Class MathArrays

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class 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.
    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method 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 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 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[] 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 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.
    • 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)
        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)
        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)
        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)
        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)
        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)
        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)
        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.
      • distance

        public static double distance​(int[] p1,
                                      int[] p2)
        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)
        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)
        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)
        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)
        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)
        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
      • checkPositive

        public static void checkPositive​(double[] in)
        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)
        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)
        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)
        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
      • 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)
        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)
        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
      • 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)
        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)
        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)
        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 weights array does not contain at least one non-zero value (applies when length is non zero)
          • 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)
        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 weights array does not contain at least one non-zero value (applies when length is non zero)
          • 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