DoubleMatrix3D
cern.colt.matrix.tdouble

## Class DoubleMatrix3D

• All Implemented Interfaces:
Serializable, Cloneable
Direct Known Subclasses:
DenseDoubleMatrix3D, SparseDoubleMatrix3D, WrapperDoubleMatrix3D

public abstract class DoubleMatrix3D
extends AbstractMatrix3D
Abstract base class for 3-d matrices holding double elements. First see the package summary and javadoc tree view to get the broad picture.

A matrix has a number of slices, rows and columns, which are assigned upon instance construction - The matrix's size is then slices()*rows()*columns(). Elements are accessed via [slice,row,column] coordinates. Legal coordinates range from [0,0,0] to [slices()-1,rows()-1,columns()-1]. Any attempt to access an element at a coordinate slice<0 || slice>=slices() || row<0 || row>=rows() || column<0 || column>=column() will throw an IndexOutOfBoundsException.

Note that this implementation is not synchronized.

See Also:
Serialized Form
• ### Method Detail

• #### aggregate

public double aggregate(DoubleDoubleFunction aggr,
DoubleFunction 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(slice,row,column)) ) and terminators are a(1) == f(get(0,0,0)), a(0)==Double.NaN.

Example:

cern.jet.math.Functions F = cern.jet.math.Functions.functions;
2 x 2 x 2 matrix
0 1
2 3

4 5
6 7

// Sum( x[slice,row,col]*x[slice,row,col] )
matrix.aggregate(F.plus,F.square);
--> 140

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:
DoubleFunctions
• #### aggregate

public double aggregate(DoubleDoubleFunction aggr,
DoubleFunction f,
DoubleProcedure cond)
Applies a function to each cell that satisfies a condition 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.
cond - a condition.
Returns:
the aggregated measure.
See Also:
DoubleFunctions
• #### aggregate

public double aggregate(DoubleDoubleFunction aggr,
DoubleFunction f,
IntArrayList sliceList,
IntArrayList rowList,
IntArrayList columnList)
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.
sliceList - slice indexes.
rowList - row indexes.
columnList - column indexes.
Returns:
the aggregated measure.
See Also:
DoubleFunctions
• #### aggregate

public double aggregate(DoubleMatrix3D other,
DoubleDoubleFunction aggr,
DoubleDoubleFunction 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(slice,row,column),other.get(slice,row,column)) ) and terminators are a(1) == f(get(0,0,0),other.get(0,0,0)), a(0)==Double.NaN.

Example:

cern.jet.math.Functions F = cern.jet.math.Functions.functions;
x = 2 x 2 x 2 matrix
0 1
2 3

4 5
6 7

y = 2 x 2 x 2 matrix
0 1
2 3

4 5
6 7

// Sum( x[slice,row,col] * y[slice,row,col] )
x.aggregate(y, F.plus, F.mult);
--> 140

// Sum( (x[slice,row,col] + y[slice,row,col])ˆ2 )
x.aggregate(y, F.plus, F.chain(F.square,F.plus));
--> 560

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:
IllegalArgumentException - if slices() != other.slices() || rows() != other.rows() || columns() != other.columns()
See Also:
DoubleFunctions
• #### assign

public DoubleMatrix3D assign(DoubleFunction function)
Assigns the result of a function to each cell; x[slice,row,col] = function(x[slice,row,col]).

Example:

matrix = 1 x 2 x 2 matrix
0.5 1.5
2.5 3.5

// change each cell to its sine
matrix.assign(cern.jet.math.Functions.sin);
-->
1 x 2 x 2 matrix
0.479426  0.997495
0.598472 -0.350783

For further examples, see the package doc.
Parameters:
function - a function object taking as argument the current cell's value.
Returns:
this (for convenience only).
See Also:
DoubleFunctions
• #### assign

public DoubleMatrix3D assign(DoubleProcedure cond,
double 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 DoubleMatrix3D assign(double 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 DoubleMatrix3D assign(double[] values)
Sets all cells to the state specified by values. values is required to have the form values[slice*row*column].

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:
IllegalArgumentException - if values.length != slices()*rows()*columns()
• #### assign

public DoubleMatrix3D assign(double[][][] values)
Sets all cells to the state specified by values. values is required to have the form values[slice][row][column] and have exactly the same number of slices, rows and columns 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:
IllegalArgumentException - if values.length != slices() || for any 0 <= slice < slices(): values[slice].length != rows() .
IllegalArgumentException - if for any 0 <= column < columns(): values[slice][row].length != columns() .
• #### assign

public DoubleMatrix3D assign(DoubleMatrix3D other)
Replaces all cell values of the receiver with the values of another matrix. Both matrices must have the same number of slices, rows and columns. 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:
IllegalArgumentException - if slices() != other.slices() || rows() != other.rows() || columns() != other.columns()
• #### assign

public DoubleMatrix3D assign(DoubleMatrix3D y,
DoubleDoubleFunction function)
Assigns the result of a function to each cell; x[row,col] = function(x[row,col],y[row,col]).

Example:

// assign x[row,col] = x[row,col]<sup>y[row,col]</sup>
m1 = 1 x 2 x 2 matrix
0 1
2 3

m2 = 1 x 2 x 2 matrix
0 2
4 6

m1.assign(m2, cern.jet.math.Functions.pow);
-->
m1 == 1 x 2 x 2 matrix
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:
IllegalArgumentException - if slices() != other.slices() || rows() != other.rows() || columns() != other.columns()
See Also:
DoubleFunctions
• #### assign

public DoubleMatrix3D assign(DoubleMatrix3D y,
DoubleDoubleFunction function,
IntArrayList sliceList,
IntArrayList rowList,
IntArrayList columnList)
Assigns the result of a function to all cells with a given indexes
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, *
sliceList - slice indexes.
rowList - row indexes.
columnList - column indexes.
Returns:
this (for convenience only).
Throws:
IllegalArgumentException - if slices() != other.slices() || rows() != other.rows() || columns() != other.columns()
See Also:
DoubleFunctions
• #### 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 DoubleMatrix3D 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 Object elements()
Returns the elements of this matrix.
Returns:
the elements
• #### equals

public boolean equals(double 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(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 DoubleMatrix3D object that has the same number of slices, rows and columns as the receiver and has exactly the same values at the same coordinates.
Overrides:
equals in class Object
Parameters:
obj - the object to compare with.
Returns:
true if the objects are the same; false otherwise.
• #### get

public double get(int slice,
int row,
int column)
Returns the matrix cell value at coordinate [slice,row,column].
Parameters:
slice - the index of the slice-coordinate.
row - the index of the row-coordinate.
column - the index of the column-coordinate.
Returns:
the value of the specified cell.
Throws:
IndexOutOfBoundsException - if slice<0 || slice>=slices() || row<0 || row>=rows() || column<0 || column>=column() .
• #### getMaxLocation

public double[] getMaxLocation()
Return maximum value of this matrix together with its location
Returns:
{ maximum_value, slice_location, row_location, column_location };
• #### getMinLocation

public double[] getMinLocation()
Returns minimum value of this matrix together with its location
Returns:
{ minimum_value, slice_location, row_location, column_location };
• #### getNegativeValues

public void getNegativeValues(IntArrayList sliceList,
IntArrayList rowList,
IntArrayList columnList,
DoubleArrayList 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:
sliceList - the list to be filled with slice indexes, can have any size.
rowList - the list to be filled with row indexes, can have any size.
columnList - the list to be filled with column indexes, can have any size.
valueList - the list to be filled with values, can have any size.
• #### getNonZeros

public void getNonZeros(IntArrayList sliceList,
IntArrayList rowList,
IntArrayList columnList,
DoubleArrayList 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 fill like: for (slice = 0..slices-1) for (row = 0..rows-1) for (column = 0..colums-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). For an example, see getNonZeros(IntArrayList,IntArrayList,IntArrayList,DoubleArrayList).

Parameters:
sliceList - the list to be filled with slice indexes, can have any size.
rowList - the list to be filled with row indexes, can have any size.
columnList - the list to be filled with column indexes, can have any size.
valueList - the list to be filled with values, can have any size.
• #### getPositiveValues

public void getPositiveValues(IntArrayList sliceList,
IntArrayList rowList,
IntArrayList columnList,
DoubleArrayList 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:
sliceList - the list to be filled with slice indexes, can have any size.
rowList - the list to be filled with row indexes, can have any size.
columnList - the list to be filled with column indexes, can have any size.
valueList - the list to be filled with values, can have any size.
• #### getQuick

public abstract double getQuick(int slice,
int row,
int column)
Returns the matrix cell value at coordinate [slice,row,column].

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): slice<0 || slice>=slices() || row<0 || row>=rows() || column<0 || column>=column().

Parameters:
slice - the index of the slice-coordinate.
row - the index of the row-coordinate.
column - the index of the column-coordinate.
Returns:
the value at the specified coordinate.
• #### like

public DoubleMatrix3D like()
Construct and returns a new empty matrix of the same dynamic type as the receiver, having the same number of slices, rows and columns. For example, if the receiver is an instance of type DenseDoubleMatrix3D the new matrix must also be of type DenseDoubleMatrix3D, if the receiver is an instance of type SparseDoubleMatrix3D the new matrix must also be of type SparseDoubleMatrix3D, 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 DoubleMatrix3D like(int slices,
int rows,
int columns)
Construct and returns a new empty matrix of the same dynamic type as the receiver, having the specified number of slices, rows and columns. For example, if the receiver is an instance of type DenseDoubleMatrix3D the new matrix must also be of type DenseDoubleMatrix3D, if the receiver is an instance of type SparseDoubleMatrix3D the new matrix must also be of type SparseDoubleMatrix3D, etc. In general, the new matrix should have internal parametrization as similar as possible.
Parameters:
slices - the number of slices the matrix shall have.
rows - the number of rows the matrix shall have.
columns - the number of columns the matrix shall have.
Returns:
a new empty matrix of the same dynamic type.
• #### like2D

public abstract DoubleMatrix2D like2D(int rows,
int columns)
Construct and returns a new 2-d matrix of the corresponding dynamic type, sharing the same cells. For example, if the receiver is an instance of type DenseDoubleMatrix3D the new matrix must also be of type DenseDoubleMatrix2D, if the receiver is an instance of type SparseDoubleMatrix3D the new matrix must also be of type SparseDoubleMatrix2D, 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.
• #### normalize

public void normalize()
Normalizes this matrix, i.e. makes the sum of all elements equal to 1.0 If the matrix contains negative elements then all the values are shifted to ensure non-negativity.
• #### set

public void set(int slice,
int row,
int column,
double value)
Sets the matrix cell at coordinate [slice,row,column] to the specified value.
Parameters:
slice - the index of the slice-coordinate.
row - the index of the row-coordinate.
column - the index of the column-coordinate.
value - the value to be filled into the specified cell.
Throws:
IndexOutOfBoundsException - if row<0 || row>=rows() || slice<0 || slice>=slices() || column<0 || column>=column() .
• #### setQuick

public abstract void setQuick(int slice,
int row,
int column,
double value)
Sets the matrix cell at coordinate [slice,row,column] 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): slice<0 || slice>=slices() || row<0 || row>=rows() || column<0 || column>=column().

Parameters:
slice - the index of the slice-coordinate.
row - the index of the row-coordinate.
column - the index of the column-coordinate.
value - the value to be filled into the specified cell.
• #### toArray

public double[][][] toArray()
Constructs and returns a 2-dimensional array containing the cell values. The returned array values has the form values[slice][row][column] and has the same number of slices, rows and columns as the receiver.

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

Returns:
an array filled with the values of the cells.
• #### toString

public String toString()
Returns a string representation using default formatting.
Overrides:
toString in class Object
See Also:
DoubleFormatter
• #### vectorize

public abstract DoubleMatrix1D vectorize()
Returns a vector obtained by stacking the columns of each slice of the matrix on top of one another.
Returns:
a vector obtained by stacking the columns of each slice of the matrix on top of one another.
• #### viewColumn

public DoubleMatrix2D viewColumn(int column)
Constructs and returns a new 2-dimensional slice view representing the slices and rows of the given column. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

To obtain a slice view on subranges, construct a sub-ranging view ( view().part(...)), then apply this method to the sub-range view. To obtain 1-dimensional views, apply this method, then apply another slice view (methods viewColumn, viewRow) on the intermediate 2-dimensional view. To obtain 1-dimensional views on subranges, apply both steps.

Parameters:
column - the index of the column to fix.
Returns:
a new 2-dimensional slice view.
Throws:
IndexOutOfBoundsException - if column < 0 || column >= columns().
See Also:
viewSlice(int), viewRow(int)
• #### viewColumnFlip

public DoubleMatrix3D viewColumnFlip()
Constructs and returns a new flip view along the column axis. What used to be column 0 is now column columns()-1, ..., what used to be column columns()-1 is now column 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.
See Also:
viewSliceFlip(), viewRowFlip()
• #### viewDice

public DoubleMatrix3D viewDice(int axis0,
int axis1,
int axis2)
Constructs and returns a new dice view; Swaps dimensions (axes); Example: 3 x 4 x 5 matrix --> 4 x 3 x 5 matrix. The view has dimensions exchanged; what used to be one axis is now another, in all desired permutations. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.
Parameters:
axis0 - the axis that shall become axis 0 (legal values 0..2).
axis1 - the axis that shall become axis 1 (legal values 0..2).
axis2 - the axis that shall become axis 2 (legal values 0..2).
Returns:
a new dice view.
Throws:
IllegalArgumentException - if some of the parameters are equal or not in range 0..2.
• #### viewPart

public DoubleMatrix3D viewPart(int slice,
int row,
int column,
int depth,
int height,
int width)
Constructs and returns a new sub-range view that is a depth x height x width sub matrix starting at [slice,row,column]; Equivalent to view().part(slice,row,column,depth,height,width); Provided for convenience only. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.
Parameters:
slice - The index of the slice-coordinate.
row - The index of the row-coordinate.
column - The index of the column-coordinate.
depth - The depth of the box.
height - The height of the box.
width - The width of the box.
Returns:
the new view.
Throws:
IndexOutOfBoundsException - if slice<0 || depth<0 || slice+depth>slices() || row<0 || height<0 || row+height>rows() || column<0 || width<0 || column+width>columns()
• #### viewRow

public DoubleMatrix2D viewRow(int row)
Constructs and returns a new 2-dimensional slice view representing the slices and columns of the given row. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

To obtain a slice view on subranges, construct a sub-ranging view ( view().part(...)), then apply this method to the sub-range view. To obtain 1-dimensional views, apply this method, then apply another slice view (methods viewColumn, viewRow) on the intermediate 2-dimensional view. To obtain 1-dimensional views on subranges, apply both steps.

Parameters:
row - the index of the row to fix.
Returns:
a new 2-dimensional slice view.
Throws:
IndexOutOfBoundsException - if row < 0 || row >= row().
See Also:
viewSlice(int), viewColumn(int)
• #### viewRowFlip

public DoubleMatrix3D viewRowFlip()
Constructs and returns a new flip view along the row axis. What used to be row 0 is now row rows()-1, ..., what used to be row rows()-1 is now row 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.
See Also:
viewSliceFlip(), viewColumnFlip()
• #### viewSelection

public DoubleMatrix3D viewSelection(DoubleMatrix2DProcedure condition)
Constructs and returns a new selection view that is a matrix holding all slices matching the given condition. Applies the condition to each slice and takes only those where condition.apply(viewSlice(i)) yields true. To match rows or columns, use a dice view.

Example:

// extract and view all slices which have an aggregate sum > 1000
matrix.viewSelection(new DoubleMatrix2DProcedure() {
public final boolean apply(DoubleMatrix2D m) {
return m.zSum > 1000;
}
});

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 DoubleMatrix3D viewSelection(int[] sliceIndexes,
int[] rowIndexes,
int[] columnIndexes)
Constructs and returns a new selection view that is a matrix holding the indicated cells. There holds view.slices() == sliceIndexes.length, view.rows() == rowIndexes.length, view.columns() == columnIndexes.length and view.get(k,i,j) == this.get(sliceIndexes[k],rowIndexes[i],columnIndexes[j]) . Indexes can occur multiple times and can be in arbitrary order. For an example see DoubleMatrix2D.viewSelection(int[],int[]).

Note that modifying the index arguments 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:
sliceIndexes - The slices of the cells that shall be visible in the new view. To indicate that all slices shall be visible, simply set this parameter to null.
rowIndexes - The rows of the cells that shall be visible in the new view. To indicate that all rows shall be visible, simply set this parameter to null.
columnIndexes - The columns of the cells that shall be visible in the new view. To indicate that all columns shall be visible, simply set this parameter to null.
Returns:
the new view.
Throws:
IndexOutOfBoundsException - if !(0 <= sliceIndexes[i] < slices()) for any i=0..sliceIndexes.length()-1.
IndexOutOfBoundsException - if !(0 <= rowIndexes[i] < rows()) for any i=0..rowIndexes.length()-1.
IndexOutOfBoundsException - if !(0 <= columnIndexes[i] < columns()) for any i=0..columnIndexes.length()-1.
• #### viewSlice

public DoubleMatrix2D viewSlice(int slice)
Constructs and returns a new 2-dimensional slice view representing the rows and columns of the given slice. The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

To obtain a slice view on subranges, construct a sub-ranging view ( view().part(...)), then apply this method to the sub-range view. To obtain 1-dimensional views, apply this method, then apply another slice view (methods viewColumn, viewRow) on the intermediate 2-dimensional view. To obtain 1-dimensional views on subranges, apply both steps.

Parameters:
slice - the index of the slice to fix.
Returns:
a new 2-dimensional slice view.
Throws:
IndexOutOfBoundsException - if slice < 0 || slice >= slices().
See Also:
viewRow(int), viewColumn(int)
• #### viewSliceFlip

public DoubleMatrix3D viewSliceFlip()
Constructs and returns a new flip view along the slice axis. What used to be slice 0 is now slice slices()-1, ..., what used to be slice slices()-1 is now slice 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.
See Also:
viewRowFlip(), viewColumnFlip()
• #### viewSorted

public DoubleMatrix3D viewSorted(int row,
int column)
Sorts the matrix slices into ascending order, according to the natural ordering of the matrix values in the given [row,column] position. This sort is guaranteed to be stable. For further information, see DoubleSorting.sort(DoubleMatrix3D,int,int) . For more advanced sorting functionality, see DoubleSorting.
Returns:
a new sorted vector (matrix) view.
Throws:
IndexOutOfBoundsException - if row < 0 || row >= rows() || column < 0 || column >= columns() .
• #### viewStrides

public DoubleMatrix3D viewStrides(int sliceStride,
int rowStride,
int columnStride)
Constructs and returns a new stride view which is a sub matrix consisting of every i-th cell. More specifically, the view has this.slices()/sliceStride slices and this.rows()/rowStride rows and this.columns()/columnStride columns holding cells this.get(k*sliceStride,i*rowStride,j*columnStride) for all k = 0..slices()/sliceStride - 1, i = 0..rows()/rowStride - 1, j = 0..columns()/columnStride - 1 . The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.
Parameters:
sliceStride - the slice step factor.
rowStride - the row step factor.
columnStride - the column step factor.
Returns:
a new view.
Throws:
IndexOutOfBoundsException - if sliceStride<=0 || rowStride<=0 || columnStride<=0 .
• #### zAssign27Neighbors

public void zAssign27Neighbors(DoubleMatrix3D B,
Double27Function function)
27 neighbor stencil transformation. For efficient finite difference operations. Applies a function to a moving 3 x 3 x 3 window. Does nothing if rows() < 3 || columns() < 3 || slices() < 3.
B[k,i,j] = function.apply(
A[k-1,i-1,j-1], A[k-1,i-1,j], A[k-1,i-1,j+1],
A[k-1,i,  j-1], A[k-1,i,  j], A[k-1,i,  j+1],
A[k-1,i+1,j-1], A[k-1,i+1,j], A[k-1,i+1,j+1],

A[k  ,i-1,j-1], A[k  ,i-1,j], A[k  ,i-1,j+1],
A[k  ,i,  j-1], A[k  ,i,  j], A[k  ,i,  j+1],
A[k  ,i+1,j-1], A[k  ,i+1,j], A[k  ,i+1,j+1],

A[k+1,i-1,j-1], A[k+1,i-1,j], A[k+1,i-1,j+1],
A[k+1,i,  j-1], A[k+1,i,  j], A[k+1,i,  j+1],
A[k+1,i+1,j-1], A[k+1,i+1,j], A[k+1,i+1,j+1]
)

x x x -     - x x x     - - - -
x o x -     - x o x     - - - -
x x x -     - x x x ... - x x x
- - - -     - - - -     - x o x
- - - -     - - - -     - x x x

Make sure that cells of this and B do not overlap. In case of overlapping views, behaviour is unspecified.

Example:

final double alpha = 0.25; final double beta = 0.75;

cern.colt.function.Double27Function f = new
cern.colt.function.Double27Function() {    public final
double apply(       double a000, double
a001, double a002,       double a010,
double a011, double a012,       double
a020, double a021, double a022,

double a100, double a101, double
a102,       double a110, double a111,
double a112,       double a120, double
a121, double a122,

double a200, double a201, double
a202,       double a210, double a211,
double a212,       double a220, double
a221, double a222) {
return beta*a111 +
alpha*(a000 + ... + a222);       } };
A.zAssign27Neighbors(B,f);

Parameters:
B - the matrix to hold the results.
function - the function to be applied to the 27 cells.
Throws:
NullPointerException - if function==null.
IllegalArgumentException - if rows() != B.rows() || columns() != B.columns() || slices() != B.slices() .
• #### zSum

public double zSum()
Returns the sum of all cells; Sum( x[i,j,k] ).
Returns:
the sum.

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