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Fast double-precision vector and matrix maths library for Java, supporting N-dimensional numeric arrays.
There is a newer version: 0.67.0
package mikera.matrixx;

import java.nio.DoubleBuffer;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Iterator;
import java.util.List;

import mikera.arrayz.Array;
import mikera.arrayz.Arrayz;
import mikera.arrayz.INDArray;
import mikera.arrayz.ISparse;
import mikera.arrayz.impl.AbstractArray;
import mikera.arrayz.impl.IDense;
import mikera.arrayz.impl.JoinedArray;
import mikera.arrayz.impl.SliceArray;
import mikera.indexz.AIndex;
import mikera.indexz.Index;
import mikera.matrixx.algo.Definite;
import mikera.matrixx.algo.Determinant;
import mikera.matrixx.algo.Inverse;
import mikera.matrixx.algo.Multiplications;
import mikera.matrixx.algo.Rank;
import mikera.matrixx.impl.ADenseArrayMatrix;
import mikera.matrixx.impl.ARectangularMatrix;
import mikera.matrixx.impl.AStridedMatrix;
import mikera.matrixx.impl.IdentityMatrix;
import mikera.matrixx.impl.ImmutableMatrix;
import mikera.matrixx.impl.MatrixBandView;
import mikera.matrixx.impl.MatrixColumnList;
import mikera.matrixx.impl.MatrixColumnView;
import mikera.matrixx.impl.MatrixElementIterator;
import mikera.matrixx.impl.MatrixRowIterator;
import mikera.matrixx.impl.MatrixRowList;
import mikera.matrixx.impl.MatrixRowView;
import mikera.matrixx.impl.SparseColumnMatrix;
import mikera.matrixx.impl.SparseRowMatrix;
import mikera.matrixx.impl.SubMatrixView;
import mikera.matrixx.impl.TransposedMatrix;
import mikera.matrixx.impl.ZeroMatrix;
import mikera.randomz.Hash;
import mikera.transformz.AAffineTransform;
import mikera.transformz.AffineMN;
import mikera.transformz.impl.IdentityTranslation;
import mikera.util.Maths;
import mikera.vectorz.AScalar;
import mikera.vectorz.AVector;
import mikera.vectorz.IOperator;
import mikera.vectorz.Op;
import mikera.vectorz.Op2;
import mikera.vectorz.Tools;
import mikera.vectorz.Vector;
import mikera.vectorz.Vectorz;
import mikera.vectorz.impl.ADenseArrayVector;
import mikera.vectorz.impl.MatrixViewVector;
import mikera.vectorz.impl.Vector0;
import mikera.vectorz.util.Constants;
import mikera.vectorz.util.DoubleArrays;
import mikera.vectorz.util.ErrorMessages;
import mikera.vectorz.util.IntArrays;
import mikera.vectorz.util.VectorzException;

/**
 * Abstract 2D matrix class. All Vectorz 2D matrices inherit from this class.
 * 
 * Implements generic version of most key matrix operations.
 * 
 * @author Mike
 */
public abstract class AMatrix extends AbstractArray implements IMatrix {
	// ==============================================
	// Abstract interface
	private static final long serialVersionUID = 4854869374064155441L;
	
	@Override
	public abstract double get(int i, int j);

	@Override
	public abstract void set(int i, int j, double value);

	// =============================================
	// Standard implementations

	@Override 
	public final double get(int row) {
		throw new VectorzException("1D get not supported on matrix!");
	}
	
	@Override 
	public final double get() {
		throw new VectorzException("0D get not supported on matrix!");
	}
	
	@Override 
	public void set(int row, double value) {
		throw new VectorzException("1D get not supported on matrix!");
	}
	
	@Override 
	public final void set(double value) {
		fill(value);
	}
	
	@Override 
	public void fill(double value) {
		int len=rowCount();
		for (int i = 0; i < len; i++) {
			getRowView(i).fill(value);
		}
	}
	
	/**
	 * Sets an element value in the matrix in an unsafe fashion, without performing bound checks
	 * The result is undefined if the row and column are out of bounds.
	 * @param i
	 * @param j
	 * @return
	 */
	public void unsafeSet(int i, int j, double value) {
		set(i,j,value);
	}
	
	/**
	 * Gets an element in the matrix in an unsafe fashion, without performing bound checks
	 * The result is undefined if the row and column are out of bounds.
	 * @param i
	 * @param j
	 * @return
	 */
	public double unsafeGet(int i, int j) {
		return get(i,j);
	}
	
	@Override
	public void clamp(double min, double max) {
		int len=rowCount();
		for (int i = 0; i < len; i++) {
			getRowView(i).clamp(min, max);
		}
	}
	
	@Override
	public void pow(double exponent) {
		int len=rowCount();
		for (int i = 0; i < len; i++) {
			AVector v=getRowView(i);
			v.pow(exponent);
		}
	}
	
	@Override
	public void square() {
		int len=rowCount();
		for (int i = 0; i < len; i++) {
			getRowView(i).square();
		}
	}
	
	@Override 
	public void set(int[] indexes, double value) {
		if (indexes.length==2) {
			set(indexes[0],indexes[1],value);
		} else {
			throw new VectorzException(""+indexes.length+"D set not supported on AMatrix");
		}
	}
	
	@Override 
	public void set(long[] indexes, double value) {
		if (indexes.length==2) {
			set(Tools.toInt(indexes[0]),Tools.toInt(indexes[1]),value);
		} else {
			throw new VectorzException(""+indexes.length+"D set not supported on AMatrix");
		}
	}
	
	@Override
	public final int dimensionality() {
		return 2;
	}
	
	/**
	 * Returns the number of dimensions required for input vectors
	 * @return
	 */
	public final int inputDimensions() {
		return columnCount();
	}
	
	/**
	 * Returns the number of dimensions required for output vectors
	 * @return
	 */
	public final int outputDimensions() {
		return rowCount();
	}
	
	@Override
	public long elementCount() {
		return ((long)rowCount())*columnCount();
	}
	
	@Override
	public final AVector slice(int row) {
		return getRowView(row);
	}
	
	@Override
	public AVector slice(int dimension, int index) {
		checkDimension(dimension);
		return (dimension==0)?getRowView(index):getColumnView(index);	
	}	
	
	@Override
	public int sliceCount() {
		return rowCount();
	}
	
	@Override
	public final List getSlices() {
		return getRows();
	}
	
    @Override
	public List getRows() {    
		return new MatrixRowList(this);
	}
    
    @Override
	public List getColumns() {    
		return new MatrixColumnList(this);
	}
	
	@Override
	public final List getSlices(int dimension) {
		checkDimension(dimension);
		return (dimension==0)?getRows():getColumns();
	}
	
	@Override
	public List getSliceViews() {	
		int rc=rowCount();
		ArrayList al=new ArrayList(rc);
		for (int i=0; i=(rc*cc))) throw new IndexOutOfBoundsException(ErrorMessages.invalidElementIndex(this,i));
		return unsafeGet((int)(i/cc),(int)(i%cc));
	}
	
	/**
	 * Returns a vector view of the leading diagonal values of the matrix
	 * @return
	 */
	public AVector getLeadingDiagonal() {
		return getBand(0);
	}
	
	public AAffineTransform toAffineTransform() {
		return new AffineMN(this,IdentityTranslation.create(rowCount()));
	}
	
	@Override
	public boolean isIdentity() {
		int rc=this.rowCount();
		int cc=this.columnCount();
		if (rc!=cc) return false;
		for (int i=0; i cols=getColumns();
	    for( int i = 0; i < n; i++ ) {
            AVector a = cols.get(i);
            if (!a.isUnitLengthVector(tolerance)) return false;
            for( int j = i+1; j < n; j++ ) {
                double val = a.dotProduct(cols.get(j));
                if ((Math.abs(val) > tolerance)) return false;
            }
        }
        
        return true;
	}

	/**
	 * Tests whether all columns in the matrix are orthonormal vectors
	 * @return
	 */
	public boolean hasOrthonormalColumns() {
		return getTranspose().innerProduct(this).epsilonEquals(IdentityMatrix.create(columnCount()));
	}
	
	/**
	 * Tests whether all rows in the matrix are orthonormal vectors
	 * @return
	 */
	public boolean hasOrthonormalRows() {
		return innerProduct(getTranspose()).epsilonEquals(IdentityMatrix.create(rowCount()));
	}
	
	@Override
	public INDArray reshape(int... dimensions) {
		int ndims=dimensions.length;
		if (ndims==1) {
			return toVector().subVector(0, dimensions[0]);
		} else if (ndims==2) {
			return Matrixx.createFromVector(asVector(), dimensions[0], dimensions[1]);
		} else {
			return Arrayz.createFromVector(toVector(), dimensions);
		}
	}
	
	public Matrix reshape(int rows, int cols) {
		return Matrixx.createFromVector(asVector(), rows, cols);
	}
	
	@Override
	public AMatrix reorder(int[] order) {
		return reorder(0,order);
	}	
	
	@Override
	public AMatrix reorder(int dim, int[] order) {
		int n=order.length;
		switch (dim) {
			case 0: {
				if (n==0) return ZeroMatrix.create(0, columnCount());
				if (IntArrays.isRange(order)) {
					return subMatrix(order[0],n,0,columnCount());
				}
				
				ArrayList al=new ArrayList(n);
				for (int si: order) {
					al.add(slice(si));
				}
				return SparseRowMatrix.wrap(al);
			}
			case 1: {
				if (n==0) return ZeroMatrix.create(rowCount(),0);
				if (IntArrays.isRange(order)) {
					return subMatrix(0,rowCount(),order[0],n);
				}
				
				ArrayList al=new ArrayList(n);
				for (int si: order) {
					al.add(slice(1,si));
				}
				return SparseColumnMatrix.wrap(al);
			}
			default: throw new IndexOutOfBoundsException(ErrorMessages.invalidDimension(this, dim));
		}
	}	
	
	@Override
	public AMatrix subMatrix(int rowStart, int rows, int colStart, int cols) {
		if ((rows==0)||(cols==0)) return ZeroMatrix.create(rows, cols);
		return new SubMatrixView(this, rowStart, colStart, rows, cols);	
	}
	
	@Override
	public final AMatrix subArray(int[] offsets, int[] shape) {
		if (offsets.length!=2) throw new IllegalArgumentException(ErrorMessages.invalidIndex(this, offsets));
		if (shape.length!=2) throw new IllegalArgumentException(ErrorMessages.illegalSize(shape));
		return subMatrix(offsets[0],shape[0],offsets[1],shape[1]);
	}
	
	@Override
	public INDArray rotateView(int dimension, int shift) {
		int n=getShape(dimension);
		
		if (n==0) return this;
		shift = Maths.mod(shift,n);
		if (shift==0) return this;
		
		int[] off=new int[2];
		int[] shp=getShapeClone();
		
		shp[dimension]=shift;
		INDArray right=subArray(off,shp);
		shp[dimension]=n-shift;
		off[dimension]=shift;
		INDArray left=subArray(off,shp);
		return left.join(right,dimension);
	}

	@Override
	public void transform(AVector source, AVector dest) {
		if ((source instanceof Vector )&&(dest instanceof Vector)) {
			transform ((Vector)source, (Vector)dest);
			return;
		}
		int rc = rowCount();
		int cc = columnCount();
		if (source.length()!=cc) throw new IllegalArgumentException(ErrorMessages.wrongSourceLength(source));
		if (dest.length()!=rc) throw new IllegalArgumentException(ErrorMessages.wrongDestLength(dest));
		for (int row = 0; row < rc; row++) {
			dest.unsafeSet(row, rowDotProduct(row,source));
		}
	}
	
	public void transform(Vector source, Vector dest) {
		int rc = rowCount();
		int cc = columnCount();
		if (source.length()!=cc) throw new IllegalArgumentException(ErrorMessages.wrongSourceLength(source));
		if (dest.length()!=rc) throw new IllegalArgumentException(ErrorMessages.wrongDestLength(dest));
		for (int row = 0; row < rc; row++) {
			dest.unsafeSet(row, rowDotProduct(row,source));
		}
	}

	@Override
	public void transformInPlace(AVector v) {
		if (v instanceof ADenseArrayVector) {
			transformInPlace((ADenseArrayVector)v);
			return;
		}
		double[] temp = new double[v.length()];
		int rc = rowCount();
		int cc = columnCount();
		if (v.length()!=rc) throw new IllegalArgumentException(ErrorMessages.incompatibleShapes(this,v));
		if (rc != cc)
			throw new UnsupportedOperationException(
					"Cannot transform in place with a non-square transformation");
		for (int row = 0; row < rc; row++) {
			temp[row] = getRow(row).dotProduct(v);
		}
		v.setElements(temp);
	}
	
	public void transformInPlace(ADenseArrayVector v) {
		double[] temp = new double[v.length()];
		int rc = rowCount();
		int cc = columnCount();
		if (v.length()!=rc) throw new IllegalArgumentException(ErrorMessages.incompatibleShapes(this,v));
		if (rc != cc)
			throw new UnsupportedOperationException(
					"Cannot transform in place with a non-square transformation");
		double[] data=v.getArray();
		int offset=v.getArrayOffset();
		for (int row = 0; row < rc; row++) {
			temp[row] = getRow(row).dotProduct(data,offset);
		}
		v.setElements(temp);
	}

	@Override
	public AVector getRow(int row) {
		return getRowView(row);
	}

	@Override
	public AVector getColumn(int column) {
		return getColumnView(column);
	}
	
	@Override
	public AVector getRowView(int row) {
		return new MatrixRowView(this, row);
	}

	@Override
	public AVector getColumnView(int column) {
		return new MatrixColumnView(this, column);
	}
	
	@Override
	public AVector getRowClone(int row) {
		int cc=columnCount();
		Vector result=Vector.createLength(cc);
		this.copyRowTo(row,result.getArray(),0);
		return result;
	}

	@Override
	public AVector getColumnClone(int column) {
		int rc=rowCount();
		Vector result=Vector.createLength(rc);
		this.copyColumnTo(column,result.getArray(),0);
		return result;
	}

	/**
	 * Sets this matrix with the element values from another matrix. Source matrix must have the same shape.
	 * @param a
	 */
	public void set(AMatrix a) {
		int rc = rowCount();
		int cc = columnCount();
		a.checkShape(rc,cc);
		for (int i = 0; i < rc; i++) {
			setRow(i,a.getRow(i));
		}
	}
	
	@Override
	public void set(INDArray a) {
		if (a instanceof AMatrix) {set((AMatrix) a); return;}	
		if (a instanceof AVector) {set((AVector)a); return;}
		if (a instanceof AScalar) {set(a.get()); return;}
		// fall back to default impl
		super.set(a);
	}
	
	/**
	 * Sets every row of this matrix with the element values from a vector.
	 * @param a
	 */
	public void set(AVector v) {
		int rc=rowCount();
		for (int i=0; i elementIterator() {
		return new MatrixElementIterator(this);
	}
	
	@Override
	public boolean isBoolean() {
		int rc=rowCount();
		for (int i=0; i iterator() {
		return new MatrixRowIterator(this);
	}
		
	@Override
	public final boolean epsilonEquals(INDArray a, double epsilon) {
		if (a instanceof AMatrix) {
			return epsilonEquals((AMatrix) a,epsilon);
		} if (a.dimensionality()!=2) {
			return false;
		} else {
			int sc=rowCount();
			if (a.sliceCount()!=sc) return false;
			for (int i=0; iConstants.PRINT_THRESHOLD) {
			Index shape=Index.create(getShape());
			return "Large matrix with shape: "+shape.toString();
		}
		
		return toStringFull();
	}

	@Override
	public String toStringFull() {
		StringBuilder sb = new StringBuilder();
		int rc = rowCount();
		sb.append("[");
		for (int i = 0; i < rc; i++) {
			if (i>0) sb.append(",\n");
			sb.append(getRow(i).toString());
		}
		sb.append("]");
		return sb.toString();
	}

	@Override
	public int hashCode() {
		// hashcode is hashcode of all doubles, row by row
		int hashCode = 1;
		int rc = rowCount();
		int cc = columnCount();
		for (int i = 0; i < rc; i++) {
			for (int j = 0; j < cc; j++) {
				hashCode = 31 * hashCode + (Hash.hashCode(unsafeGet(i, j)));
			}
		}
		return hashCode;
	}

	/**
	 * Returns the matrix values as a single reference Vector in the form [row0
	 * row1 row2....]
	 * 
	 * @return
	 */
	@Override
	public AVector asVector() {
		int rc = rowCount();
		if (rc == 0) return Vector0.INSTANCE;
		if (rc == 1) return getRowView(0);
		
		int cc= columnCount();
		if (cc==1) return getColumnView(0);

		return new MatrixViewVector(this);
	}
	
	@Override
	public List asElementList() {
		return asVector().asElementList();
	}
	
	@Override
	public AMatrix innerProduct(AMatrix a) {
		return Multiplications.multiply(this, a);
	}
	
	@Override
	public Vector innerProduct(Vector v) {
		int cc=this.columnCount();
		int rc=this.rowCount();
		v.checkLength(cc);
		Vector r=Vector.createLength(rc);
		for (int i=0; i al=getRows();
		List rl=new ArrayList(rc);
		for (AVector v: al ) {
			rl.add(v.innerProduct(a));
		}
		return SliceArray.create(rl);
	}

	@Override
	public INDArray outerProduct(INDArray a) {
		ArrayList al=new ArrayList(sliceCount());
		for (AVector s:this) {
			al.add(s.outerProduct(a));
		}
		return Arrayz.create(al);
	}
	
	/**
	 * Returns the dot product of a specific row with a vector.
	 * 
	 * Unsafe operation: performs no bounds checking
	 * @param i
	 * @param a
	 * @return
	 */
	public double rowDotProduct(int i, AVector a) {
		return getRow(i).dotProduct(a);
	}

	/**
	 * Computes the inverse of a matrix. Returns null if the matrix is singular.
	 * 
	 * Throws an Exception is the matrix is not square
	 * @param m
	 * @return
	 */
	@Override
	public AMatrix inverse() {
		return Inverse.calculate(this);
	}
	
	@Override
	public double trace() {
		int rc=Math.min(rowCount(), columnCount());
		double result=0.0;
		for (int i=0; i2) throw new IllegalArgumentException(ErrorMessages.incompatibleShapes(this, a));
			if (dims==0) {
				add(a.get());
			} else if (dims==1) {
				add(Vectorz.toVector(a));
			} else if (dims==2) {
				add(Matrixx.toMatrix(a));
			}
		}
	}
	
	/**
	 * Multiply each row in this matrix by a vector. Mutates this matrix.
	 * @param v
	 */
	public void multiply(AVector v) {
		int rc = rowCount();
		for (int i = 0; i < rc; i++) {
			getRowView(i).multiply(v);
		}
	}
	
	@Override
	public void multiply(INDArray a) {
		if (a instanceof AMatrix) {
			multiply((AMatrix)a);
		} else if (a instanceof AVector) {
			multiply((AVector)a);
		} else{
			int dims=a.dimensionality();
			if (dims==0) {
				multiply(a.get());
			} else if (dims==1) {
				multiply(Vectorz.toVector(a));
			} else if (dims==2) {
				multiply(Matrixx.toMatrix(a));
			} else {
				throw new IllegalArgumentException(ErrorMessages.incompatibleShapes(this,a));
			}
		}
	}
	
	/**
	 * Divides every row of this matrix by the given vector
	 * @param v
	 */
	public void divide(AVector v) {
		int rc=rowCount();
		for (int i=0; i2) r=r.broadcastLike(target);
		return r.clone();
	}
	
	@Override
	public INDArray broadcastCopyLike(INDArray target) {
		INDArray r=this.copy();
		if (target.dimensionality()>2) r=r.broadcastLike(target);
		return r;
	}

	/**
	 * Returns true if the matrix is the zero matrix (all components zero)
	 */
	@Override
	public boolean isZero() {
		int rc=rowCount();
		for (int i=0; i j
	 */
	public boolean isUpperTriangular() {
		int rc=rowCount();
		int cc=columnCount();
		for (int i=1; i0)?band:0;
	}
	
	protected final static int bandLength(int rc, int cc, int band) {
		if (band>0) {
			return (band0; w--) {
			if (!getBand(w).isZero()) return w;
		}
		return 0;
	}
	
	/**
	 * Computes the lower bandwidth of a matrix, i.e. the number of bands below the leading diagonal
	 * that cover all non-zero values
	 * @return
	 */
	public int lowerBandwidth() {
		for (int w=lowerBandwidthLimit(); w>0; w--) {
			if (!getBand(-w).isZero()) return w;
		}
		return 0;
	}
	
	/**
	 * Gets a specific band of the matrix, as a view vector. The band is truncated at the edges of the
	 * matrix, i.e. it does not wrap around the matrix.
	 * 
	 * @param band
	 * @return
	 */
	@Override
	public AVector getBand(int band) {
		return MatrixBandView.create(this,band);
	}
	
	public AVector getBandWrapped(int band) {
		AVector result=Vector0.INSTANCE;
		int rc=rowCount();
		int cc=columnCount();
		if (rc0) si-=rc;
			for (;si-rc; si-=cc) {
				result=result.join(getBand(si));
			}
		}
		return result;
	}
	
	/**
	 * Sets a row in a matrix to the value specified by the given vector
	 * 
	 * @param i
	 * @param row
	 */
	public void setRow(int i, AVector row) {
		getRowView(i).set(row);
	}
	
	/**
	 * Replaces a row in a matrix, adding the row to the internal structure of the matrix.
	 * 
	 * Will throw UnsupportedOperationException if not possible for the given matrix type.
	 * 
	 * @param i
	 * @param row
	 */
	public void replaceRow(int i, AVector row) {
		throw new UnsupportedOperationException("replaceRow not supported for "+this.getClass()+". Consider using an AVectorMatrix or SparseRowMatrix instance instead.");
	}
	
	/**
	 * Replaces a column in a matrix, adding the column to the internal structure of the matrix.
	 * 
	 * Will throw UnsupportedOperationException if not possible for the given matrix type.
	 * 
	 * @param i
	 * @param row
	 */
	public void replaceColumn(int i, AVector row) {
		throw new UnsupportedOperationException("replaceColumn not supported for "+this.getClass()+". Consider using a SparseColumnMatrix instance instead.");
	}
	
	/**
	 * Sets a column in a matrix. 
	 * 
	 * @param i
	 * @param row
	 */
	public void setColumn(int i, AVector col) {
		getColumnView(i).set(col);
	}

	@Override
	public abstract AMatrix exactClone();
	
	@Override
	public INDArray immutable() {
		if (!isMutable()) return this;
		return ImmutableMatrix.create(this);
	}
	
	@Override
	public AMatrix mutable() {
		if (isFullyMutable()) return this;
		return clone();
	}
	
	@Override
	public AMatrix sparse() {
		if (this instanceof ISparse) return this;
		return Matrixx.createSparse(this);
	}
	
	@Override
	public AMatrix dense() {
		if (this instanceof IDense) return this;
		return Matrix.create(this);
	}
	
	@Override
	public final Matrix denseClone() {
		return Matrix.create(this);
	}
	
	@Override 
	public void validate() {
		if (((long)rowCount())*columnCount()!=elementCount()) throw new VectorzException("Invalid Array shape?");
		super.validate();
	}

	/**
	 * Copies the elements in a selected row of this matrix to a double array
	 * @param i The index of the selected row
	 * @param dest Destination double[] array
	 * @param destOffset Offset into destination array
	 */
	public void copyRowTo(int i, double[] dest, int destOffset) {
		// note: using getRow() may be faster when overriding
		int cc=columnCount();
		for (int j=0; j= 2))
			throw new IndexOutOfBoundsException(ErrorMessages.invalidDimension(this,dimension));
	}
	
	/**
	 * Checks if this matrix has the same shape as another matrix. Throws an exception if not.
	 * @param m
	 */
	protected void checkSameShape(AMatrix m) {
		if((rowCount()!=m.rowCount())||(columnCount()!=m.columnCount())) {
			throw new IndexOutOfBoundsException(ErrorMessages.mismatch(this, m));
		}
	}
	
	/**
	 * Checks if this matrix has the same shape as another matrix. Throws an exception if not.
	 * @param m
	 */
	protected void checkSameShape(ARectangularMatrix m) {
		if((rowCount()!=m.rowCount())||(columnCount()!=m.columnCount())) {
			throw new IndexOutOfBoundsException(ErrorMessages.mismatch(this, m));
		}
	}
	
	/**
	 * Checks if this matrix has the specified shape. Throws an exception if not.
	 */
	protected void checkShape(int rows, int cols) {
		int rc=rowCount();
		int cc=columnCount();
		if((rc!=rows)||(cc!=cols)) {
			throw new IllegalArgumentException("Unexpected shape: ["+cc+","+rc+"] expected: ["+rows+","+cols+"]");
		}
	}
	
	/**
	 * Checks if the given index is valid for this matrix. Throws an exception if not.
	 */
	protected void checkIndex(int i, int j) {
		int rc=rowCount();
		int cc=columnCount();
		if ((i<0)||(i>=rc)||(j<0)||(j>=cc)) {
			throw new IndexOutOfBoundsException(ErrorMessages.invalidIndex(this, i,j));
		}
	}
	
	/**
	 * Checks if the given column index is valid for this matrix. Throws an exception if not.
	 *
	 * @return the number of columns in this matrix
	 */
	public int checkColumn(int column) {
		int cc=columnCount();
		if ((column<0)||(column>=cc)) throw new IndexOutOfBoundsException(ErrorMessages.invalidSlice(this, 1, column));
		return cc;
	}
	
	/**
	 * Checks if the given rows index is valid for this matrix. Throws an exception if not.
	 * 
	 * @return the number of rows in this matrix
	 */
	public int checkRow(int row) {
		int rc=rowCount();
		if ((row<0)||(row>=rc)) throw new IndexOutOfBoundsException(ErrorMessages.invalidSlice(this, 0, row));
		return rc;
	}

	@Override
	public void add2(AMatrix a, AMatrix b) {
		add(a);
		add(b);
	}


}