java.lang.Object
- adams.data.statistics.StatUtils

```
public class StatUtils
extends Object
```
A statistical helper class.

Author:

fracpete (fracpete at waikato dot ac dot nz)

Field Summary

Fields
Modifier and Type Field Description

protected static org.apache.commons.math3.distribution.NormalDistribution m_NormalDist
for computation.

Constructor Summary

Constructors
Constructor Description

StatUtils()

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static double`	`correlationCoefficient(double[] y1, double[] y2)`	Computes the correlation coefficient between the two data vectors and returns it.
`static double`	`correlationCoefficient(Number[] y1, Number[] y2)`	Computes the correlation coefficient between the two data vectors and returns it.
`static double`	`covariance(double[] x, double[] y)`	Computes the covariance between the two data vectors and returns it.
`static double`	`covariance(Number[] x, Number[] y)`	Computes the covariance between the two data vectors and returns it.
`static int`	`findClosest(double[] array, double toFind)`	Returns the index of the double closest to the one one is looking for in the given array.
`static int`	`findClosest(int[] array, int toFind)`	Returns the index of the integer closest to the one one is looking for in the given array.
`static int`	`findClosest(Number[] array, Number toFind)`	Returns the index of the number closest to the one one is looking for in the given array.
`static int`	`findFirst(double[] array, double toFind)`	Returns the (first) index of the double one is looking for in the given array.
`static int`	`findFirst(int[] array, int toFind)`	Returns the (first) index of the integer one is looking for in the given array.
`static int`	`findFirst(Number[] array, Number toFind)`	Returns the (first) index of the number one is looking for in the given array.
`static byte[]`	`flatten(byte[][] matrix)`	Converts the matrix into a flat array, row after row.
`static double[]`	`flatten(double[][] matrix)`	Converts the matrix into a flat array, row after row.
`static float[]`	`flatten(float[][] matrix)`	Converts the matrix into a flat array, row after row.
`static int[]`	`flatten(int[][] matrix)`	Converts the matrix into a flat array, row after row.
`static long[]`	`flatten(long[][] matrix)`	Converts the matrix into a flat array, row after row.
`static short[]`	`flatten(short[][] matrix)`	Converts the matrix into a flat array, row after row.
`static Number[]`	`flatten(Number[][] matrix)`	Converts the matrix into a flat array, row after row.
`static double`	`iqr(double[] array)`	Returns the iqr of the given array.
`static double`	`iqr(int[] array)`	Returns the iqr of the given array.
`static double`	`iqr(Number[] array)`	Returns the interquartile of the given array.
`static double[]`	`kendallTheil(double[] x, double[] y)`	Computes the Kendall-Theil robust regression of the given data points.
`static double[]`	`kendallTheil(Number[] x, Number[] y)`	Computes the Kendall-Theil robust regression of the given data points.
`static double[]`	`linearRegression(double[] x, double[] y)`	Calculates the slope and intercept between the two arrays.
`static double[]`	`linearRegression(Number[] x, Number[] y)`	Calculates the slope and intercept between the two arrays.
`static double`	`mae(double[] actual, double[] predicted)`	Computes the mean absolute error between the two data vectors and returns it.
`static double`	`mae(Number[] actual, Number[] predicted)`	Computes the mean absolute error between the two data vectors and returns it.
`static void`	`main(String[] args)`	Just for testing.
`static double`	`max(double[] array)`	Returns the (first occurrence of the) biggest value in the given array.
`static int`	`max(int[] array)`	Returns the (first occurrence of the) biggest value in the given array.
`static Number`	`max(Number[] array)`	Returns the (first occurrence of the) biggest value in the given array.
`static int`	`maxIndex(double[] array)`	Returns the (first occurrence of the) index of the cell with the biggest double.
`static int`	`maxIndex(int[] array)`	Returns the (first occurrence of the) index of the cell with the biggest int.
`static int`	`maxIndex(Number[] array)`	Returns the (first occurrence of the) index of the cell with the biggest number.
`static double`	`mean(double[] array)`	Returns the mean of the given array.
`static double`	`mean(int[] array)`	Returns the mean of the given array.
`static double`	`mean(Number[] array)`	Returns the mean of the given array.
`static double`	`median(double[] array)`	Returns the median of the given array.
`static double`	`median(int[] array)`	Returns the median of the given array.
`static double`	`median(Number[] array)`	Returns the median of the given array.
`static double`	`min(double[] array)`	Returns the (first occurrence of the) smallest value in the given array.
`static int`	`min(int[] array)`	Returns the (first occurrence of the) smallest value in the given array.
`static Number`	`min(Number[] array)`	Returns the (first occurrence of the) smallest value in the given array.
`static int`	`minIndex(double[] array)`	Returns the (first occurrence of the) index of the cell with the smallest double.
`static int`	`minIndex(int[] array)`	Returns the (first occurrence of the) index of the cell with the smallest int.
`static int`	`minIndex(Number[] array)`	Returns the (first occurrence of the) index of the cell with the smallest number.
`static double`	`normalInverse(double y0)`	Returns the value, `x`, for which the area under the Normal (Gaussian) probability density function (integrated from minus infinity to `x`) is equal to the argument `y` (assumes mean is zero, variance is one).
`static double[]`	`normalize(double[] array)`	Normalizes the given array (returns a copy).
`static double[]`	`normalize(int[] array)`	Normalizes the given array (returns a copy).
`static Double[]`	`normalize(Number[] array)`	Normalizes the given array (returns a copy), i.e., the array will sum up to 1.
`static double[]`	`normalizeRange(double[] array, double lower, double upper)`	Normalizes the given array (returns a copy), to have its values range from lower to upper bound.
`static double[]`	`normalizeRange(int[] array, double lower, double upper)`	Normalizes the given array (returns a copy), to have its values range from lower to upper bound.
`static Double[]`	`normalizeRange(Number[] array, double lower, double upper)`	Normalizes the given array (returns a copy), to have its values range from lower to upper bound.
`static double`	`normalProbability(double a)`	Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to `x` (assumes mean is zero, variance is one).
`static double`	`quartile(double[] array, double quartile)`	Returns the quartile of the given array.
`static double`	`quartile(int[] array, double quartile)`	Returns the quartile of the given array.
`static double`	`quartile(Number[] array, double quartile)`	Returns the quartile of the given array.
`static double`	`rae(double[] actual, double[] predicted)`	Computes the relative absolute error between the two data vectors and returns it.
`static double`	`rae(Number[] actual, Number[] predicted)`	Computes the relative absolute error between the two data vectors and returns it.
`static double`	`rmse(double[] actual, double[] predicted)`	Computes the root mean squared error between the two data vectors and returns it.
`static double`	`rmse(Number[] actual, Number[] predicted)`	Computes the root mean squared error between the two data vectors and returns it.
`static double[]`	`rowNorm(double[] x)`	Applies row-wise normalization to the data.
`static double[]`	`rowNorm(Number[] x)`	Applies row-wise normalization to the data.
`static double`	`rrse(double[] actual, double[] predicted)`	Computes the root relative squared error between the two data vectors and returns it.
`static double`	`rrse(Number[] actual, Number[] predicted)`	Computes the root relative squared error between the two data vectors and returns it.
`static double`	`rSquared(double[] actual, double[] predicted)`	Computes the R^2 between the two data vectors and returns it.
`static double`	`rSquared(Number[] actual, Number[] predicted)`	Computes the R^2 between the two data vectors and returns it.
`static double`	`signalToNoiseRatio(double[] x)`	Calculates the signal/noise ratio.
`static double`	`signalToNoiseRatio(Number[] x)`	Calculates the signal/noise ratio.
`static double[]`	`sort(double[] array)`	Returns a sorted copy of the array (ascending).
`static double[]`	`sort(double[] array, boolean asc)`	Returns a sorted copy of the array (ascending or descending).
`static int[]`	`sort(int[] array)`	Returns a sorted copy of the array (ascending).
`static int[]`	`sort(int[] array, boolean asc)`	Returns a sorted copy of the array (ascending or descending).
`static Number[]`	`sort(Number[] array)`	Returns a sorted copy of the array (ascending).
`static Number[]`	`sort(Number[] array, boolean asc)`	Returns a sorted copy of the array (ascending or descending).
`static double[]`	`standardize(double[] array, boolean isSample)`	Standardizes the given array (returns a copy).
`static double[]`	`standardize(int[] array, boolean isSample)`	Standardizes the given array (returns a copy).
`static Double[]`	`standardize(Number[] array, boolean isSample)`	Standardizes the given array (returns a copy).
`static double[]`	`standardScores(double[] x, boolean isSample)`	Computes the standard scores for the array.
`static double[]`	`standardScores(double[] actual, double[] predicted, boolean isSample)`	Computes the standard scores.
`static double[]`	`standardScores(Number[] x, boolean isSample)`	Computes the standard scores for the array.
`static double[]`	`standardScores(Number[] actual, Number[] predicted, boolean isSample)`	Computes the standard scores.
`static double`	`stddev(double[] array, boolean isSample)`	Returns the std deviation of the given array.
`static double`	`stddev(int[] array, boolean isSample)`	Returns the std deviation of the given array.
`static double`	`stddev(Number[] array, boolean isSample)`	Returns the std deviation of the given array.
`static gnu.trove.list.array.TIntArrayList`	`subsample(int num, double perc, long seed)`	Creates a random sub-sample of indices of a certain percentage using the specified number of entrie.
`static gnu.trove.list.array.TIntArrayList`	`subsample(int num, double perc, RandomIntegerRangeGenerator generator)`	Creates a random sub-sample of indices of a certain percentage using the specified number of entrie.
`static double`	`sum(double[] array)`	Returns sum of all the elements in the array.
`static double`	`sum(int[] array)`	Returns sum of all the elements in the array.
`static double`	`sum(Number[] array)`	Returns sum of all the elements in the array.
`static double`	`sumOfSquares(double[] array)`	Returns sum of all the squared elements in the array.
`static double`	`sumOfSquares(int[] array)`	Returns sum of all the squared elements in the array.
`static double`	`sumOfSquares(Number[] array)`	Returns sum of all the squared elements in the array.
`static byte[]`	`toByteArray(Number[] array)`	Turns the Number array into one consisting of primitive bytes.
`static byte[][]`	`toByteMatrix(Number[][] matrix)`	Turns the Number matrix into one consisting of primitive bytes.
`static double[]`	`toDoubleArray(Number[] array)`	Turns the Number array into one consisting of primitive doubles.
`static double[][]`	`toDoubleMatrix(Number[][] matrix)`	Turns the Number matrix into one consisting of primitive doubles.
`static float[]`	`toFloatArray(Number[] array)`	Turns the Number array into one consisting of primitive floats.
`static float[][]`	`toFloatMatrix(Number[][] matrix)`	Turns the Number matrix into one consisting of primitive floats.
`static int[]`	`toIntArray(Number[] array)`	Turns the Number array into one consisting of primitive ints.
`static int[][]`	`toIntMatrix(Number[][] matrix)`	Turns the Number matrix into one consisting of primitive ints.
`static long[]`	`toLongArray(Number[] array)`	Turns the Number array into one consisting of primitive longs.
`static long[][]`	`toLongMatrix(Number[][] matrix)`	Turns the Number matrix into one consisting of primitive longs.
`static Number[]`	`toNumberArray(byte[] array)`	Turns the byte array into a Byte array.
`static Number[]`	`toNumberArray(double[] array)`	Turns the double array into a Double array.
`static Number[]`	`toNumberArray(float[] array)`	Turns the float array into a Float array.
`static Number[]`	`toNumberArray(int[] array)`	Turns the int array into a Integer array.
`static Number[]`	`toNumberArray(long[] array)`	Turns the long array into a Long array.
`static Number[]`	`toNumberArray(short[] array)`	Turns the short array into a Short array.
`static Number[][]`	`toNumberMatrix(byte[][] matrix)`	Turns the Number matrix into one consisting of primitive bytes.
`static Number[][]`	`toNumberMatrix(double[][] matrix)`	Turns the primitive double matrix into one consisting of Doubles.
`static Number[][]`	`toNumberMatrix(float[][] matrix)`	Turns the primitive float matrix into one consisting of Floats.
`static Number[][]`	`toNumberMatrix(int[][] matrix)`	Turns the primitve int matrix into one consisting of Integers.
`static Number[][]`	`toNumberMatrix(long[][] matrix)`	Turns the primitive long matrix into one consisting of Longs.
`static Number[][]`	`toNumberMatrix(short[][] matrix)`	Turns the Number matrix into one consisting of primitive shorts.
`static short[]`	`toShortArray(Number[] array)`	Turns the Number array into one consisting of primitive shorts.
`static short[][]`	`toShortMatrix(Number[][] matrix)`	Turns the Number matrix into one consisting of primitive shorts.
`static gnu.trove.map.TByteIntMap`	`uniqueCounts(byte[] numbers)`	Returns all the unique numbers in the array.
`static gnu.trove.map.TDoubleIntMap`	`uniqueCounts(double[] numbers)`	Returns all the counts for the unique numbers in the array.
`static gnu.trove.map.TFloatIntMap`	`uniqueCounts(float[] numbers)`	Returns all the unique numbers in the array.
`static gnu.trove.map.TIntIntMap`	`uniqueCounts(int[] numbers)`	Returns all the unique numbers in the array.
`static gnu.trove.map.TLongIntMap`	`uniqueCounts(long[] numbers)`	Returns all the unique numbers in the array.
`static gnu.trove.map.TShortIntMap`	`uniqueCounts(short[] numbers)`	Returns all the unique numbers in the array.
`static byte[]`	`uniqueValues(byte[] numbers)`	Returns all the unique numbers in the array.
`static double[]`	`uniqueValues(double[] numbers)`	Returns all the unique numbers in the array.
`static float[]`	`uniqueValues(float[] numbers)`	Returns all the unique numbers in the array.
`static int[]`	`uniqueValues(int[] numbers)`	Returns all the unique numbers in the array.
`static long[]`	`uniqueValues(long[] numbers)`	Returns all the unique numbers in the array.
`static short[]`	`uniqueValues(short[] numbers)`	Returns all the unique numbers in the array.

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

- Field Detail
  - m_NormalDist
```
protected static org.apache.commons.math3.distribution.NormalDistribution m_NormalDist
```
    for computation.
- Constructor Detail
  - StatUtils
```
public StatUtils()
```
- Method Detail
  - toNumberArray
```
public static Number[] toNumberArray(byte[] array)
```
    Turns the byte array into a Byte array.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toNumberArray
```
public static Number[] toNumberArray(short[] array)
```
    Turns the short array into a Short array.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toNumberArray
```
public static Number[] toNumberArray(int[] array)
```
    Turns the int array into a Integer array.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toNumberArray
```
public static Number[] toNumberArray(long[] array)
```
    Turns the long array into a Long array.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toNumberArray
```
public static Number[] toNumberArray(float[] array)
```
    Turns the float array into a Float array.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toNumberArray
```
public static Number[] toNumberArray(double[] array)
```
    Turns the double array into a Double array.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toByteArray
```
public static byte[] toByteArray(Number[] array)
```
    Turns the Number array into one consisting of primitive bytes.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toShortArray
```
public static short[] toShortArray(Number[] array)
```
    Turns the Number array into one consisting of primitive shorts.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toIntArray
```
public static int[] toIntArray(Number[] array)
```
    Turns the Number array into one consisting of primitive ints.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toLongArray
```
public static long[] toLongArray(Number[] array)
```
    Turns the Number array into one consisting of primitive longs.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toFloatArray
```
public static float[] toFloatArray(Number[] array)
```
    Turns the Number array into one consisting of primitive floats.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - toDoubleArray
```
public static double[] toDoubleArray(Number[] array)
```
    Turns the Number array into one consisting of primitive doubles.
    
    Parameters:
    
    array - the array to convert
    
    Returns:
    
    the converted array
  - minIndex
```
public static int minIndex(Number[] array)
```
    Returns the (first occurrence of the) index of the cell with the smallest number. -1 in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the index
  - minIndex
```
public static int minIndex(int[] array)
```
    Returns the (first occurrence of the) index of the cell with the smallest int. -1 in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the index
  - minIndex
```
public static int minIndex(double[] array)
```
    Returns the (first occurrence of the) index of the cell with the smallest double. -1 in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the index
  - min
```
public static Number min(Number[] array)
```
    Returns the (first occurrence of the) smallest value in the given array. Null in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the smallest value
  - min
```
public static int min(int[] array)
```
    Returns the (first occurrence of the) smallest value in the given array. Integer.MIN_VALUE in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the smallest value
  - min
```
public static double min(double[] array)
```
    Returns the (first occurrence of the) smallest value in the given array. -Double.MAX_VALUE in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the smallest value
  - maxIndex
```
public static int maxIndex(Number[] array)
```
    Returns the (first occurrence of the) index of the cell with the biggest number. -1 in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the index
  - maxIndex
```
public static int maxIndex(int[] array)
```
    Returns the (first occurrence of the) index of the cell with the biggest int. -1 in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the index
  - maxIndex
```
public static int maxIndex(double[] array)
```
    Returns the (first occurrence of the) index of the cell with the biggest double. -1 in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the index
  - max
```
public static Number max(Number[] array)
```
    Returns the (first occurrence of the) biggest value in the given array. Null in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the biggest value
  - max
```
public static int max(int[] array)
```
    Returns the (first occurrence of the) biggest value in the given array. Integer.MAX_VALUE in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the biggest value
  - max
```
public static double max(double[] array)
```
    Returns the (first occurrence of the) biggest value in the given array. Double.MAX_VALUE in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the biggest value
  - mean
```
public static double mean(Number[] array)
```
    Returns the mean of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the mean
  - mean
```
public static double mean(int[] array)
```
    Returns the mean of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the mean
  - mean
```
public static double mean(double[] array)
```
    Returns the mean of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the mean
  - iqr
```
public static double iqr(double[] array)
```
    Returns the iqr of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the iqr
  - iqr
```
public static double iqr(int[] array)
```
    Returns the iqr of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the iqr
  - iqr
```
public static double iqr(Number[] array)
```
    Returns the interquartile of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the iqr
  - quartile
```
public static double quartile(double[] array,
                              double quartile)
```
    Returns the quartile of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    quartile - the quartile to return (0-1)
    
    Returns:
    
    the quartile
  - quartile
```
public static double quartile(int[] array,
                              double quartile)
```
    Returns the quartile of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    quartile - the quartile to return (0-1)
    
    Returns:
    
    the quartile
  - quartile
```
public static double quartile(Number[] array,
                              double quartile)
```
    Returns the quartile of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    quartile - the quartile to return (0-1)
    
    Returns:
    
    the quartile
  - median
```
public static double median(Number[] array)
```
    Returns the median of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the median
  - median
```
public static double median(int[] array)
```
    Returns the median of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the median
  - median
```
public static double median(double[] array)
```
    Returns the median of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the median
  - stddev
```
public static double stddev(Number[] array,
                            boolean isSample)
```
    Returns the std deviation of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the std deviation
  - stddev
```
public static double stddev(int[] array,
                            boolean isSample)
```
    Returns the std deviation of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the std deviation
  - stddev
```
public static double stddev(double[] array,
                            boolean isSample)
```
    Returns the std deviation of the given array. NaN is returned in case of zero-length arrays.
    
    Parameters:
    
    array - the array to work on
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the std deviation
  - normalize
```
public static Double[] normalize(Number[] array)
```
    Normalizes the given array (returns a copy), i.e., the array will sum up to 1. In case of a sum of 0, it returns null.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the normalized array
  - normalize
```
public static double[] normalize(int[] array)
```
    Normalizes the given array (returns a copy).
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the std deviation
  - normalize
```
public static double[] normalize(double[] array)
```
    Normalizes the given array (returns a copy).
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the std deviation
  - normalizeRange
```
public static Double[] normalizeRange(Number[] array,
                                      double lower,
                                      double upper)
```
    Normalizes the given array (returns a copy), to have its values range from lower to upper bound.
    
    Parameters:
    
    array - the array to work on
    
    lower - the lower bound
    
    upper - the upper bound
    
    Returns:
    
    the normalized array, null if failed to determine min/max or range is zero
  - normalizeRange
```
public static double[] normalizeRange(int[] array,
                                      double lower,
                                      double upper)
```
    Normalizes the given array (returns a copy), to have its values range from lower to upper bound.
    
    Parameters:
    
    array - the array to work on
    
    lower - the lower bound
    
    upper - the upper bound
    
    Returns:
    
    the normalized array, null if failed to determine min/max or range is zero
  - normalizeRange
```
public static double[] normalizeRange(double[] array,
                                      double lower,
                                      double upper)
```
    Normalizes the given array (returns a copy), to have its values range from lower to upper bound.
    
    Parameters:
    
    array - the array to work on
    
    lower - the lower bound
    
    upper - the upper bound
    
    Returns:
    
    the normalized array, null if failed to determine min/max or range is zero
  - standardize
```
public static Double[] standardize(Number[] array,
                                   boolean isSample)
```
    Standardizes the given array (returns a copy). Returns null if the standard deviation is zero and data cannot be standardized.
    
    Parameters:
    
    array - the array to work on
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the std deviation
  - standardize
```
public static double[] standardize(double[] array,
                                   boolean isSample)
```
    Standardizes the given array (returns a copy). Returns null if the standard deviation is zero and data cannot be standardized.
    
    Parameters:
    
    array - the array to work on
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the std deviation
  - standardize
```
public static double[] standardize(int[] array,
                                   boolean isSample)
```
    Standardizes the given array (returns a copy). Returns null if the standard deviation is zero and data cannot be standardized.
    
    Parameters:
    
    array - the array to work on
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the std deviation
  - sum
```
public static double sum(Number[] array)
```
    Returns sum of all the elements in the array.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the sum
  - sum
```
public static double sum(int[] array)
```
    Returns sum of all the elements in the array.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the sum
  - sum
```
public static double sum(double[] array)
```
    Returns sum of all the elements in the array.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the sum
  - sumOfSquares
```
public static double sumOfSquares(Number[] array)
```
    Returns sum of all the squared elements in the array.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the sum
  - sumOfSquares
```
public static double sumOfSquares(int[] array)
```
    Returns sum of all the squared elements in the array.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the sum
  - sumOfSquares
```
public static double sumOfSquares(double[] array)
```
    Returns sum of all the squared elements in the array.
    
    Parameters:
    
    array - the array to work on
    
    Returns:
    
    the sum
  - sort
```
public static Number[] sort(Number[] array)
```
    Returns a sorted copy of the array (ascending).
    
    Parameters:
    
    array - the array to sort
    
    Returns:
    
    the sorted array
  - sort
```
public static int[] sort(int[] array)
```
    Returns a sorted copy of the array (ascending).
    
    Parameters:
    
    array - the array to sort
    
    Returns:
    
    the sorted array
  - sort
```
public static double[] sort(double[] array)
```
    Returns a sorted copy of the array (ascending).
    
    Parameters:
    
    array - the array to sort
    
    Returns:
    
    the sorted array
  - sort
```
public static Number[] sort(Number[] array,
                            boolean asc)
```
    Returns a sorted copy of the array (ascending or descending).
    
    Parameters:
    
    array - the array to sort
    
    asc - if true then the data gets sorted in ascending manner, otherwise in descending manner
    
    Returns:
    
    the sorted array
  - sort
```
public static int[] sort(int[] array,
                         boolean asc)
```
    Returns a sorted copy of the array (ascending or descending).
    
    Parameters:
    
    array - the array to sort
    
    asc - if true then the data gets sorted in ascending manner, otherwise in descending manner
    
    Returns:
    
    the sorted array
  - sort
```
public static double[] sort(double[] array,
                            boolean asc)
```
    Returns a sorted copy of the array (ascending or descending).
    
    Parameters:
    
    array - the array to sort
    
    asc - if true then the data gets sorted in ascending manner, otherwise in descending manner
    
    Returns:
    
    the sorted array
  - findFirst
```
public static int findFirst(Number[] array,
                            Number toFind)
```
    Returns the (first) index of the number one is looking for in the given array. -1 is returned if not found.
    
    Parameters:
    
    array - the array to search
    
    toFind - the number to find
    
    Returns:
    
    the index
  - findFirst
```
public static int findFirst(int[] array,
                            int toFind)
```
    Returns the (first) index of the integer one is looking for in the given array. -1 is returned if not found.
    
    Parameters:
    
    array - the array to search
    
    toFind - the integer to find
    
    Returns:
    
    the index
  - findFirst
```
public static int findFirst(double[] array,
                            double toFind)
```
    Returns the (first) index of the double one is looking for in the given array. -1 is returned if not found.
    
    Parameters:
    
    array - the array to search
    
    toFind - the double to find
    
    Returns:
    
    the index
  - findClosest
```
public static int findClosest(Number[] array,
                              Number toFind)
```
    Returns the index of the number closest to the one one is looking for in the given array.
    
    Parameters:
    
    array - the array to search
    
    toFind - the number to find
    
    Returns:
    
    the index
  - findClosest
```
public static int findClosest(int[] array,
                              int toFind)
```
    Returns the index of the integer closest to the one one is looking for in the given array.
    
    Parameters:
    
    array - the array to search
    
    toFind - the integer to find
    
    Returns:
    
    the index
  - findClosest
```
public static int findClosest(double[] array,
                              double toFind)
```
    Returns the index of the double closest to the one one is looking for in the given array.
    
    Parameters:
    
    array - the array to search
    
    toFind - the double to find
    
    Returns:
    
    the index
  - correlationCoefficient
```
public static double correlationCoefficient(double[] y1,
                                            double[] y2)
```
    Computes the correlation coefficient between the two data vectors and returns it.
    
    Parameters:
    
    y1 - the first data array
    
    y2 - the second data array
    
    Returns:
    
    the computed correlation
  - correlationCoefficient
```
public static double correlationCoefficient(Number[] y1,
                                            Number[] y2)
```
    Computes the correlation coefficient between the two data vectors and returns it.
    
    Parameters:
    
    y1 - the first data array
    
    y2 - the second data array
    
    Returns:
    
    the computed correlation
  - rSquared
```
public static double rSquared(double[] actual,
                              double[] predicted)
```
    Computes the R^2 between the two data vectors and returns it.
    
    Parameters:
    
    actual - the first data array
    
    predicted - the second data array
    
    Returns:
    
    the computed correlation
  - rSquared
```
public static double rSquared(Number[] actual,
                              Number[] predicted)
```
    Computes the R^2 between the two data vectors and returns it. https://en.wikipedia.org/wiki/Coefficient_of_determination
    
    Parameters:
    
    actual - the first data array
    
    predicted - the second data array
    
    Returns:
    
    the computed correlation
  - covariance
```
public static double covariance(double[] x,
                                double[] y)
```
    Computes the covariance between the two data vectors and returns it. Cov(X,Y) = Sum((Xi-Xbar)*(Yi-Ybar)) / n with n = length of vectors, Xi the ith element of X, Yi the ith element of Y, Xbar the mean of X, Ybar the mean of Y.
    
    Parameters:
    
    x - the first data array
    
    y - the second data array
    
    Returns:
    
    the computed correlation
  - covariance
```
public static double covariance(Number[] x,
                                Number[] y)
```
    Computes the covariance between the two data vectors and returns it. Cov(X,Y) = Sum((Xi-Xbar)*(Yi-Ybar)) / n with n = length of vectors, Xi the ith element of X, Yi the ith element of Y, Xbar the mean of X, Ybar the mean of Y.
    
    Parameters:
    
    x - the first data array
    
    y - the second data array
    
    Returns:
    
    the computed correlation
  - rmse
```
public static double rmse(double[] actual,
                          double[] predicted)
```
    Computes the root mean squared error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the rmse
  - rmse
```
public static double rmse(Number[] actual,
                          Number[] predicted)
```
    Computes the root mean squared error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the rmse
  - mae
```
public static double mae(double[] actual,
                         double[] predicted)
```
    Computes the mean absolute error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the mae
  - mae
```
public static double mae(Number[] actual,
                         Number[] predicted)
```
    Computes the mean absolute error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the mae
  - rae
```
public static double rae(double[] actual,
                         double[] predicted)
```
    Computes the relative absolute error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the rae
  - rae
```
public static double rae(Number[] actual,
                         Number[] predicted)
```
    Computes the relative absolute error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the rae
  - rrse
```
public static double rrse(double[] actual,
                          double[] predicted)
```
    Computes the root relative squared error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the rrse
  - rrse
```
public static double rrse(Number[] actual,
                          Number[] predicted)
```
    Computes the root relative squared error between the two data vectors and returns it.
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    Returns:
    
    the rrse
  - standardScores
```
public static double[] standardScores(double[] x,
                                      boolean isSample)
```
    Computes the standard scores for the array.
    
    Parameters:
    
    x - the data array
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the standard scores
  - standardScores
```
public static double[] standardScores(Number[] x,
                                      boolean isSample)
```
    Computes the standard scores for the array.
    
    Parameters:
    
    x - the data array
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the standard scores
  - standardScores
```
public static double[] standardScores(double[] actual,
                                      double[] predicted,
                                      boolean isSample)
```
    Computes the standard scores. The mean/stdev are determined from the first array (actual) and the z-scores are produced for the second one (predicted).
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the standard scores
  - standardScores
```
public static double[] standardScores(Number[] actual,
                                      Number[] predicted,
                                      boolean isSample)
```
    Computes the standard scores. The mean/stdev are determined from the first array (actual) and the z-scores are produced for the second one (predicted).
    
    Parameters:
    
    actual - the second data array
    
    predicted - the first data array
    
    isSample - if true, then the sample standard deviation instead of the population standard deviation is calculated (using n-1 instead of n).
    
    Returns:
    
    the standard scores
  - signalToNoiseRatio
```
public static double signalToNoiseRatio(Number[] x)
```
    Calculates the signal/noise ratio.
    
    For more details, see Signal-to-noise ratio.
    
    Parameters:
    
    x - the input data to calculate the ratio for
    
    Returns:
    
    the ratio
  - signalToNoiseRatio
```
public static double signalToNoiseRatio(double[] x)
```
    Calculates the signal/noise ratio.
    
    For more details, see Signal-to-noise ratio.
    
    Parameters:
    
    x - the input data to calculate the ratio for
    
    Returns:
    
    the ratio
  - rowNorm
```
public static double[] rowNorm(Number[] x)
```
    Applies row-wise normalization to the data.
    
    Parameters:
    
    x - the input data
    
    Returns:
    
    the normalize data
  - rowNorm
```
public static double[] rowNorm(double[] x)
```
    Applies row-wise normalization to the data.
    
    Parameters:
    
    x - the input data
    
    Returns:
    
    the normalize data
  - normalProbability
```
public static double normalProbability(double a)
```
    Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to x (assumes mean is zero, variance is one).
    x - 1 | | 2 normal(x) = --------- | exp( - t /2 ) dt sqrt(2pi) | | - -inf. = ( 1 + erf(z) ) / 2 = erfc(z) / 2
    where z = x/sqrt(2). Computation is via the functions errorFunction and errorFunctionComplement.
    Parameters:
    
    a - the z-value
    
    Returns:
    
    the probability of the z value according to the normal pdf
  - normalInverse
```
public static double normalInverse(double y0)
```
    Returns the value, x, for which the area under the Normal (Gaussian) probability density function (integrated from minus infinity to x) is equal to the argument y (assumes mean is zero, variance is one).
    For small arguments 0 < y < exp(-2), the program computes z = sqrt( -2.0 * log(y) ); then the approximation is x = z - log(z)/z - (1/z) P(1/z) / Q(1/z). There are two rational functions P/Q, one for 0 < y < exp(-32) and the other for y up to exp(-2). For larger arguments, w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
    
    Parameters:
    
    y0 - the area under the normal pdf
    
    Returns:
    
    the z-value
  - linearRegression
```
public static double[] linearRegression(Number[] x,
                                        Number[] y)
```
    Calculates the slope and intercept between the two arrays.
    
    Parameters:
    
    x - the first array, representing the X values
    
    y - the second array, representing the Y values
    
    Returns:
    
    intercept/slope
  - linearRegression
```
public static double[] linearRegression(double[] x,
                                        double[] y)
```
    Calculates the slope and intercept between the two arrays.
    
    Parameters:
    
    x - the first array, representing the X values
    
    y - the second array, representing the Y values
    
    Returns:
    
    intercept/slope
  - kendallTheil
```
public static double[] kendallTheil(double[] x,
                                    double[] y)
```
    Computes the Kendall-Theil robust regression of the given data points. Also called Theil-Sen estimator (see here).
    
    Parameters:
    
    x - the x coordinates
    
    y - the y coordinates
    
    Returns:
    
    intercept/slope
  - kendallTheil
```
public static double[] kendallTheil(Number[] x,
                                    Number[] y)
```
    Computes the Kendall-Theil robust regression of the given data points. Also called Theil-Sen estimator (see here).
    
    Parameters:
    
    x - the x coordinates
    
    y - the y coordinates
    
    Returns:
    
    intercept/slope
  - flatten
```
public static byte[] flatten(byte[][] matrix)
```
    Converts the matrix into a flat array, row after row.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the matrix as arrawy (row after row)
  - flatten
```
public static short[] flatten(short[][] matrix)
```
    Converts the matrix into a flat array, row after row.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the matrix as arrawy (row after row)
  - flatten
```
public static int[] flatten(int[][] matrix)
```
    Converts the matrix into a flat array, row after row.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the matrix as arrawy (row after row)
  - flatten
```
public static long[] flatten(long[][] matrix)
```
    Converts the matrix into a flat array, row after row.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the matrix as arrawy (row after row)
  - flatten
```
public static float[] flatten(float[][] matrix)
```
    Converts the matrix into a flat array, row after row.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the matrix as arrawy (row after row)
  - flatten
```
public static double[] flatten(double[][] matrix)
```
    Converts the matrix into a flat array, row after row.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the matrix as arrawy (row after row)
  - flatten
```
public static Number[] flatten(Number[][] matrix)
```
    Converts the matrix into a flat array, row after row.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the matrix as arrawy (row after row)
  - toByteMatrix
```
public static byte[][] toByteMatrix(Number[][] matrix)
```
    Turns the Number matrix into one consisting of primitive bytes.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toShortMatrix
```
public static short[][] toShortMatrix(Number[][] matrix)
```
    Turns the Number matrix into one consisting of primitive shorts.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toIntMatrix
```
public static int[][] toIntMatrix(Number[][] matrix)
```
    Turns the Number matrix into one consisting of primitive ints.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toLongMatrix
```
public static long[][] toLongMatrix(Number[][] matrix)
```
    Turns the Number matrix into one consisting of primitive longs.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toFloatMatrix
```
public static float[][] toFloatMatrix(Number[][] matrix)
```
    Turns the Number matrix into one consisting of primitive floats.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toDoubleMatrix
```
public static double[][] toDoubleMatrix(Number[][] matrix)
```
    Turns the Number matrix into one consisting of primitive doubles.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toNumberMatrix
```
public static Number[][] toNumberMatrix(byte[][] matrix)
```
    Turns the Number matrix into one consisting of primitive bytes.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toNumberMatrix
```
public static Number[][] toNumberMatrix(short[][] matrix)
```
    Turns the Number matrix into one consisting of primitive shorts.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toNumberMatrix
```
public static Number[][] toNumberMatrix(int[][] matrix)
```
    Turns the primitve int matrix into one consisting of Integers.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toNumberMatrix
```
public static Number[][] toNumberMatrix(long[][] matrix)
```
    Turns the primitive long matrix into one consisting of Longs.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toNumberMatrix
```
public static Number[][] toNumberMatrix(float[][] matrix)
```
    Turns the primitive float matrix into one consisting of Floats.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - toNumberMatrix
```
public static Number[][] toNumberMatrix(double[][] matrix)
```
    Turns the primitive double matrix into one consisting of Doubles.
    
    Parameters:
    
    matrix - the matrix to convert
    
    Returns:
    
    the converted matrix
  - subsample
```
public static gnu.trove.list.array.TIntArrayList subsample(int num,
                                                           double perc,
                                                           long seed)
```
    Creates a random sub-sample of indices of a certain percentage using the specified number of entrie. Uses JavaRandomInt.
    
    Parameters:
    
    num - the maximum number of indices
    
    perc - the size of the subsample (0-1)
    
    seed - the seed value for JavaRandomInt
    
    Returns:
    
    the subsample of indices (chosen from 0 to num-1)
  - subsample
```
public static gnu.trove.list.array.TIntArrayList subsample(int num,
                                                           double perc,
                                                           RandomIntegerRangeGenerator generator)
```
    Creates a random sub-sample of indices of a certain percentage using the specified number of entrie.
    
    Parameters:
    
    num - the maximum number of indices
    
    perc - the size of the subsample (0-1)
    
    generator - the random int generator to use
    
    Returns:
    
    the subsample of indices (chosen from 0 to num-1)
  - uniqueValues
```
public static byte[] uniqueValues(byte[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueValues
```
public static short[] uniqueValues(short[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueValues
```
public static int[] uniqueValues(int[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueValues
```
public static long[] uniqueValues(long[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueValues
```
public static float[] uniqueValues(float[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueValues
```
public static double[] uniqueValues(double[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueCounts
```
public static gnu.trove.map.TByteIntMap uniqueCounts(byte[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueCounts
```
public static gnu.trove.map.TShortIntMap uniqueCounts(short[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueCounts
```
public static gnu.trove.map.TIntIntMap uniqueCounts(int[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueCounts
```
public static gnu.trove.map.TLongIntMap uniqueCounts(long[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueCounts
```
public static gnu.trove.map.TFloatIntMap uniqueCounts(float[] numbers)
```
    Returns all the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique numbers
  - uniqueCounts
```
public static gnu.trove.map.TDoubleIntMap uniqueCounts(double[] numbers)
```
    Returns all the counts for the unique numbers in the array.
    
    Parameters:
    
    numbers - the numbers to use
    
    Returns:
    
    the unique number counts (number -> count)
  - main
```
public static void main(String[] args)
```
    Just for testing.
    
    Parameters:
    
    args - ignored

Class StatUtils

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

m_NormalDist

Constructor Detail

StatUtils

Method Detail

toNumberArray

toNumberArray

toNumberArray

toNumberArray

toNumberArray

toNumberArray

toByteArray

toShortArray

toIntArray

toLongArray

toFloatArray

toDoubleArray

minIndex

minIndex

minIndex

min

min

min

maxIndex

maxIndex

maxIndex

max

max

max

mean

mean

mean

iqr

iqr

iqr

quartile

quartile

quartile

median

median

median

stddev

stddev

stddev

normalize

normalize

normalize

normalizeRange

normalizeRange

normalizeRange

standardize

standardize

standardize

sum

sum

sum

sumOfSquares

sumOfSquares

sumOfSquares

sort

sort

sort

sort

sort

sort

findFirst

findFirst

findFirst

findClosest

findClosest

findClosest

correlationCoefficient

correlationCoefficient

rSquared

rSquared