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 enum 
    MathArrays.OrderDirection
    Specification of ordering direction.
    static enum 
    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 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 Details

    • 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

      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

      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:

    • 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.

    • 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

      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

      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:

    • 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