNonNegative(long[] in)	Check that all entries of the input array are >= 0.
static void	checkNonNegative(long[][] in)	Check all entries of the input array are >= 0.
static void	checkNotNaN(double[] in)	Check that no entry of the input array is NaN.
static void	checkOrder(double[] val)	Check that the given array is sorted in strictly increasing order.
static void	checkOrder(double[] val, MathArrays.OrderDirection dir, boolean strict)	Check that the given array is sorted.
static boolean	checkOrder(double[] val, MathArrays.OrderDirection dir, boolean strict, boolean abort)	Check that the given array is sorted.
static <T extends CalculusFieldElement<T>> void	checkOrder(T[] val)	Check that the given array is sorted in strictly increasing order.
static <T extends CalculusFieldElement<T>> void	checkOrder(T[] val, MathArrays.OrderDirection dir, boolean strict)	Check that the given array is sorted.
static <T extends CalculusFieldElement<T>> boolean	checkOrder(T[] val, MathArrays.OrderDirection dir, boolean strict, boolean abort)	Check that the given array is sorted.
static void	checkPositive(double[] in)	Check that all entries of the input array are strictly positive.
static void	checkRectangular(long[][] in)	Throws MathIllegalArgumentException if the input array is not rectangular.
static double[]	concatenate(double[]... x)	Concatenates a sequence of arrays.
static double[]	convolve(double[] x, double[] h)	Calculates the convolution between two sequences.
static double	cosAngle(double[] v1, double[] v2)	Calculates the cosine of the angle between two vectors.
static double	distance(double[] p1, double[] p2)	Calculates the L2 (Euclidean) distance between two points.
static double	distance(int[] p1, int[] p2)	Calculates the L2 (Euclidean) distance between two points.
static double	distance1(double[] p1, double[] p2)	Calculates the L1 (sum of abs) distance between two points.
static int	distance1(int[] p1, int[] p2)	Calculates the L1 (sum of abs) distance between two points.
static double	distanceInf(double[] p1, double[] p2)	Calculates the L∞ (max of abs) distance between two points.
static int	distanceInf(int[] p1, int[] p2)	Calculates the L∞ (max of abs) distance between two points.
static double[]	ebeAdd(double[] a, double[] b)	Creates an array whose contents will be the element-by-element addition of the arguments.
static double[]	ebeDivide(double[] a, double[] b)	Creates an array whose contents will be the element-by-element division of the first argument by the second.
static double[]	ebeMultiply(double[] a, double[] b)	Creates an array whose contents will be the element-by-element multiplication of the arguments.
static double[]	ebeSubtract(double[] a, double[] b)	Creates an array whose contents will be the element-by-element subtraction of the second argument from the first.
static boolean	equals(byte[] x, byte[] y)	Returns true if both arguments are null or have same dimensions and all their elements are equals.
static boolean	equals(double[] x, double[] y)	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by Precision.equals(double,double).
static boolean	equals(float[] x, float[] y)	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by Precision.equals(float,float).
static boolean	equals(int[] x, int[] y)	Returns true if both arguments are null or have same dimensions and all their elements are equals.
static boolean	equals(long[] x, long[] y)	Returns true if both arguments are null or have same dimensions and all their elements are equals.
static boolean	equals(short[] x, short[] y)	Returns true if both arguments are null or have same dimensions and all their elements are equals.
static <T extends FieldElement<T>> boolean	equals(T[] x, T[] y)	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by Object.equals(Object).
static boolean	equalsIncludingNaN(double[] x, double[] y)	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by this method.
static boolean	equalsIncludingNaN(float[] x, float[] y)	Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by this method.
static boolean	isMonotonic(double[] val, MathArrays.OrderDirection dir, boolean strict)	Check that an array is monotonically increasing or decreasing.
static <T extends Comparable<? super T>> boolean	isMonotonic(T[] val, MathArrays.OrderDirection dir, boolean strict)	Check that an array is monotonically increasing or decreasing.
static double	linearCombination(double[] a, double[] b)	Compute a linear combination accurately.
static double	linearCombination(double a1, double b1, double a2, double b2)	Compute a linear combination accurately.
static double	linearCombination(double a1, double b1, double a2, double b2, double a3, double b3)	Compute a linear combination accurately.
static double	linearCombination(double a1, double b1, double a2, double b2, double a3, double b3, double a4, double b4)	Compute a linear combination accurately.
static int[]	natural(int n)	Returns an array representing the natural number n.
static double[]	normalizeArray(double[] values, double normalizedSum)	Normalizes an array to make it sum to a specified value.
static double	safeNorm(double[] v)	Returns the Cartesian norm (2-norm), handling both overflow and underflow.
static double[]	scale(double val, double[] arr)	Create a copy of an array scaled by a value.
static void	scaleInPlace(double val, double[] arr)	Multiply each element of an array by a value.
static int[]	sequence(int size, int start, int stride)	Returns an array of size integers starting at start, skipping stride numbers.
static void	shuffle(int[] list)	Shuffle the entries of the given array.
static void	shuffle(int[] list, int start, MathArrays.Position pos)	Shuffle the entries of the given array.
static void	shuffle(int[] list, int start, MathArrays.Position pos, RandomGenerator rng)	Shuffle the entries of the given array, using the Fisher–Yates algorithm.
static void	shuffle(int[] list, RandomGenerator rng)	Shuffle the entries of the given array.
static void	sortInPlace(double[] x, double[]... yList)	Sort an array in ascending order in place and perform the same reordering of entries on other arrays.
static void	sortInPlace(double[] x, MathArrays.OrderDirection dir, double[]... yList)	Sort an array in place and perform the same reordering of entries on other arrays.
static double[]	unique(double[] data)	Returns an array consisting of the unique values in data.
static boolean	verifyValues(double[] values, double[] weights, int begin, int length)	This method is used to verify that the begin and length parameters designate a subarray of positive length and the weights are all non-negative, non-NaN, finite, and not all zero.
static boolean	verifyValues(double[] values, double[] weights, int begin, int length, boolean allowEmpty)	This method is used to verify that the begin and length parameters designate a subarray of positive length and the weights are all non-negative, non-NaN, finite, and not all zero.
static boolean	verifyValues(double[] values, int begin, int length)	This method is used to verify that the input parameters designate a subarray of positive length.
static boolean	verifyValues(double[] values, int begin, int length, boolean allowEmpty)	This method is used to verify that the input parameters designate a subarray of positive length.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

scale

public static double[] scale(double val,
                             double[] arr)

Create a copy of an array scaled by a value.

Parameters:

arr - Array to scale.

val - Scalar.

Returns:

scaled copy of array with each entry multiplied by val.

scaleInPlace

public static void scaleInPlace(double val,
                                double[] arr)

Multiply each element of an array by a value.

The array is modified in place (no copy is created).

Parameters:

arr - Array to scale

val - Scalar

ebeAdd

public static double[] ebeAdd(double[] a,
                              double[] b)
                       throws MathIllegalArgumentException

Creates an array whose contents will be the element-by-element addition of the arguments.

Parameters:

a - First term of the addition.

b - Second term of the addition.

Returns:

a new array r where r[i] = a[i] + b[i].

Throws:

MathIllegalArgumentException - if the array lengths differ.

ebeSubtract

public static double[] ebeSubtract(double[] a,
                                   double[] b)
                            throws MathIllegalArgumentException

Creates an array whose contents will be the element-by-element subtraction of the second argument from the first.

Parameters:

a - First term.

b - Element to be subtracted.

Returns:

a new array r where r[i] = a[i] - b[i].

Throws:

MathIllegalArgumentException - if the array lengths differ.

ebeMultiply

public static double[] ebeMultiply(double[] a,
                                   double[] b)
                            throws MathIllegalArgumentException

Creates an array whose contents will be the element-by-element multiplication of the arguments.

Parameters:

a - First factor of the multiplication.

b - Second factor of the multiplication.

Returns:

a new array r where r[i] = a[i] * b[i].

Throws:

MathIllegalArgumentException - if the array lengths differ.

ebeDivide

public static double[] ebeDivide(double[] a,
                                 double[] b)
                          throws MathIllegalArgumentException

Creates an array whose contents will be the element-by-element division of the first argument by the second.

Parameters:

a - Numerator of the division.

b - Denominator of the division.

Returns:

a new array r where r[i] = a[i] / b[i].

Throws:

MathIllegalArgumentException - if the array lengths differ.

distance1

public static double distance1(double[] p1,
                               double[] p2)
                        throws MathIllegalArgumentException

Calculates the L₁ (sum of abs) distance between two points.

Parameters:

p1 - the first point

p2 - the second point

Returns:

the L₁ distance between the two points

Throws:

MathIllegalArgumentException - if the array lengths differ.

distance1

public static int distance1(int[] p1,
                            int[] p2)
                     throws MathIllegalArgumentException

Calculates the L₁ (sum of abs) distance between two points.

Parameters:

p1 - the first point

p2 - the second point

Returns:

the L₁ distance between the two points

Throws:

MathIllegalArgumentException - if the array lengths differ.

distance

public static double distance(double[] p1,
                              double[] p2)
                       throws MathIllegalArgumentException

Calculates the L₂ (Euclidean) distance between two points.

Parameters:

p1 - the first point

p2 - the second point

Returns:

the L₂ distance between the two points

Throws:

MathIllegalArgumentException - if the array lengths differ.

cosAngle

public static double cosAngle(double[] v1,
                              double[] v2)

Calculates the cosine of the angle between two vectors.

Parameters:

v1 - Cartesian coordinates of the first vector.

v2 - Cartesian coordinates of the second vector.

Returns:

the cosine of the angle between the vectors.

distance

public static double distance(int[] p1,
                              int[] p2)
                       throws MathIllegalArgumentException

Calculates the L₂ (Euclidean) distance between two points.

Parameters:

p1 - the first point

p2 - the second point

Returns:

the L₂ distance between the two points

Throws:

MathIllegalArgumentException - if the array lengths differ.

distanceInf

public static double distanceInf(double[] p1,
                                 double[] p2)
                          throws MathIllegalArgumentException

Calculates the L_∞ (max of abs) distance between two points.

Parameters:

p1 - the first point

p2 - the second point

Returns:

the L_∞ distance between the two points

Throws:

MathIllegalArgumentException - if the array lengths differ.

distanceInf

public static int distanceInf(int[] p1,
                              int[] p2)
                       throws MathIllegalArgumentException

Calculates the L_∞ (max of abs) distance between two points.

Parameters:

p1 - the first point

p2 - the second point

Returns:

the L_∞ distance between the two points

Throws:

MathIllegalArgumentException - if the array lengths differ.

isMonotonic

public static <T extends Comparable<? super T>> boolean isMonotonic(T[] val,
                                                                    MathArrays.OrderDirection dir,
                                                                    boolean strict)

Check that an array is monotonically increasing or decreasing.

Type Parameters:

T - the type of the elements in the specified array

Parameters:

val - Values.

dir - Ordering direction.

strict - Whether the order should be strict.

Returns:

true if sorted, false otherwise.

isMonotonic

public static boolean isMonotonic(double[] val,
                                  MathArrays.OrderDirection dir,
                                  boolean strict)

Check that an array is monotonically increasing or decreasing.

Parameters:

val - Values.

dir - Ordering direction.

strict - Whether the order should be strict.

Returns:

true if sorted, false otherwise.

checkEqualLength

public static boolean checkEqualLength(double[] a,
                                       double[] b,
                                       boolean abort)

Check that both arrays have the same length.

Parameters:

a - Array.

b - Array.

abort - Whether to throw an exception if the check fails.

Returns:

true if the arrays have the same length.

Throws:

MathIllegalArgumentException - if the lengths differ and abort is true.

checkEqualLength

public static void checkEqualLength(double[] a,
                                    double[] b)

Check that both arrays have the same length.

Parameters:

a - Array.

b - Array.

Throws:

MathIllegalArgumentException - if the lengths differ.

checkEqualLength

public static <T extends CalculusFieldElement<T>> boolean checkEqualLength(T[] a,
                                                                           T[] b,
                                                                           boolean abort)

Check that both arrays have the same length.

Type Parameters:

T - the type of the field elements

Parameters:

a - Array.

b - Array.

abort - Whether to throw an exception if the check fails.

Returns:

true if the arrays have the same length.

Throws:

MathIllegalArgumentException - if the lengths differ and abort is true.

Since:

1.5

checkEqualLength

public static <T extends CalculusFieldElement<T>> void checkEqualLength(T[] a,
                                                                        T[] b)

Check that both arrays have the same length.

Type Parameters:

T - the type of the field elements

Parameters:

a - Array.

b - Array.

Throws:

MathIllegalArgumentException - if the lengths differ.

Since:

1.5

checkEqualLength

public static boolean checkEqualLength(int[] a,
                                       int[] b,
                                       boolean abort)

Check that both arrays have the same length.

Parameters:

a - Array.

b - Array.

abort - Whether to throw an exception if the check fails.

Returns:

true if the arrays have the same length.

Throws:

MathIllegalArgumentException - if the lengths differ and abort is true.

checkEqualLength

public static void checkEqualLength(int[] a,
                                    int[] b)

Check that both arrays have the same length.

Parameters:

a - Array.

b - Array.

Throws:

MathIllegalArgumentException - if the lengths differ.

checkOrder

public static boolean checkOrder(double[] val,
                                 MathArrays.OrderDirection dir,
                                 boolean strict,
                                 boolean abort)
                          throws MathIllegalArgumentException

Check that the given array is sorted.

Parameters:

val - Values.

dir - Ordering direction.

strict - Whether the order should be strict.

abort - Whether to throw an exception if the check fails.

Returns:

true if the array is sorted.

Throws:

MathIllegalArgumentException - if the array is not sorted and abort is true.

checkOrder

public static void checkOrder(double[] val,
                              MathArrays.OrderDirection dir,
                              boolean strict)
                       throws MathIllegalArgumentException

Check that the given array is sorted.

Parameters:

val - Values.

dir - Ordering direction.

strict - Whether the order should be strict.

Throws:

MathIllegalArgumentException - if the array is not sorted.

checkOrder

public static void checkOrder(double[] val)
                       throws MathIllegalArgumentException

Check that the given array is sorted in strictly increasing order.

Parameters:

val - Values.

Throws:

MathIllegalArgumentException - if the array is not sorted.

checkOrder

public static <T extends CalculusFieldElement<T>> boolean checkOrder(T[] val,
                                                                     MathArrays.OrderDirection dir,
                                                                     boolean strict,
                                                                     boolean abort)
                                                              throws MathIllegalArgumentException

Check that the given array is sorted.

Type Parameters:

T - the type of the field elements

Parameters:

val - Values.

dir - Ordering direction.

strict - Whether the order should be strict.

abort - Whether to throw an exception if the check fails.

Returns:

true if the array is sorted.

Throws:

MathIllegalArgumentException - if the array is not sorted and abort is true.

Since:

1.5

checkOrder

public static <T extends CalculusFieldElement<T>> void checkOrder(T[] val,
                                                                  MathArrays.OrderDirection dir,
                                                                  boolean strict)
                                                           throws MathIllegalArgumentException

Check that the given array is sorted.

Type Parameters:

T - the type of the field elements

Parameters:

val - Values.

dir - Ordering direction.

strict - Whether the order should be strict.

Throws:

MathIllegalArgumentException - if the array is not sorted.

Since:

1.5

checkOrder

public static <T extends CalculusFieldElement<T>> void checkOrder(T[] val)
                                                           throws MathIllegalArgumentException

Check that the given array is sorted in strictly increasing order.

Type Parameters:

T - the type of the field elements

Parameters:

val - Values.

Throws:

MathIllegalArgumentException - if the array is not sorted.

Since:

1.5

checkRectangular

public static void checkRectangular(long[][] in)
                             throws MathIllegalArgumentException,
                                    NullArgumentException

Throws MathIllegalArgumentException if the input array is not rectangular.

Parameters:

in - array to be tested

Throws:

NullArgumentException - if input array is null

MathIllegalArgumentException - if input array is not rectangular

checkPositive

public static void checkPositive(double[] in)
                          throws MathIllegalArgumentException

Check that all entries of the input array are strictly positive.

Parameters:

in - Array to be tested

Throws:

MathIllegalArgumentException - if any entries of the array are not strictly positive.

checkNotNaN

public static void checkNotNaN(double[] in)
                        throws MathIllegalArgumentException

Check that no entry of the input array is NaN.

Parameters:

in - Array to be tested.

Throws:

MathIllegalArgumentException - if an entry is NaN.

checkNonNegative

public static void checkNonNegative(long[] in)
                             throws MathIllegalArgumentException

Check that all entries of the input array are >= 0.

Parameters:

in - Array to be tested

Throws:

MathIllegalArgumentException - if any array entries are less than 0.

checkNonNegative

public static void checkNonNegative(long[][] in)
                             throws MathIllegalArgumentException

Check all entries of the input array are >= 0.

Parameters:

in - Array to be tested

Throws:

MathIllegalArgumentException - if any array entries are less than 0.

safeNorm

public static double safeNorm(double[] v)

Returns the Cartesian norm (2-norm), handling both overflow and underflow. Translation of the minpack enorm subroutine.

The redistribution policy for MINPACK is available here, for convenience, it is reproduced below.

Minpack Copyright Notice (1999) University of Chicago. All rights reserved

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. 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.
3. The end-user documentation included with the redistribution, if any, must include the following acknowledgment: 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.
4. 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.
5. 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.

Parameters:

v - Vector of doubles.

Returns:

the 2-norm of the vector.

sortInPlace

public static void sortInPlace(double[] x,
                               double[]... yList)
                        throws MathIllegalArgumentException,
                               NullArgumentException

Sort an array in ascending order in place and perform the same reordering of entries on other arrays. For example, if x = [3, 1, 2], y = [1, 2, 3] and z = [0, 5, 7], then sortInPlace(x, y, z) will update x to [1, 2, 3], y to [2, 3, 1] and z to [5, 7, 0].

Parameters:

x - Array to be sorted and used as a pattern for permutation of the other arrays.

yList - Set of arrays whose permutations of entries will follow those performed on x.

Throws:

MathIllegalArgumentException - if any y is not the same size as x.

NullArgumentException - if x or any y is null.

sortInPlace

public static void sortInPlace(double[] x,
                               MathArrays.OrderDirection dir,
                               double[]... yList)
                        throws MathIllegalArgumentException,
                               NullArgumentException

Sort an array in place and perform the same reordering of entries on other arrays. This method works the same as the other sortInPlace method, but allows the order of the sort to be provided in the dir parameter.

Parameters:

x - Array to be sorted and used as a pattern for permutation of the other arrays.

dir - Order direction.

yList - Set of arrays whose permutations of entries will follow those performed on x.

Throws:

MathIllegalArgumentException - if any y is not the same size as x.

NullArgumentException - if x or any y is null

linearCombination

public static double linearCombination(double[] a,
                                       double[] b)
                                throws MathIllegalArgumentException

Compute a linear combination accurately. This method computes the sum of the products ai bi 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 Accurate Sum and Dot Product by Takeshi Ogita, Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

public static double linearCombination(double a1,
                                       double b1,
                                       double a2,
                                       double b2)

Compute a linear combination accurately.

This method computes a₁×b₁ + a₂×b₂ 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 Accurate Sum and Dot Product by Takeshi Ogita, Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

See Also:

linearCombination(double, double, double, double, double, double), linearCombination(double, double, double, double, double, double, double, double)

linearCombination

public static double linearCombination(double a1,
                                       double b1,
                                       double a2,
                                       double b2,
                                       double a3,
                                       double b3)

Compute a linear combination accurately.

This method computes a₁×b₁ + a₂×b₂ + a₃×b₃ 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 Accurate Sum and Dot Product by Takeshi Ogita, Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

See Also:

linearCombination(double, double, double, double), linearCombination(double, double, double, double, double, double, double, double)

linearCombination

public static double linearCombination(double a1,
                                       double b1,
                                       double a2,
                                       double b2,
                                       double a3,
                                       double b3,
                                       double a4,
                                       double b4)

Compute a linear combination accurately.

This method computes a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄ 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 Accurate Sum and Dot Product by Takeshi Ogita, Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the third term

b4 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

linearCombination(double, double, double, double), linearCombination(double, double, double, double, double, double)

equals

public static boolean equals(float[] x,
                             float[] y)

Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by Precision.equals(float,float).

Parameters:

x - first array

y - second array

Returns:

true if the values are both null or have same dimension and equal elements.

equalsIncludingNaN

public static boolean equalsIncludingNaN(float[] x,
                                         float[] y)

Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by this method.

Parameters:

x - first array

y - second array

Returns:

true if the values are both null or have same dimension and equal elements

equals

public static boolean equals(double[] x,
                             double[] y)

Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by Precision.equals(double,double).

Parameters:

x - First array.

y - Second array.

Returns:

true if the values are both null or have same dimension and equal elements.

equals

public static <T extends FieldElement<T>> boolean equals(T[] x,
                                                         T[] y)

Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by Object.equals(Object).

Type Parameters:

T - type of the field elements

Parameters:

x - First array.

y - Second array.

Returns:

true if the values are both null or have same dimension and equal elements.

Since:

4.0

equalsIncludingNaN

public static boolean equalsIncludingNaN(double[] x,
                                         double[] y)

Returns true iff both arguments are null or have same dimensions and all their elements are equal as defined by this method.

Parameters:

x - First array.

y - Second array.

Returns:

true if the values are both null or have same dimension and equal elements.

equals

public static boolean equals(long[] x,
                             long[] y)

Returns true if both arguments are null or have same dimensions and all their elements are equals.

Parameters:

x - First array.

y - Second array.

Returns:

true if the values are both null or have same dimension and equal elements.

equals

public static boolean equals(int[] x,
                             int[] y)

Returns true if both arguments are null or have same dimensions and all their elements are equals.

Parameters:

x - First array.

y - Second array.

Returns:

true if the values are both null or have same dimension and equal elements.

equals

public static boolean equals(byte[] x,
                             byte[] y)

Returns true if both arguments are null or have same dimensions and all their elements are equals.

Parameters:

x - First array.

y - Second array.

Returns:

true if the values are both null or have same dimension and equal elements.

equals

public static boolean equals(short[] x,
                             short[] y)

Returns true if both arguments are null or have same dimensions and all their elements are equals.

Parameters:

x - First array.

y - Second array.

Returns:

true if the values are both null or have same dimension and equal elements.

normalizeArray

public static double[] normalizeArray(double[] values,
                                      double normalizedSum)
                               throws MathIllegalArgumentException,
                                      MathRuntimeException

Normalizes an array to make it sum to a specified value. Returns the result of the transformation

    x ↦ x * normalizedSum / sum
 

applied to each non-NaN element x of the input array, where sum is the sum of the non-NaN entries in the input array.

Throws IllegalArgumentException if normalizedSum is infinite or NaN and ArithmeticException if the input array contains any infinite elements or sums to 0.

Ignores (i.e., copies unchanged to the output array) NaNs in the input array. The input array is unchanged by this method.

Parameters:

values - Input array to be normalized

normalizedSum - Target sum for the normalized array

Returns:

the normalized array

Throws:

MathRuntimeException - if the input array contains infinite elements or sums to zero

MathIllegalArgumentException - if the target sum is infinite or NaN

buildArray

public static <T extends FieldElement<T>> T[] buildArray(Field<T> field,
                                                         int length)

Build an array of elements.

Arrays are filled with field.getZero()

Type Parameters:

T - the type of the field elements

Parameters:

field - field to which array elements belong

length - of the array

Returns:

a new array

buildArray

public static <T extends FieldElement<T>> T[][] buildArray(Field<T> field,
                                                           int rows,
                                                           int columns)

Build a double dimension array of elements.

Arrays are filled with field.getZero()

Type Parameters:

T - the type of the field elements

Parameters:

field - field to which array elements belong

rows - number of rows in the array

columns - number of columns (may be negative to build partial arrays in the same way new Field[rows][] works)

Returns:

a new array

buildArray

public static <T extends FieldElement<T>> T[][][] buildArray(Field<T> field,
                                                             int l1,
                                                             int l2,
                                                             int l3)

Build a triple dimension array of elements.

Arrays are filled with field.getZero()

Type Parameters:

T - the type of the field elements

Parameters:

field - field to which array elements belong

l1 - number of elements along first dimension

l2 - number of elements along second dimension

l3 - number of elements along third dimension (may be negative to build partial arrays in the same way new Field[l1][l2][] works)

Returns:

a new array

Since:

1.4

convolve

public static double[] convolve(double[] x,
                                double[] h)
                         throws MathIllegalArgumentException,
                                NullArgumentException

Calculates the convolution between two sequences.

The solution is obtained via straightforward computation of the convolution sum (and not via FFT). Whenever the computation needs an element that would be located at an index outside the input arrays, the value is assumed to be zero.

Parameters:

x - First sequence. Typically, this sequence will represent an input signal to a system.

h - Second sequence. Typically, this sequence will represent the impulse response of the system.

Returns:

the convolution of x and h. This array's length will be x.length + h.length - 1.

Throws:

NullArgumentException - if either x or h is null.

MathIllegalArgumentException - if either x or h is empty.

shuffle

public static void shuffle(int[] list,
                           int start,
                           MathArrays.Position pos)

Shuffle the entries of the given array. The start and pos parameters select which portion of the array is randomized and which is left untouched.

Parameters:

list - Array whose entries will be shuffled (in-place).

start - Index at which shuffling begins.

pos - Shuffling is performed for index positions between start and either the end (if MathArrays.Position.TAIL) or the beginning (if MathArrays.Position.HEAD) of the array.

See Also:

shuffle(int[],int,Position,RandomGenerator)

shuffle

public static void shuffle(int[] list,
                           int start,
                           MathArrays.Position pos,
                           RandomGenerator rng)

Shuffle the entries of the given array, using the Fisher–Yates algorithm. The start and pos parameters select which portion of the array is randomized and which is left untouched.

Parameters:

list - Array whose entries will be shuffled (in-place).

start - Index at which shuffling begins.

pos - Shuffling is performed for index positions between start and either the end (if MathArrays.Position.TAIL) or the beginning (if MathArrays.Position.HEAD) of the array.

rng - Random number generator.

shuffle

public static void shuffle(int[] list,
                           RandomGenerator rng)

Shuffle the entries of the given array.

Parameters:

list - Array whose entries will be shuffled (in-place).

rng - Random number generator.

See Also:

shuffle(int[],int,Position,RandomGenerator)

shuffle

public static void shuffle(int[] list)

Shuffle the entries of the given array.

Parameters:

list - Array whose entries will be shuffled (in-place).

See Also:

shuffle(int[],int,Position,RandomGenerator)

natural

public static int[] natural(int n)

Returns an array representing the natural number n.

Parameters:

n - Natural number.

Returns:

an array whose entries are the numbers 0, 1, ..., n-1. If n == 0, the returned array is empty.

sequence

public static int[] sequence(int size,
                             int start,
                             int stride)

Returns an array of size integers starting at start, skipping stride numbers.

Parameters:

size - Natural number.

start - Natural number.

stride - Natural number.

Returns:

an array whose entries are the numbers start, start + stride, ..., start + (size - 1) * stride. If size == 0, the returned array is empty.

verifyValues

public static boolean verifyValues(double[] values,
                                   int begin,
                                   int length)
                            throws MathIllegalArgumentException

This method is used to verify that the input parameters designate a subarray of positive length.

• returns true iff the parameters designate a subarray of positive length
• throws MathIllegalArgumentException if the array is null or or the indices are invalid
• returns false if the array is non-null, but length is 0.

Parameters:

values - the input array

begin - index of the first array element to include

length - the number of elements to include

Returns:

true if the parameters are valid and designate a subarray of positive length

Throws:

MathIllegalArgumentException - if the indices are invalid or the array is null

verifyValues

public static boolean verifyValues(double[] values,
                                   int begin,
                                   int length,
                                   boolean allowEmpty)
                            throws MathIllegalArgumentException

This method is used to verify that the input parameters designate a subarray of positive length.

• returns true iff the parameters designate a subarray of non-negative length
• throws IllegalArgumentException if the array is null or or the indices are invalid
• returns false if the array is non-null, but length is 0 unless allowEmpty is true

Parameters:

values - the input array

begin - index of the first array element to include

length - the number of elements to include

allowEmpty - if true then zero length arrays are allowed

Returns:

true if the parameters are valid

Throws:

MathIllegalArgumentException - if the indices are invalid or the array is null

verifyValues

public static boolean verifyValues(double[] values,
                                   double[] weights,
                                   int begin,
                                   int length)
                            throws MathIllegalArgumentException

This method is used to verify that the begin and length parameters designate a subarray of positive length and the weights are all non-negative, non-NaN, finite, and not all zero.

• returns true iff the parameters designate a subarray of positive length and the weights array contains legitimate values.
• throws IllegalArgumentException if any of the following are true:
  • the values array is null
  • the weights array is null
  • the weights array does not have the same length as the values array
  • the weights array contains one or more infinite values
  • the weights array contains one or more NaN values
  • the weights array contains negative values
  • the start and length arguments do not determine a valid array
• returns false if the array is non-null, but length is 0.

Parameters:

values - the input array

weights - the weights array

begin - index of the first array element to include

length - the number of elements to include

Returns:

true if the parameters are valid and designate a subarray of positive length

Throws:

MathIllegalArgumentException - if the indices are invalid or the array is null

verifyValues

public static boolean verifyValues(double[] values,
                                   double[] weights,
                                   int begin,
                                   int length,
                                   boolean allowEmpty)
                            throws MathIllegalArgumentException

This method is used to verify that the begin and length parameters designate a subarray of positive length and the weights are all non-negative, non-NaN, finite, and not all zero.

• returns true iff the parameters designate a subarray of non-negative length and the weights array contains legitimate values.
• throws MathIllegalArgumentException if any of the following are true:
  • the values array is null
  • the weights array is null
  • the weights array does not have the same length as the values array
  • the weights array contains one or more infinite values
  • the weights array contains one or more NaN values
  • the weights array contains negative values
  • the start and length arguments do not determine a valid array
• returns false if the array is non-null, but length is 0 unless allowEmpty is true

Parameters:

values - the input array.

weights - the weights array.

begin - index of the first array element to include.

length - the number of elements to include.

allowEmpty - if true than allow zero length arrays to pass.

Returns:

true if the parameters are valid.

Throws:

NullArgumentException - if either of the arrays are null

MathIllegalArgumentException - if the array indices are not valid, the weights array contains NaN, infinite or negative elements, or there are no positive weights.

concatenate

public static double[] concatenate(double[]... x)

Concatenates a sequence of arrays. The return array consists of the entries of the input arrays concatenated in the order they appear in the argument list. Null arrays cause NullPointerExceptions; zero length arrays are allowed (contributing nothing to the output array).

Parameters:

x - list of double[] arrays to concatenate

Returns:

a new array consisting of the entries of the argument arrays

Throws:

NullPointerException - if any of the arrays are null

unique

public static double[] unique(double[] data)

Returns an array consisting of the unique values in data. The return array is sorted in descending order. Empty arrays are allowed, but null arrays result in NullPointerException. Infinities are allowed. NaN values are allowed with maximum sort order - i.e., if there are NaN values in data, Double.NaN will be the first element of the output array, even if the array also contains Double.POSITIVE_INFINITY.

Parameters:

data - array to scan

Returns:

descending list of values included in the input array

Throws:

NullPointerException - if data is null