MathArrays (Apache Commons Math 3.6.1 API)

org.apache.commons.math3.util

## Class MathArrays

- java.lang.Object
- - org.apache.commons.math3.util.MathArrays

-     public class MathArrays
      extends Object

  Arrays utilities.
  Since:
    3.0

- - ### Nested Class Summary

    Nested Classes
    Modifier and Type | Class and Description
    --- | ---
    `static interface` | `MathArrays.Function` Real-valued function that operate 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

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `static <T> T[]` | `buildArray(Field<T> field, int length)` Build an array of elements.
    `static <T> T[][]` | `buildArray(Field<T> field, int rows, int columns)` Build a double 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 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 void` | `checkPositive(double[] in)` Check that all entries of the input array are strictly positive.
    `static void` | `checkRectangular(long[][] in)` Throws DimensionMismatchException 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[]` | `copyOf(double[] source)` Creates a copy of the `source` array.
    `static double[]` | `copyOf(double[] source, int len)` Creates a copy of the `source` array.
    `static int[]` | `copyOf(int[] source)` Creates a copy of the `source` array.
    `static int[]` | `copyOf(int[] source, int len)` Creates a copy of the `source` array.
    `static double[]` | `copyOfRange(double[] source, int from, int to)` Creates a copy of the `source` array.
    `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(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` | `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.
      Since:
        3.2

    - #### 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
      Since:
        3.2

    - #### ebeAdd

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

      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:
        `DimensionMismatchException` - if the array lengths differ.
      Since:
        3.1

    - #### ebeSubtract

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

      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:
        `DimensionMismatchException` - if the array lengths differ.
      Since:
        3.1

    - #### ebeMultiply

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

      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:
        `DimensionMismatchException` - if the array lengths differ.
      Since:
        3.1

    - #### ebeDivide

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

      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:
        `DimensionMismatchException` - if the array lengths differ.
      Since:
        3.1

    - #### distance1

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

      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:
        `DimensionMismatchException` - if the array lengths differ.

    - #### distance1

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

      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:
        `DimensionMismatchException` - if the array lengths differ.

    - #### distance

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

      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:
        `DimensionMismatchException` - 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.
      Since:
        3.6

    - #### distance

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

      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:
        `DimensionMismatchException` - if the array lengths differ.

    - #### distanceInf

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

      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:
        `DimensionMismatchException` - if the array lengths differ.

    - #### distanceInf

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

      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:
        `DimensionMismatchException` - 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:
        `DimensionMismatchException` - if the lengths differ and `abort` is `true`.
      Since:
        3.6

    - #### checkEqualLength

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

      Check that both arrays have the same length.
      Parameters:
        `a` - Array.
        `b` - Array.
      Throws:
        `DimensionMismatchException` - if the lengths differ.
      Since:
        3.6

    - #### 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:
        `DimensionMismatchException` - if the lengths differ and `abort` is `true`.
      Since:
        3.6

    - #### checkEqualLength

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

      Check that both arrays have the same length.
      Parameters:
        `a` - Array.
        `b` - Array.
      Throws:
        `DimensionMismatchException` - if the lengths differ.
      Since:
        3.6

    - #### checkOrder

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

      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:
        `NonMonotonicSequenceException` - if the array is not sorted and `abort` is `true`.

    - #### checkOrder

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

      Check that the given array is sorted.
      Parameters:
        `val` - Values.
        `dir` - Ordering direction.
        `strict` - Whether the order should be strict.
      Throws:
        `NonMonotonicSequenceException` - if the array is not sorted.
      Since:
        2.2

    - #### checkOrder

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

      Check that the given array is sorted in strictly increasing order.
      Parameters:
        `val` - Values.
      Throws:
        `NonMonotonicSequenceException` - if the array is not sorted.
      Since:
        2.2

    - #### checkRectangular

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

      Throws DimensionMismatchException if the input array is not rectangular.
      Parameters:
        `in` - array to be tested
      Throws:
        `NullArgumentException` - if input array is null
        `DimensionMismatchException` - if input array is not rectangular
      Since:
        3.1

    - #### checkPositive

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

      Check that all entries of the input array are strictly positive.
      Parameters:
        `in` - Array to be tested
      Throws:
        `NotStrictlyPositiveException` - if any entries of the array are not strictly positive.
      Since:
        3.1

    - #### checkNotNaN

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

      Check that no entry of the input array is `NaN`.
      Parameters:
        `in` - Array to be tested.
      Throws:
        `NotANumberException` - if an entry is `NaN`.
      Since:
        3.4

    - #### checkNonNegative

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

      Check that all entries of the input array are >= 0.
      Parameters:
        `in` - Array to be tested
      Throws:
        `NotPositiveException` - if any array entries are less than 0.
      Since:
        3.1

    - #### checkNonNegative

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

      Check all entries of the input array are >= 0.
      Parameters:
        `in` - Array to be tested
      Throws:
        `NotPositiveException` - if any array entries are less than 0.
      Since:
        3.1

    - #### 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.
      Since:
        2.2

    - #### sortInPlace

          public static void sortInPlace(double[] x,
                         double[]... yList)
                                  throws DimensionMismatchException,
                                         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:
        `DimensionMismatchException` - if any `y` is not the same size as `x`.
        `NullArgumentException` - if `x` or any `y` is null.
      Since:
        3.0

    - #### sortInPlace

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

      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:
        `DimensionMismatchException` - if any `y` is not the same size as `x`.
        `NullArgumentException` - if `x` or any `y` is null
      Since:
        3.0

    - #### copyOf

          public static int[] copyOf(int[] source)

      Creates a copy of the `source` array.
      Parameters:
        `source` - Array to be copied.
      Returns:
        the copied array.

    - #### copyOf

          public static double[] copyOf(double[] source)

      Creates a copy of the `source` array.
      Parameters:
        `source` - Array to be copied.
      Returns:
        the copied array.

    - #### copyOf

          public static int[] copyOf(int[] source,
                     int len)

      Creates a copy of the `source` array.
      Parameters:
        `source` - Array to be copied.
        `len` - Number of entries to copy. If smaller then the source length, the copy will be truncated, if larger it will padded with zeroes.
      Returns:
        the copied array.

    - #### copyOf

          public static double[] copyOf(double[] source,
                        int len)

      Creates a copy of the `source` array.
      Parameters:
        `source` - Array to be copied.
        `len` - Number of entries to copy. If smaller then the source length, the copy will be truncated, if larger it will padded with zeroes.
      Returns:
        the copied array.

    - #### copyOfRange

          public static double[] copyOfRange(double[] source,
                             int from,
                             int to)

      Creates a copy of the `source` array.
      Parameters:
        `source` - Array to be copied.
        `from` - Initial index of the range to be copied, inclusive.
        `to` - Final index of the range to be copied, exclusive. (This index may lie outside the array.)
      Returns:
        the copied array.

    - #### linearCombination

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

      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:
        `DimensionMismatchException` - 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
      Since:
        2.2

    - #### 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.

    - #### 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.
      Since:
        2.2

    - #### normalizeArray

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

      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.

      Parameters:
        `values` - Input array to be normalized
        `normalizedSum` - Target sum for the normalized array
      Returns:
        the normalized array.
      Throws:
        `MathArithmeticException` - if the input array contains infinite elements or sums to zero.
        `MathIllegalArgumentException` - if the target sum is infinite or `NaN`.
      Since:
        2.1

    - #### buildArray

          public static <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
      Since:
        3.2

    - #### buildArray

          public static <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
      Since:
        3.2

    - #### convolve

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

      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`.
        `NoDataException` - if either `x` or `h` is empty.
      Since:
        3.3

    - #### 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.
      Since:
        3.4

    - #### 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
      Since:
        3.3

    - #### 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
      Since:
        3.3

    - #### 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
      Since:
        3.3

    - #### 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.
      Since:
        3.3

    - #### 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
      Since:
        3.6

    - #### 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
      Since:
        3.6

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