cern.colt.matrix.tint

Class IntMatrix1D

java.lang.Object

cern.colt.PersistentObject

cern.colt.matrix.AbstractMatrix

cern.colt.matrix.AbstractMatrix1D

cern.colt.matrix.tint.IntMatrix1D

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

DenseIntMatrix1D, SparseIntMatrix1D, WrapperIntMatrix1D

public abstract class IntMatrix1D
extends AbstractMatrix1D

Abstract base class for 1-d matrices (aka vectors) holding int elements. First see the package summary and javadoc tree view to get the broad picture.

A matrix has a number of cells (its size), which are assigned upon instance construction. Elements are accessed via zero based indexes. Legal indexes are of the form [0..size()-1]. Any attempt to access an element at a coordinate index<0 || index>=size() will throw an IndexOutOfBoundsException.

See Also:

Serialized Form

Method Summary

Modifier and Type	Method and Description
int	aggregate(IntIntFunction aggr, IntFunction f) Applies a function to each cell and aggregates the results.
int	aggregate(IntIntFunction aggr, IntFunction f, IntArrayList indexList) Applies a function to all cells with a given indexes and aggregates the results.
int	aggregate(IntMatrix1D other, IntIntFunction aggr, IntIntFunction f) Applies a function to each corresponding cell of two matrices and aggregates the results.
IntMatrix1D	assign(int value) Sets all cells to the state specified by value.
IntMatrix1D	assign(int[] values) Sets all cells to the state specified by values.
IntMatrix1D	assign(IntFunction f) Assigns the result of a function to each cell; x[i] = function(x[i]).
IntMatrix1D	assign(IntMatrix1D other) Replaces all cell values of the receiver with the values of another matrix.
IntMatrix1D	assign(IntMatrix1D y, IntIntFunction function) Assigns the result of a function to each cell; x[i] = function(x[i],y[i]).
IntMatrix1D	assign(IntMatrix1D y, IntIntFunction function, IntArrayList nonZeroIndexes) Assigns the result of a function to each cell; x[i] = function(x[i],y[i]).
IntMatrix1D	assign(IntProcedure cond, int value) Assigns a value to all cells that satisfy a condition.
IntMatrix1D	assign(IntProcedure cond, IntFunction f) Assigns the result of a function to all cells that satisfy a condition.
int	cardinality() Returns the number of cells having non-zero values; ignores tolerance.
IntMatrix1D	copy() Constructs and returns a deep copy of the receiver.
abstract java.lang.Object	elements() Returns the elements of this matrix.
boolean	equals(int value) Returns whether all cells are equal to the given value.
boolean	equals(java.lang.Object obj) Compares this object against the specified object.
int	get(int index) Returns the matrix cell value at coordinate index.
int[]	getMaxLocation() Return the maximum value of this matrix together with its location
int[]	getMinLocation() Return the minimum value of this matrix together with its location
void	getNegativeValues(IntArrayList indexList, IntArrayList valueList) Fills the coordinates and values of cells having negative values into the specified lists.
void	getNonZeros(IntArrayList indexList, IntArrayList valueList) Fills the coordinates and values of cells having non-zero values into the specified lists.
void	getNonZeros(IntArrayList indexList, IntArrayList valueList, int maxCardinality) Fills the coordinates and values of the first maxCardinality cells having non-zero values into the specified lists.
void	getPositiveValues(IntArrayList indexList, IntArrayList valueList) Fills the coordinates and values of cells having positive values into the specified lists.
abstract int	getQuick(int index) Returns the matrix cell value at coordinate index.
IntMatrix1D	like() Construct and returns a new empty matrix of the same dynamic type as the receiver, having the same size.
abstract IntMatrix1D	like(int size) Construct and returns a new empty matrix of the same dynamic type as the receiver, having the specified size.
abstract IntMatrix2D	like2D(int rows, int columns) Construct and returns a new 2-d matrix of the corresponding dynamic type, entirelly independent of the receiver.
abstract IntMatrix2D	reshape(int rows, int columns) Returns new IntMatrix2D of size rows x columns whose elements are taken column-wise from this matrix.
abstract IntMatrix3D	reshape(int slices, int rows, int columns) Returns new IntMatrix3D of size slices x rows x columns, whose elements are taken column-wise from this matrix.
void	set(int index, int value) Sets the matrix cell at coordinate index to the specified value.
abstract void	setQuick(int index, int value) Sets the matrix cell at coordinate index to the specified value.
void	setSize(int size) Sets the size of this matrix.
void	swap(IntMatrix1D other) Swaps each element this[i] with other[i].
int[]	toArray() Constructs and returns a 1-dimensional array containing the cell values.
void	toArray(int[] values) Fills the cell values into the specified 1-dimensional array.
java.lang.String	toString() Returns a string representation using default formatting.
IntMatrix1D	viewFlip() Constructs and returns a new flip view.
IntMatrix1D	viewPart(int index, int width) Constructs and returns a new sub-range view that is a width sub matrix starting at index.
IntMatrix1D	viewSelection(int[] indexes) Constructs and returns a new selection view that is a matrix holding the indicated cells.
IntMatrix1D	viewSelection(IntProcedure condition) Constructs and returns a new selection view that is a matrix holding the cells matching the given condition.
IntMatrix1D	viewSorted() Sorts the vector into ascending order, according to the natural ordering.
IntMatrix1D	viewStrides(int stride) Constructs and returns a new stride view which is a sub matrix consisting of every i-th cell.
int	zDotProduct(IntMatrix1D y) Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]).
int	zDotProduct(IntMatrix1D y, int from, int length) Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]).
int	zDotProduct(IntMatrix1D y, int from, int length, IntArrayList nonZeroIndexes) Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]).
int	zSum() Returns the sum of all cells; Sum( x[i] ).

Methods inherited from class cern.colt.matrix.AbstractMatrix1D

checkSize, index, size, stride, toStringShort

Methods inherited from class cern.colt.matrix.AbstractMatrix

ensureCapacity, isView, trimToSize

Methods inherited from class cern.colt.PersistentObject

clone

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Method Detail

aggregate

public int aggregate(IntIntFunction aggr,
                     IntFunction f)

Applies a function to each cell and aggregates the results. Returns a value v such that v==a(size()) where a(i) == aggr( a(i-1), f(get(i)) ) and terminators are a(1) == f(get(0)), a(0)==Int.NaN.

Example:

   cern.jet.math.Functions F = cern.jet.math.Functions.functions;
   matrix = 0 1 2 3 
 
   // Sum( x[i]*x[i] ) 
   matrix.aggregate(F.plus,F.square);
   --> 14
 
 

For further examples, see the package doc.

Parameters:

aggr - an aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.

f - a function transforming the current cell value.

Returns:

the aggregated measure.

See Also:

IntFunctions

aggregate

public int aggregate(IntIntFunction aggr,
                     IntFunction f,
                     IntArrayList indexList)

Applies a function to all cells with a given indexes and aggregates the results.

Parameters:

aggr - an aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.

f - a function transforming the current cell value.

indexList - indexes.

Returns:

the aggregated measure.

See Also:

IntFunctions

aggregate

public int aggregate(IntMatrix1D other,
                     IntIntFunction aggr,
                     IntIntFunction f)

Applies a function to each corresponding cell of two matrices and aggregates the results. Returns a value v such that v==a(size()) where a(i) == aggr( a(i-1), f(get(i),other.get(i)) ) and terminators are a(1) == f(get(0),other.get(0)), a(0)==Int.NaN.

Example:

   cern.jet.math.Functions F = cern.jet.math.Functions.functions;
   x = 0 1 2 3 
   y = 0 1 2 3 
 
   // Sum( x[i]*y[i] )
   x.aggregate(y, F.plus, F.mult);
   --> 14
 
   // Sum( (x[i]+y[i])ˆ2 )
   x.aggregate(y, F.plus, F.chain(F.square,F.plus));
   --> 56
 
 

For further examples, see the package doc.

Parameters:

aggr - an aggregation function taking as first argument the current aggregation and as second argument the transformed current cell values.

f - a function transforming the current cell values.

Returns:

the aggregated measure.

Throws:

java.lang.IllegalArgumentException - if size() != other.size().

See Also:

IntFunctions

assign

public IntMatrix1D assign(IntFunction f)

Assigns the result of a function to each cell; x[i] = function(x[i]). (Iterates downwards from [size()-1] to [0]).

Example:

   // change each cell to its sine
   matrix =   0.5      1.5      2.5       3.5 
   matrix.assign(cern.jet.math.Functions.sin);
   -->
   matrix ==  0.479426 0.997495 0.598472 -0.350783
 
 

For further examples, see the package doc.

Parameters:

f - a function object taking as argument the current cell's value.

Returns:

this (for convenience only).

See Also:

IntFunctions

assign

public IntMatrix1D assign(IntProcedure cond,
                          IntFunction f)

Assigns the result of a function to all cells that satisfy a condition.

Parameters:

cond - a condition.

f - a function object.

Returns:

this (for convenience only).

See Also:

IntFunctions

assign

public IntMatrix1D assign(IntProcedure cond,
                          int value)

Assigns a value to all cells that satisfy a condition.

Parameters:

cond - a condition.

value - a value.

Returns:

this (for convenience only).

assign

public IntMatrix1D assign(int value)

Sets all cells to the state specified by value.

Parameters:

value - the value to be filled into the cells.

Returns:

this (for convenience only).

assign

public IntMatrix1D assign(int[] values)

Sets all cells to the state specified by values. values is required to have the same number of cells as the receiver.

The values are copied. So subsequent changes in values are not reflected in the matrix, and vice-versa.

Parameters:

values - the values to be filled into the cells.

Returns:

this (for convenience only).

Throws:

java.lang.IllegalArgumentException - if values.length != size().

assign

public IntMatrix1D assign(IntMatrix1D other)

Replaces all cell values of the receiver with the values of another matrix. Both matrices must have the same size. If both matrices share the same cells (as is the case if they are views derived from the same matrix) and intersect in an ambiguous way, then replaces as if using an intermediate auxiliary deep copy of other.

Parameters:

other - the source matrix to copy from (may be identical to the receiver).

Returns:

this (for convenience only).

Throws:

java.lang.IllegalArgumentException - if size() != other.size().

assign

public IntMatrix1D assign(IntMatrix1D y,
                          IntIntFunction function)

Assigns the result of a function to each cell; x[i] = function(x[i],y[i]).

Example:

   // assign x[i] = x[i]<sup>y[i]</sup>
   m1 = 0 1 2 3;
   m2 = 0 2 4 6;
   m1.assign(m2, cern.jet.math.Functions.pow);
   -->
   m1 == 1 1 16 729
 
 

For further examples, see the package doc.

Parameters:

y - the secondary matrix to operate on.

function - a function object taking as first argument the current cell's value of this, and as second argument the current cell's value of y,

Returns:

this (for convenience only).

Throws:

java.lang.IllegalArgumentException - if size() != y.size().

See Also:

IntFunctions

assign

public IntMatrix1D assign(IntMatrix1D y,
                          IntIntFunction function,
                          IntArrayList nonZeroIndexes)

Assigns the result of a function to each cell; x[i] = function(x[i],y[i]). (Iterates downwards from [size()-1] to [0]).

Example:

   // assign x[i] = x[i]<sup>y[i]</sup>
   m1 = 0 1 2 3;
   m2 = 0 2 4 6;
   m1.assign(m2, cern.jet.math.Functions.pow);
   -->
   m1 == 1 1 16 729
 
   // for non-standard functions there is no shortcut: 
   m1.assign(m2,
      new IntIntFunction() {
         public int apply(int x, int y) { return Math.pow(x,y); }
      }
   );
 
 

For further examples, see the package doc.

Parameters:

y - the secondary matrix to operate on.

function - a function object taking as first argument the current cell's value of this, and as second argument the current cell's value of y.

nonZeroIndexes - list of indexes of non-zero values

Returns:

this (for convenience only).

Throws:

java.lang.IllegalArgumentException - if size() != y.size().

See Also:

IntFunctions

cardinality

public int cardinality()

Returns the number of cells having non-zero values; ignores tolerance.

Returns:

the number of cells having non-zero values.

copy

public IntMatrix1D copy()

Constructs and returns a deep copy of the receiver.

Note that the returned matrix is an independent deep copy. The returned matrix is not backed by this matrix, so changes in the returned matrix are not reflected in this matrix, and vice-versa.

Returns:

a deep copy of the receiver.

elements

public abstract java.lang.Object elements()

Returns the elements of this matrix.

Returns:

the elements

equals

public boolean equals(int value)

Returns whether all cells are equal to the given value.

Parameters:

value - the value to test against.

Returns:

true if all cells are equal to the given value, false otherwise.

equals

public boolean equals(java.lang.Object obj)

Compares this object against the specified object. The result is true if and only if the argument is not null and is at least a IntMatrix1D object that has the same sizes as the receiver and has exactly the same values at the same indexes.

Overrides:

equals in class java.lang.Object

Parameters:

obj - the object to compare with.

Returns:

true if the objects are the same; false otherwise.

get

public int get(int index)

Returns the matrix cell value at coordinate index.

Parameters:

index - the index of the cell.

Returns:

the value of the specified cell.

Throws:

java.lang.IndexOutOfBoundsException - if index<0 || index>=size().

getNegativeValues

public void getNegativeValues(IntArrayList indexList,
                              IntArrayList valueList)

Fills the coordinates and values of cells having negative values into the specified lists. Fills into the lists, starting at index 0. After this call returns the specified lists all have a new size, the number of non-zero values.

Parameters:

indexList - the list to be filled with indexes, can have any size.

valueList - the list to be filled with values, can have any size.

getNonZeros

public void getNonZeros(IntArrayList indexList,
                        IntArrayList valueList)

Fills the coordinates and values of cells having non-zero values into the specified lists. Fills into the lists, starting at index 0. After this call returns the specified lists all have a new size, the number of non-zero values.

In general, fill order is unspecified. This implementation fills like: for (index = 0..size()-1) do ... . However, subclasses are free to us any other order, even an order that may change over time as cell values are changed. (Of course, result lists indexes are guaranteed to correspond to the same cell).

Example:

   0, 0, 8, 0, 7
   -->
   indexList  = (2,4)
   valueList  = (8,7)
 
 

In other words, get(2)==8, get(4)==7.

Parameters:

indexList - the list to be filled with indexes, can have any size.

valueList - the list to be filled with values, can have any size.

getNonZeros

public void getNonZeros(IntArrayList indexList,
                        IntArrayList valueList,
                        int maxCardinality)

Fills the coordinates and values of the first maxCardinality cells having non-zero values into the specified lists. Fills into the lists, starting at index 0. After this call returns the specified lists all have a new size, the number of non-zero values.

In general, fill order is unspecified. This implementation fills like: for (index = 0..size()-1) do ... . However, subclasses are free to us any other order, even an order that may change over time as cell values are changed. (Of course, result lists indexes are guaranteed to correspond to the same cell).

Example:

   0, 0, 8, 0, 7
   -->
   indexList  = (2,4)
   valueList  = (8,7)
 
 

In other words, get(2)==8, get(4)==7.

Parameters:

indexList - the list to be filled with indexes, can have any size.

valueList - the list to be filled with values, can have any size.

maxCardinality - maximal cardinality

getPositiveValues

public void getPositiveValues(IntArrayList indexList,
                              IntArrayList valueList)

Fills the coordinates and values of cells having positive values into the specified lists. Fills into the lists, starting at index 0. After this call returns the specified lists all have a new size, the number of non-zero values.

Parameters:

indexList - the list to be filled with indexes, can have any size.

valueList - the list to be filled with values, can have any size.

getQuick

public abstract int getQuick(int index)

Returns the matrix cell value at coordinate index.

Provided with invalid parameters this method may return invalid objects without throwing any exception. You should only use this method when you are absolutely sure that the coordinate is within bounds. Precondition (unchecked): index<0 || index>=size().

Parameters:

index - the index of the cell.

Returns:

the value of the specified cell.

like

public IntMatrix1D like()

Construct and returns a new empty matrix of the same dynamic type as the receiver, having the same size. For example, if the receiver is an instance of type DenseIntMatrix1D the new matrix must also be of type DenseIntMatrix1D, if the receiver is an instance of type SparseIntMatrix1D the new matrix must also be of type SparseIntMatrix1D, etc. In general, the new matrix should have internal parametrization as similar as possible.

Returns:

a new empty matrix of the same dynamic type.

like

public abstract IntMatrix1D like(int size)

Construct and returns a new empty matrix of the same dynamic type as the receiver, having the specified size. For example, if the receiver is an instance of type DenseIntMatrix1D the new matrix must also be of type DenseIntMatrix1D, if the receiver is an instance of type SparseIntMatrix1D the new matrix must also be of type SparseIntMatrix1D, etc. In general, the new matrix should have internal parametrization as similar as possible.

Parameters:

size - the number of cell the matrix shall have.

Returns:

a new empty matrix of the same dynamic type.

like2D

public abstract IntMatrix2D like2D(int rows,
                                   int columns)

Construct and returns a new 2-d matrix of the corresponding dynamic type, entirelly independent of the receiver. For example, if the receiver is an instance of type DenseIntMatrix1D the new matrix must be of type DenseIntMatrix2D, if the receiver is an instance of type SparseIntMatrix1D the new matrix must be of type SparseIntMatrix2D, etc.

Parameters:

rows - the number of rows the matrix shall have.

columns - the number of columns the matrix shall have.

Returns:

a new matrix of the corresponding dynamic type.

getMaxLocation

public int[] getMaxLocation()

Return the maximum value of this matrix together with its location

Returns:

{ maximum_value, location };

getMinLocation

public int[] getMinLocation()

Return the minimum value of this matrix together with its location

Returns:

{ minimum_value, location };

reshape

public abstract IntMatrix2D reshape(int rows,
                                    int columns)

Returns new IntMatrix2D of size rows x columns whose elements are taken column-wise from this matrix.

Parameters:

rows - number of rows

columns - number of columns

Returns:

new 2D matrix with columns being the elements of this matrix.

reshape

public abstract IntMatrix3D reshape(int slices,
                                    int rows,
                                    int columns)

Returns new IntMatrix3D of size slices x rows x columns, whose elements are taken column-wise from this matrix.

Parameters:

rows - number of rows

columns - number of columns

Returns:

new 2D matrix with columns being the elements of this matrix.

set

public void set(int index,
                int value)

Sets the matrix cell at coordinate index to the specified value.

Parameters:

index - the index of the cell.

value - the value to be filled into the specified cell.

Throws:

java.lang.IndexOutOfBoundsException - if index<0 || index>=size().

setQuick

public abstract void setQuick(int index,
                              int value)

Sets the matrix cell at coordinate index to the specified value.

Provided with invalid parameters this method may access illegal indexes without throwing any exception. You should only use this method when you are absolutely sure that the coordinate is within bounds. Precondition (unchecked): index<0 || index>=size().

Parameters:

index - the index of the cell.

value - the value to be filled into the specified cell.

setSize

public void setSize(int size)

Sets the size of this matrix.

Parameters:

size -

swap

public void swap(IntMatrix1D other)

Swaps each element this[i] with other[i].

Throws:

java.lang.IllegalArgumentException - if size() != other.size().

toArray

public int[] toArray()

Constructs and returns a 1-dimensional array containing the cell values. The values are copied. So subsequent changes in values are not reflected in the matrix, and vice-versa. The returned array values has the form
for (int i=0; i < size(); i++) values[i] = get(i);

Returns:

an array filled with the values of the cells.

toArray

public void toArray(int[] values)

Fills the cell values into the specified 1-dimensional array. The values are copied. So subsequent changes in values are not reflected in the matrix, and vice-versa. After this call returns the array values has the form
for (int i=0; i < size(); i++) values[i] = get(i);

Throws:

java.lang.IllegalArgumentException - if values.length < size().

toString

public java.lang.String toString()

Returns a string representation using default formatting.

Overrides:

toString in class java.lang.Object

See Also:

IntFormatter

viewFlip

public IntMatrix1D viewFlip()

Constructs and returns a new flip view. What used to be index 0 is now index size()-1, ..., what used to be index size()-1 is now index 0. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

Returns:

a new flip view.

viewPart

public IntMatrix1D viewPart(int index,
                            int width)

Constructs and returns a new sub-range view that is a width sub matrix starting at index. Operations on the returned view can only be applied to the restricted range. Any attempt to access coordinates not contained in the view will throw an IndexOutOfBoundsException.

Note that the view is really just a range restriction: The returned matrix is backed by this matrix, so changes in the returned matrix are reflected in this matrix, and vice-versa.

The view contains the cells from index..index+width-1. and has view.size() == width. A view's legal coordinates are again zero based, as usual. In other words, legal coordinates of the view are 0 .. view.size()-1==width-1. As usual, any attempt to access a cell at other coordinates will throw an IndexOutOfBoundsException.

Parameters:

index - The index of the first cell.

width - The width of the range.

Returns:

the new view.

Throws:

java.lang.IndexOutOfBoundsException - if index<0 || width<0 || index+width>size().

viewSelection

public IntMatrix1D viewSelection(IntProcedure condition)

Constructs and returns a new selection view that is a matrix holding the cells matching the given condition. Applies the condition to each cell and takes only those cells where condition.apply(get(i)) yields true.

Example:

   // extract and view all cells with even value
   matrix = 0 1 2 3 
   matrix.viewSelection( 
      new IntProcedure() {
         public final boolean apply(int a) { return a % 2 == 0; }
      }
   );
   -->
   matrix ==  0 2
 
 

For further examples, see the package doc. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

Parameters:

condition - The condition to be matched.

Returns:

the new view.

viewSelection

public IntMatrix1D viewSelection(int[] indexes)

Constructs and returns a new selection view that is a matrix holding the indicated cells. There holds view.size() == indexes.length and view.get(i) == this.get(indexes[i]). Indexes can occur multiple times and can be in arbitrary order.

Example:

   this     = (0,0,8,0,7)
   indexes  = (0,2,4,2)
   -->
   view     = (0,8,7,8)
 
 

Note that modifying indexes after this call has returned has no effect on the view. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

Parameters:

indexes - The indexes of the cells that shall be visible in the new view. To indicate that all cells shall be visible, simply set this parameter to null.

Returns:

the new view.

Throws:

java.lang.IndexOutOfBoundsException - if !(0 <= indexes[i] < size()) for any i=0..indexes.length()-1.

viewSorted

public IntMatrix1D viewSorted()

Sorts the vector into ascending order, according to the natural ordering. This sort is guaranteed to be stable. For further information, see IntSorting.sort(IntMatrix1D). For more advanced sorting functionality, see IntSorting.

Returns:

a new sorted vector (matrix) view.

viewStrides

public IntMatrix1D viewStrides(int stride)

Constructs and returns a new stride view which is a sub matrix consisting of every i-th cell. More specifically, the view has size this.size()/stride holding cells this.get(i*stride) for all i = 0..size()/stride - 1.

Parameters:

stride - the step factor.

Returns:

the new view.

Throws:

java.lang.IndexOutOfBoundsException - if stride <= 0.

zDotProduct

public int zDotProduct(IntMatrix1D y)

Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]). Where x == this. Operates on cells at indexes 0 .. Math.min(size(),y.size()).

Parameters:

y - the second vector.

Returns:

the sum of products.

zDotProduct

public int zDotProduct(IntMatrix1D y,
                       int from,
                       int length)

Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]). Where x == this. Operates on cells at indexes from .. Min(size(),y.size(),from+length)-1.

Parameters:

y - the second vector.

from - the first index to be considered.

length - the number of cells to be considered.

Returns:

the sum of products; zero if from<0 || length<0.

zDotProduct

public int zDotProduct(IntMatrix1D y,
                       int from,
                       int length,
                       IntArrayList nonZeroIndexes)

Returns the dot product of two vectors x and y, which is Sum(x[i]*y[i]). Where x == this.

Parameters:

y - the second vector.

nonZeroIndexes - the indexes of cells in yhaving a non-zero value.

Returns:

the sum of products.

zSum

public int zSum()

Returns the sum of all cells; Sum( x[i] ).

Returns:

the sum.