ArrayMath (JSci API Documentation)

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JSci.maths
Class ArrayMath

java.lang.Object
  JSci.maths.AbstractMath
      JSci.maths.ArrayMath

public final class ArrayMath
extends AbstractMath
extends AbstractMath

Arrays are faster than object, so this class is here to take full advantage of arrays without encapsulation. All methods are safe, that is, they create copies of arrays whenever necessary This makes for slower methods, but the programmer can always define his own methods optimized for performance.

Method Summary
`static double[]`	`abs(double[] v)` Takes the absolute value of each component of an array.
`static double[][]`	`abs(double[][] v)` Takes the absolute value of each component of an array.
`static int[]`	`abs(int[] v)` Takes the absolute value of each component of an array.
`static int[][]`	`abs(int[][] v)` Takes the absolute value of each component of an array.
`static double[]`	`add(double[] w, double a)` Adds a scalar to every element in the array.
`static double[]`	`add(double[] a, double[] b)` Adds the two arrays together (componentwise).
`static double[]`	`add(double[] w, double a, double[] v, int p)` Adds to an array w, a times v where a is a scalar.
`static int[]`	`add(int[] w, double a, int[] v, int p)` Adds to an array w, a times v where a is a scalar.
`static int[]`	`add(int[] w, int a)` Adds a scalar to every element in the array.
`static int[]`	`add(int[] a, int[] b)` Adds the two arrays together (componentwise).
`static Complex[]`	`apply(ComplexMapping m, Complex[] v)` Applys a map to every component of an array.
`static Complex[][]`	`apply(ComplexMapping m, Complex[][] v)` Applys a map to every component of an array.
`static double[]`	`apply(Mapping m, double[] v)` Applys a map to every component of an array.
`static double[][]`	`apply(Mapping m, double[][] v)` Applys a map to every component of an array.
`static double[]`	`copy(double[] v)` Returns a copy of the array.
`static double[][]`	`copy(double[][] v)` Returns a copy of the array.
`static int[]`	`copy(int[] v)` Returns a copy of the array.
`static int[][]`	`copy(int[][] v)` Returns a copy of the array.
`static double`	`correlation(double[] v1, double[] v2)` Computes the (linear) correlation between two arrays.
`static double`	`correlation(int[] v1, int[] v2)` Computes the (linear) correlation between two arrays.
`static double`	`covariance(double[] v1, double[] v2)` Computes the covariance.
`static double`	`covariance(int[] v1, int[] v2)` Computes the covariance.
`static boolean`	`equals(double[] a, double[] b)` Checks if two arrays are equal within a tolerance.
`static boolean`	`equals(int[] a, int[] b)` Deprecated. Use java.util.Arrays instead.
`static double[]`	`extract(int k0, int k1, double[] invect)` Extracts a sub-array (will invert the resulting array if k0 > k1).
`static int[]`	`extract(int k0, int k1, int[] invect)` Extracts a sub-array (will invert the resulting array if k0 > k1).
`static double[]`	`invert(double[] v)` Inverts an array from left to right.
`static int[]`	`invert(int[] v)` Inverts an array from left to right.
`static boolean`	`isSquare(double[][] a)`
`static boolean`	`isSquare(int[][] a)`
`static boolean`	`isSquare(java.lang.Object[][] a)`
`static double`	`mass(double[] v)` Returns the sum of the elements of the array.
`static int`	`mass(int[] v)` Returns the sum of the elements of the array.
`static double`	`max(double[] v)` Returns the maximum of an array.
`static double`	`max(double[][] v)` Returns the maximum of an array.
`static int`	`max(int[] v)` Returns the maximum of an array.
`static int`	`max(int[][] v)` Returns the maximum of an array.
`static double`	`mean(double[] v)` Computes the mean.
`static double`	`mean(int[] v)` Computes the mean.
`static double`	`median(double[] v)` Computes the median of an array.
`static int`	`median(int[] v)` Computes the median of an array.
`static double`	`min(double[] v)` Returns the minimum of an array.
`static double`	`min(double[][] v)` Returns the minimum of an array.
`static int`	`min(int[] v)` Returns the minimum of an array.
`static int`	`min(int[][] v)` Returns the minimum of an array.
`static double[]`	`mod(Complex[] v)` Returns the componentwise modulus of an array of Complex numbers.
`static double[][]`	`mod(Complex[][] v)` Returns the componentwise modulus of an array of Complex numbers.
`static double`	`norm(double[] data)` Computes the L2 norm of an array (Euclidean norm or "length").
`static double`	`norm(int[] data)` Computes the L2 norm of an array (Euclidean norm or "length").
`static double[]`	`normalize(double[] v)` Renormalizes the array so that its L2 norm is 1 (up to computational errors).
`static double[]`	`padding(int n0, int pos, double[] v)` Fills in with zero to get to the desired length; original array with be at the specified position.
`static int[]`	`padding(int n0, int pos, int[] v)` Fills in with zeroes to get to the specified length; original array with be at the specified position
`static double`	`percentile(double[] v, double p)` Gives the percentile of an array.
`static double`	`percentile(double[] v, double p, boolean isSorted)`
`static double`	`percentile(int[] v, double p)` Gives the percentile of an array.
`static double`	`percentile(int[] v, double p, boolean isSorted)`
`static void`	`print(double[] v)` Prints an array to screen.
`static void`	`print(double[][] v)` Prints an array to screen.
`static void`	`print(int[] v)` Prints an array to screen.
`static void`	`print(int[][] v)` Prints an array to screen.
`static double[]`	`range(double b)` Generates an array going for 0 to b with steps of size 1.
`static double[]`	`range(double a, double b)` Generates an array going for a to b inclusively with steps of size 1.
`static double[]`	`range(double a, double b, double step)` Generates an array going for a to b with steps of size step.
`static int[]`	`range(int b)` Generates an array going for 0 to b with steps of size 1.
`static int[]`	`range(int a, int b)` Generates an array going for a to b with steps of size 1.
`static int[]`	`range(int a, int b, int step)` Generates an array going for a to b with steps of size step.
`static double[]`	`scalarMultiply(double a, double[] v)` Multiplies every component of an array by a scalar.
`static double[]`	`scalarMultiply(double a, int[] v)` Multiplies every component of an array by a scalar.
`static double[]`	`scalarMultiplyFast(double a, double[] v)` Fast scalar multiplication for sparse arrays.
`static double[]`	`scalarMultiplyFast(double a, int[] v)` Fast scalar multiplication for sparse arrays.
`static double`	`scalarProduct(double[][] w0, double[][] w1)` Computes the scalar product of two array as if they were matrices.
`static double`	`scalarProduct(double[] w0, double[] w1)` Computes the scalar product of two array as if they were vectors.
`static double`	`scalarProduct(int[][] w0, int[][] w1)` Computes the scalar product of two array as if they were matrices.
`static int`	`scalarProduct(int[] w0, int[] w1)` Computes the scalar product of two array as if they were vectors.
`static double[]`	`setLengthFromBeginning(double[] data, int length)` Sets an array to the specified length scraping or padding the end if necessary.
`static int[]`	`setLengthFromBeginning(int[] data, int length)` Sets an array to the specified length scraping or padding the end if necessary.
`static double[]`	`setLengthFromEnd(double[] data, int length)` Sets an array to the specified length scraping or padding the beginning if necessary.
`static int[]`	`setLengthFromEnd(int[] data, int length)` Sets an array to the specified length scraping or padding the beginning if necessary.
`static double[]`	`sortMaxToMin(double[] v)` Returns a sorted array from the maximum to the minimum value.
`static int[]`	`sortMaxToMin(int[] v)` Returns a sorted array from the maximum to the minimum value.
`static double[]`	`sortMinToMax(double[] v)` Returns a sorted array from the minimum to the maximum value.
`static int[]`	`sortMinToMax(int[] v)` Returns a sorted array from the minimum to the maximum value.
`static double`	`standardDeviation(double[] v)` Computes the standard deviation of an array.
`static double`	`standardDeviation(int[] v)` Returns the standard deviation of an array.
`static double[]`	`subtract(double[] a, double[] b)` Subtracts the two arrays together (componentwise)
`static int[]`	`subtract(int[] a, int[] b)` Subtracts the two arrays together (componentwise).
`static double`	`sumModSqrs(Complex[] v)`
`static double`	`sumModSqrs(Complex[][] v)`
`static double`	`sumSquares(double[] data)` Sums the squares of all components; also called the energy of the array.
`static double`	`sumSquares(double[][] data)` Sums the squares of all components; also called the energy of the array.
`static int`	`sumSquares(int[] data)` Sums the squares of all components; also called the energy of the array.
`static int`	`sumSquares(int[][] data)` Sums the squares of all components; also called the energy of the array.
`static java.lang.String`	`toString(double[] array)` Returns a comma delimited string representing the value of the array.
`static java.lang.String`	`toString(double[][] array)` Returns a comma delimited string representing the value of the array.
`static java.lang.String`	`toString(int[] array)` Returns a comma delimited string representing the value of the array.
`static java.lang.String`	`toString(int[][] array)` Returns a comma delimited string representing the value of the array.
`static double[][]`	`transpose(double[][] M)` Takes the transpose of an array (like the matrix operation).
`static int[][]`	`transpose(int[][] M)` Takes the transpose of an array (like the matrix operation).
`static double`	`variance(double[] v)` Computes the variance.
`static double`	`variance(int[] v)` Computes the variance.

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

Method Detail

isSquare

public static boolean isSquare(double[][] a)

isSquare

public static boolean isSquare(int[][] a)

isSquare

public static boolean isSquare(java.lang.Object[][] a)

apply

public static double[] apply(Mapping m,
                             double[] v)

Applys a map to every component of an array.

apply

public static double[][] apply(Mapping m,
                               double[][] v)

Applys a map to every component of an array.

apply

public static Complex[] apply(ComplexMapping m,
                              Complex[] v)

Applys a map to every component of an array.

apply

public static Complex[][] apply(ComplexMapping m,
                                Complex[][] v)

Applys a map to every component of an array.

normalize

public static double[] normalize(double[] v)

Renormalizes the array so that its L2 norm is 1 (up to computational errors).

setLengthFromEnd

public static double[] setLengthFromEnd(double[] data,
                                        int length)

Sets an array to the specified length scraping or padding the beginning if necessary.

setLengthFromBeginning

public static double[] setLengthFromBeginning(double[] data,
                                              int length)

Sets an array to the specified length scraping or padding the end if necessary.

copy

public static double[] copy(double[] v)

Returns a copy of the array.

copy

public static double[][] copy(double[][] v)

Returns a copy of the array.

variance

public static double variance(double[] v)

Computes the variance.

covariance

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

Computes the covariance.

correlation

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

Computes the (linear) correlation between two arrays. Squaring this result and multiply by 100 gives you the percentage of correlation.

mean

public static double mean(double[] v)

Computes the mean.

standardDeviation

public static double standardDeviation(double[] v)

Computes the standard deviation of an array.

sortMinToMax

public static double[] sortMinToMax(double[] v)

Returns a sorted array from the minimum to the maximum value.

sortMaxToMin

public static double[] sortMaxToMin(double[] v)

Returns a sorted array from the maximum to the minimum value.

percentile

public static double percentile(double[] v,
                                double p)

Gives the percentile of an array.

Parameters:: v - an unsorted array; p - percentile, must be between 0 and 1
Throws:: java.lang.IllegalArgumentException - if parameter. p is not between 0 and 1.

percentile

public static double percentile(double[] v,
                                double p,
                                boolean isSorted)

median

public static double median(double[] v)

Computes the median of an array. If the array contains an even number of elements, then the mean of the lower and upper medians is returned.

equals

public static boolean equals(double[] a,
                             double[] b)

Checks if two arrays are equal within a tolerance.

abs

public static double[] abs(double[] v)

Takes the absolute value of each component of an array.

abs

public static double[][] abs(double[][] v)

Takes the absolute value of each component of an array.

max

public static double max(double[] v)

Returns the maximum of an array.

max

public static double max(double[][] v)

Returns the maximum of an array.

min

public static double min(double[] v)

Returns the minimum of an array.

min

public static double min(double[][] v)

Returns the minimum of an array.

mod

public static double[] mod(Complex[] v)

Returns the componentwise modulus of an array of Complex numbers.

mod

public static double[][] mod(Complex[][] v)

Returns the componentwise modulus of an array of Complex numbers.

sumModSqrs

public static double sumModSqrs(Complex[] v)

sumModSqrs

public static double sumModSqrs(Complex[][] v)

norm

public static double norm(double[] data)

Computes the L2 norm of an array (Euclidean norm or "length").

sumSquares

public static double sumSquares(double[] data)

Sums the squares of all components; also called the energy of the array.

sumSquares

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

Sums the squares of all components; also called the energy of the array.

scalarProduct

public static double scalarProduct(double[] w0,
                                   double[] w1)

Computes the scalar product of two array as if they were vectors.

Throws:: java.lang.IllegalArgumentException - if the don't have the same length

scalarProduct

public static double scalarProduct(double[][] w0,
                                   double[][] w1)

Computes the scalar product of two array as if they were matrices.

Throws:: java.lang.IllegalArgumentException - if the don't have the same length

extract

public static double[] extract(int k0,
                               int k1,
                               double[] invect)

Extracts a sub-array (will invert the resulting array if k0 > k1).

Parameters:: k0 - location of the first component; k1 - location of the last component

invert

public static double[] invert(double[] v)

Inverts an array from left to right.

padding

public static double[] padding(int n0,
                               int pos,
                               double[] v)

Fills in with zero to get to the desired length; original array with be at the specified position.

Parameters:: n0 - length of the new array.; pos - position of the old array.

add

public static double[] add(double[] w,
                           double a,
                           double[] v,
                           int p)

Adds to an array w, a times v where a is a scalar. Since v can be smaller then w, we must specified the position at which v will be added.

Parameters:: a - scalar.; p - position.

add

public static double[] add(double[] w,
                           double a)

Adds a scalar to every element in the array.

transpose

public static double[][] transpose(double[][] M)

Takes the transpose of an array (like the matrix operation).

Throws:: java.lang.IllegalArgumentException - if the array is not a matrix

range

public static double[] range(double a,
                             double b,
                             double step)

Generates an array going for a to b with steps of size step. If it can't get to the value b in a finite number of steps, it gets as close as possible (a can be larger or smaller than b)

Parameters:: step - size of steps, must be positive.; a - first value of array.; b - last value of array.
Throws:: java.lang.IllegalArgumentException - if step is negative of if a=b.

range

public static double[] range(double a,
                             double b)

Generates an array going for a to b inclusively with steps of size 1. a can be smaller or larger than b.

range

public static double[] range(double b)

Generates an array going for 0 to b with steps of size 1. 0 can be smaller or larger than b.

add

public static double[] add(double[] a,
                           double[] b)

Adds the two arrays together (componentwise).

Throws:: java.lang.IllegalArgumentException - if the two arrays don't have the same length.

subtract

public static double[] subtract(double[] a,
                                double[] b)

Subtracts the two arrays together (componentwise)

Throws:: java.lang.IllegalArgumentException - if the two arrays don't have the same length.

scalarMultiply

public static double[] scalarMultiply(double a,
                                      double[] v)

Multiplies every component of an array by a scalar.

toString

public static java.lang.String toString(double[] array)

Returns a comma delimited string representing the value of the array.

toString

public static java.lang.String toString(double[][] array)

Returns a comma delimited string representing the value of the array.

mass

public static double mass(double[] v)

Returns the sum of the elements of the array.

scalarMultiplyFast

public static double[] scalarMultiplyFast(double a,
                                          double[] v)

Fast scalar multiplication for sparse arrays.

print

public static void print(double[] v)

Prints an array to screen.

print

public static void print(double[][] v)

Prints an array to screen.

setLengthFromEnd

public static int[] setLengthFromEnd(int[] data,
                                     int length)

Sets an array to the specified length scraping or padding the beginning if necessary.

setLengthFromBeginning

public static int[] setLengthFromBeginning(int[] data,
                                           int length)

Sets an array to the specified length scraping or padding the end if necessary.

copy

public static int[] copy(int[] v)

Returns a copy of the array.

copy

public static int[][] copy(int[][] v)

Returns a copy of the array.

variance

public static double variance(int[] v)

Computes the variance.

covariance

public static double covariance(int[] v1,
                                int[] v2)

Computes the covariance.

correlation

public static double correlation(int[] v1,
                                 int[] v2)

Computes the (linear) correlation between two arrays. Squaring this result and multiply by 100 gives you the percentage of correlation.

mean

public static double mean(int[] v)

Computes the mean.

standardDeviation

public static double standardDeviation(int[] v)

Returns the standard deviation of an array.

sortMinToMax

public static int[] sortMinToMax(int[] v)

Returns a sorted array from the minimum to the maximum value.

sortMaxToMin

public static int[] sortMaxToMin(int[] v)

Returns a sorted array from the maximum to the minimum value.

toString

public static java.lang.String toString(int[] array)

Returns a comma delimited string representing the value of the array.

toString

public static java.lang.String toString(int[][] array)

Returns a comma delimited string representing the value of the array.

percentile

public static double percentile(int[] v,
                                double p)

Gives the percentile of an array.

Parameters:: v - an unsorted array; p - percentile, must be between 0 and 1
Throws:: java.lang.IllegalArgumentException - if parameter p is not between 0 and 1.

percentile

public static double percentile(int[] v,
                                double p,
                                boolean isSorted)

Parameters:: isSorted - true if the array is already sorted into ascending numerical order.

median

public static int median(int[] v)

Computes the median of an array. If the array contains an even number of elements, the lower median is returned.

equals

public static boolean equals(int[] a,
                             int[] b)

Deprecated. Use java.util.Arrays instead.

Use java.util.Arrays instead. Check if two arrays are equal.

abs

public static int[] abs(int[] v)

Takes the absolute value of each component of an array.

abs

public static int[][] abs(int[][] v)

Takes the absolute value of each component of an array.

max

public static int max(int[] v)

Returns the maximum of an array.

max

public static int max(int[][] v)

Returns the maximum of an array.

min

public static int min(int[] v)

Returns the minimum of an array.

min

public static int min(int[][] v)

Returns the minimum of an array.

norm

public static double norm(int[] data)

Computes the L2 norm of an array (Euclidean norm or "length").

sumSquares

public static int sumSquares(int[] data)

Sums the squares of all components; also called the energy of the array.

sumSquares

public static int sumSquares(int[][] data)

Sums the squares of all components; also called the energy of the array.

scalarProduct

public static int scalarProduct(int[] w0,
                                int[] w1)

Computes the scalar product of two array as if they were vectors.

Throws:: java.lang.IllegalArgumentException - if the don't have the same length.

scalarProduct

public static double scalarProduct(int[][] w0,
                                   int[][] w1)

Computes the scalar product of two array as if they were matrices.

Throws:: java.lang.IllegalArgumentException - if the don't have the same length.

extract

public static int[] extract(int k0,
                            int k1,
                            int[] invect)

Extracts a sub-array (will invert the resulting array if k0 > k1).

Parameters:: k0 - location of the first component.; k1 - location of the last component.

invert

public static int[] invert(int[] v)

Inverts an array from left to right.

padding

public static int[] padding(int n0,
                            int pos,
                            int[] v)

Fills in with zeroes to get to the specified length; original array with be at the specified position

Parameters:: n0 - length of the new array.; pos - position of the old array.

add

public static int[] add(int[] w,
                        double a,
                        int[] v,
                        int p)

Adds to an array w, a times v where a is a scalar. Since v can be smaller then w, we must specified the position at which v will be added.

Parameters:: a - scalar.; p - position.; w - longer array.; v - shorter array.
Throws:: java.lang.IllegalArgumentException - if the second array is not shorter than the first one.

add

public static int[] add(int[] w,
                        int a)

Adds a scalar to every element in the array.

range

public static int[] range(int a,
                          int b)

Generates an array going for a to b with steps of size 1. a can be smaller or larger than b.

range

public static int[] range(int b)

Generates an array going for 0 to b with steps of size 1. 0 can be smaller or larger than b.

range

public static int[] range(int a,
                          int b,
                          int step)

Generates an array going for a to b with steps of size step. If it can't get to the value b in a finite number of steps, it gets as close as possible (a can be larger or smaller than b)

Parameters:: step - size of steps, must be positive; a - first value of array; b - last value of array
Throws:: java.lang.IllegalArgumentException - if step is negative or if a=b.

transpose

public static int[][] transpose(int[][] M)

Takes the transpose of an array (like the matrix operation).

Throws:: java.lang.IllegalArgumentException - if the array is not a matrix

add

public static int[] add(int[] a,
                        int[] b)

Adds the two arrays together (componentwise).

Throws:: java.lang.IllegalArgumentException - if the two arrays don't have the same length.

subtract

public static int[] subtract(int[] a,
                             int[] b)

Subtracts the two arrays together (componentwise).

Throws:: java.lang.IllegalArgumentException - if the two arrays don't have the same length.

mass

public static int mass(int[] v)

Returns the sum of the elements of the array.

scalarMultiply

public static double[] scalarMultiply(double a,
                                      int[] v)

Multiplies every component of an array by a scalar.

scalarMultiplyFast

public static double[] scalarMultiplyFast(double a,
                                          int[] v)

Fast scalar multiplication for sparse arrays.

print

public static void print(int[] v)

Prints an array to screen.

print

public static void print(int[][] v)

Prints an array to screen.

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JSci.maths Class ArrayMath

isSquare

isSquare

isSquare

apply

apply

apply

apply

normalize

setLengthFromEnd

setLengthFromBeginning

copy

copy

variance

covariance

correlation

mean

standardDeviation

sortMinToMax

sortMaxToMin

percentile

percentile

median

equals

abs

abs

max

max

min

min

mod

mod

sumModSqrs

sumModSqrs

norm

sumSquares

sumSquares

scalarProduct

scalarProduct

extract

invert

padding

add

add

transpose

range

range

range

add

subtract

scalarMultiply

toString

toString

mass

scalarMultiplyFast

print

print

setLengthFromEnd

setLengthFromBeginning

copy

copy

variance

covariance

correlation

mean

standardDeviation

sortMinToMax

sortMaxToMin

toString

toString

percentile

percentile

median

equals

abs

abs

max

max

min

min

JSci.maths
Class ArrayMath