/*
Copyright (c) 1999 CERN - European Organization for Nuclear Research.
Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose 
is hereby granted without fee, provided that the above copyright notice appear in all copies and 
that both that copyright notice and this permission notice appear in supporting documentation. 
CERN makes no representations about the suitability of this software for any purpose. 
It is provided "as is" without expressed or implied warranty.
*/
package cern.colt.matrix;

import cern.colt.list.DoubleArrayList;
import cern.colt.list.IntArrayList;
import cern.colt.matrix.impl.AbstractMatrix3D;
/**
Abstract base class for 3-d matrices holding <tt>double</tt> elements.
First see the <a href="package-summary.html">package summary</a> and javadoc <a href="package-tree.html">tree view</a> to get the broad picture.
<p>
A matrix has a number of slices, rows and columns, which are assigned upon instance construction - The matrix's size is then <tt>slices()*rows()*columns()</tt>.
Elements are accessed via <tt>[slice,row,column]</tt> coordinates.
Legal coordinates range from <tt>[0,0,0]</tt> to <tt>[slices()-1,rows()-1,columns()-1]</tt>.
Any attempt to access an element at a coordinate <tt>slice&lt;0 || slice&gt;=slices() || row&lt;0 || row&gt;=rows() || column&lt;0 || column&gt;=column()</tt> will throw an <tt>IndexOutOfBoundsException</tt>.
<p>
<b>Note</b> that this implementation is not synchronized.

@author wolfgang.hoschek@cern.ch
@version 1.0, 09/24/99
*/
public abstract class DoubleMatrix3D extends AbstractMatrix3D {
/**
 * Makes this class non instantiable, but still let's others inherit from it.
 */
protected DoubleMatrix3D() {}
/**
Applies a function to each cell and aggregates the results.
Returns a value <tt>v</tt> such that <tt>v==a(size())</tt> where <tt>a(i) == aggr( a(i-1), f(get(slice,row,column)) )</tt> and terminators are <tt>a(1) == f(get(0,0,0)), a(0)==Double.NaN</tt>.
<p>
<b>Example:</b>
<pre>
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
</pre>
For further examples, see the <a href="package-summary.html#FunctionObjects">package doc</a>.

@param aggr an aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.
@param f a function transforming the current cell value.
@return the aggregated measure.
@see cern.jet.math.Functions
*/
public double aggregate(cern.colt.function.DoubleDoubleFunction aggr, cern.colt.function.DoubleFunction f) {
	if (size()==0) return Double.NaN;
	double a = f.apply(getQuick(slices-1,rows-1,columns-1));
	int d = 1; // last cell already done
	for (int slice=slices; --slice >= 0; ) {
		for (int row=rows; --row >= 0; ) {
			for (int column=columns-d; --column >= 0; ) {
				a = aggr.apply(a, f.apply(getQuick(slice,row,column)));
			}
			d = 0;
		}
	}
	return a;
}
/**
Applies a function to each corresponding cell of two matrices and aggregates the results.
Returns a value <tt>v</tt> such that <tt>v==a(size())</tt> where <tt>a(i) == aggr( a(i-1), f(get(slice,row,column),other.get(slice,row,column)) )</tt> and terminators are <tt>a(1) == f(get(0,0,0),other.get(0,0,0)), a(0)==Double.NaN</tt>.
<p>
<b>Example:</b>
<pre>
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])^2 )
x.aggregate(y, F.plus, F.chain(F.square,F.plus));
--> 560
</pre>
For further examples, see the <a href="package-summary.html#FunctionObjects">package doc</a>.

@param aggr an aggregation function taking as first argument the current aggregation and as second argument the transformed current cell values.
@param f a function transforming the current cell values.
@return the aggregated measure.
@throws	IllegalArgumentException if <tt>slices() != other.slices() || rows() != other.rows() || columns() != other.columns()</tt>
@see cern.jet.math.Functions
*/
public double aggregate(DoubleMatrix3D other, cern.colt.function.DoubleDoubleFunction aggr, cern.colt.function.DoubleDoubleFunction f) {
	checkShape(other);
	if (size()==0) return Double.NaN;
	double a = f.apply(getQuick(slices-1,rows-1,columns-1),other.getQuick(slices-1,rows-1,columns-1));
	int d = 1; // last cell already done
	for (int slice=slices; --slice >= 0; ) {
		for (int row=rows; --row >= 0; ) {
			for (int column=columns-d; --column >= 0; ) {
				a = aggr.apply(a, f.apply(getQuick(slice,row,column), other.getQuick(slice,row,column)));
			}
			d = 0;
		}
	}
	return a;
}
/**
 * Sets all cells to the state specified by <tt>values</tt>.
 * <tt>values</tt> is required to have the form <tt>values[slice][row][column]</tt>
 * and have exactly the same number of slices, rows and columns as the receiver.
 * <p>
 * The values are copied. So subsequent changes in <tt>values</tt> are not reflected in the matrix, and vice-versa.
 *
 * @param    values the values to be filled into the cells.
 * @return <tt>this</tt> (for convenience only).
 * @throws IllegalArgumentException if <tt>values.length != slices() || for any 0 &lt;= slice &lt; slices(): values[slice].length != rows()</tt>.
 * @throws IllegalArgumentException if <tt>for any 0 &lt;= column &lt; columns(): values[slice][row].length != columns()</tt>.
 */
public DoubleMatrix3D assign(double[][][] values) {
	if (values.length != slices) throw new IllegalArgumentException("Must have same number of slices: slices="+values.length+"slices()="+slices());
	for (int slice=slices; --slice >= 0;) {
		double[][] currentSlice = values[slice];
		if (currentSlice.length != rows) throw new IllegalArgumentException("Must have same number of rows in every slice: rows="+currentSlice.length+"rows()="+rows());
		for (int row=rows; --row >= 0;) {
			double[] currentRow = currentSlice[row];
			if (currentRow.length != columns) throw new IllegalArgumentException("Must have same number of columns in every row: columns="+currentRow.length+"columns()="+columns());
			for (int column=columns; --column >= 0;) {
				setQuick(slice,row,column,currentRow[column]);
			}
		}
	}
	return this;
}
/**
 * Sets all cells to the state specified by <tt>value</tt>.
 * @param    value the value to be filled into the cells.
 * @return <tt>this</tt> (for convenience only).
 */
public DoubleMatrix3D assign(double value) {
	for (int slice=slices; --slice >= 0;) {
		for (int row=rows; --row >= 0;) {
			for (int column=columns; --column >= 0;) {
				setQuick(slice,row,column,value);
			}
		}
	}
	return this;
}
/**
Assigns the result of a function to each cell; <tt>x[slice,row,col] = function(x[slice,row,col])</tt>.
<p>
<b>Example:</b>
<pre>
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
</pre>
For further examples, see the <a href="package-summary.html#FunctionObjects">package doc</a>.

@param function a function object taking as argument the current cell's value.
@return <tt>this</tt> (for convenience only).
@see cern.jet.math.Functions
*/
public DoubleMatrix3D assign(cern.colt.function.DoubleFunction function) {
	for (int slice=slices; --slice >= 0; ) {
		for (int row=rows; --row >= 0; ) {
			for (int column=columns; --column >= 0; ) {
				setQuick(slice,row,column, function.apply(getQuick(slice,row,column)));
			}
		}
	}
	return this;
}
/**
 * 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 <i>as if</i> using an intermediate auxiliary deep copy of <tt>other</tt>.
 *
 * @param     other   the source matrix to copy from (may be identical to the receiver).
 * @return <tt>this</tt> (for convenience only).
 * @throws	IllegalArgumentException if <tt>slices() != other.slices() || rows() != other.rows() || columns() != other.columns()</tt>
 */
public DoubleMatrix3D assign(DoubleMatrix3D other) {
	if (other==this) return this;
	checkShape(other);
	if (haveSharedCells(other)) other = other.copy();
	
	for (int slice=slices; --slice >= 0;) {
		for (int row=rows; --row >= 0;) {
			for (int column=columns; --column >= 0;) {
				setQuick(slice,row,column,other.getQuick(slice,row,column));
			}
		}
	}
	return this;
}
/**
Assigns the result of a function to each cell; <tt>x[row,col] = function(x[row,col],y[row,col])</tt>.
<p>
<b>Example:</b>
<pre>
// 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
</pre>
For further examples, see the <a href="package-summary.html#FunctionObjects">package doc</a>.

@param y the secondary matrix to operate on.
@param function a function object taking as first argument the current cell's value of <tt>this</tt>,
and as second argument the current cell's value of <tt>y</tt>,
@return <tt>this</tt> (for convenience only).
@throws	IllegalArgumentException if <tt>slices() != other.slices() || rows() != other.rows() || columns() != other.columns()</tt>
@see cern.jet.math.Functions
*/
public DoubleMatrix3D assign(DoubleMatrix3D y, cern.colt.function.DoubleDoubleFunction function) {
	checkShape(y);
	for (int slice=slices; --slice >= 0; ) {
		for (int row=rows; --row >= 0; ) {
			for (int column=columns; --column >= 0; ) {
				setQuick(slice,row,column, function.apply(getQuick(slice,row,column), y.getQuick(slice,row,column)));
			}
		}
	}
	return this;
}
/**
 * Returns the number of cells having non-zero values; ignores tolerance.
 */
public int cardinality() {
	int cardinality = 0;
	for (int slice=slices; --slice >= 0;) {
		for (int row=rows; --row >= 0;) {
			for (int column=columns; --column >= 0;) {
				if (getQuick(slice,row,column) != 0) cardinality++;
			}
		}
	}
	return cardinality;
}
/**
 * Constructs and returns a deep copy of the receiver.
 * <p>
 * <b>Note that the returned matrix is an independent deep copy.</b>
 * The returned matrix is not backed by this matrix, so changes in the returned matrix are not reflected in this matrix, and vice-versa. 
 *
 * @return  a deep copy of the receiver.
 */
public DoubleMatrix3D copy() {
	return like().assign(this);
}
/**
 * Returns whether all cells are equal to the given value.
 *
 * @param     value the value to test against.
 * @return    <tt>true</tt> if all cells are equal to the given value, <tt>false</tt> otherwise.
 */
public boolean equals(double value) {
	return cern.colt.matrix.linalg.Property.DEFAULT.equals(this,value);
}
/**
 * Compares this object against the specified object.
 * The result is <code>true</code> if and only if the argument is 
 * not <code>null</code> and is at least a <code>DoubleMatrix3D</code> object
 * that has the same number of slices, rows and columns as the receiver and 
 * has exactly the same values at the same coordinates.
 * @param   obj   the object to compare with.
 * @return  <code>true</code> if the objects are the same;
 *          <code>false</code> otherwise.
 */
public boolean equals(Object obj) {
	if (this == obj) return true;
	if (obj == null) return false;
	if (!(obj instanceof DoubleMatrix3D)) return false;

	return cern.colt.matrix.linalg.Property.DEFAULT.equals(this,(DoubleMatrix3D) obj);
}
/**
 * Returns the matrix cell value at coordinate <tt>[slice,row,column]</tt>.
 *
 * @param     slice   the index of the slice-coordinate.
 * @param     row   the index of the row-coordinate.
 * @param     column   the index of the column-coordinate.
 * @return    the value of the specified cell.
 * @throws	IndexOutOfBoundsException if <tt>slice&lt;0 || slice&gt;=slices() || row&lt;0 || row&gt;=rows() || column&lt;0 || column&gt;=column()</tt>.
 */
public double get(int slice, int row, int column) {
	if (slice<0 || slice>=slices || row<0 || row>=rows || column<0 || column>=columns) throw new IndexOutOfBoundsException("slice:"+slice+", row:"+row+", column:"+column);
	return getQuick(slice,row,column);
}
/**
 * Returns the content of this matrix if it is a wrapper; or <tt>this</tt> otherwise.
 * Override this method in wrappers.
 */
protected DoubleMatrix3D getContent() {
	return this;
}
/**
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.
<p>
In general, fill order is <i>unspecified</i>.
This implementation fill like: <tt>for (slice = 0..slices-1) for (row = 0..rows-1) for (column = 0..colums-1) do ... </tt>.
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 {@link DoubleMatrix2D#getNonZeros(IntArrayList,IntArrayList,DoubleArrayList)}.

@param sliceList the list to be filled with slice indexes, can have any size.
@param rowList the list to be filled with row indexes, can have any size.
@param columnList the list to be filled with column indexes, can have any size.
@param valueList the list to be filled with values, can have any size.
*/
public void getNonZeros(IntArrayList sliceList, IntArrayList rowList, IntArrayList columnList, DoubleArrayList valueList) {
	sliceList.clear(); 
	rowList.clear(); 
	columnList.clear(); 
	valueList.clear();
	int s = slices;
	int r = rows;
	int c = columns;
	for (int slice=0; slice < s; slice++) {
		for (int row=0; row < r; row++) {
			for (int column=0; column < c; column++) {
				double value = getQuick(slice,row,column);
				if (value != 0) {
					sliceList.add(slice);
					rowList.add(row);
					columnList.add(column);
					valueList.add(value);
				}
			}
		}
	}
}
/**
 * Returns the matrix cell value at coordinate <tt>[slice,row,column]</tt>.
 *
 * <p>Provided with invalid parameters this method may return invalid objects without throwing any exception.
 * <b>You should only use this method when you are absolutely sure that the coordinate is within bounds.</b>
 * Precondition (unchecked): <tt>slice&lt;0 || slice&gt;=slices() || row&lt;0 || row&gt;=rows() || column&lt;0 || column&gt;=column()</tt>.
 *
 * @param     slice   the index of the slice-coordinate.
 * @param     row   the index of the row-coordinate.
 * @param     column   the index of the column-coordinate.
 * @return    the value at the specified coordinate.
 */
public abstract double getQuick(int slice, int row, int column);
/**
 * Returns <tt>true</tt> if both matrices share at least one identical cell.
 */
protected boolean haveSharedCells(DoubleMatrix3D other) {
	if (other==null) return false;
	if (this==other) return true;
	return getContent().haveSharedCellsRaw(other.getContent());
}	
/**
 * Returns <tt>true</tt> if both matrices share at least one identical cell.
 */
protected boolean haveSharedCellsRaw(DoubleMatrix3D other) {
	return false;
}	
/**
 * Construct and returns a new empty matrix <i>of the same dynamic type</i> as the receiver, having the same number of slices, rows and columns.
 * For example, if the receiver is an instance of type <tt>DenseDoubleMatrix3D</tt> the new matrix must also be of type <tt>DenseDoubleMatrix3D</tt>,
 * if the receiver is an instance of type <tt>SparseDoubleMatrix3D</tt> the new matrix must also be of type <tt>SparseDoubleMatrix3D</tt>, etc.
 * In general, the new matrix should have internal parametrization as similar as possible.
 *
 * @return  a new empty matrix of the same dynamic type.
 */
public DoubleMatrix3D like() {
	return like(slices,rows,columns);
}
/**
 * Construct and returns a new empty matrix <i>of the same dynamic type</i> as the receiver, having the specified number of slices, rows and columns.
 * For example, if the receiver is an instance of type <tt>DenseDoubleMatrix3D</tt> the new matrix must also be of type <tt>DenseDoubleMatrix3D</tt>,
 * if the receiver is an instance of type <tt>SparseDoubleMatrix3D</tt> the new matrix must also be of type <tt>SparseDoubleMatrix3D</tt>, etc.
 * In general, the new matrix should have internal parametrization as similar as possible.
 *
 * @param slices the number of slices the matrix shall have.
 * @param rows the number of rows the matrix shall have.
 * @param columns the number of columns the matrix shall have.
 * @return  a new empty matrix of the same dynamic type.
 */
public abstract DoubleMatrix3D like(int slices, int rows, int columns);
/**
 * Construct and returns a new 2-d matrix <i>of the corresponding dynamic type</i>, sharing the same cells.
 * For example, if the receiver is an instance of type <tt>DenseDoubleMatrix3D</tt> the new matrix must also be of type <tt>DenseDoubleMatrix2D</tt>,
 * if the receiver is an instance of type <tt>SparseDoubleMatrix3D</tt> the new matrix must also be of type <tt>SparseDoubleMatrix2D</tt>, etc.
 *
 * @param rows the number of rows the matrix shall have.
 * @param columns the number of columns the matrix shall have.
 * @param rowZero the position of the first element.
 * @param columnZero the position of the first element.
 * @param rowStride the number of elements between two rows, i.e. <tt>index(i+1,j)-index(i,j)</tt>.
 * @param columnStride the number of elements between two columns, i.e. <tt>index(i,j+1)-index(i,j)</tt>.
 * @return  a new matrix of the corresponding dynamic type.
 */
protected abstract DoubleMatrix2D like2D(int rows, int columns, int rowZero, int columnZero, int rowStride, int columnStride);
/**
 * Sets the matrix cell at coordinate <tt>[slice,row,column]</tt> to the specified value.
 *
 * @param     slice   the index of the slice-coordinate.
 * @param     row   the index of the row-coordinate.
 * @param     column   the index of the column-coordinate.
 * @param    value the value to be filled into the specified cell.
 * @throws	IndexOutOfBoundsException if <tt>row&lt;0 || row&gt;=rows() || slice&lt;0 || slice&gt;=slices() || column&lt;0 || column&gt;=column()</tt>.
 */
public void set(int slice, int row, int column, double value) {
	if (slice<0 || slice>=slices || row<0 || row>=rows || column<0 || column>=columns) throw new IndexOutOfBoundsException("slice:"+slice+", row:"+row+", column:"+column);
	setQuick(slice,row,column,value);
}
/**
 * Sets the matrix cell at coordinate <tt>[slice,row,column]</tt> to the specified value.
 *
 * <p>Provided with invalid parameters this method may access illegal indexes without throwing any exception.
 * <b>You should only use this method when you are absolutely sure that the coordinate is within bounds.</b>
 * Precondition (unchecked): <tt>slice&lt;0 || slice&gt;=slices() || row&lt;0 || row&gt;=rows() || column&lt;0 || column&gt;=column()</tt>.
 *
 * @param     slice   the index of the slice-coordinate.
 * @param     row   the index of the row-coordinate.
 * @param     column   the index of the column-coordinate.
 * @param    value the value to be filled into the specified cell.
 */
public abstract void setQuick(int slice, int row, int column, double value);
/**
 * Constructs and returns a 2-dimensional array containing the cell values.
 * The returned array <tt>values</tt> has the form <tt>values[slice][row][column]</tt>
 * and has the same number of slices, rows and columns as the receiver.
 * <p>
 * The values are copied. So subsequent changes in <tt>values</tt> are not reflected in the matrix, and vice-versa.
 *
 * @return an array filled with the values of the cells.
 */
public double[][][] toArray() {
	double[][][] values = new double[slices][rows][columns];
	for (int slice=slices; --slice >= 0;) {
		double[][] currentSlice = values[slice];
		for (int row=rows; --row >= 0;) {
			double[] currentRow = currentSlice[row];
			for (int column=columns; --column >= 0;) {
				currentRow[column] = getQuick(slice,row,column);
			}
		}
	}
	return values;
}
/**
 * Returns a string representation using default formatting.
 * @see cern.colt.matrix.doublealgo.Formatter
 */
/* freehep-jaida
public String toString() {
	return new cern.colt.matrix.doublealgo.Formatter().toString(this);
}
*/
/**
 * Constructs and returns a new view equal to the receiver.
 * The view is a shallow clone. Calls <code>clone()</code> and casts the result.
 * <p>
 * <b>Note that the view is not a deep copy.</b>
 * The returned matrix is backed by this matrix, so changes in the returned matrix are reflected in this matrix, and vice-versa. 
 * <p>
 * Use {@link #copy()} if you want to construct an independent deep copy rather than a new view.
 *
 * @return  a new view of the receiver.
 */
protected DoubleMatrix3D view() {
	return (DoubleMatrix3D) clone();
}
/**
Constructs and returns a new 2-dimensional <i>slice view</i> 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.
<p>
To obtain a slice view on subranges, construct a sub-ranging view (<tt>view().part(...)</tt>), then apply this method to the sub-range view.
To obtain 1-dimensional views, apply this method, then apply another slice view (methods <tt>viewColumn</tt>, <tt>viewRow</tt>) on the intermediate 2-dimensional view.
To obtain 1-dimensional views on subranges, apply both steps.

@param column the index of the column to fix.
@return a new 2-dimensional slice view.
@throws IndexOutOfBoundsException if <tt>column < 0 || column >= columns()</tt>.
@see #viewSlice(int)
@see #viewRow(int)
*/
public DoubleMatrix2D viewColumn(int column) {
	checkColumn(column);
	int sliceRows = this.slices;
	int sliceColumns = this.rows;

	//int sliceOffset = index(0,0,column);
	int sliceRowZero = sliceZero;
	int sliceColumnZero = rowZero + _columnOffset(_columnRank(column));
	
	int sliceRowStride = this.sliceStride;
	int sliceColumnStride = this.rowStride;
	return like2D(sliceRows,sliceColumns,sliceRowZero,sliceColumnZero,sliceRowStride,sliceColumnStride);
}
/**
Constructs and returns a new <i>flip view</i> along the column axis.
What used to be column <tt>0</tt> is now column <tt>columns()-1</tt>, ..., what used to be column <tt>columns()-1</tt> is now column <tt>0</tt>.
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

@return a new flip view.
@see #viewSliceFlip()
@see #viewRowFlip()
*/
public DoubleMatrix3D viewColumnFlip() {
	return (DoubleMatrix3D) (view().vColumnFlip());
}
/**
Constructs and returns a new <i>dice view</i>; 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.

@param axis0 the axis that shall become axis 0 (legal values 0..2).
@param axis1 the axis that shall become axis 1 (legal values 0..2).
@param axis2 the axis that shall become axis 2 (legal values 0..2).
@return a new dice view.
@throws IllegalArgumentException if some of the parameters are equal or not in range 0..2.
*/
public DoubleMatrix3D viewDice(int axis0, int axis1, int axis2) {
	return (DoubleMatrix3D) (view().vDice(axis0,axis1,axis2));
}
/**
Constructs and returns a new <i>sub-range view</i> that is a <tt>depth x height x width</tt> sub matrix starting at <tt>[slice,row,column]</tt>;
Equivalent to <tt>view().part(slice,row,column,depth,height,width)</tt>; 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. 

@param     slice   The index of the slice-coordinate.
@param     row   The index of the row-coordinate.
@param     column   The index of the column-coordinate.
@param     depth   The depth of the box.
@param     height   The height of the box.
@param     width   The width of the box.
@throws	IndexOutOfBoundsException if <tt>slice<0 || depth<0 || slice+depth>slices() || row<0 || height<0 || row+height>rows() || column<0 || width<0 || column+width>columns()</tt>
@return the new view.
		
*/
public DoubleMatrix3D viewPart(int slice, int row, int column, int depth, int height, int width) {
	return (DoubleMatrix3D) (view().vPart(slice,row,column,depth,height,width));
}
/**
Constructs and returns a new 2-dimensional <i>slice view</i> 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.
<p>
To obtain a slice view on subranges, construct a sub-ranging view (<tt>view().part(...)</tt>), then apply this method to the sub-range view.
To obtain 1-dimensional views, apply this method, then apply another slice view (methods <tt>viewColumn</tt>, <tt>viewRow</tt>) on the intermediate 2-dimensional view.
To obtain 1-dimensional views on subranges, apply both steps.

@param row the index of the row to fix.
@return a new 2-dimensional slice view.
@throws IndexOutOfBoundsException if <tt>row < 0 || row >= row()</tt>.
@see #viewSlice(int)
@see #viewColumn(int)
*/
public DoubleMatrix2D viewRow(int row) {
	checkRow(row);
	int sliceRows = this.slices;
	int sliceColumns = this.columns;
	
	//int sliceOffset = index(0,row,0);
	int sliceRowZero = sliceZero ;
	int sliceColumnZero = columnZero + _rowOffset(_rowRank(row));
	
	int sliceRowStride = this.sliceStride;
	int sliceColumnStride = this.columnStride;
	return like2D(sliceRows,sliceColumns,sliceRowZero,sliceColumnZero,sliceRowStride,sliceColumnStride);
}
/**
Constructs and returns a new <i>flip view</i> along the row axis.
What used to be row <tt>0</tt> is now row <tt>rows()-1</tt>, ..., what used to be row <tt>rows()-1</tt> is now row <tt>0</tt>.
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

@return a new flip view.
@see #viewSliceFlip()
@see #viewColumnFlip()
*/
public DoubleMatrix3D viewRowFlip() {
	return (DoubleMatrix3D) (view().vRowFlip());
}
/**
Constructs and returns a new <i>selection view</i> that is a matrix holding the indicated cells.
There holds <tt>view.slices() == sliceIndexes.length, view.rows() == rowIndexes.length, view.columns() == columnIndexes.length</tt> and 
<tt>view.get(k,i,j) == this.get(sliceIndexes[k],rowIndexes[i],columnIndexes[j])</tt>.
Indexes can occur multiple times and can be in arbitrary order.
For an example see {@link DoubleMatrix2D#viewSelection(int[],int[])}.
<p>
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. 

@param  sliceIndexes   The slices of the cells that shall be visible in the new view. To indicate that <i>all</i> slices shall be visible, simply set this parameter to <tt>null</tt>.
@param  rowIndexes   The rows of the cells that shall be visible in the new view. To indicate that <i>all</i> rows shall be visible, simply set this parameter to <tt>null</tt>.
@param  columnIndexes   The columns of the cells that shall be visible in the new view. To indicate that <i>all</i> columns shall be visible, simply set this parameter to <tt>null</tt>.
@return the new view.
@throws IndexOutOfBoundsException if <tt>!(0 <= sliceIndexes[i] < slices())</tt> for any <tt>i=0..sliceIndexes.length()-1</tt>.
@throws IndexOutOfBoundsException if <tt>!(0 <= rowIndexes[i] < rows())</tt> for any <tt>i=0..rowIndexes.length()-1</tt>.
@throws IndexOutOfBoundsException if <tt>!(0 <= columnIndexes[i] < columns())</tt> for any <tt>i=0..columnIndexes.length()-1</tt>.
*/
public DoubleMatrix3D viewSelection(int[] sliceIndexes, int[] rowIndexes, int[] columnIndexes) {
	// check for "all"
	if (sliceIndexes==null) {
		sliceIndexes = new int[slices];
		for (int i=slices; --i >= 0; ) sliceIndexes[i] = i;
	}
	if (rowIndexes==null) {
		rowIndexes = new int[rows];
		for (int i=rows; --i >= 0; ) rowIndexes[i] = i;
	}
	if (columnIndexes==null) {
		columnIndexes = new int[columns];
		for (int i=columns; --i >= 0; ) columnIndexes[i] = i;
	}
	
	checkSliceIndexes(sliceIndexes);
	checkRowIndexes(rowIndexes);
	checkColumnIndexes(columnIndexes);
	
	int[] sliceOffsets = new int[sliceIndexes.length];
	int[] rowOffsets = new int[rowIndexes.length];
	int[] columnOffsets = new int[columnIndexes.length];
	
	for (int i=sliceIndexes.length; --i >= 0; ) {
		sliceOffsets[i] = _sliceOffset(_sliceRank(sliceIndexes[i]));
	}
	for (int i=rowIndexes.length; --i >= 0; ) {
		rowOffsets[i] = _rowOffset(_rowRank(rowIndexes[i]));
	}
	for (int i=columnIndexes.length; --i >= 0; ) {
		columnOffsets[i] = _columnOffset(_columnRank(columnIndexes[i]));
	}
	
	return viewSelectionLike(sliceOffsets,rowOffsets,columnOffsets);
}
/**
Constructs and returns a new <i>selection view</i> that is a matrix holding all <b>slices</b> matching the given condition.
Applies the condition to each slice and takes only those where <tt>condition.apply(viewSlice(i))</tt> yields <tt>true</tt>.
To match rows or columns, use a dice view.
<p>
<b>Example:</b>
<br>
<pre>
// extract and view all slices which have an aggregate sum > 1000
matrix.viewSelection( 
&nbsp;&nbsp;&nbsp;new DoubleMatrix2DProcedure() {
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;public final boolean apply(DoubleMatrix2D m) { return m.zSum > 1000; }
&nbsp;&nbsp;&nbsp;}
);
</pre>
For further examples, see the <a href="package-summary.html#FunctionObjects">package doc</a>.
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa. 

@param  condition The condition to be matched.
@return the new view.
*/
public DoubleMatrix3D viewSelection(DoubleMatrix2DProcedure condition) {
	IntArrayList matches = new IntArrayList();
	for (int i=0; i < slices; i++) {
		if (condition.apply(viewSlice(i))) matches.add(i);
	}
	
	matches.trimToSize();
	return viewSelection(matches.elements(), null, null); // take all rows and columns
}
/**
 * Construct and returns a new selection view.
 *
 * @param sliceOffsets the offsets of the visible elements.
 * @param rowOffsets the offsets of the visible elements.
 * @param columnOffsets the offsets of the visible elements.
 * @return  a new view.
 */
protected abstract DoubleMatrix3D viewSelectionLike(int[] sliceOffsets, int[] rowOffsets, int[] columnOffsets);
/**
Constructs and returns a new 2-dimensional <i>slice view</i> 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.
<p>
To obtain a slice view on subranges, construct a sub-ranging view (<tt>view().part(...)</tt>), then apply this method to the sub-range view.
To obtain 1-dimensional views, apply this method, then apply another slice view (methods <tt>viewColumn</tt>, <tt>viewRow</tt>) on the intermediate 2-dimensional view.
To obtain 1-dimensional views on subranges, apply both steps.

@param slice the index of the slice to fix.
@return a new 2-dimensional slice view.
@throws IndexOutOfBoundsException if <tt>slice < 0 || slice >= slices()</tt>.
@see #viewRow(int)
@see #viewColumn(int)
*/
public DoubleMatrix2D viewSlice(int slice) {
	checkSlice(slice);
	int sliceRows = this.rows;
	int sliceColumns = this.columns;
	
	//int sliceOffset = index(slice,0,0);
	int sliceRowZero = rowZero;
	int sliceColumnZero = columnZero + _sliceOffset(_sliceRank(slice));

	int sliceRowStride = this.rowStride;
	int sliceColumnStride = this.columnStride;
	return like2D(sliceRows,sliceColumns,sliceRowZero,sliceColumnZero,sliceRowStride,sliceColumnStride);
}
/**
Constructs and returns a new <i>flip view</i> along the slice axis.
What used to be slice <tt>0</tt> is now slice <tt>slices()-1</tt>, ..., what used to be slice <tt>slices()-1</tt> is now slice <tt>0</tt>.
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

@return a new flip view.
@see #viewRowFlip()
@see #viewColumnFlip()
*/
public DoubleMatrix3D viewSliceFlip() {
	return (DoubleMatrix3D) (view().vSliceFlip());
}
/**
Sorts the matrix slices into ascending order, according to the <i>natural ordering</i> of the matrix values in the given <tt>[row,column]</tt> position.
This sort is guaranteed to be <i>stable</i>.
For further information, see {@link cern.colt.matrix.doublealgo.Sorting#sort(DoubleMatrix3D,int,int)}.
For more advanced sorting functionality, see {@link cern.colt.matrix.doublealgo.Sorting}.
@return a new sorted vector (matrix) view.
@throws IndexOutOfBoundsException if <tt>row < 0 || row >= rows() || column < 0 || column >= columns()</tt>.
*/
/* freehep-jaida
public DoubleMatrix3D viewSorted(int row, int column) {
	return cern.colt.matrix.doublealgo.Sorting.mergeSort.sort(this,row,column);
}
*/
/**
Constructs and returns a new <i>stride view</i> which is a sub matrix consisting of every i-th cell.
More specifically, the view has <tt>this.slices()/sliceStride</tt> slices and <tt>this.rows()/rowStride</tt> rows and <tt>this.columns()/columnStride</tt> columns 
holding cells <tt>this.get(k*sliceStride,i*rowStride,j*columnStride)</tt> for all <tt>k = 0..slices()/sliceStride - 1, i = 0..rows()/rowStride - 1, j = 0..columns()/columnStride - 1</tt>.
The returned view is backed by this matrix, so changes in the returned view are reflected in this matrix, and vice-versa.

@param sliceStride the slice step factor.
@param rowStride the row step factor.
@param columnStride the column step factor.
@return a new view.
@throws	IndexOutOfBoundsException if <tt>sliceStride<=0 || rowStride<=0 || columnStride<=0</tt>.
*/
public DoubleMatrix3D viewStrides(int sliceStride, int rowStride, int columnStride) {
	return (DoubleMatrix3D) (view().vStrides(sliceStride, rowStride, columnStride));
}
/**
 * Applies a procedure to each cell's value.
 * Iterates downwards from <tt>[slices()-1,rows()-1,columns()-1]</tt> to <tt>[0,0,0]</tt>,
 * as demonstrated by this snippet:
 * <pre>
 * for (int slice=slices; --slice >=0;) {
 *    for (int row=rows; --row >= 0;) {
 *       for (int column=columns; --column >= 0;) {
 *           if (!procedure.apply(get(slice,row,column))) return false;
 *       }
 *    }
 * }
 * return true;
 * </pre>
 * Note that an implementation may use more efficient techniques, but must not use any other order.
 *
 * @param procedure a procedure object taking as argument the current cell's value. Stops iteration if the procedure returns <tt>false</tt>, otherwise continues. 
 * @return <tt>false</tt> if the procedure stopped before all elements where iterated over, <tt>true</tt> otherwise. 
 */
private boolean xforEach(final cern.colt.function.DoubleProcedure procedure) {
	for (int slice=slices; --slice >= 0;) {
		for (int row=rows; --row >= 0;) {
			for (int column=columns; --column >= 0;) {
				if (!procedure.apply(getQuick(slice,row,column))) return false;
			}
		}
	}
	return true;
}
/**
 * Applies a procedure to each cell's coordinate.
 * Iterates downwards from <tt>[slices()-1,rows()-1,columns()-1]</tt> to <tt>[0,0,0]</tt>,
 * as demonstrated by this snippet:
 * <pre>
 * for (int slice=slices; --slice >=0;) {
 *    for (int row=rows; --row >= 0;) {
 *       for (int column=columns; --column >= 0;) {
 *           if (!procedure.apply(slice,row,column)) return false;
 *       }
 *    }
 * }
 * return true;
 * </pre>
 * Note that an implementation may use more efficient techniques, but must not use any other order.
 *
 * @param procedure a procedure object taking as first argument the current slice, as second argument the current row, and as third argument the current column. Stops iteration if the procedure returns <tt>false</tt>, otherwise continues. 
 * @return <tt>false</tt> if the procedure stopped before all elements where iterated over, <tt>true</tt> otherwise. 
 */
private boolean xforEachCoordinate(final cern.colt.function.IntIntIntProcedure procedure) {
	for (int column=columns; --column >= 0;) {
		for (int slice=slices; --slice >=0;) {
			for (int row=rows; --row >= 0;) {
				if (!procedure.apply(slice,row,column)) return false;
			}
		}
	}
	return true;
}
/**
27 neighbor stencil transformation. For efficient finite difference operations.
Applies a function to a moving <tt>3 x 3 x 3</tt> window.
Does nothing if <tt>rows() < 3 || columns() < 3 || slices() < 3</tt>.
<pre>
B[k,i,j] = function.apply(
&nbsp;&nbsp;&nbsp;A[k-1,i-1,j-1], A[k-1,i-1,j], A[k-1,i-1,j+1],
&nbsp;&nbsp;&nbsp;A[k-1,i,  j-1], A[k-1,i,  j], A[k-1,i,  j+1],
&nbsp;&nbsp;&nbsp;A[k-1,i+1,j-1], A[k-1,i+1,j], A[k-1,i+1,j+1],

&nbsp;&nbsp;&nbsp;A[k  ,i-1,j-1], A[k  ,i-1,j], A[k  ,i-1,j+1],
&nbsp;&nbsp;&nbsp;A[k  ,i,  j-1], A[k  ,i,  j], A[k  ,i,  j+1],
&nbsp;&nbsp;&nbsp;A[k  ,i+1,j-1], A[k  ,i+1,j], A[k  ,i+1,j+1],

&nbsp;&nbsp;&nbsp;A[k+1,i-1,j-1], A[k+1,i-1,j], A[k+1,i-1,j+1],
&nbsp;&nbsp;&nbsp;A[k+1,i,  j-1], A[k+1,i,  j], A[k+1,i,  j+1],
&nbsp;&nbsp;&nbsp;A[k+1,i+1,j-1], A[k+1,i+1,j], A[k+1,i+1,j+1]
&nbsp;&nbsp;&nbsp;)

x x x - &nbsp;&nbsp;&nbsp; - x x x &nbsp;&nbsp;&nbsp; - - - - 
x o x - &nbsp;&nbsp;&nbsp; - x o x &nbsp;&nbsp;&nbsp; - - - - 
x x x - &nbsp;&nbsp;&nbsp; - x x x ... - x x x 
- - - - &nbsp;&nbsp;&nbsp; - - - - &nbsp;&nbsp;&nbsp; - x o x 
- - - - &nbsp;&nbsp;&nbsp; - - - - &nbsp;&nbsp;&nbsp; - x x x 
</pre>
Make sure that cells of <tt>this</tt> and <tt>B</tt> do not overlap.
In case of overlapping views, behaviour is unspecified.
</pre>
<p>
<b>Example:</b>
<pre>
final double alpha = 0.25;
final double beta = 0.75;

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

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double a100, double a101, double a102,
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double a110, double a111, double a112,
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double a120, double a121, double a122,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double a200, double a201, double a202,
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double a210, double a211, double a212,
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double a220, double a221, double a222) {
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;return beta*a111 + alpha*(a000 + ... + a222);
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}
};
A.zAssign27Neighbors(B,f);
</pre>
	
@param B the matrix to hold the results.
@param function the function to be applied to the 27 cells.
@throws NullPointerException if <tt>function==null</tt>.
@throws IllegalArgumentException if <tt>rows() != B.rows() || columns() != B.columns() || slices() != B.slices() </tt>.
*/
public void zAssign27Neighbors(DoubleMatrix3D B, cern.colt.function.Double27Function function) {
	if (function==null) throw new NullPointerException("function must not be null.");
	checkShape(B);
	if (rows<3 || columns<3 || slices<3) return; // nothing to do
	int r = rows-1;
	int c = columns-1;
	double a000, a001, a002;
	double a010, a011, a012;
	double a020, a021, a022;

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

	double a200, a201, a202;
	double a210, a211, a212;
	double a220, a221, a222;
	
	for (int k=1; k<slices-1; k++) {
		for (int i=1; i<r; i++) {
			a000=getQuick(k-1,i-1,0); a001=getQuick(k-1,i-1,1); 
			a010=getQuick(k-1,i,  0); a011=getQuick(k-1,i,  1); 
			a020=getQuick(k-1,i+1,0); a021=getQuick(k-1,i+1,1); 

			a100=getQuick(k-1,i-1,0); a101=getQuick(k  ,i-1,1); 
			a110=getQuick(k  ,i,  0); a111=getQuick(k  ,i,  1); 
			a120=getQuick(k  ,i+1,0); a121=getQuick(k  ,i+1,1); 

			a200=getQuick(k+1,i-1,0); a201=getQuick(k+1,i-1,1); 
			a210=getQuick(k+1,i,  0); a211=getQuick(k+1,i,  1); 
			a220=getQuick(k+1,i+1,0); a221=getQuick(k+1,i+1,1); 

			for (int j=1; j<c; j++) {
				// in each step 18 cells can be remembered in registers - they don't need to be reread from slow memory
				// in each step 9 instead of 27 cells need to be read from memory.
				a002=getQuick(k-1,i-1,j+1);
				a012=getQuick(k-1,i,  j+1);
				a022=getQuick(k-1,i+1,j+1);
				
				a102=getQuick(k  ,i-1,j+1);
				a112=getQuick(k  ,i,  j+1);
				a122=getQuick(k  ,i+1,j+1);
				
				a202=getQuick(k+1,i-1,j+1);
				a212=getQuick(k+1,i,  j+1);
				a222=getQuick(k+1,i+1,j+1);
				
				B.setQuick(k,i,j, function.apply(
					a000, a001, a002,
					a010, a011, a012,
					a020, a021, a022,
					
					a100, a101, a102,
					a110, a111, a112,
					a120, a121, a122,
					
					a200, a201, a202,
					a210, a211, a212,
					a220, a221, a222));
				
				a000=a001; a001=a002;
				a010=a011; a011=a012;
				a020=a021; a021=a022;

				a100=a101; a101=a102;
				a110=a111; a111=a112;
				a120=a121; a121=a122;

				a200=a201; a201=a202;
				a210=a211; a211=a212;
				a220=a221; a221=a222;			
			}
		}
	}
}
/**
 * Returns the sum of all cells; <tt>Sum( x[i,j,k] )</tt>.
 * @return the sum.
 */
public double zSum() {
	if (size()==0) return 0;
	return aggregate(cern.jet.math.Functions.plus,cern.jet.math.Functions.identity);
}
}