Class Vector

Static class Vector. Defines a set of extension methods that operates mainly on single-dimensional arrays.
Inheritance
System.Object
Vector
Inherited Members
System.Object.Equals(System.Object)
System.Object.Equals(System.Object, System.Object)
System.Object.GetHashCode()
System.Object.GetType()
System.Object.MemberwiseClone()
System.Object.ReferenceEquals(System.Object, System.Object)
System.Object.ToString()
Namespace: Mars.Numerics
Assembly: Mars.Numerics.dll
Syntax
public static class Vector

Methods

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Copy<T>(T[])

Creates a shallow copy of the array.
Declaration
public static T[] Copy<T>(this T[] vector)
Parameters
Type Name Description
T[] vector
Returns
Type Description
T[]
Type Parameters
Name Description
T
See Also
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Create<T>(T[])

Creates a vector with the given starting values.
Declaration
public static T[] Create<T>(params T[] values)
Parameters
Type Name Description
T[] values The initial values for the vector.
Returns
Type Description
T[]
Type Parameters
Name Description
T
See Also
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Create<T>(Int32, T)

Creates a vector with the given dimension and starting value.
Declaration
public static T[] Create<T>(int size, T value)
Parameters
Type Name Description
System.Int32 size The number of elements in the vector.
T value The initial values for the vector.
Returns
Type Description
T[]
Type Parameters
Name Description
T
See Also
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Create<T>(Int32, T[])

Creates a vector with the given dimension and starting value.
Declaration
public static T[] Create<T>(int size, T[] values)
Parameters
Type Name Description
System.Int32 size The number of elements in the vector.
T[] values The initial values for the vector.
Returns
Type Description
T[]
Type Parameters
Name Description
T
See Also
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CreateAs<T>(T[])

Creates a vector with the shape of the given vector.
Declaration
public static T[] CreateAs<T>(T[] vector)
Parameters
Type Name Description
T[] vector The vector whose shape should be copied.
Returns
Type Description
T[]
Type Parameters
Name Description
T
See Also
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Dot(Sparse<Double>, Sparse<Double>)

Gets the inner product (scalar product) between two vectors (a'*b).
Declaration
public static double Dot(this Sparse<double> a, Sparse<double> b)
Parameters
Type Name Description
Sparse<System.Double> a A vector.
Sparse<System.Double> b A vector.
Returns
Type Description
System.Double The inner product of the multiplication of the vectors.
See Also
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EnumerableRange(Double, Double, Double)

Enumerates through a range (like Python's xrange function).
Declaration
public static IEnumerable<double> EnumerableRange(double a, double b, double stepSize)
Parameters
Type Name Description
System.Double a The inclusive lower bound of the range.
System.Double b The exclusive upper bound of the range.
System.Double stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Double>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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EnumerableRange(Double, Double, Int32)

Enumerates through a range (like Python's xrange function).
Declaration
public static IEnumerable<double> EnumerableRange(double a, double b, int stepSize)
Parameters
Type Name Description
System.Double a The inclusive lower bound of the range.
System.Double b The exclusive upper bound of the range.
System.Int32 stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Double>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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EnumerableRange(Double, Double)

Enumerates through a range (like Python's xrange).
Declaration
public static IEnumerable<double> EnumerableRange(double a, double b)
Parameters
Type Name Description
System.Double a The inclusive lower bound of the range.
System.Double b The exclusive upper bound of the range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Double>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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EnumerableRange(Double)

Enumerates through a range (like Python's xrange function).
Declaration
public static IEnumerable<double> EnumerableRange(double n)
Parameters
Type Name Description
System.Double n The exclusive upper bound of the range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Double>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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EnumerableRange(Int32, Int32, Double)

Enumerates through a range (like Python's xrange function).
Declaration
public static IEnumerable<double> EnumerableRange(int a, int b, double stepSize)
Parameters
Type Name Description
System.Int32 a The inclusive lower bound of the range.
System.Int32 b The exclusive upper bound of the range.
System.Double stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Double>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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EnumerableRange(Int32, Int32, Int32)

Enumerates through a range (like Python's xrange function).
Declaration
public static IEnumerable<int> EnumerableRange(int a, int b, int stepSize)
Parameters
Type Name Description
System.Int32 a The inclusive lower bound of the range.
System.Int32 b The exclusive upper bound of the range.
System.Int32 stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Int32>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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EnumerableRange(Int32, Int32)

Enumerates through a range (like Python's xrange).
Declaration
public static IEnumerable<int> EnumerableRange(int a, int b)
Parameters
Type Name Description
System.Int32 a The inclusive lower bound of the range.
System.Int32 b The exclusive upper bound of the range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Int32>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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EnumerableRange(Int32)

Enumerates through a range (like Python's xrange function).
Declaration
public static IEnumerable<int> EnumerableRange(int n)
Parameters
Type Name Description
System.Int32 n The exclusive upper bound of the range.
Returns
Type Description
System.Collections.Generic.IEnumerable<System.Int32>
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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GetIndices<T>(T[])

Creates a vector containing every index that can be used to address a given array, in order.
Declaration
public static int[] GetIndices<T>(this T[] array)
Parameters
Type Name Description
T[] array The array whose indices will be returned.
Returns
Type Description
System.Int32[] A vector of the same size as the given array containing all vector indices from 0 up to the length of array.
Type Parameters
Name Description
T
Examples
double[] a = { 5.3, 2.3, 4.2 };
int[] idx = a.GetIndices(); // output will be { 0, 1, 2 }
See Also
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Histogram(Int32[], Int32[])

Counts how many times an integer label appears in a vector (i.e. creates an histogram of integer values assuming possible values start at zero and go up to the maximum value of in the vector).
Declaration
public static int[] Histogram(this int[] labels, int[] result)
Parameters
Type Name Description
System.Int32[] labels An array containing the integer labels to be counted.
System.Int32[] result The histogram to were the counts will be added. This vector should have been zeroed out before being passed to this method.
Returns
Type Description
System.Int32[] The same vector result passed as an argument.
See Also
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Interval(DoubleRange, Int32)

Creates an interval vector (like NumPy's linspace function).
Declaration
public static double[] Interval(this DoubleRange range, int steps)
Parameters
Type Name Description
DoubleRange range
System.Int32 steps
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.linspace function. For a similar method that accepts a step size instead of a number of steps, see Range(Int32, Int32).

See Also
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Interval(IntRange, Int32)

Creates an interval vector (like NumPy's linspace function).
Declaration
public static int[] Interval(this IntRange range, int steps)
Parameters
Type Name Description
IntRange range
System.Int32 steps
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.linspace function. For a similar method that accepts a step size instead of a number of steps, see Range(Int32, Int32).

See Also
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Interval(Double, Double, Int32, Boolean)

Creates an interval vector (like NumPy's linspace function).
Declaration
public static double[] Interval(double a, double b, int steps, bool includeLast = true)
Parameters
Type Name Description
System.Double a
System.Double b
System.Int32 steps
System.Boolean includeLast
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.linspace function. For a similar method that accepts a step size instead of a number of steps, see Range(Int32, Int32).

See Also
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Interval(Double, Double)

Creates an interval vector (like NumPy's linspace function).
Declaration
public static double[] Interval(double a, double b)
Parameters
Type Name Description
System.Double a
System.Double b
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.linspace function. For a similar method that accepts a step size instead of a number of steps, see Range(Int32, Int32).

See Also
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Interval(Int32, Int32, Int32, Boolean)

Creates an interval vector (like NumPy's linspace function).
Declaration
public static int[] Interval(int a, int b, int steps, bool includeLast = true)
Parameters
Type Name Description
System.Int32 a
System.Int32 b
System.Int32 steps
System.Boolean includeLast
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.linspace function. For a similar method that accepts a step size instead of a number of steps, see Range(Int32, Int32).

See Also
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Interval(Int32, Int32)

Creates an interval vector (like NumPy's linspace function).
Declaration
public static int[] Interval(int a, int b)
Parameters
Type Name Description
System.Int32 a
System.Int32 b
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.linspace function. For a similar method that accepts a step size instead of a number of steps, see Range(Int32, Int32).

See Also
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Ones(Int32)

Creates a one-valued vector.
Declaration
public static double[] Ones(int size)
Parameters
Type Name Description
System.Int32 size The number of elements in the vector.
Returns
Type Description
System.Double[] A vector of the specified size.
See Also
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Ones<T>(Int32)

Creates a zero-valued vector.
Declaration
public static T[] Ones<T>(int size)
Parameters
Type Name Description
System.Int32 size The number of elements in the vector.
Returns
Type Description
T[] A vector of the specified size.
Type Parameters
Name Description
T The type of the vector to be created.
See Also
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Random(Int32, Double, Double)

Creates a vector with uniformly distributed random data.
Declaration
public static double[] Random(int size, double min, double max)
Parameters
Type Name Description
System.Int32 size
System.Double min
System.Double max
Returns
Type Description
System.Double[]
See Also
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Random(Int32, Int32, Int32)

Creates a vector with uniformly distributed random data.
Declaration
public static int[] Random(int size, int min, int max)
Parameters
Type Name Description
System.Int32 size
System.Int32 min
System.Int32 max
Returns
Type Description
System.Int32[]
See Also
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Random(Int32)

Creates a vector with uniformly distributed random data.
Declaration
public static double[] Random(int size)
Parameters
Type Name Description
System.Int32 size
Returns
Type Description
System.Double[]
See Also
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Range(DoubleRange, Double)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(this DoubleRange range, double stepSize)
Parameters
Type Name Description
DoubleRange range The range from where values should be created.
System.Double stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(DoubleRange, Int32)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(this DoubleRange range, int stepSize)
Parameters
Type Name Description
DoubleRange range The range from where values should be created.
System.Int32 stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(DoubleRange)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(this DoubleRange range)
Parameters
Type Name Description
DoubleRange range The range from where values should be created.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(IntRange, Double)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(this IntRange range, double stepSize)
Parameters
Type Name Description
IntRange range The range from where values should be created.
System.Double stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(IntRange, Int32)

Creates a range vector (like NumPy's arange function).
Declaration
public static int[] Range(this IntRange range, int stepSize)
Parameters
Type Name Description
IntRange range The range from where values should be created.
System.Int32 stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(IntRange)

Creates a range vector (like NumPy's arange function).
Declaration
public static int[] Range(this IntRange range)
Parameters
Type Name Description
IntRange range The range from where values should be created.
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Double, Double, Double)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(double a, double b, double stepSize)
Parameters
Type Name Description
System.Double a The inclusive lower bound of the range.
System.Double b The exclusive upper bound of the range.
System.Double stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Double, Double, Int32)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(double a, double b, int stepSize)
Parameters
Type Name Description
System.Double a The inclusive lower bound of the range.
System.Double b The exclusive upper bound of the range.
System.Int32 stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Double, Double)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(double a, double b)
Parameters
Type Name Description
System.Double a The inclusive lower bound of the range.
System.Double b The exclusive upper bound of the range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Double)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(double n)
Parameters
Type Name Description
System.Double n The exclusive upper bound of the range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Int32, Int32, Double)

Creates a range vector (like NumPy's arange function).
Declaration
public static double[] Range(int a, int b, double stepSize)
Parameters
Type Name Description
System.Int32 a The inclusive lower bound of the range.
System.Int32 b The exclusive upper bound of the range.
System.Double stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Double[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Int32, Int32, Int32)

Creates a range vector (like NumPy's arange function).
Declaration
public static int[] Range(int a, int b, int stepSize)
Parameters
Type Name Description
System.Int32 a The inclusive lower bound of the range.
System.Int32 b The exclusive upper bound of the range.
System.Int32 stepSize The step size to be taken between elements. This parameter can be negative to create a decreasing range.
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Int32, Int32)

Creates a range vector (like NumPy's arange function).
Declaration
public static int[] Range(int a, int b)
Parameters
Type Name Description
System.Int32 a The inclusive lower bound of the range.
System.Int32 b The exclusive upper bound of the range.
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Range(Int32)

Creates a range vector (like NumPy's arange function).
Declaration
public static int[] Range(int n)
Parameters
Type Name Description
System.Int32 n The exclusive upper bound of the range.
Returns
Type Description
System.Int32[]
Remarks

The Range methods should be equivalent to NumPy's np.arange method, with one single difference: when the intervals are inverted (i.e. a > b) and the step size is negative, the framework still iterates over the range backwards, as if the step was negative.

This function never includes the upper bound of the range. For methods that include it, please see the Interval(Int32, Int32) methods.

See Also
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Sample(Double, Double)

Returns a vector of the specified percentage of the populationSize containing non-repeating indices in the range [0, populationSize) in random order.
Declaration
public static double[] Sample(double percentage, double populationSize)
Parameters
Type Name Description
System.Double percentage The percentage of the population to sample.
System.Double populationSize The non-inclusive maximum number an index can have.
Returns
Type Description
System.Double[]
Examples
  var a = Vector.Sample(0.3, 10);  // a possible output is { 1, 7, 4 };
  var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };

  foreach (var i in Vector.Sample(0.2, 6))
  {
     // ...
  }
See Also
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Sample(Double, Int32)

Returns a vector of the specified percentage of the populationSize containing non-repeating indices in the range [0, populationSize) in random order.
Declaration
public static int[] Sample(double percentage, int populationSize)
Parameters
Type Name Description
System.Double percentage The percentage of the population to sample.
System.Int32 populationSize The non-inclusive maximum number an index can have.
Returns
Type Description
System.Int32[]
Examples
  var a = Vector.Sample(0.3, 10);  // a possible output is { 1, 7, 4 };
  var b = Vector.Sample(1.0, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };

  foreach (var i in Vector.Sample(0.2, 6))
  {
     // ...
  }
See Also
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Sample(Double)

Returns a vector containing indices (0, 1, 2, ..., n - 1) in random order. The vector grows up to to size, but does not include size among its values.
Declaration
public static double[] Sample(double size)
Parameters
Type Name Description
System.Double size The size of the sample vector to be generated.
Returns
Type Description
System.Double[]
Examples
  var a = Vector.Sample(3);  // a possible output is { 2, 1, 0 };
  var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };

  foreach (var i in Vector.Sample(5))
  {
     // ...
  }
See Also
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Sample(Int32, Double)

Returns a vector of the specified sampleSize containing non-repeating indices in the range [0, populationSize) in random order.
Declaration
public static double[] Sample(int sampleSize, double populationSize)
Parameters
Type Name Description
System.Int32 sampleSize The size of the sample vector to be generated.
System.Double populationSize The non-inclusive maximum number an index can have.
Returns
Type Description
System.Double[]
Remarks
In other words, this return a sample of size k from a population of size N, where k is the parameter sampleSize and N is the parameter populationSize.
Examples
  var a = Vector.Sample(3, 10);  // a possible output is { 1, 7, 4 };
  var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };

  foreach (var i in Vector.Sample(5, 6))
  {
     // ...
  }
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Sample(Int32, Int32)

Returns a vector of the specified sampleSize containing non-repeating indices in the range [0, populationSize) in random order.
Declaration
public static int[] Sample(int sampleSize, int populationSize)
Parameters
Type Name Description
System.Int32 sampleSize The size of the sample vector to be generated.
System.Int32 populationSize The non-inclusive maximum number an index can have.
Returns
Type Description
System.Int32[]
Remarks
In other words, this return a sample of size k from a population of size N, where k is the parameter sampleSize and N is the parameter populationSize.
Examples
  var a = Vector.Sample(3, 10);  // a possible output is { 1, 7, 4 };
  var b = Vector.Sample(10, 10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };

  foreach (var i in Vector.Sample(5, 6))
  {
     // ...
  }
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Sample(Int32)

Returns a vector containing indices (0, 1, 2, ..., n - 1) in random order. The vector grows up to to size, but does not include size among its values.
Declaration
public static int[] Sample(int size)
Parameters
Type Name Description
System.Int32 size The size of the sample vector to be generated.
Returns
Type Description
System.Int32[]
Examples
  var a = Vector.Sample(3);  // a possible output is { 2, 1, 0 };
  var b = Vector.Sample(10); // a possible output is { 5, 4, 2, 0, 1, 3, 7, 9, 8, 6 };

  foreach (var i in Vector.Sample(5))
  {
     // ...
  }
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Sample<T>(T[], Int32, Boolean)

Draws a random sample from a group of observations, with or without repetitions.
Declaration
public static T[] Sample<T>(this T[] values, int size, bool replacement = false)
Parameters
Type Name Description
T[] values The observation vector.
System.Int32 size The size of the sample to be drawn (how many samples to get).
System.Boolean replacement Whether to sample with replacement (repeating values) or without replacement (non-repeating values).
Returns
Type Description
T[] A vector containing the samples drawn from values.
Type Parameters
Name Description
T The type of the observations.
See Also
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Scale(Double, IRange<Double>, IRange<Double>)

Converts values from one scale to another scale.
Declaration
public static double Scale(this double value, IRange<double> fromRange, IRange<double> toRange)
Parameters
Type Name Description
System.Double value
IRange<System.Double> fromRange
IRange<System.Double> toRange
Returns
Type Description
System.Double
See Also
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Scale(Double, IRange<Double>, IRange<Int32>)

Converts values from one scale to another scale.
Declaration
public static int Scale(this double value, IRange<double> fromRange, IRange<int> toRange)
Parameters
Type Name Description
System.Double value
IRange<System.Double> fromRange
IRange<System.Int32> toRange
Returns
Type Description
System.Int32
See Also
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Scale(Double, Double, Double, Double, Double)

Converts a value from one scale to another scale.
Declaration
public static double Scale(this double value, double fromMin, double fromMax, double toMin, double toMax)
Parameters
Type Name Description
System.Double value
System.Double fromMin
System.Double fromMax
System.Double toMin
System.Double toMax
Returns
Type Description
System.Double
See Also
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Scale(Double, Double, Double, Int32, Int32)

Converts a value from one scale to another scale.
Declaration
public static int Scale(this double value, double fromMin, double fromMax, int toMin, int toMax)
Parameters
Type Name Description
System.Double value
System.Double fromMin
System.Double fromMax
System.Int32 toMin
System.Int32 toMax
Returns
Type Description
System.Int32
See Also
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Scale(Double[], IRange<Double>, IRange<Double>, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this double[] values, IRange<double> fromRange, IRange<double> toRange, double[] result)
Parameters
Type Name Description
System.Double[] values
IRange<System.Double> fromRange
IRange<System.Double> toRange
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Double[], IRange<Double>, IRange<Double>)

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this double[] values, IRange<double> fromRange, IRange<double> toRange)
Parameters
Type Name Description
System.Double[] values
IRange<System.Double> fromRange
IRange<System.Double> toRange
Returns
Type Description
System.Double[]
See Also
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Scale(Double[], IRange<Double>, IRange<Int32>, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this double[] values, IRange<double> fromRange, IRange<int> toRange, int[] result)
Parameters
Type Name Description
System.Double[] values
IRange<System.Double> fromRange
IRange<System.Int32> toRange
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Double[], IRange<Double>, IRange<Int32>)

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this double[] values, IRange<double> fromRange, IRange<int> toRange)
Parameters
Type Name Description
System.Double[] values
IRange<System.Double> fromRange
IRange<System.Int32> toRange
Returns
Type Description
System.Int32[]
See Also
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Scale(Double[], IRange<Double>, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this double[] values, IRange<double> toRange, double[] result)
Parameters
Type Name Description
System.Double[] values
IRange<System.Double> toRange
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Double[], IRange<Int32>, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this double[] values, IRange<int> toRange, int[] result)
Parameters
Type Name Description
System.Double[] values
IRange<System.Int32> toRange
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Double[], Double, Double, Double, Double, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this double[] values, double fromMin, double fromMax, double toMin, double toMax, double[] result)
Parameters
Type Name Description
System.Double[] values
System.Double fromMin
System.Double fromMax
System.Double toMin
System.Double toMax
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Double[], Double, Double, Double, Double)

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this double[] values, double fromMin, double fromMax, double toMin, double toMax)
Parameters
Type Name Description
System.Double[] values
System.Double fromMin
System.Double fromMax
System.Double toMin
System.Double toMax
Returns
Type Description
System.Double[]
See Also
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Scale(Double[], Double, Double, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this double[] values, double toMin, double toMax, double[] result)
Parameters
Type Name Description
System.Double[] values
System.Double toMin
System.Double toMax
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Double[], Double, Double, Int32, Int32, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this double[] values, double fromMin, double fromMax, int toMin, int toMax, int[] result)
Parameters
Type Name Description
System.Double[] values
System.Double fromMin
System.Double fromMax
System.Int32 toMin
System.Int32 toMax
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Double[], Double, Double, Int32, Int32)

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this double[] values, double fromMin, double fromMax, int toMin, int toMax)
Parameters
Type Name Description
System.Double[] values
System.Double fromMin
System.Double fromMax
System.Int32 toMin
System.Int32 toMax
Returns
Type Description
System.Int32[]
See Also
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Scale(Double[], Double, Double)

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this double[] values, double toMin, double toMax)
Parameters
Type Name Description
System.Double[] values
System.Double toMin
System.Double toMax
Returns
Type Description
System.Double[]
See Also
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Scale(Double[], Int32, Int32, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this double[] values, int toMin, int toMax, int[] result)
Parameters
Type Name Description
System.Double[] values
System.Int32 toMin
System.Int32 toMax
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Double[], Int32, Int32)

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this double[] values, int toMin, int toMax)
Parameters
Type Name Description
System.Double[] values
System.Int32 toMin
System.Int32 toMax
Returns
Type Description
System.Int32[]
See Also
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Scale(Int32, IRange<Int32>, IRange<Double>)

Converts values from one scale to another scale.
Declaration
public static double Scale(this int value, IRange<int> fromRange, IRange<double> toRange)
Parameters
Type Name Description
System.Int32 value
IRange<System.Int32> fromRange
IRange<System.Double> toRange
Returns
Type Description
System.Double
See Also
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Scale(Int32, IRange<Int32>, IRange<Int32>)

Converts values from one scale to another scale.
Declaration
public static int Scale(this int value, IRange<int> fromRange, IRange<int> toRange)
Parameters
Type Name Description
System.Int32 value
IRange<System.Int32> fromRange
IRange<System.Int32> toRange
Returns
Type Description
System.Int32
See Also
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Scale(Int32, Int32, Int32, Double, Double)

Converts a value from one scale to another scale.
Declaration
public static double Scale(this int value, int fromMin, int fromMax, double toMin, double toMax)
Parameters
Type Name Description
System.Int32 value
System.Int32 fromMin
System.Int32 fromMax
System.Double toMin
System.Double toMax
Returns
Type Description
System.Double
See Also
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Scale(Int32, Int32, Int32, Int32, Int32)

Converts a value from one scale to another scale.
Declaration
public static int Scale(this int value, int fromMin, int fromMax, int toMin, int toMax)
Parameters
Type Name Description
System.Int32 value
System.Int32 fromMin
System.Int32 fromMax
System.Int32 toMin
System.Int32 toMax
Returns
Type Description
System.Int32
See Also
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Scale(Int32[], IRange<Double>, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this int[] values, IRange<double> toRange, double[] result)
Parameters
Type Name Description
System.Int32[] values
IRange<System.Double> toRange
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Int32[], IRange<Int32>, IRange<Double>, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this int[] values, IRange<int> fromRange, IRange<double> toRange, double[] result)
Parameters
Type Name Description
System.Int32[] values
IRange<System.Int32> fromRange
IRange<System.Double> toRange
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Int32[], IRange<Int32>, IRange<Double>)

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this int[] values, IRange<int> fromRange, IRange<double> toRange)
Parameters
Type Name Description
System.Int32[] values
IRange<System.Int32> fromRange
IRange<System.Double> toRange
Returns
Type Description
System.Double[]
See Also
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Scale(Int32[], IRange<Int32>, IRange<Int32>, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this int[] values, IRange<int> fromRange, IRange<int> toRange, int[] result)
Parameters
Type Name Description
System.Int32[] values
IRange<System.Int32> fromRange
IRange<System.Int32> toRange
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Int32[], IRange<Int32>, IRange<Int32>)

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this int[] values, IRange<int> fromRange, IRange<int> toRange)
Parameters
Type Name Description
System.Int32[] values
IRange<System.Int32> fromRange
IRange<System.Int32> toRange
Returns
Type Description
System.Int32[]
See Also
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Scale(Int32[], IRange<Int32>, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this int[] values, IRange<int> toRange, int[] result)
Parameters
Type Name Description
System.Int32[] values
IRange<System.Int32> toRange
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Int32[], Double, Double, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this int[] values, double toMin, double toMax, double[] result)
Parameters
Type Name Description
System.Int32[] values
System.Double toMin
System.Double toMax
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Int32[], Double, Double)

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this int[] values, double toMin, double toMax)
Parameters
Type Name Description
System.Int32[] values
System.Double toMin
System.Double toMax
Returns
Type Description
System.Double[]
See Also
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Scale(Int32[], Int32, Int32, Double, Double, Double[])

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this int[] values, int fromMin, int fromMax, double toMin, double toMax, double[] result)
Parameters
Type Name Description
System.Int32[] values
System.Int32 fromMin
System.Int32 fromMax
System.Double toMin
System.Double toMax
System.Double[] result
Returns
Type Description
System.Double[]
See Also
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Scale(Int32[], Int32, Int32, Double, Double)

Converts values from one scale to another scale.
Declaration
public static double[] Scale(this int[] values, int fromMin, int fromMax, double toMin, double toMax)
Parameters
Type Name Description
System.Int32[] values
System.Int32 fromMin
System.Int32 fromMax
System.Double toMin
System.Double toMax
Returns
Type Description
System.Double[]
See Also
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Scale(Int32[], Int32, Int32, Int32, Int32, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this int[] values, int fromMin, int fromMax, int toMin, int toMax, int[] result)
Parameters
Type Name Description
System.Int32[] values
System.Int32 fromMin
System.Int32 fromMax
System.Int32 toMin
System.Int32 toMax
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Int32[], Int32, Int32, Int32, Int32)

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this int[] values, int fromMin, int fromMax, int toMin, int toMax)
Parameters
Type Name Description
System.Int32[] values
System.Int32 fromMin
System.Int32 fromMax
System.Int32 toMin
System.Int32 toMax
Returns
Type Description
System.Int32[]
See Also
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Scale(Int32[], Int32, Int32, Int32[])

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this int[] values, int toMin, int toMax, int[] result)
Parameters
Type Name Description
System.Int32[] values
System.Int32 toMin
System.Int32 toMax
System.Int32[] result
Returns
Type Description
System.Int32[]
See Also
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Scale(Int32[], Int32, Int32)

Converts values from one scale to another scale.
Declaration
public static int[] Scale(this int[] values, int toMin, int toMax)
Parameters
Type Name Description
System.Int32[] values
System.Int32 toMin
System.Int32 toMax
Returns
Type Description
System.Int32[]
See Also
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Shuffle<T>(T[])

Shuffles an array.
Declaration
public static void Shuffle<T>(this T[] array)
Parameters
Type Name Description
T[] array
Type Parameters
Name Description
T
See Also
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Shuffled<T>(T[])

Shuffles an array.
Declaration
public static T[] Shuffled<T>(this T[] array)
Parameters
Type Name Description
T[] array
Returns
Type Description
T[]
Type Parameters
Name Description
T
See Also
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Sort<T>(T[], Boolean, Boolean)

Sorts the elements of an entire one-dimensional array using the given comparison.
Declaration
public static void Sort<T>(this T[] values, bool stable = false, bool asc = true)
    where T : IComparable<T>
Parameters
Type Name Description
T[] values
System.Boolean stable
System.Boolean asc
Type Parameters
Name Description
T
See Also
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Sort<T>(T[], Comparison<T>, Boolean, Boolean)

Sorts the elements of an entire one-dimensional array using the given comparison.
Declaration
public static void Sort<T>(this T[] values, Comparison<T> comparison, bool stable = false, bool asc = true)
Parameters
Type Name Description
T[] values
System.Comparison<T> comparison
System.Boolean stable
System.Boolean asc
Type Parameters
Name Description
T
See Also
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Sort<T>(T[], out Int32[], Boolean, ComparerDirection)

Sorts the elements of an entire one-dimensional array using the given comparison.
Declaration
public static void Sort<T>(this T[] values, out int[] order, bool stable = false, ComparerDirection direction = ComparerDirection.Ascending)
    where T : IComparable<T>
Parameters
Type Name Description
T[] values
System.Int32[] order
System.Boolean stable
ComparerDirection direction
Type Parameters
Name Description
T
See Also
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Sorted<T>(T[], Boolean, Boolean)

Sorts the elements of an entire one-dimensional array using the given comparison.
Declaration
public static T[] Sorted<T>(this T[] values, bool stable = false, bool asc = true)
    where T : IComparable<T>
Parameters
Type Name Description
T[] values
System.Boolean stable
System.Boolean asc
Returns
Type Description
T[]
Type Parameters
Name Description
T
See Also
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Zeros(Int32)

Creates a zero-valued vector.
Declaration
public static double[] Zeros(int size)
Parameters
Type Name Description
System.Int32 size The number of elements in the vector.
Returns
Type Description
System.Double[] A vector of the specified size.
See Also
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Zeros<T>(Int32)

Creates a zero-valued vector.
Declaration
public static T[] Zeros<T>(int size)
Parameters
Type Name Description
System.Int32 size The number of elements in the vector.
Returns
Type Description
T[] A vector of the specified size.
Type Parameters
Name Description
T The type of the vector to be created.
See Also

See Also