MathArrays (patrius 4.0 API)

java.lang.Object
- fr.cnes.sirius.patrius.math.util.MathArrays

```
public final class MathArrays
extends Object
```
Arrays utilities.

Since:

3.0

Version:

$Id: MathArrays.java 18108 2017-10-04 06:45:27Z bignon $

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.

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`	`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`	`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[]`	`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`	`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 int[]`	`sequence(int size, int start, int stride)` Returns an array of `size` integers starting at `start`, skipping `stride` numbers.
`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.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

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

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

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

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

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

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

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.

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

checkRectangular
```
public static void checkRectangular(long[][] in)
```
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)
```
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

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

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.

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

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
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.
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.
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.
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)
```
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)
```
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.

linearCombination
```
public static double linearCombination(double[] a,
                       double[] b)
```
Compute a linear combination accurately. This method computes the sum of the products a_i b_i 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:
Σ_i a_i b_i.

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)
```
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

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

Class MathArrays

Nested Class Summary

Method Summary

Methods inherited from class java.lang.Object

Method Detail

ebeAdd

ebeSubtract

ebeMultiply

ebeDivide

distance1

distance1

distance

distance

distanceInf

distanceInf

isMonotonic

isMonotonic

checkOrder

checkOrder

checkOrder

checkRectangular

checkPositive

checkNonNegative

checkNonNegative

safeNorm

sortInPlace

sortInPlace

copyOf

copyOf

copyOf

copyOf

linearCombination

linearCombination

linearCombination

linearCombination

equals

equalsIncludingNaN

equals

equalsIncludingNaN

normalizeArray

buildArray

buildArray

natural

sequence