[Serializable]
[DataContract]
public abstract class Vector : IList<double>, ICollection<double>, IReadOnlyList<double>, IReadOnlyCollection<double>, IEnumerable<double>, IEnumerable, SettableTo<Vector>, ICloneable, CanSetAllElementsTo<double>, SettableToPower<Vector>, SettableToProduct<Vector>, SettableToProduct<Vector, Vector>, SettableToWeightedSum<Vector>

Remarks

This class includes factory methods for instantiating Vectors of different Sparsity specifications. Beyond this initial construction, application code does not need to know the the sparsity, and most operations can be done via this general base class which will handle sparsity correctly.

Properties

Count

Number of elements in vector

Declaration

public virtual int Count { get; protected set; }

Property Value

Type	Description
Int32

IsApproximate

True if this vector is approximate (sparse only)

Declaration

public bool IsApproximate { get; }

Property Value

Type	Description
Boolean

IsDense

True if this vector is dense

Declaration

public bool IsDense { get; }

Property Value

Type	Description
Boolean

IsExact

True if this vector is exact (dense or sparse)

Declaration

public bool IsExact { get; }

Property Value

Type	Description
Boolean

IsReadOnly

Is read only

Declaration

public virtual bool IsReadOnly { get; }

Property Value

Type	Description
Boolean

IsSparse

True if is this vector is sparse (exact or approximate)

Declaration

public bool IsSparse { get; }

Property Value

Type	Description
Boolean

Item[Int32]

Gets and sets an element.

Declaration

public virtual double this[int index] { get; set; }

Parameters

Type	Name	Description
Int32	index

Property Value

Type	Description
Double

Sparsity

The Sparsity specification of this vector.

Declaration

public Sparsity Sparsity { get; protected set; }

Property Value

Type	Description
Sparsity

Methods

All(Converter<Double, Boolean>)

Tests if all elements in the vector satisfy the specified condition.

Declaration

public abstract bool All(Converter<double, bool> fun)

Parameters

Type	Name	Description
Converter<Double, Boolean>	fun

Returns

Type	Description
Boolean

Any(Vector, Func<Double, Double, Boolean>)

Test if any corresponding elements in this and that vector satisfy a condition

Declaration

public virtual bool Any(Vector that, Func<double, double, bool> fun)

Parameters

Type	Name	Description
Vector	that
Func<Double, Double, Boolean>	fun

Returns

Type	Description
Boolean

Any(Converter<Double, Boolean>)

Tests if any elements in the vector satisfy the specified condition.

Declaration

public abstract bool Any(Converter<double, bool> fun)

Parameters

Type	Name	Description
Converter<Double, Boolean>	fun

Returns

Type	Description
Boolean

Append(Vector)

Return a new vector which is the concatenation of this vector and a second vector.

Declaration

public virtual Vector Append(Vector second)

Parameters

Type	Name	Description
Vector	second	Second vector

Returns

Type	Description
Vector

Append(Double)

Appends an item to a vector - returns a new vector

Declaration

public virtual Vector Append(double item)

Parameters

Type	Name	Description
Double	item

Returns

Type	Description
Vector

CheckCompatible(Vector, String)

Checks that a given vector is the same size as this vector. Throws an exception if not with the given string

Declaration

protected virtual void CheckCompatible(Vector that, string paramName)

Parameters

Type	Name	Description
Vector	that	The vector to check
String	paramName

Clone()

Clones this vector - return as a vector

Declaration

public virtual Vector Clone()

Returns

Type	Description
Vector

Concat(Vector, Vector)

Create a vector by concatenating two vectors.

Declaration

public static Vector Concat(Vector first, Vector second)

Parameters

Type	Name	Description
Vector	first	First vector
Vector	second	Second vector

Returns

Type	Description
Vector	A new vector with all elements of the first vector followed by all elements of the second vector.

Constant(Int32, Double)

Create a dense vector of given length with elements all equal to a specified value

Declaration

public static Vector Constant(int count, double value)

Parameters

Type	Name	Description
Int32	count	Number of elements in vector
Double	value	value for each element

Returns

Type	Description
Vector

Constant(Int32, Double, Sparsity)

Create a vector of given length with elements all equal to a specified value

Declaration

public static Vector Constant(int count, double value, Sparsity sparsity)

Parameters

Type	Name	Description
Int32	count	Number of elements in vector
Double	value	value for each element
Sparsity	sparsity	The Sparsity specification.

Returns

Type	Description
Vector

Contains(Double)

Returns true if the Vector contains the specified item value

Declaration

public virtual bool Contains(double item)

Parameters

Type	Name	Description
Double	item

Returns

Type	Description
Boolean

Copy(Vector)

Create a vector as a copy of another vector.

Declaration

public static Vector Copy(Vector that)

Parameters

Type	Name	Description
Vector	that	The source vector - can be dense or sparse

Returns

Type	Description
Vector

Remarks

Sparsity of created vector matches that of source vector

Copy(Vector, Sparsity)

Create a vector as a copy of another vector with a given target sparsity

Declaration

public static Vector Copy(Vector that, Sparsity sparsity)

Parameters

Type	Name	Description
Vector	that	The source vector - can be dense or sparse
Sparsity	sparsity	The Sparsity specification.

Returns

Type	Description
Vector

CopyTo(Double[], Int32)

Copies this vector to the given array starting at the specified index in the target array

Declaration

public virtual void CopyTo(double[] array, int index)

Parameters

Type	Name	Description
Double[]	array	The target array
Int32	index	The start index in the target array

CountAll(Converter<Double, Boolean>)

Returns the number of elements in the vector which satisfy a given condition.

Declaration

public abstract int CountAll(Converter<double, bool> fun)

Parameters

Type	Name	Description
Converter<Double, Boolean>	fun	The condition for the elements to satisfy.

Returns

Type	Description
Int32	The number of elements in the vector which satisfy the condition.

EnsureDense(Vector)

Declaration

protected DenseVector EnsureDense(Vector vector)

Parameters

Type	Name	Description
Vector	vector

Returns

Type	Description
DenseVector

Equals(Object)

Determines object equality.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
Object	obj	Another (DenseVector) object.

Returns

Type	Description
Boolean	True if equal.

Overrides

Object.Equals(Object)

EqualsAll(Double)

Tests if all elements are equal to a given value.

Declaration

public virtual bool EqualsAll(double value)

Parameters

Type	Name	Description
Double	value	The value to test against.

Returns

Type	Description
Boolean	True if all elements are equal to `value`.

FindAll(Converter<Double, Boolean>)

Returns an enumeration over the indices and values of all elements which satisfy the specified condition. Indices are returned in sorted order.

Declaration

public abstract IEnumerable<ValueAtIndex<double>> FindAll(Converter<double, bool> fun)

Parameters

Type	Name	Description
Converter<Double, Boolean>	fun	A function to check if the condition is satisfied.

Returns

Type	Description
IEnumerable<ValueAtIndex<Double>>	An enumeration over the indices and values of all elements which satisfy the specified condition.

FindFirstIndex(Converter<Double, Boolean>)

Returns the index of the first element that satisfies satisfy a given condition.

Declaration

public abstract int FindFirstIndex(Converter<double, bool> fun)

Parameters

Type	Name	Description
Converter<Double, Boolean>	fun	The condition for the element to satisfy.

Returns

Type	Description
Int32	The zero-based index of the first occurrence of an element that matches the conditions defined by match, if found; otherwise, �1.

FindLastIndex(Converter<Double, Boolean>)

Returns the index of the last element that satisfiessatisfy a given condition.

Declaration

public abstract int FindLastIndex(Converter<double, bool> fun)

Parameters

Type	Name	Description
Converter<Double, Boolean>	fun	The condition for the element to satisfy.

Returns

Type	Description
Int32	The zero-based index of the last occurrence of an element that matches the conditions defined by match, if found; otherwise, �1.

FromArray(Double[])

Constructs a dense vector from an array.

Declaration

public static Vector FromArray(params double[] data)

Parameters

Type	Name	Description
Double[]	data	1D array of elements.

Returns

Type	Description
Vector

Remarks

The array data is copied into new storage. The size of the vector is taken from the array.

FromArray(Double[], Sparsity)

Constructs a vector from an array.

Declaration

public static Vector FromArray(double[] data, Sparsity sparsity)

Parameters

Type	Name	Description
Double[]	data	1D array of elements.
Sparsity	sparsity	The Sparsity specification.

Returns

Type	Description
Vector

Remarks

The array data is copied into new storage. The size of the vector is taken from the array.

FromArray(Int32, Double[], Int32)

Constructs a vector from part of an array.

Declaration

public static Vector FromArray(int count, double[] data, int start)

Parameters

Type	Name	Description
Int32	count	The number of elements in the vector.
Double[]	data	Storage for the vector elements.
Int32	start	The starting index in the array for the vector elements.

Returns

Type	Description
Vector

Remarks

Throws an exception if Data is null, start < 0, or count < 0.

FromArray(Int32, Double[], Int32, Sparsity)

Constructs a vector from part of an array.

Declaration

public static Vector FromArray(int count, double[] data, int start, Sparsity sparsity)

Parameters

Type	Name	Description
Int32	count	The number of elements in the vector.
Double[]	data	Storage for the vector elements.
Int32	start	The starting index in the array for the vector elements.
Sparsity	sparsity	The Sparsity specification.

Returns

Type	Description
Vector

Remarks

Throws an exception if Data is null, start < 0, or count < 0.

FromList(IList<Double>)

Constructs a vector from a list. Maintains sparsity.

Declaration

public static Vector FromList(IList<double> list)

Parameters

Type	Name	Description
IList<Double>	list	List to create vector from.

Returns

Type	Description
Vector

GetEnumerator()

Gets a typed enumerator which yields the vector elements

Declaration

public virtual IEnumerator<double> GetEnumerator()

Returns

Type	Description
IEnumerator<Double>

GetHashCode()

Gets a hash code for the instance.

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32	The code.

Overrides

Object.GetHashCode()

GreaterThan(Vector)

Tests if this vector is strictly greater than a second vector.

Declaration

public virtual bool GreaterThan(Vector that)

Parameters

Type	Name	Description
Vector	that	The value to test against.

Returns

Type	Description
Boolean	True if each element is strictly greater than the corresponding element of `that`.

GreaterThan(Double)

Tests if all elements are strictly greater than a given value.

Declaration

public virtual bool GreaterThan(double value)

Parameters

Type	Name	Description
Double	value	The value to test against.

Returns

Type	Description
Boolean	True if all elements are strictly greater than `value`.

GreaterThanOrEqual(Vector)

Tests if this vector is than or equal to a second vector.

Declaration

public virtual bool GreaterThanOrEqual(Vector that)

Parameters

Type	Name	Description
Vector	that	The value to test against.

Returns

Type	Description
Boolean	True if each element is greater than or equal to the corresponding element of `that`.

GreaterThanOrEqual(Double)

Tests if all elements are greater than or equal to a given value.

Declaration

public virtual bool GreaterThanOrEqual(double value)

Parameters

Type	Name	Description
Double	value	The value to test against.

Returns

Type	Description
Boolean	True if all elements are greater than or equal to `value`.

IndexAtCumulativeSum(Double)

Returns the index of the first element at which the sum of all elements so far is greater than a particular value. Useful for finding the median of a Discrete distribution.

Declaration

public virtual int IndexAtCumulativeSum(double targetSum)

Parameters

Type	Name	Description
Double	targetSum	The sum of interest

Returns

Type	Description
Int32	The index of the element where `targetSum` is exceeded or -1 if `targetSum` cannot be exceeded.

IndexOf(Double)

Returns the index of the first occurence of the given value in the array. Returns -1 if the value is not in the array

Declaration

public virtual int IndexOf(double item)

Parameters

Type	Name	Description
Double	item	The item to check for

Returns

Type	Description
Int32	Its index in the array

IndexOfAll(Converter<Double, Boolean>)

Returns an enumeration over the indices of all elements which satisfy the specified condition. Indices are returned in sorted order.

Declaration

public IEnumerable<int> IndexOfAll(Converter<double, bool> fun)

Parameters

Type	Name	Description
Converter<Double, Boolean>	fun	A function to check if the condition is satisfied.

Returns

Type	Description
IEnumerable<Int32>	An enumeration over the indices of all elements which satisfy the specified condition.

IndexOfMaximum()

Returns the index of the maximum element.

Declaration

public virtual int IndexOfMaximum()

Returns

Type	Description
Int32	The index of the maximum element.

IndexOfMinimum()

Returns the index of the minimum element.

Declaration

public virtual int IndexOfMinimum()

Returns

Type	Description
Int32	The index of the minimum element.

Inner(Vector)

Returns the inner product of this vector with another vector.

Declaration

public virtual double Inner(Vector that)

Parameters

Type	Name	Description
Vector	that	Second vector, which must have the same size as `this`.

Returns

Type	Description
Double	Their inner product.

Inner(Vector, Converter<Double, Double>)

Returns the inner product of a function of this vector with a second vector.

Declaration

public virtual double Inner(Vector that, Converter<double, double> fun)

Parameters

Type	Name	Description
Vector	that	Second vector, which must have the same size as `this`.
Converter<Double, Double>	fun	Function to convert the elements of the second vector

Returns

Type	Description
Double	Their inner product.

Inner(Converter<Double, Double>, Vector, Converter<Double, Double>)

Returns the inner product of a function of this vector with a function of a second vector.

Declaration

public virtual double Inner(Converter<double, double> thisFun, Vector that, Converter<double, double> thatFun)

Parameters

Type	Name	Description
Converter<Double, Double>	thisFun	Function to convert the elements of this vector
Vector	that	Second vector, which must have the same size as `this`.
Converter<Double, Double>	thatFun	Function to convert the elements of that vector

Returns

Type	Description
Double	Their inner product.

InnerProduct(Vector, Vector)

Returns the inner product of two vectors.

Declaration

public static double InnerProduct(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a
Vector	b

Returns

Type	Description
Double	The inner product.

LessThan(Vector)

Tests if this vector is strictly less than a second vector.

Declaration

public virtual bool LessThan(Vector that)

Parameters

Type	Name	Description
Vector	that	The value to test against.

Returns

Type	Description
Boolean	True if each element is strictly less than the corresponding element of `that`.

LessThan(Double)

Tests if all elements are strictly less than a given value.

Declaration

public virtual bool LessThan(double value)

Parameters

Type	Name	Description
Double	value	The value to test against.

Returns

Type	Description
Boolean	True if all elements are strictly less than `value`.

LessThanOrEqual(Vector)

Tests if this vector is less than or equal to a second vector.

Declaration

public virtual bool LessThanOrEqual(Vector that)

Parameters

Type	Name	Description
Vector	that	The value to test against.

Returns

Type	Description
Boolean	True if each element is strictly less than or equal to the corresponding element of `that`.

LessThanOrEqual(Double)

Tests if all elements are less than or equal to a given value.

Declaration

public virtual bool LessThanOrEqual(double value)

Parameters

Type	Name	Description
Double	value	The value to test against.

Returns

Type	Description
Boolean	True if all elements are less than or equal to `value`.

LogSumExp()

Returns the log of the sum of exponentials of the elements of the vector computed to high accuracy

Declaration

public virtual double LogSumExp()

Returns

Type	Description
Double

Max()

Returns the maximum of the elements in the vector

Declaration

public virtual double Max()

Returns

Type	Description
Double

Max(Converter<Double, Double>)

Returns the maximum of a function of the elements in the vector

Declaration

public virtual double Max(Converter<double, double> fun)

Parameters

Type	Name	Description
Converter<Double, Double>	fun

Returns

Type	Description
Double

MaxDiff(Vector)

Returns the maximum absolute difference between this vector and another vector.

Declaration

public virtual double MaxDiff(Vector that)

Parameters

Type	Name	Description
Vector	that	The second vector.

Returns

Type	Description
Double	`max(abs(this[i] - that[i]))`. Matching infinities or NaNs do not count. If `this` and `that` are not the same size, returns infinity.

Remarks

This routine is typically used instead of Equals, since Equals is susceptible to roundoff errors.

MaxDiff(Vector, Double)

Returns the maximum relative difference between this vector and another.

Declaration

public virtual double MaxDiff(Vector that, double rel)

Parameters

Type	Name	Description
Vector	that	The second vector.
Double	rel	An offset to avoid division by zero.

Returns

Type	Description
Double	`max(abs(this[i] - that[i])/(abs(this[i]) + rel))`. Matching infinities or NaNs do not count. If `this` and `that` are not the same size, returns infinity.

Remarks

This routine is typically used instead of Equals, since Equals is susceptible to roundoff errors.

Median()

Returns the minimum of the elements in the vector

Declaration

public virtual double Median()

Returns

Type	Description
Double

Min()

Returns the minimum of the elements in the vector

Declaration

public virtual double Min()

Returns

Type	Description
Double

Min(Converter<Double, Double>)

Returns the minimum of a function of the elements in the vector

Declaration

public virtual double Min(Converter<double, double> fun)

Parameters

Type	Name	Description
Converter<Double, Double>	fun

Returns

Type	Description
Double

Outer(Vector)

Returns the outer product of this vector with another vector.

Declaration

public virtual Matrix Outer(Vector that)

Parameters

Type	Name	Description
Vector	that	Second vector.

Returns

Type	Description
Matrix	Their outer product.

PredivideBy(LowerTriangularMatrix)

Gets the solution to Ax=b, where A is a lower triangular matrix, and b is this vector. Equivalent to the left-division x = A\b.

Declaration

public virtual Vector PredivideBy(LowerTriangularMatrix A)

Parameters

Type	Name	Description
LowerTriangularMatrix	A	A lower triangular matrix.

Returns

Type	Description
Vector	`this`

Remarks

this is used as the right-hand side vector b, and it also receives the solution. Throws an exception if A is singular.

PredivideBy(PositiveDefiniteMatrix)

Premultiply this vector by the inverse of a positive definite matrix

Declaration

public virtual Vector PredivideBy(PositiveDefiniteMatrix A)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	A

Returns

Type	Description
Vector

PredivideBy(UpperTriangularMatrix)

Gets the solution to Ax=b, where A is an upper triangular matrix, and b is this vector. Equivalent to the left-division x = A\b.

Declaration

public virtual Vector PredivideBy(UpperTriangularMatrix A)

Parameters

Type	Name	Description
UpperTriangularMatrix	A	An upper triangular matrix.

Returns

Type	Description
Vector	`this`

Remarks

this is used as the right-hand side vector b, and it also receives the solution. Throws an exception if A is singular.

PredivideByTranspose(LowerTriangularMatrix)

Gets the solution to A'x=b, where A is a lower triangular matrix, and b is this vector. Equivalent to the left-division x = A'\b.

Declaration

public virtual Vector PredivideByTranspose(LowerTriangularMatrix A)

Parameters

Type	Name	Description
LowerTriangularMatrix	A	A lower triangular matrix.

Returns

Type	Description
Vector	`this`

Remarks

this is used as the right-hand side vector b, and it also receives the solution. Throws an exception if A is singular.

Reduce(Double, Vector, Vector, Func<Double, Double, Double, Double, Double>)

Reduce method. Operates on this vector and two other vectors

Declaration

public virtual double Reduce(double initial, Vector a, Vector b, Func<double, double, double, double, double> fun)

Parameters

Type	Name	Description
Double	initial	Initial value
Vector	a	A second vector
Vector	b	A third vector
Func<Double, Double, Double, Double, Double>	fun

Returns

Type	Description
Double

Reduce(Double, Vector, Func<Double, Double, Double, Double>)

Reduce method. Operates on this vector and that vector

Declaration

public virtual double Reduce(double initial, Vector that, Func<double, double, double, double> fun)

Parameters

Type	Name	Description
Double	initial	Initial value
Vector	that	A second vector
Func<Double, Double, Double, Double>	fun	Reduction function taking partial result, current element, and current element of `that`

Returns

Type	Description
Double

Reduce(Double, Func<Double, Double, Double>)

Reduce method. Operates on this vector

Declaration

public virtual double Reduce(double initial, Func<double, double, double> fun)

Parameters

Type	Name	Description
Double	initial	Initial value
Func<Double, Double, Double>	fun	Reduction function taking partial result and current element

Returns

Type	Description
Double

Scale(Double)

Multiplies this vector by a scalar.

Declaration

public virtual void Scale(double scale)

Parameters

Type	Name	Description
Double	scale	The scalar.

Remarks

this receives the product. This method is a synonym for SetToProduct(this, scale)

SetAllElementsTo(Double)

Sets all elements to a given value.

Declaration

public virtual void SetAllElementsTo(double value)

Parameters

Type	Name	Description
Double	value	The new value.

SetSubvector(Int32, Vector)

Set a subvector of this to another vector.

Declaration

public virtual void SetSubvector(int startIndex, Vector that)

Parameters

Type	Name	Description
Int32	startIndex	The index of the first element of this to copy to.
Vector	that	A vector whose length is at most `this.Count - startIndex`.

SetTo(Vector)

Copies values from a Vector to this vector

Declaration

public virtual void SetTo(Vector that)

Parameters

Type	Name	Description
Vector	that

SetTo(IEnumerable<Double>)

Copies values from an Enumerable to this vector

Declaration

public virtual void SetTo(IEnumerable<double> that)

Parameters

Type	Name	Description
IEnumerable<Double>	that

SetTo(Double[])

Copies values from an array.

Declaration

public virtual void SetTo(double[] values)

Parameters

Type	Name	Description
Double[]	values	An array whose length matches `this.Count`.

SetToDiagonal(Matrix)

Sets this vector to the diagonal of a matrix.

Declaration

public virtual void SetToDiagonal(Matrix m)

Parameters

Type	Name	Description
Matrix	m	A matrix with Rows==Cols==this.Count.

SetToDifference(Vector, Vector)

Sets this vector to the difference of two vectors

Declaration

public virtual Vector SetToDifference(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector, which must have the same size as `this`.
Vector	b	Second vector, which must have the same size as `this`.

Returns

Type	Description
Vector	`this`

Remarks

this receives the difference, and must already be the correct size. a and/or b may be the same object as this. If this and a/b occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToDifference(Vector, Double)

Set this vector to another vector minus a constant

Declaration

public virtual Vector SetToDifference(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	The other vector
Double	b	The constant

Returns

Type	Description
Vector

Remarks

Assumes the vectors are compatible

SetToDifference(Double, Vector)

Set this vector to a constant minus another vector

Declaration

public virtual Vector SetToDifference(double a, Vector b)

Parameters

Type	Name	Description
Double	a	The constant
Vector	b	The other vector

Returns

Type	Description
Vector

Remarks

Assumes the vectors are compatible

SetToFunction(Vector, Vector, Func<Double, Double, Double>)

Sets the elements of this vector to a function of the elements of two vectors

Declaration

public virtual Vector SetToFunction(Vector a, Vector b, Func<double, double, double> fun)

Parameters

Type	Name	Description
Vector	a	The first vector
Vector	b	The second vector
Func<Double, Double, Double>	fun	The function which maps two doubles to a double

Returns

Type	Description
Vector

Remarks

Assumes the vectors are compatible

SetToFunction(Vector, Converter<Double, Double>)

Sets the elements of this vector to a function of the elements of a given vector

Declaration

public virtual Vector SetToFunction(Vector that, Converter<double, double> fun)

Parameters

Type	Name	Description
Vector	that	The given vector
Converter<Double, Double>	fun	The function which maps doubles to doubles

Returns

Type	Description
Vector

Remarks

Assumes the vectors are compatible

SetToPower(Vector, Double)

Sets this vector to the elementwise power of another vector.

Declaration

public virtual void SetToPower(Vector that, double exponent)

Parameters

Type	Name	Description
Vector	that	A vector, which must have the same size as `this`. Can be `this`.
Double	exponent	A scalar.

Remarks

this receives the product, and must already be the correct size.
If this and that occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToProduct(Matrix, Vector)

Set this vector to the product of a matrix by a vector (i.e. A*x).

Declaration

public virtual Vector SetToProduct(Matrix A, Vector x)

Parameters

Type	Name	Description
Matrix	A	A matrix.
Vector	x	A vector. Cannot be `this`.

Returns

Type	Description
Vector	`this`

Remarks

this receives the product, and must already be the correct size. If this and A/x occupy overlapping portions of the same source array, the results are undefined.

SetToProduct(Vector, Matrix)

Sets this vector to the product of a vector by a matrix (i.e. x*A).

Declaration

public virtual Vector SetToProduct(Vector x, Matrix A)

Parameters

Type	Name	Description
Vector	x	A vector. Cannot be `this`.
Matrix	A	A matrix.

Returns

Type	Description
Vector	`this`

Remarks

this receives the product, and must already be the correct size. If this and A/x occupy overlapping portions of the same source array, the results are undefined.

SetToProduct(Vector, Vector)

Sets this vector to the elementwise product of two other vectors.

Declaration

public virtual void SetToProduct(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	Must have the same size as `this`. Can be `this`.
Vector	b	Must have the same size as `this`. Can be `this`.

Remarks

this receives the product, and must already be the correct size.
If this and a occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToProduct(Vector, Double)

Sets this vector to a vector times a scalar.

Declaration

public virtual Vector SetToProduct(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	A vector, which must have the same size as `this`. Can be `this`.
Double	b	A scalar.

Returns

Type	Description
Vector	`this`

Remarks

this receives the product, and must already be the correct size.
If this and a occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToRatio(Vector, Vector)

Sets this vector to the elementwise ratio of two other vectors.

Declaration

public virtual Vector SetToRatio(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	Must have the same size as `this`. Can be `this`.
Vector	b	Must have the same size as `this`. Can be `this`.

Returns

Type	Description
Vector	`this`

Remarks

this receives the product, and must already be the correct size.
If this and a occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToSubarray(Double[], Int32)

Copies values from an array.

Declaration

public virtual void SetToSubarray(double[] values, int startIndex)

Parameters

Type	Name	Description
Double[]	values	An array whose length is at least `this.Count + startIndex`.
Int32	startIndex	The index of the first value in `values` to copy.

SetToSubvector(Vector, Int32)

Copies value from a vector.

Declaration

public virtual void SetToSubvector(Vector that, int startIndex)

Parameters

Type	Name	Description
Vector	that	A vector whose length is at least `this.Count + startIndex`.
Int32	startIndex	The index of the first value in `that` to copy.

SetToSum(Vector, Vector)

Sets this vector to the elementwise sum of two other vectors.

Declaration

public virtual Vector SetToSum(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector, which must have the same size as `this`.
Vector	b	Second vector, which must have the same size as `this`.

Returns

Type	Description
Vector	`this`

Remarks

this receives the sum, and must already be the correct size. a and/or b may be the same object as this. If this and a/b occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToSum(Vector, Double)

Sets this vector to another vector plus a scalar.

Declaration

public virtual Vector SetToSum(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	A vector, which must have the same size as `this`. Can be the same object as `this`.
Double	b	A scalar.

Returns

Type	Description
Vector	`this`

Remarks

this receives the sum, and must already be the correct size. If this and a occupy distinct yet overlapping portions of the same source array, the results are undefined.

SetToSum(Double, Vector, Double, Vector)

Set this vector to a linear combination of two other vectors

Declaration

public virtual void SetToSum(double aScale, Vector a, double bScale, Vector b)

Parameters

Type	Name	Description
Double	aScale	The multiplier for vector a
Vector	a	First vector, which must have the same size as `this`.
Double	bScale	The multiplier for vector b
Vector	b	Second vector, which must have the same size as `this`.

Remarks

Subvector(Vector, Int32, Int32)

Copy a subvector.

Declaration

public static Vector Subvector(Vector source, int startIndex, int count)

Parameters

Type	Name	Description
Vector	source	A vector whose length is at least `count + startIndex`.
Int32	startIndex	The index of the first value in `source` to copy.
Int32	count	The number of elements to copy.

Returns

Type	Description
Vector	A Vector of length `count`

Subvector(Int32, Int32)

Create a subvector of this vector

Declaration

public virtual Vector Subvector(int startIndex, int count)

Parameters

Type	Name	Description
Int32	startIndex
Int32	count

Returns

Type	Description
Vector

Sum()

Returns the sum of all elements.

Declaration

public virtual double Sum()

Returns

Type	Description
Double

Sum(Converter<Double, Double>)

Returns the sum of a function of all elements.

Declaration

public virtual double Sum(Converter<double, double> fun)

Parameters

Type	Name	Description
Converter<Double, Double>	fun

Returns

Type	Description
Double

Sum(Converter<Double, Double>, Vector, Converter<Double, Boolean>)

Returns the sum of a function of this vector filtered by a function of a second vector.

Declaration

public virtual double Sum(Converter<double, double> fun, Vector that, Converter<double, bool> cond)

Parameters

Type	Name	Description
Converter<Double, Double>	fun	Function to convert the elements of this vector
Vector	that	Second vector, which must have the same size as `this`.
Converter<Double, Boolean>	cond	Function to convert the elements of that vector to give the filter condition

Returns

Type	Description
Double	The filtered and mapped sum

SumI()

Returns the sum of over zero-based index * element.

Declaration

public virtual double SumI()

Returns

Type	Description
Double

SumISq()

Returns the sum of over square of index^2 times element.

Declaration

public virtual double SumISq()

Returns

Type	Description
Double

ToArray()

Converts this vector to an array of doubles

Declaration

public virtual double[] ToArray()

Returns

Type	Description
Double[]

ToString()

Converts this sparse vector into a human readable string

Declaration

public override string ToString()

Returns

Type	Description
String

Overrides

Object.ToString()

ToString(String)

String representation of vector with a specified format for each element

Declaration

public virtual string ToString(string format)

Parameters

Type	Name	Description
String	format

Returns

Type	Description
String

ToString(String, String)

String representation of vector with a specified format and delimiter

Declaration

public virtual string ToString(string format, string delimiter)

Parameters

Type	Name	Description
String	format
String	delimiter

Returns

Type	Description
String

ToString(String, String, Func<Int32, String>)

String representation of vector with a specified format and delimiter and a function for converting integers to display strings.

Declaration

public virtual string ToString(string format, string delimiter, Func<int, string> intToString)

Parameters

Type	Name	Description
String	format
String	delimiter
Func<Int32, String>	intToString

Returns

Type	Description
String

Zero(Int32)

Creates a dense vector of given length with elements all 0.0

Declaration

public static Vector Zero(int count)

Parameters

Type	Name	Description
Int32	count	Number of elements in vector

Returns

Type	Description
Vector

Zero(Int32, Sparsity)

Creates a vector of given length with elements all 0.0

Declaration

public static Vector Zero(int count, Sparsity sparsity)

Parameters

Type	Name	Description
Int32	count	Number of elements in vector
Sparsity	sparsity	The Sparsity specification.

Returns

Type	Description
Vector

Operators

Addition(Vector, Vector)

Returns the sum of two vectors.

Declaration

public static Vector operator +(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Vector	The sum.

Addition(Vector, Double)

Add a scalar to every element of a vector.

Declaration

public static Vector operator +(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	A vector.
Double	b	A scalar.

Returns

Type	Description
Vector	A vector with the sum.

Division(Vector, Vector)

Returns the ratio of two vectors

Declaration

public static Vector operator /(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Vector	The difference.

Division(Vector, Double)

Divides every element of a vector by a scalar.

Declaration

public static Vector operator /(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	A vector.
Double	b	A scalar.

Returns

Type	Description
Vector	A new vector with the ratio.

Equality(Vector, Vector)

Equality operator.

Declaration

public static bool operator ==(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Boolean	True if the vectors have the same size and element values.

ExclusiveOr(Vector, Double)

Returns a vector to some power.

Declaration

public static Vector operator ^(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	A vector.
Double	b	A scalar.

Returns

Type	Description
Vector	A new vector with this[i] = Math.Pow(a[i],b).

GreaterThan(Vector, Vector)

Greater than operator.

Declaration

public static bool operator>(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Boolean	True if each element in the first vector is greater than the corresponding element in the second vector.

GreaterThan(Vector, Double)

Greater than operator.

Declaration

public static bool operator>(Vector a, double value)

Parameters

Type	Name	Description
Vector	a	Vector.
Double	value	Value to compare against.

Returns

Type	Description
Boolean	True if each element is greater than given value.

GreaterThanOrEqual(Vector, Vector)

Greater than or equal to operator.

Declaration

public static bool operator >=(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Boolean	True if each element in the first vector is not less than the corresponding element in the second vector.

GreaterThanOrEqual(Vector, Double)

Greater than or equal to operator.

Declaration

public static bool operator >=(Vector a, double value)

Parameters

Type	Name	Description
Vector	a	Vector.
Double	value	Value to compare against.

Returns

Type	Description
Boolean	True if each element is not less than given value.

Inequality(Vector, Vector)

Inequality operator.

Declaration

public static bool operator !=(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Boolean	True if vectors are not equal.

LessThan(Vector, Vector)

Less than operator.

Declaration

public static bool operator <(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Boolean	True if each element in the first vector is less than the corresponding element in the second vector.

LessThan(Vector, Double)

Less than operator.

Declaration

public static bool operator <(Vector a, double value)

Parameters

Type	Name	Description
Vector	a	Vector.
Double	value	Value to compare against.

Returns

Type	Description
Boolean	True if each element is less than given value.

LessThanOrEqual(Vector, Vector)

Less than or equal to operator.

Declaration

public static bool operator <=(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Boolean	True if each element in the first vector is not greater than the corresponding element in the second vector.

LessThanOrEqual(Vector, Double)

Less than or equal to operator.

Declaration

public static bool operator <=(Vector a, double value)

Parameters

Type	Name	Description
Vector	a	Vector.
Double	value	Value to compare against.

Returns

Type	Description
Boolean	True if each element is not greater than given value.

Multiply(Vector, Vector)

Returns the elementwise product of two vectors.

Declaration

public static Vector operator *(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a
Vector	b

Returns

Type	Description
Vector	A new vector with the product.

Multiply(Vector, Double)

Multiplies every element of a vector by a scalar.

Declaration

public static Vector operator *(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	A vector.
Double	b	A scalar.

Returns

Type	Description
Vector	A new vector with the product.

Multiply(Double, Vector)

Multiply every element of this vector by a scalar.

Declaration

public static Vector operator *(double b, Vector a)

Parameters

Type	Name	Description
Double	b	A scalar.
Vector	a	A vector.

Returns

Type	Description
Vector	A new vector with the product.

Subtraction(Vector, Vector)

Returns the difference of two vectors

Declaration

public static Vector operator -(Vector a, Vector b)

Parameters

Type	Name	Description
Vector	a	First vector.
Vector	b	Second vector.

Returns

Type	Description
Vector	The difference.

Subtraction(Vector, Double)

Subtracts a scalar from each element of a vector.

Declaration

public static Vector operator -(Vector a, double b)

Parameters

Type	Name	Description
Vector	a	First vector.
Double	b	A scalar.

Returns

Type	Description
Vector	The difference.

Subtraction(Double, Vector)

Subtracts a scalar from each element of a vector.

Declaration

public static Vector operator -(double a, Vector b)

Parameters

Type	Name	Description
Double	a	First vector.
Vector	b	A scalar.

Returns

Type	Description
Vector	The difference.

UnaryNegation(Vector)

Returns a vector which is the unary negation of a vector.

Declaration

public static Vector operator -(Vector a)

Parameters

Type	Name	Description
Vector	a	The vector to negate.

Returns

Type	Description
Vector	The negation of a.

Explicit Interface Implementations

ICollection<Double>.Add(Double)

Declaration

void ICollection<double>.Add(double item)

Parameters

Type	Name	Description
Double	item

ICollection<Double>.Clear()

Declaration

void ICollection<double>.Clear()

ICollection<Double>.Remove(Double)

Declaration

bool ICollection<double>.Remove(double item)

Parameters

Type	Name	Description
Double	item

Returns

Type	Description
Boolean

IList<Double>.Insert(Int32, Double)

Declaration

void IList<double>.Insert(int index, double item)

Parameters

Type	Name	Description
Int32	index
Double	item

IList<Double>.RemoveAt(Int32)

Declaration

void IList<double>.RemoveAt(int index)

Parameters

Type	Name	Description
Int32	index

IEnumerable.GetEnumerator()

Declaration

IEnumerator IEnumerable.GetEnumerator()

Returns

Type	Description
IEnumerator

ICloneable.Clone()

Declaration

object ICloneable.Clone()

Returns

Type	Description
Object

Implements

System.Collections.Generic.IList<T>

System.Collections.Generic.ICollection<T>

System.Collections.Generic.IReadOnlyList<T>

System.Collections.Generic.IReadOnlyCollection<T>

System.Collections.Generic.IEnumerable<T>

System.Collections.IEnumerable

SettableTo<T>

System.ICloneable

CanSetAllElementsTo<T>

SettableToPower<T>

SettableToProduct<T>

SettableToProduct<T, U>

SettableToWeightedSum<T>

Extension Methods

CollectionExtensions.AddRange<T>(ICollection<T>, IEnumerable<T>)

CollectionExtensions.ContainsAll<T>(ICollection<T>, IEnumerable<T>)

CollectionExtensions.ContainsAny<T>(ICollection<T>, IEnumerable<T>)

EnumerableExtensions.ForEach<T>(IEnumerable<T>, Action<T>)

EnumerableExtensions.ForEach<T>(IEnumerable, Action<T>)

EnumerableExtensions.ForEach<T>(IEnumerable<T>, Action<Int32, T>)

EnumerableExtensions.ForEach<T>(IEnumerable, Action<Int32, T>)

EnumerableExtensions.Sum<TSource>(IEnumerable<TSource>, Func<TSource, UInt32>)

EnumerableExtensions.Sum<TSource>(IEnumerable<TSource>, Func<TSource, UInt64>)

EnumerableExtensions.ValueEquals<T>(IEnumerable<T>, IEnumerable<T>)

EnumerableExtensions.IndexOf<T>(IEnumerable<T>, T)

EnumerableExtensions.IndexOf<T>(IEnumerable, T)

EnumerableExtensions.FindIndex<T>(IEnumerable<T>, Predicate<T>)

EnumerableExtensions.FindIndex<T>(IEnumerable, Predicate<T>)

EnumerableExtensions.FindAllIndex<T>(IEnumerable<T>, Predicate<T>)

EnumerableExtensions.IndexOfAll<T>(IEnumerable<T>, T)

EnumerableExtensions.Skip<T>(IEnumerable<T>, Int32, out List<T>)

EnumerableExtensions.CopyTo<T>(IEnumerable<T>, T[], Int32)

EnumerableExtensions.ToReadOnlyList<T>(IEnumerable<T>)

IEnumerableExensions.EnumerableReduce<T, TRes>(IEnumerable<T>, TRes, Func<TRes, T, TRes>, Func<TRes, T, Int32, TRes>)

IEnumerableExensions.EnumerableSum<T>(IEnumerable<T>, Func<T, Double>)

IEnumerableExensions.ListZip<TFirst, TSecond, TResult>(IList<TFirst>, IEnumerable<TSecond>, Func<TFirst, TSecond, TResult>)

IEnumerableExensions.ListZip<TFirst, TSecond, TThird, TResult>(IList<TFirst>, IEnumerable<TSecond>, IEnumerable<TThird>, Func<TFirst, TSecond, TThird, TResult>)

IEnumerableExensions.ListZip<TFirst, TSecond, TThird, TFourth, TResult>(IList<TFirst>, IList<TSecond>, IList<TThird>, IList<TFourth>, Func<TFirst, TSecond, TThird, TFourth, TResult>)

IListExtensions.IsSparse<T>(IList<T>)

IListExtensions.ListSelect<T, T2>(IList<T>, Func<T, T2>)

IListExtensions.ListReduce<T, TRes>(IList<T>, TRes, Func<TRes, T, TRes>)

IListExtensions.ListReduce<T, T2, TRes>(IList<T>, IEnumerable<T2>, TRes, Func<TRes, T, T2, TRes>)

IListExtensions.ToVector(IList<Double>)

IListExtensions.SetTo<T>(IList<T>, IEnumerable<T>)

IListExtensions.SetTo(IList<Double>, IEnumerable<Double>)

IListExtensions.AsReadOnly<T>(IList<T>)

ReadOnlyArray.ToReadOnlyArray<T>(IEnumerable<T>)