package mikera.matrixx;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Iterator;
import java.util.List;
import java.util.Random;
import mikera.arrayz.INDArray;
import mikera.indexz.Index;
import mikera.matrixx.impl.ADiagonalMatrix;
import mikera.matrixx.impl.AStridedMatrix;
import mikera.matrixx.impl.ColumnMatrix;
import mikera.matrixx.impl.DenseColumnMatrix;
import mikera.matrixx.impl.DiagonalMatrix;
import mikera.matrixx.impl.IdentityMatrix;
import mikera.matrixx.impl.ScalarMatrix;
import mikera.matrixx.impl.SparseColumnMatrix;
import mikera.matrixx.impl.SparseRowMatrix;
import mikera.matrixx.impl.StridedMatrix;
import mikera.matrixx.impl.ZeroMatrix;
import mikera.util.Rand;
import mikera.vectorz.AVector;
import mikera.vectorz.Tools;
import mikera.vectorz.Vector3;
import mikera.vectorz.Vectorz;
import mikera.vectorz.impl.SparseIndexedVector;
import mikera.vectorz.util.ErrorMessages;
import mikera.vectorz.util.VectorzException;
import us.bpsm.edn.parser.Parseable;
import us.bpsm.edn.parser.Parser;
import us.bpsm.edn.parser.Parsers;
/**
* Static method class for matrices
*
* @author Mike
*/
public class Matrixx {
private static final long SPARSE_ELEMENT_THRESHOLD = 100000;
private final static Random rand=new Random();
/**
* Creates an identity matrix
*/
public static AMatrix createIdentityMatrix(int dimensions) {
return createImmutableIdentityMatrix(dimensions);
}
/**
* Creates a sparse, immutable identity matrix. This is the most efficient format for identity matrices
*/
public static IdentityMatrix createImmutableIdentityMatrix(int dimensions) {
return IdentityMatrix.create(dimensions);
}
/**
* Creates a fully mutable identity matrix
*/
public static AMatrix createMutableIdentityMatrix(int dimensions) {
AMatrix m = newMatrix(dimensions, dimensions);
for (int i = 0; i < dimensions; i++) {
m.unsafeSet(i, i, 1.0);
}
return m;
}
/**
* Coerce an object to a matrix format, on a best effort basis.
*
* Can handle:
* - Existing matrices
*/
@SuppressWarnings("unchecked")
public static AMatrix toMatrix(Object o) {
if (o instanceof AMatrix) {
return (AMatrix) o;
} else if (o instanceof AVector) {
return ColumnMatrix.wrap((AVector) o);
} else if (o instanceof Iterable<?>) {
List<INDArray> al = Tools.toList((Iterable<INDArray>) o);
return createFromVectors(al);
}
throw new UnsupportedOperationException("Can't convert to matrix: "
+ o.getClass());
}
/**
* Creates a sparse matrix from the given matrix, ignoring zeros
*/
public static AMatrix createSparse(AMatrix m) {
int rc=m.rowCount();
int cc=m.columnCount();
if ((rc==0)||(cc==0)) return ZeroMatrix.create(rc, cc);
return SparseRowMatrix.create(m);
}
/**
* Creates a sparse matrix of the given size, initially zero-filled. Uses row-based storage by default
*/
public static SparseRowMatrix createSparse(int rowCount, int columnCount) {
return SparseRowMatrix.create(rowCount,columnCount);
}
/**
* Creates a sparse matrix from the given matrix, ignoring zeros. Uses row-based storage by default
*/
public static SparseRowMatrix createSparseRows(Iterable<AVector> rows) {
Iterator<AVector> rowIterator=rows.iterator();
return createSparseRows(rowIterator);
}
/**
* Creates a sparse matrix from the given iterator. Each vector in the iterator will be copied to
* a row in the new sparse matrix
*/
public static ArrayList<AVector> createSparseArray(Iterator<AVector> vecIterator) {
AVector v0=vecIterator.next();
int len = v0.length();
ArrayList<AVector> vecList = new ArrayList<AVector>();
vecList.add(v0);
while (vecIterator.hasNext()) {
AVector v = vecIterator.next();
if ((v == null) || (v.isZero()))
v = Vectorz.createZeroVector(len);
else
v = v.sparseClone();
vecList.add(v.sparseClone());
}
return vecList;
}
public static SparseRowMatrix createSparseRows(Iterator<AVector> rowIterator) {
return SparseRowMatrix.wrap(createSparseArray(rowIterator));
}
public static SparseColumnMatrix createSparseColumns(Iterator<AVector> colIterator) {
return SparseColumnMatrix.wrap(createSparseArray(colIterator));
}
/**
* Create a sparse array, given an Index of column positions and AVector of corresponding values for each row in the sparse array
* Performs a defensive copy of underlying data.
*/
public static AMatrix createSparse(int columnCount, Index[] indexes,
AVector[] weights) {
int rowCount = indexes.length;
if (rowCount != weights.length)
throw new IllegalArgumentException("Length of indexes array must match length of weights array");
SparseRowMatrix sm=SparseRowMatrix.create(rowCount, columnCount);
for (int i = 0; i < rowCount; i++) {
sm.replaceRow(i, SparseIndexedVector.wrap(columnCount, indexes[i].clone(), weights[i].toDoubleArray()));
}
return sm;
}
/**
* Creates a SparseColumnMatrix from the given matrix, ignoring zeros
*/
public static SparseColumnMatrix createSparseColumns(AMatrix m) {
int cc = m.columnCount();
AVector[] cols = new AVector[cc];
for (int i = 0; i < cc; i++) {
cols[i] = Vectorz.createSparse(m.getColumn(i));
}
return SparseColumnMatrix.wrap(cols);
}
/**
* Creates a SparseRowMatrix matrix from the given matrix, ignoring zeros
*/
public static AMatrix createSparseRows(AMatrix m) {
if (m.rowCount()==0) return ZeroMatrix.create(0, m.columnCount());
return SparseRowMatrix.create(m);
}
/**
* Creates a SparseRowMatrix matrix from the given INDArray, ignoring zeros
*/
public static SparseRowMatrix createSparseRows(INDArray a) {
if (!(a.dimensionality()==2)) throw new IllegalArgumentException(ErrorMessages.incompatibleShape(a));
int rc=a.getShape(0);
int cc=a.getShape(1);
SparseRowMatrix m=SparseRowMatrix.create(rc,cc);
for (int i=0; i<rc; i++) {
AVector v=a.slice(i).sparseClone().asVector();
if (!v.isZero()) {
m.replaceRow(i, v);
}
}
return m;
}
/**
* Creates an immutable zero-filled matrix
*/
public static ZeroMatrix createImmutableZeroMatrix(int rows, int columns) {
return ZeroMatrix.create(rows, columns);
}
public static ADiagonalMatrix createScaleMatrix(int dimensions,
double factor) {
DiagonalMatrix im = new DiagonalMatrix(dimensions);
for (int i = 0; i < dimensions; i++) {
im.unsafeSet(i, i, factor);
}
return im;
}
/**
* Creates a scalar matrix with the given scale factor. Scalar matrices are efficient,
* lightweight and immutable.
*/
public static ADiagonalMatrix createScalarMatrix(int dimensions,
double factor) {
if (factor==1.0) return IdentityMatrix.create(dimensions);
return ScalarMatrix.create(dimensions, factor);
}
/**
* Creates a diagonal scaling matrix with the given scale factors for each dimension
*/
public static DiagonalMatrix createScaleMatrix(double... scalingFactors) {
int dimensions = scalingFactors.length;
DiagonalMatrix im = new DiagonalMatrix(dimensions);
for (int i = 0; i < dimensions; i++) {
im.unsafeSet(i, i, scalingFactors[i]);
}
return im;
}
/**
* Creates a diagonal matrix, using the given diagonal values. Performs a defensive copy of the data.
*/
public static DiagonalMatrix createDiagonalMatrix(double... diagonalValues) {
int dimensions = diagonalValues.length;
DiagonalMatrix im = new DiagonalMatrix(dimensions);
im.getLeadingDiagonal().setElements(diagonalValues);
return im;
}
/**
* Creates a diagonal matrix using the given vector of values on the main diagonal.
*/
public static DiagonalMatrix createDiagonalMatrix(AVector diagonalValues) {
return DiagonalMatrix.wrap(diagonalValues.toDoubleArray());
}
/**
* Creates a 3D rotation matrix for a given angle or rotation in radians around an axis vector.
* The axis vector need not be normalised.
*/
public static Matrix33 createRotationMatrix(Vector3 axis, double angle) {
return createRotationMatrix(axis.x, axis.y, axis.z, angle);
}
public static Matrix33 createRotationMatrix(double x, double y, double z,
double angle) {
double d = Math.sqrt(x * x + y * y + z * z);
if (d==0.0) return Matrix33.createIdentityMatrix();
double ca = Math.cos(angle);
double u=x, v=y, w=z;
if (d!=1.0) {
double s=1.0/d;
u = x *s;
v = y *s;
w = z *s;
}
double sa = Math.sin(angle);
return new Matrix33(u * u + (1 - u * u) * ca,
u * v * (1 - ca) - w * sa, u * w * (1 - ca) + v * sa, u * v
* (1 - ca) + w * sa, v * v + (1 - v * v) * ca, v * w
* (1 - ca) - u * sa, u * w * (1 - ca) - v * sa, v * w
* (1 - ca) + u * sa, w * w + (1 - w * w) * ca);
}
public static Matrix33 createRotationMatrix(AVector v, double angle) {
if (!(v.length() == 3))
throw new VectorzException(
"Rotation matrix requires a 3d axis vector");
return createRotationMatrix(v.unsafeGet(0), v.unsafeGet(1),
v.unsafeGet(2), angle);
}
public static Matrix33 createXAxisRotationMatrix(double angle) {
return createRotationMatrix(1, 0, 0, angle);
}
public static Matrix33 createYAxisRotationMatrix(double angle) {
return createRotationMatrix(0, 1, 0, angle);
}
public static Matrix33 createZAxisRotationMatrix(double angle) {
return createRotationMatrix(0, 0, 1, angle);
}
public static Matrix22 create2DRotationMatrix(double angle) {
return Matrix22.createRotationMatrix(angle);
}
public static Matrix createRandomSquareMatrix(int dimensions) {
Matrix m = createSquareMatrix(dimensions);
fillRandomValues(m);
return m;
}
public static Matrix createRandomSquareMatrix(int dimensions, Random rand) {
Matrix m = createSquareMatrix(dimensions);
fillRandomValues(m,rand);
return m;
}
public static AMatrix createRandomMatrix(int rows, int columns) {
AMatrix m = newMatrix(rows, columns);
fillRandomValues(m);
return m;
}
public static AMatrix createRandomMatrix(int rows, int columns, Random rand) {
AMatrix m = newMatrix(rows, columns);
fillRandomValues(m,rand);
return m;
}
/**
* Creates an empty (zero-filled) mutable matrix of the specified size
*
* @param rows
* @param columns
* @return
*/
public static AMatrix newMatrix(int rows, int columns) {
if (rows==columns) {
if (rows == 1) return new Matrix11();
if (rows == 2) return new Matrix22();
if (rows == 3) return new Matrix33();
}
if (rows*((long)columns)>SPARSE_ELEMENT_THRESHOLD) return createSparse(rows,columns);
return Matrix.create(rows, columns);
}
/**
* Creates a new matrix using the elements in the specified vector.
* Truncates or zero-pads the data as required to fill the new matrix
* @param data
* @param rows
* @param columns
* @return
*/
public static Matrix createFromVector(AVector data, int rows, int columns) {
Matrix m = Matrix.create(rows, columns);
int n=Math.min(rows*columns, data.length());
data.copyTo(0, m.data, 0, n);
return m;
}
/**
* 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
*/
public AMatrix createInverse(AMatrix m) {
return m.inverse();
}
/**
* Creates a zero-filled matrix with the specified number of dimensions for both rows and columns
* @param dimensions
* @return
*/
private static Matrix createSquareMatrix(int dimensions) {
return Matrix.create(dimensions, dimensions);
}
/**
* Extracts a lower triangular matrix from a matrix
*/
public static AMatrix extractLowerTriangular(AMatrix a) {
int rc=a.rowCount();
if (rc>a.columnCount()) throw new IllegalArgumentException("Too few columns in matrix");
AMatrix r=Matrixx.newMatrix(rc,rc);
for (int i=0; i<rc; i++) {
for (int j=0; j<=i; j++) {
r.unsafeSet(i, j, a.unsafeGet(i, j));
}
}
return r;
}
/**
* Extracts an upper triangular matrix from a matrix
*/
public static AMatrix extractUpperTriangular(AMatrix a) {
int cc=a.rowCount();
if (cc>a.rowCount()) throw new IllegalArgumentException("Too few rows in matrix");
AMatrix r=Matrixx.newMatrix(cc,cc);
for (int i=0; i<cc; i++) {
for (int j=i; j<cc; j++) {
r.unsafeSet(i, j, a.unsafeGet(i, j));
}
}
return r;
}
/**
* Creates a mutable deep copy of a matrix
*/
public static Matrix create(AMatrix m) {
return new Matrix(m);
}
/**
* Create a matrix from a list of rows
*
* @param rows
* @return
*/
public static Matrix create(List<Object> rows) {
int rc = rows.size();
AVector firstRow = Vectorz.create(rows.get(0));
int cc = firstRow.length();
Matrix m = Matrix.create(rc, cc);
m.setRow(0, firstRow);
for (int i = 1; i < rc; i++) {
m.setRow(i, Vectorz.create(rows.get(i)));
}
return m;
}
/**
* Creates a mutable copy of a matrix
*/
public static AMatrix create(IMatrix m) {
int rows = m.rowCount();
int columns = m.columnCount();
AMatrix result = newMatrix(rows, columns);
result.set(m);
return result;
}
/**
* Fills a matrix with uniform random numbers
* @param m
*/
public static void fillRandomValues(AMatrix m) {
int rows = m.rowCount();
int columns = m.columnCount();
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
m.unsafeSet(i, j, rand.nextDouble());
}
}
}
/**
* Fills a matrix with uniform random numbers, using the specified Random instance
* @param m
*/
public static void fillRandomValues(AMatrix m, Random rand) {
int rows = m.rowCount();
int columns = m.columnCount();
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
m.unsafeSet(i, j, rand.nextDouble());
}
}
}
/**
* Create a matrix using as array of vectors which represent the data for each row
* @param data
* @return
*/
public static AMatrix createFromVectors(INDArray... data) {
int rc = data.length;
int cc = (rc == 0) ? 0 : data[0].sliceCount();
AMatrix m = newMatrix(rc, cc);
for (int i = 0; i < rc; i++) {
m.setRow(i, data[i].asVector());
}
return m;
}
/**
* Create a matrix using a list of vectors as the data for each row
* @param data
* @return
*/
public static AMatrix createFromVectors(List<INDArray> data) {
int rc = data.size();
int cc = (rc == 0) ? 0 : data.get(0).sliceCount();
AMatrix m = newMatrix(rc, cc);
for (int i = 0; i < rc; i++) {
m.setRow(i,data.get(i).asVector());
}
return m;
}
// ====================================
// Edn formatting and parsing functions
private static Parser.Config getMatrixParserConfig() {
return Parsers.defaultConfiguration();
}
/**
* Parse a matrix in edn format
*
* @param ednString
* @return
*/
public static AMatrix parse(String ednString) {
Parser p = Parsers.newParser(getMatrixParserConfig());
Parseable ps = Parsers.newParseable(ednString);
@SuppressWarnings("unchecked")
List<List<Object>> data = (List<List<Object>>) p.nextValue(ps);
int rc = data.size();
int cc = (rc == 0) ? 0 : data.get(0).size();
AMatrix m = newMatrix(rc, cc);
for (int i = 0; i < rc; i++) {
List<Object> row=data.get(i);
for (int j = 0; j < cc; j++) {
m.unsafeSet(i, j, Tools.toDouble(row.get(j)));
}
}
return m;
}
public static Matrix deepCopy(AMatrix m) {
return create(m);
}
public static AMatrix create(Object... vs) {
return create(Arrays.asList(vs));
}
public static Matrix create(double[][] data) {
return Matrix.create(data);
}
/**
* Wraps double[] data in a strided matrix of the most efficient available type.
*
* @param array
* @param arrayOffset
* @param reverse
* @param reverse2
* @return
*/
public static AStridedMatrix wrapStrided(double[] data, int rows, int cols, int offset, int rowStride, int colStride) {
if ((offset==0)&&(data.length==rows*cols)) {
if ((rows<=1)||(cols<=1)||((cols==rowStride)&&(colStride==1))) {
return Matrix.wrap(rows, cols, data);
}
if ((rows==colStride)&&(rowStride==1)) {
return DenseColumnMatrix.wrap(rows, cols, data);
}
}
return StridedMatrix.wrap(data, rows, cols, offset, rowStride, colStride);
}
public static AMatrix createSparse(Iterable<INDArray> slices) {
INDArray slice1=slices.iterator().next();
int cc=slice1.sliceCount();
ArrayList<AVector> al=new ArrayList<AVector>();
for (INDArray a:slices) {
if ((a.dimensionality()!=1)||(a.sliceCount()!=cc)) throw new IllegalArgumentException(ErrorMessages.incompatibleShape(a));
al.add(a.sparse().asVector());
}
return SparseRowMatrix.create(al);
}
}